FACTA UNIVERSITATIS

Series: Mechanical Engineering Vol. 19, No 4, 2021, pp. 613 - 632

https://doi.org/10.22190/FUME210106020K

© 2021 by University of Niš, Serbia | Creative Commons License: CC BY-NC-ND

Original scientific paper

ON THE INFLUENCE OF MULTIPLE EQUILIBRIUM

POSITIONS ON BRAKE NOISE

Sebastian Koch, Emil Köppen, Nils Gräbner, Utz von Wagner

Chair of Mechatronics and Machine Dynamics, Technische Universität Berlin, Germany

these nonlinear effects that the actual research focuses on is the limit cycle behavior

representing squeal. In contrast to this, the actual paper considers the influence of the

equilibrium position established while applying the brake pressure. The elements of the

brake, namely, the carrier, caliper and pad, are highly nonlinear and elastically coupled

and allow for multiple equilibrium positions depending e.g. on the initial conditions and

transient application of the brake pressure while the frictional contact between the pads

and the disk may excite small amplitude self-excited vibrations around this equilibrium,

i.e. squeal. The current paper establishes a method and corresponding setup, to measure

the position engaged by the brake components using an optical 3D-measuring system.

Subsequently, it is demonstrated that in fact different equilibrium positions can be

Correlation

Received January 06, 2021 / Accepted February 15, 2021

Corresponding author: Sebastian Koch

Chair of Mechatronics and Machine Dynamics, Technische Universität Berlin, Einsteinufer 5, 10587 Berlin

E-mail: koch@tu-berlin.de

614 S. KOCH, E. KÖPPEN, N. GRÄBNER, U.V. WAGNER

1. INTRODUCTION

Brake squeal and other brake noises are typical examples for NVH (Noise, Vibration,

Harshness) problems in the automotive industry. These phenomena in general do not represent

temperature during such experiments has a strong influence on the squealing behavior, see e.g.

[3]. Therefore, the necessary number of tests to classify the brake in such manner is extensive,

e.g. [4]. The situation becomes more complicated by the fact that there is a possibility for

squealing to sometimes occur and sometimes not even during the tests with the identical

operation parameters [5-7]. Ref. [6] mainly considers thereby changes in the direction in which

the brake components obviously capture significantly different positions as well as the

corresponding influence on the squealing behavior.

The state of the art procedure to experimentally classify the squealing behavior of the

suspension are mounted on a dynamo test bench. A huge amount of braking operations is

performed on different parameters, while the noise level is recorded to categorize whether

equilibrium position. Obviously, the equations of motion of this linearized model depend

on this equilibrium position. The linear model is finally used for a complex eigenvalue

analysis (CEA). Since these models contain, if correctly set up, the mechanism of self-

excitation due to the friction forces between the disk and the pad, there is a possibility of

instability of the equilibrium position and the mode shapes with eigenvalues with a positive

real part are considered as modes potentially associated with squealing [9]. However, linear

instability does not represent the observed behavior of a squealing brake, as unstable

solutions in linear models show an increasing amplitude above all boundaries with time

while the real brake squealing is represented by a more or less stationary behavior with

distinct frequencies and finite amplitudes. Therefore, the behavior observed in the brake

of the limit cycles are irrelevant for noise, the problem of brake squeal would be solved.

Another reason is that nonlinearities can play a key role, when it comes to the desired

predictive character of the simulation methods. In [11] it is shown that the mode shape

belonging to the largest positive eigenvalue real part is not necessarily the one occurring

On the Influence of Multiple Equilibrium Positions on Brake Noise 615

in the limit cycle, as nonlinearities may limit that mode much earlier than another mode

shape with a smaller positive real part.

As a conclusion, nonlinearities are essential for the description of brake squeal and may

play a key role for its suppression. Nevertheless, as the description above makes obvious,

nonlinearities, if actually considered, are so far considered in detail only at one place of the

simulation process, namely in limiting the increasing vibrations. Another obvious point,

where nonlinearities play a role, is in determining the equilibrium position. Here, in general,

screwdriver on them. Sometimes it is visible with the naked eye that the position of the brake

parts is not the same after this manipulation as it was before, so that a new equilibrium

position has been reached, possibly with decisive influence on the noise behavior.

For both types of above mentioned influences of nonlinearities, the initial conditions

play an essential role in determining which solution appears. With respect to the limit cycle,

the initial conditions decide in the case of coexistent stable limit cycle and stable trivial

solution about the appearance of squealing [20], but the same happens, if different

equilibrium positions are possible due to nonlinearities, where the stability behaviors may

differ from each other. In reality, nonlinearities affect the noise behavior in both cases and

the dependence on the initial conditions is the explanation why brake squeal sometimes

that different equilibrium positions can be established depending on the initial conditions,

respectively the state of the brake before the brake pressure is applied. Additionally, there

might be some influence of external excitation on the engaged equilibrium position.

As experiments show, the concept of one engaged stationary equilibrium position is an

idealization in simulations, as these equilibrium positions may also change periodically

during the turning of the disk due to disk wobbling or other imperfections. Nevertheless,

the following investigations show that there is significant dependence of the occurrence of

squealing on the (medium) absolute and relative positions of the brake parts; they also show

that significant different positions are possible even for constant operation parameters.

In the metrological investigation it is necessary to consider that the changes in the

616 S. KOCH, E. KÖPPEN, N. GRÄBNER, U.V. WAGNER

The paper is structured as follows. First, the developed test bench is presented. The test

setup comprises an optical 3D measuring system filming the brake. The position data of

respective parts can be determined using digital image correlation (DIC). This method

allows the determination of the position of many points on the structure for low frequencies

(quasi static) and comparatively large displacements. Based on this, two test series are

presented. Test series number one is used to investigate whether changes in equilibrium

position can occur under almost identical parameters for braking torque, speed and temperature

2. EXPERIMENTAL SETUP

The main task of the experimental setup is to detect differences in the equilibrium

position of the examined floating caliper disk brake while the disk is rotating at a specific

speed and a specific brake pressure is applied. Especially the brake components carrier,

caliper and pad are considered. Furthermore, the test bench must be able to detect squealing

events and to record the corresponding parameters, namely rotational speed, brake torque,

respectively, brake pressure and temperature.

Fig. 1 Left: main components, i.e. the carrier, caliper and pad of the investigated industrial

(Fig. 16 left) in the serial setup was omitted in these two first test series. Nevertheless,

On the Influence of Multiple Equilibrium Positions on Brake Noise 617

similar effects are also observed when the clamp is mounted, as demonstrated in a third

test series. The entire control of the brake pressure and rotational speed is done manually.

Compared to industrial test benches this set up does not allow the investigation of high

rotational speeds or high torques and, therefore, it is not capable of analyzing the brake

performance. Nevertheless, brake squeal generally requires only low rotational speeds and

torques. The main advantage of this set-up is that most parts of the brake are perfectly

recorded by the 3D-system makes it possible to determine the spatial movement of these

point markers by using DIC for homologous point tracking in all three dimensions. The

equipment used is state of the art.

Fig. 2 Details of the test bench [23]. Left: 3D-system, single camera, angle sensor and

mounting for the coordinate system. Right: accelerometers, temperature sensor and

point markers

Nevertheless, the computation algorithm as described in [24] for the determination of

displacement data shall be briefly sketched. The glued-on point markers are identified and

tracked via image recognition techniques. The center of the point determines the position