Abstract
Piston friction is one of the important but complicated sources of energy loss of a hydraulic axial piston machine. In this paper, two formulas are derived for estimating instantaneous piston friction force and average piston friction moment loss. The derived formula can be applicable for piston guides with or without bushing as well as for axial piston machines of motoring and pumping operations. Through the formula derivation, a typical curve shape of friction force found from several experimental measurements during one revolution of a machine is clearly explained in this paper that it is mainly due to the equivalent friction coefficient dependent on its angular position. Stribeck curve effect can easily be incorporated into the formula by replacing outer and inner friction coefficients at both edges of a piston with the coefficient given by Manring (1999) considering mixed/boundary lubrication effects. Novel feature of the derived formula is that it is represented only by physical dimensions of a machine, hence it allows to estimate the piston friction force and loss moment of a machine without hardworking experimental test.
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Abbreviations
- a p :
-
Piston acceleration,w 2Rp tan α cos θ
- A p :
-
Piston area, πd2 p/4
- d p :
-
Diameter of piston
- F :
-
Force acting on each part of a machine
- f p :
-
Equivalent friction coefficient w.r.t.F rp
- Frp :
-
Total radial force acting on a piston
- h p :
-
Gap height between piston and cylinder
- h s :
-
Gap height of slipper and swash plate
- l bf :
-
Length between ball joint and piston guide
- l f :
-
Piston guide length,l Fo orl F0+Zp
- lBo :
-
Distance between origin and ball joint at ODP
- l co :
-
Distance of cylinder block from origin O
- l p :
-
Length of piston
- M :
-
Moment generated by each force
- m p :
-
Piston mass
- N :
-
Normal reaction force of piston
- Δ p :
-
Difference of piston and housing pressure
- γ si ,γ so :
-
Inner, outer radius of slipper sealing ring
- R p :
-
Pitch circle radius of pistons
- V g :
-
Geometric displacement, 2ApRp tan α
- υ p :
-
Piston velocity,wR P tan α sin θ
- Z p :
-
Piston displacement,R p tan α(1-cos θ)
- α:
-
Tilting angle of swash plate
- θ:
-
ngular position of a piston, i.e. phase angle
- λp :
-
Equivalent friction coefficient w.r.t.F pp
- μ:
-
Viscosity of hydraulic oil
- μ o ,μ i :
-
Outer, inner piston friction coefficient
- ω:
-
Rotational speed in rad/sec
References
Gradshteyn, I. S. and Ryzhik, I. M., 2000, Table of Integrals, Series, and Products, 6th Ed., Academic Press.
Heon-Sul Jeong, 2003, Preliminary Design of a Hydraulic Piston Motor for Achieving an User-Defined Optimal Efficiency Point, 1st International Conf. on Computational Methods in Fluid Power Technology, Melbourne Autralia, 26–28 November.
Jaroslav Ivantysyn, Monika Ivantysynova, HydroStatic Pumps and Motors, Akademia Books International, ISBN 81-85522-16-2, 2001.
Kim, J.-Y., Kim, J.-W., Cho, M.-R. and Han, D.-C., 2002, “Frictional Characteristics of Piston Ring Pack with Consideration of Mixed Lubrication: Parametric Investigation,”KSME Int. Journal, Vol. 16 No. 4, pp. 468–475.
Noah D. Manring, 1999, “Friction Forces Within the Cylinder Bores of Swash Plate Type Axial Piston Pumps and Motors,”ASME Journal of Dynamic Systems, Measurement and Control, Vol 121, pp. 531–537.
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Jeong, HS., Kim, HE. On the instantaneous and average piston friction of swash plate type hydraulic axial piston machines. KSME International Journal 18, 1700–1711 (2004). https://doi.org/10.1007/BF02984318
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DOI: https://doi.org/10.1007/BF02984318