Advertisement

Nonlinear Dynamics

, Volume 98, Issue 3, pp 1999–2018 | Cite as

Frictional impact analysis of an elastoplastic multi-link robotic system using a multi-timescale modelling approach

  • Yunian ShenEmail author
  • Ye Kuang
  • Wei Wang
  • Yuhang Zhao
  • Jiongcan Yang
  • Ali Tian
Original paper
  • 54 Downloads

Abstract

Considering tangential contact compliance, material nonlinearity and contact nonlinearity, an efficient multi-timescale computational approach (MCA) is presented to analyse the contact forces and transient wave propagation generated by the frictional impact of an elastoplastic multi-link robotic system. In the formulation of the MCA, a rigid multibody dynamic equation is derived to calculate the large overall motion without a unilateral contact constraint (large timescale) and the nonlinear finite element dynamic equation, including the penalty function algorithm, is given to calculate the contact force and stress wave propagation (small timescale). An experimental test for a manipulator’s oblique impact against a rough moving plate is also introduced. The accuracy, convergence and efficiency of the MCA are validated by a comparison with the pure finite element method (FEM) solution and experimental data. The error between the MCA and pure FEM solutions for the first peak value of the normal contact force \(F_{\mathrm{n}}\) is less than 1.5%. The total time cost of the MCA is only 0.705% of the pure FEM. The numerical results also show that the presented MCA can effectively depict the transmission and reflection of the impact-induced waves at the middle hinge. In addition, the influences of the structural compliance, the velocity of plate \(v_{\mathrm{plate}}\) and the coefficient of friction \(\mu \) on the transient responses are investigated. The peak value of \(F_{\mathrm{n}}\) will increase as \(v_{\mathrm{plate}}\) increases, which has a strong relationship with the so-called dynamic self-locking phenomenon. Due to the large structural compliance of the rod, the “succession collisions” phenomenon (i.e. multiple contacts in a very short time) can be captured during an oblique impact event, and the normal relative motion at the local contact zone may experience two transitions between compression and restitution during a single contact process. The tangential stick-slip motion occurs as a reverse phenomenon. All investigations show that the MCA has sufficient accuracy to analyse the frictional impact of flexible robotic manipulators.

Keywords

Frictional impact Stick-slip Wave propagation Elastic–plastic Transient responses 

Notes

Acknowledgements

The authors would like to thank the Robotics and Intelligent Machine Lab, NUST. This work was supported by the National Natural Science Foundation of China (Grant No. 11572157). This support is gratefully acknowledged.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest concerning the publication of this manuscript.

