Design and Modeling of Fluid Power Systems
ME 597/ABE 591 Lecture 4
Dr. Monika Ivantysynova MAHA Professor Fluid Power Systems MAHA Fluid Power Research Center Purdue University
SICFP05, June 1-3, 2005, Linkping
Content
Displacement machines design principles & scaling laws Power density comparison between hydrostatic and electric machines
Volumetric losses, effective flow, flow ripple, flow pulsation
Steady state characteristics of an ideal and real displacement machine Torque losses, torque efficiency
Dr. Monika Ivantysynova
Design and Modeling of Fluid Power Systems, ME 597/ABE 591
Historical Background SICFP05, June 1-3, 2005, Linkping
Hydrostatic transmissiom
Williams und Janney
Archimedes
230 0 1500
Pascal
1651 1600 1700
Bramah
1795 1800 1905 1900 2000
Kepler
Vane pump
Ramelli
Gear pump
Axial Piston Pump
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3
Dr. Monika Ivantysynova
Design and Modeling of Fluid Power Systems, ME 597/ABE 591
SICFP05, June 1-3, 2005, Linkping Displacement machine
due to compressibility of a real fluid
p 2 , Qe
Pumping
Adiabatic expansion
VB
Te , n p1
Adiabatic compression
Suction
Vmin=VT
with VT .. dead volume
KA.. adiabatic bulk modulus
Dr. Monika Ivantysynova
Design and Modeling of Fluid Power Systems, ME 597/ABE 591
Displacement machine SICFP05, June 1-3, 2005, Linkping due to viscosity & compressibility of a real fluid
Pressure drop between displacement chamber and port Port pressure Port pressure
Pressure in displacement chamber
Pressure in displacement chamber
Pump
Dr. Monika Ivantysynova
Motor
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Design and Modeling of Fluid Power Systems, ME 597/ABE 591
Power Density SICFP05, June 1 -3, 2005, Linkping
Electric Motor
Hydraulic Motor
F e
r r
F h
b b
I
Fe I B L sin
J b h
with I current [A]
J current density [A/m2]
Fh
T
p L h
p L h r
B magnetic flux density [ T ] or [Vs/m2] Torque:
I B L sin
r
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Dr. Monika Ivantysynova
Design and Modeling of Fluid Power Systems, ME 597/ABE 591
Example SICFP05, June 1-3, 2005, Linkping Power:
For electric motor follows: For hydraulic motor follows:
P
P
T 2
I B L r 2
n
n
assuming =90
p L h r 2
n
Hydraulic Motor
Force density:
Electric Motor
Fe L h
6 -2
J b h B L L h
-2 3
J b B
Fh L h
4
7.6 10 A m 1.8Vs m
Dr. Monika Ivantysynova
3 10 m 4.1 10 Pa
up to 5 107 Pa
Design and Modeling of Fluid Power Systems, ME 597/ABE 591
with a cross section area of conductor: 9
10 6 m2
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Mass /June Power Ratio SICFP05, 1-3, 2005, Linkping Electric Machine
mass = power Positive displacement machines (pumps & motors) are: 10 times lighter min. 10 times smaller much smaller mass moment of inertia (approx. 70 times) much better dynamic behavior of displacement machines
Dr. Monika Ivantysynova
Positive displacement machine
0.1 1 kg/kW
1 . 15 kg/kW
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Design and Modeling of Fluid Power Systems, ME 597/ABE 591
Axial Piston Pumps SICFP05, June 1-3, 2005, Linkping
Cylinder block Pitch radius R Outlet
Inlet p 2 , Qe
Swash plate Piston
Valve plate (distributor)
Cylinder block
Te , n Piston stroke = f (,R) Variable displacement pump Requires continous change of
Dr. Monika Ivantysynova 10
p1
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Design and Modeling of Fluid Power Systems, ME 597/ABE 591
Bent Axis & Swash Plate Machines SICFP05, June 1-3, 2005, Linkping
Torque generation on cylinder block
Torque generation on swash plate
Swash plate design FR
FR
Fp
FR FN
Fp
FN
Driving flange must cover radial force
FR
Fp
FN
Fp
FN
FR
FR Fp FN
Radial force FR exerted on piston!
