基于格林函数的轮轨缺陷对轮轨垂向动态相互作用的研究

Investigation on Wheel-Rail Vertical Dynamic Interaction Due to Wheel-rail Imperfections Based on Green's Function Method

在轮轨垂向耦合振动模型中,把钢轨考虑成离散支撑的连续的铁木辛科梁,用一系悬挂和二系悬挂把在钢轨上滚动的车轮、1/4构架质量块和1/8车体质量块连接起来作为简化的车辆模型。为了高效精确地研究不同车轮和钢轨缺陷对轮轨垂向动态相互作用的影响,对钢轨在移动载荷作用下的运动方程进行拉普拉斯变换,用格林函数法求解其在频域上的响应解,再通过反傅里叶变换求得钢轨在时域内的振动响应。考虑不同工况下车轮的扁疤、多边形化缺陷和钢轨的波磨缺陷,用非线性赫兹接触理论和数值迭代方法计算轮轨垂向冲击力。结果表明:应用格林函数法可以高效准确地求解轮轨垂向动态响应,为在高频范围内研究轮轨作用提供了理论基础。

The wheel-rail vertical coupled vibration model was established, in which the rail was considered as a continuous Timoshenko beam discretely supported. The lumped masses of wheel, a quarter of bogie frame and one eighth of carbody were connected using primary and secondary suspensions respectively, and this subsystem was taken as a simplified vehicle model. In order to efficiently and accurately investigate the effects of wheel and rail defects on vertical dynamic interaction between wheel and rail, Laplace transform was implemented for the motion equations of the rail under a moving load, and those motion equations were solved in the frequency domain by Green＇s function method, then inverse Fourier transform was carried out to obtain vibration response of rail in the time domain. Wheel-rail vertical impact forces due to wheel fiat, wheel polygonalization and rail corrugation in various cases were calculated by numerical iterations according to the nonlinear Hertzian contact theory. Results show that the vertical wheel-rail dynamic response can be solved by the Green function method accurately and efficiently, and it provides a theoretical foundation for the research of wheel-rail interaction in the range of high frequency.