DESIGN OF WOUND FIELD SYNCHRONOUS MACHINES AND HYBRID

EXCITATION SYNCHRONOUS MACHINES FOR ELECTRIC VEHICLE

TRACTION WITH BRUSHLESS CAPACITIVE FIELD EXCITATION

BY

ANTONIO DI GIOIA

Submitted in partial fulfillment of the

requirements for the degree of
Doctor of Philosophy in Electrical Engineering
in the Graduate College of the
Illinois Institute of Technology

Approved
Advisor

Chicago, Illinois
May 2018




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 ACKNOWLEDGMENT

To Marta.

Qual è ’l geometra che tutto s’affige

per misurar lo cerchio, e non ritrova,

pensando, quel principio ond’elli indige

Dante - Paradiso, XXXIII 133 - 135

iii
 TABLE OF CONTENTS

Page

ACKNOWLEDGEMENT . . . . . . . . . . . . . . . . . . . . . . . . . iii

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

LIST OF SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii

LIST OF ACRONYMS . . . . . . . . . . . . . . . . . . . . . . . . . . xxi

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxii

CHAPTER
1. STATE OF THE ART . . . . . . . . . . . . . . . . . . . . 1

1.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . 1
1.2. Hybrid and Pure Electric Vehicles . . . . . . . . . . . . 1
1.3. Synchronous Machine Topologies . . . . . . . . . . . . 8
1.4. Electric Machine Optimization . . . . . . . . . . . . . . 17
1.5. Proposed Contributions . . . . . . . . . . . . . . . . . 20

2. ANALYTICAL FRAMEWORK . . . . . . . . . . . . . . . 26

2.1. Sizing Equations . . . . . . . . . . . . . . . . . . . . 26

2.2. Machine Losses Analysis . . . . . . . . . . . . . . . . . 46
2.3. Machine Design Figures of Merit . . . . . . . . . . . . . 47

3. MULTI-PHYSICS MACHINE MODELING . . . . . . . . . . 50

3.1. Analytical Method . . . . . . . . . . . . . . . . . . . 50

3.2. Software Architecture . . . . . . . . . . . . . . . . . . 55
3.3. Electro-Magnetic FEA . . . . . . . . . . . . . . . . . 66
3.4. Thermal FEA . . . . . . . . . . . . . . . . . . . . . . 79
3.5. Mechanical FEA . . . . . . . . . . . . . . . . . . . . 85

4. PROTOTYPES DESIGN PROCESS . . . . . . . . . . . . . 90

4.1. WFSM Prototype 1 . . . . . . . . . . . . . . . . . . . 90

4.2. WFSM Prototype 2 . . . . . . . . . . . . . . . . . . . 98
4.3. HESM Prototype 1 . . . . . . . . . . . . . . . . . . . 114

5. PROTOTYPES EXPERIMENTAL RESULTS . . . . . . . . 140

5.1. WFSM Prototype 1 . . . . . . . . . . . . . . . . . . . 140

iv
 5.2. WFSM Prototype 2 . . . . . . . . . . . . . . . . . . . 167
5.3. HESM Prototype 1 . . . . . . . . . . . . . . . . . . . 184

6. CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . 206

6.1. Summary . . . . . . . . . . . . . . . . . . . . . . . . . 206

6.2. Contribution . . . . . . . . . . . . . . . . . . . . . . . 207
6.3. Future Work . . . . . . . . . . . . . . . . . . . . . . . 210

APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

A. HESM PROTOTYPE LAMINATION SPECIFICATIONS . . . 214

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220

v
 LIST OF TABLES

Table Page

1.1 Automotive Electrical Machine Comparison . . . . . . . . . . . . 9

3.1 Typical ATF Physical Properties . . . . . . . . . . . . . . . . . 81

4.1 WFSM Prototype 1 Input Geometric Parameter Ranges . . . . . . 91

4.2 WFSM Prototype 1 Optimization Hard Constraints . . . . . . . . 92

4.3 WFSM Prototype 1 Optimization Objectives . . . . . . . . . . . 92

4.4 Candidates Design Geometric and Physical Parameters . . . . . . 94

4.5 Candidate Design Output Characteristics and Figures of Merit . . . 95

4.6 WFSM Prototype 1 Winding Design - Limit Operating Conditions . 96

4.7 WFSM Prototype 1 Stator Winding Design . . . . . . . . . . . . 97

4.8 WFSM Prototype 1 Rotor Winding Design . . . . . . . . . . . . 97

4.9 WFSM Prototype 1 Materials Mechanical Properties . . . . . . . 98

4.10 WFSM Prototype 2 Input Geometric Parameter Ranges . . . . . . 99

4.11 WFSM Prototype 2 Optimization Hard Constraints . . . . . . . . 100

4.12 WFSM Prototype 2 Optimization Objectives . . . . . . . . . . . 100

4.13 WFSM Prototype 2 MonteCarlo Parameter Ranges . . . . . . . . 102

4.14 Prototype 2 Rotor Winding Design . . . . . . . . . . . . . . . . 105

4.15 HESM CCD Constraint List . . . . . . . . . . . . . . . . . . . 115

4.16 HESM Stator Winding Design . . . . . . . . . . . . . . . . . . 124

4.17 HESM Prototype Wound Rotor Winding Design . . . . . . . . . . 125

4.18 HESM Prototype Mechanical Material Properties . . . . . . . . . 134

5.1 WFSM 1 Unsaturated Machine Equivalent Circuit Parameters . . . 149

5.2 WFSM Prototype 1 Machine Physical Data . . . . . . . . . . . . 154

5.3 WFSM 2 Unsaturated Machine Equivalent Circuit Parameters . . . 172

5.4 WFSM Prototype 2 Machine Physical Data . . . . . . . . . . . . 182

vi
5.5 HESM Unsaturated Machine Equivalent Circuit Parameters . . . . 199

5.6 HESM Prototype Machine Weights . . . . . . . . . . . . . . . . 204

5.7 HESM Prototype Machine Physical Data . . . . . . . . . . . . . 205

vii
 LIST OF FIGURES

Figure Page

1.1 Central composite designs, CCC is for circumscribed, CCI for in-
scribed and CCF face centered cases. . . . . . . . . . . . . . . 19

2.1 Stator geometric parameters for analytical sizing of the machine . 30

2.2 Wound field rotor geometric parameters for analytical sizing of the
machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.3 Permanent magnet rotor geometric parameters for analytical sizing

of the machine . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.1 Flow diagram of the linear analytical model. . . . . . . . . . . . 52

3.2 Flow diagram of the nonlinear analytical model. . . . . . . . . . 54

3.3 Flow diagram of the FEA software implementation for a single ma-
chine simulation. . . . . . . . . . . . . . . . . . . . . . . . . 58

3.4 Stator template 1. . . . . . . . . . . . . . . . . . . . . . . . . 66

3.5 Flexible rotor template 1, pole body shape options. . . . . . . . . 69

3.6 Flexible rotor template 1, option C of the pole body is shown. . . 70

3.7 Flexible rotor template 1, decision tree used to generate the pole
body shape. . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

3.8 Flexible rotor template 2, barrier definition. . . . . . . . . . . . 74

3.9 Flexible PM rotor template 1, barrier definition. . . . . . . . . . 75

3.10 Flexible PM rotor template 2, barrier definition. . . . . . . . . . 77

3.11 Magnetic flux density distribution of the model used for FEMM
simulation (right) validation against MagNet results (left). . . . . 78

3.12 Simulated static (left) and transient (right) torque comparison, FEMM
and MagNet denote the two electromagnetic solvers used. . . . . . 78

3.13 Simulated radial component of the magnetic flux density in a stator

tooth (left) and Simulated tangential component of the magnetic
flux density in the stator yoke mid-arc (right), FEMM and MagNet
denote the two electromagnetic solvers used.. . . . . . . . . . . . 79

viii
3.14 Motor-CAD thermal circuit overview, showing steady state temper-
atures. Note: the elements are color coded with stator iron in red,
stator copper in yellow, rotor iron in cyan, rotor copper in light or-
ange, spray cooling in pink, shaft and bearings in grey and machine
housing in blue. . . . . . . . . . . . . . . . . . . . . . . . . . 82

3.15 Motor-CAD thermal circuit detail, showing modifications to the ro-

tor thermal circuit inside the green boxes (Front circuit). Note:
The thermal resistance R 103 connects the average rotor tempera-
ture Rotor F (134) to the fluid spray inlet RotC FluidSpray F (48). 83

3.16 Motor-CAD thermal circuit detail, showing modifications to the sta-

tor thermal circuit inside the green boxes (Front circuit). Note: The
user-customized thermal resistances R44384, R44726 and R44749
connect the teeth and yoke of the stator to the fluid spray inlet
FluidSpray End F (44). . . . . . . . . . . . . . . . . . . . . . 88

3.17 Wound field prototype 1 rotor lamination stack, von Mises stress on
the lamination structure, endcaps and winding are modeled in the
simulation but shown in transparency to highlight the lamination
stresses [26]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

4.1 Torque density versus goodness √PTlosses

avg
(Average Torque/Plosses)
for 8 pole 48 slot single layer WFSM designs from the final multi-
objective optimization run [26]. The dot coloring represents which
hard constraints the design meets. . . . . . . . . . . . . . . . . 93

4.2 Magnetic flux density distribution of the final three candidate designs. 93

4.3 WFSM prototype 1 finalized geometry used for the prototype multi-
physics characterization, the loading corresponds to the maximum
current densities and predicts 192 Nm torque output. . . . . . . . 96

4.4 WFSM prototype 2 differential evolution optimization results, the

full population is marked in black, the Pareto front in red and the
prototype in yellow. . . . . . . . . . . . . . . . . . . . . . . . 101

4.5 WFSM prototype 2 base case geometry resulting from the differen-
tial evolution optimization and input for the MonteCarlo extended
optimization. . . . . . . . . . . . . . . . . . . . . . . . . . . 101

4.6 WFSM prototype 2 extended optimization results on the full load

torque torque versus stator voltage per turn, the geometries resulting
in low ripple are marked in blue, the Pareto front in red and the
prototype design in yellow. . . . . . . . . . . . . . . . . . . . 103

ix
4.7 WFSM prototype 2 extended optimization results on the stator volt-
age per turns versus partial load efficiency, the geometries resulting
in low ripple are marked in blue, the Pareto front in red and the
prototype design in yellow. . . . . . . . . . . . . . . . . . . . 103

4.8 WFSM prototype 2 finalized geometry resulting from the extended

optimization. . . . . . . . . . . . . . . . . . . . . . . . . . . 104

4.9 Predicted results, MTPA shaft torque at base speed of 4000 RPM. 106

4.10 Predicted results, MTPA voltage for the machine design speed range
of 0 to 12000 RPM. . . . . . . . . . . . . . . . . . . . . . . . 107

4.11 Predicted results, MTPA current angle for the machine design speed
range of 0 to 12000 RPM. . . . . . . . . . . . . . . . . . . . . 108

4.12 Predicted results, stator copper losses map for the machine design
speed range of 0 to 12000 RPM at MTPA current angle. . . . . . 109

4.13 Predicted results, rotor copper losses map for the machine design
speed range of 0 to 12000 RPM at MTPA current angle. . . . . . 110

4.14 Predicted results, core losses map for the machine design speed range
of 0 to 12000 RPM at MTPA current angle. . . . . . . . . . . . 110

4.15 Predicted results, efficiency map for the machine design speed range
of 0 to 12000 RPM at MTPA current angle. . . . . . . . . . . . 111

4.16 Predicted results, ripple map for the machine design speed range of
0 to 12000 RPM at MTPA current angle. . . . . . . . . . . . . 111

4.17 WFSM Prototype 2, predicted vonMises stress on the rotor lamina-

tions (Maximum value 367 MPa) at maximum speed of 12000 RPM.
Note: endcaps and windings have been simulated but are not shown. 112

4.18 WFSM Prototype 2, predicted deformation on the rotor laminations

(Maximum value 21μm) at maximum speed of 12000 RPM. Note:
endcaps and windings have been simulated but are not shown. . . 113

4.19 HESM response surface model results, peak value of the fundamental
airgap magnetic flux density (B̂g1,nl ), B WF denotes the wound field
rotor (top) and B PM the permanent magnet rotor (bottom). Note:
the vertical blue dashed line and the value below the y-axis labels
mark the prototype, the green dots the FEA simulations and the
red curve the best fit of simulations. . . . . . . . . . . . . . . . 117

x
4.20 HESM response surface model results, average value of the transient
torque, T WF denotes the wound field machine (middle), T PM the
permanent magnet machine (bottom) and T (HRd) the hybrid ma-
chine with equal WF and PM rotor stack lengths (50% hybridization
ratio). Note: the vertical blue dashed line and the value below the y-
axis labels mark the prototype, the green dots the FEA simulations
and the red curve the best fit of simulations. . . . . . . . . . . . 119

4.21 HESM response surface model results, physical sizes of the stator.
Note: the vertical blue dashed line and the value below the y-axis
labels mark the prototype, the green dots the FEA simulations and
the red curve the best fit of simulations, the red horizontal dotted
line in the Stator Envelope Radius is the allowed maximum value. 120

4.22 HESM response surface model results for 50% hybridization ra-
tio, Power Density loss denotes the power density reduction due
to the rotor end turns (top), GPD the gravimetric power density of
the HESM (middle) and VPD the volumetric power density of the
HESM (bottom). Note: the vertical blue dashed line and the value
below the y-axis labels mark the prototype, the green dots the FEA
simulations and the red curve the best fit of simulations. . . . . . 122

4.23 HESM predicted results, voltage map on the torque-speed plane. . 128

4.24 HESM predicted results, rotor copper losses map on the torque-
speed plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

4.25 HESM predicted results, stator copper losses map on the torque-
speed plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

4.26 HESM predicted results, stator iron losses map on the torque-speed
plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

4.27 HESM predicted results, total losses map on the torque-speed plane. 131

4.28 HESM predicted results, efficiency map on the torque-speed plane,

CPSR is shown in red. . . . . . . . . . . . . . . . . . . . . . . 132

4.29 HESM predicted results, efficiency map of the pure IPMSM corre-
sponding to the lamination design extended to the full stack on the
torque-speed plane, ideal CPSR is shown in red. . . . . . . . . . 132

4.30 HESM predicted results, efficiency map of the pure WFSM corre-
sponding to the lamination design extended to the full stack on the
torque-speed plane, CPSR is shown in red. . . . . . . . . . . . . 133

4.31 HESM predicted results, MTPA current angle map on the torque-
speed plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

xi
4.32 HESM predicted results, power factor map on the torque-speed
plane for MTPA current angles of Figure 4.31. . . . . . . . . . . 135

4.33 HESM predicted results, torque ripple map on the torque-speed

plane for MTPA current angles of Figure 4.31. . . . . . . . . . . 136

4.34 HESM predicted results, WF section torque map on the rotor current-
stator current plane for MTPA current angles at 4000 RPM. . . . 136

4.35 HESM predicted results, PM section torque map on the rotor current-
stator current plane for MTPA current angles at 4000 RPM. . . . 137

4.36 HESM predicted results, total torque map on the rotor current-
stator current plane for MTPA current angles at 4000 RPM. . . . 137

4.37 HESM prototype, predicted von Mises stress on the PM rotor lam-
inations (Maximum value 153 MPa) at maximum speed of 12000
RPM. Note: magnets, end plates and bolts have been simulated but
are not shown. . . . . . . . . . . . . . . . . . . . . . . . . . 138

4.38 HESM prototype, predicted deformation on the PM rotor lamina-

tions (Maximum value 31μm) at maximum speed of 12000 RPM.
Note: magnets, end plates and bolts have been simulated but are
not shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

4.39 HESM prototype, predicted vonMises stress on the WF rotor lam-

inations (Maximum value 147 MPa) at maximum speed of 12000
RPM. Note: endcaps and windings have been simulated but are not
shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

4.40 HESM prototype, predicted deformation on the WF rotor lamina-

tions (Maximum value 30μm) at maximum speed of 12000 RPM.
Note: endcaps and windings have been simulated but are not shown. 139

5.1 Wound field prototype 1 rotor lamination stack. . . . . . . . . . 142

5.2 Wound field prototype 1 rotor lamination stack fitted with PEEK
endcaps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

5.3 Wound field prototype 1 stator and rotor assembly after winding. . 144

5.4 Wound field prototype 1 stator and rotor after insertion (machine
non drive-end). . . . . . . . . . . . . . . . . . . . . . . . . . 145

5.5 Wound field prototype 1 stator and rotor after insertion (machine
non drive-end). . . . . . . . . . . . . . . . . . . . . . . . . . 146

5.6 Wound field prototype 1 non drive-end view with capacitive power
coupler installed. . . . . . . . . . . . . . . . . . . . . . . . . 155

xii
5.7 WFSM Prototype 1 measured bearing and windage losses. ATF
Spray is denoted by PB,Spray , HBM refers to the digital output of
the torque meter, WT1800 to the analog output. . . . . . . . . . 155

5.8 WFSM prototype 1 measured (Experimental dataset) and simulated

(MagNet and FEMM simulated datasets referring to the solvers)
open circuit voltages. . . . . . . . . . . . . . . . . . . . . . . 156

5.9 Measured and simulated open circuit core losses, Magnet denotes
the transient solution results, FEMM the static reconstruction with
two core losses models, Steinmetz and CAL2. . . . . . . . . . . 156

5.10 WFSM prototype 1 predicted and experimentally measured equiv-

alent circuit parameters, field, Lf , and mutual Lm . FEMM denotes
the simulation data results. . . . . . . . . . . . . . . . . . . . 157

5.11 WFSM prototype 1 predicted and experimentally measured equiva-

lent circuit parameters, stator d and q axis inductances, Ld and Lq .
FEMM denotes the simulation data results. . . . . . . . . . . . 157

5.12 Wound field synchronous machine testing dynamometer setup. . . 158

5.13 WFSM prototype 1 experimental results, shaft torque at 4000 RPM,

red dots are experimental measurements, surface is the FEMM sim-
ulation result. . . . . . . . . . . . . . . . . . . . . . . . . . . 158

5.14 WFSM prototype 1 simulated (left) and experimental results (right),

current angle of the maximum torque for a given field and stator
current at 4000 RPM. . . . . . . . . . . . . . . . . . . . . . . 159

5.15 Measured WFSM prototype 1 power factor at the current angle

corresponding to maximum torque at 4000 RPM. . . . . . . . . . 159

5.16 Measured WFSM prototype 1 efficiency results at 4000 RPM using

Yokogawa PX8000. The temperature of the stator windings ranged
between 45 to 100 ◦ C. Efficiencies are for maximum torque current
angles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

5.17 Predicted WFSM prototype 1 efficiency at a winding temperature

of 70 ◦ C as a function of field and stator currents at maximum
torque current angle at 4000 RPM. The efficiency is calculated from
the net mechanical power output divided the result of power output
summed to the total copper losses. The net mechanical power output
is obtained subtracting the estimated bearing and core losses from
the simulated electromagnetic torque, averaged over one rotation. . 161

xiii
5.18 Experimental and simulated temperature at 4000 RPM, housing de-
notes the external surface of the machine shell on the active length,
ambient the room temperature during testing. . . . . . . . . . . 162

5.19 Experimental and simulated temperature of the middle of the coil at

4000 RPM, A and B denote the phases in which the thermocouple
is installed, Center the midpoint of the stator slot axially(45 mm
from both ends of the machine), Front the drive-end axial position
(30 mm from the end turns inside the stack), Rear the non-drive
end axial position (30 mm from the end turns). . . . . . . . . . 162

5.20 Experimental and simulated temperature of the end turns connec-

tions at 4000 RPM, Front denotes the drive-end axial position, Rear
the non-drive end axial position. . . . . . . . . . . . . . . . . . 163

5.21 Experimental and simulated temperature of the yoke-side liner at

4000 RPM, Center denotes midpoint of the stator slot axially (45
mm from both ends of the machine), Front the drive-end axial posi-
tion (30 mm from the end turns inside the stack), Rear the non-drive
end axial position (30 mm from the end turns). . . . . . . . . . 163

5.22 Experimental and simulated temperature of the tooth-side liner at

4000 RPM, Center denotes midpoint of the stator slot axially (45
mm from both ends of the machine), Front the drive-end axial posi-
tion (30 mm from the end turns inside the stack), Rear the non-drive
end axial position (30 mm from the end turns) . . . . . . . . . . 164

5.23 Experimental and simulated temperature of the spray cooling fluid

inlet and outlet at 4000 RPM. . . . . . . . . . . . . . . . . . . 164

5.24 Experimental estimation and simulated average temperature of the

rotor winding and brushes system at 4000 RPM, the experimental
estimation drops to 20◦ C when the rotor circuit is opened, marking
the end of the loading test. . . . . . . . . . . . . . . . . . . . 165

5.25 Experimental measurement and simulated temperature difference

between inlet and outlet of the spray cooling fluid (Top) and flow
rate (Bottom) at 4000 RPM. . . . . . . . . . . . . . . . . . . 165

5.26 Experimental measurement and simulated spray cooling fluid heat

extraction (Top) and machine losses (Bottom) at 4000 RPM. . . . 166

5.27 Wound field prototype 2 rotor lamination stack, the flux barrier is
clearly visible at the center of the poles. . . . . . . . . . . . . . 168

5.28 Wound field prototype 2 rotor lamination stack fitted with PEEK
endcaps, drive-end view. . . . . . . . . . . . . . . . . . . . . . 168

xiv
5.29 Wound field prototype 2 rotor after winding and poles connection
to varistors for surge protection, non drive-end view. . . . . . . . 169

5.30 Wound field prototype 2 rotor assembly, drive-end view. . . . . . 170

5.31 WFSM prototype 2 measured and simulated stator open circuit volt-
ages, FEMM denotes the FEA solver used. . . . . . . . . . . . . 171

5.32 WFSM prototype 2 measured and simulated open circuit core losses,
FEMM denotes the FEA solver used. . . . . . . . . . . . . . . 172

5.33 WFSM prototype 2 predicted and experimentally measured equiv-

alent circuit parameters, Field inductance Lf , Variac denotes the
data obtained at 60 Hz, Open Circuit is the result of experimental
back-emf measurement post-processing. . . . . . . . . . . . . . 174

5.34 WFSM prototype 2 predicted and experimentally measured equiva-

lent circuit parameters, mutual inductance Lm , Variac denotes the
data obtained at 60 Hz, Open Circuit is the result of experimental
back-emf measurement post-processing. . . . . . . . . . . . . . 174

5.35 WFSM prototype 2 predicted and experimentally measured equiva-

lent circuit parameters, Stator inductances Lq . . . . . . . . . . . 175

5.36 WFSM prototype 2 predicted and experimentally measured equiva-

lent circuit parameters, Stator inductance, Ld . . . . . . . . . . . 175

5.37 WFSM prototype 2 experimental results, MTPA shaft torque at

base speed of 4000 RPM. . . . . . . . . . . . . . . . . . . . . 177

5.38 WFSM prototype 2 simulation results, MTPA shaft torque at base

speed of 4000 RPM. . . . . . . . . . . . . . . . . . . . . . . . 177

5.39 WFSM prototype 2 experimental results, current angle γ of the max-

imum torque for a given field and stator current at 4000 RPM. . . 178

5.40 WFSM prototype 2 simulation results, current angle of γ the maxi-

mum torque for a given field and stator current at 4000 RPM. . . 178

5.41 WFSM prototype 2 measured power factor at the maximum torque

current angle at 4000 RPM. . . . . . . . . . . . . . . . . . . . 180

5.42 WFSM prototype 2 simulated power factor at the maximum torque

current angle at 4000 RPM. The power factor is obtained from the
simulation voltage angle offset from the imposed current simulation,
calculated from the reconstructed transient field solution . . . . . 180

5.43 WFSM prototype 2 measured torque at the maximum torque per

volt at 4000 RPM. . . . . . . . . . . . . . . . . . . . . . . . 181

xv
5.44 WFSM prototype 2 experimental results current angle at the maxi-
mum torque per volt operating points at 4000 RPM. . . . . . . . 181

5.45 WFSM prototype 2 measured efficiency results at 4000 RPM for

maximum torque current angles. . . . . . . . . . . . . . . . . . 183

5.46 WFSM prototype 2 simulated efficiency results at 4000 RPM for

maximum torque current angles. . . . . . . . . . . . . . . . . . 183

5.47 HESM prototype, assembly of PM rotor and magnet insertion into

the laminations fitted on the hub, the insertion of the third pack of
four of laminations is shown. . . . . . . . . . . . . . . . . . . . 186

5.48 HESM prototype, completed PM rotor assembly after fitting the end
plates, bolted connections and dowel pins insertion. . . . . . . . . 186

5.49 HESM prototype, WF rotor connection of the winding. . . . . . . 188

5.50 HESM prototype, hybrid excitation rotor assembly and bearings

fitted on the shaft. . . . . . . . . . . . . . . . . . . . . . . . 188

5.51 HESM prototype, insertion of the rotor assembly in the stator housing. 189

5.52 HESM prototype, non drive-end view of the machine assembly, brushes
and slip rings assembly. . . . . . . . . . . . . . . . . . . . . . 190

5.53 Hybrid excitation synchronous machine testing dynamometer setup. 194

5.54 Measured and simulated open circuit voltages as a function of the

WF rotor excitation. . . . . . . . . . . . . . . . . . . . . . . 194

5.55 HESM prototype bearing and windage power losses estimated from
experimental measurement in the speed range 40 to 4000 RPM. . . 195

5.56 HESM prototype measured WF section core losses, simulated losses

refers to the mapping at 20◦ C, the PM section core losses have been
estimated as the average of the two experimental data series. . . . 196

5.57 Measured bearing, windage and total core losses for the speed range
of interest as a function of the WF excitation. . . . . . . . . . . 197

5.58 Measured and simulated rotor copper losses as a function of the WF

excitation. . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

5.59 HESM prototype predicted and experimentally measured equivalent

circuit parameters, mutual inductance Lm . . . . . . . . . . . . . 200

xvi
5.60 HESM prototype predicted and experimentally measured equivalent
circuit parameters, Field, Lf inductance. FEMM denotes the simu-
lation results, step the step voltage test and variac the line-fed variac
test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

5.61 Predicted and experimental results, shaft torque versus torque angle:
continuous line simulated, triangles ripple range, square experimen-
tal data at 2400 RPM, 50 A stator current and 2.5 A rotor current. 202

5.62 HESM prototype measured and simulated power factor at 2400

RPM and 50 A peak stator current, PM denotes the operation at
0 A field current, HE the operation at 2,5 A field current. FEMM
denotes simulation data, EXP experimental results. . . . . . . . 203

5.63 HESM prototype measured and simulated efficiency at 2400 RPM

and 50 A peak stator current, PM denotes the operation at 0 A field
current, HE the operation at 2,5 A field current. FEMM denotes
simulation data, EXP experimental results. . . . . . . . . . . . 203

A.1 HESM prototype stator laminations specification, laser weld notch

detail. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

A.2 HESM prototype permanent magnet rotor laminations specification,

teeth specification detail. . . . . . . . . . . . . . . . . . . . . 216

A.3 HESM prototype permanent magnet rotor laminations specification,

magnet tolerancing and step-skew verification. . . . . . . . . . . 217

A.4 HESM prototype permanent magnet rotor laminations specification,

finalized lamination. . . . . . . . . . . . . . . . . . . . . . . . 218

A.5 HESM prototype wound field rotor laminations specification. . . . 219

xvii
 LIST OF SYMBOLS

Symbol Definition

m Phases

p Pole pairs

q Slots per pole per phase

z Stator slots; z = 2mpq

Rg Airgap radius [mm]

Sg Airgap surface [mm−2 ]

Vg Airgap volume [mm−3 ]

L Stack length [mm]

π
αp Half pole angular span; αp = 2p
[rad]

π
αS Half stator slot angular span; αS = 2mpq
[rad]

2πRg
τp Pole pitch; τp = 2p
[mm]

Φ Magnetization flux [Wb]

RSo Stator outer radius [mm]

RSi Stator inner radius [mm]

kSi Stator-rotor split ratio

dSy Stator yoke depth [mm]

τSy Stator yoke pole pitch [mm]

kSy Stator yoke ratio

wSt Stator tooth thickness [mm]

dSt Stator slot depth [mm]

xviii
wSo Stator slot opening [mm]

kSo Stator slot opening ratio

RSb Stator slot bottom radius [mm]

kds Stator slot shape factor

θSt Stator tooth tip angle [rad]

dSo Stator opening depth [mm]

kSt Stator tooth thickness ratio

kwν Winding factor of the ν-th harmonic

LS,et Stator winding end-turn length [mm]

δ0 Minimum airgap [mm]

RRo Rotor outer radius (at minimum airgap) [mm]

θM AX Pole tip angle with respect to axis of rotation [rad]

δM AX Maximum airgap (at pole tip) [mm]; δM AX = δ(θM AX )

RRt Rotor radius at the pole tip [mm]; RRt = RRo − δM AX

RRo Rotor outer radius (at minimum airgap) [mm]

Rsh Shaft radius [mm]

RRt Rotor radius at pole tip [mm]

wRq Rotor tip distance from q-axis [mm]

kRq Rotor tip distance ratio

wRn Rotor pole neck thickness [mm]

kRn Rotor pole neck ratio

dRy Rotor yoke depth [mm]

xix
 τRy Rotor yoke pitch [mm]

kRy Rotor yoke ratio

RRy Rotor radius at the yoke; RRy = Rsh + dRy [mm]

kRw Rotor winding aspect ratio

kRq Rotor tip distance ratio

w(Rq,X) Rotor tip distance from q-axis, case X [mm]

lX Pole body length thickness, case X [mm]

lth Required pole body thickness length [mm]

LR,et Rotor winding end-turn length [mm]

BX Magnetic flux density of surface X [T]

HX Magnetic field intensity of path X [Am− 1]

MX Magnetic flux density of surface X [mm]

σS Stator current density [Amm−2 ]

kCu,S Stator slot copper fill

σR Rotor current density [Amm−2 ]

kCu,R Rotor slot copper fill

λ Flux linkage [Wb-turns]

xx
 LIST OF ACRONYMS

Acronym Definition

WFSM Wound Field Synchronous Machine

PMSM Permanent Magnet Synchronous Machine

HESM Hybrid Excitation Synchronous Machine

ICE Internal Combustion Engine

HEV Hybrid Electric Vehicle

EV Electric Vehicle

ATF Automatic Transmission Fluid

FEA Finite Element Analysis

AFM Axial Flux Machines

RFM Radial Flux Machines

xxi
 ABSTRACT

The focus of this dissertation is to describe the electromagnetic modeling and

optimization, mechanical modeling, thermal simulation and experimental characteri-

zation of two prototype permanent magnet-free high power density wound field syn-

chronous machines (WFSMs) and one prototype of permanent magnet-wound field

hybrid excitation synchronous machine (HESM) for electric and hybrid-electric vehi-

cle traction applications. The WFSMs and HESM are designed for brushless rotor

field excitation using an axial flux hydrodynamic capacitive power coupler (CPC) but

can also be operated with a brush and slip rings excitation system. A flexible design

environment has been developed for large scale multi-objective optimization of the

machines, particularly focusing on the use of a static electro-magnetic solver, FEMM,

and the extension of the software routines to reconstruct the transient behavior of

rotating electrical machines.

