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车轮踏面优化设计是轨道交通系统的基本问题。根据车轮踏面优化模型的建立及其求解方法,车轮踏面优化设计的数值研究方法可以分为两类,即单目标优化设计方法和多目标优化设计方法。在综述轮轨踏面同步设计法、扩展方法、基于轮轨接触曲线的滚动半径差法和基于接触角曲线法等单目标优化方法的基础上,论证了车轮踏面优化是一个多目标优化问题,并给出了建立车轮踏面多目标优化模型的思路。车轮踏面多目标优化需要求解带约束的非凸不可微规划问题,求解精度和效率直接决定优化结果的可靠性和实用性。现有的求解方法包括遗传算法和拟高斯方法。针对现有计算方法存在计算量大、易早熟、收敛慢的缺点,提出求解车轮踏面多目标优化问题的响应面方法。该方法利用多项式响应面逼近目标函数和约束函数,避免了优化过程中由于数值求导带来的迭代振荡问题;同时该方法具有计算量小、收敛快的优点。以降低轮轨磨耗为目的对车轮踏面进行优化的实例表明,响应面方法能有效的优化车轮踏面。最后对车轮踏面这一课题的发展方向进行了展望。
Wheel tread optimization design is the basic problem of the rail transit system. According to the establishment of wheel tread optimization model and its solution method, the numerical research methods of wheel tread optimization design can be divided into two categories, that is, single-objective optimization design method and multi-objective optimization design method. Based on the review of wheel-rail tread synchronization design method, extension method, rolling radius difference method based on wheel-rail contact curve and single-objective optimization method based on contact angle curve method, it is proved that wheel tread optimization is a multi-objective optimization problem. The idea of establishing multi-objective optimization model of wheel tread is given. Multi-objective optimization of wheel tread requires solving non-convex and non-differentiable programming problems with constraints. Solving accuracy and efficiency directly determine the reliability and practicability of the optimization results. Existing solutions include genetic algorithms and quasi-Gaussian methods. Aiming at the shortcomings of large computational complexity, precocious maturity and slow convergence, the existing response surface method is proposed to solve the multi-objective optimization problem of wheel tread. This method uses the polynomial response surface to approximate the objective function and the constraint function, and avoids the problem of iterative oscillation caused by numerical derivation in the optimization process. At the same time, this method has the advantages of small computation and fast convergence. The example of optimizing the wheel tread with the aim of reducing wheel and rail wear shows that the response surface method can effectively optimize the wheel tread. Finally, the prospect of the development of the wheel tread is discussed.