| The understanding, prediction, and prevention of automotive/aircraft disc brake vibration and noise is a difficult and challenging problem because of the complex nature of the brake system, involving tribological and dynamic aspects as well as a large number of design parameters. Therefore, in spite of extensive research employing sophisticated experimental and analytical techniques, no model has successfully described the squeal phenomenon and the prevention of its occurrence is far from reality. The purpose of this research is to establish an innovative analytical model to understand the fundamental causes of brake vibration and noise, and to provide new insights into the brake squeal generation mechanism.; Based on the key results reported in the literature, a mathematical model which is nonlinear, nonconservative, time-dependent, and subjected to quasiperiodic excitations is established to examine the vibration and instability of the brake rotor-pad system. Applying a linearized model first, the effects of various system parameter such as the coefficient of friction, number of nodal diameters of the spinning brake rotor, pad end conditions, and geometry of the brake caliper on the stability are investigated. The full nonlinear model is then examined. For the first time, nonlinearity resulting from the contact mechanics between the disc and pad predicts a possible irregular motion (chaotic vibration) of the brake pad in the neighborhood of resonance. This chaotic behavior is identified and quantitatively measured by applying Poincaré maps, Fourier spectra, and Lyapunov exponents. It is found that these chaotic motions emerge as a result of successive Hopf bifurcations characterized by the torus breakdown and torus doubling routes as the excitation frequency varies. Besides, as a subject of future research work related to disc brake vibration and noise, a general form of mathematical model for a spinning disk subjected to a distributed frictional traction is developed based on the Mindlin's thick plate theory. This model also includes the effect of rotor rigid body motion which is often encountered in the lower frequency ranges. Moreover, the plane stress state due to distributed in-plane loading is obtained in a closed form by expressing the solution in a Fourier series. This rotor model can be applied to other spinning disk applications with similar loading conditions such as high speed gyroscopes and turbines. |
