me597-lecture4-07
DESCRIPTION
DESIGNING AND MODELLING OF FLUID SYSTEMSTRANSCRIPT
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Dr. Monika Ivantysynova
MAHA Professor Fluid Power Systems
Design and Modeling of Fluid Power SystemsME 597/ABE 591 Lecture 4
MAHA Fluid Power Research Center
Purdue University
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 5912
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
Content
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 5913
Historical Background
Williams und Janney
Hydrostatic transmissiom
15
Gear pump Axial Piston Pump
230 1795 1905
0 1700 1900 2000
1651
1600 18001500
Archimedes Pascal Bramah
Ramelli Kepler Vane pump
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 5914
Displacement machine
2
BVPumping
Suction
Vmin=VT with VT .. dead volume
Adiabatic compression
Adiabatic expansion
due to compressibility of a real fluid
KA.. adiabatic bulk modulus
Te , n
p1
p2, Qe
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 5915
Displacement machine
due to viscosity & compressibility of a real fluid
3
Pump Motor
Port pressure Port pressure
Pressure in
displacement
chamber
Pressure in
displacement
chamber
Pressure drop between displacement chamber and port
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 5916
sinLBIFe hLpFh
F
b
Fe
B
h
Power Density
Electric MotorHydraulic Motor
with I current [A]
B magnetic flux density [ T ] or [Vs/m2]
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Torque:
hbJI
J current density [A/m2]
rLBIT sin rhLpT
r
r
b
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 5917
Example
Power: nTTP 2
For electric motor follows: assuming =90
For hydraulic motor follows:
Force density: Electric Motor Hydraulic Motor
BbJhL
LBhbJ
hL
Fe
with a cross section area of conductor: 26
m109
Pa105 toup7
34
phL
Fh
nrLBIP 2
nrhLpP 2
Pa101.4m103mVs8.1mA106.743-2-26
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 5918
Mass / Power Ratio
Electric Machine Positive displacement machine
mass
power= 1 . 15 kg/kW 0.1 1 kg/kW
10 times lighter
min. 10 times smaller
much smaller mass moment of inertia (approx. 70 times)
Positive displacement machines (pumps & motors) are:
much better dynamic behavior of displacement machines
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 59110
Axial Piston Pumps
Te , n
p1
p2, Qe
Inlet
Outlet
Swash plate Piston Valve plate
(distributor)
Cylinder block
Cylinder block Pitch radius R
Piston stroke = f (,R)
Variable displacement pump
Requires continous change of
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 59111
Bent Axis & Swash Plate Machines
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Torque generation on cylinder block
FR
FR
FR
Fp
Fp
Fp
FN
FN
FN
Torque generation on swash plate
Swash plate design
Bent axis machines
Radial force FR exerted on piston!
Driving flange must
cover radial forceFp
FN
FN
FN
Fp
FR
FR
FR
Fp
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 5911219
Axial Piston Pumps
Openings in cylinder bottom
In case of plane valve plate
In case of spherical valve plate
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 5911320
Axial Piston Pumps
OutletInlet
Inlet opening Outlet opening
Plane valve plate
Plane valve plate
Connection of displacement chambers with suction and pressure port
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 5911421
Axial Piston Pumps
InletOutlet
Kinematic reversal: pump with rotating swash plate Check valves fulfill
distributor functionSuction valve
Pressure
valve for
each cy-
linder
can only work as pump
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 59116
ideal displacement machine
Steady state characteristics
8
Displacement volume of a variable displacement machine: maxVV
constn
0
P
p
const
const
0
P
n
constp
0
T
p
constconstn
0
Q const
p
constn
0
Q
n
const
constp
0
T const
n
constp
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 59118
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: 31.140
9033
0V
V
Maximal shaft speed of the larger pump:
Torque of the larger pump: Nm 25.5732
m1090Pa1040
2
3-66Vp
T
Maximal volume flow rate:
l/min 343.5/min m 3435.0rpm 8.3816/revm 1090336
maxmax nVQ
Power of the larger pump:
rpm 8.3816rpm 500031.11
0
1nn
31
kW229s60
1m 0.3435Pa1040
1-36QpP
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 59119
Real Displacement Machine
Te , n
p1
p2, Qe
QSi
QSe
Inlet
Outlet
Distributor
Cylinder
Piston
Effective Flow rate:
Effective torque: Se TVp
T2
max
QSe external volumetric losses
QSi internal volumetric losses
TS torque losses
10
QS volumetric lossesSe QnVQ max
12 ppp
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 59120
Volumetric Losses
QSL external and internal volumetric losses = flow through laminar
resistances:
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Te , n
p1
p2, Qe
QSi
QSe
external internal
volumetric losses
losses due to
compressibility
losses due to
Incomplete
filling
pCQSL
),( pfDynamic viscosity
Assuming const. gap height
SfSK
m
j
Sij
n
i
SeiS QQQQQ11
12
3phb
Q
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 59121
Volumetric Losses
Effective volume flow rate is reduced due to compressibility of the fluid
BV
Pumping
Suction
BCA
ppK
BB eVV
1
1
simplified
A
BBK
pVV
BSK VnQ with n pump speed
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C
B A
C
B
dpKV
dV 1BC
A
BC ppK
VV1
lnln
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 59122
Steady state characteristics
of a real displacement machine
Effective volumetric flow rate Sie QQQ
nVnVQi max
13
,,, VnpfQS ture...tempera
nmin
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 59123
Steady state characteristics
Effective mass flow at pump outlet QmeLoss component due to
compressibility does not
occur!