The prototypes are designed to operate with a spray cooling system with auto-

matic transmission fluid (ATF Dexron VI) in order to reach power densities compara-

ble to the commercial permanent magnet synchronous machines (PMSMs) for similar

applications. The spray cooling system was simulated with a commercial software

(MotorCAD) and the modeling approach validated with experimental characteriza-

tion. The spray cooling system was modified to include thermal circuit paths that

emerged during the testing of the prototypes and integrated in the current release of

the software.

The experimental characterization shows promising results, with peak output

power at a base speed of 4,000 RPM exceeding 80 kW for the WFSM prototypes, and

a continuous power output of 60 kW with the spray cooling system. The prototyped

WFSMs achieve volumetric and specific torque and power densities of 17.22 Nm/l,

4.69 Nm/kg, 7.19 kW/l, and 1.95 kW/kg.

xxii
 The experimental data collected for the HESM prototype shows a no-load

rotor-side flux weakening capability that enables constant power speed ratio of 10:1

during operation and provides a flexible platform for machine characterization and

advanced control development for one monoaxial and one biaxial hybrid excitation

synchronous machine configurations. The design of the HESM prototype was obtained

with an integration of analytical sizing equations for the initial exploration of the

design space and FEA methods for detailed modeling of the final prototype features.

xxiii
 1

CHAPTER 1

STATE OF THE ART

The state of the art review has been divided in three sections to address

the general characteristics of hybrid and electric drive systems, the synchronous ma-

chines topologies utilized in the industry for traction applications and electric machine

optimization tools that are employed both industrially and in research, for ease of

comparison with the proposed contributions of this work at the end of this chapter.

1.1 Introduction

This work is organized in five Chapters and one Appendix. Chapter 1 presents

the state of the art review to give context to the development of the main focus

regarding the electric machine design. Chapter 2 discusses the theoretical framework

for the development of sizing equations for design space exploration, machine losses

and figures of merit used in the machine optimization. Chapter 3 is an overview of the

finite element analysis (FEA) methods employed to model the machine prototypes,

including an overview of the simulation code architecture and integration of the multi-

physics external solvers to the central Matlab data processing. Chapter 4 details the

design process and modeling results for each of the machine prototypes realized.

Finally, Chapter 5 presents the construction and characterization of the prototypes

and a comparison of the experimental results with the simulation predictions.

1.2 Hybrid and Pure Electric Vehicles

The global diffusion of internal combustion engines changed transportation,

the society and the environment surrounding the world population in ways that few

other technologies have in the past. The renewed interest on technological develop-

ment, resource conservation and environmental effects of the automotive industry has

brought investments and research to the development of electric and hybrid electic
 2

vehicles. Although the vast majority of vehicles in use today rely on internal com-

bustion engines alone, the development of alternative technical solutions created a

market for integrated internal combustion and electrical drive trains and purely elec-

trical ones. A brief presentation of the technologies relevant to this work is reviewed

in the following subsections.

1.2.1 Drive Train Topologies. Three main categories of hybrid electric drive

trains that are currently employed, are identified by the propulsion power flows be-

tween the internal combustion engine (ICE) [31], the battery, the electric motor and

the electric generator (when present). The series topology has the ICE mechanically

decoupled from the transmission, the power flow is in series (hence the name) from

the ICE, to a generator (mechanical to electrical power conversion) and from the gen-

erator and batteries to the electric traction motor. During regenerative braking the

traction motor can recharge the batteries to increase the system efficiency and driving

range. The parallel hybrid configuration has both the ICE and the traction motor

mechanically connected to the transmission, the energy source for the electric motor

is a battery pack, while the generator component is not present. The power flow to

the wheels is in parallel and, depending on the configuration, the electric drive can

be operated as a generator. For instance, if the parallel operation is obtained with

an electric motor (e.g. rear axle) and a traditional ICE (e.g. front axle), the parallel

operation is obtained through forces exchanged with the road pavement (e.g. with

the vehicle coasting at low speed the ICE is operated at the maximum efficiency point

and the electric motor/generator recharges the batteries with the excess power). The

series-parallel is an integration of the previous topologies, using mechanical couplers

it is possible to obtain the previous traction power flows, but additional combinations

are possible.

Another classification is the one most commonly used by the original equip-
 3

ment manufacturers (OEM) in the automotive industry and is related to the position

of the electric motor in the hybrid electric power train. The acronym for this classi-

fication is P followed by a number from 0 to 4, where P stands for powertrain and

the number for the position of the electric traction motor in the transmission, larger

numbers mean that the motor is closer to the wheels. The P0 configuration has the

electric motor connected directly to the ICE via a belt system and often it includes

the starter function. The P1 has the electric motor mechanically connected directly

to the output of the ICE (the crankshaft), while the P2 configuration interposes a

clutch and a fixed gear ratio between the two components, to decouple the shafts and

the operating speeds. In the P3, the electric machine is integrated in the transmission

gearbox or it is placed immediately after it, so that the gear ratio can be changed

during operation (with respect to the previous case) and the engine and motor can

be mechanically decoupled. Finally, for the P4, the electric motor is integrated in

an independent axle from the engine, either before the differential or after it. Hub

motors also fall under this category, since the machine is integrated in the wheels

hub.

This second classification scheme in certain measure applies to pure electric

vehicles (EV), in the sense that the size, speed and torque of the electrical machine

are affected in the same way given the position in the transmission. In principle, the

closer the electric motor is to the wheel, the lower the operating speed. In terms of

operation, electric vehicles rely on the power flow from the battery to the traction

motor and on regenerative braking to recover the kinetic energy.

1.2.2 Components. In the previous section the electrical machines have been

defined as motors or generators to underline the main function in the traction sys-

tem. In reality, the operation is reversible and the traction motor can be used as a

generator, for instance to recover the braking kinetic energy, and the machine defined
 4

as generator can contribute to the traction power (in the series-parallel configuration,

where a mechanical connection allows this power flow). The main difference in the

design is affected by the powertrain P classification, since the same power density

can be obtained with a smaller motor if the base speed in increased, that is reducing

the need for torque density. The drawback of base speed increase is the mechanical

stresses that the machine incurs, the need for additional gearing and also the voltage

availability from the electric drive.

1.2.3 Electric Vehicle Traction Motors. The traction motor characteristics

of interest for vehicular design are mostly the ability to operate at peak torque from

standstill and in general the ability to provide constant power over a wide range of

speeds (changing the stator-side excitation frequency) without the need for variable

gear ratios that ICEs have. The motor design requirements are in great part affected

by the addition of weight and the occupied volume in the powertrain, so that high

specific torque density and power density are sought after to reduce the impact of the

motor on the vehicle assembly. The electric motor power output is also a fundamen-

tal sizing requirement, since it will affect directly the vehicle maximum speed and

performance, however, the main advantage with respect to ICEs is the overloading

capability of the machine. In other words the electric motor can be sized for the

average power required by the vehicle traction power requirement (one half or less

than the peak power) and loaded above nominal intermittently for short periods of

time, if suitable thermal management is present. Additional system requirements

(that affect the sizing of inverter drive, insulation and thermal management) are the

terminal voltage and currents. Depending on the topology selected, the motor may

be minimized but the inverter size may negatively offset the gain. Comprehensive

overviews of the technologies are given in [131] and [33], a brief review of traction

motor technologies is presented in the following, with main advantages and disadvan-

tages relative to each other:

 5

• Induction machines (IM) with cast or squirrel cage rotors are the most

widespread machines in industrial applications, because of their relatively sim-

ple and robust rotor construction, lower material cost, common availability of

the materials and industrial maturity of production processes. The rotor circuit

is passive and excited from the stator side field, so that no electrical connection

is needed to access the rotor winding, in almost all applications constructed to

obtain a short circuited topology (for this reason also addressed as cage), and

it also results in the machine rotor demagnetization in the event of stator-side

faults, making it passively safer than PMSMs and WFSMs. For good thermal

management, the rotor circuit can be overloaded more than the ones in other

topologies (e.g. WFSMs) since the whole circuit is passive and there is limited

risk to damage its components. The rotor operating voltage is so low that the

insulation is obtained with the natural surface oxidation layer at the interface

between the circuit and the laminations. The drawbacks are mainly linked to

the inability to operate at very wide constant power speed range and high power

factor, generating the need for an oversized inverter drive in the system design

and for this reason they are not utilized as much as traction machines as in other

applications. However, some notable exception to this trend are some General

Motors Corporation machines [59] and EV manufacturer Tesla Inc. [10], in the

latter case the rotor is equipped with a fabricated copper cage manufactured to

reduce rotor conduction losses.

• Wound field synchronous machines (WFSM) are widely used in generator

applications since the output voltage can be regulated changing the rotor exci-

tation current. Renewed interest in these machines for traction applications is

due to the inherent high constant power speed range (CPSR), obtained with the

rotor flux regulation and the absence of rare earth magnets, the price of which

is highly volatile. Additionally, the power factor is considerably higher than

 6

the IM case, so that the size of the inverter is generally smaller, although this

advantage may be offset by the need for an additional power electronics circuit

to regulate the rotor excitation current. The presence of rotor copper losses,

on the other hand, requires a dedicated cooling system to extract said losses

from the rotor and avoid damaging the winding and power electronic compo-

nents connected to the rotor circuit. Commercially, WFSMs have been used in

Renault S.A. vehicles [104]. Initally, the WFSMs were produced by Continental

A.G. in Europe, but the most recent models have been internalized by Renault.

• Permanent magnet synchronous machines (PMSM) are the most widely

used for traction applications, given the generally high power density that can

be obtained from this machine type. The weight of the permanent magnets

is generally much smaller than the IM cage or the field winding of a WFSM

machine of the same power range, allowing to decrease the rotor weight and

inertia. The main disadvantage of this type of machine is that the only possi-

bility to regulate the flux is to use the stator current to counter the magnetic

field produced by the magnets, that results in design compromises to obtain a

wide constant power speed range, high base speed power factor and the need to

expend stator current to reduce the machine back-EMF above the base speed.

Another issue with vehicular applications is the uncontrolled braking in case

of inverter drive fault, where a short circuit in the traction drive can trigger

alternating torque from the motor. In the following sections, additional details

are presented regarding synchronous machines for a direct comparison of the

prototypes developed in this work with commercially available traction motors.

• Reluctance machines employ a different torque production mode from the

more widely used synchronous machines, i.e. in PMSMs and WFSMs only a

fraction of the torque is obtained from the reluctance, while this group of ma-
 7

chines mainly exploit the reluctance torque. Academically some switched re-

luctance (SRM [117], [127] and [41]) and synchronous reluctance machines

(SynRM, [85] and [41]) have been proposed for electric vehicle applications.

The same groups presented above can be realized as radial flux machines (RFM) or

axial flux machines (AFM), referring to the main direction of the magnetic flux at the

airgap. Commercially, RFMs make up almost the totality of the market, but a case

has been made academically for the potential for higher power densities of AFMs ([19])

but in general the practical implementation is more complex than RFMs. Hovewer,

a review of AFMs is given in [39]. Additionally, some complex geometries, usually

referred to as flux switching and transverse flux machines, present more complex flux

lines.

1.2.4 Cooling System. In order to obtain high torque density in the electri-

cal machines, a suitable cooling method and thermal management strategy must be

identified, to guarantee the integrity of the component and potentially gain in per-

formance, efficiency and material cost. The effectiveness of a cooling method can be

evaluated from the current density (measured in Amm−2 ) in the conductors that can

be maintaned without damaging the insulation or cause a thermal runaway of the

machine components. A very general classification is given by cooling fluid:

• Air cooled machines are widely employed both in natural and forced convection

for its simplicity of implementation. The air heat exchange coefficients and the

indirect cooling of the machine components allow a use of continuous current

densities in the range of 3-7 Amm−2 [99].

• Water or ethylene glycol and water solutions (anti-freeze) is also a cost-effective

and available cooling fluid, usually it is employed for larger power densities with

respect to the previous case, either for direct cooling of the conductors, using
 8

channels in the windings or indirect cooling with a water jacket that encloses

the machine stator. The current densities are improved to the range of 7-10

Amm−2 [99].

• The oil spray cooling system provides direct cooling of the copper end-turns

of the machine and, given the good thermal conductivity of the material, can

effectively manage the temperature of the conductors to avoid damaging the

insulation. The operating fluids are usually mineral oils, such as automatic

transmission fluid (ATF), motor oil or transformer oil. Several methods have

been developed, especially in the aviation industry, but most of the research is

protected as trade secrets and the actual experimental data is not accessible to

the general public. In recent years, interest has grown in the automotive sector

to explore this group of systems and also national laboratories have received

funding (in particular NREL) to provide models and experimental data to the

industry [54]. Current densities exceeding 20 Amm−2 can be achieved.

1.3 Synchronous Machine Topologies

Several classifications are possible for the family of machines defined as syn-

chronous, since the torque production is only stable when the stator and rotor fields

rotate at the same angular speed, the one used in the following refers to the rotor

excitation modality. The three main branches of the synchronous machines family

tree can be considered depending on the machine magnetization type, that is electri-

cally excited (WFSMs), permanent magnet excitation (PMSMs), and no excitation

(synchronous reluctance machines, or SynRMs). The last branch has not yet been

used commercially for automotive applications and therefore will be described in the

following section regarding academic contribution on the subject. Additionally, a

group of machines denominated hybrid excitation synchronous machines are realiz-

able, where a combination of two excitation types is possible. In the following sections
 9

the three relevant cases of WFSM, PMSM and HESM are presented more in detail.

As a general power density comparison of machines the data summarized in Table

1.1, is comparable with the ranges presented in [72]. The performance of the ma-

chines is reported in [18]-[6] for the Toyota Prius 2009 IPMSM motor, the Remy

PMSM HVH250-090 [12] and the BRUSA HSM1 [16] power densities. Additionally,

the WFSM prototypes developed for this work are included for ease of comparison

[26].

Table 1.1. Automotive Electrical Machine Comparison

Machine Parameters Prius [18] HVH250 [12] HSM1 [16] WFSM [26]
Peak Power (kW) 60 170 125 80
Peak Efficiency (%) 96 95 96 95
Mass (kg) 37 49 52 41
Power Density (kW kg−1 ) 1.62 3.47 2.40 1.95

1.3.1 Wound Field Synchronous Machines. The wound field synchronous

machines are divided in two main groups, salient and non-salient, referring to the

torque production mechanisms utilized for the machine operation. A salient machine

will produce a larger part of the output torque with respect to the non-salient one with

the reluctance torque mechanism, where the rotor tends to align to the least reluctance

path to minimize the potential energy of the magnetic field. Salient machines will

also show a difference in the values of the d-axis and q-axis inductances in the dq0

equivalent circuit of the machine, with the d-axis inductance being larger than the

q-axis, while the non-salient machine inductances are approximately equal in the

two axis. Both machine groups produce synchronous torque obtained by holding the

machine electromagnetic rotating fields orthogonal. An additional classification is

obtained specifying the rotor excitation method employed:

• Brush and slip rings implementation is the most common in commercial appli-
 10

cations, where graphite brushes slide on bronze slip rings to feed DC current to

the rotor circuit during the rotation (brushed excitation [104]).

• Inductive couplers using stator harmonics and rotor auxiliary windings ([2], [4],

[5] and [128]) or rotating transformers, in either axial ([73], [74], [77] and [112]),

radial ([47], [55], [69], [111], [121], [119], [118], [120], [122] and [124]) or three-

dimensional ([83], [84] and [98]) flux configurations, transfer the static circuit

electrical power into a magnetic field that crosses the airgap for a contactless

power transfer.

• Capacitive power couplers, also available in axial or radial ([23], [24], [80], [81]

and [82]) flux configurations, transfer power across the airgap via an AC electric

field generated by the capacitor plates electrical charges.

• Resonant inductive and capacitive systems, combine the previous two power

transfer mechanism to increase the power density and to allow higher oper-

ating frequencies and size reduction for the power electronics (using resonant

converters [25]).

The last three implementations are usually referred to as brushless excita-

tion systems and they transfer power across an airgap with AC excitation, which is

then converted into DC current using rotating rectifier systems, in [25] a list and

comparison of wireless power transfer methods and prototypes is given. The main

advantage of these group of machines with respect to the PMSMs is that the field

excitation is controlled separately from the stator excitation (hence the alternative

nomenclatures of the machines group, separately excited or electrically excited syn-

hcronous machines, SESM and EESM respectively), allowing for a direct control of

the back-EMF from the rotor side and consequently a theoretically infinite flux weak-

ening region and a controllable magnetization of the field circuit, that can avoid or
 11

mitigate the uncontrolled generator operation (UGO [38] or UCG [51]) during faults.

In addition, potential advantages are related to the active power factor control of the

machine available for this group (using a rotor excitation strategy) and economically

an advantage may arise in terms of costs, since the material cost of the windings is

lower than permanent magnet materials, but at the same time the production costs

for the winding process may offset this potential advantage. On the other hand, the

drawback is the system-level addition of components, inherently lower power density

and efficiency due to rotor iron saturation and rotor copper losses. The rotor copper

losses main drawback is due to the need for an efficient heat extraction from the

rotating components on the whole machine operating range.

At least one commercially available product uses a system of brushes [104] and

was developed for EV and HEV applications by Continental AG and Renault SA and

integrated in the Zoe and Fluence vehicles. One group of solutions for inductive brush-

less implementations applied to salient WFSMs has been explored in [47], [46] and

[112], where rotating tranformers have been designed. Both solutions were proposed

as a commercial product [16] and given the separation of the magnetic paths for rotor

excitation via a rotating transformer and a conventional stator these solutions decou-

ple the stator and rotor electromagnetic design from the excitation system design.

For lower power rating, ferritic pot-core transformers have been proposed in [74], [69]

and [111] for academic research. Other proposed topologies make use of a coupled de-

sign of stator harmonic generation and rotor auxiliary windings, that power the main

rotor excitation winding: [2] with a single auxiliary rotor winding and stator-side

active harmonic injection, [4] and [5] with auxiliary rotor windings and tooth-wound

concentrated stator winding to passively provide excitation harmonics and [128] with

multiple auxialiary windings, modified rotor structure and tooth-wound concentrated

stator winding. These solutions would allow the integration of contactless excitation

in the machine structure, avoiding the addition of other components to the system,
 12

but forcing some constraints on the overall design.

A good overview of methods and prototypes in capacitive wireless transfer is

given in [25]. From the same author, a capacitive power transfer coupler has been

proposed in [24] for a wound field generator application, demonstrating the feasibility

of fractional kW operation. An updated version of the prototype in [80] was used

during the development of part of this project to excite the first prototype rotor,

transferring more than 1 kW to the rotor circuit [26].

In terms of WFSM modeling for simulation and optimization, in [48] a model-

ing barrier and pole shape for increased saliency using finite element analisys (FEA)

is presented, in [44] the FEA is coupled with a genetic algorithm optimization and

ferritic magnet assisted WFSM is investigated (little details on the optimization pro-

cedure are presented). Also in [75] and [76] barriers for saliency enhancements are

investigated with FEA models, [106] investigates generator operation improvement

with flux barriers FEA models and [20] proposes a saliency ratio enhancement FEA

model.

Non-conventional WFSM topologies are proposed in [27], where a yoke-wound

machine is proposed, [57] and [103] propose doubly-salient WFSM (stator and rotor

have salient poles and concentrated windings) for traction application as a hub-motor.

In the last two references, the modeling is carried out with analytical modeling based

on inductance estimation.

Another series of publications proposes and expands a magnetic equivalent cir-

cuit (MEC) modeling of WFSMs, [7] links the model to a population-based algorithm

for optimization. The resulting prototype has been used in [123] for investigation of

Pareto-optimal excitation strategy and additions to the model were made in [71] to

model dispersed fluxes and end-effects.

 13

Additional analytic modeling of WFSM and FEA verification of the models

are proposed in [114] for a motor designed and modeled in [53] and [52], and yet

different modeling approaches are investigated in [105] and [57] to integrate control

considerations for WFSM use in vehicle applications.

Other approaches are focused on the efficiency optimization through machine

topology modeling, such as [68] for a population-based FEA characterization and [21]

for a single prototype analyzed for efficiency and high field weakening range. Finally,

coupled electromagnetic and mechanical simulation for vibration and noise modeling

were presented in [97].

1.3.2 Permanent Magnet Synchronous Machines. The saliency classification

is also used in the PMSM group of machines, the notable difference is that the saliency

characteristic is inverted, meaning that the q-axis inductance is typically larger than

the d-axis one for salient PMSMs. Additional classifications address the position of

the magnets in the rotor structure, such as surface permanent magnets (SPMSM,

where the magnet material is directly facing the machine airgap) and interior perma-

nent magnets (IPMSM, where the magnets are placed inside the rotor laminations).

Overall, SPMSMs tend to exhibit higher torque density, machine linearity under load

and magnet losses and mechanical stress than the IPMSMs for the same rotor tip

speed, due to the higher magnet material utilization. Conversely, IPMSMs tend to

have larger flux dispersion in the rotor lamination (leakage fluxes that do not link

with the stator windings) and considerable effort in the design is aimed at reducing

this drawback, compatibly with the mechanical integrity and stresses of the machine,

employing flux barriers or differential grain orientation in the laminations. In the

traction applications IPMSMs are more widely used, the reasons are that a higher

CPSR can be obtained, a more advantageous reluctance torque characteristic. A

comparison between IPMSM and SPMSM machines is given in [102].

 14

The permanent magnets themselver are divided in several groups, notably fer-

ritic, AlNiCo (Aluminium Nickel Cobalt) and rare earth permanent magnets (SmCo

and NdFeB). The groups are listed in order of magnetic energy product (BH)max , the

maximum product of the strength of the magnet magnetic field (remanence Br ) and

the magnet resistance to demagnetization (coercivity Hc ). As an order of magnitude,

ferritic and AlNiCo magnets have about one tenth of the energy product of rare earth

permanent magnets. Additionally, the Curie temperature is a temperature at which

the magnet loses its ability to produce a magnetic field. For this parameter the rare

earth materials have a wide utilization range, where the SmCo can reach the highest

temperatures (1̃000 K) with about half of the NdFeB magnetic energy product (with

Curie temperatures around 500 to 650 K). In general, the coercivity is reduced at the

increase of the magnet temperature, reducing the flux generated.

This group of machines is the most widely used in traction applications and

usually considered as the comparison baseline for alternative structures proposed both

in literature and in the industry. Several reviews are available, also at the commercial

level, for instance [125], [65] and [107] list a large number of mass-production vehicles

and the electric or hybrid traction characteristics, including motor power density

references. General Motors Corporation has a policy of machine design disclosure that

provided academically relevant papers and reviews of the company developments, in

particular [100] and [101] presents design details for the Spark as compared to Nissan

Leaf and presents the design for a mild-hybrid vehicle electrical traction, while [89]

and [58] are related to the Chevrolet Bolt and Volt design respectively and [32] gives

details on the cooling and mechanical design of a prototype. Other manufacturers

provide data sheets with some details on the machine capability (e.g. BorgWarner

[12]).

Moreover, an ongoing benchmarking activity is carried out by Oak Ridge Na-

 15

tional Laboratory (ONRL) and funded by the United States Department of Energy

(DOE), in order to characterize machine drives available on the market, such as Toyota

Prius [18] and Camry [17]. Other academic work focuses on comparing the leading

IPMSM technology to possible alternatives, such as switched reluctance machines

([127] and [67]) or a WFSM and PMSM design in [103].

Finally some academic work relevant to this project, for example [34] describes

an IPMSM salient pole shaping FEA-assisted optimization with nondimensional ge-

ometric parameters.

1.3.3 Hybrid Excitation Synchronous Machines. This group combines two or

more excitation methods to reach a compromise between high constant power speed

ratio at a high power factor of the WFSM (reducing the VA sizing of the inverter

drive) and the power density and low rotor losses obtainable with PMSMs. Several

combinations are possible and are attracting interest in the academic environments

since the disadvantages of one topology can be be mitigated by the hybridization with

another.

Many topologies have been proposed with separate or integrated wound field

(WF) and permanent magnet (PM) poles or multiple rotors. Hybrid excitation ma-

chine overviews with a broad spectrum of implementations are given in [42] and [35].

The previouse references offer a classification of series and parallel excitation systems.

In particular, for axial flux machines a design methodology for dual-rotor machines

[38] and a flux weakening control strategy demonstrated very wide constant power

operation in open-loop [37] and closed-loop control [15].

Additional reviews and modeling resources are given in [3] including a flux-

switching alternator prototype. Also [1] presents a review, FEA and lumped param-

eter modeling of WFSM-PMSM hybrids.

 16

In [11] a quantitative review of prototypes for automotive applications is given,

a qualitative review of machines and excitation methods is available in [94] and finally

in [63] some alternated-pole hybrids are reviewed, as part of the research work on series

hybrid excitation generators from the same research group ([60], [61], [64] and [62] in

publication order). For mixed-pole solutions, where the permanent magnets and the

wound field are integrated into a single pole, several solutions have been proposed

such as [108] with a biaxial excitation, [126] with a permanent magnet placed between

wound pole and one publication addressed the AFM design [13].

A different approach altogether in pole integrated hybrids is the group of

machines denominated PM-assisted SynRM, in [41], [40], [95], [22], [96], [78], [9]

and [8]. These works are more relevant to the following derivation for the large-

scale optimization methods employed than for the machine topology, that will not be

presented in more depth.

A general theory valid for both AFMs and RFMs has been derived for the

operation of single-axis and bi-axial configurations, meaning that the magnetic axis

of the permanent magnet and the wound field excitations can be modified to address

constant power speed, power factor correction capability, torque capability and high

speed power losses requirements [14]. The conclusions of the work on axial machines

can be extended to radial machines, where different basic topologies are proposed

in literature. The coaxial rotor HESM prototype presented here in detail (Section

2.1) has been used to derive the model of the machine and has been realized as

the parallel hybrid excitation synchronous machine (parallel WFSM-IPMSM hybrid).

The prototype presented in this work will be detailed in Section 4.3 for the design

process and in Section 5.3 for the experimental characterization. In literature, a

similar topology that presents two coaxial rotors on the same shaft, one excited

with a wound field and the other with both permanent magnets and wound field in
 17

series, was first derived in [91], for a 2-pole 750 VA machine (series-parallel excitation

WFSM-IPMSM hybrid) and later a similar concept was modeled as a parallel WFSM-

SPMSM hybrid generator in [70]. The advantage of this structure, presented in this

dissertation, is that parallel excitation fluxes are generated, allowing the design of the

two rotors separately. Moreover, with respect to the prototype in [91] where the rotor

winding extends under the PM rotor section, the one developed for this work allows

the relative angle modification between the PM and WF airgap fields. This flexibility

in the mechanical design allows to test two configurations, monoaxial excitation of

PM and WF on the same axis (dPMWF using the nomenclature from [14]) and one

biaxial excitation case, with WF excitation and PM fixed power factor (dWFqPM,

also in [14]) compensation with a single prototype.

1.4 Electric Machine Optimization

A brief overview of optimization methods relevant to this work is given in this

section. For electric machine optimization, an extensive review and benchmarking of

optimization algorithms is given in [29].

1.4.1 Differential Evolution Algorithm. The algorithm proposed by R. Storn

and K. Price in [113] was adapted to parallel operation for this work, previously it

has been used for several PMSM optimization papers (e.g. [93] using parametric

geometries). Additional modifications to the FEA setup allow for a computationally-

efficient solution of the magnetic fields of the loaded machine, taking advantage of

spatial and time symmetries, detailed in [109] and in [110] for multi-objective opti-

mizations involving case-studies of PMSM machines with concentrated windings. In

general terms, a differential evolution optimization algorithm considers a population

divided in generations (that is iterations) in which each member is defined by a vector

of input parameters. After all the members in a generation are simulated to calcu-

late the cost function, the members with the smallest cost functions are perturbed
 18

matematically emulating the natural mutation and crossover and are used as an input

for the next iteration. For machine design application, usually a selection of the best

members in the distribution is applied, to identify a Pareto front of the design trade-

off. The division in generations allows for a parallelization of the algorithm execution

at the level of the member calculations, since the only interactions between members

occur when the full generation cost function has been evaluated.

1.4.2 MonteCarlo Algorithm. The MonteCarlo algorithm was first proposed

by N. Metropolis and S. Ulam in [87] for the solution of differential equation with

statistical methods. The underlying assumption is that randomized trial and error

tests over a very large number of cases, a probability distribution can be found, rep-

resentative of the system under analysis. The modeling of the physical system will be

divided in selecting stocastically the input values and calculating a cost function from

a set of deterministic relationships that describe the system. The practical applica-

tion to machine design often involves generating a parametric geometry in which the

parameters are chosen randomly in a range that generates realizable geometries, and

then the FEA simulation will solve the resulting electromagnetic problem, obtaining

the cost function associated to the test. This algorithm is inherently parallel, since

to each set of input values corresponds a set of output cost functions and each test is

independent from the rest.

1.4.3 Design of Experiments Algorithms. The design of experiments (DOE) is

a method to identify a set of input points in an n-dimensional space in order to define a

set of experiments in a given range of the input variable and to derive (for the resulting

outcomes of the experiments) a response surface (RS), that is fitting a polinomial to

the results and estimating the variance of the test ([56]). The main application of this

method in the machine design is to capture an approximated analytical correlation

between different machine figures of merit, and to explore the design space before
 19

using a global optimization algorithm. The limitation in the practical use of this

method is that the number of function evaluations for a wide number of factors

increases as a factorial function. However, it requires limited calculation time for a

limited number of inputs and it can be adapted to different domains, namely with

a circumscribed (CCC), inscribed (CCI) or face centered (CCF) central composite

design [92]. The names are descriptive of the tests carried out in each method, the

CCC extends outside the minimum and maximum range of each input variable (in

two dimension circumscribing the square obtained at the intesection of minima and

maxima of the inputs), the CCI considers only cases inside of the domain boundaries

(in two dimension a circle is centered around the midpoint of each dimension range

and a square is inscribed in the circle) and the face centered considers cases at the

intersection of minima and maxima of the domain dimensions and an additional point

at the middle of each segment connecting the previous points. A graphical depiction

of the domains in two dimensions is given in Figure 1.1.

Figure 1.1. Central composite designs, CCC is for circumscribed, CCI for inscribed
and CCF face centered cases.

1.4.4 Extended Optimization Algorithm. The extended optimization algo-

rithm combines two or more of the previous algorithms to identify the design space

region where the optimal machine is found and executes one or more additional opti-
 20

mization runs to include additional features. For instance, the optimization of the full

machine including barriers may require longer simulation time due to the optimization

problem complexity and parameter number, on the other hand, splitting the process

in two parts (i.e. identifying the optimal machine stack length to diameter ratio

first and optimizing flux barriers later) can reduce the designer effort while allowing

for incremental improvement of the prototypes. As an example found in literature,

P. Zhang, G. Sizov, D. Ionel and D. Demerdash present a combination of response

surface modeling (CCD to identify the significant design variable and their ranges)

and of differential evolution optimization to find the Pareto front of a distribution

of spoke-type IPMSMs in [129] and a comparison of optimized geometries for three

types of IPMSMs in [130].

