Background Information

A sliding system such as automotive disk brake or transmission clutch involves two or more sliding bodies which are nominally conforming over some contact area. An imperfection might disturb the otherwise uniform pressure distribution and hence the frictional heat generation. This produces non-uniform thermoelastic distortion and further non-uniformity in the contact pressure distribution. If the sliding speed is sufficiently high, the thermal-mechanical feedback process is unstable, leading eventually to the localization of the load in a small region of the nominal contact area of the sliding surfaces. This phenomenon, generally known as thermoelastic instability or TEI, was first discovered and explained by Barber (1967, 1969) in sliding systems involving frictional heating. TEI has long been recognized as imposing design constraints on high performance systems such as aircraft brakes, but interest in the phenomenon in the automotive industry is more recent, being prompted by changes in braking materials and other design improvements.

In the HotSpotter, a finite element method is developed for determining the critical sliding speed for TEI 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 wave number. The Fourier reduction method developed in HotSpotter permits a remarkably efficient solution of the frictional thermoelastic stability problem for systems in which the geometry is axisymmetric. The power of the method is demonstrated by the multidisk clutch example, direct numerical simulation of which would represent an extremely challenging computational problem. Values are obtained for the critical sliding or rotational speed and also for the exponential growth rate of each mode when operating above the critical speed. The method is easily applied to other examples and can therefore be used to assess the effect of design modifications such as changes in geometry and material properties on the thermoelastic stability of multidisk brakes and clutches.

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