Verification Process of Cylindrical Contact Force Models for Internal Contact Modeling

Authors: Cândida M. Pereira, Amílcar L. Ramalho, Jorge A. Ambrósio

Abstract:

In the numerical solution of the forward dynamics of a multibody system, the positions and velocities of the bodies in the system are obtained first. With the information of the system state variables at each time step, the internal and external forces acting on the system are obtained by appropriate contact force models if the continuous contact method is used instead of a discrete contact method. The local deformation of the bodies in contact, represented by penetration, is used to compute the contact force. The ability and suitability with current cylindrical contact force models to describe the contact between bodies with cylindrical geometries with particular focus on internal contacting geometries involving low clearances and high loads simultaneously is discussed in this paper. A comparative assessment of the performance of each model under analysis for different contact conditions, in particular for very different penetration and clearance values, is presented. It is demonstrated that some models represent a rough approximation to describe the conformal contact between cylindrical geometries because contact forces are underestimated.

Keywords: Clearance joints, Contact mechanics, Contact dynamics, Internal cylindrical contact, Multibody dynamics.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1063076

References:

[1] R.S. Haines, Survey: 2-dimensional motion and impact at revolute joints, Mechanism and Machine Theory, 15, pp. 361-370, 1980.
[2] J.A. Zukas, T. Nicholas, L.B. Greszczuk, D. R. Curran, Impact Dynamics, John Wiley and Sons, New York, New York, 1982.
[3] R.R. Ryan, ADAMS-Multibody System Analysis Software, Multibody Systems Handbook, Berlin, Springer-Verlag, 1990.
[4] R.C. Smith, E.J. Haug, DADS-Dynamic Analysis and Design System, Multibody Systems Handbook, Berlin, Springer-Verlag, 1990.
[5] W. Schiehlen, Multibody system dynamics: roots and perspectives, Multibody System Dynamics, 1, 149-188, 1997.
[6] C.L. Bottasso, P. Citelli, A. Taldo, C.G. Franchi, Unilateral Contact Modeling with Adams, In International ADAMS User-s Conference, Berlin, Germany, November 17-18, 11p, 1999.
[7] B.M. Bahgat, M.O.M. Osman, T.S. Sankar, On the effect of bearing clearances in the dynamic analysis of planar mechanisms, Journal of Mechanical Engineering Science, 21(6), 429-437, 1979.
[8] M.T. Bengisu, T. Hidayetoglu, A. Akay, A theoretical and experimental investigation of contact loss in the clearances of a four-bar mechanism, J. of Mech., Trans. and Automation in Design, 108, 237-244, 1986.
[9] K. Soong, B.S. Thompson, A theoretical and experimental investigation of the dynamic response of a slider-crank mechanism with radial clearance in the gudgeon-pin joint, J. of Mechanical Design, 112, 183- 189, 1990.
[10] S. Earles, O. Kilicay, A design criterion for maintaining contact at plain bearings, In Proceedings of the Institution of Mechanical Engineers, 194, 249-258, 1980.
[11] L.D. Seneviratne, S.W.E. Earles, Chaotic Behaviour Exhibited During contact Loss in a Clearance Joint in a Four-bar Mechanism, Mechanism and Machine Theory, 27(3), 307-321, 1992.
[12] M.-J. Tsai, T.-H. Lai, Kinematic sensitivity analysis of linkage with joint clearance based on transmission quality, Mechanism and Machine Theory, 39(11), 1189 -1206, 2004.
[13] J.F. Deck, S. Dubowsky, On the limitations of predictions of the dynamic response of machines with clearance connections, Journal of Mechanical Design, 116, 833-841, 1994.
[14] J. Rhee, A. Akay, Dynamic response of a revolute joint with clearance, Mechanism and Machine Theory, 31 (1), 121-134, 1996.
[15] S. Shivaswamy, H.M. Lankarani, Impact Analysis of Plates Using Quasi-Static Approach, J. of Mechanical Design, 119, 376-381, 1997.
[16] P.A. Ravn, Continuous analysis method for planar multibody systems with joint clearance, Multibody System Dynamics, 2, 1-24, 1998.
[17] P. Ravn, S. Shivaswamy, B. J. Alshaer, H. Lankarani, Joint Clearances with Lubricated Long Bearings in Multibody Mechanical Systems, Journal of Mechanical Design, 122, 484-488, 2000.
