a review on axial piston pump technologies · 2019-07-01 · ccefp summit at purdue in honor of...

CCEFP Summit at Purdue in Honor of Monika IvantysynovaCover Slide …

Purdue University, June 4-6, 2019

N.D. Manring Slide # 1

A REVIEW ON AXIAL PISTON PUMP TECHNOLOGIES

Noah D. ManringGlen A. Barton Professor for Fluid PowerMechanical and Aerospace Engineering

University of Missouri

CCEFP Summit at Purdue in Honor of Monika IvantysynovaAgenda …



AGENDA

1. My history of knowing Monika and Jaro

2. A few of Monika’s contributions to the field of axial piston pump research

3. Physical limitations for the bandwidth frequency of an axial piston pump

CCEFP Summit at Purdue in Honor of Monika IvantysynovaHistory of Knowing Monika …



MY HISTORY OF KNOWING MONIKA AND JARO

CCEFP Summit at Purdue in Honor of Monika IvantysynovaFirst Meeting …



1955 - 2018

Our first meeting … 1995 – Ames Iowa

CCEFP Summit at Purdue in Honor of Monika IvantysynovaSecond Meeting …



Our second meeting … 1996 – Neumunster, Germany

CCEFP Summit at Purdue in Honor of Monika IvantysynovaSubsequent Meetings …



Subsequent meetings … 2004 and beyond

CCEFP Summit at Purdue in Honor of Monika IvantysynovaContributions …



A FEW OF MONIKA’S CONTRIBUTIONS TO THE FIELD OF AXIAL PISTON PUMP RESEARCH

CCEFP Summit at Purdue in Honor of Monika IvantysynovaMost Recent Paper …



1955 - 2018

Most Recent Paper …

Williams, K., and M. Ivantysynova. 2019. Approximate stochastic differentialdynamic programming for hybrid vehicle energy management. Journalof Dynamic Systems, Measurement and Control. Vol. 141 051003-1-9


• Hydraulic hybrid vehicles• Energy management• Proper charge of the energy storage system

CCEFP Summit at Purdue in Honor of Monika IvantysynovaMost Recent Paper …


CCEFP Summit at Purdue in Honor of Monika IvantysynovaSeminal Book…



1955 - 2018

Seminal Book …

Ivantysyn, J, and M. Ivantysynova. 2003. Hydrostatic Pump and Motors:Principles, Design, Performance, Modelling, Analysis, Control andTesting. First English Edition. (First published in German, 1993.) TechBooks International. New Delhi, India.




“The main objective of this book is to provide a

comprehensive account for design and analysis of

hydrostatic pumps and motors similar to the

popular technical literature in the classical

branches of mechanical engineering like turbines,

centrifugal pumps, compressors and internal

combustion engines.”




“The aim of this book is not only to give the

reader the possibility to understand the working

principles of hydrostatic pumps and motors but he

should also be able to use modern computational

methods for the design and analysis of

displacement machines as well as fluid power

systems.”




1. Piston pumps

2. Gear pumps

3. Screw pumps

4. Vane pumps

5. Efficiency

6. Control


1955 - 2018

Most Cited Paper …

Wieczorek, U., and M. Ivantysynova. 2002. Computer aided optimization ofbearing and sealing gaps in hydrostatic machines – The simulation toolCASPAR. International Journal of Fluid Power. Vol. 3, No. 1, pp. 7-20

CCEFP Summit at Purdue in Honor of Monika IvantysynovaMost Cited Paper …



• CASPAR

• (CAlculation of Swash Plate Type Axial Piston Pump and MotoR)

• “For the first time it is possible to calculate the gap flow and thus the losses due to viscous friction and leakage in all gaps of the rotating group of a swash plate machine with the here presented simulation tool CASPAR.”

• Iterates until it finds the piston eccentricity, etc.

• Highest leakage on the low pressure side of the pump

• Accounts for local viscosity changes (leakage and friction)

• Correlates well with experimental results






1. Introduction

2. Simulation tool

3. Calculation of gap flow

4. Pressure in the displacement chamber

5. Motion equation

6. Simulation results

a. Piston

b. Slipper

c. Cylinder block

d. Total losses

e. Swash plate moment

7. Conclusion




Introduction …

• Conducted at the Technical University of Hamburg-

Harburg (2nd stint, 1999-2004)

• Volumetric and friction losses

• Numerical solutions for PDEs (Reynolds equation and

Energy equation)

• “For the first time it is possible to calculate the gap

flow and thus the losses due to viscous friction and

leakage in all gaps of the rotating group of a swash

plate machine with the here presented simulation tool

CASPAR.”




