A new instability index for unstable mode selection in squeal prediction by complex eigenvalue analysis

During these last decades the modal instability of systems, generated by frictional contact forces, has been the subject of a huge amount of works in friction induced vibration literature. Linear and nonlinear numerical analyses have been largely investigated to predict and reproduce squeal vibrations. While nonlinear transient analysis needs large computational efforts, results of Complex Eigenvalue Analysis (CEA) suffer from an over-prediction issue and it is not able to predict correctly the mode that will become effectively unstable in case of several unstable eigenvalues. Because the CEA has been adopted as an efficient tool for brake design, a more reliable index is here proposed, from the CEA outputs and energetic considerations, to identify the mode that will become effectively unstable. A modular lumped model is developed to reproduce friction induced vibrations. The use of the eigenvalue real part, as discriminant of the system instability, is here combined with information coming from the eigenvectors, projected on the equilibrium position, to account for the energy flows involved in the squeal phenomena. This approach allows to define a Modal Absorption Index (MAI). The MAI allows for comparing unstable modes of the same system and is applied in this paper to predict, by CEA outputs, the unstable mode that will effectively result in squeal vibrations.