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Recursive formulations for multibody systems with frictional joints based on the interaction between bodies

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Abstract

In practice, the clearances of joints in a great number of mechanical systems are well under control. In these cases, some of the existing methods become unpractical because of the little differences in the order of magnitude between relative movements and computational errors. Assuming that the effects of impacts are negligible, we proved that both locations and forces of contacts in joints can be fully determined by parts of joint reaction forces. Based on this fact, a method particularly suited for multibody systems possessing frictional joints with tiny clearances is presented. In order to improve the efficiency of computation, recursive formulations are proposed based on the interactions between bodies. The proposed recursive formulations can improve the computation of joint reaction forces. With the methodology presented in this paper, not only the motion of bodies in a multibody system but also the details about the contacts in joints, such as forces of contacts and locations of contact points, can be obtained. Even with the assumption of impact free, the instants of possible impacts can be detected without relying upon any ambiguous parameters, as indicated by numerical examples in this paper.

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References

  1. Flores, P., Ambrósio, J., Claro Pimenta, J., Lankarani, H.: Kinematics and Dynamics of Multibody Systems with Imperfect Joints: Models and Case Studies. Springer, Dordrecht (2008)

    MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  3. Glocker, C., Pfeiffer, F.: Dynamical systems with unilateral contacts. Nonlinear Dyn. 3(4), 245–259 (1992)

    Article  MathSciNet  Google Scholar 

  4. Glocker, C., Pfeiffer, F.: Multiple impacts with friction in rigid multibody systems. Nonlinear Dyn. 7(4), 471–497 (1995)

    Article  MathSciNet  Google Scholar 

  5. Glocker, C., Pfeiffer, F.: Complementarity problems in multibody systems with planar friction. Arch. Appl. Mech. 63(7), 452–463 (1993)

    MATH  Google Scholar 

  6. Glocker, C., Studer, C.: Formulation and preparation for numerical evaluation of linear complementarity systems in dynamics. Multibody Syst. Dyn. 13(4), 447–463 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  7. Leine, R.I., van Campen, D.H., Glocker, C.: Nonlinear dynamics and modeling of various wooden toys with impact and friction. J. Vib. Control 9(1–2), 25–78 (2003)

    MATH  MathSciNet  Google Scholar 

  8. Glocker, C.: Concepts for modeling impacts without friction. Acta Mech. 168(1–2), 1–19 (2004)

    Article  MATH  Google Scholar 

  9. Djerassi, S.: Collision with friction; Part A: Newton’s hypothesis. Multibody Syst. Dyn. 21(1), 37–54 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  10. Djerassi, S.: Collision with friction; Part B: Poisson’s and Stornge’s hypotheses. Multibody Syst. Dyn. 21(1), 55–70 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  11. Najafabadi, S.A.M., Kövecses, J., Angeles, J.: Impacts in multibody systems: modeling and experiments. Multibody Syst. Dyn. 20(2), 163–176 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  12. Schiehlen, W., Seifried, R.: Three approaches for elastodynamic contact in multibody systems. Multibody Syst. Dyn. 12(1), 1–16 (2004)

    Article  MATH  Google Scholar 

  13. Pang, J., Trinkle, J.C.: Complementarity formulations and existence of solutions of dynamic multi-rigid-body contact problems with Coulomb friction. Math. Program. 73(2), 199–226 (1996)

    Article  MathSciNet  Google Scholar 

  14. Trinkle, J.C., Tzitzoutis, J., Pang, J.S.: Dynamic multi-rigid-body systems with concurrent distributed contacts: theory and examples. Philos. Trans. Math. Phys. Eng. Sci. Ser. A 359(1789), 2575–2593 (2001)

    Article  MATH  Google Scholar 

  15. Pfeiffer, F., Foerg, M., Ulbrich, H.: Numerical aspects of non-smooth multibody dynamics. Comput. Methods Appl. Mech. Eng. 195(50–51), 6891–6908 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  16. Förg, M., Pfeiffer, F., Ulbrich, H.: Simulation of unilateral constrained systems with many bodies. Multibody Syst. Dyn. 14(2), 137–154 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  17. Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M., Koshy, C.S.: A study on dynamics of mechanical systems including joints with clearance and lubrication. Mech. Mach. Theory 41(3), 247–261 (2006)

    Article  MATH  Google Scholar 

  18. Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M.: Influence of the contact-impact force model on the dynamic response of multibody systems. Proc. Inst. Mech. Eng., Part-K J. Multi-body Dyn. 220(1), 21–34 (2006)

    Google Scholar 

  19. Gonthier, Y., McPhee, J., Lange, C., Piedboeuf, J.C.: A regularized contact model with asymmetric damping and dwell-time dependent friction. Multibody Syst. Dyn. 11(3), 209–233 (2004)

