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Journal of Mechanical Science and Technology

, Volume 21, Issue 1, pp 83–97 | Cite as

A novel performance model given by the physical dimensions of hydraulic axial piston motors: Model derivation

  • Heon-Sul Jeong
Article

Abstract

Since Wilson (1948) had firstly developed steady-state flow rate and moment loss model for hydraulic piston machines, several authors tried to make precise performance models. However, Huhtala (1997) discussed the strength and weakness of some existing models comparing with measurement data and concluded unfortunately that any model is not accurate enough for wide operating ranges. For a hydraulic axial piston motor of swash plate design with rotating cylinder, new performance formula is derived in this paper through theoretical study on leakages and friction losses of three facing gaps and other non-negligible losses. And efficiency surface of an example motor is estimated and extension of the formula for hydraulic pumps is discussed. A novel feature of the derived model is that all coefficients are given by the physical dimensions of a motor, hence allowing calculation and analysis of the performance of a motor in mind.

Key Words

Leak Flow Loss Hydro-Mechanical loss Volumetric Mechanical and Overall Efficiency Performance Coefficient Model Hydraulic Axial Piston Motor 

Nomenclature

Ao

Opening area of a piston port

aP

Piston accelerationw 2 R P tan α cos θ

AP

Cross-section area of a piston, πd p 2 /4

AVN

Opening area of the valve port notch

ASp

Side view area of a slipper and piston outside of cylinder block

bV1,bB2

Inner, outer breadth of the valve plate sealing ring

C

Performance coefficient related with leak-age

Cd

Discharge coefficient of an orifice

CV

Breadth of the valve delivery/return port

Cw

Drag coefficient of a cylindrical bar

dB

Diameter of a piston bore

dBr

Diameter of the support bearing

dP

Diameter of a piston

eP

Breadth of the piston port edge

F

Force acting on several parts of a machine

f

Friction coefficient

fP,hP

Friction coefficient and gap height between a piston and cylinder hole

hs

Gap height between slipper and swash plate

hR

Gap height between valve plate and cylinder

K

Performance coefficient related with moment loss

l

Length of several parts

lB

Length of a piston bore

lC

Length of the cylinder block

lF

Length of piston guide,l Fo orl Fo +Z P

lFo

Length of a piston guide or bushing at ODP

M, ML

Moment, moment loss produced by several forces

M2

Output moment of a motor

mP

Mass of a piston

n

Rotational speed of a motor in HZ,w/2π

p

Piston chamber pressure

p1

Inlet pressure of a motor

p2

Outlet pressure of a motor

pe

Pressure inside of a motor enclosure

Δp

Pressure difference,p-p e orp 1-p 2

Q, QL

Flow, leak flow through several parts

rsi,rso

Inner, outer radius of the slipper sealing ring

rV1,rV2

Inner, outer radius of the valve plate inner sealing ring

rV3,rV4

Inner, outer radius of the valve plate outer sealing ring

Rc

Radius of the cylinder block

RH

Inner radius of a motor housing

RP

Pitch circle radius of pistons

Vg

Motor geometric displacement

2APRP tan α VP

Piston velocity,wR P tan α sin θ

z

Number of pistons in a motor

Zo

Piston number located at delivery port side

ZP

Piston displacement,R P tan α(1−cosθ)

α

Tilting angle of the swash plate

β

Bulk modulus of hydraulic oil

ρ

Density of hydraulic oil

ΔθVn

Angle of the valve port notch opened

θ

Angular position of a piston or motor

ηhm

Hydro-mechanical efficiency of a motor

ηt

Overall efficiency of a motor

ηv

Volumetric efficiency of a motor

λP

Equivalent friction coefficient of a piston

μ

Viscosity of hydraulic oil

ω

Rotational speed of a motor in rad/sec,2πn

Subscript

aP

Piston acceleration

Br

Support bearing

c

Fluid compressibility

C

Cylinder block

ch

Churning, swirl

CH

Cylinder and motor housing

fP,fS

Friction force on a piston, slipper

o

Miscellaneous

p

Pressure dependent term

P

Piston

pBr

Pressure on bearings

pP

Piston pressure

PP

Piston port

PSP

Piston port, slipper and piston

S

Slipper pad or swash plate

SP

Slipper pad, slipper and piston

V

Valve plate

VN

Valve port control notch

vBr

Velocity of bearings

vP

Piston velocity

μP, μS, μV

Viscosity in a piston, slipper, valve plate

ωP

Centrifugal force of a piston

μ

Viscosity dependent term

ρ

Density dependent term

Superscript

Fluctuating value of total flow rate or moment

-

Average value of total flow rate or moment

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References

  1. Dal-Sik Jang, 1997,Verlustanalyse an Axial-kolbeneinheiten, Dissertation, Aachen, ISBN 3-89653-252-9.Google Scholar
  2. Gradshteyn, I. S. and Ryzhik, I. M., 2000,Table of Integrals, Series, and Products, 6th Ed., Academic Press.Google Scholar
  3. Heon-Sul Jeong, Hyoung-Eui Kim, Bo-Sik Kang, Dong-Soo Jeong and Young-Bum Lee, 2003, “Preliminary Design of Hydraulic Piston Motors for Achieving an User-Defined Optimal Efficiency point,”1st Int. Conf. on Computational Methods in Fluid Power Technology, Melbourne Autralia, pp. 613–624.Google Scholar
  4. Heon-Sul Jeong and Hyung-Eui Kim, 2004, “On the Instantaneous and Average Piston Friction of Swash Plate Type Hydraulic Axial Piston Machines,”KSME International Journal, Vol. 18, No. 10, pp. 1700–1711.Google Scholar
  5. Heon-Sul Jeong, 2006, “A Novel Performance Model Given by the Physical Dimensions of Hydraulic Axial Piston Motors: Experimental Analysis,”to appear in Journal of Mechanical Science and Technology. Jaroslav Ivantysyn and Monika Ivantysynova,2001, Hydrostatic Pumps and Motors, Akademia Books International, ISBN 81-85522-16-2.Google Scholar
  6. Kalevi Huhtala, 1997, “Matti Vilenius, Comparison of Steady State Models of Hydraulic Pump,”5th Scandinavian International Conference on Fluid Power, Linkoping, Sweden.Google Scholar
  7. Shuyan Liu and Weige Yan, 1998, “Analytical Solution for Laminar Viscous Flow in the Gap Between Parallel Rotary Disks,”Journal of Beijing Institute of Technology, Vol. 7, No. 2, pp. 113–119.Google Scholar
  8. Wilson, W. E., 1948, “Performance Criteria for Positive Displacement Pumps and Fluid Motors,”ASME Semi-annual Meeting, paper No. 48-SA-14.Google Scholar

Copyright information

© The Korean Society of Mechanical Engineers (KSME) 2007

Authors and Affiliations

  1. 1.School of Mechanical EngineeringKunsan National University, KunsanChonbukKorea

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