Skip to main content
SpringerLink
Log in

Study of the effect of contact force model on the dynamic response of mechanical systems with dry clearance joints: computational and experimental approaches

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

The main objective of this work is to present a computational and experimental study on the contact forces developed in revolute clearance joints. For this purpose, a well-known slider-crank mechanism with a revolute clearance joint between the connecting rod and slider is utilized. The intra-joint contact forces that are generated at these clearance joints are computed by considering several different elastic and dissipative approaches, namely those based on the Hertz contact theory and the ESDU tribology-based cylindrical contacts, along with a hysteresis-type dissipative damping. The normal contact force is augmented with the dry Coulomb’s friction force. In addition, an experimental apparatus is used to obtained some experimental data in order to verify and validate the computational models. From the outcomes reported in this paper, it is concluded that the selection of the appropriate contact force model with proper dissipative damping plays a significant role in the dynamic response of mechanical systems involving contact events at low or moderate impact velocities.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Ravn, P., Shivaswamy, S., Alshaer, B.J., Lankarani, H.M.: Joint clearances with lubricated long bearings in multibody mechanical systems. J. Mech. Des. 122, 484–488 (2000)

    Article  Google Scholar 

  2. Flores, P., Lankarani, H.M., Ambrósio, J., Claro, J.C.P.: Modelling lubricated revolute joints in multibody mechanical systems. Proc. Inst. Mech. Eng., Proc., Part K, J. Multi-Body Dyn. 218(4), 183–190 (2004)

    Google Scholar 

  3. Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M.: Dynamic behaviour of planar rigid multibody systems including revolute joints with clearance. Proc. Inst. Mech. Eng., Proc., Part K, J. Multi-Body Dyn. 221(2), 161–174 (2007)

    Google Scholar 

  4. Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M.: Translational joints with clearance in rigid multibody systems. J. Comput. Nonlinear Dyn. 3(1), 0110071 (2008)

    Article  Google Scholar 

  5. Erkaya, S., Uzmay, I.: Investigation on effect of joint clearance on dynamics of four-bar mechanism. Nonlinear Dyn. 58, 179–198 (2009)

    Article  MATH  Google Scholar 

  6. Erkaya, S., Uzmay, İ.: Determining link parameters using genetic algorithm in mechanisms with joint clearance. Mech. Mach. Theory 44, 222–234 (2009)

    Article  MATH  Google Scholar 

  7. Flores, P.: Modeling and simulation of wear in revolute clearance joints in multibody systems. Mech. Mach. Theory 44(6), 1211–1222 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Tian, Q., Zhang, Y., Chen, L., Yang, J.: Simulation of planar flexible multibody systems with clearance and lubricated revolute joints. Nonlinear Dyn. 60, 489–511 (2010)

    Article  MATH  Google Scholar 

  9. Flores, P., Lankarani, H.M.: Spatial rigid-multi-body systems with lubricated spherical clearance joints: modeling and simulation. Nonlinear Dyn. 60, 99–114 (2010)

    Article  MATH  Google Scholar 

  10. Brutti, C., Coglitore, C., Valentini, P.P.: Modeling 3D revolute joint with clearance and contact stiffness. Nonlinear Dyn. 66(4), 531–548 (2011)

    Article  Google Scholar 

  11. Tian, Q., Liu C., Machado, M., Flores, P.: A new model for dry and lubricated cylindrical joints with clearance in spatial flexible multibody systems. Nonlinear Dyn. 64, 25–47 (2011)

    Article  Google Scholar 

  12. Liu, C., Tian, Q., Hu, H.: Dynamics and control of a spatial rigid-flexible multibody system with multiple cylindrical clearance joints. Mech. Mach. Theory 52, 106–129 (2012)

    Article  Google Scholar 

  13. Flores, P., Lankarani, H.M.: Dynamic response of multibody systems with multiple clearance joints. J. Comput. Nonlinear Dyn. 7(3), 031003 (2012)

    Article  Google Scholar 

  14. Erkaya, S.: Prediction of vibration characteristics of a planar mechanism having imperfect joints using neural network. J. Mech. Sci. Technol. 26(5), 1419–1430 (2012)

