Advertisement

Nonlinear Dynamics

, Volume 88, Issue 1, pp 131–143 | Cite as

A validated model for a pin-slot clearance joint

  • Luka Skrinjar
  • Janko Slavič
  • Miha Boltežar
Original Paper

Abstract

The numerical modeling of joints with a certain amount of clearance and a subsequent validation of the model are important for accurate multibody simulations. For such validated modeling, not only the kinematic constraints, but also the contact models, are important. If a joint has no clearance, it is assumed to be ideal. However, in real applications, there is frequently some clearance in the joints. Adding clearance and kinematic conditions to a pin-slot joint significantly increases the number of kinematic and contact parameters. Consequently, the resulting kinematics and the contact forces can vary significantly with regard to the selection of those parameters. This research covers the development of a validated model for a pin-slot clearance joint. Different kinematic constraints and contact models are discussed. The presented model is an experimentally validated one for a pin-slot clearance joint that is commonly used in safety-critical applications like electrical circuit breakers. Special attention is given to the Hertz, Kelvin–Voigt, Johnson, and Lankarani–Nikravesh contact models. When comparing different contact models within numerical approaches and comparing the results with experimental data, significant differences in the results were observed. With a validated model of a pin-slot clearance joint, a physically consistent numerical simulation was obtained.

Keywords

Clearance joints Multibody dynamics Contact models Measured impact forces 

Notes

Acknowledgements

The authors acknowledge the partial financial support of the Slovenian Research Agency (research core funding No. P2-0263)

