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An approximate analysis method for brake squeal is presented. Using MSC/NASTRAN a geometric nonlinear solution is run using a friction stiffness matrix to model the contact between the pad and rotor. The friction coefficient can be pressure dependent. Next, linearized complex modes are found where the interface is set in a slip condition. Since the entire interface is set sliding, it produces the maximum friction work possible during the vibration. It is a conservative measure for stability evaluation. An averaged friction coefficient is measured and used during squeal. Dynamically unstable modes are found during squeal. They are due to friction coupling of neighboring modes. When these modes are decoupled, they are stabilized and squeal is eliminated. Good correlation with experimental results is shown. It will be shown that the complex modes baseline solution is insensitive to the type of variations in pressure and velocity that occur in a test schedule.

A new procedure for component mode synthesis has been developed where the residual flexibility effects due to modes truncated from the analysis are properly accounted for. Superelement disk storage is minimized in the new method by saving the boundary and transformation matrices only. A special DMAP was developed to save the transformation matrices for data recovery degrees of freedom only. An external superelement is created with a small read only data base. Using this method with a frozen body design, full vehicle models can run on desktop workstations. The number of design iterations that an analyst can do in a given time is increased dramatically in the new method.

Techniques have been developed to model friction induced vibration and these were applied to the brake moan of a vehicle. A vehicle system model and the MSC/NASTRAN solutions for geometric nonlinear and complex modes were modified by DMAP for friction input. To assess stability, a position of steady sliding equilibrium was found. Then a complex modes solution was done to find negatively damped modes. Mode shape animation of all the unstable modes showed that there was a 90° out of phase vibration. This produced a design modification on a test vehicle which stabilized the vibration and eliminated brake moan.