Skip to main content
Log in

A continuous analysis method of planar rigid-body mechanical systems with two revolute clearance joints

  • Published:
Multibody System Dynamics Aims and scope Submit manuscript

Abstract

In this paper we are interested in the dynamic behavior of a slider-crank mechanism with single and two revolute clearance joints. Due to the clearance existence in the revolute joints, it is important to choose an appropriate contact force model in analyzing the dynamic response of a slider-crank mechanism with clearances. The dynamic equations are established by combining the Newton–Euler equations with modified contact force model and improved Coulomb friction force model, and the Baumgarte stabilization approach is used to improve the numerical stability. According to numerical and experimental results, the method of continuous contact can be verified to be reasonable. Comparing dynamic the response between one clearance joint and two clearance joints in a crank-slider mechanism, it is easy to find a significant mutual coupling region due to the presence of two clearance joints by simply contact figures. The dynamic response in a mechanism with two clearance joints is not a simple superposition of that in mechanism with one clearance joint. Therefore, all the joints in a multibody system should be modeled as clearance joints.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

References

  1. Varedi, S.M., Daniali, H.M., Dardel, M., Fathi, A.: Optimal dynamic design of a planar slider-crank mechanism with a joint clearance. Mech. Mach. Theory 86, 191–200 (2015)

    Article  Google Scholar 

  2. Funabashi, H., Ogawa, K., Horie, M.: A dynamic analysis of mechanisms with clearances. Bull. JSME 21(161), 1652–1659 (1978)

    Article  Google Scholar 

  3. Miedema, B., Mansour, W.M.: Mechanical joints with clearance: a three-mode model. J. Manuf. Sci. Eng. 98(4), 1319–1323 (1976)

    Google Scholar 

  4. Ravn, P.: A continuous analysis method for planar multibody systems with joint clearance. Multibody Syst. Dyn. 2(1), 1–24 (1998)

    Article  MATH  Google Scholar 

  5. Muvengei, O., 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)

    Article  MathSciNet  Google Scholar 

  6. Bai, Z.F., Zhao, Y.: A hybrid contact force model of revolute joint with clearance for planar mechanical systems. Int. J. Non-Linear Mech. 48, 15–36 (2013)

    Article  Google Scholar 

  7. Erkaya, S., Uzmay, İ.: Experimental investigation of joint clearance effects on the dynamics of a slider-crank mechanism. Multibody Syst. Dyn. 24(1), 81–102 (2010)

    Article  MATH  Google Scholar 

  8. Schwab, A.L., Meijaard, J.P., Meijers, P.: A comparison of revolute joint clearance models in the dynamic analysis of rigid and elastic mechanical systems. Mech. Mach. Theory 37(9), 895–913 (2002)

    Article  MATH  Google Scholar 

  9. 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 

  10. Muvengei, O., Kihiu, J., Ikua, B.: Dynamic analysis of planar rigid-body mechanical systems with two-clearance revolute joints. Nonlinear Dyn. 73(1), 259–273 (2013)

    Article  MathSciNet  Google Scholar 

  11. 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), 325–338 (2013)

    Article  Google Scholar 

  12. Machado, M., Costa, J., Seabra, E., Flores, P.: The effect of the lubricated revolute joint parameters and hydrodynamic force models on the dynamic response of planar multibody systems. Nonlinear Dyn. 69(1), 635–654 (2012)

    Article  Google Scholar 

  13. Tian, Q., Sun, Y., Liu, C., Hu, H., Flores, P.: ElastoHydroDynamic lubricated cylindrical joints for rigid-flexible multibody dynamics. Comput. Struct. 114–115, 106–120 (2013)

    Article  Google Scholar 

  14. Flores, P., Lankarani, H.: Dynamic response of multibody systems with multiple clearance joints. J. Comput. Nonlinear Dyn. 7(3), 1–13 (2012)

