Modeling of Non-ideal Variable Pitch Valve Springs for Use in Automotive Cam Optimization

  • Henry Yau
  • Richard W. Longman
Conference paper


Optimal control theory has been studied for use in developing valve trains in engines to minimize vibration and wear. Previous works have concentrated on the optimization of the cam lobe profile using an ideal linear spring model for the valve spring. The ideal linear spring model cannot capture the variations in spring stiffness that occur at high speeds due to the internal spring dynamics. By using a multiple-mass lumped-parameter spring, greater accuracy may be obtained in simulation. In addition, such a model allows for the introduction of spring pitch to be included as an additional optimization parameter. In this paper, a simple multi-mass variable pitch spring model is developed to be used in valve pitch optimization as well as cam profile optimization.


Contact Force Optimal Control Theory Spring Stiffness Variable Pitch Spring Coil 
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  1. 1.
    H.G. Bock, R.W. Longman, J.P. Schlöder, and M.J. Winckler. Synthesis of automotive cams using multiple shooting-SQP methods for constrained optimization. In W. Jäger and H.-J. Krebs, editors, Mathematics - Key Technology for the Future. Springer, 2003.Google Scholar
  2. 2.
    M. Chew, F. Freudenstein, and R.W. Longman. Application of optimal control theory to the synthesis of high-speed cam-follower systems: Parts 1 and 2. Transactions of the ASME, 105(1):576–591, 1981.Google Scholar
  3. 3.
    S. Dubowsky and F. Freudenstein. Dynamic analysis of mechanical systems with clearances part 1: Formulation of dynamic model. Journal of Engineering for Industry, 93(1):305–309, 1971.CrossRefGoogle Scholar
  4. 4.
    D. Elgin. Automotive camshaft dynamics. CAM Design Handbook, pages 529–543, 2003.Google Scholar
  5. 5.
    A. Fujimoto, H Higashi, N Osawa, H Nakai, and T Mizukami. Valve jump prediction using dynamic simulation on direct acting valve train. Technical Report 2007-19, Advanced Powertrain Development Dept. Mitsubishi Motors, 2007.Google Scholar
  6. 6.
    B. C. Fabien, R.W. Longman, and F. Freudenstein. The design of high-speed dwell-rise-dwell cams using linear quadratic optimal control theory. Journal of Mechanical Design, 116:867–874, 1994.CrossRefGoogle Scholar
  7. 7.
    F. Freudenstein, M. Mayurian, and E.R. Maki. Energy efficient cam-follower systems. ASME Journal of Mechanisms, Transmissions, and Automation in Design, 105:681–685, 1983.Google Scholar
  8. 8.
    S. Faik and H. Witteman. Modeling of impact dynamics: A literature survey. In International ADAMS User Conference, 2000.Google Scholar
  9. 9.
    K.H. Hunt and F.R.E. Crossley. Coefficient of restitution interpreted as damping in vibroimpact. ASME Journal Of Applied Mechanics, 42(2):440–445, 1975.CrossRefGoogle Scholar
  10. 10.
    R. W. Longman J.-G. Sun and F. Freudenstein. Objective functions for optimal control in cam follower systems. International Journal for Manufacturing Science and Technology, 8(2), 2006.Google Scholar
  11. 11.
    T. Kitada and M. Kuchita. Development of vibration calculation code for engine valve-train. Technical Report 2008-20, Advanced Powertrain Development Dept. Mitsubishi Motors, 2008.Google Scholar
  12. 12.
    D.B. Leineweber. The theory of MUSCOD in a nutshell. IWR-Preprint 96-19, Universität Heidelberg, 1996.Google Scholar
  13. 13.
    H. M. Lankarani and P. E. Nikravesh. A contact force model with hysteresis damping for impact analysis of multibody systems. Journal of Mechanical Design, 112:369–376, 1990.CrossRefGoogle Scholar
  14. 14.
    Y. Lin and A.P. Pisano. General dynamic equations of helical springs with static solution and experimental verification. ASME Journal Of Applied Mechanics, 54:910–917, 1987.CrossRefGoogle Scholar
  15. 15.
    J. Lee and D.J. Thompson. Dynamic stiffness formulation, free vibration and wave motion of helical springs. Journal of Sound and Vibration, 239(2):297–320, 2001.CrossRefGoogle Scholar
  16. 16.
    N. Milovanovic, R. Chen, and J. Turner. Influence of variable valve timings on the gas exchange process in a controlled auto-ignition engine. Journal of Automobile Engineering, 218(D):567–583, 2004.Google Scholar
  17. 17.
    S. Mclaughlin and I. Hague. Development of a multi-body simulation model of a winston cup valvetrain to study valve bounce. Proceedings of the Institution of Mechanical Engineers, 216(K):237–248, 2002.Google Scholar
  18. 18.
    S. Mennicke, R.W. Longman, M.S. Chew, and H.G. Bock. A cad package for high speed automotive cam design based on direct multiple shooting control techniques. ASME Proceedings Design Engineering Technical Conference, 2004.Google Scholar
  19. 19.
    S. Mennicke, R.W. Longman, M.S. Chew, and H.G. Bock. High speed automotive cam design using direct multiple shooting control techniques. ASME Proceedings Design Engineering Technical Conference, 2004.Google Scholar
  20. 20.
    R. Norton. Cam Design and Manufacturing Handbook. Industrial Press, New York, 1st edition, 2002.Google Scholar
  21. 21.
    K. Oezguer and F. Pasin. Separation phenomenon in force closed cam mechanisms. Mechanical Machine Theory, 31(4):487–499, 1996.CrossRefGoogle Scholar
  22. 22.
    D. Pearson and W. H. Wittrick. An exact solution for the vibration of helical springs using a bernoulli-euler model. International journal of mechanical sciences, 28(2):83–96, 1986.zbMATHCrossRefGoogle Scholar
  23. 23.
    A. Sinopoli. Dynamics and impact in a system with unilateral constraints the relevance of dry friction. Meccanica, 22(4):210–215, 1987.zbMATHCrossRefGoogle Scholar
  24. 24.
    J.G. Sun, R.W. Longman, and R. Freudenstein. Determination of appropriate cost functionals for cam-follower design using optimal control theory. In Proceedings of the 1984 American Control Conference, pages 1799–1800, San Diego, Calif., 1984. American Automatic Control Council.Google Scholar
  25. 25.
    M.H. Wu and W.Y. Hsu. Modelling the static and dynamic behavior of a conical spring by considering the coil close and damping effects. Journal of Sound and Vibration, 214(1):17–28, 1998.CrossRefGoogle Scholar
  26. 26.
    T.L. Wang W. Jiang and W.K. Jones. The forced vibrations of helical springs. International Journal of Mechanical Sciences, 34(7):549–562, 1992.zbMATHCrossRefGoogle Scholar
  27. 27.
    D.J. Zhu and C.M. Taylor. Tribological Analysis and Design of a Modern Automobile Cam and Follower. Wiley and Sons, Suffolk UK, 1st edition, 2001.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Columbia UniversityNew YorkUSA

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