Friction, Instability and Parametric Studies of a Nonlinear Model for an Aircraft Brake Whirl Analysis

Abstract This paper presents a research devoted to the study of instability phenomena in non-linear model with a constant brake friction coefficient. The condition of stability is based on the resolution of a generalized eigenvalue problem and the limit cycle amplitude are determined by the center manifold reduction. A model is presented for the analysis of whirl mode vibration in aircraft braking systems. In this study, a non-linear material behaviour of the brake heat stack is considered. This non-linearity is expressed as a polynomial. The model does not require the use of brake negative damping and predicts that instability can occur with a constant brake friction coefficient. The center manifold approach is used to obtain equations for the limit cycle amplitude. 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.