Rotary Transformer with Ferrite Core

for Brushless Excitation of Synchronous Machines

S.-A. Vip, J.-N. Weber, A. Rehfeldt, B. Ponick

Abstract—Salient-pole synchronous machines (SPSYM) rotatory

transformer
combine a high power density with high efficiency over a wide I2
speed range. In contrast to permanent magnet synchronous
machines (PMSM), the field excitation can be controlled actively.
UDC rotor
Due to the adjustable excitation, flux-weakening is possible with winding
reduced losses. The efficiency at partial load and at high speed
can be improved. Furthermore, faults, such as short circuit
currents, are easier to handle. These attributes qualify SPSYM
as a promising alternative to PMSM for electrically powered
vehicles. In order to achieve this additional degree of freedom, Fig. 1: Basic concept of contactless transmission system for
electrical power needs to be transferred to the rotating part
of the motor. Established slip ring transmission systems are SPSYM
sensitive to ambient conditions such as humidity or impure
contacts. Moreover, the limited reliability of contact based
systems amplifies the desire to develop contactless transmission excites the rotary transformer with a periodic AC current. The
systems. transformer transfers the electrical energy across the air gap.
In this paper, the electromagnetic design of a rotary transformer
On the rotating side, a AC/DC converter rectifies the output
with a ferrite core intended to transfer the excitation current is
discussed. High frequency effects (skin- and proximity effect), current of the transformer. The DC current I2 (index 2 for
leakage inductances and the waveform of the transformer rotor, index 1 for stator) excites the SPSYM. The waveforms
currents are considered in an automated design process. This of the transformer currents on both sides, as well as the
process combines analytical calculations and 2D FEM simu- operating frequency of the converters, have a certain impact
lations to determine an optimal design. In a final step, the
on the copper losses Pv,cu and the iron losses Pv,fe . Moreover,
calculated results are compared with measurements performed
on a prototype. the fragile core material ferrite limits the possible mechanical
design of the rotary transformer. Taking these constraints into
account, an automated design process for rotary transformers
I. I NTRODUCTION is presented in this paper.

C Ontactless transmission systems are designed to over-

come the disadvantages of conventional contact based
systems. The desire to achieve a longer lifetime, an increased
rotor winding
Φh rotor

reliability and a reduced sensitivity to ambient influences

leads to brushless transmission systems [1]. In addition to
that, contactless systems allow compact designs. Whereas air gap
conductive systems, due to the necessary maintenance, have
to be installed outside of the motor’s housing, contactless sys- stator winding stator
tems might allow the integration into the machine’s housing
or inside a hollow shaft.
The rotary transformer requires a relatively large air
gap, resulting in non negligible leakage effects and a high Φh
magnetizing current [2]. Fig. 1 shows the basic concept Fig. 2: Design of the rotary transformer
of the proposed transmission system. A DC/AC converter
S.-A. Vip is with Institute for Drive Systems and Power Electronics
at Leibniz Universität Hannover, Germany (e-mail: stephan.vip@ial.uni- II. E LECTROMAGNETIC D ESIGN
hannover.de).
J.-N. Weber is with Institute for Drive Systems and Power Electronics A. Constructive constraints and design
at Leibniz Universität Hannover, Germany (e-mail: niklas.weber@ial.uni- Constructive constraints such as the axial length lax , the
hannover.de).
A. Rehfeldt is with Institute for Drive Systems and Power Electronics at outer diameter dout , the desired airgap length lλ or the
Leibniz Universität Hannover, Germany (e-mail: alexander.rehfeldt@ial.uni- rotational speed n limit the possible designs. Ferrite’s main
hannover.de). disadvantages are the sensitivity towards a tensile stress,
B. Ponick is with Institute for Drive Systems and Power Electron-
ics at Leibniz Universität Hannover, Germany (e-mail: ponick@ial.uni- compared to electrical steel [3] and high production toler-
hannover.de). ances. On the other hand, it has a high electrical resistance

l-))) 
 rotating
stationary
Rac1 Lσ1 Lσ2 
Rac2

i1 i2 Lf
iμ
UDC u1
Lh
Rf

Fig. 3: Full bridge forward converter topology

which allows to operate the transformer at a higher frequency. not grow in size for the integration of the rotary transformer.
Accordingly, the size of the transformer can be reduced.
To avoid a high tensile stress, the rotary transformer is de-
signed with an external rotor. An internal rotor would require
an additional bandage. This would increase the effective air
gap length resulting in a reduced main inductance Lh and a
higher magnetizing current Iμ . Fig. 2 presents a cross section
of the rotary transformer, indicating the position of the stator,
the rotor and the windings. Two L-shaped ferrite cores form
the magnetic circuit. The main flux path is illustrated by the
main flux Φh . The flux crosses the air gap in radial direction.
The L-shaped cores are comparatively easy to manufacture
and favor a coaxial configuration of the stator and rotor
coil resulting in a better coupling of the coils [4],[5]. The
coils are assembled from flat copper band as shown in Fig
4. Copper band windings offer a high filling factor and a
constant voltage stress between each turn [6].
Fig. 5: Hollow shaft integration

