Linear and Nonlinear Energy Analysis of a Minimal Model for Brake Squeal

The simulative assessment of brake squeal is commonly performed by applying the complex eigenvalue analysis (CEA) to large finite-element-method (FEM) models. Despite many advantages, this method has two major drawbacks: First, the resulting negative damping value gives no quantitative measure for the actual squeal propensity and second, no reliable experimental technique to measure the negative damping is available. Therefore, a direct validation and comparison of simulated and experimental squeal propensity is not possible. In this work, the energy analysis of friction-induced vibrations, proposed by Guan et al. [1] and Wagner et al. [2], is considered to overcome these drawbacks. Equations for computing the mechanical work proportions of a general multi-degrees-of-freedom (DOF) system, including the external work, are derived. These work proportions are compared to the results of the CEA for a self-excited linear and nonlinear two-DOF system exhibiting a mode coupling instability. It is shown that the work proportions of the linear and nonlinear system yield to the same stability boundaries as the CEA. The energy analysis enables the separate investigation of the dissipative and exciting work. In addition, the external work was found to predict the onset of an instability even before its actual occurrence.     «

The simulative assessment of brake squeal is commonly performed by applying the complex eigenvalue analysis (CEA) to large finite-element-method (FEM) models. Despite many advantages, this method has two major drawbacks: First, the resulting negative damping value gives no quantitative measure for the actual squeal propensity and second, no reliable experimental technique to measure the negative damping is available. Therefore, a direct validation and comparison of simulated and experimental squ...     »