Flexible Wiper System Dynamic Instabilities: Modelling and Experimental Validation

Chevennement–Roux, Carine; Dreher, Thomas; Alliot, Patrick; Aubry, Evelyne; Lainé, Jean-Pierre; Jézéquel, L.

doi:10.1007/s11340-006-9027-3

Cited by 31 publications

(25 citation statements)

References 8 publications

(8 reference statements)

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“…This sensitivity seems in changes of stability properties and thus in the amplitude of the self friction-induced vibrations. Moreover, it has been demonstrated that the friction coefficient admits strong dispersions [20,21]. Thus it is also necessary to take account of the uncertainty of the friction coefficient in order to ensure the robustness of the stability analysis and the prediction of self friction-induced vibrations.…”

Section: Introductionmentioning

confidence: 99%

Prediction of Random Self Friction-Induced Vibrations in Uncertain Dry Friction Systems Using a Multi-Element Generalized Polynomial Chaos Approach

Nechak¹,

Berger²,

Aubry³

2012

Journal of Vibration and Acoustics

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The prediction of self friction-induced vibrations is of major importance in the design of dry friction systems. This is known to be a challenging problem since dry friction systems are very complex nonlinear systems. Moreover, it has been shown that the friction coefficients admit dispersions depending in general on the manufacturing process of dry friction systems. As the dynamic behavior of these systems is very sensitive to the friction parameters, it is necessary to predict the friction-induced vibrations by taking into account the dispersion of friction. So, the main problem is to define efficient methods which help to predict friction-induced vibrations by taking into account both nonlinear and random aspect of dry friction systems. The multi-element generalized polynomial chaos formalism is proposed to deal with this question in a more general setting. It is shown that, in the case of friction-induced vibrations obtained from long time integration, the proposed method is efficient by opposite to the generalized polynomial chaos based method and constitutes an interesting alternative to the prohibitive Monte Carlo method.

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Section: Introductionmentioning

confidence: 99%

Prediction of Random Self Friction-Induced Vibrations in Uncertain Dry Friction Systems Using a Multi-Element Generalized Polynomial Chaos Approach

Nechak¹,

Berger²,

Aubry³

2012

Journal of Vibration and Acoustics

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“…The non-linear static solution corresponds to the origin of the system (26). So, the eigenvalues  of the linearized system can be found by solving the characteristic equation:…”

Section: Parametric Study Of Stabilitymentioning

confidence: 99%

“…This confirms the improvement of the accuracy given by the non-intrusive methods. Fig.12 In a previous step, polynomial chaos was used intrusively and non-intrusively to estimate the first and second order statistics of the dynamic behaviour of the friction system (26) …”

Section: Non-intrusive Approachmentioning

confidence: 99%

A polynomial chaos approach to the robust analysis of the dynamic behaviour of friction systems

Nechak

Berger²,

Aubry³

2011

European Journal of Mechanics - A/Solids

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To cite this version:Lyes Nechak, Sébastien Berger, Evelyne Aubry. A polynomial chaos approach to the robust analysis of the dynamic behaviour of friction systems. Abstract-This paper presents a dynamic behaviour study of non-linear friction systems subject to uncertain friction laws. The main aspects are the analysis of the stability and the associated non-linear amplitude around the steady-state equilibrium. As friction systems are highly sensitive to the dispersion of friction laws, it is necessary to take into account the uncertainty of the friction coefficient to obtain stability intervals and to estimate the extreme magnitudes of oscillations. Intrusive and nonintrusive methods based on the polynomial chaos theory are proposed to tackle these problems. The efficiency of these methods is investigated in a two degree of freedom system representing a drum brake system. The proposed methods prove to be interesting alternatives to the classic method such as parametric studies and Monte Carlo based techniques.

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“…In carrying out CEA, the computational model is usually considered as deterministic, and the fixed friction coefficient is applied. However, the friction coefficient is known to have strong dispersion characteristics depending on the operation conditions [7], and should be modeled as a random parameter. In addition, most physical systems are subject to uncertainties concerning the input parameters, such as the material properties and geometry, and the contact conditions.…”

Section: Introductionmentioning

confidence: 99%

A Combined Nonstationary Kriging and Support Vector Machine Method for Stochastic Eigenvalue Analysis of Brake Systems

Lee

Park

2019

Applied Sciences

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This paper presents a new metamodel approach based on nonstationary kriging and a support vector machine to efficiently predict the stochastic eigenvalue of brake systems. One of the difficulties in the mode-coupling instability induced by friction is that stochastic eigenvalues represent heterogeneous behavior due to the bifurcation phenomenon. Therefore, the stationarity assumption in kriging, where the response is correlated over the entire random input space, may not remain valid. In this paper, to address this issue, Gibb's nonstationary kernel with step-wise hyperparameters was adopted to reflect the heterogeneity of the stochastic eigenvalues. In predicting the response for unsampled input, the support vector machine-based classification is utilized. To validate the performance, a simplified finite element model of the brake system is considered. Under various types of uncertainties, including different friction coefficients and material properties, stochastic eigenvalue problems are investigated. Through numerical studies, it is seen that the proposed method improves accuracy and robustness compared to conventional stationary kriging.Carlo simulation (MCS), a sensitivity-based approach, polynomial chaos expansion (PCE), and kriging (Gaussian process). MCS [8] is a sampling-based technique which is considered the most robust method for uncertainty quantifications. However, since a large number of samples must be drawn to obtain sufficient accuracy, the computational cost becomes prohibitive. The sensitivity-based method [9] is a low-order Taylor expansion method that approximates the solution near the input parameters. Although this method is computationally efficient, the obtained solution will be inaccurate under large parameter variabilities.PCE and kriging are metamodel (surrogate model) -based techniques that replace the original model with an easy-to-evaluate function. PCE [10], also known as a spectral approach, is a regression-based methods that approximates the model by multivariate polynomials. Kriging [11] is an interpolation-based approach in which the model is assumed to be a realization of a Gaussian process. Since metamodel-based methods can be applied to various levels of uncertainty, numerous studies have utilized them to solve stochastic eigenvalue problems in brake systems [12][13][14][15].However, despite previous studies, it remains challenging to apply PCE and kriging to brake systems with the mode-coupling phenomenon. Since eigenvalues exhibit nonsmooth behavior around the bifurcation point, PCE is not adequate for capturing local solution accuracy. Several studies have tackled this issue by applying multi-element PCE [16], a wavelet basis [17]. Although kriging interpolates each sample and reflects the local characteristics, to the authors' knowledge, previous studies have all been based on the stationarity assumption, which means that the smoothness of response is entirely correlated throughout the random input space. Therefore, for mode-coupling problems where the stationarity a...

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Flexible Wiper System Dynamic Instabilities: Modelling and Experimental Validation

Cited by 31 publications

References 8 publications

Prediction of Random Self Friction-Induced Vibrations in Uncertain Dry Friction Systems Using a Multi-Element Generalized Polynomial Chaos Approach

Prediction of Random Self Friction-Induced Vibrations in Uncertain Dry Friction Systems Using a Multi-Element Generalized Polynomial Chaos Approach

A polynomial chaos approach to the robust analysis of the dynamic behaviour of friction systems

A Combined Nonstationary Kriging and Support Vector Machine Method for Stochastic Eigenvalue Analysis of Brake Systems

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