Skip to main content
SpringerLink
Log in

Modeling and simulation of the nonsmooth planar rigid multibody systems with frictional translational joints

  • Published:
Multibody System Dynamics Aims and scope Submit manuscript

Abstract

The main purpose of this paper is to present a modeling and simulation method for the rigid multibody system with frictional translational joints. The small clearance between a slider and guide is considered. The geometric constraints of the translational joints are treated as bilateral constraints and the impacts between sliders and guides are neglected when the clearance sizes of the translational joints are very small. The contact situations of the normal forces acting on the sliders are described by inequalities and complementarity conditions, while the frictional contacts are characterized by a set-valued force law of the type of Coulomb’s law for dry friction. The dynamic equations of the multibody systems with normal and tangential contact forces are written on the acceleration-force level using the Lagrange multiplier technique. The problem of the transitions of the contact situation of the normal forces acting on sliders and the transitions of the stick-slip of the sliders in the system is formulated as a horizontal linear complementarity problem (HLCP), which is solved by event-driven method. Baumgarte’s stabilization method is used to decrease the constraint drift. Finally, two typical mechanisms are considered as demonstrative application examples. The numerical results obtained show some dynamical behaviors of the systems with frictional translational joints and constraint stabilization effect.

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

Access this article

Log in via an institution

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
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

References

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  4. Zhao, Z., Liu, C.S.: The analysis and simulation for three-dimensional impact with friction. Multibody Syst. Dyn. 18, 511–530 (2007)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  8. Liu, T., Wang, M.Y., Low, K.H.: Non-jamming conditions in multi-contact rigid-body dynamics. Multibody Syst. Dyn. 22, 269–295 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Flores, P., Ambrósio, J., Claro, J.C.P., Lankarani, H.M.: Translational joints with clearance in rigid multibody systems. J. Comput. Nonlinear Dyn. 3, 011007 (2008)

    Article  Google Scholar 

  10. Al-Dwairi, A.F., Al-Nawafleh, M.A., Al-Lubani, S.E., Al-Ghathian, F.M.: Lagrangian modeling and analysis of the dynamics of frictional winding mechanisms. Multibody Syst. Dyn. 26(2), 175–190 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  11. Paul, B.: Kinematics and Dynamics of Planar Machinery. Prentice-Hall, Englewood Cliffs (1982)

    Google Scholar 

  12. Pfeiffer, F.: The idea of complementarity in multibody dynamics. Arch. Appl. Mech. 72(11–12), 807–816 (2003)

    MATH  Google Scholar 

  13. Pfeiffer, F., Glocker, C.: Multibody Dynamics with Unilateral Constraints. Wiley, New York (1996)

    Book  Google Scholar 

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

    MATH  Google Scholar 

  15. 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, 165–190 (2010)

    Article  MathSciNet  Google Scholar 

  16. Anitescu, M., Hart, G.D.: A constraint-stabilized time-stepping approach for rigid multibody dynamics with joints, contact and friction. Int. J. Numer. Methods Eng. 60, 2335–2371 (2004)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  18. Flores, P., Machado, M., Seabra, E., Silva, M.T.: A parametric study on the Baumgarte stabilization method for forward dynamics of constrained multibody systems. J. Comput. Nonlinear Dyn. 6, 011019 (2011)

    Article  Google Scholar 

  19. Wang, Q., Peng, H., Zhuang, F.: A constraint-stabilized method for multibody dynamics with friction-affected translational joints based on HLCP. Discrete Continuous. Dyn. Syst. Ser. B 16, 589–605 (2011)

    MathSciNet  MATH  Google Scholar 

  20. Blajer, W.: Methods for constraint violation suppression in the numerical simulation of constrained multibody systems—a comparative study. Comput. Methods Appl. Mech. Eng. 200(13–16), 1568–1576 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  21. Klepp, H.J.: The existence and uniqueness of solutions for a single-degree-of-freedom system with two friction-affected sliding joints. J. Sound Vib. 185(2), 364–371 (1995)

    Article  MathSciNet  Google Scholar 

  22. Leine, R.I., Van Campen, D.H., Glocker, C.: Nonlinear dynamics and modeling of various wooden toys with impact and friction. J. Sound Control 9, 25–78 (2003)

    MATH  Google Scholar 

  23. Blajer, W.: On the determination of joint reactions in multibody mechanisms. J. Mech. Des. 126, 341–350 (2004)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  25. Braun, D.J., Goldfarb, M.: Eliminating constraint drift in the numerical simulation of constrained dynamical systems. Comput. Methods Appl. Mech. Eng. 198, 3151–3160 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  26. Schäfer, U.: Verification methods for the horizontal linear complementarity problem. Proc. Appl. Math. Mech. 8, 10799–10800 (2008)

    Article  Google Scholar 

  27. Lemke, C.E.: Some pivot schemes for the linear complementarity problem. Math. Program. Stud. 7, 15–35 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  28. Cottle, R.W., Pang, J.S., Stone, R.E.: The Linear Complementarity Problem. Academic Press, Boston (1992)

    MATH  Google Scholar 

Download references

Acknowledgements

This work is supported by a grant from National Natural Science Foundation of China (No. 11072014). The authors would also like to express sincere appreciation to the anonymous reviewers for their insightful comments and suggestions on an earlier draft of this paper.

Author information

Authors and Affiliations

  1. School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, 100191, Beijing, P.R. China

    Fangfang Zhuang & Qi Wang

Authors
  1. Fangfang Zhuang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qi Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fangfang Zhuang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhuang, F., Wang, Q. Modeling and simulation of the nonsmooth planar rigid multibody systems with frictional translational joints. Multibody Syst Dyn 29, 403–423 (2013). https://doi.org/10.1007/s11044-012-9328-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11044-012-9328-5

Keywords

Search

Navigation