1.5 Proposed Contributions

1.5.1 Multi-Solver Optimization Software. The proposed contribution on

machine optimization software addresses the implementation of a multi-solver, multi-

physics design environment developed for the initial WFSM prototype project and

extended to the simulation of PMSMs and HESMs. In particular, a flexible, modu-

lar software architecture has been devised to interface the simulation code developed

in the Matlab language to two electromagnetic solvers (FEMM [86] and Infolytica

MagNet [49]) and one thermal simulator (Motor Design Limited MotorCAD [90])

via ActiveX commands and Visual Basic (VBA) scripts [88]. The modularity of this

software allows for integration of additional solvers, provided that a model drawing

and setting interface is enabled remotely. Several research groups developed similar

software, but usually the focus is on the electromagnetic design alone and the scope

is limited to the implementation of one machine structure (e.g. Syr-E used in [79] for

SynRM). The software developed for this work, on the other hand, allows for par-

allel development of the parametric template of the machine by different developers

 21

and provides a set of standardized functions to interface to the external FEA solvers,

passing only the data structure needed for simulation. In principle, all operations

could be integrated in Matlab, but the use of external solvers optimized for speed

provides a simulation and development time reduction. The simulation results ob-

tained with FEMM and MagNet have been validated in the early development stage

in order to take advantage of the parallelization of the FEMM solver (that allows

unlimited licenses to be used at the same time) without sacrificing the accuracy of

the modeling.

In particular, the proposed contributions to this topic area are the following:

• Modular software architecture for different multi-physics solvers that allow:

– Parallelization of several solver instances for simulation speed increase.

– Coupling to optimization algorithms such as differential evolution and re-

sponse surface modeling.

– Expandable and robust data-structure that can be interfaced to additional

solvers with minimal development effort.

• Flexible geometric templates with parametrized non-dimensional factors for:

– Ease of comparison between different synchronous machine types (e.g.

WFSM, IPMSM and SPMSM, HESM).

– Testing and optimization with different optimization algorithms and meth-

ods.

– Generation of similar geometries (preserving the ratios between machine

components) for different physical envelopes.

• Transient reconstruction using an open-source static solver to obtain:

 22

– Transient reconstruction from static solutions of time-dependent and rotation-

dependent machine parameters (e.g. voltage and core losses).

– Comparable loss estimation compared to commercial software.

– Machine loss mapping at any operating speed with transient reconstruction

post-processing.

1.5.2 High Power Density WFSM. The integration of the WFSM prototype

1 with a brushless capacitive excitation demonstrated the feasibility of this excita-

tion method on a high-power density wound field synchronous machine, that exceeds

the metrics imposed by the DOE USDRIVE 2020 electric motors technical targets

of 30kW continuous power, 55 kW peak power for 18 seconds, 1.6 kW/kg and 5.7

kW/liter [30] (the weight of the machine includes all the active materials and shaft,

the volume is the total volume that encloses the machine active materials). These

power densities are comparable to commercially available IPMSM (e.g. [18]) and

WFSMs (e.g. [104]). To the knowledge of the author, the prototype was the first

one to be operated with the CPC technology [82] and it was expressly designed to

meet the requirements imposed by the capacitive power coupler [26], additionally,

the research related to the thermal modeling of ATF spray-cooled WFSM is the first

published material on the subject.

In particular, the proposed contributions to this topic area are the following:

• Design of an ATF spray cooled WFSM which meets DOE USDRIVE 2020

targets for power and power density.

• Design of a WFSM that can be operated with a novel capacitive power coupler.

• Modeling of a large range of rotor flux barrier types and positions in the rotor

pole, including permanent magnet insertion.

 23

• Improved spray cooling thermal models which take into account:

– Spray cooling effect on rotor iron core temperatures.

– Spray cooling effect on stator iron core temperatures.

– Experimental calibration of the improved thermal model.

1.5.3 Analytical Model for Hybrid Excitation Optimization. The work

on permanent magnet-free WFSM machines has been expanded in the perspective of

future machine development with the design of one prototype of reduced permanent

magnet hybrid excitation machine. The machine modeling development effort is mo-

tivated by the possibility of finding a compromise between machine torque and power

density (in which PM machines are superior when employing high temperature grade,

rare-earth permanent magnets) and flux regulation capability. The proposed design

procedure uses firstly an analytical sizing model to identify the design tradeoffs and

design space region for the optimal candidates (e.g. electromagnetic loading, power

and mass), secondly it uses the FEA software routines to identify additional machine

details (e.g. torque ripple, iron saturation and leakage fluxes). This approach com-

bines a fast and coarse analytical approach that reaches general conclusions with a

refined numerical simulation for particular test cases, reducing the overall develop-

ment and simulation time with respect to either of the two methods used for the

whole design process.

In particular, the proposed contributions to this topic area are given in the

following:

• Adapted existing analytical sizing methods to hybrid excitation machines.

• Modeling and characterization of a radial flux machine electromagnetically

equivalent to the axial flux machine proposed in [38].

 24

• Verified the sizing model within the tolerance of electromagnetic material prop-

erties uncertainties against FEA models.

• Final design modeled with high accuracy, coupling the analytical model to the

FEA simulation and mapping routine capabilities previously presented.

1.5.4 Hybrid Excitation Machine for Controls Development. The proposed

radial flux hybrid excitation synchronous machine is meant to provide a platform for

advanced controls development of this particular machine topology that provides ad-

vantages in terms of options for the design of high power density, reduced permanent

magnet content machines. The projected use with an efficient spray cooling system

allows the development of drive cycle gains in terms of losses and increased constant

power speed range with respect to the PMSM structure and efficiency and power den-

sity with respect to the WFSM. During the design phase, the rotor structure has been

developed with the option to operate the machine in monoaxial and biaxial excitation

configurations, so that a single prototype can be used to represent different machine

types. The compromise is that the hybridization ratio has been chosen to obtain

a theoretically infinite constant power speed range in the monoaxial configuration

(bound by peak power output performance metrics) and oversizing the permanent

magnet excitation portion for the biaxial excitation. This design choice is motivated

for the proof-of-concept research on biaxial hybrid excitation and has the potential

to motivate additional research on the topic in the future.

In particular, the proposed contributions to this topic area are the following:

• Design and prototyping of a parallel rotor, radial flux HESM which meets DOE

USDRIVE 2020 targets for power and power density, conceptually similar to

the structure patented by Ecoair Corp for alternators [116] (9 kW peak power

at 28 V constant output and 5:1 CPSR).

 25

• Mechanical design for easy adaptation of a single prototype for testing monoax-

ial and biaxial hybrid excitation concepts.

• Experimental characterization of a radial flux HESM for high CPSR capability

(10:1 at no-load).

• Experimental characterization of equivalent circuit parameters of HESM for

machine control development.

 26

CHAPTER 2

ANALYTICAL FRAMEWORK

In this chapter the fundamental concepts of machine analytical modeling are

examined. In order to compare Wound Field Synchronous Machines (WFSMs) and

Permanent Magnet Synchronous Machines (PMSMs), sizing equations derived and

compared, in the effort of showing the advantages and disadvantages of the different

topologies. Finally, a hybrid excitation machine analytical sizing is proposed, with

the intent of enabling previous research in the field of Axial Flux Machines to be

extended to Radial Flux Machines.

2.1 Sizing Equations

Using a basic modeling of the machine airgap it is possible to identify the

loading characteristic and main figures of merit before more detailed modeling of

the machine and FEA simulation (Chapter 3.3). The sizing equation approach is

a classical method originally proposed by V. B. Honsinger in [43], adapted by S.

Huang, J. Luo, F. Leonardi and T. A. Lipo in [45] and extended to include thermal

consideration by A. Cavagnino, M. Lazzari, F. Profumo and A. Tenconi in [19]. This

technique is widely employed for initial exploration of the design space, as it allows

for rapid results and provides insight into the design tradeoffs.

2.1.1 Airgap Flux Density Model. The excitation is the main characteristic

that sets apart the PMSM and WFSM. For wound field excitation, an additional

control handle is available to direcly set the excitation flux, while for permanent

magnet excitation, the stator has to be used for flux weakening at high speed in order

to maintain the operation inside the voltage limit. It follows that in the no-load

condition, the nominal rotor current will provide the magnetization flux, while the

permanent magnets always generate the flux that is imposed by the magnetic circuit.
 27

The following hypotheses are needed to reduce the complexity of the analysis and

compare the resulting figures of merit:

1. The two machines have the same airgap thickness δ0 , stack length L and airgap

radius Rg , therefore the same the same available rotor airgap surface Sg , rotor

volume Vg and airgap MMF drop Mδ0 .

2. In the no-load condition (stator current set to zero), the same peak airgap flux

is obtained for the fundamental harmonic with PMs and nominal rotor current

respectively, Φ̂g,0 → Φ̂g,P M (IS = 0) = Φ̂g,W F (IR,n , IS = 0)

3. The linear stator current density for the fundamental harmonic at the airgap is

also the same, so that AS1,W F = AS1,P M .

4. The magnetic flux tubes in the iron sections have infinite permeability, so that

the corresponding reluctance is null and the flux experiences no MMF drop.

5. The field orientation is guaranteed by an ideal regulator that keeps the rotor

and stator fields orthogonal, therefore the nominal loading angle sets the current

vector on the machine q-axis and the rotor excitation flux on the d-axis.

Once the first hypothesis is established, the second can be referred to the

first harmonic peak magnetic flux density over the airgap surface (B̂g1,P M ), that is

formalized in Eq. 2.1. The third hypothesis is introduced to maintain the same

stator equivalent excitation on the airgap, in order to allow the hybridization of the

machine in the following derivation. The last two hypothesis simplify the analysis in

order to obtain a linear system on which the superposition theorem can be applied,

and to consider only the alignment torque component. This last simplification affects

the torque capability in the modeling, but avoids taking into account the reluctance

component of the torque, that would result in opposite nominal current vector angles

(lagging or aligned to the q-axis for the WFSM and leading for the PMSM).
 28

B̂g1,P M (IS = 0)Sg = B̂g1,W F (IR,n , IS = 0)Sg (2.1)

Under these assumptions, the torque of radial flux machines can be expressed

as the integral of the force over the airgap, resulting in Eq. 2.2. The modeling has

been adapted from [19].

√
Tem = 2πRg2 LB̂g1 AS1 (2.2)

In terms of this idealized machine, several metrics can be derived. An example

for peak magnetization flux B̂g1,P M = 0.9T and a rotor volume of 2.6 liters yields a

torque of 199 Nm for 60 kAm− 1. The values in the example are obtained from

experience with previously designed high power density electrical machines of a similar

size.

In the following derivations, the actual stack length can be obtained from the

net lamination length with Eq. 2.3, where Lstack physical length of the assembled

stack and kF e the stacking factor (considered equal to 0.95).

L = Lstack kF e (2.3)

Since the iron core saturation is not considered in this basic model, the torque

grows linearly with the stator current density.

It is possible to take into account additional effects, removing some of the

simplifying assumptions, but the increase in complexity will be analyzed after the

main design space for optimal candidates is identified. This combined method allows

for a fast, although coarse, search on the initial premises, but reduces the development

effort, in order to focus on the main aspects of machine characterization.

 29

2.1.2 Stator Sizing Equations. In order to characterize the main machine

metrics taking into account the effect of the iron structure on the behavior under

load, a set of sizing equations have been derived. According to the model chosen for

torque calculation (Eq. 2.2), all machine parameters depend on a given value of peak

fundamental airgap magnetic flux B̂g1 and the root mean square of the fundamental

component of linear current density AS1 . The stator non-dimensional ratios are given

by the conservation of magnetic flux over the flux tubes. The relative sizes of the

sections in the flux tubes are given by the ratio between the peak values of the

sinusoidal magnetic flux density in the flux tube and at the airgap. The physical

dimensions of the stator presented in the following are depicted in Figure 2.1 for a

sample geometry.

The pole pitch (τp ) of Eq. 2.4 is the airgap line used for integration of the

magnetic flux density.

2πRg
τp = (2.4)
2p

The peak airgap flux of a pole (Φ̂) with sinusoidal flux distribution has been

adapted from [99] and it represents the main machine magnetization flux. All the

following development will refer to the machine parameter of Eq. 2.5.

 L  τp  
x 2 B̂g1
Φ̂ = B̂g1 cos π dx dl = B̂g1 τp L = 2Rg L (2.5)
0 −τp τp π p

The resulting airgap magnetic flux density is then obtained manipulating Eq.

2.5 to fit the model of ideal torque.

Φ̂ p
B̂g1 = (2.6)
τp R g L
 30

Figure 2.1. Stator geometric parameters for analytical sizing of the machine

At this point the actual machine topology needs to be simplified. It will

assumed that the stator is composed of two structures, one radial and one tangential,

with respect to the plane orthogonal to the machine rotational axis. The radial

structure is a stator tooth flux where, based on hypothesis 4, we assume flux to be

present only on the teeth.

The tooth is defined by the pitch at the airgap τSt and the width wSt (a straight

tooth geometry is assumed). For each pole, the flux can be obtained integrating over

the tooth sections in Eq. 2.7.

 31

 L  τp  
x 2 wSt zL 2
Φ̂ = B̂St cos π dx dl = B̂St = B̂St wSt Lmq (2.7)
0 −τp τSt π 2p π

With simple manipulation of Eq. 2.7, the peak value of the tooth flux density

is obtained in Eq. 2.8.

Φ̂ π
B̂St = (2.8)
2 wSt Lmq

The axial structure is the stator yoke flux of a pole, the yoke is defined by it

depth in the radial direction, dSy . Since the flux splits over 2 identical stator yokes

for each pole, the integral of Eq. 2.9 carries a 0.5 constant coefficient.

 L  dSy
Φ̂ = B̂Sy dr dl = 2B̂Sy dSy L (2.9)
0 0

Φ̂ 1
B̂Sy = (2.10)
2 dSy L

With the derivation of the stator flux tubes, a link between geometry and

magnetic flux density has been established. In order to model all the variables that

appear in the torque equation, an analogous model for the currents needs to be

defined. Approaching the problem from the machine terminal currents, conductors

and winding factor, the root mean square value of linear current density can be

expressed as in Eq. 2.11.

2mpqNS IS kw1
AS1 = (2.11)
2πRg

Where NS is the number of turns in series and kw1 the first harmonic winding

factor. Once the main flux has been modeled and linked to the geometric variables,
 32

it is necessary to derive non-dimensional ratios in order to generalize the analysis to

machines of different sizes. This approach allows for the use of a limited number of

dimensional inputs (namely the airgap radius Rg and stack length L) and sweep the

normalized ratios in order to find an optimal group of machine candidates.

One possible derivation of the yoke depth to airgap radius ratio kSy is carried

out in Eq. 2.12 imposing the non-dimensional constraint on the magnetic flux peak

values:

B̂g Φ̂ p 2 pdSy
kSy = = dSy L = (2.12)
B̂Sy 2 Rg L Φ̂ Rg

When used in the machine definition, the yoke thickness is calculated from the

non-dimensional ratio.

kSy Rg
dSy = (2.13)
p

Moreover, the corresponding yoke pole pitch is derived from the mean path

across the yoke with Eq. 2.14.

 
dSy π
τSy = Rg + (2.14)
2 p

For the stator tooth width, the corresponding sizing process is illustrated in

Eqs. 2.15 and 2.16.

B̂g Φ̂ p 2 wSt zL wSt zL

kSt = = = (2.15)
B̂St 2 Rg L π Φ̂ 2p 2πRg

2πkSt Rg
wSt = (2.16)
z
 33

Finally, the link between the magnetic flux and stator current is derived. The

simplified geometry only takes into account the flux-carrying iron and the current-

carrying copper. For a given stator tooth section, it is possible to split the iron and

copper assigning to them corresponding tangential and radial variables. The modeling

choice is to give the tooth iron size a tangential control of the geometry (Eq. 2.16)

while the net stator copper area ACu,S of Eq. 2.17 will extend radially to meet the

cross-sectional size required to generate the linear current density of Eq. 2.18, taking

into account the winding window ASW and slot fill kCu,S . In other words, the iron

section is constant and set with a magnetic constraint (the ratio between tooth and

airgap flux densities) while the copper area meets the thermal requirement extending

only radially.

ASW kCu,S
ACu,S = (2.17)
z

Combining the equations we obtain, discounting the fraction of the stator

inner perimeter that is occupied by the teeth (wSt z), the stator slot depth will be

proportional to linear current density, the cross-sectional area current density σS and

the slot shape factor kds .

2πRg AS1
ASW = (2.18)
kCu,S kw1 σS

That is, a rectangular winding window cross-sectional area is transformed into

a slot shaped area (using kds ) and is then divided by the perimeter fraction left free

by the teeth on the stator inner surface as formulated in 2.19.

ASW AS1
dSt = = (2.19)
2πRg (1 − kSt )kds kCu,S kw1 kds (1 − kSt )σS
 34

for the particular case of equal split between copper and iron, the formulation

of [45] is obtained in Eq. 2.20 .

2ASW
dSt = (2.20)
2πRg kds

At this point, regardless of the rotor excitation details, the outer stator size

can be obtained with Eq. 2.21, in order to model the actual machine power density

in the following derivation.

Ro = Rg + dSt + dSy (2.21)

The other factor that has an effect on the machine envelope is the axial length.

A correlation presented in [19] has been used in Eq. 2.22.

π dSt
LS,et = (Rg + ) (2.22)
2p 2

To analyze the rotor, an analogous process can be utilized, but the two excita-

tion types (permanent magnet and wound field) forces us to take a different approach.

In terms of excitation flux generation, the wound field and the permanent magnet can

be equated to an ideal magneto-motive force generator and an ideal magnetic flux

generator in parallel with the magnet reluctance, respectively. Using an electrical

analogy of the magnetic model, this corresponds to an ideal voltage source (wound

field) and to an ideal current source in parallel with a resistor (permanent magnet).

2.1.3 Wound Field Rotor Sizing Equations. The rotor excitation is here

presented for the WFSM case, where a winding must be electrically excited in order

to magnetize the machine. Refer to Figure 2.2 for a graphic presentation of the wound

field rotor geometry derived in the following.

 35

Figure 2.2. Wound field rotor geometric parameters for analytical sizing of the ma-
chine

The rotor yoke derivation follows the same principle of the stator yoke. The

corresponding formulas for peak flux, peak airgap flux density and non-dimensional

ratios are Eqs. 2.23 to 2.25.

 L  dRy
Φ̂ = B̂Ry dr dl = 2B̂Ry dRy L (2.23)
0 0

Φ̂ 1
B̂Ry = (2.24)
2 dRy L

B̂g Φ̂ p 2 pdRy L
kRy = = dRy L = (2.25)
B̂Ry 2 Rg L π Φ̂ 2πRg

The corresponding dimensional value is derived in Eq. 2.26 for the rotor yoke

thickness and in Eq. 2.27 for the mean path length.

 36

kRy Rg
dRy = (2.26)
p

π
τRy = (Rsh + dRy ) (2.27)
p

The choice of sizing the rotor neck before the winding has been made in order

to prioritize iron saturation over current density. The flux in the neck (of width wRn )

is affected by the pole shaping in the pole body flux tube, this reflects in the use of
4
a π
constant to correctly scale the flux integral of Eq. 2.28 (cfr. Chapter 3 of [99]).

 L  dRy
4
Φ̂ = B̂Rn dr dl = B̂Rn wRn L (2.28)
0 0 π

The peak value of the neck magnetic flux density (B̂Rn ) of 2.29 is very im-

portant to determine the yoke saturation. In terms of excitation, this will limit the

maximum amount of excitation flux produced by the rotor. Moreover, demagnetizing

flux will affect the machine operation.

Φ̂π 1
B̂Rn = (2.29)
4 wRn L

Thus, the non-dimensional factor derived in 2.30 is the corresponding design

variable in the sizing of the machine.

B̂g Φ̂ p 4 2p wRn
kRn = =( ) ( )wRn L = (2.30)
B̂Rn 2 Rg L Φπ π Rg

The rotor neck width of Eq. 2.31 is directly related to the airgap radius via

the non-dimensional ratio.

 37

πRg kRn
wRn = (2.31)
2p

On the other hand, the neck radial dimension is also affected by the current

density and the rotor copper fill, since the rotor winding can only occupy the space

left free by the rotor neck. In particular, Eq. 2.32 assumes that the winding shape

is rectangular, in order to try to minimize the axial extension of the rotor end turns.

The same principle used for the stator winding window is applied, but in this case

the peak value of the current is used (DC excitation) and two areas are available on

both sides of the neck, resulting in the (2) constant factor.

√
AS1 2
dRn = (2.32)
kCu,R (1 − kRn )σR

For the rotor pole a different flux integration must be derived since the rotor

shape affects the airgap thickness and in turn the magnetic flux. The resulting Eq.
2
2.33 takes the inverse cosine pole shaping into account thanks to the π
factor, as

presented in [99].

 L  τRp
2
Φ̂ = B̂Rp dr dl = B̂Rp τRp L (2.33)
0 0 π

The rotor pole magnetic flux density can have a complex relation to the ge-

ometry, due to the interaction of the stator and rotor magnetic fields. This can be

simplified considering the no-load condition (where no interaction is present) and the

geometric relationship between the rotor and stator magnetic pole arcs, resulting in

Eq. 2.34.

τRp
B̂Rp = (2.34)
τp
 38

The resulting ratio of Eq. 2.35 is only representative of the no-load case, but

sufficient for the scope of the initial sizing.

B̂g ˆ
πΦ p 2 τRp
kRp = =( ) ( )τRp L = (2.35)
B̂Rp 2 Rg L π Φ̂ τp

Moreover, the dimensional values of the rotor pole flux tube are completed

considering the rotor shaping function and deriving the pole body thickness in Eq.

2.36, and the corresponding tangential extension in Eq. 2.37.

δ0
dRp = (2.36)
cos(kRp π2 )

π
hRp = Rg sin(kRp ) (2.37)
2

Finally, the rotor end turns must be evaluated in order to estimate the rotor

axial extension, since these connection will exceed the stack length. Two correlations

are proposed, the first one (Eq. 2.38 ) assumes a trapezoidal winding window and

a constant bending radius, related to the maximum winding window use. This re-

lationship is useful in designing a WFSM, since it does not exceed the stator axial

extension, while at the same time providing the largest bending radius for the wire.

In other words, the axial extension is maximized in order to minimize the bending

radius.

π
LR,et = hRp sin(kRp ) (2.38)
2p

The opposite is true for the correlation of Eq. 2.39. In this case the axial

extension of the end turns are minimized, using a bending radius compatible with
 39

the wire sizes considered for the design. This correlation has been used to derive the

figures of merit for HESM, since it is desirable to reduce the impact on the dead space

between the wound and permanent magnet rotors.

ARW
LR,et = + Rbend (2.39)
dRn

2.1.4 Permanent Magnet Rotor Sizing Equations. The PMSM considered in

this work is a Interior Permanent Magnet Synchronous Machine (IPMSM) topology.

Two magnet configurations have been modeled and analyzed in order to model the

machine performance. The two configurations share the pole and yoke sizing with the

WFSM, while the magnet shape affects the flux and magnet thickness and therefore is

analyzed separately. The permanent magnet rotor geometry for the simplified fluxes

is shown in Figure 2.3. The actual machine geometry will be derived in the section

relative to the FEA simulation.

Figure 2.3. Permanent magnet rotor geometric parameters for analytical sizing of the
machine

The first configuration to be explored is that of a flat bar magnet, for which the

proposed sizing method is presented. Starting from the magnetic equivalent circuit,
 40

the magnet can be modeled as magnetic flux generator in parallel with the magnetic

permeance. The airgap and stator load reluctances are connected to the magnetic

flux generator creating a closed circuit that allows the calculation of the magnet

requirements. The flux tubes derivation approach is to simplify the magnetic circuit

to take into account the airgap and permanent magnet alone. The iron MMF drops

will be taken into account as an increase of the airgap MMF, linearizing the circuit

around the operating point of the magnet. This approach is valid to calculate the

no-load magnetization of the machine and only in case of linear iron characteristic

if the machine is also loaded from the stator. For non-linear iron characteristic, a

numerical solver is needed to take into account the saturation effects. The magnet

and airgap flux tubes are derived first. The airgap surface is obtained integrating the

airgap radius over the pole angular coordinate θ and the length of the machine (Eq.

2.40)

 L  θp
π
Sg = Rg dθ dl = Rg L (2.40)
0 0 p

The following step is to calculate, with a similar procedure, the surface occu-

pied by the magnets (Eq. 2.41 ) where kP M is defined as a ratio of the permanent

magnet surface to the airgap surface (Eq. 2.42 ). The assumption is that no leak-

age flux reduces the flux at the airgap, this simplification is acceptable due to the

insertion of air barriers to the sides of the magnets.

 L θp k P M
2 kP M π
SP M = −θp kP M
Rg dθ dl = R g L = τP M L (2.41)
0 2
p

SP M
kP M = (2.42)
Sg

The airgap and permanent magnet permeances (Λg and ΛP M respectively) that

result from this method are explicitly defined in Eqs. 2.43 and 2.44. The parallel
 41

connection of the permeances represents the simplified magnetic circuit (ΛT OT,0 ) to

which the magnet is connected as a source of magnetic flux (Eq. ).

μ0 Sg
Λg = (2.43)
δ0

μ0 μr,P M SP M
ΛP M = (2.44)
dP M

Λg ΛP M μ0 μr,P M kP M Sg μ0 Sg
ΛT OT,0 = = = (2.45)
Λg + ΛP M μr,P M kP M δ0 + dP M δ0 + μr,PdM
PM
kP M

The resulting no-load flux is calculated from the no-load airgap flux density

and the magnet MMF of Eq. 2.46.

Φ0 = ΛT OT,0 MP M = ΛT OT,0 Hc dP M (2.46)

The previous expression is modified to extract the the fundamental frequency

component as the first harmonic in the Fourier series (Eq. 2.48)

4 νπ(1 − kpr )
ksh,ν = cos(kP M ) (2.47)
νπ 2

4 π
ksh,B = sin(kP M ) (2.48)
π 2

Combining Eqs. 2.46 and 2.48, the no-load magnetic flux density is obtained

in Eq. 2.49.

dP M
Φ̂0 μ
= Bˆag = ksh,B Br dP Mr,P M (2.49)
Sg μ
+ δ0
r,P M
 42

Inverting Eq. 2.49 to express the magnet thickness, the magnet sizing equation

is finally obtained for this case.

δ0
dP M = ksh,B Br 1
(2.50)
μr,P M Bag
− μr,P M kP M

Additional parameters are the magnet depth in the rotor pole and the yoke

radius calculation. The yoke radius equation is in all identical to Eq. 2.26, and also

the resulting flux tube has the same parameters. The magnet depth has been assumed

to be corresponding to the projection of the pole q-axis on the d-axis (Eq. 2.51)

π
dRp = Rg (1 − cos( )) (2.51)
2p

For the V-shaped configuration of the magnets, two factors need to be taken

into account and modified with respect to the previous case: the angle that the

magnets span in the pole (equivalent to the flat bar case kP M of Eq. 2.42) and

the angle between the two magnets (αP M ). This additional parameter will set the

inclination of the magnet, the smaller the angle between the magnets, the larger the

depth of the V-shaped configuration (and the quantity of permanent magnet material

that can be used in the rotor pole) will be.

αP M = kRα π (2.52)

THe V-shaped configuration has been used to design the HESM prototype and

in presented in detail in Section 3.3, Figure 3.10.

2.1.5 Monoaxial dPMWF Hybrid Excitation. To approach the problem of

sizing for hybrid excitation, the classification proposed by G. Borocci, F. Giulii Cap-

poni, G. De Donato and F. Caricchi in [14] has been employed. The reference model
 43

proposes a general approach for hybrid excitation machines in which the excitation

is classified as monoaxial if the permanent magnet excitation flux and the wound

field excitation flux are both oriented on the machine magnetic d-axis (dPMWF ex-

citation). Many other cases are possible for biaxial excitation, where the excitation

fluxes can be directed on either the d-axis and q-axis, generated with multiple wind-

ings or permanent magnet structures. In particular, the combination of d-axis wound

field excitation flux and q-axis permanent magnet excitation flux is presented here

(dWFqPM excitation).

The model assumes a simplified machine model that disregards resistive volt-

age drops, leakage fluxes and saturation effects and the conclusion (from manipulation

of the machine model in the dq0 transformation) is that a hybridization ratio can be

defined for the magnetic d-axis and q-axis of the machine (Eqs. 2.53 and 2.53 )

λP M,pu,d
HRd = (2.53)
λen,pu,d

λP M,pu,q
HRq = (2.54)
λen,pu,q

Where λ is the flux linkage and the subscripts have the following meaning:

PM for permanent magnet, pu for per unit, d and q for the magnetic axes of the

machine. The subscript e refers to the back emf, so that λen,pu,d refers to the linkage

flux that generates the nominal back emf, in per units on the magnetic d-axis. In

the following derivations, omitting the reference axis (d or q) will refer to the vector

composition of the two components.

The sizing approach is based on the consideration that in general the PM and

WF peak airgap flux density may be different, while the airgap pole pitch (derived in

the sizing equations as τp ) is fixed. The d-axis hybridization ratio is proportional to

 44

the stack length of the two excitation systems section according to Eq. 2.55.

LP M B̂ag,P M
HRd  (2.55)
LP M B̂ag,P M LW F B̂ag,W F

Since one side of the WF rotor end turns (of length LR,et ) will be placed inside

of the machine, the stack length L will be reduced in the rotor by this amount, giving

the available length (Eq. 2.56). The available length can at this point be expressed

as the sum of the WF and PM rotor sections lengths.

Lav = L − LR,et = LP M + LW F (2.56)

In general, the hybridization ratio can assume any value between zero (WF

machine) and one (PM machine) and a length ratio parameter kL can be defined to

link the electromagnetic sizing to the geometric sizing of the two sections (Eq. 2.57).

LW F 1 − HRd Bag,P M
kL =  (2.57)
LP M HRd Bag,W F

Assuming the same airgap flux density (the hypotesis made to derive the sizing

equations), the two stack lengths are calculated in Eqs. 2.58 and 2.59

Lav
LP M = (2.58)
1 + kL

Lav kL
LW F = (2.59)
1 + kL

To obtain a hybrid machine with theoretically infinite constant power speed

ratio (CPSR), a suitable hybridization must be chosen. Comparing the machine

 45

noload back-EMF at base speed and at the maximum speed, a general relationship

can be obtained. At the corner point operation, the rated flux and base speed are

obtained, resulting in Eq. 2.60

eb = ωb λen,pu,d = ωb (λP M,pu,d + λW F,pu,d (If,n )) (2.60)

At any speed above the base, the symbol ωpu in the constant power speed

range (CPSR) will be used. For the maximum speed in the flux weakening region, a

similar equation can be obtained, where the WF flux is reducing the total rotor flux

(Eq. 2.61).

ec = ωpu (λP M,pu,d − λW F,pu,d (If )) (2.61)

Imposing the constraint of constant value of the back-EMF at base speed (Eq.

2.60) and at maximum CPSR speed (Eq. 2.61) can be obtained equating the base

speed in per unit to one (Eq. 2.62). This derivation is referred to a rotor excitation

circuit capable of bidirectional power flow and a rotor-only flux weakening strategy

(i.e. without using the stator current for flux regulation).

ωpu − 1
λW F,pu,d = λP M,pu,d (2.62)
ωpu + 1

Summing the PM flux linkage λP M,pu,d on both sides of Eq. 2.62, the definition

of the hybridization ratio can be made explicit (Eq. 2.63) with simple manipulations.

 
ωpu − 1
λW F,pu,d + λP M,pu,d = λP M,pu,d +1 (2.63)
ωpu + 1

The relationship between the maximum CPSR that can be obtained with a
 46

given hybridization ratio can then be expressed as in Eq. 2.64.

