The problem of squealing brakes is still a major challenge for design engineers. The noise problem referred to as brake squeal is caused by a transfer of energy from the movement of the vehicle into vibrations of the brake system, which itself emits acoustic waves. The excitation mechanism for the vibration of the system lies in the interaction of the brake pads and the disk. In order to predict whether a brake system is likely to squeal, it is necessary to have reliable models. Whereas in many industrial applications finite element models have become an ac- cepted tool to predict the mechanical behavior of structures, this goal has not yet been achieved in the context of brake squeal. The reason for this is twofold. First, the modeling of a frictional contact is generally a difficult task. Second, it is a challenge to set up consistent finite ele- ment models including prescribed movements of individual parts, as for example the rigid body rotation of the brake disk.
Many of the finite element models for brakes that are used in industry today are studied using the so called complex eigenvalue analysis. This is however problematic, since it is only appli- cable if the linearized equations of motion have constant coefficients. However, considering a rotating body in contact with a stationary body, equations of motion with constant coefficients only arise if the rotating body is rotationally symmetric. Therefore, if in the context of brake squeal rotationally nonsymmetric disks are to be studied, the equations of motion will have periodic coefficients. Even though the stability analysis of linear equations of motion having periodic coefficients is well established, appropriate solvers are not available in today’s com- mercial finite element codes and different approaches have to be developed.
The present analysis is devoted to the combination of advantages of a semi-analytic modeling procedure, with the flexibility of finite element codes to deal with complex geometries. The mechanism causing brake squeal has been studied and well described using analytic models with emphasis on the contact geometry and a consistent formulation of the contact forces. On the other hand, in the analytic models, the geometry of the brake disk is only modeled as a rotating plate, which is a rather crude approximation. Using finite element codes it is possible to perform a modal analysis for almost arbitrary geometries of the brake rotor. Therefore in this paper mass and stiffness parameters of a finite element model are used as input data for a semi-analytical contact model. In this way rotationally nonsymmetric brake disks are studied and modifications of the disk are evaluated. Summarizing, the proposed method should be a first step towards reliable models for brake squeal allowing for the consideration of complex geometries of the brake rotor, inhibiting the excitation mechanism and avoiding squeal. | English |