Analytical investigation of steady-state stability and Hopf-bifurcations occurring in sliding friction oscillators with application to low-frequency disc brake noise

摘要

This article presents an analytical investigation on stability and local bifurcation behavior due to exponentially decaying friction characteristics in the sliding domain of a simple friction oscillator, which is commonly referred to as "mass-on-a-belt"-oscillator. Friction is described by a friction coefficient which in the sense of Stribeck depends on the relative velocity between the two tribological partners. For such a characteristic the stability and bifurcation behavior are discussed. It is shown, that the system can undergo a subcritical Hopf-bifurcation from an unstable steady-state fixed-point to an unstable limit cycle, which separates the basins of the stable steady-state fixed-point and the self-sustained stick-slip limit cycle. Therefore, only a local examination of the eigenvalues at the steady-state, as is the classical approach when investigating conditions for the onset of friction-induced vibrations, may not give the whole picture, since the stable region around the steady-state fixed-point may be rather small. Furthermore, the results of above considerations are applied to a brake-noise problem. It is found that, in contrast to squeal, a decaying friction characteristic may be a satisfying explanation for the onset low-frequency groan. The analytical results are compared with experimental measurements.