On the Effect of Track Irregularities on the Dynamic Response of Railway Vehicles

The steady state response for models of a six-axle locomotive running on a sinusoidally irregular track has been investigated. Two mathematical models have been set up, a full model for the “stationary” vehicle in which creep between wheels and rails was neglected, and a full model for the “moving” vehicle in which creep forces, gravity stiffness effects and wheel tread profiles were considered. The use of the generalized method of complex algebra to obtain the steady state response of the railway vehicle components to varying input frequencies was used. The results given in this paper are for the case of sinusoidal lateral track irregularities only, but the method is general enough to allow also for vertical track irregularities. For the “stationary” vehicle the input frequency is increased from zero to 3 cycles per second. For the “moving” vehicle the input frequency is a function of the track wave length and the vehicle forward speed and is given in terms of the vehicle speed. The frequency response curves are computer plotted in each case. For the “moving” vehicle, responses for the cases of both new and worn wheels are obtained. The natural frequencies for the full model are also calculated. The results obtained show the effect of the creep forces and the condition of the wheels on the steady state response. It is recommended that slip and corresponding creep forces, wheel tread and rail profiles, and the gravity stiffness effect be included in the steady state response analysis of railway vehicles to track irregularities. The analysis may be used to check the response of any proposed design for a railway vehicle to economically attractive track irregularities. It may also be used to adjust geometry, spring rates and damping characteristics in order to maximize operating speeds while providing optimum damping for the trucks and body motions. This paper illustrates and describes the mathematical models used; gives generalized form for the differential equations of motion and the methods of solution. The equations of motion for the wheelsets are derived in detail including the creep forces and the wheel tread profiles.