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Preprint 16-2015

Numerical methods for parametric model reduction in the simulation of disk brake squeal

Source file is available as :   Portable Document Format (PDF)

Author(s) : Nils Gräbner , Volker Mehrmann , Sarosh Quraishi , Christian Schröder , Utz Von Wagner

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 16-2015

MSC 2000

65F15 Eigenvalues, eigenvectors
65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
65P40 Nonlinear stabilities

Abstract :
We present numerical methods for model reduction in the numerical simulation of disk brake squeal. Automotive disk brake squeal is a high frequency noise phenomenon based on self excited vibrations. Our method is based on a variation of the proper orthogonal decomposition method and involves the solution of a large scale, parametric eigenvalue problem. Several important challenges arise, some of which can be traced back to the finite element modeling stage. Compared to the current industrial standard our new approach is more accurate in vibration prediction and achieves a better reduction in model size. This comes at the price of an increased computational cost, but it still gives useful results when the traditional method fails to do so. We illustrate the results with several numerical experiments, some from real industrial models, some from simpler academic models. These results indicate where improvements of the current black box industrial codes are advisable.

Keywords : brake squeal, quadratic eigenvalue problem, complex eigenvalue analysis, model reduction, damped systems, modeling errors, proper orthogonal decomposition

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