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Railway wheel axle experiences the problem of hunting above a critical velocity, which is a kind of self-excited oscillation. This paper investigates the linear and non-linear stability analysis of wheel axle constrained within a fixed bogie frame. From the linear analysis the critical velocity of the system with the existing parameters is found to be 268 km/hr. The influence of different parameters on stability of the system is further investigated in present study. Nonlinear analysis provides additional information compared with linear systems. Nonlinear analysis provides several stable solutions with a single set of parameters and each stable solution is function of the initial conditions. Using domains for initial conditions i.e. domains for attraction, chances for existence for stable solutions is determined. Present nonlinear analysis indicates that for vehicle velocity range from the critical velocity 366 km/hr to 392 km/hr, two stable solutions coexist i.e. the trivial solution with limit cycle solution and for the range of velocities beyond 392 km/hr one stable solution exist.

The study deals with the design of the automotive suspension system to better dynamic characteristics in an uncertain operating atmosphere. Vehicle design parameters are to be optimized to achieve better passengers comfort, vehicle body stability, and road holding as the measure of suspension system performance improvement. The design of experiments gives the optimum parametric combination in the domain on the basis of vertical body acceleration data obtained by simulation of a 2-DOF nonlinear quarter car model. Moreover, the nonlinear hysteric behavior foremost design parameters have been characterized through the theoretical and experimental analysis in order to validate the design and to check the analogical viability of the derived model. Finally, the proposed methodology ascertains the optimum design of the suspension system in the time and cost-effective manner. The developed passive design of car suspension system exhibits excellent vibrational characteristics and convinces the acceptable range of vehicle vibration as suggested by ISO-2631-1997.