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Theoretical Investigations of Brake Judder

Ams A., Schmalfuss C., Wedig W.

Machine Dynamics Problems

2000

Vol. 24, No. 1

9-13

The disc brake of a car will be considered as a linear timevariant model with one degree of freedom and will be described by the equation of motion [formula] Herein, the parameter ω1 denotes the natural frequency of the linear oscillator, D and B are damping coefficients. The coordinate x describes the displacement of the grake pad and the coordinate s gives the position of the contact point between the pad and the disc [omega]0 is a frequency parameter, μ is the friction coefficient (Coulomb) and the function u(s) describes the roughness of the disc surface. Time derivatives are abbreviated by dots and dash is a derivative with respect to s. Harmonic and stochastic excitations will be discussed. The first part is devoted to the harmonic case. With the Floquet theory a stability map will be calculated. This stability map shows stable and unstable regions in dependency on the velocity of the disc. The second part discusses stochastic excitations. To determine the asymptotic stability of the zero position one has to calculate the top Lyapunov exponent of the system. This part explains a computational method to calculate these exponents. The calculated Lyapunov exponents are shown in a stability map.