Multibody System Dynamics

, Volume 22, Issue 2, pp 133–144 | Cite as

Dynamic simulation of crankshaft multibody systems

  • C. B. Drab
  • H. W. Engl
  • J. R. Haslinger
  • G. Offner
  • R. U. Pfau
  • W. Zulehner


General multibody system approaches are often not sufficient for specific situations in applications to yield an efficient and accurate solution. We concentrate on the simulation of the crankshaft dynamics which is characterized by flexible bodies and force laws describing the interaction between the bodies. The use of the floating frame of reference approach in our model leads to an index-2 DAE system. The algebraic constraints originate from the reference conditions and the normalization equation for the quaternions. For the time integration of this system, two aspects have to be taken into account: firstly, for efficiency exploiting the structure of the system and using parallelization. Secondly, consistent initial values also with respect to a related index-3 system have to be computed in order to compute missing initial velocities and to reduce transient phenomena.


Automotive application Multibody systems Dynamic simulation Differential-algebraic equations Backward differentiation formula 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    ABAQUS: ABAQUS Theory Manual, Version 6.7. ABAQUS (2007) Google Scholar
  2. 2.
    Barrett, R., Berry, M., Chan, T.F., Demmel, J., Donato, J., Dongarra, J., Eijkhout, V., Pozo, R., Romine, C., Van der Vorst, H.: Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, 2nd edn. SIAM, Philadelphia (1994) Google Scholar
  3. 3.
    Bottema, O., Roth, B.: Theoretical Kinematics. Dover, New York (1990) MATHGoogle Scholar
  4. 4.
    Brenan, K.E., Campbell, S.L., Petzold, L.R.: Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. SIAM, Philadelphia (1996) MATHGoogle Scholar
  5. 5.
    Bulirsch, R., Stoer, J.: Introduction to Numerical Analysis. Springer, New York (2002) MATHGoogle Scholar
  6. 6.
    De Veubeke, B.F.: The dynamics of flexible bodies. Int. J. Eng. Sci. 14, 895–913 (1976) MATHCrossRefGoogle Scholar
  7. 7.
    Drab, C.B.: Dynamic simulation of power train related systems. PhD Thesis. Johannes Kepler Universität Linz, Linz (2007) Google Scholar
  8. 8.
    Drab, C.B., Haslinger, J.R., Offner, G., Pfau, R.U.: Comparison of the classical formulation with the reference conditions formulation for dynamic flexible multibody systems. ASME J. Comput. Nonlinear Dyn. 2, 337–343 (2007) CrossRefGoogle Scholar
  9. 9.
    Eberhard, P.: Kontaktuntersuchungen durch hybride Mehrkörpersystem/Finite Element Simulationen. Shaker, Aachen (2000) Google Scholar
  10. 10.
    Eich-Soellner, E., Führer, C.: Numerical Methods in Multibody Dynamics. Teubner, Stuttgart (1998) MATHGoogle Scholar
  11. 11.
    Eizenberger, T.: Dynamic simulation of flexible structures undergoing large gross motion. PhD Thesis. Johannes Kepler Universität Linz, Linz (2003) Google Scholar
  12. 12.
    AVL GmbH: AVL-EXCITE, Theory, Version 7.0.4. AVL, Graz (2007) Google Scholar
  13. 13.
    Führer, C., Wallrapp, O.: A computer-oriented method for reducing linearized multibody system equations by incorporating constraints. Comput. Methods Appl. Mech. Eng. 46, 169–175 (1984) MATHCrossRefGoogle Scholar
  14. 14.
    Hairer, E., Nørsett, S.P., Wanner, G.: Solving Ordinary Differential Equations I: Nonstiff Problems. Springer, New York (2000) Google Scholar
  15. 15.
    Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems. Springer, New York (2002) Google Scholar
  16. 16.
    Jackson, K.R., Sacks-Davis, R.: An alternative implementation of variable step-size multistep formulas for stiff ODEs. ACM Trans. Math. Softw. 3, 295–318 (1980) CrossRefMathSciNetGoogle Scholar
  17. 17.
    Krasser, J.: Thermoelastohydrodynamische Analyse dynamisch belasteter Radialgleitlager. PhD Thesis, Technische Universität Graz, Graz (1996) Google Scholar
  18. 18.
    Kuipers, J.B.: Quaternions and Rotation Sequences. Princeton University Press, Princeton (1999) MATHGoogle Scholar
  19. 19.
    Lalor, N.: Experimental statistical energy analysis: A tool for the reduction of machinery noise. In: Proceedings of the E.J. Richards Memorial Session at the 131st ASA Meeting (1996) Google Scholar
