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1. 北京航空航天大学中法工程师学院, 北京 100083;
2. 中航工业金城南京机电液压工程研究中心, 南京 211140

Oil film analysis of swash plate/slipper pair based on CFD
MA Jiming1 , SHEN Yayong1, LI Qilin2
1. Sino-French Engineer School, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;
2. Jincheng Nanjing Electrical and Hydraulic Engineering Research Center of AVIC, Nanjing 211140, China
Abstract: The 3-D Navier-Stokes equations and arbitrary Lagrangian-Eulerian (ALE) method are firstly used to present the oil film analysis method based on computational fluid dynamics (CFD), which can describe the correlation among slipper structure parameters, running conditions and oil film thickness. Then, the oil film thicknesses of a slipper bearing under 24 different running conditions are obtained by simulation method. A function is consequently obtained based on the simulation results, which can express the relationships between running conditions (temperature, rotation speed, and outlet preesure) and oil film thickness. Furthermore, an equation of hydraulic dynamic parameter is provided and used to express the oil film thickness analytically. Based on the CFD simulation results, the parameter is proven to be only related with the oil viscosity (temperature) under fixed design structure, and unrelated with other running conditions, such as rotation, pressure, and so on. It is convenient for designer to derive the oil film thickness expression equation. Finally, we compared the oil film thicknesses obtained from analytical and CFD methods, and the results show that the presented method is feasible.
Key words: piston pump     swash plate/slipper pair     oil film     computational fluid dynamics     lubrication
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1 滑靴副油膜特性分析流程

 图 1 柱塞/滑靴装配件 Fig. 1 Piston/slipper assembly

 图 2 滑靴副油膜厚度分析流程 Fig. 2 Oil film thickness analysis procedure of slipper pair

2 基于CFD的油膜厚度计算 2.1 计算域描述及控制方程

 图 3 滑靴副结构示意图 Fig. 3 Computational domain of slipper structure

u(x,y,z,0)=w(x,y,z,0)

uA(x,y,z,t)=w(x,y,z,t)

uB(x,y,z,t)=0

pinin(x,y,z,t)·n

poutout(x,y,z,t)·n

w(x,y,z,t)=dr/dt,r·w=0,r×w=rω

2.2 ALE描述下的计算域与驱动方程

ALE方法融合了拉格朗日描述和欧拉描述[30],是处理自由边界和动边界问题的有效方法[27, 31]。由于滑靴副CFD仿真考虑了柱塞泵的旋转等诸多因素,导致滑靴副计算域的边 界条件较为复杂。通过ALE方法可将动边界问题转化为静止边界问题,使问题简化。

g(x,y,z,t)是欧拉描述下的方程,ALE描述方法将方程从欧拉描述的坐标系(x,y,z)转换到参考坐标系(xr,yr,zr)中,ALE转换见式(3)、式(4)[27]

ALE描述下滑靴副的边界条件如下。

u(x,y,z,0)=0

uA(xr,yr,zr,t)=0

uB(x,y,z,t)=wr(xr,yr,zr,t)

pinin(xr,yr,zr,t)·n

poutout(xr,yr,zr,t)·n

wr(xr,yr,zr,t)=dr/dt
r·wr=0,r×wr=rω

2.3 解算方法

2.4 滑靴副网格划分与CFD仿真

 图 4 滑靴副CFD仿真的几何模型网格划分 Fig. 4 Geometrical mesh of CFD model of slipper pair

 图 5 滑靴副压力分布 Fig. 5 Pressure distribution of slipper pair
2.5 油膜厚度的计算结果

 图 6 工况对滑靴副油膜压力分布的影响 Fig. 6 Effect of running condition on oil film pressure distribution of slipper pair

 图 7 24种工况下的滑靴分离力 Fig. 7 Separation force on slipper under 24 different running conditions

 图 8 油膜厚度与工况关系 Fig. 8 Relationship between oil film thickness and running condition
3 油膜厚度的影响因素分析 3.1 液动力参数

 图 9 24种工况下液动力参数G Fig. 9 Hydrodynamic parameter G under 24 different running conditions

3.2 基于液动力参数的油膜厚度分析

 图 10 40℃时CFD与式(15)计算的油膜厚度h Fig. 10 Oil film thickness h obtained from CFD and Eq. (15) (temperature=40℃)
4 结 论