 
ωpu + 1 1 1
HRd = = 1+ (2.64)
2ωpu 2 ωpu

The conclusion for this derivation is that a hybrid machine with theoretically

infinite CPSR can be obtained imposing an HRd smaller or equal to 0.5. Conversely,

for a CPSR of 3, an HRd of 0.67 would be the maximum limit for rotor-only flux

weakening. The hybridization ratio of 0.5 was chosen for the prototype since it makes

no assumption on the stator strategy in use, but further strategies are possible.

2.2 Machine Losses Analysis

2.2.1 Lumped Parameter Thermal Analysis. The thermal equivalent circuit

model employs an analogy between the thermal transient equation of the system that

is being modeled and an equivalent electric circuit, in order to use tha same techniques

available for electrical systems. The main difference is that the thermal circuits are

in general non-linear, so a temperature dependence of several parameters must be

specified to obtain reasonable prediction of the system behavior. The similitude is

generally defined as an analogy of the current in the circuit with the heat flow (exten-

sive physical property), the voltage representing the temperature (intensive physical

property) and the impedance with a thermal impedance, with similar meaning of re-

sistance (a quantitative measure of the difficulty to force a heat flow through a given

section of the system) and capacity (the thermal inertia of the system or portion of

it).

2.2.2 Iron Losses Modeling. Modeling the iron losses in electrical machines

has been an interest of designers since the initial development of this branch of engi-

neering. Surprisingly enough, one of the first models, Steinmetz equation, is still in

use today with slight modifications to better model the hysteresis and eddy current
 47

phenomena of losses in the electrical steel material. The additional modification pro-

vided in this work is to consider each harmonic of the induction field separately when

evaluating the losses of the machine. Additionally, another method called CAL2 has

been implemented [50], where loss coefficients for hysteresis and eddy currents are

functions of the frequency and flux density levels.

2.3 Machine Design Figures of Merit

2.3.1 Torque Density. Volumetric torque density and specific torque density as

the following:

Tout
ρT,W = (2.65)
Mmachine

Tout
ρT,V = (2.66)
Vmachine

Where M is the mass of the machine, and T is the net output torque.

2.3.2 Power Density. Volumetric power density and specific power density as the

following:

Pmech
ρP,W = = ρT,W ωmech (2.67)
Mmachine

Pmech
ρP,W = = ρT,V ωmech (2.68)
Mmachine

Where P is the mechanical power output of the machine. The power densities

can also be obtained multiplying the torque densities by the mechanical rotational

speed in radians per second.

 48

2.3.3 Machine Goodness. This machine figure of merit is adapted from the

motor constant usually employed to compare the performance in servo motors and

BLDC motors, is the ratio between the torque produced and the square root of copper

losses. For the motor prototypes presented in the following, the modification applied

is to consider the square root of the total losses, since the losses are copper-dominated

the two versions do not differ dramatically.

Pmech
MG =  (2.69)
Ploss,T OT

2.3.4 Power Factor . The power factor is the fraction of real electrical power over

the apparent power absorbed by the machine. It is a fundamental parameter in the

specification of power electronic converters that need to interface to the machine, since

the power converter terminal current determines the losses. Comparing two machines,

the one with the larger power factor can be controlled with a smaller power converter,

i.e. a smaller apparent power rating in VA.

P
pf = cos(φ) = (2.70)
Q

2.3.5 Constant Power Speed Ratio. The constant power speed ratio (CPSR)

is a metric for the ability of a machine to operate above the base speed. The CPSR

is defined as the ratio between the base speed and the maximum speed at which the

machine can be operated (Eq. 2.71).

ωmax
CP SR = (2.71)
ωn

The base speed is defined as the speed at which the machine terminal voltage

reaches the nominal value. Since the voltage depends linearly on the speed and the
 49

linkage flux (Eq. 2.72 ), to operate at speeds above nominal, the flux must be reduced.

The flux weakening methods depend on the available machine controls, for instance

in PMSM machines the excitation is not controlled, therefore the only option is to

use part of the stator flux to buck the rotor flux. Theoretically, the machine has an

infinite CPSR, but is practically limited in the design stage by the negative effect is

has on power factor at base speed.

Eˆm = ωkw NS Φ̂m (2.72)

On the other hand, for machines that can control the excitation level (WFSM,

DFIG or separately excited DC machines), it is possible to reduce the magnetization

flux from the rotor or combining the stator and rotor flux weakening strategies.

2.3.6 Torque Ripple. The torque ripple is the variation of produced torque during

the rotation of the machine. It is an important parameter for traction motors, since it

directly affects vehicle vibration and passenger comfort. In order to model the torque

ripple, the machine rotation must be considered, since the reluctance changes as a

function of the rotor position with respect to the stator teeth.

 50

CHAPTER 3

MULTI-PHYSICS MACHINE MODELING

In this chapter the simulation systems are presented as an overview of the

design tools employed to obtain the machine prototypes. The analytical (Section 3.1)

and electromagnetic FEA (Section 3.2) presented here have been used in the sizing

of the machines described in detail in the following Chapter 4. Electromagnetic,

thermal and mechanical modeling were used to predict the behavior of the prototype

machines, and the methods presented here have been validated with experimental

results in Chapter 5.

Additionally, the software architecture implementation is presented for the

electromagnetic section, including the machine templates used in the following design

and a comparison of results used to verify the implementations in different solvers.

Finally, the thermal and mechanical simulations are presented along with the

external solvers employed.

3.1 Analytical Method

The analytical method employs the sizing equations derived in the previous

Section 2.1. A first approach considered a linearized iron material and was used

to test the coupling of the geometrical parameters to the FEA simulation model.

In the second iteration of the development, a nonlinear solver was used with the

same material characteristic implemented in the FEA solver, in order to obtain more

accurate first approximation results from the sizing equation system. The analytical

method and the FEA can be run separately or in parallel.

3.1.1 Linear Iron with Superposition. Using the theoretical modeling of the

flux tubes, the simplest model is to account for linear iron MMF drops, in order to

take advantage of the superposition theorem for the stator and rotor magnetic fields
 51

and their resultants. The flux tubes are described in the Section 2.1 alongside with

the sizing equations. The linearized version can also be implemented in the FEA

solver and will be presented in the Section 3.2.

A diagram of the program flow for the analytical simulation is presented in

Figure 3.1, on the left. The input values are the dimensional physical quantities that

define the ideal machine of Eq. 2.2, that is the airgap radius Rg , the stack length L, the

fundamental airgap flux density B̂g1 and the linear current density AS1 . In addition

to these dimensional values, the set of nondimensional ratios defined in Section 2.1

is used to define each flux tube taken into account during the geometry calculation.

The right side of Figure 3.1 is a simplified representation of the FEA process, to

emphasize that the the same material properties are set for both methods. The full

FEA function list is given in Section 3.1.

The resulting dimensional geometry is used to calculate the MMF drops in

each section and then the magnetic flux. Once the machine is sized and the material

characteristic calculated for the operating point, the figures of merit of Section 2.3

are calculated. The same geometric data is drawn in the FEA simulator described in

detail in Section 3.2 and set with linear material, in order to compare the results and

calibrate the analytical model.

The linear method is very limited in the conclusions that can be drawn from

it, since usually at least some part of the machine iron is saturated in actual operating

conditions. However, in broad terms, it can help in setting an idealized maximum

limit for the machine performance.

3.1.2 Nonlinear Iron. The limitations introduced by the linear iron model can be

compensated taking into account a DC BH curve of the material. The consequence

is that the superposition method cannot be applied and a numerical solver is needed
 52

Figure 3.1. Flow diagram of the linear analytical model.

to calculate the machine fields under load.

In terms of physical simulation of the machine, this method approximates to a

lumped parameter the FEA field solution, enabling a more detailed characterization.

The main limitation of this method is the implementation time, since in order to

represent details in the machine structures, the equivalent circuit development and

flux tube modeling complicates much faster than a purely numerical implementation.

The approach that has been taken is to model the machine in terms of equation
 53

systems with the minimum set of parameters to identify the range in which to search

for the optimal machine in terms of metrics such as weight or power density. In the

following, the magnetic equivalent circuit implementations of the PMSM, WFSM and

HESM are presented. The applied method is outlined first, then the specific cases are

detailed.

The simulation flow diagram is given in Figure 3.2 and, comparing it to the

linear case of Figure 3.1, it can be noted that the materials characteristic differs.

In terms of implementation this means that instead of a single calculation as for

the linear case, a system of equations is solved iterating on the nonlinear material

characteristic.

For the wound field excitation, the no-load characteristic is obtained for the

desired value of airgap flux density B̂g1,nl of Eq. 2.6, meaning that the MMF drops

M are calculated for each flux tube with the non-dimensional ratios of the stator and

rotor.

In particular, for the stator pole the total MMF drop is given in Eq. 3.1 as

the sum of the tooth and yoke MMF drops (obtained as the product of magnetic

field intensity H and the length of the paths dSt of Eq. 2.19 and τSy of Eq. 2.14

respectively). Each magnetic field intensity is obtained from the BH curve of the

material point corresponding to the flux tube magnetic field density B.

MS,nl = HSt (B̂St,nl )dSt + HSy (B̂Sy,nl )τSy (3.1)

For the airgap drop, the air permeability is considered, being linear in any

case. The resulting MMF drop is calculated in Eq. 3.2.

 54

Figure 3.2. Flow diagram of the nonlinear analytical model.

4
Mδ0 ,nl = B̂g1,nl δ0 (3.2)
πμ0

For the wound field rotor, the rotor yoke, neck and pole flux tubes are con-

sidered to obtain the total MMF drop of Eq. 3.3, considering also in this case the

magnetic field intensity of each path as a function of magnetic field density and ma-

terial characteristic, and the path lenghts τRy , dRn and dRp respectively.
 55

MR,nl = HRy (B̂Ry,nl )τRy + HRn (B̂Rn,nl )dRn + HRp (B̂Rp,nl )dRp (3.3)

The total MMF drop is then calculated from the sum of each contribution

and the rotor Ampere-turns are thus obtained to compensate the MMF drops and

generate the no-load airgap flux. Being system with a single source of magnetomotive

force, a single iteration results in the no-load solution of the analytical model.

Mnl = MS,nl + Mδ0 ,nl + MR,nl (3.4)

For the full-load operation, the same process is carried out, but an iterative

solution is needed. Since the airgap always behaves linearly, the stator and rotor flux

contributions are calculated from the Ampere-turns set via the linear current density

AS1 and the Mnl of Eq. 3.4 and summed in quadrature to obtain the magnetic flux

density at full load B̂g1,f l . The hypothesis made in the theoretical background is that

the two fields are maintaned in quadrature during the machine operation.

The process for the MMF calculation is repeated, but in this case the values of

flux density in each section are those corresponding to the B̂g1,f l . An iterative process

is needed to convergence to a single value of airgap flux density, scaled in each section

of the machine via the nondimensional ratios.

A similar process is applied to the PM rotor, but given that the magnet ex-

citation is not controllable in this topology, the MMF is the one resulting from the

magnet thickness in the direction of magnetization of Eq. 2.49. Additionally, the

V-shaped topology yields, for the constraints imposed on the solution, a sufficient

rotor yoke size is obtained on the magnets side.

3.2 Software Architecture

 56

The machine finite element analysis simulation code is organized on a modular

basis, in order to reuse common functions for different synchronous machine geome-

tries and types, e.g. wound field, internal permanent magnet and surface permanent

magnet . Each simulation is considered as an independent thread of calculation,

meaning that the full characterization is independent of other concurrent simulations

and allows for parallelization of several threads. The implementation relies on Matlab

acting as a server to interface the machine geometry and materials to external FEA

solvers, retrieve the resulting data, organizing it into a data structure, post-process

and display it in a graphical or textual result to the user.

A graphical representation of the program flow for each machine simulation is

given in Figure 3.3, corresponding on the expansion of the right branches of Figures

3.1 and 3.2 for the linear and nonlinear iron setup, respectively. The simulation code

is implemented in as a set of functions designed to interact and respond to different

settings, based on a data structure common to the whole machine simulation.

The scope of the functions is reflected on the fraction of the data structure

that each function can access and modify. The high-level functions for the simulations

are the following:

1. Initialization: Matlab loads all the functions, input data and external material

properties and initialize the communication with the solvers.

2. Geometry generation: Matlab calculates all the dimensional values that de-

fine the machine geometry from one or more templates.

3. Drawing and Setting: Matlab creates the geometry in the external FEA

solver and assigns materials and stimuli (current or voltage inputs). In this

section is also possible to export the machine geometry for the mechanical sim-

ulation.
 57

4. Static Solution: the FEA solves the magneto-static problem for different cur-

rent angles and the solver output is loaded into the Matlab data (torque, flux

linkages etc.).

5. Transient Solution: the FEA rotates the rotor geometry for each simulation

point set in the initialization, updates the stator currents and solves the series

of problems and Matlab loads the results.

6. Post-Processing: Matlab post-processes the transient data for different speeds

to obtain frequency-dependent parameters (losses and back-emf)

7. MotorCAD: for the thermal interface two accesses are provided, one loads a

fixed geometry and edits the losses details for the simulation to be performed,

the other sets the full model of the machine from the default machine model

(geometry, cooling system and losses).

In the following section, further details of the implementation and the tem-

plate used in the actual machine designs are presented. The ”dot notation”, when

employed, symbolizes that each variable contains further sub-variables, so that the

data can be accessed by a user-friendly nomenclature and broken down to basic data

types (numerical, string or boolean).

3.2.1 Modular Function Implementation. The Initialization uses a Matlab

structure, a format for a database, organized as nested field and data types. The

main database object for a machine is called a Member or Design and it contains all

the characteristics of the machine. The following list briefly describes all the top level

sub-objects that are edited during a machine simulation, called data structure fields

in Matlab.

1. status: is a collection of all the simulation options for static and transient
 58

Figure 3.3. Flow diagram of the FEA software implementation for a single machine
simulation.

electromagnetic FEA, thermal simulation and technical drawing plotting to in-

terface to mechanical FEA.

2. machine: is organized with all the machine-level common values, such as poles,

phases, number of slots etc.

3. stator: contains the stator template and is populated during the geometry

generation with the dimensional values, lines, arcs and material block charac-

terization for the generated areas.

4. rotor: is populated with the rotor template and in the geometry section lines,
 59

arcs and material block characterization.

5. airgap: for the rotation, this sub-object is updated with a specialized code to

impose the correct boundary conditions.

6. boundaries: is populated with the initial boundary characteristic, in this way

the previous geometry characteristics can be mirrored and copy-rotated to rep-

resent the minimum machine symmetry, while the boundaries are imposed with

an even or odd periodicity.

7. materials: lists all the material properties that will be used in the simulation,

either by reference to the external solver library or to a Matlab data format.

8. circuits: collects the convention used for circuit representation, and stores

the excitation levels used for static and transient simulation

9. results: is divided into sub-objects where the electromagnetic and thermal

simulation results are stored.

Each of these sub-objects (fields) will be explained in detail in the following

sections. The fundamental concept to follow is that each field is accessed at the

sub-function level, so that specific functions are applied to it. For instance, the lines

and arcs that are part of the stator and rotor objects are rotated by the same

low-level function, but the items are organized in separate objects so that they can

be debugged together. Additionally, it is possible to have several templates in the

same Design, so for instance an asymmetric rotor can be built using different values

or even templates for the two halves of the pole.

Following the list at the start of this section, a more detailed view is given

for the sub-objects and the data they contain. The status object controls how the

simulation is run, several options are available to modify the sections of simulation
 60

code that is executed at a given time. The options that are involved directly in this

outline of the simulation software are listed here for convenience:

1. run parallel: in this field a boolean is stored that allows the parallel execution

of several simulations at the same time.

2. electromagnetic solver: this value sets the interface to the electromagnetic

solver (FEMM or MagNet) and executes specialized functions to interface to

the external software.

3. EM problem.static: the EM problem stores all the data to set the simulation

in the external FEA solver, the dot notation indicates that an additional sub-

object is nested inside the main one.

4. EM problem.transient: similarly to the previous point, contains the data to set

up the transient simulation, for instance the number of points in the rotation,

the angular span and the equivalent frequency for the reconstruction of the

frequency-dependent parameters (e.g. voltage and core losses).

Throughout the code execution, status is called upon and flags are updated to

check the execution flow. This is a debug tool since it records where the program fails

to execute, or it can activate several times a section of the code itself. For example,

in a mapping routine, the same geometry is drawn once per each parallel thread, then

a static simulation can be executed several times (in order to save the drawing time)

since the static solution utilizes a fixed rotor position and the excitation level alone

is modified.

The Geometry generation phase accesses the Design fields created in the

Initialization phase and calculates the geometry that will be drawn in the external

software for simulation in the Drawing and Setting phase. The machine sub-object
 61

contains all the machine-level data used in the drawing phase. These information is

detailed in the following list:

1. poles: number of poles of the machine p.

2. phases: number of phases of the machine m.

3. slots perpolephase: number of slots in half a phase belt q, using the first

three values of this list, the number of slots corresponding to one pole of the

machine and the pole angular pitch are set for all of the following, i.e. the total

number of slots is z = mpq.

4. stator current density, rotor current density: the current density in the

net copper area are specified, since it has a strong correlation with the cooling

capabilities.

5. stator fill factor, rotor fill factor: represents the fraction of net cop-

per in the winding window, allowing to convert the current density into terminal

current ampere-turns.

6. lamination stacking factor: is the stacking fill factor for the laminations,

usually comprised between 0.9 and 0.97, in order to scale the actual iron stack

with the mechanical core length.

7. core length: is the actual physical length of the machine for the specified lam-

ination stacking factor, the simulation will use the net iron to calculate torque

(for instance) while this value is used for volume and coil lengths calculations.

8. arcdetail, linedetail, meshsize: these parameters control the mesh ap-

pearance of arcs, lines and surface meshing, allowing for separate control of

different sections of the machine (for instance the shaft has a low quality mesh

of 5 mm elements while the airgap has a higher quality with 0.1 mm)
 62

9. winding: a subroutine defines the winding as a series of circuit names and

number of turns, in order to represent synthetically several possible windings,

in order to test different configurations.

The machine geometry is composed of all the machine points, lines, arcs,

material and circuit definition locations. For ease of development, stator, rotor, airgap

and boundaries structures have been separated into four sub-functions, each of which

generates the corresponding geometry. The machine pole pairs, p, and number of

stator slots, z = mpq, are first defined, so that the pole and slot pitch are fixed (αp

and αs respectively).

For the stator and rotor the same structure is employed in order to reuse

the same geometric functions (rotation, translation, drawing etc.). The content of

these objects is listed in the following:

1. template.type: specifies which template is in use, for instance 1 will activate

the wound field machine template, 101 a flat-bar IPMSM template.

2. template.input variables: is a input list of the dimensional and non-dimensional

parameters used to calculate the points, lines and arcs that generate the geomet-

ric structure, a list of stator and rotor templates is given after the description

of the program flow in this section with the parameters description.

3. geometry.lines: is the output lists of lines created in the code, specialized

functions access this sub-object to rotate, calculate intersections and translate

segments when the template is duplicated.

4. geometry.arcs: is analogous to the previous field for lines but deals with arcs,

that are defined by terminal points and the curvature.

 63

5. geometry.areas: output surfaces are stored for mass calculation associating

each area to the materials specified in geometry.blocks.

6. geometry.blocks: assigns to a simulation area the physical characteristics of

the materials and circuits and a name string, so that is can be accessed sep-

arately to model different materials, changing only the input, this allows for

compatibility to different external solvers without changing the program struc-

ture, only the data passed, while the string is more user-friendly for filtering

and debugging purposes.

7. geometry.sample points: are geometric points defined for each area in order

to sample the field and used for the core loss estimation in the Post-Processing

phase.

The airgap template is simply a list of airgap arcs used to control directly

the meshing and to sample the airgap magnetic fields, while the boundaries are con-

structed as lines or arcs with particular boundary conditions (Dirichlet, Periodic and

Anti-periodic) that allows the full machine to be simulated with the least common

multiple of rotor and stator poles in the FEA field (increasing the speed of the overall

simulation without affecting its accuracy).

Once the geometry is finalized, the Drawing and Setting phase will use

the objects materials and circuits to link the Matlab variables to the physical

properties and excitation level used in the solver. Each geometry object is translated

into ActiveX commands that interface to the external software (drawing) and then

the properties are assigned for each area (setting). A single drawing function is called

upon for each of the geometry objects, allowing an efficient code reutilization. For

instance, the variable materials.iron contains the BH curve of the iron material

used for the simulation, and a list of cases can be explored with ease, changing the
 64

values stored in the Matlab object instead of defining each case separately in the

external solver. Moreover, the same plotting and post-processing functions can be

run for different cases presenting the data to the user.

The actual simulation results fields are updated during the Static Solution

and Transient Solution phases and then stored in the results sub-object. The

Static Solution routine updates each circuit excitation level, simulates the machine

fields and updates the following structure:

1. results.static.sample points: contains the field values in each geometric

point specified, allowing to test the saturation of the iron with a limited number

of runs.

2. results.static.flux linkage: samples each of the circuits for flux linkage

and is used to calculate inductances in the post-processing, corresponding to

the excitation level set in the circuits field.

3. results.static.torque: contains the rotor torque for each excitation level, a

post-processing is set up to calculate the MTPA angle from the static samples.

Other data is stored separately with additional fields under results, such as the

MTPA angle, the full set of input stator angles and three tests run to calculate the

flux at the airgap in different operating conditions (open stator with rotor excitation,

open rotor with d-axis stator excitation and open rotor with q-axis excitation).

In the results also the Transient Solution output is contained. This func-

tion will rotate the rotor geometry, update the boundaries that are displaced and

execute a field solution in the external FEA software. For FEMM the only solver

available is a magneto-static, so the data will reconstruct the rotation with discrete

steps as a quasi-static approximation. Infolytica MagNet has a built-in transient

 65

solver, so it is sufficient to set the rotation speed and axis and it will provide a post-

processed list of outputs (namely voltages and losses) that can be obtained in FEMM

only after processing these results. The results is updated to store the following

data:

1. results.transient.torque: stores the angle of rotation, the torque for each

step, the average and the ripple torque.

2. results.transient.flux linkage: is analogous to the static but it is used to

calculate the voltage input necessary to obtain the current excitation set in the

electromagnetic simulation. For both the currently implemented solvers, the

voltages are post-processed after the transient simulation is completed, so that

the frequency can be set arbitrarily in a mapping process.

3. results.transient.sample points: contains the induction field sampling used

to assess saturation and core losses of the machine.

The Post-Processing phase is applied to the FEMM results and uses the

results structure to obtain core losses (with Steinmetz and CAL2 models) and cop-

per losses. This function is implemented separately because the input speed and

frequency affects the losses, and for the same excitation level, a mapping can be ob-

tained running the function several times for different desired speeds. In terms of

execution time this process is much faster, as an order of magnitude than solving the

full electromagnetic problem for each frequency. For instance, the simulation time for

30 steps rotation lasts around 30 seconds, while a sweep of 30 speeds of the machine

lasts around 1 second.

Finally, the MotorCAD function translates the geometry and losses to inter-

face to the MotorCAD WFSM thermal model and runs the thermal simulation. Two
 66

options are available, either to run a static solution or to specify a custom duty cycle.

More details to the thermal simulation environment are given in Section 3.4.

3.3 Electro-Magnetic FEA

3.3.1 Matlab Geometry Templates. The stator template of Figure 3.4 is a syn-

thetic representation of the one used for the WFSM machine prototype optimizations.

The non-dimensional ratios, denoted with k, are organized into a parameter hierarchy

that is reflected in the sequence of calculation. In order to generate a unique geomet-

ric case and to give priority to some geometrical features over others (e.g. the stator

yoke depth is considered more important than the tooth tip thickness) the order may

be changed for different templates. It should be noted that the parameters presented

here do not correspond exactly to the ones derived in the analytical method. In this

context the derivation does not follow a preset model of the machine fluxes, but a

pure parametric geometric entity definition.

Figure 3.4. Stator template 1.

The resulting dimensional parameters listed in Fig. 3.4 are the stator inner

radius, RSi , and the stator yoke depth, dSy , are calculated from two split ratios, kSi
 67

and kSy , of the stator outer radius, RSo (Eqs. 3.5 and 3.6 ).

RSi = kSi RSo (3.5)

1 − kSi
dSy = kSy RSo (3.6)
1 + kSy

Then a stator tooth thickness, wSt , and stator slot opening, wSo , are imposed

with two additional ratios, kSt and kSo , and half stator slot angular span, αs . The

values of these geometric entities are limited by the intersection of inner stator radius

and parallel tooth surfaces.

wSt = RSi sin(kSt αs ) (3.7)

 
wSt
wSo = kSo RSi tan(αs ) (3.8)
cos(αs )

The stator slot depth is also derived from these parameters, since the tooth

geometry is needed to calculate surfaces and volumes, in turn used to derive the iron

weight and winding window cross-sectional areas.

1 − kSi
dSt = RSo (3.9)
1 + kS y

The slot bottom radius RSb is derived from the intersection of a 90 degrees

spanning arc, which starts at the stator yoke minimum depth, and ends with the

parallel tooth line intersection.

(RSi + dSt ) tan(αs ) − wS t

cos(αs )
RSb = (3.10)
1 + tan(αs )
 68

Finally, a tooth tip thickness and angle are imposed to link the inner stator

circumference to the straight tooth (dSo and θSt respectively).

dSo = kSo dSt (3.11)

The tooth tip angle θSt is the least important in the hierarchy, and it is cal-

culated as a fraction of the maximum allowable angle of the segment connecting

the tooth tip and the straight tooth. The corresponding segment is calculated from

the intersection of the stator tooth line (with slope tan(αs )) and a segment of slope

tan(θSt )

  
π RSb − wSo
θSt = ktt − arctan (3.12)
2 dSt − RSb − dSo

The rotor template has been designed with a similar concept, but additional

flexibility has been added, allowing points to merge and collapse. Fig. 3.5 shows the

four possible types of rotor pole shoe shapes, allowing the exploration of different

electromagnetic and mechanical trade-offs. The template presented in the following

has been used to optimize the first WFSM prototype and to design the wound field

section of the HESM, interfacing the template variables with the analytical design

equation method.

For each given airgap length and pole shaping function, different cross-sectional

areas of the pole shoe are possible. The areas are obtained multiplying the stack length

by the pole thickness (denoted lA through lD for the respective rotor type). A stress

concentration estimation has been derived from an exploratory stress analysis design

of experiments and forces the geometry generation engine to meet the requirement of

a minimum thickness of the pole in order to guarantee its mechanical integrity. The

rotor geometry type in Fig. 3.5 is obtained following the corresponding flowchart in
 69

Figure 3.5. Flexible rotor template 1, pole body shape options.

Fig. 3.7 (for case C the full list of parameters is given in Figure 3.6). The common

feature of the geometry is the pole shape of the surface facing the airgap, defined by

a minimum airgap thickness, δ0 , and an inverse cosine pole function. In Eq. 3.13, θp

is an azimuthal coordinate spanning counterclockwise from the horizontal axis to a

fraction of the pole pitch θmax < π2 .

(RSi − δ0 )
RRo (θp ) = (3.13)
cos(θp )

The maximum value of the coordinate, θmax , is calculated taking into account
π
that the inverse cosine tends to zero when θp approaches 2
and that in turn would

force the airgap to approach infinity. For practical code implementation, the value

chosen for the development has been of 85 electrical degrees, corresponding to a max-

imum airgap thickness of approximately 25 times δ0 . During the geometry generation

process, the actual fraction of the pole shape generated in this phase is controlled by

the parameter kX as in Eq. 3.15.

 70

θX = kX θmax (3.14)
δ0
δM AX = (3.15)
θX

Consequently, the rotor tip airgap thickness will be calculated with Eq. 3.13,

setting at the same time the rotor tip radius RRt .

RRt = RSi − δM AX (3.16)

The rotor tip is now characterized by a pole thickness and a distance from the

magnetic q-axis (lA in Fig. 3.5 and wRq,A in Fig. 3.6).

Figure 3.6. Flexible rotor template 1, option C of the pole body is shown.
 71

The distance from the magnetic q-axis is calculated with Eq. 3.17, where kRq

is the nondimensional ratio controlling this parameter as a fraction of the pole tip

distance from the q-axis.

RRt
wRq,A = kRq (3.17)
tan(θM AX )

In order to meet contrasting requirements of mechanical stiffness (bigger pole

body) and reduction of rotor leakage flux (smaller pole body), the geometry can morph

into one of the four cases of Fig. 3.5 in order to meet two constraints: the required
∗
minimum distance from the rotor interpolar axis wRq and the required minimum pole
∗
thickness, lth . These parameters are also expressed as a ratio, and the values are

derived from a mechanical analysis carried out to identify the mechanical limits of

the wound rotor structure.

Following the flowchart of Fig. 3.7, the distance from the q axis of case A

(wRq,A of Eq. 3.17 ) is calculated and compared to the required minimum value,
∗
wRq (step 1). If the first constraint is met, the pole thickness is checked (step 2)

and the type A rotor is finalized if the pole thickness is larger than the required

minimum value. In other words, passing the test at step 1 and 2 of Fig. 3.7 will

result in a case A geometry. The other possible outcome is that the thickness of the

pole is not sufficient. The geometry routine will then add a horizontal segment that
∗
extends until it intersects the line parallel to the q-axis and offset by the value wRq .

If the increased pole thickness, lB , meets the constraints, case B is finalized (step

5) since both constraints are met simultaneously. This corresponds to passing the

test in step 1, failing the test in step 2 and passing the test in step 5 of Fig. 3.7.

At step 5 it is also possible to fail the thickness requirement, the last option left is

to follow the line parallel to the q-axis (step 6) and check again the pole thickness

thus obtained (step 7). The geometry of case C is finalized when the added thickness
 72

is sufficient, otherwise the geometry is discarded. Cases A, B and C all meet the

prescribed distance from the q-axis by geometric definition. However, at step 1, the
∗
geometry may fail the wRq test and a case D geometry is attempted. In this pole

option, RRt and θX are calculated again imposing the intersection of the pole shape

to the prescribed q-axis distance, then a segment parallel to it is added (step 3) and

the obtained pole thickness is tested (step 6). Passing the test at step 6 means to

finalize a case D rotor, failing it will discard the geometry. Regardless of the pole

body case that is selected, the rotor neck thickness is calculated imposing a neck

thickness parameter, wRn , (defined as a fraction of the pole rotor tip height) and a

yoke radius, RRy (defined as a fraction of the pole rotor tip radial distance from the

shaft center), Fig. 3.6.

wRn = kRn RRt sin(θX ) (3.18)

RRy = Rshaf t + kRy (RRt − Rshaf t ) = Rshaf t + dRy (3.19)

The second rotor template is presented to show the additions made to simulate

the candidates to the second WFSM machine prototype optimization. The structure

of the geometry generation is in all identical to the previous case, but modifications

were made to the first step of the pole profile definition, allowing a multiplier to

be employed in the inverse cosine rule of Eq. 3.13, that becomes Eq. 3.20 with the

addition of the parameter kshape . The resulting geometry can allow a larger or smaller

saliency of the pole, with respect to the basic formulation of prototype 1.