    Article  Google Scholar 

  15. Erkaya, S., Uzmay, I.: Effects of balancing and flexibility on dynamics of a planar mechanism having joint clearance. Sci. Iran. B 19(3), 483–490 (2012)

    Article  Google Scholar 

  16. Olyaei, A.A., Ghazavi, M.R.: Stabilization slider-crank mechanism with clearance joints. Mech. Mach. Theory 53, 17–29 (2012)

    Article  Google Scholar 

  17. Bai, Z.F., Zhao, Y.: Dynamics modeling and quantification analysis of multibody systems including revolute clearance joints. Precis. Eng. 36, 554–567 (2012)

    Article  Google Scholar 

  18. Bai, Z.F., Zhao, Y.: Dynamic behaviour analysis of planar mechanical systems with clearance in revolute joints using a new hybrid contact force model. Int. J. Mech. Sci. 54, 190–205 (2012)

    Article  Google Scholar 

  19. Muvengei, O., Kihiu, J., Ikua, B.: Numerical study of parametric effects on the dynamic response of planar multi-body systems with differently located frictionless revolute clearance joints. Mech. Mach. Theory 53, 30–49 (2012)

    Article  Google Scholar 

  20. Chaker, A., Mlika, A., Laribi, M.A., Romdhane, L., Zeghloul, S.: Clerance and manufacturing errors’ effects on the accuracy of the 3-RCC spherical parallel manipulator. Eur. J. Mech. A, Solids 37, 86–95 (2013)

    Article  Google Scholar 

  21. Haines, R.S.: Survey: 2-Dimensional motion and impact at revolute joints. Mech. Mach. Theory 15, 361–370 (1980)

    Article  Google Scholar 

  22. Flores, P.: A parametric study on the dynamic response of planar multibody systems with multiple clearance joints. Nonlinear Dyn. 61(4), 633–653 (2010)

    Article  MATH  Google Scholar 

  23. Soong, K., Thompson, B.S.: A theoretical and experimental investigation of the dynamic response of a slider-crank mechanism with radial clearance in the gudgeon-pin joint. J. Mech. Des. 112, 183–189 (1990)

    Article  Google Scholar 

  24. Lankarani, H.M., Koshy, S., Kanetkar, G., Flores, P., Claro, J.C.P., Ambrósio, J.: Experimental study on multibody systems with clearance joints. In: The Second Asian Conference on Multibody Dynamics 2004, Olympic Parktel, Seoul, Korea, August 1–4, p. 6 (2004)

    Google Scholar 

  25. Flores, P.: Dynamic analysis of mechanical systems with imperfect kinematic joints. PhD dissertation, University of Minho, Guimarães, Portugal (2004)

  26. Koshy, C.S.: Characterization of mechanical systems with real joints and flexible links. PhD dissertation, Wichita State University, Wichita, Kansas, USA (2006)

  27. Khemili, I., Romdhane, L.: Dynamic analysis of a flexible slider-crank mechanism with clearance. Eur. J. Mech. A, Solids 27(5), 882–898 (2008)

    Article  MATH  Google Scholar 

  28. Erkaya, S., Uzmay, I.: Experimental investigation of joint clearance effects on the dynamics of a slider-crank mechanism. Multibody Syst. Dyn. 24, 81–102 (2010)

    Article  MATH  Google Scholar 

  29. Flores, P., Koshy, C.S., Lankarani, H.M., Ambrósio, J., Claro, J.C.P.: Numerical and experimental investigation on multibody systems with revolute clearance joints. Nonlinear Dyn. 65(4), 383–398 (2011)

    Article  Google Scholar 

  30. Machado, M., Moreira, P., Flores, P., Lankarani, H.M.: Compliant contact force models in multibody dynamics: evolution of the Hertz contact theory. Mech. Mach. Theory 53, 99–121 (2012)

    Article  Google Scholar 

  31. Ravn, P.: Analysis and synthesis of planar mechanical systems including flexibility, contact and joint clearance. PhD dissertation, DCAMM Report No. S78, Technical University of Denmark, Lyngby, Denmark (1998)

  32. Lankarani, H.M., Nikravesh, P.E.: A contact force model with hysteresis damping for impact analysis of multibody systems. J. Mech. Des. 112, 369–376 (1990)

