Disk brake squeal prediction using the ABLE algorithm

Abstract

Disk brake squeal noise is mainly due to unstable friction-induced vibration. A typical disk brake system includes two pads, a rotor, a caliper and a piston. In order to predict if a disk brake system will generate squeal, the finite element method (FEM) is used to simulate the system. At the contact interfaces between the pads and the rotor, the normal displacement is continuous and Coulomb's friction law is applied. Thus, the resulting FEM matrices of the dynamic system become unsymmetric, which will yield complex eigenvalues. Any complex eigenvalue with a positive real part indicates an unstable mode, which may result in squeal. In real-world applications, the FEM model of a disk brake system usually contains tens of thousands of degrees of freedom (d.o.f.s). Therefore any direct eigenvalue solver based on the dense matrix data structure cannot efficiently perform the analysis, mainly due to its huge memory requirement and long computation time. It is well known that the FEM matrices are generally sparse and hence only the non-zeros of the matrices need to be stored for eigenvalue analysis. A recently developed iterative method named ABLE is used in this paper to search for any unstable modes within a certain user-specified frequency range. The complex eigenvalue solver ABLE is based on an adaptive block Lanczos method for sparse unsymmetric matrices. Numerical examples are presented to demonstrate the formulation and the eigenvalues are compared to the results from the component modal synthesis (CMS).