(RSi − δ0 )
RRo (θp ) = (3.20)
kshape cos(θp )

In addition to this, a magnetic flux barrier has been designed to be inserted in

 73

Figure 3.7. Flexible rotor template 1, decision tree used to generate the pole body
shape.

the rotor neck, to try and replicate results found in literature on performance increases

to the machine through reluctance enhancement. The modular implementation of the

software allows the barrier to be defined in a sub-region of the rotor, and therefore

the barrier effect can be activated or deactivated from the simulation setup without

any change in code execution. The barrier graphic definition is given in Figure 3.8,

where the parameter Y sets the barrier thickness and the fillet radii as a fraction of

the neck thickness, X1 sets the distance from the the shaft and X2 the distance to the

previously defined rotor surface, both distances are expressed in terms of the rotor

radial size, that is Rro − Rshaf t . In order to obtain a realizable geometry, the random

generation during the optimization code execution is filtered for a minimum size of

0.25 mm, so that the resulting simulation model may express or not this feature. For
 74

ease of postprocessing and tracking of performace, a software flag is also raised to

easily filter the simulation results obtained with or without the barrier.

Figure 3.8. Flexible rotor template 2, barrier definition.

Two additional rotor templates were used to design the PM section of the

HESM machine, since the WF section is identical to the protoype 2 template, with-

out the magnetic flux barrier. The main difference is that the template has been

coupled with the sizing equation, meaning that the purely mathematical model of

the fluxes has been used to derive dimensional values, then converted to the correct

non-dimensional ratios used in the FEA section. This is necessary to be able to reuse

previous development and avoid ad hoc dimensional implementations of the machine.

The definition of the magnet includes a handle to the magnetizing direction, although

it has been fixed in the radial direction for the development given that the standard

magnets are usually magnetized on the direction of one of the surfaces. An option for

rotor pole shaping with an offset circle has been explored, but was not used for the

optimization of the prototype because of the loss in airgap magnetic flux density it

caused and is not presented here. The geometry generation process differs from the
 75

previous ones in the central part of the pole, because there is no need to fit a winding

around the pole, but flux barriers are necessary to avoid shorting the magnetization

flux instead.

A sample geometry of the flat bar PM template 1 is shown in Figure 3.9, where

the rotor outer radius is simply an arc that spans one half of the pole and of constant

radius equal to the stator inner radius subtracted of the airgap thickness (Eq. 3.21).

RRo = Rsi − δ0 (3.21)

Figure 3.9. Flexible PM rotor template 1, barrier definition.

The magnet is defined by an angular span occupied (τP M of Eq. 2.41), since

this parameter was defined in the sizing equations, and the extrema of the rectan-
 76

gular magnet area are calculated imposing the magnet thickness resulting from the

equations (dP M of Eq. 2.50) in the radial direction (Fig. 3.9). The magnet depth,

yoke size and shaft radius are also defined according to the sizing equations of Section

2.1. Two additional parameters have been added to size the air barriers to the side

of the magnet, dRbt and dRbr , that allow to change the tangential and radial thickness

of the iron bridges connecting the pole tip to the rest of the lamination. These two

parameters are defined as dimensional ones, meaning that a prescribed thickness can

be calculated from the mechanical FEA and imposed to obtain the necessary rigidity.

The remaining segments connecting the magnet region to the lamination are calcu-

lated imposing the intersection of a radial and a vertical segment to the prescribed

barrier thicknesses.

The V-shaped PM machine template 2 is portrayed in Figure 3.10, with iden-

tical meaning of the symbols from the previous one. The main difference regards

the magnets shape, since the pole depth of the flat bar case will be enlarged by the

magnets disposition. An additional parameter is defined (αP M of Eq. 2.52) as the

angular opening between the magnets.

3.3.2 FEMM and Infolytica MagNet Comparison. In order to validate

the FEMM results and reconstruction method, Infolytica MagNet has been used to

simulate the same geometry and operating conditions. In the following, the results

of the comparison are presented.

The geometry for the simulation is identical for the two cases, being generated

before the simulation is initialized (Fig. 3.11). The magnetic flux distribution for

each step is also coherent between the two cases, since the same silicon steel material

characteristic has been imposed to the two simulations. The main difference is in the

actual data transfer from Matlab to the solvers, since the MagNet implementation

takes advantage of Visual Basic scripts to draw the geometry elements, while FEMM
 77

Figure 3.10. Flexible PM rotor template 2, barrier definition.

has a LUA procedure linked to Matlab functions.

Additionally, the MagNet simulation is entirely setup in the simulation setup

stage (after drawing the geometry) while FEMM is initialized with default values and

updated only when necessary. This implementation allows for additional solvers to

be linked to the code base according to the external software setup.

The comparison of results included a static simulation and a transient simu-

lation, for which the electromagnetic torque are shown in Figure 3.12. For the static

solution very good agreement can be observed, while for the transient solution it

can be noted that the MagNet results have higher frequency ripple. This difference

can be explained by the MagNet use of higher order elements and additional mesh

refinement, that allow the modeling of higher order torque harmonics. Mreover, the
 78

(a) MagNet (b) FEMM

Figure 3.11. Magnetic flux density distribution of the model used for FEMM simula-
tion (right) validation against MagNet results (left).

FEMM transient solution is a composition of static solutions and the torque harmonic

bandwith is limited by the number of rotation steps. However, for the FEMM rota-

tion during the transient, the number of steps was set to 45 (one mechanical degree

discretization) in order to correctly represent the 21st torque harmonic. This value

has been chosen for a compromise between precision and execution speed, considering

also the mechanical damping effect of the rotor inertia during rotation.

(a) Static Torque (b) Transient Torque

Figure 3.12. Simulated static (left) and transient (right) torque comparison, FEMM
and MagNet denote the two electromagnetic solvers used.
 79

Finally, for the transient solution, the magnetic flux density in the machine

sections have been compared (Fig. 3.13). This validation is necessary to correctly

model the iron losses resulting from the post-processing of the two simulation results.

Also in this case there is very good agreement on the solvers results, so that for the

same loss model it is expected to obtain the same core losses result. MagNet offers

a post-processed value of losses in the GUI (using a modified Steinmetz equation

model) that takes into account all the elements in a given region, while for FEMM

a flux sampling point (that represents the whole region) has been implemented in

the transient solution. The results also in this case agree, even though the Matlab

implementation for losses calculation offers access to low-level functions and there-

fore a better flexibility that can include several loss models. An element-by-element

implementation could potentially yield a more accurate solution, but at the cost of

sampling and execution time.

(a) Tooth Flux (b) Yoke Flux

Figure 3.13. Simulated radial component of the magnetic flux density in a stator
tooth (left) and Simulated tangential component of the magnetic flux density in
the stator yoke mid-arc (right), FEMM and MagNet denote the two electromagnetic
solvers used..

3.4 Thermal FEA

In the current implementation of the simulation software, the thermal sim-

 80

ulation is linked to a single external program. The geometry is trasferred to the

Motor-CAD template via an ActiveX interface and populated with the simulation

results from the electromagnetic routines. Additional solvers may be integrated in

the future for thermal FEA analysis.

3.4.1 Motor-CAD. Motor-CAD (Copyright 2000-2017

c Motor Design Limited)

is an electromagnetic and thermal simulation software used in this project to estimate

and predict the thermal performance of the machines and the cooling system. The

model used for thermal modeling is that of a lumped parameter thermal circuit, in

which each element of the simulation is characterized by a temperature, thermal re-

sistance and capacitance and the heat flows are calculated for the specified equivalent

circuit. Some modifications of the thermal circuit were necessary to properly repre-

sent the prototype machines, in particular the spray cooling jets directed to different

parts of the machine. The built-in model uses an implementation of the submerged

double jet impingment method to calculate the heat exchange of the spray [28]. Ma-

terial properties can be defined to use any fluid of which the physical properties are

known. The heat exchange model employs an equivalent heat transfer coefficient that

depends on the geometry wet surface S, thermal power Pth , surface temperature Tsurf

and spray temperature Tspray (Eq. 3.22, [28]).

Pth
h= (3.22)
2(Tsurf − Tspray )S

In particular, the density, thermal conductivity, specific heat capacity and

kinematic viscosity of the fluid allows the calculation of two figures of merit that

characterise the two different processes of heat exchange over the impingment region

(direct spray flow) and the wall jet region (indirectly affected by the liquid jet). The

actual calculation is not directly accessible to the user and uses an experimental char-

acterization (Womac correlation) that takes into account the Reynolds and Nusselt
 81

numbers of the jet spray, the nozzle and heat exchange region geometries and is used

to derive the heat transfer coefficient. However, the model implementation is linear

with the wet area, so that a calculated coefficient can be modified for parts of the

geometry in order to add or update heat exchange resistances and model customized

systems.

The data representative of a typical ATF are listed in Table 3.1 [66]. It can

be noted the large variation of kinematic viscosity at higher temperatures, while the

density and specific heat are almost constant in the range of operation.

Table 3.1. Typical ATF Physical Properties

Parameters Values
Temperature 0◦ C 40◦ C 100◦ C 150◦ C
Density [kg m-3 ] 880 853 816 788
-1 -1
Specific Heat [J kg K ] 1800 2012 2219 2428
2 -1 -6 -6 -6
Kinematic Viscosity [m s ] 270.7 * 10 33.9 * 10 7.1 * 10 3.3 * 10-6

Figure 3.14 depicts the default overview thermal model of a WFSM machine,

it can be noted that the spray cooling thermal path (labeled EW-Spray, in pink) is

connected to the stator end-turns. The default model at the start of this project

(Motor-CAD version 9.4.3) included only stator and rotor end-turns thermal paths,

and a spray cooling method with constant inlet temperature.

The modifications to the default model for this project are related with the

stator and rotor core wet areas, that is the iron parts of the machine that are cooled

by the spray even though the bulk of the flow is aimed the copper end turns. An

additional modification was necessary to take into account an equivalent input-output

model for the heat exchanger present in the experimental setup, that refrigerates the

inlet fluid before spraying the machine components, using a constant temperature

water supply on the secondary and that is placed outside the machine shell.
 82

Figure 3.14. Motor-CAD thermal circuit overview, showing steady state tempera-
tures. Note: the elements are color coded with stator iron in red, stator copper in
yellow, rotor iron in cyan, rotor copper in light orange, spray cooling in pink, shaft
and bearings in grey and machine housing in blue.

In a first revision of the thermal model, it emerged from the calibration that

the rotor winding temperature simulation exceeded the experimental data. Initially,

a constant thermal resistance was added to represent the heat exchange between the

ATF spray and the rotor core. Since the heat exchange model is linear with the

wet area, the constant thermal resistance value was obtained from the wet surfaces

ratios between the coils end-turns and the iron core exposed to the fluid flow and

the average end-turns heat exchange coefficient calculated from the software. The

resulting simulation results matched approximately the experimental data and this

modification was included as a feature of the software (starting from Motor-CAD

version 10.2.3), allowing resistance variations with temperature and fluid flow during
 83

the simulations and therefore a more accurate modeling. The modifications included

in the detailed thermal circuit are shown in Figure 3.15

Figure 3.15. Motor-CAD thermal circuit detail, showing modifications to the rotor
thermal circuit inside the green boxes (Front circuit). Note: The thermal resistance
R 103 connects the average rotor temperature Rotor F (134) to the fluid spray inlet
RotC FluidSpray F (48).

Additional changes were made to the thermal circuit to include thermal paths

also connecting the spray cooling to the stator core, with the same approximate

method described for the rotor modification. Additionally, a script has been used to

link the inlet temperature of the spray to the heat extracted from the machine. A

detailed view of the stator modifications is shown in Figure 3.16, where the front inlet

of the fluid spray is connected with custom thermal paths to the teeth and yoke of

the stator core. The labels C1 and C2 are representative of the cuboid representation
 84

of the stator end turns, that is, two coils and the adjancent teeth were modeled with

a geometric relationship between the Motor-CAD model and the prototype machine

end turns shape. The same modification was operated on the rear end of the machine

equivalent circuit.

The script runs during the transient solution on a drive cycle and adjusts the

inlet spray temperature using a feedback from the average temperature in the simu-

lated return path. In the actual experimental setup, a heat exchanger is connected

to the ATF closed circuit on the primary and to a constant temperature inlet water

supply. Since the pump is operated at constant power, the spray flow rate depends

on the cooling fluid viscosity and density (that decrease for increasing temperatures).

An empirical correlation between the ATF temperature and flow rate has been

calculated for the experimental setup, employing a linear fit of the experimental

measurements, the average fit of the flow rate as a function of the inlet temperature
˙ F is the flow rate and TAT F,in is the spray temperature
is given in Eq. 3.23, where VA T

between the heat exchanger and before the spray ring section. The experimental data

shows an hysteretic behavior, meaning that the flow rate is slightly different during the

heating and cooling section of the machine heat run test (within 10% of the average).

However, the correlation utilizes the average of the two paths with a tolerance of 10%

on the actual flow value as acceptable simplification.

V̇AT F (TAT F,in ) = 0.0993941TAT F,in − 0.558666 [dm3 s−1 ] (3.23)

During the duty cycle simulation of the machine, the losses, initial tempera-

tures and coolant flow rate are imposed to the circuit, the thermal net is solved at each

step and the customized script is run. The operations carried out in the customized

simulations are to save the coolant flow rate at the current simulation step V̇AT F,t ,
 85

the spray inlet and outlet temperatures (TAT F,out,t and TAT F,in,t ) and to calculate the

heat extracted from the machine Q̇t (Eq. 3.24).

Q̇t = ρAT F,t V̇AT F,t (TAT F,in,t )cP,AT F (TAT F,out,t − TAT F,in,t ) (3.24)

After the initialization, the thermal power Q̇t of the previous step is subtracted

from the previous step temperature TAT F,out,t corresponding to an heat exchanger

correlation (that takes into account the fluid heat capacity cP,AT F and flow rate V̇AT F,t )

to update the inlet temperature TAT F,in,t+1 and flow rate V̇AT F,t set in the simulation

(Eq. 3.25). The calibration of the model is presented in Section 5.1, along with the

experimental data.

Q̇t
TAT F,in,t+1 = TAT F,out,t − (3.25)
ρAT F,t V̇AT F,t (TAT F,in,t )cP,AT F

This simple exchanger model relies on the assumption that the heat extracted

changes with a time constant sufficiently larger than the simulation step, and that

the spray cooling fluid in the reservoir has a small thermal capacity compared to the

machine and heat exchanger. The model can be further refined to obtain a closer

representation of the system, but the results confirm the assumptions made, within

the tolerance set on the flow rate.

Both additions to the model have been proposed as modifications of the equiv-

alent thermal circuit model and will be integrated in the Motor-CAD simulation in a

future release.

3.5 Mechanical FEA

The mechanical modeling of the rotor structures has been carried out in dif-

ferent context, an initial design of experiments was prepared to identify the most
 86

significant machine parameters and their effects on the structural integrity during

operation, subsequently every prototype design, selected for its electromagnetic char-

acteristics, was modeled in 3D solid modeling software in order to verify the safety

factors expected of the rotating parts.

3.5.1 SolidWorks. The WFSM prototype 1 mechanical performance charac-

terization was explored for the initial study and verified for the finalized prototype

using the commercial software package SolidWorks (Copyright 1997-2015

c Dassault

Systemes SolidWorks Corporation). The rotor material properties were modeled as

a composite, modifying the axial and radial stiffness to better represent the stack

assembly [36]. The lamination material, M250-35A Grade according to EN 10106

standard [115], has a nominal Youngs Modulus of 185 GPa for the bulk material, but

it was lowered in the radial direction to 176 GPa and to 76 GPa in the axial direction,

assuming a bonded lamination assembly. The yield stress was set at 455 MPa and

the Poisson’s ratio at 0.21

The field winding was represented by the geometry of the actual winding

and a density scaled with a fill factor (ratio of the copper volume divided by the

winding window) of 50%. The calculation identified the von Mises stress (Fig. 3.17),

safety factors, and displacement at 12,000 RPM and 15,000 RPM. The speed of

12,000 RPM is considered the maximum design speed of the motor. A response

surface was calculated from generating test cases from the same templates used in the

electromagnetic modeling, and the resulting linear regression used in the optimization

phase to estimate the structural integrity. In case of projected failure as modeled by

the correlation, the test case is eliminated from the electromagnetic optimization and

marked as an unfeasible case. The minimum safety factor to allow a test case in the

final candidate design has been set at 1.9 at 12,000 RPM. The WFSM prototype 1

finalized geometry results are presented here as an example of mechanical modeling

 87

(Fig. 3.17). Considering the yield stress of the material of 450 MPa, at 12 kRPM the

machine can resist the maximum stresses.

3.5.2 Abaqus. For the mechanical design feasibility the Abaqus software was also

employed (Copyright 2005-2015

c Dassault Systemes), due to license availability of

the SolidWorks solver during the design process of the HESM prototype. The stress-

strain simulation was additionally used as a verification of the SolidWorks results

previously obtained. There are some differences in the final results using the two

commercial packages, most probably due to the meshing quality.

 88

Figure 3.16. Motor-CAD thermal circuit detail, showing modifications to the stator
thermal circuit inside the green boxes (Front circuit). Note: The user-customized
thermal resistances R44384, R44726 and R44749 connect the teeth and yoke of the
stator to the fluid spray inlet FluidSpray End F (44).
 89

Figure 3.17. Wound field prototype 1 rotor lamination stack, von Mises stress on
the lamination structure, endcaps and winding are modeled in the simulation but
shown in transparency to highlight the lamination stresses [26].
 90

CHAPTER 4

PROTOTYPES DESIGN PROCESS

This chapter describes the process followed to design the machine prototypes.

The equations and FEA software of the previous chapters have been employed in

three different cases, two WFSM machines and one HESM machine prototype. The

first prototype sizing has been obtained from a Differential Evolution Optimization

algorithm (DEOpt), modified to meet mechanical requirements and reduce stress con-

centration in some critical sections of the machine lamination. The second prototype

has been obtained from a two-steps extended optimization process, this combines an

initial sizing of the machine with the DEOpt algorithm and then a MonteCarlo opti-

mization run to size a magnetic flux barrier in the rotor pole. The last prototype took

advantage of an analytical modeling to identify the design region for each rotor of the

machine in order to obtain a wide rotor-side flux weakening region, then modifications

have been incorporated in the initial design to include permanent magnet flux barri-

ers and a step-skew in the PM rotor section, with the intent of improving the magnet

utilization and reduce the torque ripple. The method for this modifications is a sur-

face response modeling, with a Central Composite Design (CCD) method. Finally,

for each prototype, a map of the predicted performance in the torque versus speed

plane is presented as part of the design process to motivate the choices of winding

structures and sizing, since all the machines are designed for high CPSR operation.

4.1 WFSM Prototype 1

The first WFSM prototype has been designed using the WFSM Stator and

Rotor templates 1, described in detail in Section 3.2. The templates were linked to

the parallelized differential evolution optimization routine and tested for the non-

dimensional parameters to be used in the machine design through central composite

designs to identify the limits on the parameters that allow the generation of realizable
 91

geometries and to be able to place the CPC inside the end-turns inner radius.

After extensive test runs of the differential evolution optimizer to identify the

best design region, the input geometric parameter ranges have been specified as per

Table 4.1. The field current values have been chosen from current densities achievable

in industrial prototypes. Further limitations on the torque ripple were imposed as

constraints to increase the convergence speed to the optimal region of the design space

(Table 4.2), since a low values is desired for traction applications. With regards to

the hard constraints of Table 4.2, the conclusion of the preliminary optimization runs

is that these limits act as additional objectives until suitable population is found, and

afterwards keep undesired mutations out of the final distribution, especially when

specifying a torque range instead of a single value to avoid oversized machines.

Table 4.1. WFSM Prototype 1 Input Geometric Parameter Ranges

Parameter Name Range Units
Dimensional Parameters
Axial Length 50 to 200 mm
Airgap 0.5 to 1.0 mm
Stator Outer Diameter 80 to 220 mm
Stator Current Density 15 to 30 A/mm2
Rotor Current Density 10 to 25 A/mm2

Non-dimensional Parameters
ksi 0.5 to 0.8 pu
kwt 0.3 to 0.85 pu
kwso 0.3 to 0.8 pu
kys 0.3 to 0.8 pu
khn 0.15 to 0.85 pu
kth 0.05 to 0.40 pu
kry 0.15 to 0.50 pu
krwind 0.25 to 0.95 pu
kq 0.1 to 0.3 pu
 92

In general, during the optimization test runs has been observed that adding

hard constraints speed up convergence more than increasing the number of optimiza-

tion objectives. The final optimization run specifications have been run in parallel on

two machines with a variation in the number of optimization objectives used. One

optimization was run with a single objective (torque density maximization) while the

other parallel optimization was run with multiple objectives, maximizing torque den-
Tavg
sity and ”goodness” √ (Table 4.3). The final prototype has been selected from
Plosses

this second optimization run, also the population data presented in the following refer

to the optimization with multiple objectives.

Table 4.2. WFSM Prototype 1 Optimization Hard Constraints

Hard Constraint Value Units
Torque Ripple <5 % Per Unit
Average Electromagnetic Torque (Minimum) >140 Nm
Average Electromagnetic Torque (Maximum) <150 Nm
Rotor Ohmic Losses (Maximum) <2500 W
Stator Total Losses (Maximum) <6000 W

Table 4.3. WFSM Prototype 1 Optimization Objectives

Objectives Dimensions Goal
1/Torque Density V
TAV G
m3 N m−1 Minimize
√ 1
1/Goodness PLosses
TAV G
Wth N m−1
2
Minimize

4.1.1 Differential Evolution Optimization. The multi-objective optimization

version with 75 members per generation evolving over 75 generations yielded an overall

better final population from which a shortlist of wound field synchronous machine

designs has been extracted for a more detailed analysis of their characteristics. In

Fig. 4.1(a) all the 5625 tested cases are represented in the torque density/goodness

plane. The populations are color coded to show if various constraints where satisfied.
 93

In Fig. 4.1(b), all designs which meet all hard constraints are highlighted in blue while

design that do not meet the hard constraints are turned white. The local Pareto front

is show in red, for ease of comparison of the best members that have been added to

the candidate shortlist. All the candidate designs presented in Figure 4.1 have a

base speed of 4 kRPM, but an additional candidate with 3 kRPM base speed has

been selected for the final analysis and prototype selection from the single-objective

simulation (candidate 9 in Figure 4.2 and Tables 4.4 and 4.5 ).

(a) Full population (b) Shortlist

Figure 4.1. Torque density versus goodness √PTlosses

avg
(Average Torque/Plosses) for 8
pole 48 slot single layer WFSM designs from the final multi-objective optimization
run [26]. The dot coloring represents which hard constraints the design meets.

4.1.2 Prototype Selection. The down selected machine designs for further study

are shown in Fig. 4.2. The candidate design geometric and physical parameters are

listed in Table 4.4 and output characteristics and figures of merit in Table 4.5.

(a) #5 (b) #6 (c) #9

Figure 4.2. Magnetic flux density distribution of the final three candidate designs.
 94

Table 4.4. Candidates Design Geometric and Physical Parameters

Machine Parameters #5 (62/30) #6 (47/29) #9 (31/28)
Stator Radius (Diameter) 136 mm (272) 124 mm (248) 133 mm (266)
Rotor Radius (Diameter) 100 mm (200) 89 mm (178) 99.6 mm (199)
Length 84.3 mm 87.4 mm 106.82 mm
Min. Airgap Length 0.998 mm 0.955 mm 0.963 mm
Max CPC Radius (Diameter) 67 mm (134) 61 mm (122) 74 mm (148)
Stator Current Density 15.9 A/mm2 18.1 A/mm2 22.0 A/mm2
Rotor Current Density 12.9 A/mm2 16.9 A/mm2 15.1 A/mm2
Mass 34.06 kg 28.40 kg 38.76 kg
Estimated Stress 305 MPa 260 MPa 274 MPa

The candidate design #6 was selected for construction as prototype 1 because

of its superior power density metrics compared to the other candidate designs. The

performance characteristics of the candidate design #6 are compared between the

static reconstruction technique used in FEMM and a transient analysis performed in

Infolytica MagNet. All results are given at the base speed with peak values of required

torque (maximum stator and rotor currents, 18 and 17 MA/m2 respectively). Very

close agreement is seen between the FEMM and MagNet predictions. After settling

on candidate #6 for prototype 1 a check stress analysis was performed. To avoid

potential failure spots in the corners of the pole shoes at the connection to the pole

neck additional fillets were added.

4.1.3 Electromagnetic Characterization. Detailed torque and voltage per

turn mappings based on the prototype 1 model were completed to aid the winding

optimization and aid controls development. The maps were completed by sweeping

the stator and rotor current densities (σS from 8 to 20 A/mm2 and σR from 2 to 20

A/mm2) with the current angle varied between -65 Degrees and 80 Degrees with 5

Degree intervals.
 95

Table 4.5. Candidate Design Output Characteristics and Figures of Merit

Machine Parameters #5 (62/30) #6 (47/29) #9 (31/28)
Base Speed [RPM] 4000 4000 3000
Base Frequency [Hz] 267 267 200
Torque Average [Nm] 140.5 141.2 203.4
Peak Power [kW] 58.54 59.13 63.90
Gross Volume [liters] 4.869 4.231 5.928
Torque Density [Nm/liter] 28.87 33.36 34.31
Vol Power Density [kW/liter] 12.09 13.97 10.78
Mass Power Density [kW/kg] 1.73 2.08 1.65
Stator Iron Losses [W] 441 430 434
Stator Copper Losses [W] 1640 1884 2218
Rotor Copper Losses [W] 1383 1817 1829
Total Losses [kW] 3.5 4.1 4.5
Efficiency 94.4 % 93.4 % 93.4 %
Torque Ripple [Nm] - % 6.78 - 4.84 % 6.97 - 4.94 % 10.03 - 4.94 %

Based on the voltage per turn maps two operating conditions have been ana-

lyzed to optimize the design of the prototype 1 winding:

1. Rated peak operating point at the base speed (4 kRPM): MTPA angle, peak

torque (142 Nm)

2. End of the constant power speed range (CPSR) (12 kRPM): MTPV angle, peak

torque (42 Nm)

For the end of the constant power speed range the torque and voltage mapping

help determine the winding where the terminal current is minimized to keep the cost

of the inverter reasonable. To minimize the current rating of the inverter switches and

avoid risks with circulating currents caused by winding imbalance all coil groups were

connected in series. The voltage of the machine must be kept below the maximum
 96

allowed by the inverter. The operating conditions characterization is given in Table

4.6. The high speed operating point, 12 kRPM, at the end of the constant power

speed range operating point was found by searching the torque maps as a function of

the current angle, stator, and rotor current densities for combinations which satisfied

the torque requirement for constant power while minimizing the voltage per turn.

Figure 4.3. WFSM prototype 1 finalized geometry used for the prototype multi-
physics characterization, the loading corresponds to the maximum current densities
and predicts 192 Nm torque output.

Table 4.6. WFSM Prototype 1 Winding Design - Limit Operating Conditions

Speed σS σR Curtent Angle Torque Voltage per turn
4 kRPM A
18 Amm-2 17 Amm-2 20 degrees 142.9 Nm 7.7 V
12 kRPM B
13 Amm-2 11 Amm-2 60 degrees 42.45 Nm 10.6 V
A B
Base Speed, Maximum Speed

4.1.4 Winding Design. Based on the two operating points windings were designed

to meet dynamometer DC link voltage limits. Winding models have been constructed
 97

to estimate the stator and rotor winding parameters and compared to commercial

software results, Table ?? and Table 4.8. High but reasonable slot fills are specified.

Table 4.7. WFSM Prototype 1 Stator Winding Design

Parameter Design Motorsolve MotorCAD
Turns per pole per phase 4 4 4
Slot fill factor 40.10 % 40.10 % 39.44 %
End Winding Length [mm] 90.4 102.0 103.4
Winding resistance [Ω/ph] 0.0153 0.0163 n.a.
Phase voltage [VRMS] (12 kRPM) 240 255 n.a.
Phase current [ARMS] (12 kRPM) 195 195 n.a.

Table 4.8. WFSM Prototype 1 Rotor Winding Design

Parameter Design Motorsolve MotorCAD
Slot fill factor 44.91 % 44.90 % 52.91 %
End Winding Length [mm] 55.7 60.8 69.1
Winding Window [mm 2 ] 191 191 191
Turns per pole 239 n.a. n.a.
◦
Winding resistance 100 C [Ω] 32.66 33.9 n.a.
Phase Voltage [VDC ] (4 kRPM) 225.5 227.1 n.a.
Phase current [ADC ] (4 kRPM) 6.7 6.7 n.a.

The finalized winding designs allow the machine to be operated in the full

range of the converter and additionally to be overloaded on the rotor side when

operating with brushes. This condition has been instrumental in modeling the thermal

operation of the machine under load and the spray cooling system. The stator winding

is characterized by 4 turns in series for each of the 8 coils. To combine ease of

manufacturing with a high slot fill, the wire size chosen is AWG 16, with 10 strands

in hand. The rotor winding main limitation is the CPC terminal current, that is the

reason to choose a very large number of turns (239) on the rotor. Additionally, to
 98

favor a higher fill of the coil sides, a smaller wire with respect to the stator has been

preferred, the AWG 21.5.

4.1.5 Mechanical Design and Structural Analysis. The materials properties

used in the mechanical simulations are listed in Table 4.9, the steel properties have

been modified to take into account the effect of rotor lamination as previosly presented

in Section 3.5. It should be noted that the actual geometry of the coil was used, but

the copper density was adjusted to reflect the fill factor achievable in random wound

coils (50% of net copper).

This geometry differs slightly from the optimizer output, because initial results

of the mechanical modeling showed a stress concentration at the base of the pole and

between the yoke and the neck of the rotor. For this reason, fillets were added to

the geometry and the machine was simulated with increasing radii of the fillets until

the stress at the maximum speed dropped below the prescribed safety factor fo 1.9.

The results of the finalized geometry are given as an example in Figure 3.17 and this

finalized geometry was used to map the performance of the machine at the base speed,

presented for convenience of comparison in Section 5.1 relative to the experimental

characterization.

Table 4.9. WFSM Prototype 1 Materials Mechanical Properties

Parameter M250-35A Copper PEEK
Density [kg m-3 ] 7850 8960 1320
A
Young modulus [GPa] 175.85 117 5.475
Elastic limit [MPa] 450 139 95
Poisson’s ratio [p.u.] 0.21 0.36 0.38
A
Radial Yong Modulus, Axial simulated value is 75.76 GPa

4.2 WFSM Prototype 2

For the prototype 2 design, a two-step extended optimization was carried out,
 99

using the stator template and the flexible rotor template of Figure 3.8. In the initial

optimization with the differential evolution algorithm, the air barrier at the center of

the rotor pole was omitted and it was used on the second part of the optimization,

carried out with a MonteCarlo method. For both simulations, the stator is unchanged

from the previous design.

4.2.1 Differential Evolution Optimization. Table 4.10 shows the setup for the

first step in the machine optimization. The rotor structure differs from the previous

version because an additional parameter for the rotor saliency was added, kshape ,

in the attempt to increase the reluctance torque of the machine. Additionally, the

optimization constraints and optimization objectives are presented in Tables 4.11 and

4.12. The difference from the WFSM prototype 1 is here in the torque limits imposed,

since a larger power density is sought after.

