Stochastic characterization of friction-induced vibration

Stochastic characteristics of friction-induced vibration are investigated especially for a pin-on-disc system and a brake disc.; The experimental investigation are performed at low disc speed based on a representative pin-disc apparatus. The interfacial forces between the rotating disc and the stationary pin (friction element assembly) are found to be essentially non-stationary and non-Gaussian wide band random processes. When the disc rotates cock-wise, the mechanism of sprag-slip is demonstrated to be main reason for severe squeal. The natural frequency of the pin is always time-dependent, indicating that the pin possesses time varying boundary conditions.; For the vibration of the pin, depending on its different condition at the fixed end of the pin. The analytical model of the pin is treated as a cantilever beam with inhomogeneous boundary conditions or a rigid bar with a torsional spring attached at fixed end. The former is solved using variable transformation technique for the first mode of the beam and associated stochastic stability condition is obtained. The latter, incorporated with linear and nonlinear friction-velocity models that are developed based on the experimental data. The analysis of both models are carried out using the stochastic averaging method. The problem of noise-induced transition is examined for nonlinear model. For the piecewise linear friction-velocity model, the complete probabilistic description of the pin's dynamic behavior is derived in a closed form and corresponding stochastic stability conditions are studied in detail.; For the disc vibration, the general equations of motion for a rotating disc under stationary distributed in-plane frictional loads is established using Hamilton's principle on the basis of Mindlin theory. Under either deterministic or random follower-type frictional loads, response characteristics such as stability conditions, critical speed, vibration type, and response statistics are studied analytically and numerically. As an important result of this study, circumferential oscillation of the disc is also responsible for vibration and noise of disc brakes besides transverse deflection.