Abstract: For the problem of using the experience and experiment method to match the wheel-rail shape in engineering, an optimization and visualization algorithm is presented for the geometrical shape matching in the wheel-rail contact system. The algorithm of the subsection cubic spline interpolation is adopted to fit the wheel-rail profiles curves, and curve boundary is got by the finite difference method；furthermore, the wheel-rail contact positions are figured out by computing the roll angles of wheelset iteratively with the dichotomy. Based on MATLAB and Visual C++, the wheel-rail contact geometrical parameters are calculated and visualized dynamically. The method achieves a quantitative analysis between equivalent conicity and lateral displacement of wheelset, then, it provides a new optimization method for the wheel-rail match. The simulation results show the algorithm is of the strong robustness and generality.

Key words: wheel-rail match, wheel-rail contact, visualization, spline interpolation, hybrid programming

摘要： 针对目前工程上采用经验和试验方法确定轮轨外形匹配的问题，提出了轮轨接触的几何外形匹配优化及其可视化算法。算法用三次样条曲线拟合轮轨外形，差分法确定插值边界条件；采用二分法迭代求解轮对侧滚角解算出轮轨接触点位置，进而得到轮轨接触几何参数；利用MATLAB及Visual C++动态地将计算结果可视化。该算法实现了轮对等效锥度与横移量的定量分析，为轮轨匹配优化提供了新的方法，仿真结果表明，该算法具有较强的鲁棒性和通用性。

关键词: 轮轨匹配, 轮轨接触, 可视化, 样条插值, 混合编程