1) 基于CFD和数值仿真方法开展柱塞泵滑靴副油膜特性分析,可以综合考虑滑靴副结构形式、尺寸参数和环境工况对油膜的综合影响,具有全面性。其中基于液动力参数的油膜厚度分析方法,通过解析手段定量直观描述油膜厚度与工况参数之间的函数关系。

2) 在滑靴副结构尺寸固定的情况下,滑靴副油膜厚度与环境工况之间的关系可以通过液动力参数进行定量描述。针对特定的滑靴副,液动力参数只与介质温度(黏度)相关。

3) 鉴于通过实验手段直接测量滑靴副油膜特性难度较大,本文关于油膜厚度的分析结论可以通过对比不同工况下的磨损情况(和油膜厚度密切相关)进行验证。

 [1] 张斌. 轴向柱塞泵的虚拟样机及油膜压力特性研究[D].杭州:浙江大学,2009:75-97. ZHANG B.Study on virtual prototype and pressure characteristics of oil film for axial piston pump[D].Hangzhou:Zhejiang University,2009:75-97(in Chinese). Cited By in Cnki (43) [2] 李迎兵. 轴向柱塞泵滑靴油膜特性研究[D].杭州:浙江大学,2011:23-35. LI Y B.Study on characteristics of oil film for slipper pair of axial piston pumps[D].Hangzhou:Zhejiang University,2011:23-35(in Chinese). Cited By in Cnki (10) [3] HOOKE C J,LI K Y.The lubrication of slippers in axial piston pumps and motors-the effect of tilting couples[J].Journal of Mechanical Engineering Science,1989,203(53):343-350. Click to display the text [4] KOC E,HOOKE C J.Considerations in the design of partially hydrostatic slipper bearings[J].Tribology International,1997,30(11):815-823. Click to display the text [5] MANRING N D,WRAY C L, DONG Z.Experimental studies on the performance of slipper bearings within axial piston pumps[J].Journal of Tribology,2004,126(3):511-518. Click to display the text [6] CANBULUT F. The experimental analyses of the effects of the geometric and working parameters on the circular hydrostatic thrust bearings[J].JSME International Journal,2005,48(4):715-722. Click to display the text [7] FISHER M J. A theoretical determination of some characteristics of a tilted hydrostatic slipper bearing[R].[S.l.]:British Hydromechanics Research Association,1962. [8] 庄欠伟,周华,艾青林.轴向柱塞泵滑靴副润滑特性实验台的研制[J].机床与液压,2005(3):113-115. ZHUANG Q W,ZHOU H,AI Q L.Development of experiment rig for lubricate film of the slipper pad in axial piston pumps[J].Machine Tools & Hydraulics,2005(3):113-115(in Chinese). Cited By in Cnki (11) [9] 艾青林,周华,张增猛,等.轴向柱塞泵配流副与滑靴副润滑特性试验系统的研制[J].液压与气动,2004(11):22-25. AI Q L,ZHOU H,ZHANG Z M, et al.Development of lubricating characteristics testing system of friction pair in axial piston pump[J].Chinese Hydraulics & Pneumatics,2004(11):22-25(in Chinese). Cited By in Cnki (30) [10] NIE L, HUANG G H,LI Y R.Tribological study on hydrostatic slipper bearing with annular orifice damper for water hydraulic axial piston motor[J].Tribology International,2006,39(11):1342-1354. Click to display the text [11] 马纪明,李齐林,任春宇,等.轴向柱塞泵/滑靴副润滑磨损的影响因素分析[J].北京航空航天大学学报,2015,41(3):405-410. MA J M,LI Q L,REN C Y,et al.Influence factors analysis on wear of hydraulic axial piston pump/slipper pair[J].Journal of Beijing University of Aeronautics and Astronautics,2015,41(3):405-410(in Chinese). Cited By in Cnki (2) [12] MA J M,CHEN J,LI J.Wear analysis of swash plate/slipper pair of axis piston hydraulic pump[J].Tribology International,2015,90:467-472. Click to display the text [13] IBOSHI N,YAMAGUCHI A.Characteristics of a slipper bearing for swash plate type axial piston pumps and motors,theoretical analysis[J].Bulletin of the JSME,1982,25(428):1921-1930. [14] IBOSHI N. Characteristics of a slipper bearing for swash plate type axial piston pumps and motors,design method for a slipper with a minimum power loss in fluid lubrication[J].Bulletin of the JSME,1986,129(254):2529-2538. [15] BERGADA J M,KUMAR S,DAVIES D L,et al.A complete analysis of axial piston pump leakage and output flow ripples[J].Applied Mathematical Modeling,2012,36(4):1731-1751. Click to display the text [16] SCHENK A,IVANTYSYNOVA M.A transient fluid structure interaction