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

doi:10.1007/s11465-021-0671-1

Front. Mech. Eng.

2022, Vol. 17

Issue (2) : 15 https://doi.org/10.1007/s11465-021-0671-1

RESEARCH ARTICLE

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

Qun CHAO^1,²(

), Jianfeng TAO¹, Chengliang LIU¹, Zhengliang LI³

¹. State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
². State Key Laboratory of Fluid Power and Mechatronic Systems, School of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China
³. Liyuan Hydraulic (Suzhou) Co., Ltd., Suzhou 215131, China

Download: PDF(4793 KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

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.

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

Corresponding Author(s): Qun CHAO

About author:

Tongcan Cui and Yizhe Hou contributed equally to this work.

Just Accepted Date: 18 March 2022 Issue Date: 29 April 2022

Cite this article:

Qun CHAO,Jianfeng TAO,Chengliang LIU, et al. Development of an analytical model to estimate the churning losses in high-speed axial piston pumps[J]. Front. Mech. Eng., 2022, 17(2): 15.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-021-0671-1
https://academic.hep.com.cn/fme/EN/Y2022/V17/I2/15

Fig.1 Power losses in three commercial axial piston motors at variable rotational speeds.

Fig.3 Schematic of the rotating parts immersed in oil.

Tab.1 Geometric dimensions of the rotating parts [17]

Fig.4 Photos of (a) specific churning test rig and (b) simplified rotating parts.

Fig.5 Mean squared error of the drag torque acting on the cylinder block as a function of coefficient λ₂.

Fig.6 Drag torque acting on the cylinder block—Comparisons between different analytical models and the experimental measurements in Ref. [17].

Fig.7 Radial gap effects on the drag coefficient of the cylinder block.

Fig.8 Fitting curve of f(Re_p) versus the nominal Reynolds number.

Fig.9 Drag torque acting on the pistons—Comparisons between different analytical models and the experimental measurements in Ref. [17].

Fig.10 Shielding effects on the reduction in piston drag coefficient.

Tab.2 Statistical results of k_p for a series of commercial axial piston pumps

Fig.11 Comparison of the total drag torque acting on the cylinder block and pistons between the presented analytical model and experimental measurements in Ref. [17].

C_dc	Drag coefficient of the cylinder block
C_dp	Drag coefficient of a single piston
C_D	Reynolds number-related drag coefficient of a single circular cylinder
d_p	Piston diameter
f(Re_p)	A function of the Reynolds number
k_p	Dimensionless relative gap between two adjacent pistons
k_r	Dimensionless relative gap between the pump casing and the cylinder block
L_c	Cylinder block length
L_p	Piston length
m	Number of operating points
N	Piston number
R_c	Cylinder block external radius
R_ca	Casing internal radius
R_p	Piston pitch circle radius
Re_c	Reynolds number associated with the cylinder block rotation
Re_p	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
T_c	Drag torque acting on the rotating cylinder block
T_cm	Calculated drag torque acting on the cylinder block at rotational speed of $ω m$
$T c m ′$	Measured drag torque acting on the cylinder block at rotational speed of $ω m$
T_p	Calculated drag torque acting on all pistons
$T p ′$	Measured drag torque acting on all pistons
V_c	Cylinder block volume
V_oil	Casing fluid volume
ζ	Volume ratio between the casing fluid and the cylinder block
λ_i (i = 1, 2, …, 6)	Constant coefficients determined from experimental data in principle
$ν$	Kinematic viscosity
ρ	Fluid density
$ω$	Rotational speed

