Effect of Geometry on Thermoelastic Instability in Disk Brakes and Clutches

Abstract

The finite element method is used to reduce the problem of thermoelastic instability (TEI) for a brake disk to an eigenvalue problem for the critical speed. Conditioning of the eigenvalue problem is improved by performing a preliminary Fourier decomposition of the resulting matrices. Results are also obtained for two-dimensional layer and three-dimensional strip geometries, to explore the effects of increasing geometric complexity on the critical speeds and the associated mode shapes. The hot spots are generally focal in shape for the three-dimensional models, though modes with several reversals through the width start to become dominant at small axial wavenumbers n, including a “thermal banding” mode corresponding to n = 0. The dominant wavelength (hot spot spacing) and critical speed are not greatly affected by the three-dimensional effects, being well predicted by the two-dimensional analysis except for banding modes. Also, the most significant deviation from the two-dimensional analysis can be approximated as a monotonic interpolation between the two-dimensional critical speeds for plane stress and plane strain as the width of the sliding surface is increased. This suggests that adequate algorithms for design against TEI could be developed based on the simpler two-dimensional analysis.