Railway carriage simulation model to study the influence of vertical secondary suspension stiffness on ride comfort of railway carbody

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Abstract
A mathematical model of a railway carriage moving on tangent tracks is constructed by deriving the equations of motion concern the model in which single-point and two-point wheel–rail contacts are considered. The presented railway carriage model comprises front and rear simple conventional bogies with two leading and trailing wheelsets attached to each bogie. The railway carriage is modeled using 31 degrees of freedom which govern vertical displacement, lateral displacement, roll angle, and yaw angle dynamic response of wheelset, whereas vertical displacement, lateral displacement, roll angle, pitch angle, and yaw angle dynamic response carbody and each of the two bogies were also studied. Linear stiffness and damping parameters of longitudinal, lateral, and vertical primary and secondary suspensions are provided to the railway carriage model. Combination of linear Kalker’s theory and non-linear Heuristic model is adopted to calculate the creep forces introduced at wheel and rail contact patch area. Computer-aided simulation is constructed to solve the governing differential equations of the mathematical model using Runge–Kutta fourth-order method. Principle of limit cycle and phase plane approach is applied to realize the stability and evaluate the concerning critical hunting velocity at which the railway carriage starts to hunt. The numerical simulation model is used to study the influence of vertical secondary suspension spring stiffness on the ride passenger comfort of railway carbody at speeds below and at critical hunting velocity. High magnitudes of vertical secondary spring stiffness suspension introduce undesirable roll and yaw dynamic responses in which affect ride passenger comfort at critical hunting velocity.

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