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A nonlinear transient finite element method was developed to analyze brake squeal occurrence. It overcomes the drawbacks associated with the conventional methods such as modal analysis and complex eigenvalue analysis. It includes the prediction of contact surface variation during the braking process and the complex friction phenomena at rotor-pad interfaces. A new solid element was also developed to suit the brake squeal analysis. A fast Fourier transformation (FFT) was employed to convert the results in the time domain generated from nonlinear transient analysis into the frequency domain to identify the frequencies associated with noise. Good correlation, between the squeal frequencies predicted by the proposed method and those obtained from tests, has been established.

An eight-noded hexahedral element is developed for linear and nonlinear analyses, which can be also used to analyze bending and sheet metal forming problems. The development is based on the formulation of multiple-point quadrature elements proposed by Liu, Hu and Belytschko [1]. In this new element, one-point quadrature, instead of four-point or eight-point quadrature, is used so that computational time is substantially reduced without adversely effecting the accuracy. Hourglass control is included in the element formulation to suppress spurious modes. The volumetric locking for nearly-incompressible material, as well as the shear locking in bending problems are also eliminated. Several examples are presented to demonstrate the performance of this element.

A new method to predict brake squeal occurrence was developed by MSC under contract to Ford Motor Company. The results indicate that the stability characteristics of this disc brake assembly are governed mainly by the frictional properties between the pads and rotor. The stability is achieved when the friction coefficient of the pads is decreasing as the contact force increases. Based on the results, a stable brake system can be obtained without changing the brake structure by incorporating the appropriate frictional coefficient in the brake system. The method developed here can be also used as a tool to test the quality of any brake design in the early design stage.