点接触EHL二次压力峰和中心压力拟合公式
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摘要
基于求解点接触弹流润滑(EHL)问题的高效直接算法,研究了点接触EHL状态下载荷、速度、材料参数对二次压力峰和中心压力的影响,在对大量数值解结果进行分析和回归的基础上,给出了二次压力峰和中心压力对载荷、速度、材料参数关系的拟合公式,并对拟合公式的精确性进行了检验,结果显示,在相当宽的参数范围内,所提出的拟合公式的计算结果与数值解的相对误差小于10%,为研究零件在点接触EHL状态下的最大应力及疲劳寿命预测提供了一个简单而实用的工具。
This paper presents a study on the effect of operating parameters on the pressure spike and central pressure under point contact Elastohydrodynamic Lubrication( EHL) state with a high effective iterative algorithm.Through making regression analysis for a amount of numerical results,two simple fitting formulas of pressure spike and central pressure are proposed for the operating parameters( dimensionless load, speed, and material parameter). The accuracy of the formulas is examined and it shows that in a wide range of operating parameters,the relative error between the fitting formulas and numerical solution is less 10 than percent. The current study provides a simple and useful tool for calculating maximum stress and fatigue life prediction of mechanical parts working under the point contact EHL state.
This paper presents a study on the effect of operating parameters on the pressure spike and central pressure under point contact Elastohydrodynamic Lubrication( EHL) state with a high effective iterative algorithm.Through making regression analysis for a amount of numerical results,two simple fitting formulas of pressure spike and central pressure are proposed for the operating parameters( dimensionless load, speed, and material parameter). The accuracy of the formulas is examined and it shows that in a wide range of operating parameters,the relative error between the fitting formulas and numerical solution is less 10 than percent. The current study provides a simple and useful tool for calculating maximum stress and fatigue life prediction of mechanical parts working under the point contact EHL state.
引文
[1]刘坤,吴磊.ANSYS有限元方法精解[M].北京:国防工业出版社,2005Liu K,Wu L.ANASYS finite element method solution[M].Beijing:National Defence Industry Press,2005(in Chinese)
[2]Brebbia C A.The boundary element method for engineers[M].London:Pentech Press,1978
[3]王丽彪,任家骏,吴风林,等.三维弹性接触问题边界元法的研究[J].山西机械,2001,(1):6-7,10Wang L B,Ren J J,Wu F L,et al.Research on the boundary element of three dimensional elastic contact problem[J].Shanxi Machinery,2001,(1):6-7,10(in Chinese)
[4]Dowson D,Higginson G R.Elastohydrodynamic lubrication[M].Oxford:P ergam on P ress,1 9 6 6
[5]温诗铸,杨沛然.弹性流体动力润滑[M].北京:清华大学出版社,1992Wen S Z,Yang P R.Elastohydronamic lubrication[M].Beijing:Tsinghua University Press,1992(in Chinese)
[6]Houpert L,Ioannides E,Kuypers J C,et al.The effect of the EHD pressure spike on rolling bearing fatigue[J].Journal of Tribology,1987,109(3):444-450
[7]Bissett E J,Glander D W.A highly accurate approach that resolves the pressure spike of elastohydrodynamic lubrication[J].Journal of Tribology,1988,110(2):241-246
[8]Hamrock B J,Pan P,Lee R T.Pressure spikes in elastohydrodynamically lubricated conjunctions[J].Journal of Tribology,1988,110(2):279-284
[9]Venner C H,Ten Napel W E.Numerical calculations of the pressure spike in elastohydrodynamic lubrication[J].Lubrication Science,1990,2(4):321-335
[10]Hamrock B J,Lee R T,Houpert L G.Paper VII(i)Parametric study of performance parameters in elastohydrodynamic lubricated line contacts[C]//Proceedings of the 13th Leeds-Lyon Symposium on Tribology.Leeds:The University of Leeds,1987,11:199-206
[11]Pan P,Hamrock B J.Simple formulas for performance parameters used in elastohydrodynamically lubricated line contacts[J].Journal of Tribology,1989,111(2):246-251
