Mechanical APDL Structural Analysis Guide

3.7.3. Brake Squeal (Prestressed Modal) Analysis

Vehicle brakes can generat e several kinds of noises. Among them is squeal, a noise in the 1-12 kHz
range. It is commonly accepted that brake squeal is initiated by instability due to the friction forces,
leading to self-excited vibrations.

To predict the onset of instability, you can perform a modal analysis of the prestressed structure. This
type of analysis typically involves 3-D surface-to-surface contact between the brake pad and the rotating
disk. The applicable contact elements are CONTA173,CONTA174, and CONTA175.

An unsymmetric stiffness matrix is a result of the friction coupling between the brake pad and disc; this
may lead to complex eigenfrequencies. If the real part of the complex frequency is positive, then the
system is unstable as the vibrations grow exponentially over time.

Three different methods to perform a brake squeal analysis are presented here:
3.7.3.1. Full Nonlinear Perturbed Modal Analysis
3.7.3.2. Partial Nonlinear Perturbed Modal Analysis
3.7.3.3. Linear Non-prestressed Modal Analysis

A full nonlinear perturbed modal analysis is the most accurat e method for modeling the brake squeal
problem. This method uses nonlinear static solutions to both establish the initial contact and compute
the sliding contact.

A partial nonlinear perturbed modal analysis is used when a nonlinear solution is required to establish
contact but a linear analysis can be used to compute the sliding contact.

A linear non-prestressed modal analysis is effective when the stress-stiffening effects are not critical.
This method requires less run time than the other two methods, as no nonlinear base solution is required.
The contact-stiffness matrix is based on the initial contact status.

Each method involves several solution steps. The table below outlines the differences between the
methods. Since the eigensolution step is the most computationally intensive step, the QRDAMP eigen-
solver (MODOPT,QRDAMP) is generally recommended for fast turnaround time in a parametric brake
squeal study environment. However, since this solver approximates the unsymmetric stiffness matrix
by symmetrizing it, the unsymmetric eigensolver (MODOPT,UNSYM) should be used to verify the eigen-
frequencies and mode shapes.

Method Base Static Analysis Modal Analysis

(Linear Perturbation Analysis or

Linear Modal Analysis)

First Solve Second Solve First Solve Second Solve

QR damped or un-

symmetric modal

analysis

Establish initial

contact status;

compute prestress

effects

Linear perturba-

tion modal solu-

tion

Generate unsym-

metric matrix

Force frictional

sliding (CMRO-

TATE command)

Full nonlinear

solution

Full nonlinear per-

turbed modal ana-

lysis

and perform a full

nonlinear solution

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Modal Analysis Examples