Innovative squeak noise prediction: An approach using the harmonic balance method and a variable normal contact force

Abstract A flawless interior acoustics is a customer requirement in automotive industry. Any disturbing noise e.g. squeak or rattle must be avoided to meet the customer’s expectations regarding quality. This work presents an improved approach to predict squeak noise. For this purpose, a test rig generating the underlying stick-slip phenomenon by harmonic excitation is used and a corresponding finite element model is built describing the system’s dynamic behavior. The Harmonic Balance Method is applied for solving the nonlinear equations of motion. The major difference to previous approaches consists in the implementation of a contact algorithm allowing variable normal forces in the contact domain. The calculated nonlinear system response is compared to existing methods using a constant normal force. The proposed method is capable of predicting odd harmonics, which is a significant improvement in assessing squeak noise. Furthermore, good agreement between simulation and experiment is observed which validates the approach.

[1]  Malte Krack,et al.  Harmonic Balance for Nonlinear Vibration Problems , 2020, Mathematical Engineering.

[2]  T. Caughey,et al.  Classical Normal Modes in Damped Linear Dynamic Systems , 1960 .

[3]  J. Sinou,et al.  Generalized Modal Amplitude Stability Analysis for the prediction of the nonlinear dynamic response of mechanical systems subjected to friction-induced vibrations , 2020 .

[4]  A. Papangelo,et al.  Self-excited vibrations due to viscoelastic interactions , 2020 .

[5]  Earl H. Dowell,et al.  Multi-Harmonic Analysis of Dry Friction Damped Systems Using an Incremental Harmonic Balance Method , 1985 .

[6]  Steffen Marburg,et al.  Estimation of Radiated Sound Power: A Case Study on Common Approximation Methods , 2009 .

[7]  Alberto Cardona,et al.  A multiharmonic method for non‐linear vibration analysis , 1994 .

[8]  S. Marburg,et al.  Calculation of the Response of a Periodically Excited Beam with Frictional Contact Using Harmonic Balance Method , 2016 .

[9]  J. Griffin,et al.  An Alternating Frequency/Time Domain Method for Calculating the Steady-State Response of Nonlinear Dynamic Systems , 1989 .

[10]  Jens Weber,et al.  Squeak & Rattle Correlation in Time Domain using theSAR-LINE™ Method , 2012 .

[11]  Sebastian Oberst,et al.  Guidelines for numerical vibration and acoustic analysis of disc brake squeal using simple models of brake systems , 2013 .

[12]  D. J. Ewins,et al.  Effects of Damping and Varying Contact Area at Blade-Disk Joints in Forced Response Analysis of Bladed Disk Assemblies , 2006 .

[13]  Fabrice Thouverez,et al.  Vibration Prediction of Bladed Disks Coupled by Friction Joints , 2017 .

[14]  S. Marburg,et al.  Matching experimental and three dimensional numerical models for structural vibration problems with uncertainties , 2018 .

[15]  J. Sinou,et al.  An adaptive harmonic balance method for predicting the nonlinear dynamic responses of mechanical systems—Application to bolted structures , 2010 .

[16]  Benny Rediers,et al.  Squeak and Rattle - State of the Art and Beyond , 1999 .

[17]  Steffen Marburg,et al.  Squeak Noise Prediction of a Door Trim Panel Using Harmonic Balance Method , 2020 .

[18]  Raj Sohmshetty,et al.  Automotive Body Structure Enhancement for Buzz, Squeak and Rattle , 2004 .

[19]  Rikard Söderberg,et al.  Defining perceived quality in the automotive industry: an engineering approach. , 2015 .

[20]  Alan G. Haddow,et al.  Quantitative Prediction of Rattle in Impacting System , 1997 .

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

[22]  M. Bampton,et al.  Coupling of substructures for dynamic analyses. , 1968 .

[23]  Stefano Zucca,et al.  Nonlinear dynamics of mechanical systems with friction contacts: Coupled static and dynamic Multi-Harmonic Balance Method and multiple solutions , 2014, 1811.07543.

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

[25]  H. Ouyang,et al.  Friction-induced vibration considering multiple types of nonlinearities , 2020, Nonlinear Dynamics.

[26]  Sebastian Oberst,et al.  On the potential of uncertainty analysis for prediction of brake squeal propensity , 2016 .

[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]  Rikard Söderberg,et al.  Corporate and Customer Understanding of Core Values Regarding Perceived Quality: Case Studies on Volvo Car Group and Volvo Group Truck Technology , 2014 .

[29]  Pascal Reuss,et al.  The influence of joints on friction induced vibration in brake squeal , 2015 .

[30]  J. B. Fahnline,et al.  A lumped parameter model for the acoustic power output from a vibrating structure , 1996 .

[31]  Robert S. Brines,et al.  N-Hance: Software for Identification of Critical BSR Locations in Automotive Assemblies using Finite Element Models , 2003 .

[32]  David J. Ewins,et al.  MODELLING TWO-DIMENSIONAL FRICTION CONTACT AND ITS APPLICATION USING HARMONIC BALANCE METHOD , 1996 .

[33]  Walter Sextro,et al.  Spatial Dynamics of Tuned and Mistuned Bladed Disks with Cylindrical and Wedge-Shaped Friction Dampers , 2003 .

[34]  Sebastian Oberst,et al.  Deep learning for brake squeal: Brake noise detection, characterization and prediction , 2021 .

[35]  Christophe Pierre,et al.  HYBRID FREQUENCY-TIME DOMAIN METHODS FOR THE ANALYSIS OF COMPLEX STRUCTURAL SYSTEMS WITH DRY FRICTION DAMPING , 2003 .

[36]  Dominik Süß,et al.  Investigation of a jointed friction oscillator using the Multiharmonic Balance Method , 2015 .