轮轨接触几何约束方程迭代算法研究  

Research on the Iteration Algorithm of the Wheel and Rail Contact Geometry Constraint Equations

作　　者：王建斌[1] 姚鑫 张大福[1] 李大地[1] 屈升 WANG Jianbin;YAO Xin;ZHANG Dafu;LI Dadi;QU Sheng(State key laboratory of traction power,Southwest Jiaotong University,Chengdu 610031)

机构地区：[1]西南交通大学牵引动力国家重点实验室,成都610031

出　　处：《机械工程学报》2024年第2期234-242,共9页Journal of Mechanical Engineering

基　　金：国家自然科学基金(U1934202);牵引动力国家重点实验室自主课题(2021TPL-T09)资助项目。

摘　　要：轮轨磨耗演变仿真需要在动力学程序中实时更新型面曲线,在每个动力学积分步中实现轮轨接触几何快速计算是核心算法。研究轮轨接触几何约束方程Newton迭代求解接触点算法,根值迭代的收敛性取决于初值与目标值的距离以及约束方程雅可比矩阵数值稳定性,极值迭代的收敛性取决于增量步在超曲面梯度的前进方向,约束方程哈希矩阵为半正定。基于迭代收敛影响因素,从型面曲线与导曲线平滑参数、Newton迭代缩放系数和迭代起点取值范围三方面研究轮轨接触几何迭代算法的稳定条件与参数选择区间。采用局部支撑特性的非均匀有理B样条曲线描述轮轨型面,局部控制点的变化不会引起全局形状的改变。以接触斑横轴尺寸为高斯平滑窗口对型面和导曲线进行平滑处理,满足雅可比矩阵数值稳定性要求。为避免轮缘接触区迭代增量越界振荡,选择缩放系数0.5以满足收敛速度和稳定性要求。基于Newton迭代分形研究不同接触区的无条件收敛稳定域,迭代初始参数选在目标点为中心±3mm的邻域可确保收敛稳定。It is necessary to update profiles for real-time wheel rail wear simulations of which the key procedure is to realize rapid computation of wheel rail contact geometry at each integration step of dynamic equations.Iteration algorithm for the geometry constraint equations is studied for positioning contact points.The convergence of the finding roots of the algebraic equations depends on the distance between the initial estimates and the real roots,and the numerical stability of the computing the inverse the Jacobian matrix.The convergence of the finding extremes depends on the direction of the Newton incremental step indicated by the definite of the Hessian matrix.Based on the convergence conditions,a robust iteration algorithm for computing wheel rail contact geometry is built including smoothing algorithm for profiles and the derivative curves,damping factor of Newton’s method and initial estimates domains with unconditional stability.Non-unform rational B spline(NURBS)is adopted for wheel rail profiles functions as local variations of the curve function could not change the global curve,and it is the key feature for local wear simulation.Gauss filter of which the kernel function that has the same window size with the contact patch is adopted for smoothing the profiles and derivative curves.For avoiding overstep the curve boundary,damped Newton’s method with the step size scale factor 0.5 is chosen based on the convergence rate and stability.Based on the Newton iteration fractal,the unconditional stable domain of the initial estimates of the contact points is±3 mm respect to the center of the target contact point.

关 键 词：轮轨接触几何 NEWTON方法 非均匀有理B样条曲线 高斯平滑 迭代分形 

分 类 号：U260[机械工程—车辆工程]