考虑热弹性变形的角接触球轴承微观热弹流分析
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摘要
运用点接触热弹性流体动压润滑理论,考虑了润滑油膜温升变化引起的角接触球轴承中滚珠和内圈接触表面的热弹性变形和表面随机粗糙度的影响,提出了一种计入热弹性变形和随机粗糙度影响的角接触球轴承热弹性流体动压润滑分析方法.该方法通过将热弹性变形进行热力转换,得到了滚珠和内圈接触表面的材料线热膨胀系数,计算修正了滚珠和内圈表面因油膜温度场变化引起的热弹性变形,求得了计入热弹性变形和表面粗糙度后的油膜压力、油膜厚度、油膜温升以及热弹性变形等主要润滑特性,研究了内圈转速、滑滚比和滚珠数量的变化对油膜厚度和油膜压力的影响规律,结果表明:最大热弹性变形量与最小油膜厚度处在同一量级,并且内圈转速、滑滚比和滚珠数量的变化对油膜厚度和压力会产生明显的影响.进一步对比分析了几种算法下的最小膜厚,验证了计入热弹性变形的数值算法的可行性.
By considering the thermal elastic deformation and random surface roughness of contact surface between ball and inner race of angular contact ball bearing caused by lubricant temperature rise, a numerical method for analyzing point contact thermal elastohydrodynamic lubrication of angular contact ball bearing was proposed based on the point contact thermal elastohydrodynamic lubrication theory. According to heat transfer of thermal elastic deformation, the material line thermal expansion coefficients of contact surface between rolling ball and inner race were obtained, the thermal elastic deformation caused by lubricant temperature rise was modified. The oil film pressure, the oil film thickness, the oil film temperature rise and the thermal deformation were calculated by considering thermal elastic deformation and random surface roughness. The effects of different rotational speeds of the inner race, slide-to-roll ratios and number of rolling balls on the oil film thickness and the oil film pressure were studied. The results show that thermal elastic deformation and minimum oil film thickness were in the same order of magnitude, and the rotational speeds of the inner race, slide-to-roll ratios and number of rolling balls had profound influences on lubrication performance.Furthermore, the minimum film thickness of several algorithms was compared and analyzed, and the feasibility of the numerical algorithm considering thermal elastic deformation was verified.
By considering the thermal elastic deformation and random surface roughness of contact surface between ball and inner race of angular contact ball bearing caused by lubricant temperature rise, a numerical method for analyzing point contact thermal elastohydrodynamic lubrication of angular contact ball bearing was proposed based on the point contact thermal elastohydrodynamic lubrication theory. According to heat transfer of thermal elastic deformation, the material line thermal expansion coefficients of contact surface between rolling ball and inner race were obtained, the thermal elastic deformation caused by lubricant temperature rise was modified. The oil film pressure, the oil film thickness, the oil film temperature rise and the thermal deformation were calculated by considering thermal elastic deformation and random surface roughness. The effects of different rotational speeds of the inner race, slide-to-roll ratios and number of rolling balls on the oil film thickness and the oil film pressure were studied. The results show that thermal elastic deformation and minimum oil film thickness were in the same order of magnitude, and the rotational speeds of the inner race, slide-to-roll ratios and number of rolling balls had profound influences on lubrication performance.Furthermore, the minimum film thickness of several algorithms was compared and analyzed, and the feasibility of the numerical algorithm considering thermal elastic deformation was verified.
引文
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[11]Shi Xiujiang,Wang Liqin,Zheng Dezhi.Thermal EHL analysis of aero-engine mainshaft ball bearing with dynamic characteristics[J].Tribology,2015,35(4):415-422(in Chinese)[史修江,王黎钦,郑德志.考虑动力学特性的航空发动机主轴球轴承热弹流分析[J].摩擦学学报,2015,35(4):415-422].doi:10.16078/j.tribology.2015.04.009.
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[14]Wang Yanshuang,Deng Sier,Yang Haisheng,et al.Effects of nonnewtonian behavior of lubricants on the thermal elastohydrodynamic lubrication in heavily loaded point contacts[J].Journal of Aerospace Power,2009,24(3):683-689(in Chinese)[王燕霜,邓四二,杨海生,等.非牛顿特性对重载点接触热弹流润滑的影响[J].航空动力学报,2009,24(3):683-689].
[15]Shi X J,Wang L Q,Mao Y Z,et al.Coupling study on dynamics and TEHL behavior of high-speed and heavy-load angular contact ball bearing with spinning[J].Tribology International,2015,88:76-84.doi:10.1016/j.triboint.2015.03.011.
