Investigation of the tire in-plane vibration property using an improved ring model

Abstract

The paper investigates the in-plane vibration property of static and rotating tires with the proposed tire model. The tire model is based on the linear ring model, and a mathematical approach is proposed to handle the tire contact problem. With this improvement, the tire model allows for directly calculating the eigenmodes of a loaded tire by solving its eigenvalue problem. A group of simulations is carried out using this improved ring model. For a static (not rotating) tire, the eigenfrequency and corresponding mode shape are investigated under both unloaded and loaded conditions. For a rotating tire, the effect of rotational speed on the eigenfrequencies of unloaded and loaded tires are modeled, and the results are observed using co-rotating and non-rotating reference frames. The main original contribution of this work is an evaluation of the quantitative relationship between unloaded and loaded conditions using modal assurance criterion (MAC) or improved modal assurance criterion (IMAC) analyses on both static and rotating tires. For a static tire, the eigenmodes can be classified into rigid ring modes and flexible ring modes, according to their mode shape and MAC evaluation results. For a rotating tire, the eigenfrequency and mode shape could vary with increasing rotational speed and behave differently in non-rotating and co-rotating reference frames. In a non-rotating frame, the IMAC value percentages for a loaded tire vary with increasing rotational speed, especially in the frequency veering ranges. In a co-rotating frame, the IMAC value variations for loaded modes are weaker than those seen in a non-rotating frame.