滚动体几何相似条件在轴承边界元法中的应用
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摘要
滚动轴承作为多物体接触系统,具有高度的非线性。为了求解滚动轴承的三维载荷分布,考虑所有滚动体的形状和边界条件相同,利用几何相似条件通过初始位置滚动体的离散模型,得到其他滚动体的离散数据。将所有滚动体看作是一个物体,轴承系统可以用3个物体无摩擦接触边界元法进行模拟计算。考虑全部滚动体作为一个整体的特殊性,叙述了边界积分方程和耦合的矩阵方程的建立,编制了基于滚动体几何相似条件的轴承边界元法Fortran源程序。利用该程序对轧机四列圆锥滚子轴承进行数值模拟,得到轴承的接触压力和载荷,滚动体接触宽度和接触滚动体个数,并说明了方法的有效性。
As a multi-object contact system,roller bearing is highly non-linear.To solve its three-dimensional distribution of pressure and load,we establish a discrete model of the initial location roller;other rollers' discrete data can be obtained because they have geometrically similar conditions.Based on the three-dimensional,elastic contact boundary element method(BEM),all bearing rollers can be described as one object;therefore,the roller bearing problem of a multi-object contact system can be simplified to the problem of a three-object contact system.Considering the specificity of all bearing rollers described as one object,the boundary integral equation and coupling matrix equation are established.A bearing-BEM program using Fortran language is compiled based on geometrically similar roller conditions;with this method,a mill four-row tapered roller bearing is simulated.The bearing contact pressure and load,the rollers' contact widths and the number of contact rollers are obtained,certifying the method's validity.
As a multi-object contact system,roller bearing is highly non-linear.To solve its three-dimensional distribution of pressure and load,we establish a discrete model of the initial location roller;other rollers' discrete data can be obtained because they have geometrically similar conditions.Based on the three-dimensional,elastic contact boundary element method(BEM),all bearing rollers can be described as one object;therefore,the roller bearing problem of a multi-object contact system can be simplified to the problem of a three-object contact system.Considering the specificity of all bearing rollers described as one object,the boundary integral equation and coupling matrix equation are established.A bearing-BEM program using Fortran language is compiled based on geometrically similar roller conditions;with this method,a mill four-row tapered roller bearing is simulated.The bearing contact pressure and load,the rollers' contact widths and the number of contact rollers are obtained,certifying the method's validity.
引文
[1]陈家庆,周海,徐琳琳.滚动轴承载荷分布问题的理论研究进展[J].北京石油化工学院学报,2000(1):51-56.(CHEN Jia-qing,ZHOU Hai,XU Lin-lin.Review of theoretical research on the load distribution in roller bearing[J].Journal of Beijing Institute of Petrochemical Technology,2000(1):51-56.(in Chinese))
[2]Zhou X Y,Wang H R,Jiang Z D.Influence of lubrication performance on the service life of rolling mill bearings[J].International Journal of Plant Engineering and Management,2006,11(3):184-192.
[3]赵春江,葛世东,王建梅,等.基于矩阵表达的高速角接触球轴承动态特性求解方法[J].四川大学学报(工程科学版),2009,41(1):197-201.(ZHAO Chun-jiang,GE Shi-dong,WANG Jian-mei,et al.A method of solving dynamic character of high-speed angular-contact ball bearing in matrix form[J].Journal of Sichuan University(Engineering Science Edition),2009,41(1):197-201.(in Chinese))
[4]李德信,徐健学.非线性转子2轴承系统的周期解及近似解析表达式[J].计算力学学报,2004,21(5):557-563.(LI De-xin,XU Jian-xue.Periodic solution and its approx imate analytic expressions of the nonlinear rotor-bearing system[J].Chinese Journal of Computational Mechanics,2004,21(5):557-563.(in Chinese))
[5]王槐,代霜.大接触角推力球轴承接触的有限元仿真研究[J].计算机仿真,2013,30(1):305-309.(WANG Huai,DAI Shuang.Study on contact finite element simulation of the high-angular contact thrust ball bearing[J].Computer Simulation,2013,30(1):305-309.(in Chinese))
[6]童宝宏,刘颖,苏荭.滚动轴承动态接触特性数值模拟中若干问题[J].机械工程学报,2012,48(21):116-123.(TONG Bao-hong,LIU Ying,SU Hong.Some issues in numerical simulation of dynamic contacting nature of roller bearing[J].Journal of Mechanical Engineering,2012,48(21):116-123.(in Chinese))
[7]陈泽军,肖宏,杨霞.HC轧机辊间接触与辊系变形的Taylor级数多极边界元数学规划解析[J].计算力学学报,2011,28(1):84-90.(CHEN Ze-jun,XIAO Hong,YANG Xia.Analysis of contacy and roll system deformation of HC mill by Taylor series multipole BEM mathematical programming method[J].Chinese Journal of Computational Mechanics,2011,28(1):84-90.(in Chinese))
[8]于春宵,申光宪.规划-迭代型弹塑性摩擦接触多极边界元法[J].计算力学学报,2008,25(1):65-71.(YU Chun-xiao,SHEN Guang-xian.Program-iteration pattern fast multipole BEM for elasto-plastic contact with friction[J].Chinese Journal of Computational Mechanics,2008,25(1):65-71.(in Chinese))
[9]Shen G X,Shu X D,Li M.The 3-d boundary element method of roller bearing by plate element analogue[J].Acta Mechanica Solida Sinica,2001(3):83-89.