[16]Wang X P,Liu Y C,Zhu D.Numerical solution of mixed thermal elastohydrodynamic lubrication in point contacts with threedimensional surface roughness[J].ASME Journal of Tribology,2017,139(1):011501.
[17]Vinogradov O.Using modified potential to account for non-zero temperature in molecular statics for crystals[J].Computational Materials Science,2008,41(4):493-497.doi:10.1016/j.commatsci.2007.05.013.
[18]Li G,Vinogradov O,Gubanov A.A modified Morse potential accounting for non-zero temperature in molecular statics for Nickel crystals[J].Computational Materials Science,2012,62:126-130.doi:10.1016/j.commatsci.2012.05.040.
[19]Miao Enming,Xu Zhishang,Zhou Xiaoshuai,et al.Simulation of thermal deformation of cylindrical mechanical parts bounded by boundary constraint based on conversion mechanism of thermal into mechanics[J].Optics and Precision Engineering,2015,23(2):504-511(in Chinese)[苗恩铭,徐祗尚,周小帅,等.基于热力转换机理仿真圆柱体零件形体边界约束的热弹性变形[J].光学精密工程,2015,23(2):504-511].
[20]Yang P R,Wen S Z.A generalized Reynolds equation for nonnewtonian thermal elasto-hydrodynamic lubrication[J].ASMEJournal of Tribology,1990,112(4):631-636.doi:10.1115/1.2920308.
[21]Roelands C J A.Correlation aspects of viscosity temperature pressure relationship of lubrication oils[D].Netherlands:Delft University of Technology,1966.
[22]Dowson D,Higginson G R.Elastohydrodynamic lubrication[M].Oxford:Pergamon Press,1977.
[23]Takeuti Y,Zaima S,Noda N.Thermal stresses problems in industry1:On thermoelastic distortion in machining metals[J].Thermal Stresses,1978,1(2):199-210.doi:10.1080/01495737808926943.
[24]Ozisk M N[America].Heat conduction[M].Translated by Yu Changming.Beijing:Higher Education Press,1983:83-107(in Chinese)[M.N.奥齐西克[美].热传导[M].俞昌铭,译.北京:高等教育出版,1983:83-107].
[25]Wang Honggang.Introduction to thermal elasticity[M].Beijing:Tsinghua University Press,1989:191-236(in Chinese)[王洪纲.热弹性力学概论[M].北京:清华大学出版社,1989:191-236].
[26]Gu Chaohao.Mathematical physics equation[M].Beijing:Higher Education Press,2002:147-183(in Chinese)[谷超豪.数学物理方程[M].北京:高等教育出版社,2002:147-183].
[27]Xiong Wanli,Zhao Zisheng,Zhou Yang,et al.Research on dynamic stiffness of ball bearings considering ferrule deformation and elastohydrodynamic lubrication[J].China Mechanical Engineering,2015,26(11):1421-1428(in Chinese)[熊万里,赵紫生,周阳,等.计入套圈变形和润滑影响的球轴承动刚度研究[J].中国机械工程,2015,26(11):1421-1428].doi:10.3969/j.issn.1004-132X.2015.11.001.
[28]Huang Ping.Numerical calculation methods of elastohydrodynamic lubrication[M].Beijing:Tsinghua University Press,2013:95-123(in Chinese)[黄平.弹性流体动压润滑数值计算方法[M].北京:清华大学出版社,2013:95-123].
[29]Fei Yetai.The theory and application of mechanical thermal elastic deformation[M].Beijing:National Defense Industry Press,2009:190-225(in Chinese)[费业泰.机械热弹性变形理论及应用[M].北京:国防工业出版社,2009:190-225].
[30]Hamrock B J,Dowson D.Isothermal elastohydrodynamic lubrication of point contacts,part III:fully flooded results[J].ASMEJournal of Lubrication Technology,1977,99(2):261-276.doi:10.1115/1.3453063.
[31]Zhai Wenjie,Zhang Pengshun.Thermal EHL film performance of point contact and the modified formula of minimum film thickness[J].Mechanical Design,1995(7):27-29(in Chinese)[翟文杰,张平顺.全膜点接触热弹流的油膜特性及最小膜厚热修正公式[J].机械设计,1995(7):27-29].
[2]Zhang S G,Wang W Z,Zhao Z Q.Elastohydrodynamic lubrication analysis of point contacts with consideration of material inhomogeneity[J].ASME Journal of Tribology,2014,136(4):041501.doi:10.1115/1.4027750.