Fp
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FN
Bent axis machines
Design and Modeling of Fluid Power Systems, ME 597/ABE 591
Dr. Monika Ivantysynova
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Axial Piston Pumps SICFP05, June 1-3, 2005, Linkping
Openings in cylinder bottom In case of plane valve plate
In case of spherical valve plate
Dr. Monika Ivantysynova
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Design and Modeling of Fluid Power Systems, ME 597/ABE 591
Axial Piston Pumps SICFP05, June 1-3, 2005, Linkping
Plane valve plate Inlet opening Outlet opening
Plane valve plate Inlet Outlet
Connection of displacement chambers with suction and pressure port
Dr. Monika Ivantysynova 13
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Design and Modeling of Fluid Power Systems, ME 597/ABE 591
Axial Piston Pumps SICFP05, June 1-3, 2005, Linkping
Kinematic reversal: pump with rotating swash plate Check valves fulfill distributor function Suction valve
Pressure valve for each cylinder
Outlet
Dr. Monika Ivantysynova
Inlet
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can only work as pump
Design and Modeling of Fluid Power Systems, ME 597/ABE 591
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Steady state characteristics SICFP05, June 1-3, 2005, Linkping
ideal displacement machine
Displacement volume of a variable displacement machine:
const p const
n const const
Vmax
const p const
n
const n const
p
p const const
n
const n const
p
Dr. Monika Ivantysynova
n
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Design and Modeling of Fluid Power Systems, ME 597/ABE 591
SICFP05, June 1-3, 2005, Linkping Example
The maximal shaft speed of a given pump is 5000 rpm. The displacement volume of this pump is V= 40cm3/rev. The maximal working pressure is given with 40 MPa. Using first order scaling laws, determine: - the maximal shaft speed of a pump with 90 cm3/rev - the torque of this larger pump - the maximal volume flow rate of this larger pump - the power of this larger pump For the linear scaling factor follows:
3
V V0
1
90 40
1.31
Maximal shaft speed of the larger pump: n
n0
1.31 1 5000 rpm 3816 .8 rpm
Torque of the larger pump: T
p V 2
40 10 6 Pa 90 10 -6 m 3 2
573.25 Nm
Maximal volume flow rate: Qmax V nmax 90 10 6 m 3 /rev 3816.8 rpm 0.3435 m 3 /min 343.5 l/min 1 -1 6 3 p Q 40 10 Pa 0.3435 m s 229 kW Power of the larger pump: P 60
Dr. Monika Ivantysynova
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Design and Modeling of Fluid Power Systems, ME 597/ABE 591
SICFP05, June 1-3, 2005, Linkping Real Displacement Machine
Cylinder Distributor Inlet Piston Outlet p 2 , Qe
p2
p1
Te , n
QSe
QSi
p1
QSe external volumetric losses QSi internal volumetric losses Effective Flow rate: Effective torque:
Dr. Monika Ivantysynova
Qe
Vmax n QS
QS volumetric losses TS torque losses
Design and Modeling of Fluid Power Systems, ME 597/ABE 591
Te
p 2
Vmax
10
19
TS
Volumetric Losses SICFP05, June 1-3, 2005, Linkping
n m
QS
i 1
QSei
j 1
QSij
QSK
QSf
losses due to Incomplete p2, Qe filling Te , n QSe p1 QSi
external
internal volumetric losses
losses due to compressibility
QSL external and internal volumetric losses = flow through laminar resistances: b h3 p Q p 12
QSL
Assuming const. gap height Dynamic viscosity
Dr. Monika Ivantysynova
f ( , p)
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Design and Modeling of Fluid Power Systems, ME 597/ABE 591
SICFP05, June 1-3,Losses 2005, Linkping Volumetric
Effective volume flow rate is reduced due to compressibility of the fluid
C
dV V B
VB
1 dp KA
1 pC p B KA
ln VC
ln VB
1 pC KA
VB
pB
Pumping
VB 1 e
simplified
VB
p VB KA
Suction
QSK
VB
with n pump speed
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Dr. Monika Ivantysynova
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Design and Modeling of Fluid Power Systems, ME 597/ABE 591
SICFP05, June 1-3, 2005, Linkping Steady state characteristics
of a real displacement machine
Qi
V n
Vmax n
Effective volumetric flow rate
Qe
Qi QS
nmin
QS
Dr. Monika Ivantysynova
p, n,V ,
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...temperature
Design and Modeling of Fluid Power Systems, ME 597/ABE 591
Steady state characteristics SICFP05, June 1-3, 2005, Linkping
Effective mass flow at pump outlet Qme Loss component due to compressibility does not occur!