Table 4.10. WFSM Prototype 2 Input Geometric Parameter Ranges

Parameter Name Range Units
Dimensional Parameters
Axial Length 91 mm
Airgap 0.5 to 1.0 mm
Stator inner Diameter 178 mm
Stator Outer Diameter 254 mm
Stator Current Density 15 to 30 A/mm2
Rotor Current Density 10 to 20 A/mm2

Non-dimensional Parameters
kth 0.05 to 0.4 pu
kry 0.2 to 0.75 pu
kq 0.01 to 0.4 pu
kshape 0.7 to 0.95 pu
khn 0.45 to 0.8 pu
kX 0.01 to 0.9 pu
 100

Table 4.11. WFSM Prototype 2 Optimization Hard Constraints

Hard Constraint Value Units
Torque Ripple <5 % Per Unit
Average Electromagnetic Torque (Minimum) >180 Nm
Average Electromagnetic Torque (Maximum) <200 Nm
Rotor Ohmic Losses (Maximum) <1500 W
Stator Total Losses (Maximum) <6000 W

Table 4.12. WFSM Prototype 2 Optimization Objectives

Objectives Dimensions Goal
1/Torque Density V
TAV G
m3 N m−1 Minimize
√ 1
1/Goodness PLosses
TAV G
Wth N m−1
2
Minimize

Figure 4.4 shows the results of the optimization run on the losses versus power

density plane. Since some approximated thermal model was available from the WFSM

prototype 1 characterization, the total machine losses limit was set at 6 kW, and the

machine was selected as the one with the highest power density below this value. The

simulation results of the base case for the extended optimization of Figure 4.5 shows

the flux density plot at the peak operating point.

4.2.2 MonteCarlo Extended Optimization. The second part of the optimiza-

tion dealt with the sizing of the pole barrier at the center of the rotor pole. In this

optimization run the rest of the geometry is fixed and the optimizer does not set

directly objectives or constraints, it only generates cases and simulates two operating

points of the machine, to try and approximate the characterization of the machine at

full load and partial load. The barrier size parameter ranges are given in Table 4.13,

where it can be noticed that the ranges are very large for the horizontal parameters. In

order to avoid unfeasible geometries, a filter is applied to the machines for which these

parameters generate an unfeasible geometry. Since the base case machine had been
 101

Figure 4.4. WFSM prototype 2 differential evolution optimization results, the full
population is marked in black, the Pareto front in red and the prototype in yellow.

Figure 4.5. WFSM prototype 2 base case geometry resulting from the differential
evolution optimization and input for the MonteCarlo extended optimization.
 102

mapped before the MonteCarlo simulation, a loading characteristic was obtained and

imposed to the simulation of the machines with the barrier. The values for the partial

load excitation in the stator and rotor were 12 Amm−2 and 9 Amm−2 respectively,

while the peak power point was simulated at the stator and rotor current desities of

24 Amm−2 and 17 Amm−2 respectively. The partial load excitation thermal loading

would allow the machine to operate continously, and also the expected power output

was estimated to exceed the continuous power requirement of 30 kW.

Table 4.13. WFSM Prototype 2 MonteCarlo Parameter Ranges

Parameter Name Range Units
Non-dimensional Parameters
kY 0.05 to 0.2 pu
kX1 0.05 to 0.3 pu
kX2 0.1 to 0.95 pu

The results from the MonteCarlo optimization were filtered and analyzed to

identify two Pareto fronts of the machines meeting low ripple requirements (less than

5%), the tradeoff in Figure 4.6 is between full torque output at base speed and the

stator turn voltage, used to ensure the operability of the machine with an existing

stator. The prototype selected shows a small torque increment and voltage reduction

with respect to the base case. The other tradeoff considered in the selection is between

the stator turn voltage and the partial load efficiency of Figure 4.7, since in this

comparison the machines with lower peak torque output can give an advantage in

terms of continuous power loading efficiency. The simulated machine selected for

prototyping is the compromise between these two factors and is shown in Figure 4.8.

4.2.3 Winding Design. The stator winding has the same characteristics of the

WFSM prototype 1. For the rotor, an increased number of turns allows the machine

to be operated with reduced stress on the capacitive power coupler. The details on
 103

Figure 4.6. WFSM prototype 2 extended optimization results on the full load torque
torque versus stator voltage per turn, the geometries resulting in low ripple are
marked in blue, the Pareto front in red and the prototype design in yellow.

Figure 4.7. WFSM prototype 2 extended optimization results on the stator voltage
per turns versus partial load efficiency, the geometries resulting in low ripple are
marked in blue, the Pareto front in red and the prototype design in yellow.
 104

Figure 4.8. WFSM prototype 2 finalized geometry resulting from the extended opti-
mization.
 105

the rotor winding design are reported in Table 4.14.

Table 4.14. Prototype 2 Rotor Winding Design

Parameter Design MotorCAD
Slot fill factor 46.7 % 48 %
End Winding Length [mm] 51 –
Winding Window [mm2 ] 226 226
Turns per pole 325 n.a.
◦
Winding resistance 20 C [Ω] 39.31 n.a.
◦
Winding resistance 100 C [Ω] 58.78 n.a.
Phase Voltage [VDC] (4 kRPM) 312 n.a.
Phase current [ADC] (4 kRPM) 5.31 n.a.
Phase Voltage [VDC] (12 kRPM) 158 n.a.
Phase current [ADC] (12 kRPM) 2.70 n.a.

4.2.4 Electromagnetic Characterization. The post-processing of the recon-

structed transient FEMM electromagnetic solution, allows for the calculation of the

whole speed range mapping of the machine. In order to derive the efficiency mapping,

the machine losses need to be estimated. For the output power, the electromagnetic

torque is subtracted of the bearing and windage losses, and as power input, the cop-

per and iron losses are summed to the net output. Since the machine losses are

copper-dominated, the temperature is an important factor for its scaling. The oper-
◦
ating temperature chosen to model the losses is 70 C, in order to compare to the

experimental results.

The predicted torque as a function of stator and rotor current is shown in Fig.

4.9. The motor output power is then obtained for different speeds multiplying the

torque by the shaft speed. However, not all points are feasible because of the stator

voltage constraints.

In the following figures, all the components that take part into the motor
 106

Figure 4.9. Predicted results, MTPA shaft torque at base speed of 4000 RPM.

efficiency calculation are represented inside the voltage limit, and the values corre-

sponding to the MTPA torque are used. The phase voltage map of Fig 4.10 shows

a large area between the 300 Vpk and the nominal 350 Vpk range. This is because

the algorithm used to construct the mapping searches for voltages that meet the

maximum voltage requirement even if the angle exceeds the MTPA.

This detail can be observed closely in Fig. 4.11. From the previous modeling

of the machine we know that the MTPA angle is in the range 15 to 30 degrees for a

wide operating area of the machine, while the MTPV is closer to the range 40 to 45

degrees. In the torque-speed plane we can see that the maximum power output up to

the base speed is obtained for current angles close to the MTPA, while the operating

points close to the voltage limit shift closer to the MTPV current angle.

The predicted stator copper losses of Figure 4.12 are the largest component

in the machine losses, but these are acceptable thanks to an efficient direct cooling
 107

Figure 4.10. Predicted results, MTPA voltage for the machine design speed range of
0 to 12000 RPM.

of the stator end turns via ATF spray. Comparing this losses map to the rotor

equivalent (Fig. 4.13), it can be noted that the peak torque is reached in the region

with approximately equal loading of the two circuits, up to the base speed at which

the rotor flux is weakened to reduce the terminal voltage. Above the base speed,

stator currents could be kept to the maximum allowed value, but the corresponding

operating point is not the one with maximum torque per ampere.

The stator core losses have been calculated from the simulated field distribu-

tions, sampled in each iron section of the stator (Fig. 4.14). It can be noted that

the order of these losses is approximately one tenth of the stator copper losses and

even though it is not negligible, shows that a dedicated cooling system (e.g. a water

jacket) is not required to directly extract the core losses.

The resulting efficiency is represented in the same torque-speed plane in Figure

4.15. The efficiency has been calculated as the net power output (electromagnetic
 108

Figure 4.11. Predicted results, MTPA current angle for the machine design speed
range of 0 to 12000 RPM.

torque times speed subtracted of the iron losses) divided by the sum of the net power

output and the total copper losses. A wide area of efficiency above 94% is present

below the required output of 150 Nm (to exceed the peak power requirement of 55

kW), this region should be the target of the continuous operation of the machine

when integrated into a vehicle transmission and ultimately the reason for choosing

to model the machine at partial load, selecting the most efficient that met all other

requirements.

Finally, the torque ripple simulated values are shown in Fig. 4.16. It can be

observed that for the whole operating area of the machine, a low ripple below 11 %

is predicted.

4.2.5 Mechanical Design and Structural Analysis. The WFSM prototype 2

materials specifications are the same as the the WFSM prototype 1 (Table 4.9), but
 109

Figure 4.12. Predicted results, stator copper losses map for the machine design speed
range of 0 to 12000 RPM at MTPA current angle.

the finalized machine simulation has been carried out in Abaqus instead of Solidworks.

The von Mises stress is shown in Figure 4.17 and the displacement in Figure 4.18.

The stress concentration is located at the center of the stack, on the fillet connecting

the rotor neck with the pole expansion.

 110

Figure 4.13. Predicted results, rotor copper losses map for the machine design speed
range of 0 to 12000 RPM at MTPA current angle.

Figure 4.14. Predicted results, core losses map for the machine design speed range of
0 to 12000 RPM at MTPA current angle.
 111

Figure 4.15. Predicted results, efficiency map for the machine design speed range of
0 to 12000 RPM at MTPA current angle.

Figure 4.16. Predicted results, ripple map for the machine design speed range of 0 to
12000 RPM at MTPA current angle.
 112

Figure 4.17. WFSM Prototype 2, predicted vonMises stress on the rotor laminations
(Maximum value 367 MPa) at maximum speed of 12000 RPM. Note: endcaps and
windings have been simulated but are not shown.
 113

Figure 4.18. WFSM Prototype 2, predicted deformation on the rotor laminations

(Maximum value 21μm) at maximum speed of 12000 RPM. Note: endcaps and
windings have been simulated but are not shown.
 114

4.3 HESM Prototype 1

The HESM prototype initial design was obtained with the sizing equations

presented in Chapter 3.1 and refined with the FEA methods presented in Chapter 3.3.

The sizing method employed is presented in the following and provides a design space

analytical characterization followed by a combinatorial method using FEA simulations

and, after the choice of prototype, a mapping of the finalized prototype. The mapping

is followed by the mechanical analysis of the rotor structures for mechanical integrity

verification at the design maximum speed of 12000 RPM.

4.3.1 Analytical Sizing Equations. The analytical sizing equation system

provides a distribution of machine cases that meet the no-load fundamental airgap

flux of 0.9 T (B̂g1,nl ), airgap volume of 2.5 liters and a stator linear current density

of 60 kARMS m−1 . The idealized electromagnetic torque produced is equal to 190 Nm

(Eq. 2.2) for all the cases analyzed.

In order to generate a design space in the nonlinear analytical model (see

Section3.1), three variables are selected: the airgap radius Rg , the yoke depth ratio kSy

and the tooth width ratio kSt . The analytical model distribution has been obtained

combining several CCF central composite designs, for a total of 540 cases examined

(one order of magnitude less than the differential evolution algorithms used in the

WFSM prototypes optimization). The airgap radius has been swept between 60 and

100 mm, with 16 steps of 2.7 mm, the yoke ratios assumed 6 values in the range from

0.67 to 1.0 and the 6 tooth ratios were in the range 0.5 to 0.82, both with increments

of 0.064 . The corresponding no-load peak magnetic flux density is calculated from

Eqs. 2.8 and 2.10 respectively, to be in the range 0.9 T to 1.34 T for the yoke peak

value and the range 1.1 T to 1.8 T in the most saturated tooth.

Additional constraints are introduced to derive the design space characteriza-

 115

tion, since sweeping these parameters as variables would increase exponentially the

number of cases examined and therefore the execution time of the FEA simulation.

The full list of constraints and values is given in Table 4.15, with a link to the relevant

design equation.

Table 4.15. HESM CCD Constraint List

Constraint Name Symbol Value Reference
Phases m 3 Eq. 2.11
Pole Pairs p 4 Eq. 2.11
Slot per Pole per Phase m 2 Eq. 2.11
Number of Teeth z 48 Eq. 2.17
Airgap thickness δ0 0.75 mm Eq. 3.2
Slot Shape Factor kds 0.85 Eq. 2.19
A
Winding Factor kw1 0.966 Eq. 2.19
Lamination Stacking Factor kF e 0.95 Eq. 2.3
Stator Fill Factor kCu,S 0.40 Eq. 2.17
−2
Stator Current Density σS 24 Amm Eq. 2.17
Rotor Yoke Ratio kRy 0.8 Eq. 2.25
Rotor Neck Ratio kRn 0.7 Eq. 2.30
PM Pole Span Ratio kP M 0.8 Eq. 2.41
PM Angle Ratio kRα 0.6 Eq. 2.52
WF Pole Span Ratio kRp 0.9 Eq. 2.35
Rotor Fill Factor kCu,R 0.45 Eq. 2.32
−2
Rotor Current Density σR 18 Amm Eq. 2.32
A
First harmonic

4.3.2 FEA Modeling. For the detailed modeling of the machine, the templates

presented in Section 3.3 were employed. In particular the stator and wound field

rotor templates are the same as the WFSM prototypes, while the PM template is the

second presented, with a V-shaped permanent magnet configuration (Fig. 3.10). The

flat-bar version of the PM rotor was used for the initial model calibration, but the

V-shaped version was preferred, as more representative of the PM machines used in

 116

automotive traction applications.

Each of the analytical sizing geometries were exported to the FEA solver and

modeled .The comparison of the results are shown in Figures 4.19 to 4.22. The full set

of results is a four-dimensional surface in the design space previously defined, but it

has been projected on the airgap radius versus results plane for ease of presentation.

Plotting the distribution on the stator tooth axis yields a quadratic function, since

this parameter affects both the outer diameter (slot depth) and the winding area.

The stator yoke yields an approximately linear fit. The last two projections were

omitted in order to highlight the main dependency of the parameters on the airgap

radius.

Figure 4.19 shows the peak value of the fundamental for airgap flux density

at no-load, obtained from the FEA simulations. The vertical spread of results is

the result of the interaction between the three input factors, resulting in a spread of

about 10% around the value of 1 T for the PM rotor and of about 7% around the

value of 0.95 T for the WF rotor. A possible explanation for this behavior is the

sizing equation process, since the WF excitation level is set after the calculation of

the projected MMF drops in the machine, while the PM sizing is mostly related to the

linear reluctances of the permanent magnet and airgap. Potentially, the PM sizing

could be improved with an iterative method that takes into account additional MMF

drops, but this sizing tolerance was deemed sufficiently accurate for the purpose of

this work.

The resulting FEA torque is shown in Figure 4.20 for the HESM, WFSM and

PMSM. The comparison has been obtained calculating the WFSM and PMSM torque

for two machines with the same rotor and stator stack lengths. The HESM torque

is obtained scaling the active length of the two rotors (operating with the stator and

rotor fluxes in quadrature) and subtracting the wound field end-turn length from the
 117

Figure 4.19. HESM response surface model results, peak value of the fundamental
airgap magnetic flux density (B̂g1,nl ), B WF denotes the wound field rotor (top)
and B PM the permanent magnet rotor (bottom). Note: the vertical blue dashed
line and the value below the y-axis labels mark the prototype, the green dots the
FEA simulations and the red curve the best fit of simulations.
 118

available stack. This cost of the hybridization is also shown in Figure 4.22 as a power

density loss.

The projected machine physical dymensions are represented in Figure 4.21

and have been obtained from the analytical model, using correlations between the

end turns and the end turns arc. The stator envelope volume is larger than the

airgap volume because for the same stack length, the stator end turns are summed to

the length and the machine outer diameter is considered. The stator envelope radius

is the sum of the airgap radius, the tooth depth and the yoke thickness.

It should be noted that the maximum stator diameter available for testing

is limited to 254 mm, so all candidate designs above this limit were excluded from

further investigation.

Finally, Figure 4.22 shows the power density of the hybrid machines obtained

subtracting the rotor end turns length from the avalable stack length (show in the top

plot as power density loss), and dividing the net avalaible stack equally between the

PM and WF rotors. In terms of sizing parameters this corresponds to a hybridization

factor on the d-axis of 50%. It can be noted that for a smaller radius, a larger

gravimetric power density could be obtained with respect to the prototype (marked

as a vertical blue dashed line in all of the plots). Additionally, it can be noted

that the power density cost decreases slightly more than linearly with the airgap

radius, because two factors (the rotor end turn arc and the length to diameter ratio)

interact at larger stack length for the same airgap volume. Moreover, the gravimetric

power density has a maximum value at an intermediate airgap radius in the range

considered, even though the power density loss is larger than the one at the minimum

airgap radius.

The choice of airgap radius is motivated by compatibility with the previous

 119

Figure 4.20. HESM response surface model results, average value of the transient
torque, T WF denotes the wound field machine (middle), T PM the permanent
magnet machine (bottom) and T (HRd) the hybrid machine with equal WF and
PM rotor stack lengths (50% hybridization ratio). Note: the vertical blue dashed
line and the value below the y-axis labels mark the prototype, the green dots the
FEA simulations and the red curve the best fit of simulations.
 120

Figure 4.21. HESM response surface model results, physical sizes of the stator. Note:
the vertical blue dashed line and the value below the y-axis labels mark the proto-
type, the green dots the FEA simulations and the red curve the best fit of simula-
tions, the red horizontal dotted line in the Stator Envelope Radius is the allowed
maximum value.
 121

prototypes and it should also be noted that the prototype geometry is the one with

highest power density that also meets the maximum stator size constraints for the

airgap radius size. The input parameter values for the candidate HESM machine

selected as prototype are Rg equal to 89 mm, kSy equal to 0.8733 (corresponding to

1 T peak flux in the yoke at no-load) and kSt equal to 0.6298 (corresponding to 1.4

T peak flux in the most saturated tooth at no-load).

The projected weight used in the calculation of the power density does not

include the shaft, but using similar components sizes (from the WFSM designs), it

can be inferred that the full assembly can meet the DOE USDRIVE 2020 targets of

1.6 kW kg-1 .

The maximum power density could be obtained, if not constrained by other

factors, for an airgap radius of 76 mm and the smallest yoke and tooth factors (0.67

and 0.5 respectively), but would also produce the lowest torque in the range and gain

at most a 20% in power density (potentially less due to the effect of the shaft weight).

The model yields, for this combination, a stack length of 137 mm, a stator outer

diameter of 216 mm and a machine length, including end turns, of 206 mm.

4.3.3 Prototype Selection. Since the HESM prototype needs to be compatible

with the available testing equipments and previous prototypes as a design require-

ment, the airgap radius has been fixed at the value of 89 mm, corresponding to 100

mm of stator stack length for the desired airgap cylindrical volume of 2.5 liters. For

this airgap radius value, the tooth and yoke have been sized as the combination that

results in the maximum power density for a stator outer diameter of 254 mm (size

limit of the existing stator shell available for testing). Due to the uncertainty linked

to the rotor end turns and the tolerance needed for thermal expansion of the winding,

a precautionary stack length increase of 6 mm was performed, with marginal effect

on the machine parameters.

 122

Figure 4.22. HESM response surface model results for 50% hybridization ratio, Power
Density loss denotes the power density reduction due to the rotor end turns (top),
GPD the gravimetric power density of the HESM (middle) and VPD the volumetric
power density of the HESM (bottom). Note: the vertical blue dashed line and
the value below the y-axis labels mark the prototype, the green dots the FEA
simulations and the red curve the best fit of simulations.
 123

The PM section barriers were subject to an additional optimization, in or-

der to address the leakage flux in the rotor lamination and the torque ripple. The

process followed is again a central composite design, this time with the barriers di-

mensional values and selecting the combination that resulted in maximum torque

output (each of the cases examined performances fell in a range of -5% to +5% of

the initial prototype). Hovewer, the PM section torque ripple exceeded the design

constraint of 10%, so an additional modification, a step-skewing of the lamination,

was performed. Since this modification does affects marginally the terminal voltage,

it will be presented after the winding design section.

4.3.4 Winding Design. The stator winding for the HESM prototype is similar

to the WFSM prototypes already presented. A distributed winding with two slots

per pole per phase was selected also in this case to obtain relatively low harmonic

content, but the smaller terminal voltage obtained from the simulation allowed the

use of an additional turn per pole.

The field winding can be operated as 250 turns / 5.16 A (series connection)

nominal either with brushes or CPC excitation or as 125 turns / 10.32 A (parallel

connection) with brushes to generate the nominal airgap peak flux density of 1 T.

The circuit simulation results are given in Table 4.17, where the Design column shows

the data for the series connection and the MotorCAD column shows the data for

the parallel connection (used to calculate the thermal lumped parameter circuit of

the machine). Field voltages and currents must meet the DC power source limits,

therefore are referred to the maximum allowed temperature of 150◦ C.

4.3.5 PM section step-skewing. The PM section stack length was subject

to additional modifications with respect to the initial model. In order to reduce the

torque and flux harmonic, a step-skew was operated on this structure. The lamination

specifications are shown in Figure A.4, where it can be noted that a single lamination
 124

Table 4.16. HESM Stator Winding Design

Parameter Design
Turns per pole per phase 5
Design slot fill factor 40 %
Stack Length [mm] 106
End Winding Arc LengthA [mm] 121
A
End Winding Axial Length [mm] 38
Estimated winding resistance 20◦ C [Ω/ph] 0.0378
Estimated winding resistance 150◦ C [Ω/ph] 0.0566
B
Phase voltage [VRMS ] (4 kRPM) 233
B
Phase current [ARMS ] (4 kRPM) 147
Phase voltageC [VRMS ] (12 kRPM) 233
Phase currentC [ARMS ] (12 kRPM) 147
A
Referred to each coil on each side
B
Field current 5 ADC (maximum flux boosting)
C
Field current -1 ADC (flux weakening)

is cut, but the key and drill holes align to generate a total offset equal to a half a slot

pitch (corresponding to a continuous skew of one slot pitch) while at the same time

allowing for assembly in either direction.

The drill holes and cutouts have been added for structural and weight reduction

reasons. The drill holes allow an insertion of through-bolts to two steel end plates,

used to compress the lamination and magnets assembly and in part to provide further

mechanical strength to the lamination pole (i.e. to reduce the stress on the flux

barriers). The bolts and plates have been selected from non-ferromagnetic, austenitic

steels that present high resistance to corrosion, in view of the prototype use with the

ATF spray-cooling system.

Additionally, the permanent magnet material initally used for the machine

sizing (764AP) was not available at the moment of the lamination production. A
 125

Table 4.17. HESM Prototype Wound Rotor Winding Design

Parameter Design MotorCAD
Electrical connection Series Parallel
Design slot fill factor 40.23 % 40 %
End Winding Axial LengthA [mm] 10 10
Winding Window [mm] 202 202
Turns per pole 125 250
Parallel coils per pole 2 1
Estimated winding resistance 20◦ C [Ω] 18.72 9.36
◦
Estimated winding resistance 150 C [Ω] 28.00 14.00
Nominal Field Voltage [VDC ] 193.19 96.60
Nominal Field current [ADC ] 5.16 10.32
A
Referred to each coil on each side

different magnet grade (N42SH) was modeled and purchased for the prototype imple-

mentation, with small changes in the machine performance. The available standard

size in the magnetization direction was equal to 3.175 mm, approximately 6% larger

than the size obtained from the machine sizing.

The permanent magnet thickness used for the prototype is approximately half

of the commercial machines of comparable power rating (e.g. Toyota Prius 2010 are

7.16 mm in the magnetization direction [18]). An explanation for this difference is the

need, in PM machines, to avoid demagnetization of the rotor. For the HESM machine

the demagnetization can be addressed with the control of the WF rotor, limiting the

demagnetizing current.

However, a simulation was conducted on the final machine geometry and per-

manent magnet material (N42SH), showing that the magnet can survive demagneti-

zation with a demagnetizing current of 1500 At from the stator (approximately 50%

larger than the nominal), at 100◦ C derated performance. The same test at 20◦ C
 126

resulted in the demagnetization of the magnets corners for currents exceeding 2000

At (approximately double the nominal current).

4.3.6 Electromagnetic Characterization. The hybrid excitation prototype

mapping is more complex than the previous wound field prototypes since the rotor

is composed by three sections, the WFSM and the two step-skewed PM subsections.

The PM subsections have been simulated from the finalized geometry and offset in

the angular direction so as to correctly represent the reluctance harmonics and their

cancellation.

The mapping process was divided into three simulation, to take into account all

the contributions to the excitation of the machine. For each of the two PM sections,

an equivalent PMSM with the full stack length has been simulated (100 mm of net core

length, accounting for the lamination stacking factor) for 30 steps of stator current

densities ranging from 0 to 30 Amm-2 (corresponding to 40% stator overload) and 20

current angles in the range -25 to 70 electrical degrees, with a 5 degrees increment. A

total of 1,200 transient solutions were simulated in approximately 5 hours (on a 8 core

machine running 8 parallel threads) to obtain the full PMSM mapping. The PM rotor

post-processing operates a composition of the two step-skewed sections based on the

stack length, summing each of the simulation results of interest (e.g. voltage, transient

torque during rotation etc.). In addition, for each of the 40 speeds considered (from

1 to 20,001 RPM with a 500 RPM increment), the losses and voltages are calculated,

in order to generated the machine maps presented in the following. The final 48,000

points of the mapping relative to speed can be obtained in approximately 1 minute

of calculation time.

For the WF section, a similar mapping has been simulated, with the addition

of 16 steps of rotor current density for the field excitation modeling (from 0 to 22

Amm-2 , corresponding to a 50% overload of the rotor circuit). Also for the wound
 127

field, a WFSM was simulated for the full stack length, in order to compare the HESM

to this solution and it was post-processed for the same speeds as the PMSM. The total

execution time for the WFSM transient simulations was approximately 41 hours for

the 9,600 transient simulations (due to larger database saving time) while the post-

process is executed in less than 20 minutes for the final 384,000 operating points.

In order to model performance with field enhancement and weakening of the

HESM, an additional post-processing operated a composition of the PMSM and

WFSM maps. For each step of the mapping (i.e. a 4D matrix indexed on rotor

current density, stator current density, current angle and speed), all the variables of

interest where scaled by the actual active stack lenght of 44 mm for each of the ro-

tors, summing or subtracting the component due to the WFSM to generate the field

boosting and weakening regions, centered on the field no-load solution. For instance,

the motoring WF section torque was summed and subtracted to each value of the

PM section corresponding to the same stator current, current angle and speed. The

same process was applied to voltage, core losses and rotor copper losses. The stator

copper losses, on the other hand, are the same for both machines, given the initial

assumption of modeling the WFSM and PMSM separately for the same stack length.

This final result database for the HESM machine is composed of 816,000 op-

erating points, and the individual results have been filtered and plotted to describe

the predicted performance of the machine at the MTPA value for the PM and WF

rotor excitations aligned on the magnetic d-axis. In principle, the performance for

any offset between the rotor magnetic axes can be derived from the existing dataset.

The relevant section of these data that have been experimentally tested is presented

in Section 5.3.

Figure 4.24 shows the terminal voltage on the torque-speed plane for the HESM

prototype. In order to plot the results on this plane, a binning algorithm has been
 128

used to discretize the torque in the y axis, inside each group of data, the maximum

efficiency point has been selected, usually close to the MTPA point. The DC bus

voltage is fixed at 350 V, so that a line-to-line voltage of 300 V can be obtained from

the inverter (corresponding to the stator overloaded condition). The jagged lines

in the wide flux weakening region are due to the map discretization. This voltage

limitation has been imposed on all of the following graphs, discarding operating points

that produce a voltage larger than the acceptable values of Figure 4.24.

Figure 4.23. HESM predicted results, voltage map on the torque-speed plane.

The efficiency calculation for the HESM is presented starting from the com-

ponents of the efficiency expression. The rotor copper losses of the WF section are

shown in Figure 4.24, while the stator copper losses are plotted in Figure 4.25. Both

losses characteristic show a similar behavior as the WFSM prototypes, as it should

be expected, and also in this case a temperature of 70◦ C has been assumed.

The stator iron losses are presented in Figure 4.25 and are summed to the

total copper losses to derive machine losses map of Figure 4.27. The efficiency is then
 129

Figure 4.24. HESM predicted results, rotor copper losses map on the torque-speed
plane.

Figure 4.25. HESM predicted results, stator copper losses map on the torque-speed
plane.
 130

calculated from the output power (multiplying x and y axis values), subtracting the

core and bearing losses (from previous prototypes data) and dividing by the total

copper losses.

For the efficiency plots, the HESM, IPMSM and WFSM are presented sepa-

rately (Figs. 4.28, 4.29 and 4.30 respectively), to allow for a comparison between the

three topologies. The ideal constant power speed ratio has also been overimposed to

the efficiency maps (up to a 5:1 ratio from the 4000 RPM base speed), in order to

highlight the characteristic of these machines in terms of flux weakening. Comparing

the plots it can be noted that both the HESM and WFSM can be operated at high

CPSR (other than for a notch above 14 kRPM due to low field current resolution)

while the PMSM is more limited in this sense. In practice the PMSM could be op-

erated at higher CPSR imposing a larger component of stator current to reduce the

permanent magnets flux, but the simulation angle was limited in the original data set

(Fig. 4.31).

Additional variables modeled in the machine mapping are the MTPA current

angle (Fig. 4.31), the power factor (4.31) and the torque ripple in the transient

solution (4.33). These plots show that the metrics are met for high power factor in a

wide operating range for a low torque ripple (above 20 Nm torque production), while

the torque angle shows that up to base speed the MTPA angle is close to 20 degrees,

above the base speed the voltage constraint is met only for increasingly high values.

Finally, the last set of plots show the produced torque on the stator current

versus rotor current plane, at the base speed of 4000 RPM (other than for voltage

limitation, this torque distribution is the same used to plot the previous maps).

Figure 4.34 shows the maximum motoring torque produced by the WF section in

every intersection corresponding to the value of excitation current and stator current.

The axis are scaled for terminal ampere-turns, where for the stator current 1400 At
 131

Figure 4.26. HESM predicted results, stator iron losses map on the torque-speed
plane.

Figure 4.27. HESM predicted results, total losses map on the torque-speed plane.
 132

Figure 4.28. HESM predicted results, efficiency map on the torque-speed plane, CPSR
is shown in red.

Figure 4.29. HESM predicted results, efficiency map of the pure IPMSM correspond-
ing to the lamination design extended to the full stack on the torque-speed plane,
ideal CPSR is shown in red.
 133

Figure 4.30. HESM predicted results, efficiency map of the pure WFSM corresponding
to the lamination design extended to the full stack on the torque-speed plane, CPSR
is shown in red.

correspond to 33 Amm-2 current density in the stator copper, and the maximum rotor

current density of 22 Amm-2 corresponds to 2000 At excitation. Figure 4.35 shows the

same sweep for the PM section, that is independent from the WF torque production,

and Figure 4.36 is the composition of the two, assuming the net motoring torque.

It can be noted that in the negative excitation region, the machine can behave like

a motor from the torque production point of view, but the PM rotor will produce

positive torque while the WF rotor will behave as a brake.

4.3.7 Mechanical Design and Structural Analysis. The structural integrity of

the rotors have been verified with an Abaqus simulation for each case. The material

properties, similar to the ones of the previous WFSM prototypes but with the addition

of the permanent magnet material, are shown in Table 4.18.

The simulation results for the PM rotor are shown in Figures 4.37 and 4.38,

for the von Mises stress and deformation, respectively. The magnets, through bolts
 134

Figure 4.31. HESM predicted results, MTPA current angle map on the torque-speed
plane.

