# Contribution Analysis of Assembled Brake System to Reduce Squealing
## 1 Introduction  
The noise of an assembled brake system continues to be a problem throughout the automotive industry despite efforts to reduce its occurrence. Consistent customer complaints result in high annual warranty costs. More importantly, customer dissatisfaction may result in the loss of future business. Nowadays, the noise of an assembled brake system has been given various names that provide definitions of the sound emitted, such as grinding, granting, moaning, squeaking, squealing, and wire brush. Squealing is the most common and annoying noise of an assembled brake system. It is defined as noise with a frequency of 1 kHz or higher with excessively high and irritating sound pressure levels [1, 2]. Squealing is generally caused by friction-induced, self-excited, and self-sustained vibrations generated in a short time by a rotating disk. It is widely accepted that squealing is caused by the dynamic instability of an assembled brake system [3, 4]. Substantial research has been conducted on the squealing of assembled brake systems. Although the mechanism of squealing is still unknown, there has been much research on many aspects of the problem [5]. [PERSON] and [PERSON] [6] measured the sound and vibration signals of a brake system by using a brake dynamometer. The experimental results showed that disk run-out resulting from the misalignment of the brake disk varies with the brake line pressure and becomes an important factor in the generation of brake squealing. [PERSON] et al. [7] and [PERSON] et al. [8] investigated the cause of squealing and proposed design modifications for reducing it. Several approaches can be used to predict squealing using a simulation model of a brake system [9, 10]. To estimate the dynamic stability of the noise, modal correlation, nonlinear static analysis, and complex eigenvalue analysis have been performed. [PERSON] et al. [11] analyzed squealing using computer-aided engineering to design an antisquealing assembled brake system. In another study, design modifications were evaluated by applying arobust design optimization algorithm, and a solution was derived by changing the shape of a brake pad [12]. [PERSON] et al. [13] developed a new design study process for brake squeal development. The goal of the research was to apply a modal domain analysis approach to minimize design iterations using finite-element (FE) models, and a method for calculating complex eigenvalues to reduce the solution time was developed. [PERSON] et al. [14] suggested a new approach combining component contribution and eigenvalue sensitivity analysis to reduce brake squealing. [PERSON] et al. [15] demonstrated a quantitative method for defining system mode shapes using the concept of modal participation factors. This method was implemented in a front-assembled brake system to identify the modal coupling mechanism associated with high-frequency squealing. The contribution analysis concept is extremely efficient for the selection of design modification targets for complex systems, such as vehicle systems, and studies have been conducted to address harsh vibration problems [16; 17]. Recent studies have focused on the brake problems related to squealing. [PERSON] et al. [18] evaluated the influence of damping variations in the brake pad and disk using an FE model, and [PERSON] et al. [19] focused on the effect of multiscale contact localization at a simplified pad on a disk system. [PERSON] et al. [20] evaluated the efficiency of the double modal synthesis method in predicting squealing, and [PERSON] et al. [21] calculated the friction coefficient of the brake system from a microscale model and transferred it to a macroscale multibody simulation. In this study, harsh squealing was overcome by modifying the brake pad configuration, and the contribution analysis concept was used to find the most influential part, the brake pad, through the obtained spectral response vectors of the assembled brake module.