    Article  MATH  Google Scholar 

  20. Bing, S., Ye, J.: Dynamic analysis of the reheat-stop-valve mechanism with revolute clearance joint in consideration of thermal effect. Mech. Mach. Theory 43(12), 1625–1638 (2008)

    Article  MATH  Google Scholar 

  21. Srivastava, N., Haque, I.: Clearance and friction-induced dynamics of chain CVT drives. Multibody Syst. Dyn. 19(3), 255–280 (2008)

    Article  MATH  Google Scholar 

  22. Orden, J.C.G.: Analysis of joint clearances in multibody systems. Multibody Syst. Dyn. 13(4), 401–420 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  23. Liu, C.S., Zhang, K., Yang, L.: Normal force-displacement relationship of spherical joints with clearances. J. Comput. Nonlinear Dyn. 1(2), 160–167 (2006)

    Article  Google Scholar 

  24. Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M.: Translational joints with clearance in rigid multibody systems. J. Comput. Nonlinear Dyn. 3(1), 0110071-10 (2008)

    Google Scholar 

  25. Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M.: Dynamics of multibody systems with spherical clearance joints. J. Comput. Nonlinear Dyn. 1(3), 240–247 (2006)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  28. Inna, S., Yuning, Z.: A contact force solution for non-colliding contact dynamics simulation. Multibody Syst. Dyn. 16(3), 263–290 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  29. Paul, B.: Kinematics and Dynamics of Planar Machinery. Prentice-Hall, Englewood Cliffs (1979)

    Google Scholar 

  30. Hall, A.S.: Notes on Mechanism Analysis. Waveland Press Inc., Long Grove (1986)

    Google Scholar 

  31. Haug, E.J., Wu, S.C., Yang, S.M.: Dynamics of mechanical systems with Coulomb friction stiction, impact and constraint addition-deletion—I and II. Mech. Mach. Theory 21(5), 401–425 (1986)

    Article  Google Scholar 

  32. Bae, D.S., Haug, E.J.: A recursive formulation for constrained mechanical system dynamics. I. Open loop systems. Mech. Struct. Mach. 15(3), 359–382 (1987)

    Article  Google Scholar 

  33. Bae, D.S, Haug, E.J.: A recursive formulation for constrained mechanical system dynamics: Part II. Closed loop systems. Mech. Des. Struct. Mach. 15(4), 481–506 (1987)

    Article  Google Scholar 

  34. Kim, S.S., Haug, E.J.: A recursive formulation for flexible multibody dynamics. I. Open loop systems. Comput. Methods Appl. Mech. Eng. 71(3), 293–314 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  35. Kim, S.S., Haug, E.J.: A recursive formulation for flexible multibody dynamics. II. Closed-loop systems. Comput. Methods Appl. Mech. Eng. 74(3), 251–269 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  36. Hwang, Y.L.: Dynamic recursive decoupling method for closed-loop flexible mechanical systems. Int. J. Non-Linear Mech. 41(10), 1181–1190 (2006)

    Article  Google Scholar 

  37. Featherstone, R.: The calculation of robot dynamics using articulated-body inertias. Int. J. Robot. Res. 2(1), 13–30 (1983)

    Article  Google Scholar 

  38. Wittenburg, J.: Dynamics of Multibody Systems: Dynamics of Systems of Rigid Bodies. Springer, Berlin (2007)

    Google Scholar 

  39. Featherstone, R.: Robot Dynamics Algorithms. Kluwer Academic, Dordrecht (1987)

    Google Scholar 

  40. Leine, R.I., Glocker, Ch.: A set-valued force law for spatial Coulomb–Contensou friction. Eur. J. Mech.-A/Solids 22(2), 193–216 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  41. Leine, R.I., van de Wouw, N.: Stability properties of equilibrium sets of non-linear mechanical systems with dry friction and impact. Nonlinear Dyn. 51(4), 551–583 (2008)

    Article  MATH  Google Scholar 

  42. Pennestri, E., Valentini, P.P., Vita, L.: Multibody dynamics simulation of planar linkages with Dahl friction. Multibody Syst. Dyn. 17(4), 321–347 (2007)

    Article  MathSciNet  Google Scholar 

  43. Rooney, G.T., Deravi, P.: Coulomb friction in mechanism sliding joints. Mech. Mach. Theory 17(3), 207–211 (1982)

    Article  Google Scholar 

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, 116024, Dalian, China

    Zhaohui Qi, Yongsheng Xu & Xiaoming Luo

  2. Department of Mechanical Engineering, University of New Brunswick, NB, E3B 5A3, Fredericton, Canada

    Shengji Yao

Authors
  1. Zhaohui Qi
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  2. Yongsheng Xu
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  3. Xiaoming Luo
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  4. Shengji Yao
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Correspondence to Zhaohui Qi.

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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, 133–166 (2010). https://doi.org/10.1007/s11044-010-9213-z

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  • DOI: https://doi.org/10.1007/s11044-010-9213-z

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