Simulation tool …

• Numerical solutions for PDEs (Reynolds equation and

Energy equation)

• Iteration is done to solve the motion equation

(eccentricity for pistons)

• MATLAB programing plus the graphical user interface




Calculation of gap flow …

• Laminar flow is assumed (low Reynolds number)

• 2 dimensional Reynolds equation is solved numerically

• Negative pressures are set to zero

• Local changes in viscosity are calculated using a model

that adjusts for local pressure and temperature

• Energy equation is solved numerically to calculate the

local temperatures

• Incompressible fluid

• Finite volume method is used to solve the PDEs

(Pantankar 1980)




Pressure in the displacement chamber …

• Pressure-rise-rate equation with fluid compressibility

• Leakage calculations (3 places) coupled to the PDE

solution for gap flow

• Simple model for valve-plate flow

• 75cc test machine

• Correlates well with experiments




Motion equation …

• Static equation of forces acting on the piston (inertia is

neglected)

• Squeeze film equations are used to create an ODE for

modeling the motion of the piston in the radial

direction

• Eccentricity in 2 places, in 2 directions is calculated

• If metal-to-metal contact is found, the piston is

assumed to deform elastically

• Effects of hydrodynamic lubrication were not

considered at this stage …




Simulation results – piston …

• Gap height is calculated as shown in the figure

• “During the high-pressure phase the leakage flow is

less than during the low-pressure phase. This can be

explained by the fact that Couette flow has a stronger

influence than Poiseuille flow.”

• Piston friction forces (not shown here) are comparable

to measurements taken on a special test rig.




Simulation results – slipper …

• Leakage flow during low pressure is larger than the

leakage during high pressure




Simulation results – cylinder block …

• Tilting moment resisted by the valve plate

• Fluid film thicknesses ~ 2 microns

• Torque loss ~ 22 Nm




Simulation results – total losses …

• Experimental leakage ~ 1.70 lpm

• Experimental power loss due to friction ~ 10.07 kW

(CASPER: 8.77 kW)




Simulation results – swash plate moment …

• Average moment for the considered operating point is

17.98 Nm




Conclusion …

• Leakage and viscous friction have been simulated

using a sophisticated numerical program

• Elastohydrodynamic effects are not included here …

• A tool for improving the design, to improve the

efficiency of the machine

• “A simulation tool cannot replace experiments.”

CCEFP Summit at Purdue in Honor of Monika IvantysynovaBandwidth Frequency …



PHYSICAL LIMITATIONS FOR THE BANDWIDTH FREQUENCY OF AN AXIAL PISTON PUMP


CCEFP Summit at Purdue in Honor of Monika IvantysynovaBandwidth Frequency Paper (Manring and Mehta) …


Physical Limitations for the Bandwidth Frequency of a Pressure

Controlled, Axial-Piston Pump

Noah D. Manring and Viral S. Mehta

Journal of Dynamic Systems, Measurement, and Control

November 2011, Vol 133, 061005-1-12

Dedicated to Monika




Pump Description




Analysis




Discharge pressure …

,h d

p d d

V dPQ Q P

dt

Pressure rise-rate equation …

Pump flow …

tan( ),

p

p

N A rQ

Discharge flow model …

,o od p dQ Q P

where .

p

p p p

N A rQ G G

Summary …

( ) ( ) .

o

h dd d p o

V dPP P G

dt




Swash-plate angle… Angular momentum …

Bias actuator force …

Control actuator force …

Continued on the next slide …

2

21

,N

b b c c n n

n

d dI C F L F L R l

dt dt

2

2.b b d b o

dF M L P A F k L

dt

2

2.c c c c

dF M L P A

dt

Slipper reaction …

2

2

2

sin( ) 2 cos( )

sin( ) ,

n p n p n

p n n p

d dR M r M r

dt dt

M r P A




Swash-plate angle…

Equation of motion …

where the following identities have been used …

Piston pressure terms must be studied …

22 2 2 2 2

2

1

[ ]2 2

( ) sin( ) ,

b c p p

N

d b c c o p n n

n

N d d NI M M L M r C k L M r

dt dt

P A P A L F L A r P

2

1 1

sin ( ) and sin( )cos( ) 0 .2

N N

n n n

n n

N




(Piston pressure …)Discontinuous approximation …

Integral average …

2 2

( )( / 2)

2 2

3

2 2

( ) 3 3( 3 / 2)