    Article  Google Scholar 

  33. Shigley, J.E., Mischke C.R.: Mechanical Engineering Design. McGraw-Hill, New York (1989)

    Google Scholar 

  34. Timoshenko, S.P., Goodier, J.N.: Theory of Elasticity. McGraw-Hill, New York (1970)

    MATH  Google Scholar 

  35. Johnson, K.L.: One hundred years of Hertz contact. Proc. Inst. Mech. Eng. 196, 363–378 (1982)

    Article  Google Scholar 

  36. Hertz, H.: Über die Berührung fester elastischer Körper. J. Reine Angew. Math. 92, 156–171 (1881)

    Google Scholar 

  37. Shivaswamy, S., Lankarani, H.M.: Impact analysis of plate using quasi-static approach. J. Mech. Des. 119, 376–381 (1997)

    Article  Google Scholar 

  38. Cross, R.: The bounce of a ball. Am. J. Phys. 67, 222–227 (1999)

    Article  Google Scholar 

  39. Dietl, P., Wensing, J., van Nijen, G.C.: Rolling bearing damping for dynamic analysis of multi-body systems—experimental and theoretical results. Proc. Inst. Mech. Eng., Proc., Part K, J. Multi-Body Dyn. 214(1), 33–43 (2000)

    Google Scholar 

  40. Pereira, C.M., Ramalho, A.L., Ambrósio, J.A.: A critical overview of internal and external cylinder contact force models. Nonlinear Dyn. 63, 681–697 (2011)

    Article  Google Scholar 

  41. Goldsmith, W.: Impact—The Theory and Physical Behaviour of Colliding Solids. Arnold, London (1960)

    MATH  Google Scholar 

  42. Machado, M., Flores, P., Claro, J.C.P., Ambrósio, J., Silva, M., Completo, A., Lankarani, H.M.: Development of a planar multi-body model of the human knee joint. Nonlinear Dyn. 60, 459–478 (2010)

    Article  MATH  Google Scholar 

  43. Hunt, K.H., Crossley, F.R.E.: Coefficient of restitution interpreted as damping in vibroimpact. J. Appl. Mech. 7, 440–445 (1975)

    Article  Google Scholar 

  44. Shivaswamy, S.: Modeling contact forces and energy dissipation during impact in multibody mechanical systems. PhD dissertation, Wichita State University, Wichita, Kansas, USA (1997)

  45. ESDU 78035 tribology series, contact phenomena. I: Stresses, deflections and contact dimensions for normally loaded unlubricated elastic components. Engineering Sciences Data Unit, London, England (1978)

  46. Dubowsky, S., Freudenstein, F.: Dynamic analysis of mechanical systems with clearances, part 1: formulation of dynamic model. J. Eng. Ind. 93, 305–309 (1971)

    Article  Google Scholar 

  47. Herbert, R.G., McWhannell, D.C.: Shape and frequency composition of pulses from an impact pair. J. Eng. Ind. 99, 513–518 (1977)

    Article  Google Scholar 

  48. Lee, T.W., Wang, A.C.: On the dynamics of intermittent-motion mechanisms, part 1: dynamic model and response. J. Mech. Transm. Autom. Des. 105, 534–540 (1983)

    Article  Google Scholar 

  49. Kuwabara, G., Kono, K.: Restitution coefficient in a collision between two spheres. Jpn. J. Appl. Phys. 26, 1230–1233 (1987)

    Article  Google Scholar 

  50. Gonthier, Y., McPhee, J., Lange, C., Piedboeuf, J.-C.: A regularized contact model with asymmetric damping and dwell-time dependent friction. Multibody Syst. Dyn. 11, 209–233 (2004)

    Article  MATH  Google Scholar 

  51. Flores, P., Machado, M., Silva, M.T., Martins, J.M.: On the continuous contact force models for soft materials in multibody dynamics. Multibody Syst. Dyn. 25, 357–375 (2011)

    Article  MATH  Google Scholar 

  52. Minamoto, H., Kawamura, S.: Moderately high speed impact of two identical spheres. Int. J. Impact Eng. 38, 123–129 (2011)

    Article  Google Scholar 

  53. Yigit, A.S., Christoforou, A.P., Majeed, M.A.: A nonlinear visco-elastoplastic impact model and the coefficient of restitution. Nonlinear Dyn. 66, 509–521 (2011)

