Eigenvalue solution of thermoelastic instability problems using Fourier reduction

Abstract

A nite-element method is developed for determining the critical sliding speed for thermoelastic instability of an axisymmetric clutch or brake. Linear perturbations on the constant-speed solution are sought that vary sinusoidally in the circumferential direction and grow exponentially in time. These factors cancel in the governing thermoelastic and heat-conduction equations, leading to a linear eigenvalue problem on the two-dimensional cross-sectional domain for the exponential growth rate for each Fourier wavenumber. The imaginary part of this growth rate corresponds to a migration of the perturbation in the circumferential direction.The algorithm is tested against an analytical solution for a layer sliding between two half-planes and gives excellent agreement, for both the critical speed and the migration speed. Criteria are developed to determine the mesh re nement required to give an adequate discrete description of the thermal boundary layer adjacent to the sliding interface. The method is then used to determine the unstable mode and critical speed in geometries approximating current multi-disc clutch practice.

Transient solution of a thermoelastic instability problem using a reduced order model

“…Hot spots are then generated at the sliding interface, causing material damage, wear and low-frequency frictional vibrations [2][3][4]. Methods for determining the critical sliding speed for instability were pioneered by Burton et al [5] and have since been developed for practical brake and clutch geometries using the ÿnite element method [6,7]. However, these solutions all assume that the sliding speed is constant, whereas actual brakes and clutches operate at variable sliding speed.…”

Analysis of disc brake temperature distribution during single braking under non-axisymmetric load

“…Operation of disc brake above the certain range of the velocity may lead to thermoelastic distortions and in consequence to non-uniform pressure distribution due the interchanged moments of contact and its absence during rotation, known as thermoelastic instability (TEI) [14]. The upwind scheme in finite element formulation to prevent possible perturbations owing high Peclet number was developed [15].…”

On fatigue limit in the presence of notches: classical vs. recent unified formulations

“…Burton et al (1973) investigated the TEI problem for two sliding half-planes by determining the condition under which a small perturbation on the uniform pressure solution could grow exponentially in time. Burton's method has since been applied to both categories of thermoelastic stability problem in both analytical and numerical (finite element) form (Lee and Barber, 1993;Barber, 1995, 1996;Yi et al, 2000).…”