Nonlinearities in Friction Brake NVH - Experimental and Numerical Studies

Gräbner, Nils; Tiedemann, Merten; Wagner, Utz von; Hoffmann, Norbert

doi:10.4271/2014-01-2511

Cited by 19 publications

(19 citation statements)

References 7 publications

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“…Subcritical as well as supercritical Hopf bifurcations are often encountered in different engineering applications, e.g., aeroelastic response of airfoils with structural nonlinearities [1,2], dynamics of ball joints [3], brake squeal [4]. Engineers are generally more concerned about subcritical (hard) bifurcations as a small perturbation around the equilibrium position can lead the system to large amplitude vibration states, which the structure may not tolerate [5].…”

Section: Introductionmentioning

confidence: 99%

Subcritical bifurcation in a self-excited single-degree-of-freedom system with velocity weakening–strengthening friction law: analytical results and comparison with experiments

2017

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The dynamical behavior of a single-degreeof-freedom system that experiences friction-induced vibrations is studied with particular interest on the possibility of the so-called hard effect of a subcritical Hopf bifurcation, using a velocity weakening-strengthening friction law. The bifurcation diagram of the system is numerically evaluated using as bifurcation parameter the velocity of the belt. Analytical results are provided using standard linear stability analysis and nonlinear stability analysis to large perturbations. The former permits to identify the lowest belt velocity (v lw ) at which the full sliding solution is stable, the latter allows to estimate a priori the highest belt velocity at which large amplitude stick-slip vibrations exist. Together the two boundaries [v lw , v up ] define the range where two equilibrium solutions coexist, i.e., a stable full sliding solution and a stable stick-slip limit cycle. The model is used to fit recent experimental observations.

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Section: Introductionmentioning

confidence: 99%

Subcritical bifurcation in a self-excited single-degree-of-freedom system with velocity weakening–strengthening friction law: analytical results and comparison with experiments

2017

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Section: Introductionmentioning

confidence: 99%

“…Thus, although nonlinearities need to be studied and incorporated into the model for a true understanding of their nature [12], useful results can be obtained using a linearized finite element (FE) model, formulating the equations of motion assuming a very simplified description of the forcing term arising from a macroscopic friction law, e.g., the Coulomb law [37].…”

Section: Derivation Of the Disk Brake Modelmentioning

confidence: 99%

“…A broad overview can be found in [26], whereas numerical aspects are reviewed in [36]. Other aspects of disk brake squeal have been considered in [11,12,21,34]. Despite extensive research, however, the problem is far from being understood and, so far, satisfactory remedies have not been found that can be implemented in a systematic way.The macroscopic equations of motion arising from finite element modeling are usually considered in the formwhere M , D , and K ∈ R n×n are time invariant, parameter-dependent coefficient matrices collecting acceleration, velocity, and displacement proportional terms, respectively, and f is a vector of external forces.…”

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confidence: 99%

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Numerical methods for parametric model reduction in the simulation of disk brake squeal

Gräbner

Mehrmann

Quraishi

et al. 2016

Z. Angew. Math. Mech.

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We present numerical methods for model reduction in the numerical simulation of disk brake squeal. Automotive disk brake squeal is a high frequency noise phenomenon based on self excited vibrations. Our method is based on a variation of the proper orthogonal decomposition method and involves the solution of a large scale, parametric eigenvalue problem. Several important challenges arise, some of which can be traced back to the finite element modeling stage. Compared to the current industrial standard our new approach is more accurate in vibration prediction and achieves a better reduction in model size. This comes at the price of an increased computational cost, but it still gives useful results when the classical modal reduction method fails to do so. We illustrate the results with several numerical experiments, some from real industrial models, some from simpler academic models. These results indicate where improvements of the current black box industrial codes are advisable.

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“…For a proper simulation of this behavior, it is necessary to know the origin and the influence of the brake system's nonlinearities. It is generally known, that nonlinearities are inherent to the joints [1,2], complex friction laws [3] and the friction material of the system [4][5][6]. In this work, the influence of friction material and shim nonlinearities on the existence of a limit cycle is investigated.…”

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confidence: 99%

Nonlinear Multiple Body Models for Brake Squeal

Koch

Gräbner

Gödecker

et al. 2017

Proc Appl Math and Mech

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Brake squeal is a self-excited vibration with initially inclining amplitude reaching a limit cycle due to nonlinearities. For a proper simulation of this behavior, it is necessary to know the origin and the influence of the brake system's nonlinearities. It is generally known, that nonlinearities are inherent to the joints [1, 2], complex friction laws [3] and the friction material of the system [4][5][6]. In this work, the influence of friction material and shim nonlinearities on the existence of a limit cycle is investigated. Stiffness and damping characteristics are determined using the chair's owned DCTR [4] test rig. It is shown, how nonlinear characteristics, which are necessary for simulation, are obtained from the performed measurements. They are incorporated in a multiple body model composed of brake disk, pads, shims, carrier and calliper from which the nonlinear equations of motion are derived. For the investigation on the bifurcation behavior, the equations of motion are transformed into normal form. It is then possible to describe the bifurcation behavior with respect to parameter influences. Ultimately, with this information it is possible to show the influence of the investigated nonlinearities on brake squeal.

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Nonlinearities in Friction Brake NVH - Experimental and Numerical Studies

Cited by 19 publications

References 7 publications

Subcritical bifurcation in a self-excited single-degree-of-freedom system with velocity weakening–strengthening friction law: analytical results and comparison with experiments

Subcritical bifurcation in a self-excited single-degree-of-freedom system with velocity weakening–strengthening friction law: analytical results and comparison with experiments

Numerical methods for parametric model reduction in the simulation of disk brake squeal

Nonlinear Multiple Body Models for Brake Squeal

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