[18] Bauchau, O. A., Bottasso, C. L., Contact Conditions for Cylindrical, Prismatic, and Screw Joints in Flexible Multibody Systems, Multibody System Dynamics, 5, 251-278, 2001.
[19] P. Flores, J. Ambr├│sio, On the Contact Detection for Contact-Impact Analysis in Multibody Systems, Multibody System Dynamics, 24(1), 103-122, 2010.
[20] O. A. Bauchau, J. Rodriguez, Modeling of Joints With Clearance in Flexible Multibody Systems, Int. J. Solids Struct., 39, 41-63, 2002.
[21] A. L. Schwab, J. P. Meijaard, P. Meijers, A Comparison of Revolute Joint Clearance Models in the Dynamic Analysis of Rigid and Elastic Mechanical Systems, Mechanism and Machine Theory, 37, 895-913, 2002.
[22] G. Giraldi, I. Sharf, Literature Survey of Contact Dynamics Modelling, Mechanism and Machine Theory, 37, 1213-1239, 2002.
[23] P. Flores, J. Ambr├│sio, Revolute Joints with Clearance in Multibody Systems, Computers & Structures, 82, 1359-1369, 2004.
[24] P. Flores, J. Ambr├│sio, J. C. P. Claro, Dynamic Analysis for Planar Multibody Mechanical Systems with Lubricated Joints, Multibody System Dynamics, 12, 47-74, 2004.
[25] P. Flores, J. Ambr├│sio, J. C. P. Claro, H.M. Lankarani, Dynamics of multibody systems with spherical clearance joints, Journal of Computational Nonlinear Dynamics, 1(3), 240 -247, 2006.
[26] P. Flores, J. Ambr├│sio, J. C. P.Claro, H.M. Lankarani, C.S. Koshy, A study on dynamics of mechanical systems including joints with clearance and lubrication, Mechanism and Machine Theory, 41, 247- 261, 2006.
[27] A.R Crowthera, R. Singha, N. Zhangb, C. Chapman, Impulsive response of an automatic transmission system with multiple clearances: formulation, simulation and experiment, Journal of Sound and Vibration, 306, 444-66, 2007.
[28] P. Flores, J. Ambr├│sio, J. C. P. Claro, H. Lankarani, Kinematics and Dynamics of Multibody Systems with Imperfect Joints: Models and Case Studies, Springer, Dordrecht, The Netherlands, 2008.
[29] N. Srivastava, I. Haque, Clearance and friction-induced dynamics of chain CVT drives, Multibody Systems Dynamics, 19 (3), 255-80, 2008.
[30] G.J. Turvey, P. Wang, An FE analysis of the stresses in pultruded GRP single-bolt tension joints and their implications for joint design, Computers and Structures, 86, 1014-21, 2008.
[31] Q. Tian, Y. Zhang, L. Chen P. Flores, Dynamics of spatial flexible Multibody systems with clearance and lubricated spherical joints, Computers and Structures, 87, 913-929, 2009.
[32] T. Liu, M. Y. Wang, K. H Low, Non-jamming conditions in multicontact rigid-body dynamics, Multibody System Dynamics, 22(3), 269- 296, 2009.
[33] P. Flores, J. Ambr├│sio, J. C. P. Claro, H.M. Lankarani, C.S. Koshy, Lubricated revolute joints in rigid multibody systems, Nonlinear Dynamics, 56(3), 277-95, 2009.
[34] P. Flores, R. Leine C. Glocker, Modeling and analysis of planar rigid multibody systems with translational clearance joints based on nonsmooth dynamics approach. Multibody System Dynamics, 23(2), 165- 190, 2010.
[35] J. Choi, H.S. Ryu, C.W. Kim, J.H. Choi, An efficient and robust contact algorithm for a compliant contact force model between bodies of complex geometry, Multibody System Dynamics, 23(1), 99-120, 2010.
[36] D.M. Flickinger, A. Bowling, Simultaneous oblique impacts and contacts in multibody systems with friction, Multibody System Dynamics, 23(3), 249-262, 2010.
[37] C.-S. Liu, K. Zhang, L. Yang, Normal force-displacement relationship of spherical joints with clearances, Journal of Computational and Nonlinear Dynamics, 1, 160-167, 2006.
[38] C-S. Liu, K. Zhang, R. Yang, The FEM analysis and approximate model for cylindrical joints with clearances, Mechanism and Machine Theory, 42, 183-197, 2007.
[39] H.M. Lankarani, P.E. Nikravesh, A Contact Force Model With Hysteresis Damping for Impact Analysis of Multibody Systems, Journal of Mechanical Design, 112, 369-376, 1990.
[40] H.M. Lankarani, P.E. Nikravesh, Canonical Impulse-Momentum Equations for Impact Analysis of Multibody Systems, Journal of Mechanical Design, 114, 180-186, 1992.
[41] H.M. Lankarani, P.E. Nikravesh, Continuous Contact Force Models for Impact Analysis in Multibody Systems, Nonlinear Dynamics, 5, 193- 207, 1994.
