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

Abstract: 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.

Key words: wheel rail contact geometry, Newton’s method, non-uniform rational B spline, Gauss filter, iteration fractal