2 2

d n

d id n n

n

i n

d ii n n

P

P PP

P

P

P PP

2

1 0

sin( ) sin( ) ( ) ,2 2

N

n n n n n d i

n

N NP P d P P

Substitution …




Swash-plate angle…

Equation of motion …

where the steady-state moment for the preload of the bias spring was

substituted into the equation …

Pressure in the control actuator must be studied …

22 2

2

2 2 2

[ ]2

( )2

( ) ( / 2) ,2 o o

b c p

p o

p

b d d c c d

N d dI M M L M r C

dt dt

Nk L M r

N A rA L P P A L P P

2 2 2 ( ) ,

2 2 2o o

p co p o d i b d

N A rN AF L k L M r P P A L P




Control pressure …

Pressure rise-rate equation …

Control flow to the actuator must be studied …

.c c

c c

V dP dQ A L

dt dt




(Control flow …) Control flow …

Metering land flow …

1 2 .cQ Q Q

1 1 2 2

2 2( ) and ( ) ,d d c d c rQ A C P P Q A C P P

Linearized results …

2 ( 2 ) .c q c d cQ P P

1,2 and ,o

o

d d oq d c

do

P A C AC

P

Where the valve coefficients are given by

We need an equation of motion for the valve …




Equation of motion … Equation of motion …

Reynolds transport theorem …

Where the flow force coefficients are …

Summary …

Putting everything together …

2

1 22,v d v sp v

dM P A F k F F

dt

1 2 ( 2 ) 2 ,

c q

dc f d c f

dPF F P P

dt

2 1,2 2cos( ) and 2 cos( ) .

q o cf d d f o d

o

AP C A C

2

2( 2 ) ( ) ( 2 ) ,

q o c

dv v f d d v f d c c

d dPM k P P A P P

dt dt




Summary




1

2

2 3 4 52

6 7 7 8

ˆˆ ˆdischarge presure: ( 1) ( 1) ,

ˆ

ˆ ˆ ˆ ˆˆswash-plate motion: ( 1) ( 1) ( 1) ,ˆ ˆ

ˆ ˆˆ ˆ ˆcontrol presure: ( 1) ( 1) , andˆ ˆ

spool-valve motion

dd

d c

cd c

dPP

dt

d dP P

dt dt

dP dP P

dt dt

2

9 10 11 11 122

ˆ ˆˆ ˆ ˆ: (1 )( 1) ( 1) ,

ˆ ˆd

d c

d dPP P

dt dt

2 2

1 2 32

2 2 2

4 5 6

7 8 9 102

2 [ ]22

, , ,

22

, 2 , ,2 4

( 2 ), , , ,

2 2

o

o o

o

o

qo

o o

b c p od o

p o c d c d

p oc dpb

c d c c q

v fc d c o v

q q v d v d

NI M M L M r

P C

G A L P A L P

Nk L M r

V PN A rA

A L P A A L u

k uP A L M u

u u A P A P

11 12, and .cf c

v vA A

Nondimensional model …




Reduced order model …

1

1 2

ˆˆ 1ˆ ( 1),

ˆ ˆ ˆ( 1)

T

PdP d

dt dt

Second order system …

where …

5 7 10 11 4 7 10 11

1 2

8 10 8 10

1 (1 )( ) ( )and .

Closed form bandwidth frequency …

where …

1

22 2 2ˆ ˆ 1 2 2 2 (1 ) .bw n

1 2

1 2 1ˆ and .

ˆ2n

n




Perturbations …Closed form bandwidth frequency …

where …

1

22 2 2ˆ ˆ 1 2 2 2 (1 ) .bw n

1 2

1 2 1ˆ and .

ˆ2n

n

1 1 4 4

1 4

11 11

11

ˆ ˆˆ ˆ ( ) ( )

ˆ( ) ,

o o o

o

bw bwbw bw

o o

bw

o

Nondimensional sensitivity coefficients …




Perturbations … Results …

Closed form bandwidth frequency …

8

2 q

ocA L

u




Conclusions




1. The pressure controlled pump is a second-order, underdamped system which exhibits overshoot

and oscillation before reaching steady-state. Dominant transients are the discharge pressure and

the swash-plate angle.

2. By far, the most effective way to increase the bandwidth frequency of the pump is to REDUCE the

swept volume of the actuator, and to INCREASE the flow gain of the valve.

CCEFP Summit at Purdue in Honor of Monika IvantysynovaConcluding Remarks …



CONCLUDING REMARKS

CCEFP Summit at Purdue in Honor of Monika IvantysynovaConcluding Remarks …



1955 - 2018

1. She was a bright light in the fluid power community for over 30

years (vibrant, joyful, excited).

2. She contributed significantly to the art and science of designing axial

piston pumps and motors.

3. She was a friend to all of us.

4. She will be missed.

a review on axial piston pump technologies · 2019-07-01 · ccefp summit at purdue in honor of...

Documents