B. Electrical constraints
The purpose of a rotary transformer is to transfer electrical
power to excite the motor. The maximum output power
Pout,max is the key constraint. In addition to that, the provided
DC link voltage UDC , as well as the convention to operate
the transformer in unsaturated state, and the rotor winding
parameters of the SPSYM (Rf , Lf ) determine the electrical
design of the transformer. In order to be able to predict
Fig. 4: Exploded view of the prototype the losses, the current waveforms need to be described in
analytical expressions. Hence, the converter topology has to
The compact design of the rotary transformer makes it be predefined [8].
possible to consider new integration methods into the drive In this study, a full bridge forward converter topology
system. In high torque applications (e.g. wheel hub drives (Fig. 3) is used. The resistors Rac1 and Rac2 include the
[7]), a comparably high shaft diameter is needed. In this influence of skin and proximity effect. The inductance of
case, the contactless transmission systems could be integrated the motor’s field winding Lf acts as a smoothing reactor.
into the large hollow shaft (shown in Fig. 5). The blue part
represents the non rotating motor housing. Correspondingly,
the rotary transformer is integrated into the green hallow C. Calculation tool
shaft. The main advantage of this integration method is the The calculation process of the rotary transformer starts
utilization of unused installation space. Moreover, the rectify- with the determination of all geometric dimensions of the
ing power electronic components can be arranged inside the electromagnetic circuit. Based on the geometry, the mutual
hollow shaft too. Consequently, the housing of the motor does inductance Lh and the leakage inductances, Lσ1 , Lσ2 can


 ([10], [6], [2]), the losses are minimal for a duty cycle of
0.5. For that reason, a duty cycle close to 0.5 is desired. The
operating point can be varied by a variable DC link voltage
RM,λ1 UDC . Of course, it is possible to adjust the output power with
a variable duty cycle. However, a variable voltage is easier
to implement to execute measurements on the prototype.

The stator current i1 is the superposition of the magne-

RM,σ
tizing current iμ and the rotor coil current i2 .
N2
RM,λ2 i 1 = iμ + i 2 · (5)
N1

N2 i1
r N1 Iout + Δi

z t
Fig. 6: Proposed equivalent magnetic circuit N
− N2 Iout − Δi
1
i2
Iout
be calculated. The resulting current waveforms are analyzed
t
using Fourier series to determine the losses.
In order to estimate the inductances, the magnetic equiv- −Iout
alent circuit and its magnetic resistances RM have to be
calculated and analyzed [9]. Knowing the cross section area Δi iμ
A, the length l and the relative permeability μr of each part t
of the circuit allows to calculate the related resistance to
−Δi
l 0 αT0 T0 (1 + α)T0 2T0
RM = . (1)
μ 0 · μr · A Fig. 7: Ideal current waveforms (α = 0.5)
The magnetic resistances of the air gap (RM,λ1 ,RM,λ2 ) Taking advantage of this fact, only the Fourier coefficients
determine the inductance of the transformer. The magnetic of the currents iμ and i2 have to be calculated. The amplitude
field widens inside the air gap, resulting in a reduced resis- of the n-th harmonic for a duty cycle of 0.5 can be derived
tance. To take this fringing flux into account, the resistance of to
the air gap is calculated using the Schwarz-Christoffel trans-
formations [10]. The mutual inductance can be calculated by 4 · Δi
cμ,n = · (1 − cos(nπ)) (6)
summing up the magnetic resistance along the main flux path (nπ)2
RM,tot,h to
for the magnetizing current,
N1 · N2
Lh = . (2) 2 · Iout
RM,tot,h c2,n = · (1 − cos(nπ)) (7)
(nπ)
The number of turns of the stator coil N1 and of the
rotor coil N2 can be used to optimize the design. The stator for the rotor current and
inductance L1 is calculated with the total resistance of the  2
magnetic circuit RM,tot which includes the leakage resistance N2
c1,n = c2,n + c2μ,n (8)
RM,σ : N1

