Skip to main content
SpringerLink
Log in

A critical overview of internal and external cylinder contact force models

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

Abstract

Most of the analytical models found in the literature, to study the contact between cylindrical bodies, are based on the Hertz pressure distribution. The major shortcomings associated with these cylindrical models concern their nonlinearity. Firstly, the indentation is expressed as an implicit function of the contact force, thus a numerical iterative technique is required to evaluate the contact force for a given indentation. In a dynamic analysis code, it is implied that at each integration time step, the iterative process for the solution of the nonlinear equations has to be solved. Secondly, the current cylindrical contact models include logarithmic functions, which impose mathematical and physical limitations on their application, particularly for conformal contact conditions with lower clearance values. The validity domain of each contact model is identified in this work with relation to the clearance value and material properties of the contacting cylinders. A comparative assessment of the performance of each model is performed calculating the relative difference of each one in relation to Johnson’s model. The results show that, in general, different models exhibit distinct behavior for both the internal and external contact between cylinders. The load limit of each model and the restrictions on its application is identified using two simple examples of mechanical engineering practice in which internal contacting cylinders are involved and analyzed to include: journal bearings and roller chain drives.

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

Similar content being viewed by others

References

  1. Zukas, J.A., Nicholas, T., Greszczuk, L.B., Curran, D.R.: Impact Dynamics. Wiley, New York (1982)

    Google Scholar 

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

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  5. Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1994)

    Google Scholar 

  6. Lim, C.T., Stronge, W.J.: Oblique elastic-plastic impact between rough cylinders in plane strain. Int. J. Eng. Sci. 37, 97–122 (1999)

    Article  Google Scholar 

  7. Gugan, D.: Inelastic collision and the Hertz theory of impact. Am. J. Phys. 68(10), 920–924 (2000)

    Article  Google Scholar 

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

    Article  Google Scholar 

  9. 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 

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

    Google Scholar 

  11. ESDU-78035 Tribology Series, Contact Phenomena. I: Stresses, Deflections and Contact Dimensions for Normally-loaded Unlubricated Elastic Components, Engineering Sciences Data Unit, London (1978)

  12. Radzimovsky, E.I.: Stress distribution and strength conditions of two rolling cylinders pressed together. Bull Univ. Ill., Eng. Exp. Stn., 408 (1953)

  13. Goldsmith, W.: Impact, ‘The Theory and Physical Behaviour of Colliding Solids’. Edward Arnold, London (1960)

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  16. Lankarani, H.M., Nikravesh, P.E.: Canonical impulse-momentum equations for impact analysis of multibody systems. J. Mech. Des. 114, 180–186 (1992)

    Article  Google Scholar 

  17. Ahmed, S., Lankarani, H.M., Pereira, M.: Frictional impact analysis in open-loop multibody mechanical systems. J. Mech. Des. 121, 119–127 (1999)

    Article  Google Scholar 

  18. Lankarani, H.M.: A Poisson-based formulation for frictional impact analysis of multibody mechanical systems with open or closed kinematic chains. J. Mech. Des. 122, 489–497 (2000)

    Article  Google Scholar 

  19. Flores, P., Ambrósio, J.: On the contact detection for contact-impact analysis in multibody systems. Multibody Syst. Dyn. 24(1), 103–122 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  20. Liu, C.-S., Zhang, K., Yang, L.: Normal force-displacement relationship of spherical joints with clearances. J. Comput. Nonlinear Dyn. 1, 160–167 (2006)

    Article  Google Scholar 

  21. Liu, C.-S., Zhang, K., Yang, L.: The FEM analysis and approximate model for cylindrical joints with clearances. Mech. Mach. Theory 183–197 (2007)

  22. Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M., Koshy, C.S.: Lubricated revolute joints in rigid multibody systems. Nonlinear Dyn. 56, 277–295 (2009)

    Article  MATH  Google Scholar 

  23. Pereira, C., Ambrosio, J., Ramalho, A., Flores, P.: A methodology for the generation of models for multibody chain drives. Multibody Syst. Dyn. (2010). doi:10.1007/s11044-010-9207-x