Table 4.18. HESM Prototype Mechanical Material Properties

Parameter M15 Steel 764AP and N42SH Magnets Copper PEEK
Density [kg m-3 ] 7850 7600 8960 1320
Young modulus [GPa] 184.80 140 117 5.475
Elastic limit [MPa] 450 600 139 95
Poisson’s ratio [p.u.] 0.21 0.24 0.36 0.38

and end plates have been omitted to highlight the lamination stresses, but care has

ben taken not to exceed the safety factor in each of the elements in the assembly.

An iterative process has been used to finalize the mechanical design, and the initial

lamination modified to reduce the stresses in the pole body, using the through bolts

to compress the laminations.

Also the WF rotor section has been modeled (Figs. 4.39 and 4.40) and in this

case the stresses are reduced with respect to the previous prototypes. An explanation

for this stress reduction is that the stack length is shorter than the pure WFSM cases,
 135

Figure 4.32. HESM predicted results, power factor map on the torque-speed plane
for MTPA current angles of Figure 4.31.

and also the rotor winding geometry helps in distributing the forces along the rotor

neck.
 136

Figure 4.33. HESM predicted results, torque ripple map on the torque-speed plane
for MTPA current angles of Figure 4.31.

Figure 4.34. HESM predicted results, WF section torque map on the rotor current-
stator current plane for MTPA current angles at 4000 RPM.
 137

Figure 4.35. HESM predicted results, PM section torque map on the rotor current-
stator current plane for MTPA current angles at 4000 RPM.

Figure 4.36. HESM predicted results, total torque map on the rotor current-stator
current plane for MTPA current angles at 4000 RPM.
 138

Figure 4.37. HESM prototype, predicted von Mises stress on the PM rotor laminations
(Maximum value 153 MPa) at maximum speed of 12000 RPM. Note: magnets, end
plates and bolts have been simulated but are not shown.

Figure 4.38. HESM prototype, predicted deformation on the PM rotor laminations

(Maximum value 31μm) at maximum speed of 12000 RPM. Note: magnets, end
plates and bolts have been simulated but are not shown.
 139

Figure 4.39. HESM prototype, predicted vonMises stress on the WF rotor laminations
(Maximum value 147 MPa) at maximum speed of 12000 RPM. Note: endcaps and
windings have been simulated but are not shown.

Figure 4.40. HESM prototype, predicted deformation on the WF rotor laminations

(Maximum value 30μm) at maximum speed of 12000 RPM. Note: endcaps and
windings have been simulated but are not shown.
 140

CHAPTER 5

PROTOTYPES EXPERIMENTAL RESULTS

The experimental results of the machine designs presented in Chapter 4 are

shown here for open-circuit losses and voltage, equivalent circuit parameter identifi-

cation and machine torque production at base speed. The key differences between the

two WFSM machines are and increased saturation of the second prototype over the

first, without a corresponding torque production increase, but with a reduced rotor

terminal current necessary to magnetize the machine. On the other hand, the HESM

prototype is designed mainly for control development instead of power density metric

and it shows the flux weakening capability expected from the simulated modeling of

the machine. This enables further work on hybrid excitation synchronous machine

operation, since it allows the testing of two configurations (dPMWF and dPMqWF

as presented in Chapter 2).

5.1 WFSM Prototype 1

5.1.1 Prototype Construction and Assembly. The WFSM prototype 1 con-

struction involved the laser cutting of the stator laminations from M15-29Ga, rotor

laminations from M250-35A magnetic steel and stacking and laser welding of the

laminations. The stack construction has been contracted to an external laser cutting

company, the resulting rotor stack (Fig.5.1) has been fitted with a Polyether-Ether-

Ketone plastic (PEEK) end-cap before winding in order to provide winding end-turn

integrity at high speed and protection to the inner conductors from damage caused

by direct contact against the lamination edges (Fig. 5.2). The chemical resistance

and high operating temperature of PEEK was the main reason for this choice, since

the prototype was designed to operate in presence of ATF. The stator and rotor were

wound according to specification, the rotor was additionaly fitted to the shaft using a

hub and locknut, in order to reuse the shaft for future prototypes. The shaft and rotor
 141

assembly was balanced for operation at 12 kRPM, the maximum speed considered

for operation. The two completed components are shown in Figure 5.3, before the

stator insertion into a housing shell. Finally, the stator and rotor were fit inside the

shell (Fig. 5.4) using a lathe to insert the drive-end bearing inside the drive-end plate

seat (Fig. 5.5), with the copper coil for ATF spray already installed. The prototype

assembly was completed fitting the non drive-end plate of the machine and installing

the brushes and CPC for the field connection to the external excitation circuit (Fig.

5.6).

5.1.2 Bearing, Windage and Spray Cooling Losses. The initial characteri-

zation of the machine has been carried out with the open stator circuit. A first test

allowed to discount any torque meter offset and the bearing losses as a function of the

speed when the rotor is also kept de-energized. The equipment in use was a Yoko-

gawa WT1800 power analyzer connected to the analog output of an HBM T40 torque

flange (nominal torque range 1000 Nm) in order to capture and record the losses.

Additionally, the torque meter digital output was connected to an HBM Gensys 7

digital acquisition system integrated in the dynamometer setup. The WFSM proto-

type 1 no-load bearing and windage losses were measured with and without the ATF

spray cooling system engaged (Fig. 5.7). No significant difference between losses with

or without the ATF spray cooling can be observed for the speed range considered,

since the highest loss recorded does not exceed 1 % of the machine power output.

The HBM data sets refers to the digital acquisition system, the WT1800 data sets

refer to the the power analyzer acquisition. The bearing, windage and ATF losses

measurement could be improved by the use of a torque flange with a smaller nominal

range.

5.1.3 Open Circuit Test. Further testing was carried out energizing the rotor

circuit and measuring of the no-load back-emf, as a function of both rotor current
 142

Figure 5.1. Wound field prototype 1 rotor lamination stack.

 143

Figure 5.2. Wound field prototype 1 rotor lamination stack fitted with PEEK endcaps.
 144

Figure 5.3. Wound field prototype 1 stator and rotor assembly after winding.
 145

Figure 5.4. Wound field prototype 1 stator and rotor after insertion (machine non
drive-end).
 146

Figure 5.5. Wound field prototype 1 stator and rotor after insertion (machine non
drive-end).
 147

excitation and speed. Moreover, the mutual inductance has been derived in the no-

load condition, by post-processing the output voltage measurement (this result will

be presented in the following subsection). Finally, the torque measurement during the

back-emf test of Figure 5.8, yields the open circuit core losses (discounting the bearing,

windage and ATF spray losses). The open circuit line to line voltage and core losses

as a function of the rotor field current and speed were measured and compared with

simulation predictions, Figures 5.8 and 5.9 respectively, showing very close agreement.

Two different simulations are compared to the experimental results, FEMM denotes

the use of time-domain reconstruction from a series of static simulations at different

rotor positions, while MagNet denotes a full time-domain transient simulation. The

electromagnetic simulation details are described in detail in Section 3.2. The results

of the two solvers show a slightly different behavior, where FEMM results seem to

overestimate the voltage and the losses at low excitation current, potentially due to

the static solution results that can tend to exaggerate the saturation and imperfect

steel losses characterization. In absolute terms of losses estimation a maximum dif-

ference of 75 W is recorded at 4000 RPM, corresponding to approximately 0.2 Nm

and within the measurement tolerance of the system.

5.1.4 Equivalent Circuit Parameter Identification. With the winding defined,

the predicted machine equivalent circuit parameters were calculated both in MagNet
◦
and FEMM (predicted and measured values at 20 C in Table 5.1). The stator and

rotor resistances (Rs and Rf respectively) were measured injecting a DC current in

each winding and measuring the terminal current and voltage with two multimeters.

Four additional tests were carried out in order to estimate separately the d-axis

and q-axis stator inductances Ld and Lq, the mutual inductance Lm and the field

inductance Lf. The equipment used for this test is a single-phase line-fed variac, two

differential voltage probes and one current probe connected to a LeCroy HDO6034-MS

oscilloscope. For the first two tests, the rotor was turnes to align the field pole axis to
 148

the stator d-axis, locked in the correct position and the field winding connected to the

variac and a probe. An additional voltage probe was connected between the stator

phase A terminal and the parallel connection of phases B and C for the first test. The

machine operates as a transformer open on the secondary winding (the stator) and the

induced voltage can be recorded to estimate the Lm. The rotor impedance, discounted

of the resistive drop caused by Rf, is divided by the angular frequency to obtain the

field inductance. On the stator side, the voltage divided by the rotor current and

angular frequency yields the unsaturated mutual inductance Lm, since the large field

impedance limits the field current and no current can flow in the open-circuit stator.

For the second test, the stator side currents and voltages are measured and the field

circuit is open circuited and connected to a differential voltage probe. The d-axis

stator inductance Ld is then calculated from the imaginary part of the impedance,

while the rotor voltage gives the unsaturated mutual inductance Lm (that matches

the one previously calculated). The third and fourth tests follow the same procedure,

but the rotor is aligned to the stator q-axis and the stator differential probe connection

is between phase B and phase C terminals in series (q-axis characterization). The

results underwent the same post-processing as the previous two tests to yield the

values of Lq and yet another matching estimation on Lm and Lf. The limitation of

this approach is that of the variac current capability, in this case around 10 % of the

nominal value of stator current. This means that the values reported here are the

nominal, unsaturated inductances of the machine at 60 Hz.

Since the inductances are affected by the machine saturation, Figures 5.10 and

5.11 show the predicted values and the experimental results for field and unsaturated

mutual inductances, Fig.5.10, and d-axis and q-axis stator inductances, Fig.5.11.

However, the field nominal current is low enough to allow for testing the mutual

inductance saturation with a different method. In this test the voltage probe is

connected between one stator phase and the machine neutral, the rotor is spun on
 149

Table 5.1. WFSM 1 Unsaturated Machine Equivalent Circuit Parameters

Parameters FEMM MagNet Experimental
Lf [mH] 2330 2386 2278
Ld [mH] 0.969 0.998 0.98
Lq [mH] 0.565 0.597 0.60
Lm [mH] 32.36 32.94 33.46
Rf [Ω] 26.952 26.952 26.5
Rs [Ω] 0.0153 0.0153 0.02

a dynamometer at a known angular frequency and the field winding is fed with DC

current. The resulting voltage is postprocessed in a similar was as the test with the

variac, but in this case the angular frequency is changed to verify the previous results.

5.1.5 Dynamometer Testing. The WFSM prototype 1 characterization was

performed on a 180 kW dynamometer equipped with the torque flange previously

presented (Fig. 5.12) connecting to the field winding through slip rings and brushes.

The prototype 1 WFSM stator circuits were fed by a Semikron Semikube IGBT

Module Stack IGD-20424-P1N6-DH-FA. A custom DSP interface PCB board to the

Semikron Semikube and feedback sensors based around a Spectrum Digital TI F28335

DSP evaluation board were designed to control the inverter, regulate currents in the

stator of the WFSM and perform field oriented control. The brushes and slip rings

were connected to a manually operated Magna-Power PQ500-20 DC power supply,

interposing a snubber circuit and diode to limit overvoltages during field excitation

adjustments. To control the stator currents a discrete-time complex vector current

regulator has been implemented to decouple the stator dynamics. The WFSM effi-

ciency was measured using Yokogawa WT1800 power analyzer and the drive efficiency

with a PX8000 power analyzer. Stator phase currents were measured using Yokogawa

96031 current probes connected to the WT1800 and a LEM Ultrastab was connected

to the PX8000. Field electrical input was recorded on the two power analyzers and
 150

additionally on an oscilloscope (LeCroy HDO6034-MS) that provided a real-time field

resistance calculation. This resistance increases with temperature and gives an indica-

tion of thermal stress in the rotor, in this context it was used to avoid overtemperature

of the winding insulation.

Dynamometer test to measure torque, efficiency, and power factor mapping

was also carried out for a field currents between 1 and 7 A (1 A increment), stator

current between 50 and 300 A (with 100 A increments, all values are peak of the

sinusoidal waveform), and current angles γ from -10 to 50 degrees and for the pre-

dicted MTPA angle of 15 degrees (10 degrees increments) at 1000 to 4000 RPM with

increments of 1000 RPM. The stator temperature during the mapping was kept in

the range of 35 to 100 ◦ C. The predicted shaft torque mapping is plotted alongside

the experimental results at the base speed of 4,000 RPM, Fig.5.13. Also, the current

angle for maximum torque has been plotted in Figure5.14. Both the predicted and

experimentally measured results are in good agreement.

However, at high stator current magnitudes, above 200 A, the predicted and

measured torque begins to deviate slightly. This is most likely due to the lack of

detailed information of the BH curve of the stator core material for very high satura-

tion. It should be noted that the experimental torque data for the region with rotor

current larger than 4 A and stator current larger than 300 A have been measured from

a test of 30 seconds or longer without surpassing the winding thermal constraint of

220◦ C. This satisfies the DOE metrics for peak power and test duration, and explicitly

demonstrates the effectiveness of the cooling system. Additional thermal modeling

for steady-state operation is presented at the end of this section.

The power factor map at 4000 RPM, Fig.5.15, shows the power factor at the

current angle for maximum torque (which is not necessarily the current angle for

maximum power factor). The power factor is quite high in the high field current
 151

region of the map. Small reductions in the torque capability allow for increased

power factor (reduction of reluctance torque).

The data acquisition also allowed to calculate the motoring operation efficiency

of the machine and to compare it to the mapping obtained from FEMM simulations.

The discrepancies recorded are within 1% in excess of the estimated value, which is

compatible with the error introduced by slight deviations in the material characteri-

zation used in the simulation stage. Comparing the predicted torque production with

the measured one, the increase in measured torque is compatible with the previously

mentioned efficiency estimation error, due to the efficiency estimation procedure. In

order to derive the efficiency from the current-driven simulation, the net mechanical

output (corresponding to the electromagnetic torque production subtracted of bear-

ing and core losses) is divided by the sum of the net power output and the copper

losses.

5.1.6 Thermal Characterization. The thermal characterization of the prototype

has been carried out during the experimental campaign to refine and calibrate the

simuation model in MotorCAD in order to be able to predict the performance of the

ATF spray cooling system. The experimental data presented in the following section

are the results of a heat run, where the machine has been loaded with the contractual

peak power output (58 kW shaft power), that the machine should be able to hold

for 30 seconds. The test duration was approximately 30 minutes, in which no part of

the rotor of stator windings exceeded the rated temperature (expected life of 20,000

hours at 220◦ C). The temperature measurements were carried out interfacing to a

thermocouple reader of a Labview CompactDAQ (CDAQ) data acquisition system.

The current, voltage and torque signals were acquired via a Yokogawa WT1800 power

analyzer on the dynamometer testing bench previously mentioned. The coolant flow

waas acquired interfacing to a Badger Meter Blancett B2800 flow meter interfaced
 152

to the same CDAQ that records the thermocouple readings. The 16 thermocouple

positions were chosen in order to estimate the thermal stress on different sections of

the machine and are listed here grouped by similar positions:

1. The ambient and housing temperature were measured to provide a reference for

the power dissipated by convection (Fig. 5.18).

2. The copper winding inside the stator slots was measured in the center of the slot

for phases A and B, at the center of the stack and one third from the stack ends

both on the drive-end and non drive-end of the machine for phase A (Fig. 5.19),

the center of the slot and center of the stack should be most representative of

the hotspot of the winding.

3. The end-turns are useful to calibrate the thermal model, since most of the heat

extracted is transferred to the coolant in this area, two measurements were

recorded from the two ends of the machine (Fig.5.20).

4. The stator core temperature was also estimated, inserting three thermocouples

at the slot bottom close to the slot liner, to estimate the stator yoke temperature

during operation (Fig.5.21).

5. The stator teeth temperature is also measured with three thermocouples at the

center of the stack, one third of the stack from the drive end and non-drive end

(Fig.5.22), in contact with the slot liner on the tooth side.

6. The spray inlet and return temperatures were sampled with thermocouples in-

mersed in the connection tubing to and from the machine (Fig.5.23), giving a

direct temperature rise from which is possible to estimate the extracted heat

(Fig.5.26).
 153

7. The rotor temperature direct measurement is not easily obtained during rota-

tion, so no thermocouples were installed, however, the resistivity of the copper

is well modeled with a linear correction factor and therefore the resistance mea-

sured with the WT1800 power analyzer can be used to roughly estimate the

average temperature (Fig.5.24), the limitations are that the total resistance in-

clude the brushes and slip rings system and that the measurement can only be

obtained if the rotor is loaded.

The detailed loading of the machine can been verified from the power analyzer

and taking advantage of the previous modeling of the machine losses. The stator

active power (62 kW) subtracted of the output mechanical power (58.4 kW) gives

the total machine losses, the nominal stator resistance has been used to calculate

the stator copper losses (1000 W per phase, 3kW total, adjusted for temperature

dependency in the simulation), the remainder is core losses and bearings (500 W

and 100 W respectively) estimated from the no-load characterization. On the rotor

side, the input power has been calculated directly from the measurements, since DC

power is absorbed disregarding the initial RL transient. For the rotor temperature

scaling, the nominal resistance at 20◦ C (Rf in Table 5.1) was used, giving approxi-

mately 15◦ C/Ω. These losses and the duration of the machine loading time has been

specified in the MotorCAD model of the machine, with the necessary modifications

to the thermal circuit and taking into account the cooling system parameters and

construction details.

5.1.7 Prototype Physical Data and Metrics. The machine physical charac-

terization is presented in Table 5.2. The critical metrics for the machine torque and

power density are all meeting or exceeding the design metrics as set to meet the DOE

requirements of 1.6 kW kg−1 and 5.0 kW −1 , for a duration of the testing process

exceeding 30 seconds.
 154

Table 5.2. WFSM Prototype 1 Machine Physical Data

Machine Parameters Experimental Value
Stator Outer Diameter 254 mm
Airgap Length 0.95 mm
Rotor Outer Diameter 176 mm
Stack Length 91 mm
Peak Motoring Torque 190.55 Nm
Peak Motoring Power 79.6 kW
Peak Motoring Efficiency 95 % at 87.5 Nm, 4000 RPM
A
Mass 40.64 kg
B
Volume 11.06 
Volumetric Peak Torque Density 17.22 Nm −1
Specific Peak Torque Density 4.69 Nm kg−1
Volumetric Peak Power Density 7.19 kW −1
Specific Peak Power Density 1.95 kW kg−1
A
Includes stator, rotor and shaft
B
Volume of the cylinder that includes spray cooling rings and full machine
 155

Figure 5.6. Wound field prototype 1 non drive-end view with capacitive power coupler
installed.

Figure 5.7. WFSM Prototype 1 measured bearing and windage losses. ATF Spray is
denoted by PB,Spray , HBM refers to the digital output of the torque meter, WT1800
to the analog output.
 156

Figure 5.8. WFSM prototype 1 measured (Experimental dataset) and simulated

(MagNet and FEMM simulated datasets referring to the solvers) open circuit volt-
ages.

Figure 5.9. Measured and simulated open circuit core losses, Magnet denotes the
transient solution results, FEMM the static reconstruction with two core losses
models, Steinmetz and CAL2.
 157

Figure 5.10. WFSM prototype 1 predicted and experimentally measured equivalent

circuit parameters, field, Lf , and mutual Lm . FEMM denotes the simulation data
results.

Figure 5.11. WFSM prototype 1 predicted and experimentally measured equivalent

circuit parameters, stator d and q axis inductances, Ld and Lq . FEMM denotes
the simulation data results.
 158

Figure 5.12. Wound field synchronous machine testing dynamometer setup.

Figure 5.13. WFSM prototype 1 experimental results, shaft torque at 4000 RPM, red
dots are experimental measurements, surface is the FEMM simulation result.
 159

Figure 5.14. WFSM prototype 1 simulated (left) and experimental results (right),
current angle of the maximum torque for a given field and stator current at 4000
RPM.

Figure 5.15. Measured WFSM prototype 1 power factor at the current angle corre-
sponding to maximum torque at 4000 RPM.
 160

Figure 5.16. Measured WFSM prototype 1 efficiency results at 4000 RPM using
Yokogawa PX8000. The temperature of the stator windings ranged between 45 to
100 ◦ C. Efficiencies are for maximum torque current angles.
 161

Figure 5.17. Predicted WFSM prototype 1 efficiency at a winding temperature of

70 ◦ C as a function of field and stator currents at maximum torque current angle
at 4000 RPM. The efficiency is calculated from the net mechanical power output
divided the result of power output summed to the total copper losses. The net
mechanical power output is obtained subtracting the estimated bearing and core
losses from the simulated electromagnetic torque, averaged over one rotation.
 162

Figure 5.18. Experimental and simulated temperature at 4000 RPM, housing denotes
the external surface of the machine shell on the active length, ambient the room
temperature during testing.

Figure 5.19. Experimental and simulated temperature of the middle of the coil at 4000
RPM, A and B denote the phases in which the thermocouple is installed, Center
the midpoint of the stator slot axially(45 mm from both ends of the machine),
Front the drive-end axial position (30 mm from the end turns inside the stack),
Rear the non-drive end axial position (30 mm from the end turns).
 163

Figure 5.20. Experimental and simulated temperature of the end turns connections
at 4000 RPM, Front denotes the drive-end axial position, Rear the non-drive end
axial position.

Figure 5.21. Experimental and simulated temperature of the yoke-side liner at 4000
RPM, Center denotes midpoint of the stator slot axially (45 mm from both ends of
the machine), Front the drive-end axial position (30 mm from the end turns inside
the stack), Rear the non-drive end axial position (30 mm from the end turns).
 164

Figure 5.22. Experimental and simulated temperature of the tooth-side liner at 4000
RPM, Center denotes midpoint of the stator slot axially (45 mm from both ends of
the machine), Front the drive-end axial position (30 mm from the end turns inside
the stack), Rear the non-drive end axial position (30 mm from the end turns)

Figure 5.23. Experimental and simulated temperature of the spray cooling fluid inlet
and outlet at 4000 RPM.
 165

Figure 5.24. Experimental estimation and simulated average temperature of the rotor
winding and brushes system at 4000 RPM, the experimental estimation drops to
20◦ C when the rotor circuit is opened, marking the end of the loading test.

Figure 5.25. Experimental measurement and simulated temperature difference be-

tween inlet and outlet of the spray cooling fluid (Top) and flow rate (Bottom) at
4000 RPM.
 166

Figure 5.26. Experimental measurement and simulated spray cooling fluid heat ex-
traction (Top) and machine losses (Bottom) at 4000 RPM.
 167

5.2 WFSM Prototype 2

5.2.1 Prototype Construction and Assembly. The construction and assembly

of the second WFSM prototype follows the same process of the previous one. Since

the stator, shell and end-plates are the same, only the rotor assembly process is

presented here. The lamination stack was cut and welded by an external provider

from M-15 29 Ga electrical steel (Fig.5.27), fitted with PEEK end-caps, inserted on a

steel hub, wound and balanced by an external supplier (Fig.5.28). Once the winding

and varnishing processes were ultimated, the rotor circuit was connected to a PCB in

order to realize the connection in series of each of the poles coils and to eight damping

varistors connected in parallel to each pole, for surge protection (Fig.5.29). Finally,

the completed wound rotor was engaged to the shaft shoulder via dowel pins (to allow

an easy disassembly of the component) and pressed in place with a keyed spring and

locking nut (Fig.5.30).

5.2.2 Open Circuit Test. The second prototype characterization of bearing and

windage losses is in all identical to that of WFSM prototype 1. The data presented

in Fig. 5.7 of the previous section can be used as a reference also in this case. The

open circuit tests for the back-emf and no-load core losses of the WFSM prototype

2 have been carried out with the same method and equipment. The voltage of the

open stator has been measured and compared to the FEMM simulation results at

field excitation levels ranging from 0.5 to 8 A and speeds ranging from 1000 to 6000

RPM, with 1000 RPM increments (Fig.5.31). The main difference from the WFSM

prototype 1 is the rotor excitation capability, that has been enhanced in order to

operate the CPC at lower current and try to reduce the rotor copper losses during

operation. This has been achieved with an increase in rotor turns allowed in the

design phase by an increased rotor winding window. The nominal field current is set

by the CPC at 5 A, but the testing carried out with brushes overloaded the circuit
 168

Figure 5.27. Wound field prototype 2 rotor lamination stack, the flux barrier is clearly
visible at the center of the poles.

Figure 5.28. Wound field prototype 2 rotor lamination stack fitted with PEEK end-
caps, drive-end view.
 169

Figure 5.29. Wound field prototype 2 rotor after winding and poles connection to
varistors for surge protection, non drive-end view.
 170

Figure 5.30. Wound field prototype 2 rotor assembly, drive-end view.

 171

in order to verify the spray cooling system capability.

Figure 5.31. WFSM prototype 2 measured and simulated stator open circuit voltages,
FEMM denotes the FEA solver used.

The estimation error on open circuit core losses is compatible with the previ-

ous prototype, but in this case testing at speeds above nominal (4000 RPM) where

carried out, showing a larger deviation of the experimental losses from the simulated

characteristic. The limitation that emerges from the simulated core losses can be

attributed to the loss characteristic used to post-process the induction field intensity

obtained from the simulation. Additional testing (Epstein test of lamination strips)

would be required to characterize the core steel from which the machine is built, but

this is beyond the resources available for this work and more suitable to an industrial

product series development.

The WFSM prototype 2 field circuit has been modified to reduce the termi-

nal current (increasing the number of turns) and the effect is that the unsaturated

machine shows an increase in rotor field inductance and resistance (Table 5.3) with

respect to the WFSM prototype 1. However, the increased reluctance torque due to

the rotor pole barrier does not emerge experimentally. Perhaps the saturation level,
 172

Figure 5.32. WFSM prototype 2 measured and simulated open circuit core losses,
FEMM denotes the FEA solver used.

clearly demonstrated via field and no-load voltage at high excitation current, prevents

this advantage to be noticed.

Table 5.3. WFSM 2 Unsaturated Machine Equivalent Circuit Parameters

Parameters FEMM Experimental
Lf [mH] 5100 4750
Ld [mH] 0.969 0.98
Lq [mH] 0.565 0.60
Lm [mH] 62.15 58.64
Rf [Ω] 39.31 40.25
Rs [Ω] 0.0153 0.02

5.2.3 Equivalent Circuit Parameter Identification. The list of tests presented

in the WFSM prototype 1 have been carried out also for the second one. The resulting

inductance estimations are shown in Figures 5.33 through 5.36. The only notable

difference in the process has been an estimation of the field inductance using harmonic

currents and voltages induced in the rotor circuit. The results clearly confirm the
 173

heavy saturation of the magnetic circuit, for currents exceeding 1 A terminal current.
 174

Figure 5.33. WFSM prototype 2 predicted and experimentally measured equivalent

circuit parameters, Field inductance Lf , Variac denotes the data obtained at 60 Hz,
Open Circuit is the result of experimental back-emf measurement post-processing.

Figure 5.34. WFSM prototype 2 predicted and experimentally measured equivalent

circuit parameters, mutual inductance Lm , Variac denotes the data obtained at
60 Hz, Open Circuit is the result of experimental back-emf measurement post-
processing.
 175

Figure 5.35. WFSM prototype 2 predicted and experimentally measured equivalent

circuit parameters, Stator inductances Lq .

Figure 5.36. WFSM prototype 2 predicted and experimentally measured equivalent

circuit parameters, Stator inductance, Ld .
 176

5.2.4 Dynamometer Testing. The WFSM prototype 2 dynamometer testing has

been carried out with the same equipment and procedures as the WFSM prototype 1.

The full performance mapping under load and with spray cooling has been measured

at speeds of 2000 and 4000 RPM, rotor excitation currents ranging from 2 to 7 A (1

A increment), stator currents from 50 to 300 A (50 A peak to peak increments) and

current angles γ from -20 to 40 degrees (5 degrees increment). The comparison with

simulated data yields a substantial matching of the results, although at very high

saturation the measured torque deviates from the prediction. The motoring torque

at the MTPA is presented in Fig. 5.37, and the corresponding current angle in Fig.

5.39. Since the prototype 2 has the stator design in common with the prototype 1,

it is possible to compare the rotor performances taking into account the scaling of

the rotor excitation (prototype 2 generates 30 % more A-turns per terminal current

excitation). The conclusion is that the absolute value of torque is marginally affected,

since the machine saturation is almost total (as witnessed by the inductance satura-

tion presented in the previous section), the major difference is that the current angle

is increased, leading to the conclusion that the machine experiences a slightly larger

torque contribution from the reluctance component.

The power factor is marginally increased with respect to the first prototype,

and a slightly larger power factor is recorded at maximum torque (power factor in-

creased to 0.85 from 0.8). Also for this prototype, the power factor is improved

for higher rotor excitation, which is fundamentally limited by the cooling capability.

Overall, the power factor increase with respect to the previous prototype is limited

to about 5 %, meaning that the margin for additional power factor correction is ba-

sically inexistent at low rotor excitation. The power factor was obtained from the

impedance of the current driven simulation, using the imposed current angle and the

voltage phase the is calculated from the simulation results. This estimation of the

power factor disregards the harmonic content of the voltage (that in reality drives
 177

Figure 5.37. WFSM prototype 2 experimental results, MTPA shaft torque at base
speed of 4000 RPM.

Figure 5.38. WFSM prototype 2 simulation results, MTPA shaft torque at base speed
of 4000 RPM.
 178

Figure 5.39. WFSM prototype 2 experimental results, current angle γ of the maxi-
mum torque for a given field and stator current at 4000 RPM.

Figure 5.40. WFSM prototype 2 simulation results, current angle of γ the maximum
torque for a given field and stator current at 4000 RPM.
 179

harmonic currents into the machine stator during operation) but allows for a faster

estimation. In order to obtain a simulation closer to the reality of machine opera-

tion, a voltage-driven simulation should be performed, but the implementation poses

several difficulties in the convergence of the problem. That is, in order to implement

the voltage-driven simulation in the static solver used, the voltage imposed to the

circuit is the stimulus to a differential equation that calculates the current to set in

the static simulation for each discretized step in the rotation. The resulting current

transient in time should be at this point represented with several time stepping so-

lutions for each position of the rotation, greatly increasing the transient simulation

times. Ultimately, the estimation error is acceptable in favor of a faster execution of

the mapping procedure for the machine and a consistent reduction in development

effort.

Additional experimental data addresses the characterization of the maximum

torque per volt, which is useful for operation in the flux weakening region. It can be

observed that the maximum torque per volt of Fig. 5.43 is very similar in absolute

value to the maximum torque per ampere of Fig. 5.37, while the maximum torque

per volt current angle is larger than the MTPA equivalent result (Fig.5.44). This is

another indication of the increased reluctance torque component with respect to the

prototype 1, but the absolute gain is relatively small, due to the saturation in the

stator iron. A significant result is that the experimental MTPV torque is close to

the experimental MTPA result, denoting a capability for the machine to behave well

in the flux weakening region. Additionally, the current angle of Figure 5.44 denotes

a wide operating area with relatively small current angle and high power factor, a

predictor of suitability of the machine for flux weakening operation.

Finally, the motoring efficiency of the machine is presented in Fig. 5.45, which

shows very similar results with respect to prototype 1. The effect of a larger rotor
 180

Figure 5.41. WFSM prototype 2 measured power factor at the maximum torque
current angle at 4000 RPM.

Figure 5.42. WFSM prototype 2 simulated power factor at the maximum torque cur-
rent angle at 4000 RPM. The power factor is obtained from the simulation voltage
angle offset from the imposed current simulation, calculated from the reconstructed
transient field solution
 181

Figure 5.43. WFSM prototype 2 measured torque at the maximum torque per volt
at 4000 RPM.

