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

摘要:

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。

Abstract:

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.