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Ride quality is an important purchasing consideration for consumers. It is typically defined in terms of noise, vibration and harshness. These phenomena are a result of vibrations caused at the engine/powertrain and from the road surface, which are transmitted to the passenger cabin. To minimize such vibrations, rubber parts are used extensively at mounting points for the cabin, such as engine mountings and suspension bushings. The vehicle development process increasingly requires performance testing, including rubber parts using CAE, prior to prototype evaluation. This in turn requires a rubber material model that can accurately describe dynamic characteristics of rubber components, particularly frequency and amplitude dependency.

The present paper describes an application of non-parametric shape optimization to disc brake squeal phenomena. A main problem is defined as complex eigenvalue problem in which the real part of the complex eigenvalue causing the brake squeal is chosen as an objective cost function. The Fre´chet derivative of the objective cost function with respect to the domain variation, named as the shape derivative of the objective cost function, is evaluated using the solution of the main problem and the adjoint problem. A selection criterion of the adoptive mode number in component mode synthesis (CMS), which is used in the main problem, is presented in order to reduce the computational error in complex eigenvalue pairs. A scheme to solve the shape optimization problem is presented using an iterative algorithm based on the H1 gradient method for reshaping. For an application of the optimization method, a numerical example of a practical disc brake model is presented.

The finite element method (FEM) is effective for analyzing brake squeal phenomena. Although FEM analysis can be used to easily obtain squeal frequencies and complex vibration modes, it is difficult to identify how to modify brake structure design or contact conditions between components. Therefore, this study deals with a practical design method using sensitivity analysis to reduce brake squeal, which is capable of optimizing both the structure of components and contact conditions. A series of analysis processes that consist of modal reduction, complex eigenvalue analysis, sensitivity analysis and optimization analysis is shown and some application results are described using disk brake systems.