基于三维弹性体滚动接触理论的轮轨非平面接触算法

Wheel-rail Non-flat Contact Algorithm Based on Three-dimensional Elastic Bodies Rolling Contact Theory

基于Kalker的三维弹性体滚动接触理论,结合轮轨非平面接触几何关系,提出了最小余能方程中影响系数的修正公式。考虑轮轨非平面接触时法向与切向存在的相互作用,对最小余能方程进行离散化。以总余能最小为目标,将离散方程的求解转化为非线性规划问题,并提出了求解算法。利用有限元方法验证了所提算法的准确性。最后,研究了钢轨在不同磨耗状态下的轮轨接触特性。结果表明,在不同磨耗、相同横移量条件下,随着磨耗的增加,轮轨的轨距角接触由两点接触过渡至共形接触,最大接触应力减小,接触斑变得狭长,接触面积增大。

Based on the Kalker’s three-dimensional elastic bodies rolling contact theory and combined with the wheel-rail non-flat contact geometric relationship,the modified equation of the influence coefficient implemented in the minimum complementary energy equation was presented.Considering the interaction between the normal and the shear effects of wheel-rail non-flat contact,the minimum complementary energy equation was discretized.The solution of the discretized equation was transformed into a nonlinear programming problem with the target of the minimum of the total complementary energy,and the algorithm for solving the problem was proposed.The accuracy of the algorithm was validated with a finite element simulation.Lastly,the wheel-rail non-flat contact characteristics under different worn rail conditions were studied and the results show that,under the conditions of different wears and same lateral displacements,with the wear increasing,the wheel-rail contact occurred in the gauge corner changes from a two-point contact to a conformal contact,the corresponding maximum stress decreases,the contact patch becomes narrow and long,and the contact area increases.