model for lubrication between the slipper and swash plate in axial piston machines[C]//Proceedings of the 9th International Fluid Power Conference(9IFK),2014,1:398-409. [17] KAZAMA T,YAMAGUCHI A.Application of a mixed lubrication model for hydrostatic equipment[J].Journal of Tribology,1993,115(4):686-691. Click to display the text [18] FANG Y,SHIRAKASHI M.Mixed lubrication characteristics between the piston and cylinder in hydraulic piston pump-motor[J].Journal of Tribology,1995,117(1):80-85. Click to display the text [19] BERGADA J M,WATTON J,KUMMAR S.Pressure,flow,force,and torque between the barrel and port plate in an axial piston pump[J].Journal of Dynamic Systems Measurement and Control,2008,130(1):141-148. Click to display the text [20] 王彬,周华,杨华勇.轴向柱塞泵配流副油膜试验原理及控制特性[J].机械工程学报,2009,45(11):113-118. WANG B,ZHOU H,YANG H Y.Principle of oil film test on port pair of axial piston pump and control characteristics[J].Journal of Mechanical Engineering,2009,45(11):113-118(in Chinese). Cited By in Cnki (7) [21] BRAIDIC-MITIDIERI P,GOSMAN A D,IOANNIDES E,et al.CFD analysis of a low friction pocketed pad bearing[J].Journal of Tribology,2005,127(4):803-812. Click to display the text [22] HOUZEAUX G,CODINA R.A finite element method for the solution of rotary pumps[J].Computers & Fluids,2007,36(4):667-679. Click to display the text [23] KUMAR S,BERGADA J M,WATTON J.Axial piston pump grooved slipper analysis by CFD simulation of three-dimensional NVS equation in cylindrical coordinates[J].Computers & Fluids,2009,38(3):648-663. Click to display the text [24] KUMAR S. CFD analysis of an axial piston pump[D].Barcelona:Universidad Politecnica de Catalunya,2010:45-86. [25] ALMQVIST T,ALMQVIST A,LARSSON R.A comparison between computational fluid dynamic and Reynolds approaches for simulating transient EHL line contact[J].Tribology International,2004,37(1):61-69. Click to display the text [26] GUO Z,HIRANO T,KIRK R G.Application of CFD analysis for rotating machinery,Part 1:Hydrodynamic,hydrostatic bearings and squeeze film damper[J].ASME,2003,4(1):651-659. Click to display the text [27] DUARTE F,GORMAZ R,NATESAN S.Arbitrary Lagrangian-Eulerian method for Navier-Stokes equations with moving boundaries[J].Computer Methods in Applied Mechanics and Engineering,2004,193(45-47):4819-4836. Click to display the text [28] 张兆顺. 流体力学[M].北京:清华大学出版社,2006:53-55. ZHANG Z S.Fluid mechanics[M].Beijing:Tsinghua University Press,2006:53-55(in Chinese). [29] 李玉琳. 液压元件与系统设计[M].北京:北京航空航天大学出版社,1991:13-14. LI Y L.Hydraulic components and system design[M].Beijing:Beihang University Press,1991:13-14(in Chinese). [30] HIRT C W,AMSDEN A A,COOK J L.An arbitrary Lagrangian-Eulerian computing method for all flow speeds[J].Journal of Computational Physics,1974,14(2):227-253. Click to display the text [31] SOULAIMANI A,SAADB Y.An arbitrary Lagrangian-Eulerian finite element method for solving three-dimensional free surface flows[J].Computer Methods in Applied Mechanics and Engineering,1998,162(1-4):79-106. Click to display the text [32] CODINA R,ZIENKIEWICZ O C.CBS versus GLS stabilization of the incompressible Navier-Stokes equations and the role of the time step as stabilization parameter[J].Communications in Numerical Methods in Engineering,2002,18(2):99-112. Click to display the text

#### 文章信息

MA Jiming, SHEN Yayong, LI Qilin

Oil film analysis of swash plate/slipper pair based on CFD

Journal of Beijing University of Aeronautics and Astronsutics, 2016, 42(2): 265-272.
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0107