Analysis of a brake squeal functional model using a linear parameter varying perspective

Brake squeal is a limit cycle vibration induced by mode coupling instability that depends on operating conditions such as applied pressure, temperature, and disc velocity. This work proposes a simplified functional model of brake squeal that reproduces the main characteristics observed in a full-scale industrial test campaign: vibration growth, limit cycle saturation, vibration decay and parametric dependence. The proposed functional model differs from the well-known Hoffmann model by the introduction of a nonlinear contact law and a quasi-static pressure loading. First, using a harmonic balance perspective, non-linear forces are shown to lead to a pressure and amplitude dependent contact stiffness. This Linear Parameter Varying perspective allows complex mode computations in the pressure/amplitude domain which are then correlated with a series of transient responses of the nonlinear modes for three different pressure profiles. The chosen profiles represent usual experiments: drag where a constant pressure is applied, pressure ramps and pressure oscillations mimicking the effect of wheel spin on the contact surfaces.