EIGENVALUES EVALUATION OF GENERALLY DAMPED ELASTIC DISC BRAKE MODEL LOADED WITH NON-CONSERVATIVE FRICTION FORCE

Abstract

This paper deals with the evaluation of eigenvalues of a linear damped elastic two-degrees-of-freedom system under a non- onservative loading. As a physical interpretation of a proposed mathematical model, a simplified disk brake model is considered. A spectral analysis is performed to predict an eigenvalues bifurcation, known as the Krein collision, leading to double eigenvalues, one of them having a positive real part causing a vibration instability of the mechanical systems. This defective behaviour of eigenvalues is studied with respect to a magnitude of non-conservative Coulomb friction force, through the variation of the friction coefficient. The influence of a proportional versus general damping on the system stability is further analysed. The generalized non-symmetric eigenvalue problem calculation is employed for spectral analyses, while a modal decomposition is performed to obtain a time-domain response of the system. The analyses are compared with an experiment.

Keywords

• eigenvalues bifurcation, krein collision, non-conservative force, modal decomposition, brake squeal.