Influence of wear on thermoelastic instabilities in automotive brakes

• We introduce two new models on the interaction of thermoelastic instability (TEI) and wear: one minimal model and one model with many DOF.
• The minimal model shows different solution regimes: a periodic solution can only be found if wear is included.
• A nonlinear analysis shows that every unstable solution is a periodic solution.
• The results of the model with many DOF agrees with experimental results on the “Migrating Hot Band” phenomenon in brake systems.

In typical automotive disk brakes, two pads of organic material slide against both surfaces of a gray cast iron disk. The two materials have contrary properties with regard to elasticity, temperature and wear. One aim of this is to avoid thermoelastic instabilities (TEI) that lead to material disruption and vibrations. TEI results from local thermal expansion at regions of elevated temperature, which increases local contact pressure and destabilizes the temperature field. Common TEI models scarcely account for wear. To investigate TEI, a multi-field-problem (temperature and elastic field) must be solved. Wear can be included via boundary conditions, in terms of time-dependent contact topography and load-distribution. The basic interaction mechanisms between wear, temperature and elasticity can be explained by a minimal model that allows a nonlinear investigation and a multi-DOF-model. The inclusion of wear results in a periodic movement of hot bands that influence the effective braking radius. A nonlinear analysis shows that this periodicity is possible, although a linear model computes purely real eigenvalues. A comparison with experiments indicates that the correct stability threshold and the correct eigenform are found. The presented approach shows how wear influences the dynamics of TEI, and that a periodic motion of TEI is possible if wear is taken into account. This can only be partially described by linear models because it is highly nonlinear (local loss of contact). The approach focusses on automotive brakes, but can similarly be applied to clutches or disk brakes with multiple disks, e.g. in aircraft.