[10]杨霞,肖宏,陈泽军.基于轴承边界元法的轧机圆锥滚子轴承的载荷研究[J].应用力学学报,2014,31(1):137-143.(YANG Xia,XIAO Hong,CHEN Ze-jun.Analysing the load distribution of mill conical roller with bearing boundary element method[J].Chinese Journal of Applied Mechanics,2014,31(1):137-143.(in Chinese))
[11]杨霞.轧机圆锥滚子轴承的边界元法理论与实验研究[D].燕山大学,2011.(YANG Xia.The BEM Theory and Experiment Research of Mill Four-Row Conical Bearing[D].Yanshan University,2011.(in Chinese))
[12]Yang X,Xiao H.Three dimension multi-body contact boundary element method[A].Proceedings of the2009International Joint Conference on Computational Sciences and Optimization[C].Sanya,2009.
[13]肖宏,杨霞,陈泽军,等.赫兹接触理论在边界元法分析轧机轴承载荷中的应用[J].中国机械工程,2010,21(21):2532-2535,2540.(XIAO Hong,YANG Xia,CHEN Ze-jun,et al.Application of Hertz contact theory in analyzing the load distribution of mill roller bearing with boundary element method[J].China Mechanical Engineering,2010,21(21):2532-2535,2540.(in Chinese))
[2]Zhou X Y,Wang H R,Jiang Z D.Influence of lubrication performance on the service life of rolling mill bearings[J].International Journal of Plant Engineering and Management,2006,11(3):184-192.
[3]赵春江,葛世东,王建梅,等.基于矩阵表达的高速角接触球轴承动态特性求解方法[J].四川大学学报(工程科学版),2009,41(1):197-201.(ZHAO Chun-jiang,GE Shi-dong,WANG Jian-mei,et al.A method of solving dynamic character of high-speed angular-contact ball bearing in matrix form[J].Journal of Sichuan University(Engineering Science Edition),2009,41(1):197-201.(in Chinese))
[4]李德信,徐健学.非线性转子2轴承系统的周期解及近似解析表达式[J].计算力学学报,2004,21(5):557-563.(LI De-xin,XU Jian-xue.Periodic solution and its approx imate analytic expressions of the nonlinear rotor-bearing system[J].Chinese Journal of Computational Mechanics,2004,21(5):557-563.(in Chinese))
[5]王槐,代霜.大接触角推力球轴承接触的有限元仿真研究[J].计算机仿真,2013,30(1):305-309.(WANG Huai,DAI Shuang.Study on contact finite element simulation of the high-angular contact thrust ball bearing[J].Computer Simulation,2013,30(1):305-309.(in Chinese))
[6]童宝宏,刘颖,苏荭.滚动轴承动态接触特性数值模拟中若干问题[J].机械工程学报,2012,48(21):116-123.(TONG Bao-hong,LIU Ying,SU Hong.Some issues in numerical simulation of dynamic contacting nature of roller bearing[J].Journal of Mechanical Engineering,2012,48(21):116-123.(in Chinese))
[7]陈泽军,肖宏,杨霞.HC轧机辊间接触与辊系变形的Taylor级数多极边界元数学规划解析[J].计算力学学报,2011,28(1):84-90.(CHEN Ze-jun,XIAO Hong,YANG Xia.Analysis of contacy and roll system deformation of HC mill by Taylor series multipole BEM mathematical programming method[J].Chinese Journal of Computational Mechanics,2011,28(1):84-90.(in Chinese))
[8]于春宵,申光宪.规划-迭代型弹塑性摩擦接触多极边界元法[J].计算力学学报,2008,25(1):65-71.(YU Chun-xiao,SHEN Guang-xian.Program-iteration pattern fast multipole BEM for elasto-plastic contact with friction[J].Chinese Journal of Computational Mechanics,2008,25(1):65-71.(in Chinese))
[9]Shen G X,Shu X D,Li M.The 3-d boundary element method of roller bearing by plate element analogue[J].Acta Mechanica Solida Sinica,2001(3):83-89.
[10]杨霞,肖宏,陈泽军.基于轴承边界元法的轧机圆锥滚子轴承的载荷研究[J].应用力学学报,2014,31(1):137-143.(YANG Xia,XIAO Hong,CHEN Ze-jun.Analysing the load distribution of mill conical roller with bearing boundary element method[J].Chinese Journal of Applied Mechanics,2014,31(1):137-143.(in Chinese))
[11]杨霞.轧机圆锥滚子轴承的边界元法理论与实验研究[D].燕山大学,2011.(YANG Xia.The BEM Theory and Experiment Research of Mill Four-Row Conical Bearing[D].Yanshan University,2011.(in Chinese))
[12]Yang X,Xiao H.Three dimension multi-body contact boundary element method[A].Proceedings of the2009International Joint Conference on Computational Sciences and Optimization[C].Sanya,2009.
[13]肖宏,杨霞,陈泽军,等.赫兹接触理论在边界元法分析轧机轴承载荷中的应用[J].中国机械工程,2010,21(21):2532-2535,2540.(XIAO Hong,YANG Xia,CHEN Ze-jun,et al.Application of Hertz contact theory in analyzing the load distribution of mill roller bearing with boundary element method[J].China Mechanical Engineering,2010,21(21):2532-2535,2540.(in Chinese))