Numerical Simulation Model to Study the Dynamic Behavior of Railway Single Wheelset on Tangent Tracks with Single-point and Two-point Wheel-rail Contact

Nonlinear mathematical model of a railway single wheel-set moving on tangent tracks is constructed in which single-point and two-point wheel-rail contact has taken into consideration. The considered railway single wheelset system is modeled by 6 degrees of freedom which govern lateral displacement, vertical displacement, roll angle and yaw angle of single wheelset and lateral displacement of each left and right rails. Longitudinal, lateral and vertical primary suspensions with linear suspension characteristics are provided to the system. Combination of linear Kalker's theory and nonlinear Heuristic model has been applied to calculate the creep forces introduced on wheel and rail contact due to friction properties of the wheel-rail contact geometry. The presented nonlinear mathematical equations of motion are transformed into a set form of first order differential equations known as state space equations to be suitable for numerical integration. Computer aided-simulation is constructed to solve the transformed differential equations of the system using fourth order Runge-Kutta method. Principles of limit cycle and phase plane approach is applied to realize the stability and to evaluate the concerning critical hunting velocity of the system subjected to different parameters of wheel conicity and suspension characteristics. The numerical simulation model represents the dynamic responses on lateral, yaw, roll and vertical motions of the system moving on tangent tracks subjected to specific parameters. Single wheelset model is examined to evaluate the critical hunting velocity in which the hunting phenomenon on the system occurs under different values of wheel conicity. The results obtained that shows critical hunting velocity is proportional inversely to wheel conicity, are compared with previous model constructed by 4 degrees of freedom governed lateral displacement and yaw angle of wheelset while lateral displacement of left and right rails. Effect of vertical primary suspension spring stiffness on vertical response and on critical hunting velocity of the system is investigated. It is concluded that primary vertical spring stiffness has a compromise values must be chosen to eliminate hunting unstability and increase the critical hunting velocity of the system.