1	Q Chao , J H Zhang , B Xu , H P Huang , M Pan . A review of high-speed electro-hydrostatic actuator pumps in aerospace applications: challenges and solutions. Journal of Mechanical Design, 2019, 141( 5): 050801 https://doi.org/10.1115/1.4041582
2	Q Chao , J H Zhang , B Xu , Q N Wang , F Lyu , K Li . Integrated slipper retainer mechanism to eliminate slipper wear in high-speed axial piston pumps. Frontiers of Mechanical Engineering, 2022, 17( 1): 1
3	Q Chao , J F Tao , J B Lei , X L Wei , C L Liu , Y H Wang , L H Meng . Fast scaling approach based on cavitation conditions to estimate the speed limitation for axial piston pump design. Frontiers of Mechanical Engineering, 2021, 16( 1): 176– 185 https://doi.org/10.1007/s11465-020-0616-0
4	H Olsson. Power losses in an axial piston pump used in industrial hydrostatic transmissions. In: Proceedings of the 8th Scandinavian International Conference on Fluid Power. Tampere, 2003
5	H Theissen , S Gels , H Murrenhoff . Reducing energy losses in hydraulic pumps. In: Proceedings of the 8th International Conference on Fluid Power Transmission and Control. Hangzhou, 2013, 77– 81
6	M Zecchi , A Mehdizadeh , M Ivantysynova . A novel approach to predict the steady state temperature in ports and case of swash plate type axial piston machines. In: Proceedings of the 13th Scandinavian International Conference on Fluid Power. Linköping, 2013, 177– 187 https://doi.org/10.3384/ecp1392a18
7	B Xu , M Hu , J H Zhang , Q Su . Characteristics of volumetric losses and efficiency of axial piston pump with respect to displacement conditions. Journal of Zhejiang University-SCIENCE A, 2016, 17( 3): 186– 201 https://doi.org/10.1631/jzus.A1500197
8	M D Gao , H H Huang , X Y Li , Z F Liu . A novel method to quickly acquire the energy efficiency for piston pumps. Journal of Dynamic Systems, Measurement, and Control, 2016, 138( 10): 101004 https://doi.org/10.1115/1.4033840
9	H S Tang , Y Ren , J W Xiang . Power loss characteristics analysis of slipper pair in axial piston pump considering thermoelastohydrodynamic deformation. Lubrication Science, 2019, 31( 8): 381– 403 https://doi.org/10.1002/ls.1479
10	M M Zdravkovich . The effects of interference between circular cylinders in cross flow. Journal of Fluids and Structures, 1987, 1( 2): 239– 261 https://doi.org/10.1016/S0889-9746(87)90355-0
11	P Hishikar S K Dhiman A K Tiwari V K Gaba. Analysis of flow characteristics of two circular cylinders in cross-flow with varying Reynolds number: a review. Journal of Thermal Analysis and Calorimetry, 2022, 147(10): 5549– 5574
12	S V Singh , P Mitra , P Kumar . A study of flow interference and heat transfer between two-cylinders at different orientations. Journal of Ocean Engineering and Science, 2021, 6( 3): 248– 256 https://doi.org/10.1016/j.joes.2021.01.001
13	Z J Yang , X K Wang , J H Si , Y L Li . Flow around three circular cylinders in equilateral-triangular arrangement. Ocean Engineering, 2020, 215 : 107838 https://doi.org/10.1016/j.oceaneng.2020.107838
14	J J Yin , T Jia , D Gao , F Xiao . Numerical investigation of the patterns of the flow past nine cylinders at low Reynolds number. AIP Advances, 2020, 10( 8): 085107 https://doi.org/10.1063/5.0015541
15	R Rahmfeld , S Marsch , W Göllner , T Lang , T Dopichay , J Untch . Efficiency potential of dry case operation for bent-axis motors. In: Proceedings of the 8th International Fluid Power Conference. Dresden, 2012, 2 : 73– 86
16	B Xu , J H Zhang , Y Li , Q Chao . Modeling and analysis of the churning losses characteristics of swash plate axial piston pump. In: Proceedings of the 2015 International Conference on Fluid Power and Mechatronics (FPM). Harbin: IEEE, 2015, 22– 26 https://doi.org/10.1109/FPM.2015.7337078
17	J H Zhang , Y Li , B Xu , M Pan , F Lv . Experimental study on the influence of the rotating cylinder block and pistons on churning losses in axial piston pumps. Energies, 2017, 10( 5): 662 https://doi.org/10.3390/en10050662
18	C B Jing , J J Zhou , J C Zhou . Experimental study of churning losses in swash plate axial piston pump. Journal of Beijing Institute of Technology, 2019, 28( 3): 529– 535 https://doi.org/10.15918/j.jbit1004-0579.18029
