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Nonlinear Dynamics

, Volume 94, Issue 4, pp 2423–2440 | Cite as

Modeling and analysis of sliding joints with clearances in flexible multibody systems

  • Lingling Tang
  • Jinyang Liu
Original Paper
  • 341 Downloads

Abstract

The modeling of the sliding joint with clearance between a flexible beam and a rigid hole is investigated in this paper. The flexible beam is discretized using the three-dimensional curved Euler–Bernoulli beam element of the Absolute Nodal Coordinate Formulation, while the motion of the rigid hole is described by the Cartesian coordinates. Moreover, the cross sections of both the flexible beam and the rigid hole are assumed to be circular. The existing joints with clearances are mainly rigid joints with small clearances, and the contact detection algorithm adopted can solve only one pair of potential contact points within one section. In order to model the contact problem in the sliding joint with clearance, a new contact detection method based on the intersection of the rigid hole’s cross section and the flexible beam is proposed, which yields a two-dimensional contact detection problem. Based on the common-normal concept, the ellipse–circle contact detection problem within the hole’s cross section can be solved. The potential contact point on the hole’s cross section will be determined, and the closest point projection on the beam’s neutral axis can be defined further. The proposed contact detection method can deal with the sliding joint with large clearance and the multiple-point contact problem within one section. In addition, the penalty method is adopted to model the frictionless contact between the flexible beam and the rigid hole. Finally, two numerical examples about sliding joints with clearances, one with an initially curved beam under gravity and the other with a straight beam under zero gravity, are presented to demonstrate the influence of the clearance of sliding joint on the dynamic performance of flexible multibody systems.

Keywords

Sliding joint Clearance Contact detection Flexible multibody system 

Notes

Acknowledgements

This research was supported by General Program (Nos. 11772186, 11272203) of the National Natural Science Foundation of China, for which the authors are grateful.

