Skip to main content
Log in

An approach for modelling a clearance revolute joint with a constantly updating wear profile in a multibody system: simulation and experiment

  • Published:
Multibody System Dynamics Aims and scope Submit manuscript

Abstract

An approach for modelling a clearance revolute joint with a constantly updating wear profile in a multibody system is proposed. Before the contact analysis, the continuous geometric shape of the joint bushing is dispersed to obtain a series of uniformly distributed points of a certain density. By analysing the relative positions between the discrete points and geometric centre of the joint pin, the contact area between the bushing and pin can be estimated and the maximum contact depth can be obtained. Then, the normal contact force and the tangential friction force acting on the point of force application are calculated: after an analysis of the contact force, the wear depth on the contact discrete points is calculated based on Archard’s wear model. The location of the contact discrete point is updated to reconstruct the geometric shape of joint bushing. Finally, taking a planar slider–crank mechanism as an example, the wear characteristics and dynamic response of a revolute joint with clearance are studied by numerical simulation and experimental testing. The results verified that the extent of wear on the joint bushing profile is nonuniform, which is related to the kinetic characteristics of the mechanism. Due to wear, the joint clearance is increased, which further affects the dynamic performance of the mechanism.

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.

Institutional subscriptions

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

Similar content being viewed by others

References

  1. Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M.: Dynamic behavior of planar rigid multi-body systems including revolute joints with clearance. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 221(2), 161–174 (2007)

    Article  Google Scholar 

  2. 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 

  3. 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)

    Article  Google Scholar 

  4. Erkaya, S.: Clearance-induced vibration responses of mechanical systems: computational and experimental investigations. J. Braz. Soc. Mech. Sci. Eng. 40(2), 90 (2018)

    Article  Google Scholar 

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

    Article  Google Scholar 

  6. Erkaya, S., Doğan, S.: A comparative analysis of joint clearance effects on articulated and partly compliant mechanisms. Nonlinear Dyn. 81(1–2), 323–341 (2015)

    Article  Google Scholar 

  7. 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 

  8. 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 

  9. 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 

  10. Megahed, S.M., Haroun, A.F.: Analysis of the dynamic behavioral performance of mechanical systems with multi-clearance joints. J. Comput. Nonlinear Dyn. 7(1), 011002 (2012)

    Article  Google Scholar 

  11. Muvengei, O., Kihiu, J., Ikua, B.: Dynamic analysis of planar rigid-body mechanical systems with two-clearance revolute joints. Nonlinear Dyn. 73(1–2), 259–273 (2013)

    Article  MathSciNet  Google Scholar 

  12. 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), 031013 (2014)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  14. Xu, L.X., Li, Y.G.: Investigation of joint clearance effects on the dynamic performance of a planar 2-DOF pick-and-place parallel manipulator. Robot. Comput.-Integr. Manuf. 30(1), 62–73 (2014)

    Article  MathSciNet  Google Scholar 

  15. 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 

  16. Flores, P., Leine, R., Glocker, C.: Modeling and analysis of planar rigid multibody systems with translational clearance joints based on the non-smooth dynamics approach. Multibody Syst. Dyn. 23(2), 165–190 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  17. Qi, Z., Luo, X., Huang, Z.: Frictional contact analysis of spatial prismatic joints in multibody systems. Multibody Syst. Dyn. 26(4), 441–468 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  18. Erkaya, S., Doğan, S., Şefkatlıoğlu, E.: Analysis of the joint clearance effects on a compliant spatial mechanism. Mech. Mach. Theory 104, 255–273 (2016)

    Article  Google Scholar 

  19. Geng-xiang, W., Hong-zhao, L.I.U., Pei-sheng, D.: Dynamic modeling for a parallel mechanism considering spherical joint clearance. J. Vib. Shock 10, 009 (2014)

