Model smoothing method of contact-impact dynamics in flexible multibody systems

Abstract An original model smoothing method for contact-impact dynamics in flexible multibody system is proposed in this work. First, the model smoothing method is applied to improve the computational efficiency, in which the instant stresses of flexible bodies are replaced by the time-averaged stresses in a short time during the modeling stage, the resulting equations of motion do not contain high frequency components. In the following, the fundamental issues of continuous contact force models are discussed. A smoothing method of modeling linear complementarity problem (LCP) is proposed for the dynamic analysis of flexible multibody system. This approach takes into account the permanent contact and impact, which has the great merit that can be used straightforward without switching contact models. Numerical results show that the model smoothing method is a new effective approach for the numerical analysis of contact-impact problems in flexible multibody system.

[1]  Jacob Philippus Meijaard,et al.  Application of Runge–Kutta–Rosenbrock Methods to the Analysis of Flexible Multibody Systems , 2003 .

[2]  H. Nijmeijer,et al.  Dynamics and Bifurcations ofNon - Smooth Mechanical Systems , 2006 .

[3]  Alan Bowling,et al.  Energetically consistent simulation of simultaneous impacts and contacts in multibody systems with friction , 2009 .

[4]  Shlomo Djerassi Collision with friction; Part B: Poisson’s and Stornge’s hypotheses , 2008 .

[5]  C. Glocker,et al.  Formulation and Preparation for Numerical Evaluation of Linear Complementarity Systems in Dynamics , 2005 .

[6]  Jorge Ambrósio,et al.  Improved bushing models for general multibody systems and vehicle dynamics , 2009 .

[7]  Paulo Veríssimo,et al.  Development of generic multibody road vehicle models for crashworthiness , 2008 .

[8]  Z. Ibrahim,et al.  Adaptive order of block backward differentiation formulas for stiff ODEs , 2017 .

[9]  Gang Wang,et al.  Hybrid modeling for dynamic analysis of cable-pulley systems with time-varying length cable and its application , 2017 .

[10]  Gang Wang,et al.  An efficient model for dynamic analysis and simulation of cable-pulley systems with time-varying cable lengths , 2017 .

[11]  Henk Nijmeijer,et al.  Periodic motion and bifurcations induced by the Painlevé paradox , 2002 .

[12]  W. Sawyer,et al.  Analysis of planar multibody systems with revolute joint wear , 2010 .

[13]  Filipe Marques,et al.  A Study on the Dynamics of Spatial Mechanisms With Frictional Spherical Clearance Joints , 2016 .

[14]  Hamid M. Lankarani,et al.  Continuous contact force models for impact analysis in multibody systems , 1994, Nonlinear Dynamics.

[15]  Margarida F. Machado,et al.  On the continuous contact force models for soft materials in multibody dynamics , 2011 .

[16]  Dingguo Zhang,et al.  A regularized approach for frictional impact dynamics of flexible multi-link manipulator arms considering the dynamic stiffening effect , 2018 .

[17]  Jorge Ambrósio,et al.  A unified formulation for mechanical joints with and without clearances/bushings and/or stops in the framework of multibody systems , 2018 .

[18]  Chang-Wan Kim,et al.  An efficient and robust contact algorithm for a compliant contact force model between bodies of complex geometry , 2009 .

[19]  Mayya Tokman,et al.  Efficient integration of large stiff systems of ODEs with exponential propagation iterative (EPI) methods , 2006, J. Comput. Phys..

[20]  J. Ambrósio,et al.  Dynamic Analysis for Planar Multibody Mechanical Systems with Lubricated Joints , 2004 .

[21]  Daniel Dopico,et al.  Dealing with multiple contacts in a human-in-the-loop application , 2011 .

[22]  A. Shabana,et al.  A two-loop sparse matrix numerical integration procedure for the solution of differential/algebraic equations: Application to multibody systems , 2009 .

[23]  S. Djerassi Collision with friction; Part A: Newton’s hypothesis , 2009 .

[24]  Yunqing Zhang,et al.  Simulation of planar flexible multibody systems with clearance and lubricated revolute joints , 2010 .

[25]  Qi Wang,et al.  Modeling and simulation of planar multibody systems with revolute clearance joints considering stiction based on an LCP method , 2018, Mechanism and Machine Theory.

