Comparison of friction draft gear models for simulation in longitudinal train dynamics

The friction draft gear with hysteresis characteristics is one of the typical nonlinear elements in longitudinal train dynamics (LTD). Due to the nonlinear hysteresis of friction damping, the discontinuity between loading and unloading envelopes becomes a mathematical integration issue when adopting look-up table methods to establish draft gear models. It might cause integration divergence and wrong results if ignored. To solve this discontinuity, three different transitional strategies (velocity-dependent, intermediate slope, and smoothing approximation) are applied to building draft gear models, and the one-dimensional (1D) longitudinal train model adopting the ‘Zhai’ integration method is used. To ensure accurate results, the international benchmark cases of LTD are studied, and three draft gear models with different transitional strategies are compared in this paper. The results show that these three models can successfully work with ‘Zhai’ method in the LTD simulation to achieve the force agreement with benchmark cases. Compared to the other two models, the velocity-dependent model doesn’t exhibit good buffer deflection agreement and requires a smaller step size to achieve convergent results. Therefore, it is recommended that adopting the intermediate slope method or smoothing approximation approach avoids discontinuity problems of modelling draft gears in LTD.