    Google Scholar 

  20. Flores, P., Lankarani, H.M.: Spatial rigid-multibody systems with lubricated spherical clearance joints: modeling and simulation. Nonlinear Dyn. 60(1), 99–114 (2010)

    Article  MATH  Google Scholar 

  21. Tian, Q., Sun, Y., Liu, C., et al.: Elastohydrodynamic lubricated cylindrical joints for rigid-flexible multibody dynamics. Comput. Struct. 114, 106–120 (2013)

    Article  Google Scholar 

  22. Erkaya, S.: Experimental investigation of flexible connection and clearance joint effects on the vibration responses of mechanisms. Mech. Mach. Theory 121, 515–529 (2018)

    Article  Google Scholar 

  23. Flores, P., Ambrósio, J., Claro, J.C.P., et al.: Influence of the contact-impact force model on the dynamic response of multi-body systems. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 220(1), 21–34 (2006)

    Google Scholar 

  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)

    Article  Google Scholar 

  25. 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)

    Article  Google Scholar 

  26. Pereira, C., Ramalho, A., Ambrosio, J.: Applicability domain of internal cylindrical contact force models. Mech. Mach. Theory 78, 141–157 (2014)

    Article  Google Scholar 

  27. 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 

  28. 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(1), 190–205 (2012)

    Article  Google Scholar 

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

    Article  Google Scholar 

  30. 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 

  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)

    Article  MathSciNet  Google Scholar 

  32. Qi, Z., Xu, Y., Luo, X., et al.: Recursive formulations for multibody systems with frictional joints based on the interaction between bodies. Multibody Syst. Dyn. 24(2), 133–166 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  33. Frączek, J., Wojtyra, M.: On the unique solvability of a direct dynamics problem for mechanisms with redundant constraints and Coulomb friction in joints. Mech. Mach. Theory 46(3), 312–334 (2011)

    Article  MATH  Google Scholar 

  34. Gummer, A., Sauer, B.: Influence of contact geometry on local friction energy and stiffness of revolute joints. J. Tribol. 134(2), 021402 (2012)

    Article  Google Scholar 

  35. Ambrósio, J.A.C.: Impact of rigid and flexible multibody systems: deformation description and contact models. In: Virtual Nonlinear Multibody Systems. NATO ASI Series, vol. 103, pp. 57–81. Springer, Netherlands (2003)

    Chapter  MATH  Google Scholar 

  36. Daniel, G.B., Cavalca, K.L.: Analysis of the dynamics of a slider–crank mechanism with hydrodynamic lubrication in the connecting rod–slider joint clearance. Mech. Mach. Theory 46(10), 1434–1452 (2011)

    Article  MATH  Google Scholar 

  37. Tian, Q., Liu, C., Machado, M., et al.: A new model for dry and lubricated cylindrical joints with clearance in spatial flexible multibody systems. Nonlinear Dyn. 64(1), 25–47 (2011)

    Article  MATH  Google Scholar 

  38. Machado, M., Costa, J., Seabra, E., et al.: 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 

  39. Zhao, B., Zhang, Z.N., Fang, C.C., et al.: Modeling and analysis of planar multibody system with mixed lubricated revolute joint. Tribol. Int. 98, 229–241 (2016)

    Article  Google Scholar 

  40. Zhao, B., Dai, X.D., Zhang, Z.N., et al.: A new numerical method for piston dynamics and lubrication analysis. Tribol. Int. 94, 395–408 (2016)

    Article  Google Scholar 

  41. Mukras, S., Kim, N.H., Sawyer, W.G., et al.: Numerical integration schemes and parallel computation for wear prediction using finite element method. Wear 266(7–8), 822–831 (2009)

    Article  Google Scholar 

  42. Mukras, S., Kim, N.H., Mauntler, N.A., et al.: Analysis of planar multibody systems with revolute joint wear. Wear 268(5), 643–652 (2010)