References

  1. 1.
    Shabana, A.A.: Computational Dynamics, 3rd edn. Wiley (2009)Google Scholar
  2. 2.
    Nikravesh, P.E.: Planar Multibody Dynamics: Formulation, Programming and Applications. CRC Press (2007)Google Scholar
  3. 3.
    Nikravesh, P.E.: Computer-Aided Analysis of Mechanical Systems. Prentice-Hall (1988)Google Scholar
  4. 4.
    Love, A.E.H.: A Treatise on the Mathematical Theory of Elasticity. Library (1927)Google Scholar
  5. 5.
    Flores, P., Ambrosio, J., Pimenta, C.C.J., Lankarani, H.M.: Kinematics and Dynamics of Multibody Systems with Imperfect Joints, vol. 34 of Lecture Notes in Applied and Computational Mechanics. Springer, Berlin (2008)Google Scholar
  6. 6.
    Gilardi, G., Sharf, I.: Literature survey of contact dynamics modelling. Mech. Mach. Theory 37(10), 1213–1239 (2002)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Pfeiffer, F.: Multibody systems with unilateral constraints. J. Appl. Math. Mech. 65(4), 665–670 (2001)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Lankarani, H.M., Nikravesh, P.E.: A contact force model with hysteresis damping for impact analysis of multibody systems. J. Mech. Des. 112(3), 369–376 (1990)CrossRefGoogle Scholar
  9. 9.
    Pfeiffer, F.: Unilateral problems of dynamics. Arch. Appl. Mech. 69(8), 503–527 (1999)CrossRefMATHGoogle Scholar
  10. 10.
    Slavič, J., Boltežar, M.: Simulating multibody dynamics with rough contact surfaces and run-in wear. Nonlinear Dyn. 45(3–4), 353–365 (2006)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Khulief, Y.A.: Modeling of impact in multibody systems: an overview. J. Comput. nonlinear Dyn. 8(2), 021012 (2013)CrossRefGoogle Scholar
  12. 12.
    Flores, P., Ambrósio, J.: On the contact detection for contact-impact analysis in multibody systems. Multibody Syst. Dyn. 24(1), 103–122 (2010)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Pereira, C., Ambrosio, J., Ramalho, A.: Dynamics of chain drives using a generalized revolute clearance joint formulation. Mech. Mach. Theory 92, 64–85 (2015)CrossRefGoogle Scholar
  14. 14.
    Pereira, C., Ramalho, A., Ambrosio, J.: An enhanced cylindrical contact force model. Multibody Syst. Dyn. 35(3), 277–298 (2015)CrossRefMATHGoogle Scholar
  15. 15.
    Gummer, A., Sauer, B.: Modeling planar slider-crank mechanisms with clearance joints in RecurDyn. Multibody Syst. Dyn. 31, 127–145 (2012)Google Scholar
  16. 16.
    Erkaya, S., Doğan, S., Ulus, Ş.: Effects of joint clearance on the dynamics of a partly compliant mechanism: numerical and experimental studies. Mech. Mach. Theory 88, 125–140 (2015)CrossRefGoogle Scholar
  17. 17.
    Xu, L.: A general method for impact dynamic analysis of a planar multi-body system with a rolling ball bearing joint. Nonlinear Dyn. 78(2), 857–879 (2014)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Qi, Z., Wang, G., Zhang, Z.: Contact analysis of deep groove ball bearings in multibody systems. Multibody Syst. Dyn. 33, 115–141 (2015)Google Scholar
  19. 19.
    Xu, L., Yang, Y.: Modeling a non-ideal rolling ball bearing joint with localized defects in planar multibody systems. Multibody Syst. Dyn. 35, 409–426 (2015)Google Scholar
  20. 20.
    Zhuang, F., Wang, Q.: Modeling and simulation of the nonsmooth planar rigid multibody systems with frictional translational joints. Multibody Syst. Dyn. 29(4), 403–423 (2013)MathSciNetGoogle Scholar
  21. 21.
    Zhang, J., Wang, Q.: Modeling and simulation of a frictional translational joint with a flexible slider and clearance. Multibody Syst. Dyn. 38, 1–23 (2016)Google Scholar
  22. 22.
    Flores, P., Leine, R., Glocker, C.: Application of the nonsmooth dynamics approach to model and analysis of the contact-impact events in cam-follower systems. Nonlinear Dyn. 69(4), 2117–2133 (2012)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Hertz, H.: Ueber die Beruehrung fester elastischer Koerper. Journal fuer die reine und angewandte Mathematik 91, 156–171 (1881)Google Scholar
  24. 24.
    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)CrossRefGoogle Scholar
  25. 25.
    Ambrosio, J., Verissimo, P.: Improved bushing models for general multibody systems and vehicle dynamics. Multibody Syst. Dyn. 22(4), 341–365 (2009)CrossRefMATHGoogle Scholar
  26. 26.
    Lankarani, H.M.: Canonical equations of motion and estimation of parameters in the analysis of impact problems. Department of Aerospace and Mechanical Engineering (1988)Google Scholar
  27. 27.
