Damping optimization in simplified and realistic disc brakes
The squealing noise of automotive disc brakes arises due to friction forces in the contact interface between the brake pads and the rotating brake discs. The automotive industry aims to avoid the occurrence of high-frequency vibrations for comfort reasons by adding the damping. However, in some cases the damping must be reduced in order to optimize the stability of brakes. The equations of motion of disc brakes are nonlinear in general. In this book, a Taylor expansion yields the linearized equations of motion, which generate an eigenvalue problem for eigenvalues and corresponding eigenvectors. By using Floquet theory, the Floquet multipliers can be interpreted as eigenvalues of the monodromy matrix. The instability occurs if at least one eigenvalue has a positive real part or if at least one Floquet multiplier has absolute value greater than one, respectively. Thus, in this book, the optimization of the stability of brakes leads to an optimization of eigenvalues or Floquet multipliers. Some models of damping (Coulomb damping, viscous damping and structural damping) are used. The numerical technique of optimization is described. A minimal model of the disc brake with two degrees of freedom is analyzed to understand the qualitative stability behavior by modifying the damping matrices which have a distinct physical origin. The optimization is carried out using finite element (FE) models of simplified and realistic disc brakes. A simplified FE model of a disc brake (4600 DOF) is used to explain the optimization technique in detail. The introduced optimization method is applied to a high-dimensional, industrial disc brake model (104000 DOF), where the main aim is to optimize the structural damping factors of different brake components. As observed in the minimal model and in the simple FE model, there are limits above which adding more damping does not lead to a significant improvement of the stability of the brake system. The results of the optimization of the high-dimensional industrial FE brake model outline possibilities and disadvantages of the introduced optimization method. This book can be useful to engineers, researchers and postgraduate students.
scientific article; zbMATH DE number 6802102