### Railway Carriage Model to Study the Influence of Vertical Secondary Stiffness on Ride Comfort of Railway Carbody Running on Curved Tracks

Karim H.Ali Abood, Rasheed Ahmid Khan

#### Abstract

A mathematical model of a railway carriage running on curved tracks is constructed by deriving the equations of motion concerning the model in which single-point and two-point wheel-rail contact is considered. The presented railway carriage model comprises of front and rear simple conventional bogies with two leading and trailing wheelets attached to each bogie. The railway carriage is modeled by 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 of carbody and each of the two bogies. 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 nonlinear Heuristic model is adopted to calculate the creep forces in which 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 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 running with speeds under and at critical hunting velocity. High magnitudes of vertical secondary spring stiffness suspension introduce undesirable roll and yaw dynamic response in which affect ride passenger comfort at critical hunting velocity. Low critical hunting velocity with railway carriage running on curved tracks can be represented.

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DOI: https://doi.org/10.5539/mas.v5n2p11