Verification Process of Cylindrical Contact Force Models for Internal Contact Modeling
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.
[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.
[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.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:55606", author = "Cândida M. Pereira and Amílcar L. Ramalho and Jorge A. Ambrósio", title = "Verification Process of Cylindrical Contact Force Models for Internal Contact Modeling", 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.", volume = "7", number = "5", pages = "853-11", }