    Article  Google Scholar 

  43. Mukras, S., Kim, N.H., Mauntler, N.A., et al.: Comparison between elastic foundation and contact force models in wear analysis of planar multibody system. J. Tribol. 132(3), 031604 (2010)

    Article  Google Scholar 

  44. Li, P., Chen, W., Li, D., et al.: Wear analysis of two revolute joints with clearance in multibody systems. J. Comput. Nonlinear Dyn. 11(1), 011009 (2015)

    Article  MathSciNet  Google Scholar 

  45. Sun, D., Chen, G., Wang, T., et al.: Wear prediction of a mechanism with joint clearance involving aleatory and epistemic uncertainty. J. Tribol. 136(4), 216–223 (2014)

    Article  Google Scholar 

  46. Bai, Z.F., Zhao, Y., Chen, J.: Dynamics analysis of planar mechanical system considering revolute clearance joint wear. Tribol. Int. 64(3), 85–95 (2013)

    Article  Google Scholar 

  47. Bai, Z.F., Yang, Z., Wang, X.G.: Wear analysis of revolute joints with clearance in multibody systems. Sci. China, Phys. Mech. Astron. 56(8), 1581–1590 (2013)

    Article  Google Scholar 

  48. Su, Y., Chen, W., Tong, Y., et al.: Wear prediction of clearance joint by integrating multi-body kinematics with finite-element method. Proc. Inst. Mech. Eng., Part J J. Eng. Tribol. 224(8), 815–823 (2010)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  50. Zhao, B., Zhang, Z.N., Dai, X.D.: Modeling and prediction of wear at revolute clearance joints in flexible multibody systems. Proc. Inst. Mech. Eng., Part C, J. Mech. Eng. Sci. 228(2), 317–329 (2014)

    Article  Google Scholar 

  51. Wang, G., Liu, H., Deng, P.: Dynamics analysis of spatial multibody system with spherical joint wear. J. Tribol. 137(2), 021605 (2015)

    Article  Google Scholar 

  52. Wang, G., Liu, H.: Dynamic analysis and wear prediction of planar five-bar mechanism considering multi-flexible links and multi-clearance joints. J. Tribol. 139(5), 051606 (2017)

    Article  Google Scholar 

  53. Wang, G., Liu, H.: Three-dimensional wear prediction of four-degrees-of-freedom parallel mechanism with clearance spherical joint and flexible moving platform. J. Tribol. 140(3), 031611 (2018)

    Article  Google Scholar 

  54. Zhu, A., He, S., Zhao, J., et al.: A nonlinear contact pressure distribution model for wear calculation of planar revolute joint with clearance. Nonlinear Dyn. 88(1), 315–328 (2017)

    Article  Google Scholar 

  55. Archard, J.F.: Contact and rubbing of flat surfaces. J. Appl. Phys. 24(8), 981–988 (1953)

    Article  Google Scholar 

  56. Xu, L.X., Han, Y.C.: A method for contact analysis of revolute joints with noncircular clearance in a planar multibody system. Proc. Inst. Mech. Eng., Proc., Part K, J. Multi-Body Dyn. 230(4), 589–605 (2016)

    Google Scholar 

  57. Schmitz, T.L., Action, J.E., Burris, D.L., et al.: Wear-rate uncertainty analysis. J. Tribol. 126(4), 802–808 (2004)

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to express the sincere thanks to the referees for their valuable suggestions. This project is supported by National Natural Science Foundation of China (Grant No. 51505336) and the Fundamental Research Funds for the Central Universities (Grant No. 2018CDXYJX0019). These supports are gracefully acknowledged.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Li Xin Xu.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xu, L.X., Han, Y.C., Dong, Q.B. et al. An approach for modelling a clearance revolute joint with a constantly updating wear profile in a multibody system: simulation and experiment. Multibody Syst Dyn 45, 457–478 (2019). https://doi.org/10.1007/s11044-018-09655-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11044-018-09655-z

Keywords

Navigation