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.

具有滞后特性的摩擦缓冲器是纵向列车动力学（LTD）中典型的非线性元件之一。由于摩擦阻尼的非线性滞后，加载和卸载包络线之间的不连续性成为采用查表法建立缓冲器模型时的数学积分问题。如果忽略它可能会导致积分发散和错误的结果。为了解决这种不连续性，将三种不同的过渡策略（速度相关、中间坡度和平滑近似）应用于构建缓冲器模型，并使用采用“Zhai”积分方法的一维（1D）纵向列车模型。为确保结果准确，研究了LTD的国际基准案例，并对三种不同过渡策略的缓冲器模型进行了比较。结果表明，这三个模型可以成功地在LTD模拟中使用'Zhai'方法来实现与基准案例的力一致。与其他两个模型相比，速度相关模型没有表现出良好的缓冲偏转一致性，并且需要更小的步长来实现收敛结果。因此，建议采用中间斜率法或平滑近似法来避免LTD中的缓冲器建模不连续问题。速度相关模型没有表现出良好的缓冲偏转一致性，并且需要更小的步长来实现收敛结果。因此，建议采用中间斜率法或平滑近似法来避免LTD中的缓冲器建模不连续问题。速度相关模型没有表现出良好的缓冲偏转一致性，并且需要更小的步长来实现收敛结果。因此，建议采用中间斜率法或平滑近似法来避免LTD中的缓冲器建模不连续问题。