N12 for the stator current. Only harmonics of an odd order

L1 = . (3) exist. The loss estimation is separated into core and copper
RM,tot
losses. The Steinmetz equation
The stator leakage inductance is evaluated to
αfe
N1 Pv,fe = Cm · fsin,eq · B̂ βfe · Vfe · ktemp (9)
Lσ1 = L1 − Lh · . (4)
N2 is used to estimate the core losses. The coefficients
The rotor leakage inductance Lσ2 is determined in the Cm , αfe and βfe can be derived from the loss curves of
same way. The loss calculation is based on the ideal current the ferrite. These loss curves are usually measured with
waveforms (Fig. 7) in the stator and the rotor winding for sinusoidal excitation. Therefore, the calculation is achieved
a duty cycle of α = 0.5. As other publications point out with an equivalent sinusoidal frequency fsin,eq based on [10].


This frequency depends on the waveform of the magnetizing and rotor current
current and is given by
i2,load,n = −c2,n (14)
8
fsin,eq = (10) in load simulations for the n-th harmonic are defined in
π 2 · T0 this way. Load and no load simulations have to be done for
in this specific case. The volume of the ferrite Vfe is several harmonics. Due to the opposing current directions, the
calculated with the geometric dimensions of the magnetic magnetic fields of the stator and the rotor compensate each
circuit. The loss density of ferrite depends on the temperature. other in a load simulation. Consequently, there are mainly
This is considered by the factor ktemp which is based on leakage fields in a load simulation. In order to include skin
the temperature loss curves provided by the manufacturer. and proximity effects, each turn of the stator and the rotor
Moreover, the magnetic circuit is divided into parts with coil have to be modeled individually. Finally, the total copper
homogenous flux density. The magnetic peak flux density B̂ losses
for each part of the magnetic circuit needs to be calculated. 
First, the mutual flux is determined to Pv,cu = Pcu,load,n + Pcu,μ,n (15)
n

Φ̂h = Lh · Δi . (11) are determined by summing up the losses for each har-
monic caused by the magnetizing current Pcu,μ,n and the load
Thus, the magnetic flux density, knowing the cross section currents Pcu,load,n .
A of each part of the magnetic circuit, can be estimated to

Φ̂
B̂ = . (12) 80
N1 · A Pv,tot
For accurate results, leakage fluxes and the fringing air 60 Pv,fe
Pv /W
gap flux are considered as well. Pv,cu
40

20

0
0 2 4 6 8 10 12
Number of stator turns N1
Fig. 9: Losses at constant output power for different numbers
of turns

In addition to that, this method allows to gather the losses

individually for each turn from the simulation results. This is
used for a thermal simulation as well. To determine the total
copper losses, losses of the load and no load simulations
are superimposed. This process can be used to find optimal
designs. For instance, in Fig. 9 N1 and N2 = N1 +1 are varied
for a constant output power. On the one hand, increasing the
Fig. 8: Load (left) and no load (right) simulation number of turns implies a higher inductance. For this reason,
a minor magnetizing current is needed to magnetize the core
For the calculation of the copper losses, the 2D FEM resulting in lower core losses Pv,fe . On the other hand, the
software FEMM [11] is used. The automated generation of copper losses Pv,cu rise because of proximity and skin effects
the 2D FEM models enables parameter variations as well as well as the increasing DC resistance. Considering the total
as adjusting the currents. To determine the copper losses, losses Pv,tot , the optimal winding configuration with least
two simulations for each harmonic are done. In a no load losses can be found.
simulation, only the stator winding is excited with the mag-
netizing current. Further, the magnetizing current determines III. T HERMAL M ODEL
the magnetic flux density B in the ferrite core. Accordingly, To predict the operating temperatures, a thermal RC
the rotor current i2 is used for load simulations. The stator network is created in Simulink/PLECS (Fig. 11). Stator and
current rotor are analyzed separately. As a consequence, the heat
N2 exchange between stator and rotor is neglected. Furthermore,
i1,load,n = c2,n · (13) a stainless steel housing (orange) was modelled with a the
N1


 100 TABLE I: Prototype dimensions
Parameter Value
95 Rotor outer diameter da2 60 mm
Stator outer diameter da1 54 mm
0.5 mm
ϑ /◦ C

Air gap length lλ

90 Axial length lax 30 mm

85
transformer is operated without rotation. An ohmic-inductive
load (Lf = 12.3 mH, Rf = 10 Ω) is used for the load
80 measurements.
ϑSW ϑRW ϑSY ϑRY
Fig. 10: Stationary temperatures for peak load

constant temperature of ϑhsg = 80 ◦ C. Heat radiation as well

as convection are neglected in order to compute the worst
case.

