Effect of geometry on thermoelastic instability in disk brakes and clutches

The finite element method is used to reduce the problem of thermoelastic in stability (TEI) for a brake disk to an eigenvalue problem for the critical speed. Conditioning of the eigenvalue problem is improved by performing a p reliminary Fourier decomposition of the resulting matrices. Results are als o 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 i n shape for the three-dimensional models, though modes with several reversa ls through the width start to became dominant at small axial wavenumbers n, including a "thermal banding" mode corresponding to n = 0. The dominant wa velength (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 fro m the two-dimensional analysis can be approximated as a monotonic interpola tion between the two-dimensional critical speeds for plane stress and plane strain as the width of the sliding surface is increased. This suggests tha t adequate algorithms for design against TEI could be developed based on th e simpler two-dimensional analysis.