一种齿面接触点柔度矩阵的计算方法

Computing method for flexibility matrix of contact points on tooth surface

本文以齿面网格柔度矩阵为基础,提出一种计算接触椭圆长轴上离散点柔度矩阵的混合插值法。首先按照虚功原理,将某接触点处的法向单位载荷等效到包围它的四边形网格单元的角点上,得到该单元角点的等效载荷系数。然后依据已有的齿面网格柔度矩阵,将包围所有接触点的相关网格结点的等效位移相加,得到接触点柔度矩阵中的对应行向量。采用上述方法顺次在各接触点上施加法向单位载荷,即可形成接触点柔度矩阵。在求解齿面柔度矩阵时,发现齿面网格结点位移畸变。在位移插值时,发现当网格单元内超过两个接触点时,有可能导致接触点柔度矩阵主对角线不占优。研究表明,为了确保获得符合物理意义的接触点柔度矩阵,每个齿面网格内只能含有一个接触点。

A compound interpolation method to compute the flexibility matrix of tooth contact points（TCP） discretized along the long axis of contact ellipse is proposed on the basis of flexibility matrix of the tooth surface grid（TSG）.A normal unit load at some TCP was equal to the TSG nodes surrounding the TCP according to the principle of virtual work.The corresponding row vector in TCP flexibility matrix is formed by summing the equivalent displacement of relative TSG nodes surrounding all the TCPs based on the existing TSG flexibility matrix.With the above method,the normal unit load is brought to bear on every TCP one by one,and then the whole TCP flexibility matrix can be formed.When solving the flexibility matrix of tooth surface,a displacement distortion of TSG node was found..When interpolating displacements from TSG to TCP,the principal diagonal element of some TCP flexibility matrix might be smaller than other element of the same row if more than two TCPs occur in the same grid element.The research shows that in order to ensure that the TCP flexibility matrix fits with physical meaning one grid element must contain only one contact point.