Stability analysis of a squealing vibration model with time delay

An exact stability analysis of a squealing vibration model with time delay is carried out using Olgac's direct method. The stability regions of the model without squealing noise are identified. Sensitivity of parameters, including a natural frequency, damping and an integrated coefficient of contact and friction, to the occurrence of squealing vibration is analysed. The results show that the time delay between the varying normal force and its causing varying friction has a distinct influence on the occurrence of squeal. It is found that with an increase of the time delay, the stability regions without squeal and the unstable regions with squeal generally arise alternately. The possibility of squeal occurrence is found to increase with increasing natural frequency. It is also found that the larger the integrated coefficient, the more easily squealing vibration occurs. The nonlinear simulation result shows that the contact separation between the two sliding surfaces is a main nonlinear factor which leads to squealing vibration being bounded. Disappearance of squeal is predicted. The simulation results are compared with the test results in both time and frequency domains and is found to be in good agreement with test results. The mechanism of squeal generation, growth and disappearance is proposed.