[12]齐秀梅,高创宽.弹流润滑计算结果的回归分析[J].山西矿业学院学报,1994,12(2):171-177Qi X M,Gao C K.Regressive analysis on computational results of EHL[J].Shanxi Mining Institute Learned Journal,1994,12(2):171-177(in Chinese)
[13]汪久根.部分膜弹流的膜厚与二次压力峰公式[J].航空学报,2001,22(6):491-494Wang J G.Formulae of Film thickness and pressure spike of partial elastohydrodynamic lubrication[J].Acta Aeronautica et Astronautica Sinica,2001,22(6):491-494(in Chinese)
[14]米俊.重载点接触EHL快速算法及点接触EHL状态下二次压力峰研究[D].郑州:郑州大学,2012Mi J.Study on the fast direct iterative algorithm for heavy loaded point contact EHL and the pressure spike under the point contact EHL state[D].Zhengzhou:Zhengzhou University,2012(in Chinese)
[15]夏伯乾,张美莹.点接触弹流润滑问题的高效直接算法[J].润滑与密封,2012,37(3):16-20Xia B Q,Zhang M Y.High efficiency direct iterative algorithm for point contact EHL problems[J].Lubrication Engineering,2012,37(3):16-20(in Chinese)
[16]程正兴.数据拟合[M].西安:西安交通大学出版社,1986Cheng Z X.Data fitting[M].Xi'an:Xi'an Jiaotong University Press,1986(in Chinese)
[2]Brebbia C A.The boundary element method for engineers[M].London:Pentech Press,1978
[3]王丽彪,任家骏,吴风林,等.三维弹性接触问题边界元法的研究[J].山西机械,2001,(1):6-7,10Wang L B,Ren J J,Wu F L,et al.Research on the boundary element of three dimensional elastic contact problem[J].Shanxi Machinery,2001,(1):6-7,10(in Chinese)
[4]Dowson D,Higginson G R.Elastohydrodynamic lubrication[M].Oxford:P ergam on P ress,1 9 6 6
[5]温诗铸,杨沛然.弹性流体动力润滑[M].北京:清华大学出版社,1992Wen S Z,Yang P R.Elastohydronamic lubrication[M].Beijing:Tsinghua University Press,1992(in Chinese)
[6]Houpert L,Ioannides E,Kuypers J C,et al.The effect of the EHD pressure spike on rolling bearing fatigue[J].Journal of Tribology,1987,109(3):444-450
[7]Bissett E J,Glander D W.A highly accurate approach that resolves the pressure spike of elastohydrodynamic lubrication[J].Journal of Tribology,1988,110(2):241-246
[8]Hamrock B J,Pan P,Lee R T.Pressure spikes in elastohydrodynamically lubricated conjunctions[J].Journal of Tribology,1988,110(2):279-284
[9]Venner C H,Ten Napel W E.Numerical calculations of the pressure spike in elastohydrodynamic lubrication[J].Lubrication Science,1990,2(4):321-335
[10]Hamrock B J,Lee R T,Houpert L G.Paper VII(i)Parametric study of performance parameters in elastohydrodynamic lubricated line contacts[C]//Proceedings of the 13th Leeds-Lyon Symposium on Tribology.Leeds:The University of Leeds,1987,11:199-206
[11]Pan P,Hamrock B J.Simple formulas for performance parameters used in elastohydrodynamically lubricated line contacts[J].Journal of Tribology,1989,111(2):246-251
[12]齐秀梅,高创宽.弹流润滑计算结果的回归分析[J].山西矿业学院学报,1994,12(2):171-177Qi X M,Gao C K.Regressive analysis on computational results of EHL[J].Shanxi Mining Institute Learned Journal,1994,12(2):171-177(in Chinese)
[13]汪久根.部分膜弹流的膜厚与二次压力峰公式[J].航空学报,2001,22(6):491-494Wang J G.Formulae of Film thickness and pressure spike of partial elastohydrodynamic lubrication[J].Acta Aeronautica et Astronautica Sinica,2001,22(6):491-494(in Chinese)
[14]米俊.重载点接触EHL快速算法及点接触EHL状态下二次压力峰研究[D].郑州:郑州大学,2012Mi J.Study on the fast direct iterative algorithm for heavy loaded point contact EHL and the pressure spike under the point contact EHL state[D].Zhengzhou:Zhengzhou University,2012(in Chinese)
[15]夏伯乾,张美莹.点接触弹流润滑问题的高效直接算法[J].润滑与密封,2012,37(3):16-20Xia B Q,Zhang M Y.High efficiency direct iterative algorithm for point contact EHL problems[J].Lubrication Engineering,2012,37(3):16-20(in Chinese)
[16]程正兴.数据拟合[M].西安:西安交通大学出版社,1986Cheng Z X.Data fitting[M].Xi'an:Xi'an Jiaotong University Press,1986(in Chinese)