Ballinger, R., "A Discussion of Complex Eigenvalue Analytical Methods as They Relate to the Prediction of Brake Noise," SAE Int. J. Passeng. Cars - Mech. Syst. 9(1):183-198, 2016, doi:10.4271/2016-01-1299.
The complex eigenvalue analysis has been used by the brake research community to study friction-induced squeal in automotive disk brake assemblies. The analysis process uses a nonlinear static pre-stressed normal modes analysis simulation sequence followed by a complex eigenvalue extraction algorithm to determine the dynamic instabilities. When brake hardware exists, good correlation between analysis results and experimental data can be obtained. Consequently, complex eigenvalue analysis can be a valuable method in an effort to understand brake components that might have a propensity to influence the noise behavior of a brake system. However, when hardware does not exist and the complex eigenvalue method is asked to be predictive, it becomes a difficult, if not impossible task. This paper will focus on some of the reasons the complex eigenvalue analysis method is not a reliable predictor of friction-induced squeal in automotive disk brake assemblies. Two general areas of modelling methodology are discussed. The first area of discussion focuses on generic FEA boundary conditions that are independent of the commercial code used. Examples of generic or non-code specific boundary conditions are rotor and wheel/wheel simulator or dynamometer attachment methodology and slide pin and piston penalty contact or radial coupling definitions. The second area of discussion focuses on specific boundary conditions that are commercial code dependent. An example of a specific boundary condition is the contact stiffness scale factor specification for all prestressed contact surfaces and the resulting pre-stressed normal modes analysis results. Inappropriate choices for these generic and specific boundary conditions will render the complex eigenvalue method incapable of functioning as a predictive tool for friction-induced squeal in automotive disk brake assemblies.