STABILITY ANALYSIS AND APPLICATION OF THE CENTER MANIFOLD THEORY FOR A NONLINEAR SPRAG-SLIP MODEL

摘要

This paper presents a research devoted to the study of instability phenomena in non-linear model with a constant brake friction coefficient. We consider brake vibrations and more specifically heavy truck judder. The condition of stability is based on the resolution of a generalised eigenvalue problem and the limit cycle amplitudes are determined by the center manifold reduction. A model is presented for the analysis of a non-linear sprag-slip phenomena: the goal is to study the stability analysis and to validate the center manifold theory for a non-linear model by comparating results obtained by solving the full system and by using the center manifold approach. In this study, a non-linear stiffness is considered. This non-linearity is expressed as a polynomial with quadratic and cubic terms. The model does not require the use of brake negative coefficient, to predict the instability phenomena. The center manifold approach is used to obtain equations for the limit cycle amplitudes. The brake friction coefficient is used as unfolding parameter of the fundamental Hopf bifurcation point. The analysis shows that stable and unstable limit cycles can exist for a given constant brake friction coefficient.