[42] Y. Khulief, A. Shabana, A Continuous Force Model for the Impact Analysis of Flexible Multi-Body Systems, Mechanism and Machine Theory, 22, 213-224, 1987.
[43] S.L. Pedersen, J.M. Hansen, J.A.C. Ambr├│sio, A Roller Chain Drive Model Including Contact with Guide-Bars, Multibody System Dynamics, 12, 3, 285-301, 2004.
[44] G. Hippmann, M. Arnold, M. Schittenhelm, Efficient Simulation of Bush and Roller Chain Drives, Multibody Dynamics 2005, ECCOMAS Thematic Conference, edited by J.M. Goicolea, J. Cuadrado, J.C. García Orden, Madrid, Spain, 2005.
[45] S. Ahmed, H.M. Lankarani, M.F.O.S. Pereira, Frictional Impact Analysis in Open-Loop, Multibody Mechanical Systems, Journal of Mechanical Design, 121, 119-127, 1999.
[46] H.M. Lankarani, A Poisson-Based Formulation for Frictional Impact Analysis of Multibody Mechanical Systems with Open or Closed Kinematic Chains, Journal of Mechanical Design, 122, 489-497, 2000.
[47] K.H. Hunt, F.R. Crossley, Coefficient of restitution interpreted as damping in vibroimpact, J. of Applied Mechanics, 7, 440-445, 1975.
[48] C.T. Lim, W.J. Stronge, Oblique elastic-plastic impact between rough cylinders in plane strain, Int. J. of Eng. Science, 37, 97-122, 1999.
[49] D. Gugan, Inelastic collision and the Hertz theory of impact, American Journal of Physics, 68(10), 920-924, 2000.
[50] W. Yao, B. Chen, C. Liu, Energetic Coefficient of Restitution for Planar Impact in Multi-Rigid-Body systems With Friction, Int. J. Impact Eng., 31, 255-265, 2005.
[51] Cândida M. Pereira, Amílcar L. Ramalho, Jorge A. Ambrósio, A Critical Overview of Internal and External Cylinder Contact Force Models, Nonlinear Dynamics, 63(4), 681-697, 2011.
[52] K.L. Johnson, Contact Mechanics, Cambridge University Press, Cambridge, England, 1994.
[53] E. I. Radzimovsky, Stress distribution and strength conditions of two rolling cylinders pressed together, Eng. Exp. Sta. Univ. Ill., Bull. 408, 1953.
[54] Roark-s, Formulas for Stress & Strain, McGraw-Hill, 6th Edition, 1989.
[55] W. Goldsmith, Impact, The Theory and Physical Behaviour of Colliding Solids, Edward Arnold Ltd, London, England,1960.
[56] ESDU 78035 Tribology Series, Contact Phenomena. I: stresses, deflections and contact dimensions for normally loaded unlubricated elastic components, Eng. Sciences Data Unit, London, England, 1978.
[57] S. Dubowsky, F. Freudenstein, Dynamic analysis of mechanical systems with clearances, Part 1: formulation of dynamic model. J Eng Ind, 93 (1), 305-309, 1971.
[58] S. Dubowsky, F. Freudenstein, Dynamic analysis of mechanical systems with clearances, Part 2: dynamics response. J Eng Ind, 93(1):310-6, 1971.
[59] C. Pereira, A. Ramalho, J. Ambr├│sio, An Enhanced cylinder contact force model, Multibody System Dynamics I (submitted), 2013.
[60] M. Ciavarella, P. Decuzzi, The state of stress induced by the plane frictionless cylindrical contact 1: the case of elastic similarity, International Journal of Solids and Structures, 38, 4507-4523, 2001.
[61] M. Ciavarella, P. Decuzzi, The state of stress induced by the plane frictionless cylindrical contact. 2: the general case (elastic dissimilarity), International Journal of Solids and Structures, 38, 4523-4533, 2001.
[62] C. Pereira, A. Ramalho, J. Ambr├│sio, Conformal Cylindrical Contact Force Model Verification using a Finite Element Analysis, in B.H.V. Topping, Y. Tsompanakis, (Editors), Civil-Comp Press, Stirlingshire, UK, Paper 135, doi:10.4203/ccp.96.135, ISSN: 1759-3433, 2011.
[63] C. Pereira, A. Ramalho, J. Ambr├│sio, Experimental and Numerical Validation of an Enhanced Cylindrical Contact Force Model, Book Surface Effects and Contact Mechanics X, Edited By: J.T.M. Hosson and C.A. Brebbia, Wessex Institute of Technology, UK, Vol. 7, pp.49- 60, ISBN: 978-1-84564-530-4, 2011.
[64] BS EN ISO 286-1:2010 "Geometrical Product Specifications (GPS) - ISO code system for tolerances on linear sizes. Part 1: Basis of tolerances, deviations and fits", 2010.
[65] BS EN ISO 286-2:2010 "Geometrical Product Specifications (GPS) - ISO code system for tolerances on linear sizes. Part 2: Tables of standard tolerance classes and limit deviations for holes and shafts", 2010.