    Article  Google Scholar 

  15. Yaqubi, S., Dardel, M., Daniali, H.M., Ghasemi, M.H.: Modeling and control of crank-slider mechanism with multiple clearance joints. Multibody Syst. Dyn. 36(2), 143–167 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  16. Ben Abdallah, M.A., Khemili, I., Aifaoui, N.: Numerical investigation of a flexible slider-crank mechanism with multijoints with clearance. Multibody Syst. Dyn. 38(2), 173–199 (2016)

    Article  Google Scholar 

  17. Li, Y., Chen, G., Sun, D., Gao, Y., Wang, K.: Dynamic analysis and optimization design of a planar slider-crank mechanism with flexible components and two clearance joints. Mech. Mach. Theory 99, 37–57 (2016)

    Article  Google Scholar 

  18. Gilardi, G., Sharf, I.: Literature survey of contact dynamics modelling. Mech. Mach. Theory 37(10), 1213–1239 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  19. Pereira, C., Ambrósio, J., Ramalho, A.: Dynamics of chain drives using a generalized revolute clearance joint formulation. Mech. Mach. Theory 92, 64–85 (2015)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  21. Marques, F., Flores, P., Lankarani, H.M.: On the frictional contacts in multibody system dynamics (2015)

  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. Megahed, S.M., Haroun, A.F.: Analysis of the Dynamic Behavioral Performance of Mechanical Systems With Multi-Clearance Joints. J. Comput. Nonlin. Dyn. 7(1), 1–11 (2012)

    Article  Google Scholar 

  24. Gummer, A., Sauer, B.: Modeling planar slider-crank mechanisms with clearance joints in RecurDyn. Multibody Syst. Dyn. 31(2), 127–145 (2014)

    Article  Google Scholar 

  25. Brach, R.M.: Mechanical Impact Dynamics: Rigid Body Collisions. John Wiley and Sons, New York (1991)

    Google Scholar 

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

    Book  MATH  Google Scholar 

  27. Hunt, K.H., Crossley, F.R.E.: Coefficient of restitution interpreted as damping in vibroimpact. J. Appl. Mech. 42(2), 440–445 (1975)

    Article  Google Scholar 

  28. 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)

    Article  Google Scholar 

  29. Hu, S., Guo, X.: A dissipative contact force model for impact analysis in multibody dynamics. Multibody Syst. Dyn. 35(2), 131–151 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  30. Ye, K., Li, L., Zhu, H.: A note on the Hertz contact model with nonlinear damping for pounding simulation. Earthq. Eng. Struct. Dyn. 38(9), 1135–1142 (2009)

    Article  Google Scholar 

  31. 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(3), 357–375 (2011)

    Article  MATH  Google Scholar 

  32. Marques, F., Flores, P., Pimenta Claro, J.C., Lankarani, H.M.: A survey and comparison of several friction force models for dynamic analysis of multibody mechanical systems. Nonlinear Dyn. 86(3), 1407–1443 (2016)

    Article  MathSciNet  Google Scholar 

  33. Tian, Q., Xiao, Q., Sun, Y., Hu, H., Liu, H., Flores, P.: Coupling dynamics of a geared multibody system supported by ElastoHydroDynamic lubricated cylindrical joints. Multibody Syst. Dyn. 33(3), 259–284 (2015)

    Article  MathSciNet  Google Scholar 

  34. Erkaya, S., Uzmay, İ.: Optimization of transmission angle for slider-crank mechanism with joint clearances. Struct. Multidiscip. Optim. 37(5), 493–508 (2008)

    Article  Google Scholar 

  35. Zhang, Z., Xu, L., Flores, P., Lankarani, H.M.: A kriging model for dynamics of mechanical systems with revolute joint clearances. J. Comput. Nonlinear Dyn. 9(3), 31013 (2014)

    Article  Google Scholar 

  36. Zhang, J., Du, X.: Time-dependent reliability analysis for function generation mechanisms with random joint clearances. Mech. Mach. Theory 92, 184–199 (2015)

