Multibody System Dynamics

, Volume 26, Issue 4, pp 425–439 | Cite as

A short note for numerical analysis of dynamic contact considering impact and a very stiff spring-damper constraint on the contact point



By extending the numerical technique suggested by the author for the dynamic contact problem having a very stiff spring on the contact point, it is shown that the dynamic contact problem having a very stiff damper as well as a spring on the contact point can be time integrated without instability by imposing the time-differentiated constraints with the unconditionally stable Newmark time integration rule. It is also shown that the dynamic contact involving the repeated impacts and separations can be solved without instability by using the same time-differentiated constraints, and that the spring-damper deformation (i.e., penetration) on the contact point at the time of impact (i.e., at the first time step of contact) can be most reasonably determined by the displacement contact constraint. The special features of the present technique to solve the impact problem having a very stiff spring-damper on the contact point are that the equation of motion may be time integrated with any convenient ODE technique, and that the time step size reduction or the penetration threshold need not be considered at the time of impact.


Dynamic contact Impact Spring-damper Stiff constraint Multibody dynamics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Flores, P., Ambrosio, J., Claro, J.C.P., Lankarani, H.M.: Influence of the contact-impact force model on the dynamic response of multi-body systems. Proc. Inst. Mech. Eng., Part K, J. Multi-Body Dyn. 220, 21–34 (2006) Google Scholar
  2. 2.
    Flores, P., Ambrosio, J., Claro, J.C.P., Lankarani, H.M.: Dynamic behavior of planar rigid multi-body systems including revolute joints with clearance. Proc. Inst. Mech. Eng., Part K, J. Multi-Body Dyn. 221, 161–174 (2007) Google Scholar
  3. 3.
    Ambrosio, J., Verissimo, P.: Improved bushing models for general multibody systems and vehicle dynamics. Multibody Syst. Dyn. 22, 341–365 (2009) MATHCrossRefGoogle Scholar
  4. 4.
    Shabana, A.A., Zaazaa, K.E., Escalona, J.L., Sany, J.R.: Development of elastic force model for wheel/rail contact problems. J. Sound Vib. 269, 295–325 (2004) CrossRefGoogle Scholar
  5. 5.
    Tian, Q., Zhang, Y., Chen, L., Flores, P.: Dynamics of spatial flexible multibody systems with clearance and lubricated spherical joints. Comput. Struct. 87, 913–929 (2009) CrossRefGoogle Scholar
  6. 6.
    Flores, P., Ambrosio, J.: On the contact detection for contact-impact analysis in multibody systems. Multibody Syst. Dyn. 24, 103–122 (2010) MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Crowther, A.R., Singh, R., Zhang, N., Chapman, C.: Impulsive response of an automatic transmission system with multiple clearances: Formulation, simulation and experiment. J. Sound Vib. 306, 444–466 (2007) CrossRefGoogle Scholar
  8. 8.
    Chan, C., Pisano, A.P.: Dynamic model of a fluctuating rocker-arm ratio cam system. Trans. ASME J. Mech. Trans. Autom. Des. 109, 356–365 (1987) CrossRefGoogle Scholar
  9. 9.
    Djerassi, S.: Collision with friction; Part A: Newton’s hypothesis. Multibody Syst. Dyn. 21, 37–54 (2009) MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Djerassi, S.: Collision with friction; Part B: Poisson’s and Stronge’s hypothesis. Multibody Syst. Dyn. 21, 55–70 (2009) MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    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) MathSciNetCrossRefGoogle Scholar
  12. 12.
    Lee, K.: A stabilized numerical solution for dynamic contact of bodies having very stiff constraint on the contact point. Comput. Mech. 46, 533–543 (2010) MATHCrossRefGoogle Scholar
  13. 13.
    Vu-Quoc, L., Olsson, M.: Formulation of a basic building block model for interaction of high speed vehicles on flexible structures. J. Appl. Mech. 56, 451–458 (1989) MATHCrossRefGoogle Scholar
  14. 14.
    Lee, K.: Numerical analysis for dynamic contact between high-speed wheel and elastic beam with Coulomb friction. Int. J. Numer. Methods Eng. 78, 883–900 (2009) MATHCrossRefGoogle Scholar
  15. 15.
    Lee, K.: Analysis of dynamic contact between rotating spur gears by finite element and multi-body dynamics techniques. Proc. Inst. Mech. Eng., Part C, J. Mech. Eng. Sci. 215, 423–435 (2001) CrossRefGoogle Scholar
  16. 16.
    Lee, K.: A numerical method for dynamic analysis of vehicles moving on flexible structures having gaps. Int. J. Numer. Methods Eng. 40, 511–531 (1997) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringChonbuk National UniversityJeonjuKorea

Personalised recommendations