Investigation of chaotic instabilities in railway wheel squeal

Abstract

The occurrence of chaotic motion in a railway instability phenomenon known as wheel squeal is investigated. The analysis is motivated and applied to predicting the large amplitude friction excited oscillations of the coupled wheel and rail motion. The equations of motion reduce to two autonomous coupled nonlinear second-order systems. Instabilities of the wheel and rail motions are shown to be due to the friction coupling which at low amplitudes causes limit cycle behaviour via a Hopf bifurcation. When the amplitude grows large enough, full nonlinear creep oscillations are shown to occur causing oscillations about positive and negative sliding conditions. Chaos is shown to occur when the motion meanders and jumps between large positive and negative creep and is characterised by a Poincare map with fractal nature. The route to chaos is shown to be via quasiperiodicity. Based on this insight, necessary analytical conditions for wheel squeal chaos are developed and verified using numerical simulations over a range of angles of attack and wheel/rail contact angles. Conditions under which chaotic instability is more likely to occur are identified and discussed, including mode coupling and parametric excitation. The results may describe why some very loud occurrences of wheel squeal are not characterised by a pure tone.