Theoretical investigation of wheel/rail non-linear interaction due to roughness excitation

A study is presented of the non-linear dynamic interaction between a wheel and rail, excited by roughness on the wheel and rail contact surfaces. A moving irregularity model is used to represent the wheel/rail interaction process in the time-domain. A low order multiple degree-of-freedom system is developed to approximate the infinite track for numerical simulations. The effects of the non-linear contact on the wheel/rail dynamic interaction are investigated through calculations, analysis and comparisons with the results from a linear contact model. The difference between the non-linear and linear interactions is found to be small if the roughness level is not extremely severe and a typical static contact preload exists. The difference increases for low preloads or for high roughness amplitudes. For example, if the wheel and rail surfaces are in good condition (r.m.s. amplitudes of roughness below 15 mum), the linear model can be used without significant error for all static loads down to 25 kN (equivalent to an unloaded container wagon). When the track is corrugated with an r.m.s. amplitude of 25 mum, good agreement between linear and non-linear models is obtained for static loads of 50 kN and above, typical of passenger stock or loaded freight vehicles, but differences of up to 4 dB in one-third octave force levels are found at 25 kN. Differences between the linear and non-linear models are found to occur when the r.m.s. roughness amplitude is more than 0.35 times the static deflection of the contact zone; significant loss of contact occurs at amplitudes about 1.5 times greater than this.