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 59124
Instantaneous Pump Flow
iai fQfdt
dVQa
Instantaneous volumetric flow Qa
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Volumetric flow displaced by
a displacement chamber
k number of displacement chambers, decreasing their volume, i.e. being in the delivery stroke
The instantaneous volumetric flow is given by the sum of instantaneous flows
Qai of each displacement element:k
i
aia QQ1
2
zk z number of displacement elementsz is an even number
z is an odd number 5.02
or 5.02
zk
zk
Flow pulsation of pumps Pressure pulsation
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 59125
Flow pulsation
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mi
QQ
QQ minmax
Non-uniformity grade of volumetric flow is defined:
2
minmax QQQmi
minmax
minmax2QQ
QQQ
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 59126
Torque Losses
Se TVp
T2
max
ScSpSSS TTTTT
Torque loss due to viscous friction in gaps (laminar flow)
hgap height
Torque loss to overcome pressure drop caused in turbulent resistances
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22vv
d
lps
l
d v
flow resistance coefficient
drag coefficient
constant value
Torque loss linear dependent on pressure
effective torque required at pump shaft
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2nCT TS
pCT TpSp
nCnh
kT TTS
4 Re
3164.0turbulent
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 5912730
Steady state characteristics
of a real displacement machine
0 p
constn
TS
0
TS
p
n
constpconstn
0 p
TS
p
TS
0 p
constn
0 n
constp
TS
0 n
constp
TS
),,,( VpnfTS
Torque losses
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 59128
Steady state characteristics
n0
constp
T
Ti
TSc
TS
p
TS
TS
Effective torque Te
0T
Ti
TSc
TS
p
TS
TS
Effective torque Te
constn
p
SSie TVp
TTT2
max
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,,, VnpfTS
Effective Torque
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 5912923
cos
tan
Ry
yRb
bz
zsPPiston displacement:
cos1tanRsP
Piston stroke:
tan2 RHP
HPsP
R pitch radius
Outer dead point AT
Inner dead point IT
=0
Kinematics
Axial Piston Machine
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 59130
Kinematic Parameters
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vPau
vu
aP
Piston velocity in z-direction:
Piston acceleration in z-direction:
sintanRdt
d
d
ds
dt
dsv PPP
costan2
Rdt
d
d
dv
dt
dva PPP
Circumferential speed
Rvu
Centrifugal acceleration:
2Rau Coriolis acceleration ac is just zero, as the vector of
angular velocity and the piston velocity vP run parallel
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 5913125
Instantaneous Volumetric Flow
Geometric displacement volume:
PPg HAzV z number of pistons
In case of pistons arranged parallel to shaft axis:
tan2
2
Rd
zV Pg
Geometric flow rate: tan2
2
Rd
znQ Pg Mean value over time
Instantaneous volumetric flow:k
i
aia QQ1
aiQwith instantaneous volumetric flow of individual piston iai fQ
k number of pistons, whichare in the delivery stroke
For an ideal pump
without losses
sintanRvP
iPPpai RAAvQ sintan
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 5913226
Instantaneous Volumetric Flow
k
i
aia QQ1In case of odd number of pistons:
zk 5.0In case of even number of pistons:
zz
zk
z
zk
2for 5.02
and
0for 5.02
2
1
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 59133
z2
tan2
Q z4
tan2 z
Q
Flow & Torque Pulsation
kinematic flow and torque pulsation due to
a finite number of piston
2 with minmaxminmax
QQQ
Q
QQmi
mi
Q
2T with minmaxminmax
TT
T
TTmi
mi
T
Flow Pulsation:
Torque Pulsation
Non-uniformity grade:
Even number of pistons: Odd number of pistons:
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 59134
Piston Pumps
kinematic flow and torque pulsation due toa finite number of piston
Flow and torque pulsation frequency f:
f=znEven number of pistons:
Odd number of pistons: f=2zn
z number of pistons
Non-uniformity Even number of pistons: Odd number of pistons:
mean mean
NON-UNIFORMITY of FLOW / TORQUE
NON-UNIFORMITY of FLOW / TORQUE
Flow & Torque Pulsation
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 5913527
Flow Pulsation
Non-uniformity grade:
2 with minmaxminmax
QQQ
Q
QQmi
mi
Q
Number of pistons z
3 4 5 6 7 8 9 10 11
Non-uniformity grade
0.140 0.325 0.049 0.140 0.025 0.078 0.015 0.049 0.010
Volumetric losses Qs=f() and
Flow pulsation of a real displacement machine is much larger than the
flow pulsation given by the kinematics
,,, iS VnpfQ
Kinematic non-uniformity grade for piston machines:
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SICFP05, June 1-3, 2005, Linkping
Dr. Monika IvantysynovaDesign and Modeling of Fluid Power
Systems, ME 597/ABE 59136
0 6 0 1 2 0 1 8 0 2 4 0 3 0 0 3 6 00
2 0
4 0
6 0
8 0
1 0 0
1 2 0
1 4 0
1 6 0
1 8 0
ro ta t in g a n g le [d e g ]
Q [
l/m
in]
Q th e o K in e m a t ic N o n -u n ifo rm ity o f F lo w R a te z = 9
E f fe c t iv e F lo w R a te Q e P u m p O u t le t
Flow Pulsation
Flow pulsation leads to pressure pulsation at pump outlet
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