Some Studies on Modeling and Simulation of a Disc Brake System for Squeal Prediction

Abstract

Most mechanical systems that involve a sliding contact experience some degree of friction induced self-excited vibration. A well known example is brake squeal which is a top concern for automotive companies, who must spend huge amounts of money on warranty repairs. Brake squeal occurs above 1k Hz and below 20k Hz. The phenomena that cause brake squeal is not thoroughly understood, although a great deal of research has been dedicated to developing a better understanding of the complex problem of brake dynamics. This study developed a displacement dynamic equation of motion for brake rotor's, assuming the rotor's to be annular plates with the same modal characteristics. An analytical approach was used to solve the equation of motion of these annular discs for free vibration. The Eigen values obtained through the analytical approach were then used to obtain the natural frequencies. Experimental modal testing was also performed to determine the natural frequencies of disc and pad with free boundary conditions.

The natural frequencies of the annular disc were also obtained using the finite difference method. An algorithm was developed to describe the dynamic response of the annular disc for both a constant forcing function and a time dependent forcing function using the central difference method. The stability of the algorithm was also examined in order to obtain the time step. The importance of the finite difference technique lies in its ability to visualize the results and provide deeper insights into the dynamics of brake rotors. Computer software in C programming and Matlab was developed to solve the differential equation with the forcing function. Another advantage of this method is that any type of forcing function which is practically possible can be applied and its response calculated. The results revealed that an annular disc behaves non-linearly.

Finite element analysis was then performed to determine the dynamic characteristics (natural frequency and mode shapes) and the response of the brake model. The advantage of using this technique is that frictional forces are also taken into account. The contact analysis applied a special type of element called CONTAC49 for 3-D surfaces.

In this thesis a four degree of freedom mathematical model of the brake system based on friction characteristics and geometric non-linearity capable of representing the brake dynamics is presented. Friction induced vibration was studied by using a four degree of freedom model consisting of a disc and a pad moving in both the in-plane and transverse directions. This system takes the form of a mathematical model with two coupled equations and two uncoupled equation. The set of four differential equations can then be solved using Runge Kutta's JBM method.