Order domain analysis of speed-dependent friction-induced torque in a brake experiment

A friction-induced forced vibration problem, as excited by the geometric distortions of the brake rotor, is studied in this article. The focus is on the order domain analysis, as the speed-dependent behavior of friction torque is not well understood. First, a new laboratory experiment is constructed to simulate vehicle brake judder in a scientific and yet controlled manner. The variations in pressure and torque are measured as the rotor slows down, and the order domain tracking is used to construct shaft torque vs. speed diagrams. A quasi-linear model of the laboratory experiment is then developed to obtain an analytical solution and to estimate the torque envelope function. A nonlinear model of the laboratory experiment (with a clearance) is also investigated to examine the resonant amplitude growth. Finally, predictions are successfully compared with measurements. Several contributions emerge over the prior literature. In particular, the experimental data clearly show that multiple-orders of the rotor surface distortion profile excite the friction-induced torque, and a clearance in the torsional system controls the resonant amplitude regime. New analytical and numerical solutions provide much insight into the speed-dependent resonant amplitude growth process.