Dr. Monika Ivantysynova
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Design and Modeling of Fluid Power Systems, ME 597/ABE 591
Instantaneous Pump Flow SICFP05, June 1-3, 2005, Linkping
Instantaneous volumetric flow Qa
Qa
dV dt
Volumetric flow displaced by a displacement chamber
Qai
The instantaneous volumetric flow is given by the sum of instantaneous flows Qai of each displacement element:
k
Qa
i 1
Qai
k number of displacement chambers, decreasing their volume, i.e. being in the delivery stroke
z is an even number z is an odd number
k
k
z 2
z 0 .5 2
z number of displacement elements
or
z 0 .5 2
Pressure pulsation
Design and Modeling of Fluid Power Systems, ME 597/ABE 591
Flow pulsation of pumps
Dr. Monika Ivantysynova
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Flow pulsation SICFP05, June 1-3, 2005, Linkping
Non-uniformity grade of volumetric flow is defined:
Qmax Qmin Qmi
Qmax Qmin 2
Qmi
Qmax Qmin 2 Qmax Qmin
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Dr. Monika Ivantysynova
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Design and Modeling of Fluid Power Systems, ME 597/ABE 591
Torque Losses SICFP05, June 1-3, 2005, Linkping
TS
TS
TS
kT
TS
n
TSp TSc
CT n
constant value
Torque loss due to viscous friction in gaps (laminar flow) hgap height
Torque loss to overcome pressure drop caused in turbulent resistances
TS
CT
ps
l d
d
v2 2
v l
v2 2
Torque loss linear dependent on pressure
TSp
Te
CTp
p 2
p
Vmax TS
drag coefficient
flow resistance coefficient
0.3164
turbulent 4
Re
effective torque required at pump shaft
Dr. Monika Ivantysynova
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Design and Modeling of Fluid Power Systems, ME 597/ABE 591
Steady state characteristics SICFP05, June 1-3, 2005, Linkping
Torque losses of a real displacement machine
p const
TS
f (n, p,V , )
p const
TS
TS
TS
n const
p
n const
TS
TSp
TSp
n const
p const
p
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Dr. Monika Ivantysynova
Design and Modeling of Fluid Power Systems, ME 597/ABE 591
Steady state characteristics SICFP05, June 1-3, 2005, Linkping
Effective Torque
Te
Ti TS
p 2
Vmax
TS
Effective torque Te
n const
Effective torque Te TS
TS
TS T S TS
TS
p
TSc T
TSc
T
p const
Ti
Ti
p
Design and Modeling of Fluid Power Systems, ME 597/ABE 591
TS
Dr. Monika Ivantysynova
p, n,V ,
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Axial Machine SICFP05,Piston June 1-3, 2005, Linkping
Kinematics Piston displacement: sP
HP
sP
R tan
1 cos
sP
Outer dead point AT =0
Piston stroke:
HP
2 R tan
z
R pitch radius
b tan R y R cos
Inner dead point IT
b y
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Dr. Monika Ivantysynova
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Design and Modeling of Fluid Power Systems, ME 597/ABE 591
Kinematic Parameters SICFP05, June 1-3, 2005, Linkping
Piston velocity in z-direction:
vP ds P dt ds P d d dt R tan sin
Piston acceleration in z-direction:
aP dv P dt dv P d d dt
2
R tan
cos
vP
aP
au
Circumferential speed
vu
vu
Centrifugal acceleration:
au
Coriolis acceleration ac is just zero, as the vector of angular velocity and the piston velocity vP run parallel