References

  1. 1.
    Antonides, G.J.: Study of sep solar array modifications. Technical Report NASA-CR-157403, LMSC-D573788, Lockheed Missiles and Space Company (1978)Google Scholar
  2. 2.
    Arnold, M., Brüls, O.: Convergence of the generalized-\(\alpha \) scheme for constrained mechanical systems. Multibody Syst. Dyn. 18(2), 185–202 (2007)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Bauchau, O.A., Bottasso, C.L.: Contact conditions for cylindrical, prismatic, and screw joints in flexible multibody systems. Multibody Syst. Dyn. 5(3), 251–278 (2001)zbMATHCrossRefGoogle Scholar
  4. 4.
    Bauchau, O.A., Ju, C.: Modeling friction phenomena in flexible multibody dynamics. Comput. Methods Appl. Mech. Eng. 195(5051), 6909–6924 (2006)zbMATHCrossRefGoogle Scholar
  5. 5.
    Bauchau, O.A., Rodriguez, J.: Modeling of joints with clearance in flexible multibody systems. Int. J. Solids Struct. 39(1), 41–63 (2002)zbMATHCrossRefGoogle Scholar
  6. 6.
    Bauchau, O.A., Rodriguez, J., Chen, S.: Modeling the bifilar pendulum using nonlinear, flexible multibody dynamics. J. Am. Helicopter Soc. 48(1), 53–62 (2003)CrossRefGoogle Scholar
  7. 7.
    Belytschko, T., Liu, W.K., Moran, B., Elkhodary, K.: Nonlinear Finite Elements for Continua and Structures, 2nd edn. Wiley, Chichester (2013)zbMATHGoogle Scholar
  8. 8.
    Bronshtein, I.N., Semendyayev, K.A., Musiol, G., Mühlig, H.: Handbook of Mathematics, 6th edn. Springer, Berlin (2015)zbMATHGoogle Scholar
  9. 9.
    Chung, J., Hulbert, G.M.: A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-\(\alpha \) method. J. Appl. Mech. 60(2), 371–375 (1993)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Dmitrochenko, O., Pogorelov, D.: Generalization of plate finite elements for absolute nodal coordinate formulation. Multibody Syst. Dyn. 10(1), 17–43 (2003)zbMATHCrossRefGoogle Scholar
  11. 11.
    von Dombrowski, S.: Analysis of large flexible body deformation in multibody systems using absolute coordinates. Multibody Syst. Dyn. 8(4), 409–432 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Flores, P., Ambrósio, J., Claro, J.P., Lankarani, H.M.: Kinematics and Dynamics of Multibody Systems with Imperfect Joints. Springer, Berlin (2008)zbMATHGoogle Scholar
  13. 13.
    Flores, P., Lankarani, H.M.: Contact Force Models for Multibody Dynamics. Springer, Cham (2016)zbMATHCrossRefGoogle Scholar
  14. 14.
    Géradin, M., Cardona, A.: Flexible Multibody Dynamics: A Finite Element Approach. Wiley, Chichester (2001)Google Scholar
  15. 15.
    Gerstmayr, J., Humer, A., Gruber, P., Nachbagauer, K.: The absolute nodal coordinate formulation. In: Betsch, P. (ed.) Structure-Preserving Integrators in Nonlinear Structural Dynamics and Flexible Multibody Dynamics, pp. 159–200. Springer, Cham (2016)CrossRefGoogle Scholar
  16. 16.
    Gerstmayr, J., Sugiyama, H., Mikkola, A.: Review on the absolute nodal coordinate formulation for large deformation analysis of multibody systems. J. Comput. Nonlinear Dyn. 8(3), 031016 (2013)CrossRefGoogle Scholar
  17. 17.
    Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems. Springer, Berlin (1996)zbMATHCrossRefGoogle Scholar
  18. 18.
    Haug, E.J.: Computer Aided Kinematics and Dynamics of Mechanical Systems. Allyn and Bacon, Boston (1989)Google Scholar
  19. 19.
    Hong, D., Ren, G.: A modeling of sliding joint on one-dimensional flexible medium. Multibody Syst. Dyn. 26(1), 91–106 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Hong, J.Z.: Computational Dynamics of Multibody Systems. Higher Education Press, Beijing (1999)Google Scholar
  21. 21.
    Johnson, K.: Contact Mechanics. Cambridge University Press, Cambridge (1985)zbMATHCrossRefGoogle Scholar
  22. 22.
    Konyukhov, A., Izi, R.: Introduction to Computational Contact Mechanics. Wiley, Chichester (2015)zbMATHGoogle Scholar
  23. 23.
    Lee, S.H., Park, T.W., Seo, J.H., Yoon, J.W., Jun, K.J.: The development of a sliding joint for very flexible multibody dynamics using absolute nodal coordinate formulation. Multibody Syst. Dyn. 20(3), 223–237 (2008)zbMATHCrossRefGoogle Scholar
  24. 24.
    Liu, C., Tian, Q., Hu, H.: Dynamics and control of a spatial rigid-flexible multibody system with multiple cylindrical clearance joints. Mech. Mach. Theory 52, 106–129 (2012)CrossRefGoogle Scholar
  25. 25.
    Liu, Z., Liu, J.: Experimental validation of rigid-flexible coupling dynamic formulation for hub-beam system. Multibody Syst. Dyn. 40(3), 303–326 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    Neto, A.G., Pimenta, P.M., Wriggers, P.: A master-surface to master-surface formulation for beam to beam contact. Part I: frictionless interaction. Comput. Methods Appl. Mech. Eng. 303, 400–429 (2016)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Pappalardo, C.M., Patel, M.D., Tinsley, B., Shabana, A.A.: Contact force control in multibody pantograph/catenary systems. Proc. Inst. Mech. Eng. Part K: J. Multi-body Dyn. 230(4), 307–328 (2016)Google Scholar
  28. 28.
    Peng, Y., Zhao, Z., Zhou, M., He, J., Yang, J., Xiao, Y.: Flexible multibody model and the dynamics of the deployment of mesh antennas. J. Guid. Control Dyn. 40(6), 1499–1506 (2017)CrossRefGoogle Scholar
  29. 29.
    Shabana, A.A.: Computational Continuum Mechanics, 2nd edn. Cambridge University Press, New York (2012)zbMATHGoogle Scholar
  30. 30.
    Shabana, A.A.: Dynamics of Multibody Systems, 4th edn. Cambridge University Press, New York (2013)zbMATHCrossRefGoogle Scholar
  31. 31.
    Simo, J.C., Tarnow, N., Doblare, M.: Non-linear dynamics of three-dimensional rods: exact energy and momentum conserving algorithms. Int. J. Numer. Methods Eng. 38(9), 1431–1473 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  32. 32.
    Sonneville, V., Brüls, O., Bauchau, O.A.: Interpolation schemes for geometrically exact beams: a motion approach. Int. J. Numer. Methods Eng. 112(9), 1129–1153 (2017)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Sugiyama, H., Escalona, J.L., Shabana, A.A.: Formulation of three-dimensional joint constraints using the absolute nodal coordinates. Nonlinear Dyn. 31(2), 167–195 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  34. 34.
    Sugiyama, H., Koyama, H., Yamashita, H.: Gradient deficient curved beam element using the absolute nodal coordinate formulation. J. Comput. Nonlinear Dyn. 5(2), 021001 (2010)CrossRefGoogle Scholar
  35. 35.
    Sugiyama, H., Suda, Y.: A curved beam element in the analysis of flexible multi-body systems using the absolute nodal coordinates. Proc. Inst. Mech. Eng. Part K J. Multi-body Dyn. 221(2), 219–231 (2007)Google Scholar
  36. 36.
    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)CrossRefGoogle Scholar
  37. 37.
    Wellmann, C., Lillie, C., Wriggers, P.: A contact detection algorithm for superellipsoids based on the common-normal concept. Eng. Comput. 25(5), 432–442 (2008)zbMATHCrossRefGoogle Scholar
  38. 38.
    Yakoub, R.Y., Shabana, A.A.: Three dimensional absolute nodal coordinate formulation for beam elements: implementation and applications. J. Mech. Des. 123(4), 614–621 (2000)CrossRefGoogle Scholar
  39. 39.
    Yan, S., Xiang, W., Zhang, L.: A comprehensive model for 3d revolute joints with clearances in mechanical systems. Nonlinear Dyn. 80(1), 309–328 (2015)CrossRefGoogle Scholar
  40. 40.
    Yang, C.J., Zhang, W.H., Ren, G.X., Liu, X.Y.: Modeling and dynamics analysis of helical spring under compression using a curved beam element with consideration on contact between its coils. Meccanica 49(4), 907–917 (2014)MathSciNetzbMATHCrossRefGoogle Scholar
  41. 41.
    Yoo, W.S., Lee, J.H., Park, S.J., Sohn, J.H., Pogorelov, D., Dmitrochenko, O.: Large deflection analysis of a thin plate: computer simulations and experiments. Multibody Syst. Dyn. 11(2), 185–208 (2004)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of Naval Architecture, Ocean and Civil EngineeringShanghai Jiaotong UniversityShanghaiChina

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