基于约束方程法的轮轨接触点算法
姚鑫，王建斌，张大福，李大地，屈升
（西南交通大学 牵引动力国家重点实验室，四川 成都 610031）
摘要：基于轮轨之间的几何约束关系提出一种新的基于约束方程的牛顿迭代算法，该方法根据轮轨接触点处法向矢量方向相反、接触点坐标相同的几何约束关系建立约束方程组，采用牛顿迭代法求解非线性方程组得到轮轨接触点位置。采用Python编写了轮轨接触几何关系计算程序，用S1002CN车轮踏面与CHN60钢轨匹配接触几何关系的计算，验证该算法的有效性、准确性和效率。计算结果表明该算法能快速准确地计算轮对在任意运动姿态下与钢轨的接触点。
关键词：轮轨接触几何；约束方程；牛顿迭代法；Python
中图分类号：U260.331 文献标志码：A doi：10.3969/j.issn.1006-0316.2022.11.008
文章编号：1006-0316 (2022) 11-0056-07
Wheel-Rail Contact Point Algorithm Based on Constraint Equation Method
YAO Xin，WANG Jianbin，ZHANG Dafu，LI Dadi，QU Sheng
( State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, China )
Abstract：Based on the geometric constraint relationship between the wheel and rail, a new Newton iterative algorithm based on constraint equations is proposed. In this method, a constraint equation system is established according to the geometric constraint relationship of the wheel-rail contact point with the opposite normal vector direction and the same contact point coordinates, and the Newton iteration method is used to solve the nonlinear equation system to obtain the wheel-rail contact point position. The calculation program of wheel-rail contact geometric relationship is written in Python, and the calculation of the matching contact geometric relationship between S1002CN wheel tread and CHN60 rail is used to verify the validity, accuracy and efficiency of the algorithm. The calculation results show that the algorithm can quickly and accurately calculate the contact point between the wheelset and the rail under any motion posture.
Key words：wheel rail contact geometry；constraint equation；Newton iteration method；Python
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收稿日期：2022-04-02
基金项目：国家自然科学基金（61960206010）；牵引动力国家重点实验室自主课题（2021TPL-T09）
作者简介：姚鑫（1996－），男，浙江湖州人，硕士，主要研究方向为轮轨关系，E-mail：xinyao_1996@163.com；王建斌（1981－），男，四川成都人，博士，讲师，主要研究方向为转向架设计、车辆动力学仿真与线路试验。
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