  20. 20.
    Lötstedt, P.: On the relation between singular perturbation problems and differential-algebraic equations. Uppsala University, Dept. of Computer Sciences, Report No. 100 (1985) Google Scholar
  21. 21.
    Lubich, Ch.: Integration of stiff mechanical systems by Runge–Kutta methods. Z. Angew. Math. Phys. (ZAMP) 44, 1022–1053 (1993) MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Nikravesh, P.E.: Initial condition correction in multibody dynamics. Multibody Syst. Dyn. 18, 107–115 (2007) MATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Offner, G., Ma, M.-T., Karlsson, U., Wikstroem, A., Loibnegger, B., Priebsch, H.-H.: Quality and validation of cranktrain vibration predictions—Effect of hydrodynamic journal bearing models. MBD-MST, Loughborough (2004) Google Scholar
  24. 24.
    Offner, G., Drab, C.B., Loibnegger, B.: Application oriented dynamic simulation of elastic multibody systems. In: Goicolea, J.M., Cuadrado, J., García Orden, J.C. (eds) Proceedings of the ECCOMAS Thematic Conference “Multibody Dynamics 2005”, Madrid, Spain, 21–24 June 2005 Google Scholar
  25. 25.
    Offner, G., Eizenberger, T., Priebsch, H.H.: Separation of reference motions and elastic deformations in an elastic multi-body system. Proc. IMechE, Part K, J. Multi-body Dyn. 220, 63–75 (2006) Google Scholar
  26. 26.
    Offner, G., Lechner, M., Mahmoud, K., Priebsch, H.H.: Surface contact analysis in axial thrust bearings based on different numerical interpolation approaches. Proc. IMechE, Part K, J. Multi-body Dyn. 221, 233–245 (2007) Google Scholar
  27. 27.
    Parikyan, T., Resch, T., Priebsch, H.H.: Structured model of crankshaft in the simulation of engine dynamics with AVL/EXCITE. In: ASME Fall Technical Conference, ICE-37-3 (2001) Google Scholar
  28. 28.
    Priebsch, H.H., Krasser, J.: Simulation of the oil film behaviour in elastic engine bearings considering pressure and temperature dependent oil viscosity. In: Dowson, D., Childs, T.H.C., Taylor, C. (eds) Proceedings of the 23rd Leeds-Lyon Symposium on Tribology-Elastohydrodynamics (Leeds, UK, 1996), pp. 651–659. Elsevier, Amsterdam (1996) Google Scholar
  29. 29.
    Rasser, M.W., Resch, T., Priebsch, H.H.: Enhanced crankshaft stress calculation method. In: CIMAC Congress, Copenhagen, Denmark, May 18–22 (1998) Google Scholar
  30. 30.
    Rheinboldt, W.C., Simeon, B.: Computing smooth solutions of DAEs for elastic multibody systems. Comput. Math. Appl. 37, 69–83 (1999) MATHCrossRefMathSciNetGoogle Scholar
  31. 31.
    Schiehlen, W.: Multibody system dynamics: Roots and perspectives. Multibody Syst. Dyn. 1, 149–188 (1997) MATHCrossRefMathSciNetGoogle Scholar
  32. 32.
    Schiehlen, W.: Research trends in multibody system dynamics. Multibody Syst. Dyn. 18, 3–13 (2007) MATHCrossRefMathSciNetGoogle Scholar
  33. 33.
    Shabana, A.A.: Flexible multibody dynamics: Review of the past and recent developments. Multibody Syst. Dyn. 1, 189–222 (1997) MATHCrossRefMathSciNetGoogle Scholar
  34. 34.
    Shabana, A.A.: Vibration of Discrete and Continuous Systems. Springer, New York (1997) Google Scholar
  35. 35.
    Shabana, A.A.: Dynamics of Multibody Systems. Cambridge University Press, Cambridge (1998) MATHGoogle Scholar
  36. 36.
    Sopouch, M., Hellinger, W., Priebsch, H.-H.: Prediction of vibro-acoustics for chains and synchronous belts of reciprocating engines. Proc. IMechE, Part K, J. Multi-body Dyn. 217, 225–240 (2003) Google Scholar
  37. 37.
    Wehage, R.A., Haug, E.J.: Generalized coordinate partitioning for dimension reduction in analysis of constrained dynamic systems. J. Mech. Des. 104, 247–255 (1982) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • C. B. Drab
    • 1
  • H. W. Engl
    • 2
  • J. R. Haslinger
    • 1
  • G. Offner
    • 3
  • R. U. Pfau
    • 1
  • W. Zulehner
    • 4
  1. 1.Industrial Mathematics Competence CenterLinzAustria
  2. 2.Johann Radon Institute for Computational and Applied MathematicsAustrian Academy of SciencesLinzAustria
  3. 3.AVL List GmbHGrazAustria
  4. 4.Johannes Kepler Universität LinzLinzAustria

Personalised recommendations