Dr. Monika Ivantysynova
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Design and Modeling of Fluid Power Systems, ME 597/ABE 591
Instantaneous Flow SICFP05, June 1-3, 2005, Volumetric Linkping
Geometric displacement volume:
Vg
Vg
z AP H P
z
2 dP R tan 2
z number of pistons
In case of pistons arranged parallel to shaft axis:
2 dP R tan 2
k
For an ideal pump without losses
Geometric flow rate: Qg
n z
Mean value over time k number of pistons, which
are in the delivery stroke
Instantaneous volumetric flow:
Qa
i 1
Qai
with Qai instantaneous volumetric flow of individual piston
Qai
vP
R tan
sin
Qai
v p AP
AP R tan
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31
sin
i
Design and Modeling of Fluid Power Systems, ME 597/ABE 591
Dr. Monika Ivantysynova
SICFP05, June 1-3, 2005, Volumetric Linkping Instantaneous Flow
In case of even number of pistons: k
In case of odd number of pistons:
0.5 z
Qa
i 1
Qai
z k1 0.5 for 0 2 z z and k 2 0.5 for 2 z
Dr. Monika Ivantysynova
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Design and Modeling of Fluid Power Systems, ME 597/ABE 591
SICFP05, June 1-3, 2005, Linkping
Flow & Torque Pulsation
kinematic flow and torque pulsation due to a finite number of piston
Flow Pulsation:
Non-uniformity grade:
Q
Qmax Qmin Qmi
with Qmi
Qmax Qmin 2
Even number of pistons:
Odd number of pistons:
Q
tan
2 z
T
2 z
tan
4 z
Torque Pulsation
Tmax Tmin Tmi
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with Tmi
Tmax Tmin 2
Dr. Monika Ivantysynova
Design and Modeling of Fluid Power Systems, ME 597/ABE 591
SICFP05, June 1-3, 2005, Linkping
Flow &Pumps Torque Pulsation Piston
kinematic flow and torque pulsation due to a finite number of piston z number of pistons
Non-uniformity
mean mean
Even number of pistons:
Odd number of pistons:
NON-UNIFORMITY of FLOW / TORQUE
NON-UNIFORMITY of FLOW / TORQUE
Flow and torque pulsation frequency f: Even number of pistons:
f=zn f=2zn
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Odd number of pistons:
Dr. Monika Ivantysynova
Design and Modeling of Fluid Power Systems, ME 597/ABE 591
SICFP05, June 1-3, 2005, Linkping
Flow Pulsation
Non-uniformity grade:
Q
Qmax Qmin Qmi
3 0.140
with Qmi
Qmax Qmin 2
Kinematic non-uniformity grade for piston machines:
Number of pistons z Non-uniformity grade 4 0.325 5 0.049 6 0.140 7 0.025 8 0.078 9 0.015 10 0.049 11 0.010
Volumetric losses Qs=f() and
QS
p, n,Vi ,
Flow pulsation of a real displacement machine is much larger than the flow pulsation given by the kinematics
Dr. Monika Ivantysynova 35
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Design and Modeling of Fluid Power Systems, ME 597/ABE 591
Flow Pulsation SICFP05, June 1-3, 2005, Linkping
180 160
Q th e o K in e m a t ic N o n - u n if o r m it y o f F lo w R a te z = 9
Q [l/m in ]
140 120 100 80 60 40 20 0 0 60 120 180 240 300 360
E f f e c t iv e F lo w R a t e Q
P u m p O u tle t
r o ta tin g a n g le [d e g ]
Flow pulsation leads to pressure pulsation at pump outlet
Dr. Monika Ivantysynova
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Design and Modeling of Fluid Power Systems, ME 597/ABE 591
