Georg-Peter Ostermeyer

On the dynamics of the friction coefficient

Abstract The paper deals with the principal wear mechanism in brake systems and introduces a new dynamical model of the friction coefficient, where necessarily both friction and wear are taken into account. This model explains many open questions on the principal functionality of brake systems. In brake systems, characteristic structures are formed in the contact area by the flow of wear particles. Modulated by the friction power the wear particles are used by the system to build up hard contact patches on the brake pad. Nearly all energetic dissipation of the system is concentrated on these patches. By wear, these contact patches are destroyed after some time. So the friction coefficient is given by the equilibrium of flow of birth and death of contact patches. The resulting dynamical model describes the dynamical behaviour of the friction coefficient and the dependence of the temperature in the friction layer. This theory explains the fading effect of brake systems as well as complex hysteretic effects in the diagram of the friction coefficient versus the velocity, known from instationary measurement procedures. The structure of this theory seems to be quite general to describe other frictional systems too.

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.

Eigenschaften der Reibpaarungen im Bremsenprozess

Bremsen sind Funktionseinheiten komplexer Maschinen, die deren Bewegungsenergie, die sog. kinetische Energie, begrenzen oder verringern konnen. Ein sehr wirkungsvolles Prinzip, kinetische Energie zu verringern, ist die Nutzung der Reibung zwischen zwei Korpern. Reibung ist eine Kraft, die immer dann auftritt, wenn zwei Korper mit einer Kraft F N, der Normalkraft, gegeneinandergedruckt werden und eine Tangentialkraft F versucht, die Korper gegeneinander zu bewegen. Die Reibkraft liegt in der Kontaktflache und behindert sowohl Gleitbewegungen der Korper gegeneinander als auch den Versuch, eine Gleitbewegung zu initiieren Abb. 26.1. Ist die Gleitgeschwindigkeit v ungleich Null, so spricht man von Gleitreibung, ansonsten von Haftreibung.