[3]Wang Z J,Zhu D,Wang Q.Elastohydrodynamic lubrication of inhomogeneous materials using the equivalent inclusion method[J].ASME Journal of Tribology,2014,136(2):021501.
[4]Wang Z J,Yu C J,Wang Q.Model for elastohydrodynamic lubrication of multilayered materials[J].ASME Journal of Tribology,2015,137(1):011501.
[5]Ma Mingming,Liu Xiaoling,Zhao Huimin.Analysis on elastohydrodynamic lubrication of angle-contact ball bearings considering spinning[J].Lubrication Engineering,2017,42(1):64-70(in Chinese)[马明明,刘晓玲,赵慧敏.自旋条件下角接触球轴承的弹流润滑分析[J].润滑与密封,2017,42(1):64-70].doi:10.3969/j.issn.0254-0150.2017.01.010.
[6]Lu C Y,Liu S J.A fatigue life prediction method of rolling bearing under elliptical contact elastohydrodynamic lubrication[J].Journal of Southeast University(English Edition),2017,33(1):46-52.
[7]Yang Peiran.Numerical analysis of fluid lubrication[M].Beijing:National Defence Industry Press,1998:98-101(in Chinese)[杨沛然.流体润滑数值分析[M].北京:国防工业出版社,1998:98-101].
[8]Huang Hai,Liu Xiaoling.Analysis of thermal elastohydrodynamic lubrication for ceramic ball bearing[J].Lubrication Engineering,2012,37(6):46-51(in Chinese)[黄海,刘晓玲.陶瓷球轴承的热弹流润滑分析[J].润滑与密封,2012,37(6):46-51].doi:10.3969/j.issn.0254-0150.2012.06.011.
[9]Lu Xianjiu,Wang Youqiang,LüHui,et al.Effect of microscopic surface morphology on thermal elastohydrodynamic lubrication of angular contact ball bearing[J].Lubrication Engineering,2014,39(6):49-55(in Chinese)[卢宪玖,王优强,律辉,等.微观表面形貌对角接触球轴承热弹流润滑的影响[J].润滑与密封,2014,39(6):49-55].doi:10.3969/j.issn.0254-0150.2014.06.009.
[10]Lu Xianjiu,Wang Youqiang,Liu Bingli,et al.Analysis of microelastohydrodynamic lubrication of angular contact ball bearing considering dynamic characteristics[J].Journal of Mechanical Engineering,2014,50(23):104-111(in Chinese)[卢宪玖,王优强,刘昺丽,等.考虑动态特性的角接触球轴承微观热弹流分析[J].机械工程学报,2014,50(23):104-111].
[11]Shi Xiujiang,Wang Liqin,Zheng Dezhi.Thermal EHL analysis of aero-engine mainshaft ball bearing with dynamic characteristics[J].Tribology,2015,35(4):415-422(in Chinese)[史修江,王黎钦,郑德志.考虑动力学特性的航空发动机主轴球轴承热弹流分析[J].摩擦学学报,2015,35(4):415-422].doi:10.16078/j.tribology.2015.04.009.
[12]Shi Xiujiang,Wang Liqin,Gu Le,et al.Thermal elastohydrodynamic lubrication analysis of aero-engine mainshaft ball bearing based on quasi-dynamic[J].Journal of Aerospace Power,2016,31(1):232-240(in Chinese)[史修江,王黎钦,古乐,等.基于拟动力学的航空发动机主轴球轴承热弹流润滑分析[J].航空动力学报,2016,31(1):232-240].
[13]Zhang Binbin,Wang Jing.Analysis on thermal EHL of angular contact ball bearings under ultra-large slide-roll ratio[J].Bearing,2016(3):37-42(in Chinese)[张彬彬,王静.超大滑滚比下角接触球轴承热弹性流体动力润滑分析[J].轴承,2016(3):37-42].doi:10 .3969/j.issn.1000-3762.2016.03.012.
[14]Wang Yanshuang,Deng Sier,Yang Haisheng,et al.Effects of nonnewtonian behavior of lubricants on the thermal elastohydrodynamic lubrication in heavily loaded point contacts[J].Journal of Aerospace Power,2009,24(3):683-689(in Chinese)[王燕霜,邓四二,杨海生,等.非牛顿特性对重载点接触热弹流润滑的影响[J].航空动力学报,2009,24(3):683-689].
