LOW-FREQUENCY VIBRATIONS IN DISC BRAKES AT HIGH CAR SPEED .2. MATHEMATICAL-MODEL AND SIMULATION

In the present paper, a mathematical model is constructed for judder i n disc brakes at high speed. Vehicle suspension is modelled by means o f finite elements. Vibration modes and frequencies are derived that ca n be used in the classification of modes in main and secondary based i n the relative disc-calliper displacement; the finite element model is also used as well as in forced response analysis. Brake pads are defi ned through the friction coefficient as a function of speed, pressure, and temperature, in light of which one may consider the various braki ng conditions and types of pad. Since the line of reasoning introduces equivalent-damping terms into the equations of dynamics, these equati ons cannot be uncoupled by means of modal transformation. Two techniqu es are proposed for the solution of the problem. One of these consists in an examination of the 'main-modes' while the other is based on dir ect integration of the quasi-uncoupled equations. A computer program h as been implemented which allows the simulation of this kind of judder with different pads, brake systems and braking conditions.