19	D Hasko , L Z Shang , E Noppe , E Lefrançois . Virtual assessment and experimental validation of power loss contributions in swash plate type axial piston pumps. Energies, 2019, 12( 16): 3096 https://doi.org/10.3390/en12163096
20	J H Zhang , Y Li , B Xu , X Chen , M Pan . Churning losses analysis on the thermal-hydraulic model of a high-speed electro-hydrostatic actuator pump. International Journal of Heat and Mass Transfer, 2018, 127 : 1023– 1030 https://doi.org/10.1016/j.ijheatmasstransfer.2018.06.133
21	G A Moslått , M R Hansen , N S Karlsen . A model for torque losses in variable displacement axial piston motors. Modeling, Identification and Control, 2018, 39( 2): 107– 114 https://doi.org/10.4173/mic.2018.2.5
22	Y Huang , J Ruan , C C Zhang , C Ding , S Li . Research on the mechanical efficiency of high-speed 2D piston pumps. Processes, 2020, 8( 7): 853 https://doi.org/10.3390/pr8070853
23	Y Huang , C Ding , H Y Wang , J Ruan . Numerical and experimental study on the churning losses of 2D high-speed piston pumps. Engineering Applications of Computational Fluid Mechanics, 2020, 14( 1): 764– 777 https://doi.org/10.1080/19942060.2020.1763468
24	G Bohach. A study and optimization of a radial ball piston pump for high-speed applications. Thesis for the Master’s Degree. Minneapolis: University of Minnesota, 2021
25	Hannifin Parker. Hydraulic Saw Motor: Series F11/F12 Fixed Displacement. 2018
26	J H Zhang , Y Li , B Xu , M Pan , Q Chao . Experimental study of an insert and its influence on churning losses in a high-speed electro-hydrostatic actuator pump of an aircraft. Chinese Journal of Aeronautics, 2019, 32( 8): 2028– 2036 https://doi.org/10.1016/j.cja.2018.10.003
27	Y Li , B Xu , J H Zhang , X Chen . Experimental study on churning losses reduction for axial piston pumps. In: Proceedings of the 11th International Fluid Power Conference. Aachen, 2018, 272– 280
28	C J Hooke , K Y Li . The lubrication of overclamped slippers in axial piston pumps—centrally loaded behaviour. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 1988, 202( 4): 287– 293 https://doi.org/10.1243/PIME_PROC_1988_202_121_02
29	E Bilgen , R Boulos . Functional dependence of torque coefficient of coaxial cylinders on gap width and Reynolds numbers. Journal of Fluids Engineering, 1973, 95( 1): 122– 126 https://doi.org/10.1115/1.3446944
30	A L Gerhart J I Hochstein P M Gerhart. Munson, Young and Okiishi’s Fundamentals of Fluid Mechanics. 9th ed. Singapore: John Wiley & Sons, 2021
31	S W Chen , S Matsumoto . Influence of relative position of gears and casing wall shape of gear box on churning loss under splash lubrication condition—some new ideas. Tribology Transactions, 2016, 59( 6): 993– 1004 https://doi.org/10.1080/10402004.2015.1129568
32	C Changenet , P Velex . Housing influence on churning losses in geared transmissions. Journal of Mechanical Design, 2008, 130( 6): 062603 https://doi.org/10.1115/1.2900714
33	R Quiban , C Changenet , Y Marchesse , F Ville . Experimental investigations about the power loss transition between churning and windage for spur gears. Journal of Tribology, 2021, 143( 2): 024501 https://doi.org/10.1115/1.4047949
34	C P Enekes. Measures to increase the efficiency of axial piston machines. Dissertation for the Doctoral Degree. Aachen: RWTH Aachen University, 2012 (in German)

[1]	Qun CHAO, Haohan GAO, Jianfeng TAO, Chengliang LIU, Yuanhang WANG, Jian ZHOU. Fault diagnosis of axial piston pumps with multi-sensor data and convolutional neural network[J]. Front. Mech. Eng., 2022, 17(3): 36-.
[2]	Qun CHAO, Junhui ZHANG, Bing XU, Qiannan WANG, Fei LYU, Kun LI. Integrated slipper retainer mechanism to eliminate slipper wear in high-speed axial piston pumps[J]. Front. Mech. Eng., 2022, 17(1): 1-.
[3]	Qun CHAO, Jianfeng TAO, Junbo LEI, Xiaoliang WEI, Chengliang LIU, Yuanhang WANG, Linghui MENG. Fast scaling approach based on cavitation conditions to estimate the speed limitation for axial piston pump design[J]. Front. Mech. Eng., 2021, 16(1): 176-185.

Viewed

Full text

Abstract

Cited

Shared

Discussed