BIFURCATION ANALYSIS OF THE EFFECT OF TYRE INFLATION PRESSURE ON WHEEL SHIMMY WITH MULTIPLE TYRE PROPERTIES CONSIDERED

Abstract The shimmy oscillations of a truck’s front wheels with dependent suspension are studied to investigate how shimmy depends on changes in inflation pressure, with emphasis on the inclusion of four nonlinear tyre characteristics to improve the accuracy of the results. To this end, a three degree-of-freedom shimmy model is created which reflects pressure dependency initially only through tyre lateral force. Bifurcation analysis of the model reveals that four Hopf bifurcations are found with decreased pressures, corresponding to two shimmy modes: the yaw and the tramp modes, and there is no intersection between them. Hopf bifurcations disappear at pressures slightly above nominal value, resulting in a system free of shimmy. Further, two-parameter continuations illustrate that there are two competitive mechanisms between the four pressure-dependent tyre properties, suggesting that the shimmy model should balance these competing factors to accurately capture the effects of pressure. Therefore, the mathematical relations between these properties and inflation pressure are introduced to extend the initial model. Bifurcation diagrams computed on the initial and extended models are compared, showing that for pressures below nominal value, shimmy is aggravated as the two modes merge and the shimmy region expands, but for higher pressures, shimmy is mitigated and disappears early.