基于轮轨垂向力的波磨状态估算方法

为了探明轮轨垂向力与波磨状态之间的映射关系并采用轮轨力检测数据定量评价波磨严重程度，以中国CRTSⅡ高铁线路与服役动车组典型参数构建三维轮轨动力学有限元模型；细化波磨区段钢轨表面不平顺特征，采用高速综合检测列车在高铁波磨区段上实测轮轨垂向力时频数据验证有限元模型输出结果的准确性；模拟了车辆运行速度为300 km·h^-1时波长在40~180 mm波磨激励下的轮轨垂向力，分析了其时频域分布特性；引入轨面不平顺变化率表征波磨沿钢轨纵向的变化特性，采用非线性最小二乘法与有理式方程拟合了不同波长条件下轮轨垂向力大值与轨面不平顺变化率之间的函数关系，分析了钢轨Pinned-Pinned固有共振频率及其半值振动模态对拟合参数曲线的影响，并推导了基于轮轨垂向力的波磨谷深估算方法；该谷深估算方法在某高铁线路波磨状态监测中初步试用，共发现32个波磨区段，并对比了波磨区段上实测谷深和估算谷深。分析结果表明：谷深估算值与实测值相关系数为0.97，两者具有较高的线性相关性；在谷深估算值大于0.08 mm时，估算值与实测值之间的均方根差约为0.01mm，基于谷深估算方法作出波磨打磨整治决策时的误判率约为6.25%，说明谷深估算方法在实际高铁线路上具有较好的适用性。

Estimation method of corrugation state based on wheel-rail vertical force

In order to find out the mapping relationship between wheel-rail vertical force and corrugation state and to evaluate quantitatively the severity of the corrugation by using wheel-rail force inspection data, the typical parameters from CRTS Ⅱ high-speed railway and electric multiple units in service in China were employed to construct a three-dimensional wheel-rail dynamics finite element model. The characteristics of the irregularities on the rail surface at the corrugation section were refined, and the simulation accuracy of the constructed model was verified by the time-frequency data of the measured wheel-rail vertical force from the high-speed comprehensive inspection car at the corrugation section in the high-speed railway. On this basis, the wheel-rail vertical forces excited by the corrugation with a wavelength between 40 mm and 180 mm at the running speed of 300 km·h-1 were simulated, and their distribution characteristics in time-frequency domain were analyzed. The change rate of rail surface irregularity was introduced to characterize the changing characteristics of the corrugation along the longitudinal direction of the rail. The nonlinear least square method and rational equation were used to fit the functional relationship between the large values of the wheel-rail vertical force and the change rates of rail surface irregularity under different wavelengths. The influence of rail vibration mode of the Pinned-Pinned natural resonant frequency and its half-value on the fitting parameter curves was analyzed. A method based on the wheel-rail vertical force was derived to estimate the valley depth of the corrugation. The valley depth estimation method was tentatively tested in the high-speed railway to evaluate the corrugation, 32 sets of corrugation sections were found, and the measured and estimated valley depths at the sections were compared. Analysis results show that the correlation coefficient between the estimated and measured valley depths is 0.97, so they have a high linear correlation. The root mean square error between the estimated and measured valley depths is approximately 0.01 mm when the estimated valley depth is greater than 0.08 mm, and the misjudgment rate in making decisions on rail grinding based on the estimated valley depth is approximately 6.25%, indicating that the estimation method of valley depth has good applicability in actual high-speed railway.