References

  1. 1.
    Stronge, W.J.: Impact Mechanics. Cambridge University Press, Cambridge (2000)CrossRefGoogle Scholar
  2. 2.
    Goldsmith, W.: Impact: The Theory and Physical Behaviour of Colliding Solids. Edward Arnold Ltd, London (1960)zbMATHGoogle Scholar
  3. 3.
    Gilardi, G., Sharf, I.: Literature survey of contact dynamics modeling. Mech. Mach. Theory 37, 1213–1239 (2002)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Popov, V.L.: Contact Mechanics and Friction: Physical Principles and Applications. Berlin University of Technology, Berlin (2010)CrossRefGoogle Scholar
  5. 5.
    Han, I., Lee, Y.: Chaotic dynamics of repeated impacts in vibratory bowl feeders. J. Sound Vib. 249, 529–541 (2002)CrossRefGoogle Scholar
  6. 6.
    Würsig, B., Greene, C.R., Jefferson, T.A.: Development of an air bubble curtain to reduce underwater noise of percussive piling. Mar Environ. Res. 49, 79–93 (2000)CrossRefGoogle Scholar
  7. 7.
    Cheng, J., Xu, H.: Inner mass impact damper for attenuating structure vibration. Int. J. Solids Struct. 43, 5355–5369 (2006)CrossRefGoogle Scholar
  8. 8.
    Parker, R.G., Vijayokar, S.M., Imajo, T.: Non-linear dynamic response of a spur gear pair: modeling and experimental comparison. J. Sound Vib. 237, 435–455 (2000)CrossRefGoogle Scholar
  9. 9.
    Messaadi, M., Kermouche, G., Kapsa, P.: Numerical and experimental analysis of dynamic oblique impact: effect of impact angle. Wear 332–333, 1028–1034 (2015)CrossRefGoogle Scholar
  10. 10.
    Shen, Y., Yin, X.: Dynamic substructure analysis of stress waves generated by impacts on non-uniform rod structures. Mech. Mach. Theory 74(6), 154–172 (2014)CrossRefGoogle Scholar
  11. 11.
    Lanouette, A.M., Potvin, M.J., Martin, F., Houle, D., Therriault, D.: Residual mechanical properties of a carbon fibers/PEEK space robotic arm after simulated orbital debris impact. Int. J. Impact Eng. 84, 78–87 (2015)CrossRefGoogle Scholar
  12. 12.
    Hayne, P.O., Greenhagen, B.T., Foote, M.C., et al.: Diviner lunar radiometer observations of the LCROSS impact. Science 330, 477–479 (2010)CrossRefGoogle Scholar
  13. 13.
    Stolfia, A., Gasbarria, P., Sabatini, M.: A parametric analysis of a controlled deployable space manipulator for capturing a non-cooperative flexible satellite. Acta Astronaut. 148, 317–326 (2018)CrossRefGoogle Scholar
  14. 14.
    Flores-Abad, A., Ma, O., Pham, K., Ulrich, S.: A review of space robotics technologies for on-orbit servicing. Prog. Aerosp. Sci. 68, 1–26 (2014)CrossRefGoogle Scholar
  15. 15.
    Chapnik, B.V., Heppler, G.R., Aplevich, J.D.: Modeling impact on a one-link flexible robotic arm. IEEE Tran. Rob. Autom. 7(4), 551–561 (1991)CrossRefGoogle Scholar
  16. 16.
    Sato, A., Sato, O., Takahashi, N., Yokomichi, M.: Analysis of manipulator in consideration of impact absorption between link and projected object. Artif. Life Rob. 22, 113–117 (2017)CrossRefGoogle Scholar
  17. 17.
    Marghitu, D.B., Cojocaru, D.: Simultaneous Impact of a Two-Link Chain. Nonlinear Dyn. 77, 17–29 (2014)CrossRefGoogle Scholar
  18. 18.
    Shafei, A.M., Shafei, H.R.: Dynamic modeling of planar closed-chain robotic manipulators in flight and impact phases. Mech. Mach. Theory 126, 141–154 (2018)CrossRefGoogle Scholar
  19. 19.
    Korayem, M.H., Shafei, A.M.: A new approach for dynamic modeling of n-viscoelastic-link robotic manipulators mounted on a mobile base. Nonlinear Dyn. 79(4), 2767–2786 (2015)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Eberhart, P., Hu, B.: Advanced Contact Dynamics. Southeast University Press, Nanjing (2003)Google Scholar
  21. 21.
    Shen, Y., Stronge, W.J.: Painlevé paradox during oblique impact with friction. Eur. J. Mech. A Solid 30(4), 457–467 (2011)CrossRefGoogle Scholar
  22. 22.
    Johnson, K.L.: The bounce of ‘super ball’. Int. J. Mech. Eng. 111, 57–63 (1983)Google Scholar
  23. 23.
    Shen, Y., Gu, J.: Research on rigid body-spring-particle hybrid model for flexible beam under oblique impact with friction. J. Vib. Eng. 29(1), 1–7 (2016)Google Scholar
  24. 24.
    Matunaga, S., Koyama, J., Ohkami, Y.: Impact analysis of linked manipulator systems using wave propagation theory. In: 1998 IEEE/RSJ International Conference on Intelligent Robots and Systems, Canada, pp. 624–629 (1998)Google Scholar
  25. 25.
    Shen, Y., Yin, X.: Analysis of geometric dispersion effect of impact-induced transient waves in composite rods using dynamic substructure method. Appl. Math. Model. 40(3), 1972–1988 (2016)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Timoshenko, S.P., Goodier, J.N.: Theory of Elasticity. McGraw Hill, New York (1970)zbMATHGoogle Scholar
  27. 27.
    Yin, X., Qin, Y., Zou, H.: Transient responses of repeated impact of a beam against a stop. Int. J. Solids Struct. 44, 7323–7339 (2007)CrossRefGoogle Scholar
  28. 28.
    Hu, B., Eberhard, P., Schiehlen, W.: Symbolical impact analysis for a falling conical rod against the rigid ground. J. Sound Vib. 240(1), 41–57 (2001)CrossRefGoogle Scholar
  29. 29.
    Shi, P.: Simulation of impact involving an elastic rod. Comput. Methods Appl. Mech. Eng. 151, 497–499 (1998)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Yang, K.: A unified solution for longitudinal wave propagation in an elastic rod. J. Sound Vib. 314, 307–329 (2008)CrossRefGoogle Scholar
  31. 31.
    Zhang, L., Yin, X., Yang, J., Wang, H.: Transient impact response analysis of an elastic-plastic beam. Appl. Math. Model. 55, 616–636 (2018)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Schiehlen, W., Seifried, R., Eberhard, P.: Elastoplastic phenomena in multibody impact dynamics. Comput. Method Appl. M. 195(50–51), 6874–6890 (2006)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Zhang, X., Huang, Y., Han, W., et al.: Accurate shape description of flexible beam undergoing oblique impact based on space probe-cone docking mechanism. Adv. Space Res. 52(6), 1018–1028 (2013)CrossRefGoogle Scholar
  34. 34.
    Dong, X., Yin, X., Deng, Q., et al.: Local contact behavior between elastic and elastic-plastic bodies. Int. J Solids Struct. 150, 22–39 (2018)CrossRefGoogle Scholar
  35. 35.
    Shen, Y.: Painlevé paradox and dynamic jam of a three-dimensional elastic rod. Arch. Appl. Mech. 85, 805–816 (2015)CrossRefGoogle Scholar
  36. 36.
    Hallquist, J.O.: LS-DYNA Theory Manual. Livermore Software Technology Corporation, California (2006)Google Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Yunian Shen
    • 1
    Email author
  • Ye Kuang
    • 1
  • Wei Wang
    • 1
  • Yuhang Zhao
    • 1
  • Jiongcan Yang
    • 1
  • Ali Tian
    • 2
  1. 1.Department of Mechanics and Engineering Science, School of ScienceNanjing University of Science and TechnologyNanjingChina
  2. 2.School of Naval Architecture and Ocean EngineeringJiangsu University of Science and TechnologyZhenjiangChina

Personalised recommendations