[15]Shi X J,Wang L Q,Mao Y Z,et al.Coupling study on dynamics and TEHL behavior of high-speed and heavy-load angular contact ball bearing with spinning[J].Tribology International,2015,88:76-84.doi:10.1016/j.triboint.2015.03.011.
[16]Wang X P,Liu Y C,Zhu D.Numerical solution of mixed thermal elastohydrodynamic lubrication in point contacts with threedimensional surface roughness[J].ASME Journal of Tribology,2017,139(1):011501.
[17]Vinogradov O.Using modified potential to account for non-zero temperature in molecular statics for crystals[J].Computational Materials Science,2008,41(4):493-497.doi:10.1016/j.commatsci.2007.05.013.
[18]Li G,Vinogradov O,Gubanov A.A modified Morse potential accounting for non-zero temperature in molecular statics for Nickel crystals[J].Computational Materials Science,2012,62:126-130.doi:10.1016/j.commatsci.2012.05.040.
[19]Miao Enming,Xu Zhishang,Zhou Xiaoshuai,et al.Simulation of thermal deformation of cylindrical mechanical parts bounded by boundary constraint based on conversion mechanism of thermal into mechanics[J].Optics and Precision Engineering,2015,23(2):504-511(in Chinese)[苗恩铭,徐祗尚,周小帅,等.基于热力转换机理仿真圆柱体零件形体边界约束的热弹性变形[J].光学精密工程,2015,23(2):504-511].
[20]Yang P R,Wen S Z.A generalized Reynolds equation for nonnewtonian thermal elasto-hydrodynamic lubrication[J].ASMEJournal of Tribology,1990,112(4):631-636.doi:10.1115/1.2920308.
[21]Roelands C J A.Correlation aspects of viscosity temperature pressure relationship of lubrication oils[D].Netherlands:Delft University of Technology,1966.
[22]Dowson D,Higginson G R.Elastohydrodynamic lubrication[M].Oxford:Pergamon Press,1977.
[23]Takeuti Y,Zaima S,Noda N.Thermal stresses problems in industry1:On thermoelastic distortion in machining metals[J].Thermal Stresses,1978,1(2):199-210.doi:10.1080/01495737808926943.
[24]Ozisk M N[America].Heat conduction[M].Translated by Yu Changming.Beijing:Higher Education Press,1983:83-107(in Chinese)[M.N.奥齐西克[美].热传导[M].俞昌铭,译.北京:高等教育出版,1983:83-107].
[25]Wang Honggang.Introduction to thermal elasticity[M].Beijing:Tsinghua University Press,1989:191-236(in Chinese)[王洪纲.热弹性力学概论[M].北京:清华大学出版社,1989:191-236].
[26]Gu Chaohao.Mathematical physics equation[M].Beijing:Higher Education Press,2002:147-183(in Chinese)[谷超豪.数学物理方程[M].北京:高等教育出版社,2002:147-183].
[27]Xiong Wanli,Zhao Zisheng,Zhou Yang,et al.Research on dynamic stiffness of ball bearings considering ferrule deformation and elastohydrodynamic lubrication[J].China Mechanical Engineering,2015,26(11):1421-1428(in Chinese)[熊万里,赵紫生,周阳,等.计入套圈变形和润滑影响的球轴承动刚度研究[J].中国机械工程,2015,26(11):1421-1428].doi:10.3969/j.issn.1004-132X.2015.11.001.
[28]Huang Ping.Numerical calculation methods of elastohydrodynamic lubrication[M].Beijing:Tsinghua University Press,2013:95-123(in Chinese)[黄平.弹性流体动压润滑数值计算方法[M].北京:清华大学出版社,2013:95-123].
[29]Fei Yetai.The theory and application of mechanical thermal elastic deformation[M].Beijing:National Defense Industry Press,2009:190-225(in Chinese)[费业泰.机械热弹性变形理论及应用[M].北京:国防工业出版社,2009:190-225].
[30]Hamrock B J,Dowson D.Isothermal elastohydrodynamic lubrication of point contacts,part III:fully flooded results[J].ASMEJournal of Lubrication Technology,1977,99(2):261-276.doi:10.1115/1.3453063.
[31]Zhai Wenjie,Zhang Pengshun.Thermal EHL film performance of point contact and the modified formula of minimum film thickness[J].Mechanical Design,1995(7):27-29(in Chinese)[翟文杰,张平顺.全膜点接触热弹流的油膜特性及最小膜厚热修正公式[J].机械设计,1995(7):27-29].