| The core of wheel rail wear evolution simulation is to update the profile curve in real time in the dynamic calculation.The rapid calculation of wheel rail contact geometry in each integral step of the dynamic equation is its core.The fast iterative algorithm of wheel rail contact geometric constraint equation is studied.Based on the physical constraint relationship between the wheelset and the rail,the related constraint equations are established.Firstly,the iterative algorithm of two-dimensional constraint equation is studied without considering the shaking angle;furthermore,considering the shaking angle,the iterative algorithm of the constraint equation is extended to three-dimensional.The algorithm can solve the problem of wheel rail contact geometric relationship of wheel rail profile with different matching relationship under different motion attitude.Based on Python platform,a set of Newton iterative real-time algorithm for fast and accurate calculation of wheel rail contact geometric relationship is developed to meet the requirements of real-time updating of profile curve and small amount of calculation in the process of dynamic wear simulation.Based on this algorithm,through the motion simulation of a single wheelset system,it is verified that the algorithm is also suitable for the real-time calculation of the wheel-rail matching relationship in the vehicle dynamics simulation.The following work has been done around the algorithm:(1)Based on the requirement of real-time update of wheel-rail profile curve,in the process of vehicle dynamics simulation with variable cross-section wheel-rail matching relationship,each update profile curve will only change some data points.Therefore,the third-order non-uniform rational B-spline curve with local support characteristics is used to describe the wheel-rail profile,and the change of the local control point will not cause the change of the global shape.Due to the requirements for the derivability and smoothness of the wheel-rail profile in the calculation process,the profile and guide curve are smoothed with the horizontal axis of the contact spot as the Gaussian smoothing window to meet the numerical stability requirements of the Jacobian matrix.(2)In order to make the global calculation amount of the algorithm appropriate and the iterative increment in the flange contact area will not oscillate beyond the boundary,the Newton iterative method is improved,the damped Newton iterative algorithm is adopted,and the step size scaling coefficient is 0.5.(3)The unconditional convergence stability regions of different regions are studied based on the iterative fractal diagram.The initial geometric parameters falling in the neighborhood with the target point as the center ± 2 mm can ensure the convergence stability.Then,according to the continuity of wheel rail contact itself,the above contact point is used as the initial value of iteration,and the method of adjusting according to the transverse speed direction at the jump of contact point is adopted to meet the accuracy requirements of the algorithm for the initial value of iteration.(4)Using the measured wheel-rail profile curve,the fast iterative algorithm of the wheel-rail contact geometric constraint equation is used to calculate the measured wheel-rail matching relationship.Compared with the calculation results of the minimum distance method,the effectiveness of the algorithm is verified.Comparing the running time of the two,the fast iterative algorithm of the geometric constraint equation of wheel-rail contact has obvious advantages in efficiency.Using treads with different degrees of wear,the fast iterative algorithm of wheel-rail contact geometric constraint equation is applied to calculate the measured wheel-rail matching relationship to verify the reliability of the algorithm.(5)The Hertz contact theory is used to analyze the wheel rail contact problem and the creep rate formula,and the relevant motion simulation program is established on the python platform.Through the motion simulation of a single wheelset system,it is verified that the fast iterative algorithm of the wheel-rail contact geometric constraint equation is also suitable for the real-time calculation of the wheel-rail matching relationship in the vehicle dynamics simulation. |
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