Disk Springs

  • Vladimir Kobelev


In the current chapter the disk spring using the variation methods and equations of thin and moderately thick isotropic and anisotropic shells are investigated in closed analytical form. The equations developed here are based on common assumptions and are simple enough to be applied to the analysis. The analysis of isotropic and anisotropic thin-walled disk springs could be performed using basic spreadsheet tools, removing the need to perform an onerous finite element analysis.

The theory of linear and progressive disk wave springs is presented.


  1. Almen, J.O., Laszlo, A.: The uniform section disc spring. Trans. ASME. 58(4), 305–314 (1936)Google Scholar
  2. ANSYS.: ANSYS, Inc. Southpointe, 2600 ANSYS Drive, Canonsburg, PA 15317c (2017).
  3. Blom, A.W., Tatting, B.F., Hol, J., Gürdala, Z.: Fiber path definitions for elastically tailored conical shells. Compos. Part B. 40(1), 77–84 (2009)CrossRefGoogle Scholar
  4. Catapano, A., Desmorat, B., Vannucci, P.: Stiffness and strength optimization of the anisotropy distribution for laminated structures. J. Optim. Theory Appl. 167(1), 118–146 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  5. DIN EN 16984:2017-02.: Disc Springs—Calculation. German version EN 16984:2016 (2017)Google Scholar
  6. Dumir, P.C.: Nonlinear axisymmetric response of orthotropic thin truncated conical and spherical caps. Acta Mech. 60, 121–132 (1986)CrossRefzbMATHGoogle Scholar
  7. Fawazi, N., Lee, J.-Y., Oh, J.-E.: A load–displacement prediction for a bended slotted disc using the energy method. Proc. IMechE C J. Mech. Eng. Sci. 1–12 (2011)Google Scholar
  8. Ferrari, G.: A new calculation method for belleville disc springs with contact flats and reduced thickness. Int. J. Manuf. Mater. Mech. Eng. 3(2), 63–73 (2013)Google Scholar
  9. Hengstenberg, R.: Eigenspannungsentstehung in Tellerfedern und Schwingfestigkeit von Tellerfedern großer Scheibendicke, Diss. RWTH, Fak. Bergbau und Hüttenwesen, Aachen (1983)Google Scholar
  10. Hübner, W.: Deformationen und Spannungen bei Tellerfedern. Konstruktion. 34, 387–392 (1982)Google Scholar
  11. Hübner, W.: Large deformations of elastic conical shells. In: Axelrad, E.L., Emmerling, F.A. (eds.) Flexible Shells, pp. 257–270. Springer, Berlin (1984)CrossRefGoogle Scholar
  12. Hübner, W., Emmerling, F.A.: Axialsymmetrische große Deformationen einer elastischen Kegelschale. ZAMM. 62, 408–411 (1982)CrossRefGoogle Scholar
  13. Kobelev, V.: Exact shell solutions for conical springs. Mech. Based Des. Struct. Mach. 44(4) (2016). Doi:  10.1080/15397734.2015.1066686
  14. Kobelev, V., Hesselmann, B., Rinsdorf, A.: Corrugated spring with gradual progressive spring characteristic, US 7334784 B2, US Patent Office (2003)Google Scholar
  15. La Rosa, G., Messina, M., Risitano, A.: Stiffness of variable thickness Belleville springs. J. Mech. Des. 123(2), 294–299 (1998). doi: 10.1115/1.1357162 CrossRefGoogle Scholar
  16. Lellep, J., Polikarpus, J.: Optimization of anisotropic circular plates. In: M. Shitikova et al (Ed.). Recent Advances in Mechanical Engineering. WSEAS, pp. 40−45 (2014). ISBN: 978-960-474-402-2, 40-45Google Scholar
  17. Libai, A., Simmonds, J.G.: The Nonlinear Theory of Elastic Shells, One Spatial Dimension. Academic, London (1988)zbMATHGoogle Scholar
  18. Marsden, J.E., Hughes, T.J.R.: Mathematical Foundations of Elasticity. Dover, New York (1994)zbMATHGoogle Scholar
  19. Niepage, P.: Vergleich verschiedener Verfahren zur Berechnung von Tellerfedern—Teil I. Draht, 34, 105–108. Teil II. Draht. 34, 251–255 (1983)Google Scholar
  20. Niepage, P., Schiffner, K., Gräb, B.: Theoretische und experimentelle Untersuchungen an geschlitzten Tellerfedern. VDI-Verlag, Düsseldorf (1987)Google Scholar
  21. Rosa, G.L., Messina, M., Risitano, A.: Tangential and radial stresses of variable thickness Belleville spring. J. Mech. Des. 123(2), 294–299 (1998). doi: 10.1115/1.1357162 CrossRefGoogle Scholar
  22. Rovati, M., Taliercio, A.: Stationarity of the strain energy density for some classes of anisotropic solids. Int. J. Solids Struct. 40, 6043–6075 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  23. Saini, P.K., Kumar, P., Tandon, P.: Design and analysis of radially tapered disc springs with parabolically varying thickness. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 221(2), 151–158 (2007). doi: 10.1243/0954406JMES114 CrossRefGoogle Scholar
  24. Schremmer, G.: The slotted conical disc spring. Trans. ASME J. Eng. Ind. 95, 765–770 (1973)CrossRefGoogle Scholar
  25. Shen, W., Fang, W.: Design of a friction clutch using dual Belleville structures. ASME J. Mech. Des. 129, (2007)Google Scholar
  26. Society of Automotive Engineers.: Spring Design Manual. Part 5, SAE, HS-158, Warrendale, PA (1996)Google Scholar
  27. Tavares, S.A.: Thin conical shells with constant thickness and under axisymmetric load. Comput. Struct. 60(6), 895–921 (1996)CrossRefzbMATHGoogle Scholar
  28. Timoshenko, S., Woinowsky-Krieger, S.: Theory of Plate and Shell, 2nd edn. McGraw Hill, New York (1957)zbMATHGoogle Scholar
  29. Ventsel, E., Krauthammer, T.: Thin Plates and Shells, Theory, Analysis, and Applications. Dekker AG, Basel (2001)CrossRefGoogle Scholar
  30. Vinson, J.R.: The Behavior of Shells Composed of Isotropic and Composite Materials. Springer, Netherlands (1993)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Vladimir Kobelev
    • 1
  1. 1.Faculty of EngineeringUniversity of SiegenSiegenGermany

Personalised recommendations