Nonlinear Multiple Body Models for Brake Squeal

Koch, Sebastian; Gräbner, Nils; Gödecker, Holger; Wagner, Utz von

doi:10.1002/pamm.201710010

Cited by 4 publications

(4 citation statements)

References 5 publications

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“…Several attempts have been made in the past years to describe these effects and to investigate the resulting effects, e.g. [12][13][14][15][16][17][18][19]. These attempts are essential for several reasons.…”

Section: Introductionmentioning

confidence: 99%

On the Influence of Multiple Equilibrium Positions on Brake Noise

Koch

Köppen²,

Gräbner

et al. 2021

FU Mech Eng

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Brake noise, especially brake squeal, has been a subject of intensive research both in industry and academia for several decades. Nevertheless, the state of the art simulations does not provide a predictive tool, and extensive experimental investigations are still necessary to find an appropriate design. Actual investigations focus on the consideration of nonlinearities which are in fact essential for this phenomenon. Unfortunately, by far not all relevant effects caused by nonlinearities are known. One of 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 engaged for the same operation parameters and that the engaged position can be decisive for the occurrence of squeal. In fact, certain positions result in squeal while others do not for the same operation parameters. Taking this effect into consideration may have significant consequences for the design of brakes as well as simulation and experimental investigation of brake squeal.

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Section: Introductionmentioning

confidence: 99%

On the Influence of Multiple Equilibrium Positions on Brake Noise

Koch

Köppen²,

Gräbner

et al. 2021

FU Mech Eng

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“…In this consideration, nonlinearities limit the increasing oscillation caused by self-excitation, which finally ends in a limit cycle [6,11]. Therefore, nonlinearities resulting in the limitation of the increasing vibration are essential if the "real" brake squeal, i.e., the limit cycle, should be obtained in frequency, amplitude and sound radiation, and therefore, these nonlinearities are considered by a number of authors and publications [12][13][14][15]. For example, in [6] it is shown that the mode shape with the largest positive eigenvalue is not necessarily the one resulting in the limit cycle and therefore the squeal event.…”

Section: Introductionmentioning

confidence: 99%

On the interrelation of equilibrium positions and work of friction forces on brake squeal

2021

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Brake noise, in particular brake squeal, is a permanent topic both in industry and academia since decades. Nonlinearities play a decisive role for this phenomenon. One nonlinear effect widely ignored so far is that the brake can engage multiple equilibrium positions with severe consequences on the noise behavior. In fact in an automotive disk brake, the essential elements carrier, caliper and pad are elastically coupled with each other and their behavior is nonlinear that multiple equilibrium positions are possible. The engaged equilibrium position depends, for example, on the initial conditions, external disturbances, and the transient application of the brake pressure, and in consequence configurations with or without self-exciting characteristics of the friction forces result. Obviously, a self-exciting characteristic of the friction force is a necessary precondition for the occurrence of squeal. The authors recently published some corresponding results (Koch et al. FU Mech Eng, 2021. https://doi.org/10.22190/FUME210106020K) demonstrating that for same operating parameters with respect to brake pressure (i.e., brake torque), rotational speed and temperature the engaged equilibrium position has decisive influence whether squeal occurs or not. While in Koch et al. (2021) it has just been detected whether there is squeal or not, the excitation characteristic of the friction forces becomes, beside the engaged equilibrium position, the additional focus in the present paper. Therefore, a work criterion already successfully applied in earlier publications for squeal tendency is considered. For the experimental application of the work criterion, accelerometers have to be mounted. The accelerometers’ location to be applied can be determined in the chosen setup by the camera system anyway necessary for the measurement of the engaged equilibrium position. With this refined setup, it is possible to specify the states squeal, close to squeal and far from squeal. The test series again demonstrate the decisive influence of the engaged equilibrium position (for constant operation parameters) on the occurrence of the respective state. These findings can have consequences for simulations (consideration of multiple equilibrium positions in models and respective linearization with consequences on system’s eigenvalues), but also for the design (avoidance of equilibrium positions suspicious for squeal) and experimental setups (determination of special positions) of brakes.

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“…Both the damping term, caused by the vibrations of the transverse components of the relative velocities between the pads and the disk, and the gyroscopic terms affect the stability of the system and they both depend on the macroscopic angular velocity of the disk [5]. Besides models with continua, models with wobbling disk can also capture these terms; therefore, some models have been developed in this way to study the mechanism of brake squeal: minimal model with 2 DOFs [6], 2-DOF model with in-plane vibration of the pads [7], 6-DOF model [5] and 8-DOF model [8]. In those studies, a specialized commercial software called Autolev [9] was required to obtain the final form of the equations of motion, which is quite inconvenient for further generalization.…”

Section: Introductionmentioning

confidence: 99%

On Models With Wobbling Disk for Brake Squeal

Nguyen-Thai

Gräbner

2021

JST

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Among many mathematical models of disk brakes for the explanation of brake squeal, models with wobbling disk have their own advantage over planar models. Applying a recently developed matrix form of Euler equations in rigid body dynamics, the equations establishment process can now be performed with almost all popular computing software. Furthermore, the presented models are more generalized in terms of damping, in-plane vibration, and unsymmetrical mounting.

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Nonlinear Multiple Body Models for Brake Squeal

Cited by 4 publications

References 5 publications

On the Influence of Multiple Equilibrium Positions on Brake Noise

On the Influence of Multiple Equilibrium Positions on Brake Noise

On the interrelation of equilibrium positions and work of friction forces on brake squeal

On Models With Wobbling Disk for Brake Squeal

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