    Google Scholar 

  24. Ambrosio, J., Verissimo, P.: Improved bushing models for vehicle dynamics. Multibody Syst. Dyn. 22(4), 341–365 (2009)

    Article  MATH  Google Scholar 

  25. Ryan, R.R.: ADAMS-Multibody System Analysis Software. Multibody Systems Handbook. Springer, Berlin (1990)

    Google Scholar 

  26. Smith, R.C., Haug, E.J.: DADS-Dynamic Analysis and Design System. Multibody Systems Handbook. Springer, Berlin (1990)

    Google Scholar 

  27. Bottasso, C.L., Citelli, P., Taldo, A., Franchi, C.G.: Unilateral contact modeling with Adams. In: International ADAMS User’s Conference, Berlin, Germany, November 17–18, 11 p. (1999)

  28. Pedersen, S.L., Hansen, J.M., Ambrósio, J.: A roller chain drive model including contact with guide-bars. Multibody Syst. Dyn. 12(3), 285–301 (2004)

    Article  MATH  Google Scholar 

  29. Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M.: Influence of the contact-impact force model on the dynamic response of multi-body systems. Proc. Inst. Mech. Eng., Proc. Part K, J. Multi-Body Dyn. 220, 21–34 (2006)

    Google Scholar 

  30. Pedersen, S.L.: Simulation and analysis of roller chain drive systems. Ph.D. Dissertation, Department of Mechanical Engineering, Solid Mechanics, Technical University of Denmark, Lyngby, Denmark (2004)

  31. Silva, M., Ambrósio, J.: Human motion analysis using multibody dynamics and optimization tools. Technical Report IDMEC/CPM—2004/001’, Instituto Superior Técnico of the Technical University of Lisbon, Lisbon, Portugal (2004)

  32. Hertz, H.: On the contact of solids—on the contact of rigid elastic solids and on hardness. In: Miscellaneous Papers, pp. 146–183. Macmillan & Co., London (1896) (Translated by D.E. Jones and G.A. Schott)

    Google Scholar 

  33. Roark’s: Formulas for Stress & Strain, 6th edn. McGraw-Hill, New York (1989)

    Google Scholar 

  34. Shigley, J.E., Mischke, C.R.: Mechanical Engineering Design. 5th edn. McGraw-Hill, New York (1989)

    Google Scholar 

  35. Parker, M.A.: Drawing Standards for Computer-aided Engineering, 1st edn. England City and Guilds/Macmillan, London (1995)

    Google Scholar 

  36. General guide to the choice of journal bearing type. In: ESDU—65007. Tribology Series. Engineering Sciences Data Unit, London (1965)

  37. Marshek, K.M.: In: Shigley, J.E., Mischke, C.R. (eds.) Power Transmission Elements—A Mechanical Designers’ Workbook. McGraw-Hill, New York, pp. 159–207 (1990)

    Google Scholar 

  38. SRAMPORT—Mechanical Drives Company, Activity: Manufacture of bearings, gears, gearing and driving elements, Coimbra, Portugal

Download references

Author information

Authors and Affiliations

  1. Polytechnic Institute of Coimbra, R. Pedro Nunes, 3030-199, Coimbra, Portugal

    Cândida M. Pereira

  2. R. Luís Reis dos Santos, University of Coimbra, 3030-788, Coimbra, Portugal

    Amílcar L. Ramalho

  3. Technical University of Lisbon, Av. Rovisco Pais, 1049-001, Lisbon, Portugal

    Jorge A. Ambrósio

Authors
  1. Cândida M. Pereira
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Amílcar L. Ramalho
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jorge A. Ambrósio
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jorge A. Ambrósio.

Rights and permissions

Reprints and permissions

About this article

Cite this article

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). https://doi.org/10.1007/s11071-010-9830-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-010-9830-3

Keywords

Search

Navigation