精确求解轮轨三维几何接触的延拓方法

EXACT SOLUTION OF THREE DIMENSIONAL WHEEL/RAIL CONTACT GEOMETRY WITH CONTINUATION METHOD

本文以独立车轮和钢轨为研究对象，建立了轮轨三维几何接触的精确模型，用伪弧长延拓法追踪非线性方程组的正则解支，避免了Ｊａｃｏｂｉ矩阵奇异，解决了轮轨两点接触问题，得到车轮处于任意位形时接触点的精确位置。计算表明，延拓法具有计算效率高、通用性强的优点。最后，分别计算了ＵＩＣ６０钢轨／Ｓ１００２轮对，ＴＢ６０ｋｇ钢轨／锥形踏面、ＴＢ６０ｋｇ钢轨／磨耗形踏面轮对的几何接触关系。

In this paper,three dimensional wheel/rail contact geometry problem is studied.Based on the contact condition,a set of nonlinear equations are derived,the solution branch is followed by using pseudo arclength continuation method to avoid singularity of Jacobi matric.The contact point position including double contact points is obtained exactly.Three kinds of wheel/rail sets are calculated with this method,the advantage of worn profile wheelsets is described from the view of contact geometry.The results can be used to optimize W/R parameters,it also give the necessary data for dynamics simulation.