Fig. 12: Rotor (left) and stator (right) of the prototype

To measure the inductances, an LCR meter is utilized in

short circuit and no load operation. For the supply cables of
the stator as well as of the rotor coil, the ferrit material has to
be intermittent. This results in a reduction of the inductance
which has to be considered in the calculations. TABLE II in-
dicates that the calculation method offers sufficient accuracy
in terms of inductance prediction.

TABLE II: Comparison of measured and calculated results

Parameter Measured Calculated
Mutual inductance Lh 50.04 μH 51.7 μH
Leakage coefficient σ 7.1 % 8.4 %
Efficiency at 1000 W ηmax 96.3 % 97 %
Efficiency at 250 W ηr 96.6 % 97.1 %

Besides these initial model validations load losses were

Fig. 11: Thermal model of the transformer rotor
measured to validate the losses calculation algorithm. Fig. 13
indicates that the efficiency is more or less constant over a
The sources in the network represent the copper losses wide power range.
in the coils (yellow) and the core losses in the ferrite parts
(grey). The thermal resistors and capacities are calculated
using the geometric dimensions and the specific thermal 100
parameters of the used materials. The thermal contact resis- 98
tors, especially in the windings, are of significant importance
96
η /%

for the accuracy of the simulation. The calculations are

based on [12] and [13]. The results of this simulation for 94 calculated
Pout = 1000 W are displayed in Fig. 10. Analyzing the peak 92 measuared
temperature in stator winding ϑSW , rotor winding ϑRW , stator
yoke ϑSY , and rotor yoke ϑRY , it can be concluded that the 90
0 200 400 600 800 1,000
transformer does not exceed the permissible temperatures of
the copper, the insulation material or the ferrite. Pout /W

Fig. 13: Efficiency for varying output power

IV. M EASUREMENT R ESULTS
The developed prototype (TABLE I), separated in stator The efficiency is related only to the transformer.
and rotor, is shown in Fig. 12. In the first step, the rotary Nevertheless, the overall efficiency (including power


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V. C ONCLUSION AND O UTLOOK

B IOGRAPHIES
In this paper, the design process for a rotary transformer
with a ferrite core was presented. In a first step, the fragility
of the ferrite core material was considered in an external
rotor design. Moreover, an integration into a hollow shaft in
high torque applications was implied. Taking the converter Stephan-Akash Vip was born in Minden, Germany, in November 1989. In
topology, high frequency effects and harmonics into account, 2015, he graduated with a Master of Science in electrical engineering at
an automated design methodology was introduced. For this the Leibniz-Universität Hannover. After completing his studies, he started
working as a research associate at the Institute for Drive Systems and Power
purpose, analytical calculations were combined with 2D Electronics in Hannover in January 2016.
FEM simulations. In addition to that, a thermal model was
developed to estimate the thermal steady state. Based on mea-
surements, the thermal model has to be validated or adjusted
in the future. Finally, the calculated results were compared to
measurements. Calculated inductances and losses show good Jan-Niklas Weber was born in Hannover, Germany, in April 1987. After
accordance with the measurements. However, the calculated finishing his studies with a diploma degree in electrical engineering at
Leibniz Universität Hannover in 2013, he started working as a research
losses are slightly lower. This fact is mostly related to the associate at the Institute for Drive Systems and Power Electronics in
opening for the connection of stator and rotor coil in the Hannover.
core. In a next step, more measurements have to be done.
For instance, it is of importance to evaluate the influence of a
rotational movement. Furthermore, the design process can be
improved to overcome the differences in the loss calculation
by in depth evaluation of the measurements or by using the, Alexander Rehfeldt was born in Hannover, Germany, November 1990. He
finished his studies with a Master of Science in elelectrical engineering at
due to leakage effects, altered current waveforms for the loss Leibniz Universität Hannover 2015 and started as a research associate at the
determination. Institute for Drive Systems and Power Electronics in Hannover in 2016.


Bernd Ponick was born in Großburgwedel, Germany, in May 1964. He
received his Dipl.-Ing. degree in electrical power engineering from the
University of Hannover in 1990 and his Dr.-Ing. degree for a thesis on
electrical machines in 1994. After 9 years with the Large Drives Division
of Siemens as design engineer for large variable speed motors, head of
electrical design and Technical Director of Siemens Dynamowerk Berlin,
he is since 2003 full professor for electrical machines and drive systems at
Leibniz Universität Hannover. His main research activities are calculation
and simulation methods for electrical machines, prediction of and measures
against important parasitic effects such as magnetic noise, additional losses
or bearing currents, and new applications for electric machines, e.g. for
electric and hybrid vehicles.