A global strategy for the stability analysis of friction induced vibration problem with parameter variations

Abstract This paper presents a numerical strategy to reanalyze the modified frequency stability analysis of friction induced vibration problem. The stability analysis of a mechanical system relies on several coupling steps, namely a non-linear static analysis followed by linear and complex eigenvalue problems. We thus propose a numerical strategy to perform more rapidly multiple complex eigenvalue analyses. This strategy couples three methods namely, Fuzzy Logic Controllers to manage frictional contact problem, homotopy developments and projection techniques to reanalyze the projection matrices and component mode synthesis to calculate the modified eigensolutions. A numerical application is performed to highlight the efficiency of the strategy and a discussion is proposed in terms of precision and computational time.

[1]  Lyes Nechak,et al.  Non-intrusive generalized polynomial chaos for the robust stability analysis of uncertain nonlinear dynamic friction systems , 2013 .

[2]  Jean-Jacques Sinou,et al.  Stochastic study of a non-linear self-excited system with friction , 2013 .

[3]  Sebastian Oberst,et al.  Pad-mode-induced instantaneous mode instability for simple models of brake systems , 2015 .

[4]  Francesco Massi,et al.  A numerical investigation into the squeal instability: Effect of damping , 2011 .

[5]  Jaeyoung Kang,et al.  Finite element modelling for the investigation of in-plane modes and damping shims in disc brake squeal , 2012 .

[6]  Jean-Jacques Sinou,et al.  A double modal synthesis approach for brake squeal prediction , 2016 .

[7]  Yves Berthier,et al.  Squeaking friction phenomena in ceramic hip endoprosthesis: Modeling and experimental validation , 2015 .

[8]  H. Ouyang,et al.  Wear prediction of friction material and brake squeal using the finite element method , 2008 .

[9]  Franck Massa,et al.  Uncertain Friction-Induced Vibration Study: Coupling of Fuzzy Logic, Fuzzy Sets, and Interval Theories , 2016 .

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

[11]  B. Lallemand,et al.  Finite element analysis of frictionless contact problems using fuzzy control approach , 2015 .

[12]  Franck Massa,et al.  Structural modal reanalysis methods using homotopy perturbation and projection techniques , 2011 .

[13]  T. Tison,et al.  Using fuzzy logic control approach and model reduction for solving frictional contact problems , 2016 .

[14]  Utz von Wagner,et al.  Minimal models for disk brake squeal , 2007 .

[15]  Jean-Jacques Sinou,et al.  Transient non-linear dynamic analysis of automotive disc brake squeal – On the need to consider both stability and non-linear analysis , 2010 .

[16]  Annalisa Fregolent,et al.  Instability scenarios between elastic media under frictional contact , 2013 .

[17]  Guillaume Vermot Des Roches,et al.  Frequency and time simulation of squeal instabilities. Application to the design of industrial automotive brakes. , 2011 .

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

[19]  Charles M. Krousgrill,et al.  Comprehensive stability analysis of disc brake vibrations including gyroscopic, negative friction slope and mode-coupling mechanisms , 2009 .

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

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

[22]  Jean-Jacques Sinou,et al.  A simplified approach for the calculation of acoustic emission in the case of friction-induced noise and vibration , 2015 .

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

[24]  L. Gaul,et al.  Effects of damping on mode‐coupling instability in friction induced oscillations , 2003 .

[25]  Ebrahim H. Mamdani,et al.  An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller , 1999, Int. J. Hum. Comput. Stud..

[26]  R. Macneal.  A hybrid method of component mode synthesis , 1971 .

[27]  Jean-Jacques Sinou,et al.  A new treatment for predicting the self-excited vibrations of nonlinear systems with frictional interfaces: The Constrained Harmonic Balance Method, with application to disc brake squeal , 2009 .

[28]  Franck Massa,et al.  Multi-level homotopy perturbation and projection techniques for the reanalysis of quadratic eigenvalue problems: The application of stability analysis , 2015 .

[29]  Ulf Olofsson,et al.  On the relationships among wheel–rail surface topography, interface noise and tribological transitions , 2015 .

[30]  Laurent Dubar,et al.  A methodology for the modelling of the variability of brake lining surfaces , 2012 .

[31]  Joseph C. S. Lai,et al.  Brake squeal: a literature review , 2002 .

[32]  Louis Jezequel,et al.  Investigation of the relationship between damping and mode-coupling patterns in case of brake squeal , 2007 .

[33]  Ebrahim Mamdani,et al.  Applications of fuzzy algorithms for control of a simple dynamic plant , 1974 .

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

[35]  Jean-Jacques Sinou,et al.  Reduction strategy for a brake system with local frictional non-linearities – Application for the prediction of unstable vibration modes , 2015 .

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

[37]  Sebastian Oberst,et al.  Nonlinear transient and chaotic interactions in disc brake squeal , 2015 .

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

[39]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

[40]  K. Srinivasan,et al.  A combined approach of complex eigenvalue analysis and design of experiments (DOE) to study disc brake squeal , 2010 .

[41]  Philippe R. Spalart,et al.  Towards noise prediction for rudimentary landing gear , 2010 .

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