Shape optimization for suppressing brake squeal

The present paper describes a solution to a non-parametric shape optimization problem of a brake model to suppress squeal noise. The brake model consists of a rotor and a pad, between which Coulomb friction occurs. The main problem is defined as a complex eigenvalue problem of the brake model obtain...

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Bibliographic Details
Published in:Structural and multidisciplinary optimization 2014-12, Vol.50 (6), p.1127-1135
Main Authors: Shintani, Kohei, Azegami, Hideyuki
Format: Article
Language:English
Subjects:
Brakes
Computational Mathematics and Numerical Analysis
Cost function
Coulomb friction
Eigenvalues
Engineering
Engineering Design
Equations of motion
Industrial Application
Iterative algorithms
Iterative methods
Shape optimization
Theoretical and Applied Mechanics
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Summary:The present paper describes a solution to a non-parametric shape optimization problem of a brake model to suppress squeal noise. The brake model consists of a rotor and a pad, between which Coulomb friction occurs. The main problem is defined as a complex eigenvalue problem of the brake model obtained from the equation of motion. As an objective cost function, we use the positive real part of the complex eigenvalue generating the brake squeal. The volume of the pad is used as a constraint cost function. The Fréchet derivative of the objective cost function with respect to the domain variation, which we refer to as the shape derivative of the objective cost function, is evaluated using the solution of the main problem and the adjoint problem. A scheme by which to solve the shape optimization problem using an iterative algorithm based on the H 1 gradient method (the traction method) for reshaping is presented. Numerical results obtained using a simple rotor-pad model reveal that the real part of the target complex eigenvalue decreases monotonically, thus satisfying the volume constraint.
ISSN:1615-147X
1615-1488
DOI:10.1007/s00158-014-1102-2