滚动体几何相似条件在轴承边界元法中的应用

Application of geometrically similar roller conditions in bearing boundary element method

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.