    Article  MathSciNet  Google Scholar 

  54. Roy, A., Carretero, J.A.: A damping term based on material properties for the volume-based contact dynamics model. Int. J. Non-Linear Mech. 47(3), 103–112 (2012)

    Article  Google Scholar 

  55. Gharib, M., Hurmuzlu, Y.: A new force model for low coefficient of restitution impact. J. Appl. Mech. 79(6), 064506 (2012)

    Article  Google Scholar 

  56. Boss, M., McPhee, J.: Volumetric modelling and experimental validation of normal contact dynamic forces. J. Comput. Nonlinear Dyn. 8, 021006 (2013)

    Article  Google Scholar 

  57. Khulief, Y.A.: Modeling of impact in multibody systems: An overview. J. Comput. Nonlinear Dyn. 8, 021012 (2013)

    Article  Google Scholar 

  58. MSC Software, M.Sc. ADAMS®, Release R3, Help System (2008)

  59. Karnopp, D.: Computer simulation of stick-slid friction in mechanical dynamic systems. J. Dyn. Syst. Meas. Control 107, 100–103 (1985)

    Article  Google Scholar 

  60. Centea, D., Rahnejat, H., Menday, M.T.: Non-linear multi-body dynamic analysis for the study of clutch torsional vibrations (judder). Appl. Math. Model. 25, 177–192 (2001)

    Article  MATH  Google Scholar 

  61. Haessig, D.A., Friedland, B.: On the modelling and simulation of friction. J. Dyn. Syst. Meas. Control 113, 354–362 (1991)

    Article  Google Scholar 

  62. Ahmed, S., Lankarani, H.M., Pereira, M.F.O.S.: Frictional impact analysis in open loop multibody mechanical system. J. Mech. Des. 121, 119–127 (1999)

    Article  Google Scholar 

  63. Lankarani, H.M.: A poisson based formulation for frictional impact analysis of multibody mechanical systems with open or closed kinematic chains. J. Mech. Des. 115, 489–497 (2000)

    Article  Google Scholar 

  64. Gottschalk, S., Lin, M.C., Manocha, D.: OBBTree: a hierarchical structure for rapid interference detection. In: Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques, New Orleans, LA, USA, pp. 171–180 (1996)

    Google Scholar 

  65. Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1985)

    Book  MATH  Google Scholar 

  66. Stronge, W.J.: Impact Mechanics. Cambridge University Press, Cambridge (2000)

    Book  MATH  Google Scholar 

  67. Lankarani, H.M., Nikravesh, P.E.: Continuous contact force models for impact analysis in multibody systems. Nonlinear Dyn. 5, 193–207 (1994)

    Google Scholar 

  68. Love, A.E.H.: A Treatise on the Mathematical Theory of Elasticity, 4th edn. Dover, New York (1944)

    MATH  Google Scholar 

  69. Seifried, R., Schiehlen, W., Eberhard, P.: The role of the coefficient of restitution on impact problems in multi-body dynamics. Proc. Inst. Mech. Eng., Proc., Part K, J. Multi-Body Dyn. 224, 279–306 (2010)

    Google Scholar 

Download references

Acknowledgements

This work is supported by the Portuguese Foundation for the Science and Technology (FCT) under the research project BIOJOINTS (PTDC/EME-PME/099764/2008). The second author expresses his gratitude to Portuguese Foundation for the Science and Technology for the postdoctoral scholarship (SFRH/BPD/77831/2011).

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Wichita State University, Wichita, KS, 67260-133, USA

    C. S. Koshy & H. M. Lankarani

  2. CT2M/Centro de Tecnologias Mecânicas e de Materiais, Departamento de Engenharia Mecânica, Universidade do Minho, Campus de Azurém, 4800-058, Guimarães, Portugal

    P. Flores

Authors
  1. C. S. Koshy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Flores
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. M. Lankarani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. Flores.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Koshy, C.S., Flores, P. & Lankarani, H.M. Study of the effect of contact force model on the dynamic response of mechanical systems with dry clearance joints: computational and experimental approaches. Nonlinear Dyn 73, 325–338 (2013). https://doi.org/10.1007/s11071-013-0787-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-013-0787-x

Keywords

Search

Navigation