Prediction of Squeal Instabilities of a Finite Element Model Automotive Brake With Uncertain Structural and Environmental Parameters With a Hybrid Surrogate Model

This study focuses on the prediction of the stability behavior of an industrial automotive brake system under structural and environmental uncertainties. Uncertainties are modeled with a random distribution or an interval and are propagated with a hybrid surrogate model associating polynomial chaos and kriging. The objective is to create a surrogate model of each eigenvalue computed with the complex eigenvalue analysis (CEA). As the modes can be tracked only when unstable, the effective size of the training sets can become extremely small. Despite this limitation, it is shown the hybrid meta-model is still able to predict the stability of the brake system. Moreover, the hybrid meta-model gives a direct access to the mean and variance of the eigenvalues with respect to the design parameters without any additional Monte Carlo simulations (MCS). By considering different probability density function for the friction coefficient, it is shown it has a high influence on the stability and the latter should be accurately estimated.

[1]  Wen-Bin Shangguan,et al.  Uncertainty quantification of squeal instability under two fuzzy-interval cases , 2017, Fuzzy Sets Syst..

[2]  Andy J. Keane,et al.  Engineering Design via Surrogate Modelling - A Practical Guide , 2008 .

[3]  S. Jacobson,et al.  A study of the influence of humidity on the friction and squeal generation of automotive brake pads , 2001 .

[4]  Hui Lü,et al.  Optimization design of a disc brake system with hybrid uncertainties , 2016, Adv. Eng. Softw..

[5]  Oliver M. O’Reilly,et al.  Automotive disc brake squeal , 2003 .

[6]  T. Butlin,et al.  Friction-induced vibration: Quantifying sensitivity and uncertainty , 2010 .

[7]  Lyes Nechak,et al.  Kriging Surrogate Models for Predicting the Complex Eigenvalues of Mechanical Systems Subjected to Friction-Induced Vibration , 2016 .

[8]  R. F. Nunes,et al.  Improvement in the predictivity of squeal simulations: Uncertainty and robustness , 2014 .

[9]  J. Sinou,et al.  Robustness of stochastic expansions for the stability of uncertain nonlinear dynamical systems – Application to brake squeal , 2018, Mechanical Systems and Signal Processing.

[10]  Franck Massa,et al.  A global strategy for the stability analysis of friction induced vibration problem with parameter variations , 2017 .

[11]  Lyes Nechak,et al.  A novel hybrid surrogate model and its application on a mechanical system subjected to friction-induced vibration , 2018, Journal of Sound and Vibration.

[12]  Lyes Nechak,et al.  Squeal analysis based on the effect and determination of the most influential contacts between the different components of an automotive brake system , 2019, International Journal of Mechanical Sciences.

[13]  Sebastian Oberst,et al.  Statistical analysis of brake squeal noise , 2011 .

[14]  Paul Bannister,et al.  Uncertainty quantification of squeal instability via surrogate modelling , 2015 .

[15]  Jean-Jacques Sinou,et al.  Piecewise polynomial chaos expansion with an application to brake squeal of a linear brake system , 2013 .

[16]  A. Soom,et al.  Interactions Between Dynamic Normal and Frictional Forces During Unlubricated Sliding , 1983 .

[17]  Bruno Sudret,et al.  Global sensitivity analysis using polynomial chaos expansions , 2008, Reliab. Eng. Syst. Saf..

[18]  Hui Lü,et al.  Stability Analysis and Improvement of Uncertain Disk Brake Systems With Random and Interval Parameters for Squeal Reduction , 2015 .

[19]  Huajiang Ouyang,et al.  Numerical analysis of automotive disc brake squeal: a review , 2005 .

[20]  Hui Lü,et al.  Brake squeal reduction of vehicle disc brake system with interval parameters by uncertain optimization , 2014 .

[21]  Gerhard Müller,et al.  Uncertainty quantification applied to the mode coupling phenomenon , 2017 .

[22]  R. Ibrahim.  Friction-Induced Vibration, Chatter, Squeal, and Chaos—Part I: Mechanics of Contact and Friction , 1994 .

[23]  Raouf A. Ibrahim,et al.  Friction-Induced Vibration, Chatter, Squeal, and Chaos—Part II: Dynamics and Modeling , 1994 .

[24]  Staffan Jacobson,et al.  The effect of reduced contact area on the occurrence of disc brake squeals for an automotive brake pad , 2000 .

[25]  Staffan Jacobson,et al.  Surface characterisation of brake pads after running under silent and squealing conditions , 1999 .

[26]  Franck Massa,et al.  Experimental investigations for uncertainty quantification in brake squeal analysis , 2016 .

[27]  Lyes Nechak,et al.  Sensitivity analysis and Kriging based models for robust stability analysis of brake systems , 2015 .

[28]  D. Xiu,et al.  Modeling uncertainty in flow simulations via generalized polynomial chaos , 2003 .

[29]  Huajiang Ouyang,et al.  Statistics of complex eigenvalues in friction-induced vibration , 2015 .

[30]  S. Nacivet,et al.  Influence of structural modifications of automotive brake systems for squeal events with kriging meta-modelling method , 2019 .

[31]  Francesco Massi,et al.  Uncertainty model for contact instability prediction. , 2009, The Journal of the Acoustical Society of America.

[32]  N. Wiener.  The Homogeneous Chaos , 1938 .

[33]  Staffan Jacobson,et al.  Influence of disc topography on generation of brake squeal , 1999 .