Figure 5.44. WFSM prototype 2 experimental results current angle at the maximum
torque per volt operating points at 4000 RPM.
 182

winding combined with a larger winding window allows the peak efficiency region

to be bounded by a lower terminal current, thus reducing the stress on the rotor

excitation coupler (either CPC or brush and slip rings) but the losses in the rotor

conductors are substantially the same. Also in this case, the discrepancy arising

between the simulated and experimental values can be attributed to the torque es-

timation error, ultimately depending on the BH curve of the material used for the

modeling of the machine. The expected performance from the simulations (Fig. 5.46)

predicted around 2% more efficiency in the same region, compatible with the differ-

ence in peak torque production (experimentally 200 Nm, 205 Nm simulation) at the

peak operating point of field excitation 7 A, stator excitation 300 A, current angle 30

degrees.

5.2.5 Prototype Physical Data.

Table 5.4. WFSM Prototype 2 Machine Physical Data

Machine Parameters Experimental Value
Stator Outer Diameter 254 mm
Airgap Length 0.6 mm
Rotor Outer Diameter 176.8 mm
Stack Length 91 mm
Peak Motoring Torque 200.44 Nm
Peak Motoring Power 83.9 kW
Peak Motoring Efficiency 94 % at 112 Nm, 4000 RPM
A
Mass 40.64 kg
B
Volume 11.06 
Volumetric Peak Torque Density 18.12 Nm −1
Specific Peak Torque Density 4.93 Nm kg−1
Volumetric Peak Power Density 7.59 kW −1
Specific Peak Power Density 2.07 kW kg−1
A
Includes stator, rotor and shaft
B
Volume of the cylinder that includes spray cooling rings and full machine
 183

Figure 5.45. WFSM prototype 2 measured efficiency results at 4000 RPM for maxi-
mum torque current angles.

Figure 5.46. WFSM prototype 2 simulated efficiency results at 4000 RPM for maxi-
mum torque current angles.
 184

5.3 HESM Prototype 1

5.3.1 Prototype Construction and Assembly. The HESM prototype con-

struction is different from the previous ones since the PM rotor is magnetized before

insertion and care must be taken in order to avoid damaging the lamination stacks

during assembly, due to the permanent magnets attraction force towards the stator.

Additionally, the presence of two sub-rotors and the magnet step-skewing of the PM

section complicates the rotor assembly with respect to a conventional PM or WF ro-

tor realization. The shaft was designed for a flexible testing of the machine, meaning

that the WF rotor section key engages directly on the shaft, while the PM section is

mounted on a keyless hub, that can slide freely during assembly. It is possible, with-

out disassembling the full machine, to rotate the PM section and provide magnetic

flux on the same axis of the WF section (dPMWF HESM configuration) or to provide

a flux at 90 electrical degrees (dPMqWF and dWFqPM HESM configuration), allow-

ing the testing of 2 configurations of the hybrid excitation with a single prototype.

The PM rotor section has been assembled on a 6060 Aluminium hub similar in shape

and function to the ones used for WFSM prototypes 1 and 2 (Fig.5.47), that is to

engage on the shaft shoulder with dowel pins for testing of different prototypes. The

assembly procedure involved the following steps:

1. A non-magnetic steel (austenitic AISI 316, corrosion resistant to ATF fluid

spray) end-plate is fit to the Aluminium hub.

2. A pack of 36 laminations (cut from M-15 steel, corresponding to 12.7 mm stack

length) loose laminations were fit on the hub and tied down with AISI 316A

compression bolts to prevent deformation during the magnet insertion.

3. The permanent magnet blocks (NdFeB grade N42SH magnets, 25.4 mm x 12.7

mm x 3.175 mm, magnetized in the direction parallel to the smallest dimension)

 185

were inserted in the lamination pack, alternating North and South poles (the

magnetization polarity before insertion was checked with an F.W. Bell 5170

Tesla Meter) and checking the alternating attraction/rejection from the poles

with a test magnet after insertion.

4. The points 2 and 3 were repeated four times in total, aligning the first two packs

of laminations with the cutouts in a clockwise offset from the key, and the last

two packs aligned with a counterclokwise offset (flipping the pack), in order

to realize the step skew with a single design for the laminations and allowing

insertion of through-bolts.

5. The PM stack assembly was finalized fitting a second steel end-plate on top

of the stack, inserting 16 bolts (AISI 316 #10-32) and tying the assembly to-

gether with hexagonal locknuts (AISI 316 #10-32 and nylon ring for corrosion

resistance).

Figure 5.48 shows the finalized PM rotor section, the locknuts and the inserted

dowel pins (AISI 304) used to transmit torque to the shaft.

The WF rotor section assembly and winding were carried out by the lamination

manufacturer and an external winding facility respectively. Figure 5.49 shows the

end-connection PCB fitting on the WF rotor, the PCB can be disassembled and

substituted with a different one that allows parallel connecion of the two sub-windings

on the rotor, both PCB allow for the insertion of damping varistors across each

pole. The varistors function is to protect the winding, dampening and absorbing the

overloading that the rotor field may experience in fault conditions or step changes

in the stator current commands. The completed hybrid excitation rotor assembly is

shown in Figure 5.50, in this phase of the assembly, two insulation sheets (0.25 mm

thick polypropylene Formex GK-10) were inserted between the rotor sub-sections, to
 186

Figure 5.47. HESM prototype, assembly of PM rotor and magnet insertion into the
laminations fitted on the hub, the insertion of the third pack of four of laminations
is shown.

Figure 5.48. HESM prototype, completed PM rotor assembly after fitting the end
plates, bolted connections and dowel pins insertion.
 187

protect the WF end-turns of the winding from directly making contact against the

PM section end-plates and bolts when subject to thermal expansion. Is can also be

observed that two insulated wires are inserted in the hollow section of the shaft to be

connected to the PCB. The other connection of the wires is to the slip rings used to

transfer the rotor excitation current during rotation.

The final machine assembly in the stator housing was performed manually,

for lack of a conveniently sized lathe on the facilities. In order to avoid delamina-

tion of the stacks during the insertion, strips of slot liner insulation (0.25 mm thick

polypropylene Formex GK-10) where placed on the stator inner radius and removed

after the insertion. The process involved in the assembly was to press-fit the non

drive-end plate on the corresponding bearing and to lower the complete rotor into

the drive-end plate (Fig. 5.51), press-fitting the drive-end bearing into its seat on the

corresponding plate. Subsequently, the non-drive end plate was aligned to the shell

with dowel pins and bolted to the shell threaded holes with AISI 304 steel 1/4”-20

bolts. At this point the rotor alignment at the airgap was checked with a 0.6 mm thick

plastic feeler gauge (the closest to the designed airgap thickness of 0.75 mm) across

the accessible sides of the WF and PM rotor sections, and the protection insulating

sheet was removed. Finally, the machine assembly was mounted and aligned to the

load machine and torque meter on the dynamometer bed, completing the construc-

tion with the insertion and electrical connection of the brushes and slip rings system

(Fig. 5.52).

5.3.2 Open Circuit Test. The HESM prototype performance with slip rings

and brushes was measured on a 22 kW dynamometer with an ABB ACS880-104-

00035A-S inverter driving a Siemens 1PH8133 induction machine with a 112 Nm

(1000 lbs-in) Himmelstein 49703V(1-3)N-F-Z torque meter (Fig. 5.53). The hybrid

excitation prototype characterization of no load losses is more complex than the

 188

Figure 5.49. HESM prototype, WF rotor connection of the winding.

Figure 5.50. HESM prototype, hybrid excitation rotor assembly and bearings fitted
on the shaft.
 189

Figure 5.51. HESM prototype, insertion of the rotor assembly in the stator housing.
 190

Figure 5.52. HESM prototype, non drive-end view of the machine assembly, brushes
and slip rings assembly.
 191

previous WFSM prototypes since the PM excitation cannot be turned off in order to

isolate the bearing and windage losses from the core losses. Preferably a rotor with

non-energized magnets would be tested separately, but this was unfeasible due to

budget and time constraints. A gross estimation could be achieved using the bearing

and windage losses of the previous prototypes (given that a similar design is used for

the shaft) and subtract them from the total losses. The remainder of the losses should

then be attributed to the core losses of the section of the stator facing the PM rotor.

The experimental procedure employed to characterize this data is the open circuit

test, in which the machine is spun at different speeds and with several levels of rotor

excitation, and the machine output stator voltage and power losses (using the torque

meter reading) are recorded. However, the limited resolution of the torque meter at

such a low loading does not easily allow for a perfect attribution of each loss to its

cause. Given the limited absolute amount of such losses in the scale of the machine

power testing, a measurement tolerance of up to 1 Nm is deemed acceptable at the

highest testing speed (4000 RPM). A more precise estimation of the losses can be

achieved considering the machine model and, because the bearing and windage losses

are independent of the excitation status of the machine, we can consider these losses

to be constant with respect to the excitation level and a function of the machine speed

alone. At this point, for equal PM and WF side excitation level (i.e. corresponding

to hybrid no-load voltage double than the 0 A field current) we can assume equal core

losses for the stator WF and PM sections. In general, the total open circuit stator

losses (PHE,T OT ) of the HESM can be expressed as the sum of bearing and windage

(Pbear ), core losses of the stator section facing the PM rotor (PP M ) and core losses of

the WF section (PW F in Eq. 5.1).

PHE,T OT (ω, IW F ) = Pbear (ω) + PP M (ω) + PW F (ω, IW F ) (5.1)

 192

At this point we can calculate the loss addition due to the field induced from

the WF rotor section in the stator core as the difference between losses at a given

field excitation value and those at 0 A WF excitation (Eq. 5.2). In particular, from

the back-EMF analysis it emerged that the stator terminal voltage is doubled at the

nominal level of WF excitation current of 5 A (IW F,n ).

PW F (ω, IW F,n ) = PHE,T OT (ω, IW F,n ) − PHE,T OT (ω, IW F = 0) (5.2)

Finally, assuming that the core losses due to the two sub-rotors are equal (that

is disregarding the PM section field harmonics), the bearing losses can be estimated as

the difference between the total losses and twice the WF losses previously estimated:

Pbear (ω)  PHE,T OT (ω, IW F ) − 2PW F (ω, IW F,n ) (5.3)

The open circuit line to neutral voltage as a function of the rotor field cur-

rent and speed were measured and compared with simulation predictions, in Figure

5.54, showing very close agreement. It can be noted that the excitation current of 5

A corresponds to the no-load nominal voltage of the WF stator section, yielding a

voltage that is twice as large as the PM section (corresponding to 0 A excitation).

This dataset has been used to derive the estimated bearing losses described above.

Additionally, the saturation of the output voltage is an indicator of WF rotor iron

saturation, as predicted by the simulation mapping. Another aspect to be character-

ized is the ability of the WF rotor to control the output voltage in the flux weakening

region, that is for negative field current. The residual voltage in the experimental

data (in the order of 16 % of the nominal) can be attributed to the imperfect com-

pensation of the voltage waveform and in principle should allow a very wide flux

weakening region of about 10:1 with the correct control strategy. To better illustrate
 193

this key aspect of the hybrid excitation, another test was conducted, this time using

the speed of 400 RPM as the base speed for the machine, and manually controlling

the back-EMF (adjusting the WF excitation) in order to obtain a constant value,

corresponding to the maximum back-EMF obtained at 400 RPM and with full WF

positive excitation.

Post-processing the core losses data with the method previously presented, the

resulting losses are thus subdivided:

1. Figure 5.55 shows the estimated bearing and windage losses of the machine

discounted the measured WF section core losses and the estimated PM section

core losses.

2. Figure 5.56 shows the core losses attributed to each of the stator sections, as-

suming equal core losses for equal voltage output (field current of 5 A).

3. Figure 5.57 shows the full set of experimental and simulation results from which

the previous data is obtained.

Comparing the core losses post-process results to the previous prototypes char-

acterization, an increase of about 40 % can be observed (Fig.5.55). However, this

difference is in the order of the uncertainty associated to the torque measurement,

and in absolute value is tolerable even with simple air cooling of the machine. The

core losses originated from the rotor excitation (Fig. 5.56) as two different data series,

since the WF rotor section core losses have the same value for positive (flux boost-

ing) and negative (flux bucking) excitation flux. The estimated simulation values are

also in good accordance with the experimental results. The estimation of the PM

section core losses is the average between the ones obtained for positive and negative

excitation in the WF section.

 194

Figure 5.53. Hybrid excitation synchronous machine testing dynamometer setup.

Figure 5.54. Measured and simulated open circuit voltages as a function of the WF
rotor excitation.
 195

Figure 5.55. HESM prototype bearing and windage power losses estimated from
experimental measurement in the speed range 40 to 4000 RPM.

The full data set of Fig. 5.57 has been used to validate the simulation losses

used to derive the HESM mapping of Section4, the relevant results are also presented

here for ease of comparison. It should be noted that the simulated core losses are

summed to the estimated bearing losses for ease of comparison to the original ex-

perimental data. The small differences in estimation are most probably due to the

core material batch from which the machine was realized, and it is within tolerance

of the expected result. To improve on this modeling, expensive test are carried out

industrially to characterize the electric steel used in production, but those additional

tests are beyond the scope of this prototyping effort.

The last experimental result of the open circuit test is the rotor copper losses

characterization of Fig. 5.58. Also in this case the predicted losses are very close to

the measured rotor power.

 196

Figure 5.56. HESM prototype measured WF section core losses, simulated losses
refers to the mapping at 20◦ C, the PM section core losses have been estimated as
the average of the two experimental data series.

5.3.3 Equivalent Circuit Parameter Identification. For the unsaturated

equivalent circuit characterization, the rotor was rotated to align to the stator d-

axis, locked and the field winding connected to a differential voltage probe. The

stator winding were fed by one phase of a three-phase line-fed variac, first between

phase A and the parallel connection of phases B and C (d-axis characterization),

then between phase B and phase C terminals with the phase A terminal isolated (q-

axis characterization). The obtained values differ very little from the simulated ones,

since to avoid saturation only 5 % of the nominal value of stator current was used.

This means that the values reported here are the nominal, unsaturated inductances

of the machine at 60 Hz. Another approach at verifying the machine unsaturated

equivalent circuit parameters has been to use a direct impedance measurement with

LCR meter Keysight U1733C for the WF rotor. Moreover, the autotuning capability

of an ACS880 inverter (used on the dynamometer setup) was employed to extrapolate

 197

Figure 5.57. Measured bearing, windage and total core losses for the speed range of
interest as a function of the WF excitation.

the stator parameters. Also this test gave a good match between predicted values

and experimental results listed in Table5.5.

Additional post-processing of the data in Figure5.54 allows for an estimation

of saturated mutual inductance of the machine (Fig. 5.59), comparing the data at

different speeds and compensating for the PM induced voltage. This test is analogous

from the one described for the previous prototypes and the voltage considered for the

mutual inductance calculation is derived from the stator output voltage increase,

measured when exciting the rotor field divided by the excitation current and the

angular speed.

the decaying exponential current following the step change in field excitation

voltage

5.3.4 Dynamometer Testing. The prototype HESM stator was driven by

 198

Figure 5.58. Measured and simulated rotor copper losses as a function of the WF
excitation.

a Semikron Semikube IGBT Module Stack IGDD6-1-426-D1616-E1N6-DL-FA. The

power input to the stator is limited to 9.2 kVA, due to the use of a three-phase

Variac ( Staco Energy1520CT-3) to supply the inverter. The Semikron drive does

not have an integrated soft-start circuit and cannot be connected directly to the 480

three-phase utility supply available at the testing facility. A custom DSP interface

PCB board to the Semikron Semikube and feedback sensors connected to a Spectrum

Digital TI F28335 DSP board was designed to control the inverter, regulate currents

in the stator of the HESM, and perform field oriented control. The field winding was

connected to a Keysight E36314 DC power supply through a brush and slip rings

system and in order to protect the rotor winding from excessive field transients, each

rotor pole is equipped with varistors. Since the Keysight E36314 power supply is

limited to 50 V (corresponding to 2.5 A output), the overloading testing of the rotor

circuit has been carried out with a MAGNA SL-1000-6.0, up to a field excitation
 199

Table 5.5. HESM Unsaturated Machine Equivalent Circuit Parameters

Parameters FEMM ACS-880 Variac
Lf [mH] 1809 1571A 1799
Ld [mH] 1.493 1.54 1.433
Lq [mH] 1.333 1.46 1.398
Lm [mH] 30.87 30.82 29.72 - 31.2
A
Rf [Ω] 18.721 17.575 20.275B
Rs [Ω] 0.0378 0.0440 0.0569
A
using LCR meter Keysight U1733C
B
rotor winding resistance including brushes

of 6 A but used only for the open-circuit characterization. The WFSM and drive

electrical inputs were measured using a Keysight MSO-X 30304A oscilloscope. Stator

and rotor field circuits currents and voltages were measured using Yokogawa 701933

current probes and Yokogawa 701921 differential probes. The dynamometer setup is

shown in Fig. 5.53 with the equipment labeled accordingly. Dynamometer torque,

efficiency, and power factor mapping was also carried out for 2 values of field currents

(0 and 2.5 A), stator current magnitudes (0, 25 and 50 A), and current angles (-5

to 30 degrees with 5 degrees increment) at 400 to 2400 RPM with increments of 400

RPM. The rotor field current limitation is mostly thermal, with 2.5 A the testing

can be continuous, since the rotor movement is sufficient to limit the temperature

rise, using higher current would introduce a temperature effect or long cooling times

to avoid damaging the rotor field insulation. The stator current was limited by the

input power to the inverter capabilitym while the speed limitation is due to vibration

in the testing equipment that needs to be addressed in order to load the machine to

the base speed. The mapping was carried out within a stator temperature range of

20 to 40 ◦ C ( Nominal of 30◦ C).

The predicted shaft torque mapping is plotted alongside the experimentally

 200

Figure 5.59. HESM prototype predicted and experimentally measured equivalent

circuit parameters, mutual inductance Lm .

measured results at the speed of 2400 RPM, Figure 5.61 for the highest motoring

power reached during the testing. This operating point has a loading of 50 % on

the rotor circuit, 25 % on the stator circuit and 60 % on the nominal speed of the

machine. Both the predicted and experimentally measured results are in good agree-

ment, it should be noted that the simulated torque reported here is the net value

after considering the simulated core losses and the bearing losses fit from experimen-

tal data. The predicted and measured torque deviations are within the torque meter

resolution, but the prediction of the MTPA angle of 10◦ for hybrid operation is met.

Each test point was recorded after 10 seconds or longer, to allow the torque meter

to average the torque output. The operating points at lower power are not shown

here since the measurement signal to noise ratio is less significant. The experimental

data shown is the result of two measurements of net shaft torque: one at 0 A field

excitation (PM torque) and one at 2,5 A (HE torque), the WF torque is obtained
 201

Figure 5.60. HESM prototype predicted and experimentally measured equivalent

circuit parameters, Field, Lf inductance. FEMM denotes the simulation results,
step the step voltage test and variac the line-fed variac test.

subtracting the PM contribution from the total, since the additional stator core losses

are already discounted from the measurement.

The power factor map at 2400 RPM, Fig. 5.62, shows the power factor at the

operating conditions of the previous testing of Fig. 5.61. The power factor is above

0.8 for the whole testing, however it can be noticed that it is higher for the hybrid

excitation operation and that it approaches unity above the MTPA angle.

Finally, the efficiency of the machine is presented in Fig. 5.63, showing good

accordance with the simulated data. To obtain this data from the experimental mea-

surements, the net shaft torque was divided by the input rotor and stator active

power, measured from the oscilloscope. On the other hand, the simulated net mo-

toring power (subtracting simulated core losses and experimental bearing losses) was

divided by the sum of the net power and total copper losses.
 202

Figure 5.61. Predicted and experimental results, shaft torque versus torque angle:
continuous line simulated, triangles ripple range, square experimental data at 2400
RPM, 50 A stator current and 2.5 A rotor current.
 203

Figure 5.62. HESM prototype measured and simulated power factor at 2400 RPM
and 50 A peak stator current, PM denotes the operation at 0 A field current,
HE the operation at 2,5 A field current. FEMM denotes simulation data, EXP
experimental results.

Figure 5.63. HESM prototype measured and simulated efficiency at 2400 RPM and
50 A peak stator current, PM denotes the operation at 0 A field current, HE the op-
eration at 2,5 A field current. FEMM denotes simulation data, EXP experimental
results.
 204

5.3.5 Prototype Physical Data.

Table 5.6. HESM Prototype Machine Weights

Machine Component Active Material Weight Total Weight
Stator Shell 27.5 kg
Stator Stack 16.0 kg 16.0 kg
Stator Winding 7.5 kg 7.5 kg
Stator Assembly 23.5 kg 51.0 kg
Rotor Shaft and Bearings 4.7 kg
WF Rotor Stack 5.1 kg 5.1 kg
WF Rotor Winding 1.4 kg 1.4 kg
PM Rotor Stack 5.8 kg 7.6 kg
PM Magnets 0.5 kg 0.5 kg
Rotor Assembly 12.8 kg 19.3 kg
Machine 46.3 kg 70.3 kg
 205

Table 5.7. HESM Prototype Machine Physical Data

Machine Parameters Experimental Value
Stator Outer Diameter 254 mm
Airgap Length 0.75 mm
Rotor Outer Diameter 176.5 mm
Stator Stack Length 106 mm
WF Rotor Stack Length 44 mm
PM Rotor Stack Length 50.8 mm
Tested Motoring Torque 37 Nm
Tested Motoring Power 9.3 kW at 2400 RPM
Tested Motoring Efficiency 97 % at 37 Nm, 2400 RPM
Active Materials Mass 46.3 kg
Total Mass 70.3 kg
Volume 9.42 
Volumetric Peak Torque Density 3.93 Nm −1
Specific Peak Torque Density 0.8 Nm kg−1
Volumetric Peak Power Density 0.20 kW −1
Specific Peak Power Density 0.99 kW kg−1
 206

CHAPTER 6

CONCLUSION

6.1 Summary

During the course of this work a multi-solver, multi-physics simulation soft-

ware for electrical machine optimization has been developed. In the current state

of development the software can simulate wound field synchronous machines, per-

manent magnet synchronous machines and hybrid excitation synchronous machines

on two electromagnetic solvers (FEA) and one thermal solver (lumped parameters).

Additionally, tools are provided in the software code base to implement optimiza-

tion and analysis models for a large number of tests (in the order of 10,000 machine

models), using differential evolution optimization, response surface optimization and

MonteCarlo optimization. The mapping of a single machine is also available for a

fixed geometry and includes the electromagnetic and thermal characterization at no-

load and under load. The software was utilized to design three high power density

machine prototypes, targeting an automotive traction motor application comparable

to the PMSM industry standard. The prototypes meet or exceed the performance

metrics of DOE USDRIVE 2020, two without permanent magnet materials and one

with reduced permanent magnet materials quantity. The first prototype is a salient

pole WFSM designed to be operated with a system of brushes and slip rings or a

capacitive coupler for rotor excitation. The second prototype, also a WFSM, was

an attempt at increasing the saliency ratio with respect to the first prototype, how-

ever, the expected performance increase is not large. Both prototypes exhibit power

density comparable to commercially available traction machines. Finally, a HESM

prototype composed of two coaxial rotors (one with wound field excitation, the other

with permanent magnet excitation with interior permanent magnets) was designed

and tested. The HESM prototype can reach a power density close to the one obtained
 207

by the WFSM prototypes but has been designed with the aim of providing a control

system testing platform for monoaxial HESM and one of the possible configurations

of biaxial HESM.

6.2 Contribution

Contributions to the state-of-the-art have been made in the synchronous ma-

chine simulation software architecture, the design of high power density ATF spray

cooled wound field synchronous machines, improved models for spray cooled WFSMs,

analytical sizing coupled with FEA simulation for HESM and the design of a parallel

hybrid excitation radial flux synchronous machine. In particular, a new software has

been proposed to model and optimize different types of synchronous machines, in par-

ticular WFSMs and IPMSMs. The software capability and accuracy has been tested

with the experimental results collected from three machine prototypes. A new rotor

field excitation method has been tested with the use of a capacitive power coupler.

The behavior of the machine is not affected when the common method of excitation

with brushes and slip rings is changed to the alternative method. A radial flux, hybrid

excitation machine prototype has been tested for no-load and partial load, confirm-

ing the simulation model conclusions that it can be operated at high constant power

speed ratio and that it can be used as a platform for advanced control development.

In the following, the obtained contibutions to the state of the art are compared

to the ones proposed:

• A robust, modular software architecture linking different multi-physics solvers

simulations for synchronous machine design allowed:

– Parallel operation of up to 8 solver instances for simulation speed increase

(limited by the machine physical cores).

– Coupling to optimization algorithms with minimal adaptation of the code

 208

base, in particular differential evolution, response surface modeling and

MonteCarlo implementations were tested and used for prototype develop-

ment.

– Implementation of a standardized data-structure expanded to WFSM,

PMSM and HESM cases.

• Flexible geometric templates with parametrized non-dimensional factors were

implemented:

– WFSM, IPMSM and SPMSM templates and integrated-pole hybrid ma-

chine capability (HESM).

– Generation of geometrically similar machines (preserving the ratios be-

tween machine components) for different physical envelopes.

• Transient reconstruction tested using an open-source static solver to obtain:

– Transient reconstruction from static solutions of time-dependent and rotation-

dependent machine parameters (e.g. voltage and core losses).

– Losses and voltage calculation quality, comparable to commercial software

and in good agreement with experimental data.

– Computationally-efficient mapping at any operating speed with transient

reconstruction post-processing.

– Mapping of parallel HESM obtained post-processing multiple templates

results.

• Designed two ATF spray cooled WFSM prototypes which meet DOE USDRIVE

2020 targets for power and power density.

• Design of two WFSMs and one HESM that can be operated with a novel ca-

pacitive power coupler or slip rings and brushes.

 209

• Modeling rotor flux barriers did not yeld the expected improvements, resulting

in reduced interest for further developments in this field.

• Improved spray cooling thermal models that take into account:

– Dynamic spray cooling effect on rotor iron core temperatures, integrated

into a commercial software.

– Simplified spray cooling effect on stator iron core temperatures to approx-

imate the dynamic behavior during heat run testing.

– Experimental calibration of the improved thermal model.

• Adapted existing analytical sizing methods to hybrid excitation machines and

verified the models against FEA simulations.

• Modeling, characterization and partial load testing of a radial flux HESM elec-

tromagnetically equivalent to the axial flux machine proposed in [38].

• Final design modeled with high accuracy coupling the analytical model to the

FEA simulation and mapping routine capabilities developed in the course of

this work.

• Designed prototyped and tested a parallel rotor, radial flux HESM which pro-

duced a peak power of 9.3 kW at 2400 RPM with air cooling (limited by the

testing dynamometer).

• Verified mechanical assembly capability of testing monoaxial and biaxial hy-

brid excitation concepts on a single prototype, the monoaxial case has been

experimentally characterized in this work.

• Experimental results at no-load of the radial flux HESM demonstrate operation

up to 10:1 CPSR with rotor-only flux weakening.

 210

• Experimental results verification of the modeled equivalent circuit parameters

of the HESM prototype for machine control development.

6.3 Future Work

For future contributions to the state of the art, several development paths are

available, grouped here by area of interest in terms of simulation software develop-

ment, electrical machine topology, controls development and thermal management.

The simulation software has been designed to allow for flexibility and modularity, the

following list of topics can be integrated in the existing architecture to reuse the code

base already existing:

• Interface to additional electromagnetic solvers such as JMAG, Maxwell, COM-

SOL or Elmer to enable a benchmarking of simulation routine and identify the

best practices and models.

• Interface to structural analysis software to automatically model the machine

stress, deformation and vibration behavior.

• Interface to transient FEA thermal solvers, such as FEMM, ThermNet and

ANSYS, this future contribution is subject to availability of thermal results

from the existing prototypes testing, especially for the oil spray cooling method.

• Include additional optimization routines to benchmark the efficacy and speed

of different methods.

• Implement the software architecture in other languages such as Python for a

better control of the object-oriented programming and avoiding licensing issues

and costs.

• Implement automated winding design routines for distributed and concentrated

winding modeling.
 211

• Update the data structure management in terms of compatibility with future

Matlab versions.

• Implement of automated magnet loss calculation and demagnetization testing

routines.

• Implement virtual coils for measurement of flux linkages and leakage in various

parts of the machine to better calibrate analytical models.

• Recompile FEMM meshing routines to catch meshing errors and fail gracefully

such as to integrate error management in the software development.

• Collect actual BH curve and and core loss of silicon steel material characteriza-

tion data with standardized magnetization testing.

• Implement unit testing and regression testing for future template development.

• Improve software documentation for maintenance and future development plan-

ning.

• Update the Infolytica MagNet interface for parallelization if additional licenses

are made available for research.

• Include 3D electromagnetic modeling for fringe effects and end-turn leakage

estimation.

• Automate the structural solver interface to enable structural integrity calcula-

tion, vibration and noise modeling of the machine to be executed efficiently.

The WFSM designs provided a large quantity of data for the development of

advanced controls and cooling system development, additional topics for research are:

• Testing the HESM prototype for full power and with a spray cooling system.
 212

• Calibrating the spray cooling of the rotor from a single side in order to propose

best practices and thermal management for this machine class.

• Implementing rotor temperature estimation or direct measurement system.

• Researching the impact of different cooling fluids for spray cooling methods and

systems.

• Developing and testing sensorless control routines with different high-frequency

injected signals, both stator-side and rotor-side.

• Developing and testing additional excitation methods for the rotor winding,

such as inductive and resonant methods.

• Developing and testing a drive cycle control system to provide data for com-

parison with other machine types.

• Refining the oil spray cooling system model with experimental data, using dif-

ferent geometries for the nozzles and oil collectors.

• Integrating the existing WFSMs in a typical vehicle cooling system to provide

an additional step towards the use of such machines in industrial products.

The HESM prototype was designed to aid future control development and the

exploration of monoaxial and biaxial hybrid excitation:

• Developing and testing advanced control systems to address the operation at

high flux weakening of the machine.

• Developing and testing sensorless control routines with different high-frequency

injected signals, both stator-side and rotor-side.

• Developing and testing stator-side harmonic excitation of the rotor, taking ad-

vantage of the wound field separation in two sections.

 213

• Developing and testing thermal management solutions to allow the full power

operation of the machine, in particular modeling the cooling of the rotor circuit

from a single side of the machine.

• Integrating the existing machine in a typical vehicle setup to fully demonstrate

the advantages of the hybrid excitation in a traction application.

Additional future contributions regarding the use of different hybrid excita-

tion methods than the one presented here are also possible. The combination of

previous design data and modeling software allows the comparison and benchmark-

ing of machine designs and combination of different excitation methods, for instance

with reluctance machine, biaxial permanent magnet excitation, biaxial wound field

excitation or a combination thereof.

 214

APPENDIX A

HESM PROTOTYPE LAMINATION SPECIFICATIONS

 215

Figure A.1. HESM prototype stator laminations specification, laser weld notch detail.
 216

Figure A.2. HESM prototype permanent magnet rotor laminations specification,

teeth specification detail.
 217

Figure A.3. HESM prototype permanent magnet rotor laminations specification,

magnet tolerancing and step-skew verification.
 218

Figure A.4. HESM prototype permanent magnet rotor laminations specification,

finalized lamination.
 219

Figure A.5. HESM prototype wound field rotor laminations specification.

 220

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