Dynamics of a belt-drive system using a linear complementarity problem for the belt–pulley contact description

Abstract The aim of this study was to develop an efficient and realistic numerical model in order to predict the dynamic response of belt drives. The belt was modeled as a planar beam element based on an absolute nodal coordinate formulation. A viscoelastic material was adopted for the belt and the corresponding damping and stiffness matrices were determined. The belt–pulley contact was formulated as a linear complementarity problem together with a penalty method. This made it possible for us to accurately predict the contact forces, including the stick and slip zones between the belt and the pulley. The belt-drive model was verified by comparing it with the available analytical solutions. A good agreement was found. Finally, the applicability of the method was demonstrated by considering non-steady belt-drive operating conditions.

[1]  C. Glocker.  Formulatin of spatial contact situations in rigid multibody systems , 1999 .

[2]  P. W. Christensen,et al.  Formulation and comparison of algorithms for frictional contact problems , 1998 .

[3]  Friedrich Pfeiffer,et al.  Multibody Dynamics with Unilateral Contacts , 1996 .

[4]  Janko Slavič,et al.  A new approach to roughness-induced vibrations on a slider , 2007 .

[5]  Usik Lee,et al.  Dynamics of an Axially Moving Viscoelastic Beam Subject to Axial Tension , 2005 .

[6]  Per Lötstedt.  Mechanical Systems of Rigid Bodies Subject to Unilateral Constraints , 1982 .

[7]  Niclas Strömberg,et al.  A method for structural dynamic contact problems with friction and wear , 2003 .

[8]  Gregor Čepon,et al.  Computing the dynamic response of an axially moving continuum , 2007 .

[9]  Ahmed A. Shabana,et al.  Nonlinear dynamics of three-dimensional belt drives using the finite-element method , 2007 .

[10]  Stephen E. Bechtel,et al.  The stretching and slipping of belts and fibers on pulleys , 2000 .

[11]  Janko Slavič,et al.  Simulating Multibody Dynamics With Rough Contact Surfaces and Run-in Wear , 2006 .

[12]  S. S. Kim,et al.  QR Decomposition for State Space Representation of Constrained Mechanical Dynamic Systems , 1986 .

[13]  Takuzo Iwatsubo,et al.  THE FORMULATION AND DYNAMIC ANALYSIS OF A MULTIPLE BELT SYSTEM , 1997 .

[14]  C. Glocker,et al.  A set-valued force law for spatial Coulomb-Contensou friction , 2003 .

[15]  A. Fregolent,et al.  Parametric instability of belts: theory and experiments , 2004 .

[16]  Tamer M. Wasfy,et al.  Transient and Steady-State Dynamic Finite Element Modeling of Belt-Drives , 2002 .

[17]  David E. Stewart,et al.  Rigid-Body Dynamics with Friction and Impact , 2000, SIAM Rev..

[18]  A. Shabana,et al.  DEVELOPMENT OF SIMPLE MODELS FOR THE ELASTIC FORCES IN THE ABSOLUTE NODAL CO-ORDINATE FORMULATION , 2000 .

[19]  Ahmed A. Shabana,et al.  Application of the Absolute Nodal Coordinate Formulation to Large Rotation and Large Deformation Problems , 1998 .

[20]  Olivier A. Bauchau,et al.  On the Modeling of Friction and Rolling in Flexible Multi-Body Systems , 1999 .

[21]  Michael C. Ferris,et al.  Interfaces to PATH 3.0: Design, Implementation and Usage , 1999, Comput. Optim. Appl..

[22]  Tamer M. Wasfy,et al.  Effect of Bending Stiffness on the Dynamic and Steady-State Responses of Belt-Drives , 2002 .

[23]  A. Galip Ulsoy,et al.  Free Vibration of Serpentine Belt Drive Systems , 1996 .

[24]  Michel Saint Jean,et al.  The non-smooth contact dynamics method , 1999 .

[25]  Friedrich Pfeiffer,et al.  Elastic Modelling of Bodies and Contacts in Continuous Variable Transmissions , 2005 .

[26]  D. Stewart,et al.  AN IMPLICIT TIME-STEPPING SCHEME FOR RIGID BODY DYNAMICS WITH INELASTIC COLLISIONS AND COULOMB FRICTION , 1996 .

[27]  A. Shabana.  Computer Implementation of the Absolute Nodal Coordinate Formulation for Flexible Multibody Dynamics , 1998 .

[28]  A. Galip Ulsoy,et al.  Nonlinear Coupled Vibration Response of Serpentine Belt Drive Systems , 1996 .

[29]  A. Curnier,et al.  A model of adhesion coupled to contact and friction , 2003 .

[30]  Daniel García-Vallejo,et al.  Modeling of Belt-Drives Using a Large Deformation Finite Element Formulation , 2006 .

[31]  J. N. Fawcett.  Chain and Belt Drives - A Review , 1981 .

[32]  F. Pfeiffer,et al.  Numerical aspects of non-smooth multibody dynamics , 2006 .

[33]  Ahmed A. Shabana,et al.  Dynamics of Multibody Systems , 2020 .

[34]  M. Marques,et al.  Differential Inclusions in Nonsmooth Mechanical Problems: Shocks and Dry Friction , 1993 .

[35]  Jean W. Zu,et al.  MODAL ANALYSIS OF SERPENTINE BELT DRIVE SYSTEMS , 1999 .

[36]  A. Galip Ulsoy,et al.  Rotational Response and Slip Prediction of Serpentine Belt Drive , 1993 .

[37]  Jami J. Shah,et al.  Complex Modal Analysis of a Flat Belt Pulley System With Belt Damping and Coulomb-Damped Tensioner , 1994 .

[38]  P. Alart,et al.  A mixed formulation for frictional contact problems prone to Newton like solution methods , 1991 .

[39]  Serge Abrate,et al.  Vibrations of belts and belt drives , 1992 .

[40]  J. Domínguez,et al.  An Internal Damping Model for the Absolute Nodal Coordinate Formulation , 2005 .