    Barikloo, H., Ahmadi, E.: Dynamic properties of golden delicious and red delicious apple under normal contact force models. J. Texture Stud. 44(6), 409–417 (2013)CrossRefGoogle Scholar
  28. 28.
    Baglioni, S., Cianetti, F., Braccesi, C., De Micheli, D.M.: Multibody modelling of N DOF robot arm assigned to milling manufacturing. Dynamic analysis and position errors evaluation. J. Mech. Sci. Technol. 30(1), 405–420 (2016)CrossRefGoogle Scholar
  29. 29.
    Olsson, H.: Control systems with friction. Department of Automatic Control, Lund Institute of Technology, vol. 1045(October), p. 172 (1996)Google Scholar
  30. 30.
    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(1–2), 325–338 (2013)CrossRefGoogle Scholar
  31. 31.
    Muvengei, O., Kihiu, J., Ikua, B.: Dynamic analysis of planar multi-body systems with LuGre friction at differently located revolute clearance joints. Multibody Syst. Dyn. 28(4), 369–393 (2012)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Askari, E., Flores, P., Dabirrahmani, D., Appleyard, R.: Dynamic modeling and analysis of wear in spatial hard-on-hard couple hip replacements using multibody systems methodologies. Nonlinear Dyn. 82(1–2), 1039–1058 (2015)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Xiang, W., Yan, S., Wu, J.: A comprehensive method for joint wear prediction in planar mechanical systems with clearances considering complex contact conditions. Sci. China Technol. Sci. 58(1), 86–96 (2015)CrossRefGoogle Scholar
  34. 34.
    Flores, P., Ambrósio, J.: Revolute joints with clearance in multibody systems. Comput. Struct. 82(17–19), 1359–1369 (2004)CrossRefGoogle Scholar
  35. 35.
    Shabana, A.A., Tobaa, M., Sugiyama, H., Zaazaa, K.E.: On the computer formulations of the wheel/rail contact problem. Nonlinear Dyn. 40(2), 169–193 (2005)CrossRefMATHGoogle Scholar
  36. 36.
    Baumgarte, J.: Stabilization of constraints and integrals of motion in dynamical systems. Comput. Methods Appl. Mech. Eng. 1(1), 1–16 (1972)MathSciNetCrossRefMATHGoogle Scholar
  37. 37.
    Ambrósio, J.: Impact of rigid and flexible multibody systems: deformation description and contact models. In: Virtual Nonlinear Multibody Systems, vol. II, pp. 57–81. NATO, Advanced Study Institute (2003)Google Scholar
  38. 38.
    Flores, P., Machado, M., Seabra, E., Tavares da Silva, M.: A parametric study on the Baumgarte stabilization method for forward dynamics of constrained multibody systems. J. Comput. Nonlinear Dyn. 6(1), 011019 (2011)CrossRefGoogle Scholar
  39. 39.
    Burden, R.L., Faires, J.D.: Numerical Analysis, 9th edn. Brooks Cole (2011)Google Scholar
  40. 40.
    Flores, P., Ambrosio, J.: Revolute joints with clearance in multibody systems. Comput. Struct. 82(17–19), 1359–1369 (2004)CrossRefGoogle Scholar
  41. 41.
    Goldsmith, W.: Impact: The Theory and Physical Behaviour of Colliding Solids. Edward Arnold Ltd., London (1960)Google Scholar
  42. 42.
    Johnson, K.L.: Contact Mechanics. Cambridge University Press, London (1995)Google Scholar
  43. 43.
    Pereira, C.M., Ramalho, A.L., Ambrosio, J.: A critical overview of internal and external cylinder contact force models. Nonlinear Dyn. 63, 681–697 (2011)CrossRefGoogle Scholar
  44. 44.
    Ravn, P.: A continuous analysis method for planar multibody systems with joint clearance. Multibody Syst. Dyn. 2(1), 1–24 (1998)CrossRefMATHGoogle Scholar
  45. 45.
    Mukras, S., Kim, N.H., Mauntler, N.A., Schmitz, T.L., Sawyer, W.G.: Analysis of planar multibody systems with revolute joint wear. Wear 268(5–6), 643–652 (2010)CrossRefGoogle Scholar
  46. 46.
    Chunmei, J., Yang, Q., Ling, F., Ling, Z.: The non-linear dynamic behavior of an elastic linkage mechanism with clearances. J. Sound Vib. 249(2), 213–226 (2002)CrossRefGoogle Scholar
  47. 47.
    Coulomb, C.A.: Theories of simple machines. Mem. Math. Phys. Acad. Sci. 10, 161–331 (1785)Google Scholar
  48. 48.
    Kane, T.R., Levinson, D.A.: Dynamics: Theory and Applications, p. 402. McGraw-Hill Book Co., New York (1985)Google Scholar
  49. 49.
    Smith, S.W.: Digital Signal Processing, 2nd edn. California Technical Publishing, San Diego (1999)Google Scholar
  50. 50.
    Slavič, J., Boltežar, M.: Non-linearity and non-smoothness in multi-body dynamics: application to woodpecker toy. Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 220(3), 285–296 (2006)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.ETI Elektroelement d. d.IzlakeSlovenia
  2. 2.Faculty of Mechanical EngineeringUniversity of LjubljanaLjubljanaSlovenia

Personalised recommendations