    Article  Google Scholar 

  37. Rahmanian, S., Ghazavi, M.R.: Bifurcation in planar slider-crank mechanism with revolute clearance joint. Mech. Mach. Theory 91, 86–101 (2015)

    Article  Google Scholar 

  38. Flores, P., Ambrosio, J.: Revolute joints with clearance in multibody systems. Comput. Struct. 82(17–19), 1359–1369 (2004)

    Article  Google Scholar 

  39. Flores, P., Ambrósio, J., Claro, J.P.: Dynamic analysis for planar multibody mechanical systems with lubricated joints. Multibody Syst. Dyn. 12(1), 47–74 (2004)

    Article  MATH  Google Scholar 

  40. Brach, R.M., Goldsmith, W.: Mechanical impact dynamics: rigid body collisions. J. Eng. Ind. 113 (2) (1991)

  41. W., G.: Impact: The Theory and Physical Behaviour of Colliding Solids. University Microfilms (1978)

  42. 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(0), 99–121 (2012)

    Article  Google Scholar 

  43. Alves, J., Peixinho, N., Da Silva, M.T., Flores, P., Lankarani, H.M.: A comparative study of the viscoelastic constitutive models for frictionless contact interfaces in solids. Mech. Mach. Theory 85, 172–188 (2015)

    Article  Google Scholar 

  44. Bagci, C.: Dynamic motion analysis of plane mechanisms with Coulomb and viscous damping via the joint force analysis. J. Eng. Ind. 97(2), 551–560 (1975)

    Article  Google Scholar 

  45. Ambrósio, J.A.C.: Impact of rigid and flexible multibody systems: deformation description and contact models. In: Schiehlen, W., Valášek, M. (eds.) Virtual Nonlinear Multibody Systems, vol. 103. 57–81. Springer, Netherlands (2003)

    Chapter  Google Scholar 

  46. Nikravesh, P.E.: Computer-Aided Analysis of Mechanical Systems. Prentice Hall, Englewood Cliffs (1988)

    Google Scholar 

  47. Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M.: Spatial revolute joints with clearances for dynamic analysis of multi-body systems. Proc. Inst. Mech. Eng., Proc., Part K, J. Multi-Body Dyn. 220(4), 257–271 (2006)

    Google Scholar 

  48. Gear, C.W.: Numerical solution of differential-algebraic equations. IEEE Trans. Circuit Theory CT-18, 89–95 (1982)

    Google Scholar 

  49. Baumgarte, J.: Stabilization of constraints and integrals of motion in dynamical systems. Comput. Methods Appl. Math. 1(1), 1–16 (1972)

    MathSciNet  MATH  Google Scholar 

  50. Neto, M., Ambrósio, J.: Stabilization methods for the integration of DAE in the presence of redundant constraints. Multibody Syst. Dyn. 10(1), 81–105 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  51. Kim, J.K., Chung, I.S., Lee, B.H.: Determination of the feedback coefficients for the constraint violation stabilization method. Proc. Inst. Mech. Eng., Part C, J. Mech. Eng. Sci. 204(4), 233–242 (1990)

    Article  Google Scholar 

  52. Wilson, R., Fawcett, J.N.: Dynamics of the slider-crank mechanism with clearance in the sliding bearing. Mech. Mach. Theory 9(1), 61–80 (1974)

    Article  Google Scholar 

  53. Soong, K.: An Analytical and Experimental Study of the Elastodynamic Response Characteristics of Planar Linkage Mechanism with Bearing Clearances. Michigan State University, Flint, Michigan (1998)

    Google Scholar 

  54. Haroun, A.F., Megahed, S.M.: Simulation and experimentation of multibody mechanical systems with clearance revolute joints. Int. J. Mech. Aerosp. Eng. 6, 367–376 (2012)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yujin Hu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tan, H., Hu, Y. & Li, L. A continuous analysis method of planar rigid-body mechanical systems with two revolute clearance joints. Multibody Syst Dyn 40, 347–373 (2017). https://doi.org/10.1007/s11044-016-9562-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11044-016-9562-3

Keywords

Navigation