Understanding overall efficiency of hydrostatic pumps and motors
Pump and motor efficiency is a complex subject, to such an extent that most of the available models describing efficiency today rely on experimental data. In spite of that, mathematical models relating efficiency to pressure and angular speed have been proposed throughout the years. In all these models, volumetric and mechanical efficiencies are separately built from flow and torque losses relations. The overall efficiency model is then obtained by multiplying the volumetric and the mechanical efficiency equations. In this paper, we show that the overall efficiency equations must be developed from an energy balance and show that the simple multiplication of mechanical and volumetric efficiencies can potentially lead to inaccurate results. We then obtain a generalised equation relating the overall efficiency to pressure and angular speed for both pumps and motors and show how the resulting model can be fitted to actual experimental data.
Akers, A., Gassman, M., and Smith, R., 2006. Hydraulic
power system analysis. USA: CRC Press.
Blackburn, J.F., Reethof, G., and Shearer, J.L., 1960. Fluid
power control. USA: Technology press of M.I.T. and
John Wiley & Sons.
Costa, G.K. and Sepehri, N., 2015. Hydrostatic transmissions
and actuators – operation, modelling and applications.
UK: John Wiley & Sons.
Doddannavar, A. and Barnard, A., 2005. Practical hydraulic
systems: operation and troubleshooting for engineers and
technicians. Elsevier, US.
Dorey, R.E., 1988. Modelling of losses in pumps and
motors. First Bath International fluid power workshop,
September. UK: University of Bath, 71–97.
Esposito, A., 1980. Fluid power with applications. 4th ed.
USA: Prentice Hall.
Fitzgibbon, A.W., Pilu, M., and Fisher, R.B., 1996. Direct
least squares fitting of ellipses. IEEE transactions on
pattern analysis and machine intelligence, 21 (5), 476–
Halir, R. and Flusser, J., 1998. Numerically stable direct
least squares fitting of ellipses. Proceedings of the 6th
International conference in Central Europe on computer
graphics and visualization, Pizen, Czech Republic:
WSCG, pp 125–132.
Hall, S.J. and Steward, B.L., 2014. Comparison of steady
state flow loss models for axial piston pumps. In:
International Fluid Power Exposition (IFPE), Paper 4.1,
Las Vegas, US.
Ivantysyn, J. and Ivantysynova, M., 2000. Hydrostatic
pumps and motors, principals, designs, performance,
modeling, analysis, control and testing. New Delhi:
Academia Books International.
Jeong, H., 2007. A novel performance model given by the
physical dimensions of hydraulic axial piston motors:
model derivation. Journal of Mechanical Science and
Technology, 21 (1), 83–97. doi:10.1007/BF03161714
Jung, D.S., Kim, H.E., Jeong, H.S., Kang, B.S, Lee, Y.B., Kim, J.
K., Kang, E.S., 2005. Experimental study on the performance
estimation efficiency model of a hydraulic axial
piston motors. Proceedings of the 6th JFPS International
symposium on fluid power, TSUKUBB, 284–290. 2A3–1,
Japan Fluid Power System Society - JFPS.
Kluger, M.A., Fussner, D.R., and Roethler, B., 1996. A
performance comparison of various automatic transmission
pumping systems. SAE International congress &
exposition, Detroit, US, 33–40. doi:10.1016/S0940-2993
KohmäScher, T., et al., 2007. Improved loss modeling of
hydrostatic units: requirement for precise simulation of
mobile working machine drivelines. In: ASME 2007
International mechanical engineering congress and exposition
volume 4: design, analysis, control and diagnosis of
fluid power systems, ASME, Seattle, WA.
Manring, N.D., 2005a. Hydraulic control systems. US: John
Wiley & Sons.
Manring, N.D., 2005b. Measuring pump efficiency: uncertainty
considerations. Journal Energy Resources
Technological, 127 (4), 280–284. doi:10.1115/1.1926311
Manring, N.D., 2016. Mapping the efficiency for a hydrostatic
transmission. Journal of Dynamic Systems,
Measurement, and Control, 138, 0310041–0310048.
McCandlish, D. and Dorey, R.E., 1984. The mathematical
modeling of hydrostatic pumps and motors. Proceedings
of the Institution of Mechanical Engineers, 198B (10),
Merritt, H.E., 1967. Hydraulic control systems. US: John
Wiley & Sons.
Sauer-Danfoss, 2010. Series 40 axial piston pumps technical
information. US. October. 520L0635 Rev EJ - Sauer-
Stringer, J., 1976. Hydraulic system analysis: an introduction.
US: John Wiley & Sons.
Szpak, Z.L., Chojnacki, W., and Van Den Hengel, A., 2012.
Guaranteed ellipse fitting with the Sampson distance.
Proceedings of the 12th European conference on computer
vision, Part V, 7–13 October. Florence, Italy.
Tessmann, R.K., 1979. A leakage path model for a hydraulic
pump. The B.F.P.R Journal, 12 (1), 5–9.
Watton, J., 2009. Fundamentals of fluid power control.
Cambridge University Press, UK.
Wilson, W.E., 1946. Rotary-pump theory. ASME
Transactions, 68, 371–384.
Wilson, W.E., 1949. Performance criteria for positive-displacement
pumps and fluid motors. ASME Transactions,
Zarotti, G.L. and Nervegna, N., 1981. Pump efficiencies
approximation and modelling. 6th International fluid
power symposium, Paper C4, Cambridge, UK. 145–164.