THE EFFECT OF VARIABILITY ON INSTABILITY OF FRICTIONINDUCED VIBRATION THROUGH UNCERTAINTY ANALYSIS

摘要

Among different hypotheses about the source of brake squeal, mode-coupling theory has attracted most attention in recent years. This theory reveals how the friction force leads to asymmetric elements in the stiffness matrix and causes the system to become unstable as certain system parameters vary. A stability analysis is carried out to determine the complex eigenvalues and those with positive real parts are thought to indicate brake squeal. The complex eigenvalue analysis is known as the most efficient way for predicting brake squeal instability in terms of computation cost and time. In real braking systems, the geometry of the brake components varies from one brake to another and material properties deviate from the nominal values, due to the manufacturing processes. Assembling introduces a degree of variability. Friction and contact are major sources of uncertainty. Experimental results show the friction coefficient has a wide spread of values. The inconsistent nature of brake squeal often obscures the root cause of squeal and therefore necessitates considering the variability and uncertainty of material and geometric properties of real brake systems in order to predict brake squeal in a stochastic way. Uncertainty analysis can provide a proper foundation to take the variability and uncertainty into consideration. In contrast with deterministic approaches through which single fixed values for the output are obtained, uncertainty propagations generate a distribution for the output. In this way, it is possible to consider the variability of input parameters and then have a more reliable and realistic prediction of the system instability in terms of statistical measures. In order to gain a deeper understanding of this approach and expand the complex eigenvalue analysis approach, a simplified model of friction-induced vibration with four degrees of freedom is studied in this paper. By considering probabilistic distributions in the values of different system parameters that may represent the stiffness of the pad, abutment and calliper in a real system, and also a probabilistic distribution of the coefficient of friction, the effect of variability on the output of the system is obtained.