[26]  Dan Negrut,et al.  A Second Order Extension of the Generalized–α Method for Constrained Systems in Mechanics , 2009 .

[27]  Gerhard Hippmann,et al.  An Algorithm for Compliant Contact Between Complexly Shaped Bodies , 2004 .

[28]  Mohammad Mehdi Rashidi,et al.  A Comparison of Explicit Semi-Analytical Numerical Integration Methods for Solving Stiff ODE Systems , 2015 .

[29]  Arun K. Banerjee Flexible Multibody Dynamics: Efficient Formulations and Applications , 2016 .

[30]  R. Vijay Kumar,et al.  Analysis and simulation of mechanical systems with multiple frictional contacts , 1994 .

[31]  J. R. Cash,et al.  Review Paper: Efficient numerical methods for the solution of stiff initial-value problems and differential algebraic equations , 2003, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[32]  Jintai Chung,et al.  A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method , 1993 .

[33]  C. Glocker Energetic consistency conditions for standard impacts , 2012, Multibody System Dynamics.

[34]  Olivier Bruls,et al.  Lie group generalized-α time integration of constrained flexible multibody systems , 2012 .

[35]  Hamid M. Lankarani,et al.  A Contact Force Model With Hysteresis Damping for Impact Analysis of Multibody Systems , 1989 .

[36]  C. Glocker,et al.  Application of the nonsmooth dynamics approach to model and analysis of the contact-impact events in cam-follower systems , 2012 .

[37]  E. Haug,et al.  Dynamics of mechanical systems with Coulomb friction, stiction, impact and constraint addition-deletion—I theory , 1986 .

[38]  Qiang Tian,et al.  Dynamics of a large scale rigid–flexible multibody system composed of composite laminated plates , 2011 .

[39]  Edward J. Haug,et al.  Dynamics of mechanical systems with Coulomb friction, stiction, impact and constraint addition-deletion—II Planar systems , 1986 .

[40]  Linda,et al.  A Time Integration Algorithm forFlexible Mechanism Dynamics : TheDAE-Method , 1996 .

[41]  John McPhee,et al.  A Regularized Contact Model with Asymmetric Damping and Dwell-Time Dependent Friction , 2004 .

[42]  Cyril Feau,et al.  Experimental and numerical investigation of the earthquake response of crane bridges , 2015 .

[43]  Christoph Glocker,et al.  Modeling and analysis of rigid multibody systems with translational clearance joints based on the nonsmooth dynamics approach , 2010 .

[44]  C. Glocker Energetic consistency conditions for standard impacts , 2013, Multibody System Dynamics.

[45]  Hamid M. Lankarani,et al.  Compliant contact force models in multibody dynamics : evolution of the Hertz contact theory , 2012 .

[46]  Dan Negrut,et al.  On an Implementation of the Hilber-Hughes-Taylor Method in the Context of Index 3 Differential-Algebraic Equations of Multibody Dynamics (DETC2005-85096) , 2007 .

[47]  Filipe Marques,et al.  Modeling and analysis of friction including rolling effects in multibody dynamics: a review , 2018, Multibody System Dynamics.

[48]  Edward J. Haug,et al.  Dynamics of mechanical systems with Coulomb friction, stiction, impact and constraint addition-deletion—III Spatial systems , 1986 .

[49]  Jiri Rohn,et al.  A note on solvability of a class of linear complementarity problems , 1993, Math. Program..

[50]  Vincent Acary,et al.  Multibody systems with 3D revolute joints with clearances: an industrial case study with an experimental validation , 2017, Multibody System Dynamics.

[51]  Björn Engquist,et al.  A multiscale method for highly oscillatory ordinary differential equations with resonance , 2008, Math. Comput..

[52]  Filipe Marques,et al.  A finite element model of a 3D dry revolute joint incorporated in a multibody dynamic analysis , 2019, Multibody System Dynamics.

[53]  G. T. Rooney,et al.  Coulomb friction in mechanism sliding joints , 1982 .

[54]  M. Arnold,et al.  Convergence of the generalized-α scheme for constrained mechanical systems , 2007 .

[55]  I. Sharf,et al.  A contact force solution for non-colliding contact dynamics simulation , 2006 .

[56]  Filipe Marques,et al.  An enhanced formulation to model spatial revolute joints with radial and axial clearances , 2017 .