Hot bands and hot spots: Some direct solutions of continuous thermoelastic systems with friction

Hot bands and hot spots are thermoelastic phenomena appearing in frictional systems with high energy dissipation like brake systems or clutches. These thermoelastic instabilities are driven by the interaction of friction-induced heat in the sliding plane and thermal expansion of the materials. Systems exposed to thermoelastic instabilities show a characteristic temperature pattern that can lead to local material damage and vibrations like judder or brake torque fluctuations. While hot bands are observable by a cut through the system normal to the direction of sliding, hot spots are described by a cut parallel to the direction of sliding. When an angle parameter is introduced in a model-based description, both types of thermoelastic instabilities can be described by one single model. Such a model is presented that comprises of layers corresponding to different mechanical parts (e.g. pad, disk, homogenized cooling channels). Every layer is described by field equations for thermoelastic behavior and heat conduction. All layers basically include the same set of solutions which can analytically be found by separation of complex variables. These solutions are scaled to satisfy the boundary conditions at the contact areas between the layers. No symmetry conditions are required, but if present, they can simplify the model. The stability of one thermoelastic phenomenon under investigation is determined by evaluating the characteristic equation of the system. The appearance of hot spots or bands, their spatial distribution and movement are discussed in terms of sliding velocity and other system parameters.