Simulation of planar flexible multibody systems with clearance and lubricated revolute joints

Modeling of clearance joints plays an important role in the analysis and design of multibody mechanical systems. Based on the absolute nodal coordinate formulation (ANCF), a new computational methodology for modeling and analysis of planar flexible multibody systems with clearance and lubricated revolute joints is presented. A planar absolute nodal coordinate formulation based on the locking-free shear deformable beam element is implemented to discretize the flexible bodies. A continuous contact-impact model is used to evaluate the contact force, in which energy dissipation in the form of hysteresis damping is considered. A force transition model from hydrodynamic lubrication forces to dry contact forces is introduced to ensure continuity in the joint reaction force. A comprehensive study with different lubrication force models has also been carried out. The generalized-α method is used to solve the equations of motion and several efficient methods are incorporated in the proposed model. Finally, the methodology is validated by two numerical examples.

[1]  Ahmed A. Shabana,et al.  A continuous force model for the impact analysis of flexible multibody systems , 1987 .

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

[3]  J. Ambrósio,et al.  Elasto-plastic deformations in multibody dynamics , 1992 .

[4]  A. Shabana,et al.  Performance of the Incremental and Non-Incremental Finite Element Formulations in Flexible Multibody Problems , 2000 .

[5]  Johannes Gerstmayr,et al.  Analysis of Thin Beams and Cables Using the Absolute Nodal Co-ordinate Formulation , 2006 .

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

[7]  Steven Dubowsky,et al.  The Dynamic Modeling of Flexible Spatial Machine Systems With Clearance Connections , 1987 .

[8]  R. Nazer,et al.  Analysis of dynamic strains in tibia during human locomotion based on flexible multibody approach integrated with magnetic resonance imaging technique , 2008 .

[9]  S. Dubowsky,et al.  Design and Analysis of Multilink Flexible Mechanisms With Multiple Clearance Connections , 1977 .

[10]  J. Meijaard Efficient Numerical Integration of the Equations of Motion of Non‐Smooth Mechanical Systems , 1997 .

[11]  A. Mikkola,et al.  A new locking-free shear deformable finite element based on absolute nodal coordinates , 2007 .

[12]  Jorge Ambrósio,et al.  Application of a wheel–rail contact model to railway dynamics in small radius curved tracks , 2008 .

[13]  Peter Eberhard,et al.  Computational Dynamics of Multibody Systems: History, Formalisms, and Applications , 2006 .

[14]  Takao Kakizaki,et al.  Modeling the Spatial Dynamics of Robotic Manipulators with Flexible Links and Joint Clearances , 1993 .

[15]  Ahmed A. Shabana,et al.  Computational Continuum Mechanics , 2008 .

[16]  Jorge Ambrósio,et al.  Revolute joints with clearance in multibody systems , 2004 .

[17]  Jorge Ambrósio,et al.  Dynamics of Multibody Systems With Spherical Clearance Joints , 2005 .

[18]  Jorge Ambrósio,et al.  Lubricated revolute joints in rigid multibody systems , 2009 .

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

[20]  Jorge Ambrósio,et al.  Impact of Rigid and Flexible Multibody Systems: Deformation Description and Contact Models , 2003 .

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

[22]  Jorge Ambrósio,et al.  Translational Joints With Clearance in Rigid Multibody Systems , 2008 .

[23]  W. M. Mansour,et al.  Mechanical Joints With Clearance: A Three-Mode Model , 1976 .

[24]  Hamid M. Lankarani,et al.  Joint Clearances With Lubricated Long Bearings in Multibody Mechanical Systems , 2000 .

[25]  K. H. Hunt,et al.  Coefficient of Restitution Interpreted as Damping in Vibroimpact , 1975 .

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

[27]  C. G. Broyden A Class of Methods for Solving Nonlinear Simultaneous Equations , 1965 .

[28]  Ke Zhang,et al.  Normal Force-Displacement Relationship of Spherical Joints With Clearances , 2006 .

[29]  A. Shabana Definition of the Slopes and the Finite Element Absolute Nodal Coordinate Formulation , 1997 .

[30]  Jorge Ambrósio,et al.  A study on dynamics of mechanical systems including joints with clearance and lubrication , 2006 .

[31]  Mohamed A. Omar,et al.  A TWO-DIMENSIONAL SHEAR DEFORMABLE BEAM FOR LARGE ROTATION AND DEFORMATION PROBLEMS , 2001 .

[32]  J. Mayo,et al.  Efficient Evaluation of the Elastic Forces and the Jacobian in the Absolute Nodal Coordinate Formulation , 2004 .

[33]  Ahmed A. Shabana,et al.  A rational finite element method based on the absolute nodal coordinate formulation , 2009 .

[34]  Olivier A. Bauchau,et al.  Modeling of joints with clearance in flexible multibody systems , 2001 .

[35]  A. Mikkola,et al.  Description of Elastic Forces in Absolute Nodal Coordinate Formulation , 2003 .

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

[37]  M. S. Pereira,et al.  Frictional Impact Analysis in Open-Loop Multibody Mechanical Systems , 1999 .

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

[39]  Inna Sharf,et al.  Literature survey of contact dynamics modelling , 2002 .

[40]  A. Mikkola,et al.  A geometrically exact beam element based on the absolute nodal coordinate formulation , 2008 .

[41]  A. Shabana Computational Continuum Mechanics: Computational Geometry and Finite Element Analysis , 2008 .

[42]  Hamid M. Lankarani,et al.  Treatment of Impact with Friction in Planar Multibody Mechanical Systems , 2001 .

[43]  M. Géradin,et al.  A beam finite element non‐linear theory with finite rotations , 1988 .

[44]  A. Shabana,et al.  EFFICIENT INTEGRATION OF THE ELASTIC FORCES AND THIN THREE-DIMENSIONAL BEAM ELEMENTS IN THE ABSOLUTE NODAL COORDINATE FORMULATION , 2005 .

[45]  S. Erkaya,et al.  Determining link parameters using genetic algorithm in mechanisms with joint clearance , 2009 .

[46]  Ferdinand Freudenstein,et al.  Dynamic Analysis of Mechanical Systems With Clearances—Part 2: Dynamic Response , 1971 .

[47]  Olivier A. Bauchau,et al.  Contact Conditions for Cylindrical, Prismatic, and Screw Joints in Flexible Multibody Systems , 2001 .

[48]  Selçuk Erkaya,et al.  A neural–genetic (NN–GA) approach for optimising mechanisms having joints with clearance , 2008 .

[49]  Jingzhou Yang,et al.  An Efficient Hybrid Method for Multibody Dynamics Simulation Based on Absolute Nodal Coordinate Formulation , 2009 .

[50]  W. Philipzik Zur hydrodynamischen Theorie der Schmiermittelreibung , 1956 .

[51]  Qiang Tian,et al.  Simulation of a viscoelastic flexible multibody system using absolute nodal coordinate and fractional derivative methods , 2009 .

[52]  Arend L. Schwab,et al.  A comparison of revolute joint clearance models in the dynamic analysis of rigid and elastic mechanical systems , 2002 .

[53]  Ferdinand Freudenstein,et al.  Dynamic Analysis of Mechanical Systems With Clearances—Part 1: Formation of Dynamic Model , 1971 .