Formulation of a Linearized Model for Vehicle‐Track Interactions

In this paper, a fundamental wheel‐rail interaction (WRI) element accompanied by its coupling matrices with other vehicle‐track components have been derived taking into consideration the aspect of linearization. The key to the presented formulation is the use of the geometrical relationships of relative motions between degrees of freedom (DOFs) and energy principle. To the WRI element, both of the conditions of wheel‐rail contacts and wheel‐rail separations are allowed in the numerical computations; besides, the effects of the linear creepage and the gravitational restoring are considered in the description of wheel‐rail interactions. By comparing with an advanced three‐dimensional nonlinear model, the capability of the linear model in characterizing the response amplitude and frequency characteristic of vehicle‐track systems is demonstrated. Moreover, the method for the random vibration analysis of the linear model is presented by treating the creep coefficients as the random sources, through which the safety margin of system response can be predicted well. From the numerical examples, it is, additionally, concluded that the lateral creep coefficient holds significant influence on wheel‐rail lateral interactions and track vibrations, especially for the responses at low frequency ranges.