Approximate analytical solution of the Reynolds equation for clearance flow with pressure difference boundary conditions
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摘要: 为了获得间隙密封、滑动轴承等的液膜压力分布解析表达式,将间隙流动雷诺方程的解析解表示为特解和通解之和,其中特解表示为周向坐标函数和轴向坐标函数之和,通解表示为周向坐标函数和轴向坐标函数之积,结合分离变量法和非零压差边界条件,推导获得间隙流动雷诺方程的近似解析解。基于近似解析解计算间隙密封的液膜承载力和偏位角等参数,并与采用有限差分法的计算结果对比,其中液膜承载力偏差小于5%,偏位角偏差小于3°,而计算效率提高了数百倍。Abstract: In order to obtain the lubricant pressure distribution for clearance seal and finite length journal bearing, the Reynolds equation with pressure difference boundary conditions was solved analytically.Using the method of separation of variables in an additive and a multiplicative form, a set of particular solutions of the Reynolds equation was added in the general solution of the homogenous Reynolds equation,thus a closed form approximate analytical solution for Reynolds equation was presented.The load capacity and attitude angle of clearance seal were calculated according to the approximate analytical solution proposed, the load capacity error compared with the result calculated with finite difference method was less than 5%,and the attitude angle error was less than 3 degree and the computational efficiency increased by hundreds of times.
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[1] DUBOIS G B,OCVIRK F W.Analytical derivation and experimental evaluation of short bearing approximation of full journal bearings[R].NACA Technical Report-1157,1953. [2] SOMMERFELD A.The hydrodynamic theory of lubrication friction[J].Zeitschriftfür Angewandte Mathematik und Physik,1904,50(1/2):97-155. [3] DAGOSTINO V,SENATORE A.Analytical solution for twodimesnsional Reynolds equation for porous journal bearings[J].Industrial Lubrication and Tribology,2006,58(2):110-117. [4] WANG Y L,LIU Z S,KANG W J,et al.Approximate analytical model for fluid film force of finite length plain journal bearing[J].Journal of Mechanical Engineering Science,2011,226(5):1345-1355. [5] 王永亮,刘占生.圆瓦滑动轴承油膜力近似解析模型[J].中国电机工程学报,2011,31(29):110-117.WANG Yongliang,LIU Zhansheng.Approximate analytical model of oilfilm force for cylindrical journal bearing[J].Proceedings of CSEE,2011,31(29):101-117.(in Chinese) [6] 王永亮,刘占生,钱大帅,等.有限长椭圆瓦轴承油膜力近似解析模型[J].航空动力学报,2012,27(2):265-274.WANG Yongliang,LIU Zhansheng,QIAN Dashuai,et al.Approximate analyitical model of oilfilm force for finite length elliptical journal bearing[J].Journal of Aerospace Power,2012,27(2):265-274.(in Chinese) [7] VIGNOLO G G,BARILA D O,QUINZANI L M.Approximate analytical solution to Reynolds equation for finite length journal bearings[J].Tribology International,2011,44(10):1089-1099. [8] ZHANG Yongfang,HEI Di,LIU Cheng,et al.An approximate solution of oil film forces of turbulent finite length journal bearing[J].Tribology International,2014,74(4):110-120. [9] SFYRIS D,CHASALEVRIS A.An exact analytical solution of the Reynolds equation for the finite journal bearing lubrication[J].Tribology International,2012,55(4):46-58. [10] CHASALEVRIS A.Analytical evaluation of the static and dynamic characteristics of threelobe journal bearings with finite length[J].Journal of Tribology,2015,137(4):157-201. [11] KANEKO S.Study of the mechanism of lubrication in porous journal bearings:effects of dimensionless oilfeed pressure on static characteristics under hydrodynamic lubrication conditions[J].Journal of Tribology,1994,116(3):606-611. [12] KANEKO S,HASHIMOTO Y.Study of the mechanism of lubrication in porous journal bearings:effects of dimensionless oilfeed pressure on frictional characteristics[J].Journal of Tribology,1995,117(2):2812-2817. [13] 王丽丽,路长厚,张建川,等.高速螺旋油楔滑动轴承空穴机理的实验研究[J].振动与冲击,2012,31(5):1-6.WANG Lili,LU Changhou,ZHANG Jianchuan,et al.Experimental in vestigation on cavitation mechanism of a high speed spiral oil wedge journal bearing[J].Journal of Vibration and Shock,2012,31(5):1-6.(in Chinese) [14] DAI Huiliang,YAO Lijuan,PENG Jinli.Carrying capacity study of liquid hybrid bearing based on fluent[J].Hydromechatronics Engineering,2016,44(12):110-115. [15] 康召辉,任兴民,何尚文,等.浮环涡动对浮动环轴承油膜压力分布影响的研究[J].航空动力学报,2010,25(5):1197-1202.KANG Zhaohui,REN Xingmin,HE Shangwen,et al.Study on the effect of whirling motion of the floating ring on distribution of oil pressure in a floating ring bearing[J].Journal of Aerospace Power,2010,25(5):1197-1202.(in Chinese) [16] 马纲,席平,沈心敏,等.柔性支承浮环柱面气膜密封准动态特性分析[J].航空动力学报,2010,25(5):1190-1196.MA Gang,XI Ping,SHEN Xinmin,et al.Analysis of quasidynamic characteristics of compliant floating ring gas cylinder seal[J].Journal of Aerospace Power,2010,25(5):1190-1196.(in Chinese) [17] 谢鸿政,杨枫林.数学物理方程[M].北京:科学出版社,2001. [18] SZERI A Z.Fluid film lubrication[M].2nd ed.New York,USA:Cambridge University Press,2011. [19] VOGELPOHL G.Zur integration der Reynoldsschen gleichung für das zapfenlager endlicher breite[J].Ingenieur Archiv,1943,14(3):192-212.
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