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An Exact Solution of Torsion Problem for an Incomplete Torus with Application to Helical Springs

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Abstract

An exact analytical solution for the torsion problem of an incomplete torus with a particular form of non-circular cross-section has been found. The solution extends for the close-coiled helical spring the known solution of the torsion problems for straight cylinders with circular and elliptical cross-sections. The pitch of helix is ignored. The hollow cross-sections of the particular form also demonstrate a closed form of analytical solution. The solution can be used for analysis of helical springs with non-circular wire profile.

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References

  1. Michell, J.H., ‘The uniform torsion and flexure of incomplete torus, with application to helical springs’, Proc. London Math. Soc. 31 (1899) 130–146.

    Google Scholar 

  2. Wahl, A.M., ‘Stresses in heavy closely coiled helical springs’, Trans. ASME, J. Appl. Mech. 51 (1929) 185–200.

    Google Scholar 

  3. Göhner, O., ‘Spannungsverteilung im Querschnitt einer Schraubenfeder’, Ing.-Archiv. 1 (1930) 619–634.

    Google Scholar 

  4. Göhner, O., ‘Spannungsverteilung im Querschnitt eines gedrillten Ringstabs mit Anwendung auf Schraubenfedern’, Ing.-Archiv. 2 (1931) 381–385.

    Google Scholar 

  5. Göhner, O., ‘Die Berechnung zylindrischer Schraubenfedern’, Zeitschrift des VDI 76 (1932) 269–272.

    Google Scholar 

  6. Freiberger, W., ‘The uniform torsion of an incomplete torus’, Aust. J. Scient. Res. A2 (1949) 354–375.

    Google Scholar 

  7. Henrici, P., ‘On helical springs of finite thickness’, Quarterly Appl. Math. XIII (1955) 11, 106–110.

    Google Scholar 

  8. Muhr, T.H., ‘Zur Konstruktion von Ventilfedern in hochbeanspruchten Verbrennungsmotoren’, PhD Thesis, RWTH Aachen, Aachen, 1992.

    Google Scholar 

  9. Sato, M. et al., ‘Stress in a coil spring of arbitrary cross-section’, Trans. Jap. Soc. Mech. Engng 27 (1969) 86–88.

    Google Scholar 

  10. Sneddon, I.N. and Berry D.S., ‘The classical theory of elasticity’, In: Flügge, S. (ed.), Handbuch der Physik, Vol. VI, Springer-Verlag, New York, 1958, pp. 1–126.

    Google Scholar 

  11. Fraeijs de Veubecke, B.M., A Course in Elasticity, Springer-Verlag, New York, 1979.

    Google Scholar 

  12. Pilgram, M., ‘Die Berechnung zylindrischer Schraubenfedern’, Artilleristische Monatshefte. 79(1913) 68–88, 80(1913) 133–156, 81(1913) 221–239.

    Google Scholar 

  13. Köhler, E., Verbrennungsmotoren: Motorenmechanik, Berechnung und Auslegung des Hubkolbenmotors, Vieweg, Wiesbaden, 1998.

    Google Scholar 

  14. Fuchs, H.O., ‘High Efficiency Coil Springs with Equalized Stresses’, Metal Improvement Equipment Co., Los Angeles, 1959.

    Google Scholar 

  15. Nagaya, K., ‘Stress analysis of a cylindrical coil spring of arbitrary cross section. (1st Report)’, Bull. JSME 29 (1986) 1664–1678.

    Google Scholar 

  16. Matsumoto, Y. et al., Wire for Coiled Spring, United States Patent Number 4735403, 1988

  17. Muhr, T.H., ‘New technologies for engine valve springs’, SAE Paper 930912, New Engine Design and Engine Component Technology, SAE SP-972 (1993) 199–208.

  18. Kamiya, N. and Kita, E., ‘Boundary element method for quasi-harmonic differential equation with application to stress analysis and shape optimization of helical spring’, Computers Struct. 37 (1990) 81–86.

    Google Scholar 

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Author notes

  1. V. Kobelev (Privat-Dozent)

    Present address: Institute of Mechanics and Control Engineering, University of Siegen, FB 11, Paul-Bonatz Str. 9-11, Siegen, D-57068, Germany

Authors and Affiliations

  1. Fa. Mubea KG, P.O. Box 360, Lübecker Str. 10, D-57427, Attendorn, Germany

    V. Kobelev (Privat-Dozent)

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Kobelev, V. An Exact Solution of Torsion Problem for an Incomplete Torus with Application to Helical Springs. Meccanica 37, 269–282 (2002). https://doi.org/10.1023/A:1020108922684

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