Development of an analytical model to estimate the churning losses in high-speed axial piston pumps

Abstract

The axial piston pumps in aerospace applications are often characterized by high-speed rotation to achieve great power density. However, their internal rotating parts are fully immersed in the casing oil during operation, leading to considerable churning losses (more than 10% of total power losses) at high rotational speeds. The churning losses deserve much attention at the design stage of high-speed axial piston pumps, but accurate analytical models are not available to estimate the drag torque associated with the churning losses. In this paper, we derive the analytical expressions of the drag torque acting on the key rotating parts immersed in oil, including the cylinder block and the multiple pistons in a circular array. The calculated drag torque agrees well with the experimental data over a wide range of rotational speeds from 1500 to 12000 r/min. The presented analytical model provides practical guidelines for reducing the churning losses in high-speed axial piston pumps or motors.

Graphical abstract

Keywords

axial piston pump / rotating parts / high rotational speed / churning losses / drag torque

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Nomenclature

Cdc	Drag coefficient of the cylinder block
Cdp	Drag coefficient of a single piston
CD	Reynolds number-related drag coefficient of a single circular cylinder
dp	Piston diameter
f(Rep)	A function of the Reynolds number
kp	Dimensionless relative gap between two adjacent pistons
kr	Dimensionless relative gap between the pump casing and the cylinder block
Lc	Cylinder block length
Lp	Piston length
m	Number of operating points
N	Piston number
Rc	Cylinder block external radius
Rca	Casing internal radius
Rp	Piston pitch circle radius
Rec	Reynolds number associated with the cylinder block rotation
Rep	Nominal Reynolds number of a single piston
R(ζ)	Remainder term of the Maclaurin series
t	Gap height between the cylinder block and the casing
Tc	Drag torque acting on the rotating cylinder block
Tcm	Calculated drag torque acting on the cylinder block at rotational speed of {\omega }_m
T_{\text{c}m}^{\prime }	Measured drag torque acting on the cylinder block at rotational speed of {\omega }_m
Tp	Calculated drag torque acting on all pistons
T_{\text{p}}^{\prime }	Measured drag torque acting on all pistons
Vc	Cylinder block volume
Voil	Casing fluid volume
ζ	Volume ratio between the casing fluid and the cylinder block
λi (i = 1, 2, …, 6)	Constant coefficients determined from experimental data in principle
\nu	Kinematic viscosity
ρ	Fluid density
\omega	Rotational speed

Acknowledgements

This study was supported by the National Key R&D Program of China (Grant No. 2021YFB2011902), the National Natural Science Foundation of China (Grant No. 52005323), the National Postdoctoral Program for Innovative Talents (Grant No. BX20200210), and the China Postdoctoral Science Foundation (Grant No. 2019M660086).

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