Skip to main content
Top

2021 | OriginalPaper | Chapter

6. Coiling of Helical Springs

Author : Vladimir Kobelev

Published in: Durability of Springs

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this chapter the method for calculation of residual stress and plastic bending and torsion moments for combined bending-torsion load is developed. The Bernoulli’s hypothesis is assumed for the deformation of the bar. The analysis was provided using deformational theory of plasticity with a nonlinear stress strain law describing active plastic deformation (SAE AE-22, Sect. 8.3.33). The curvature and twist of the bar during the plastic loading increase proportionally, such that the ratio curvature to twist remains constant. The complete solutions based on this approximate material law provide closed analytical solution. The unloading is linear elastic. This chapter is the primary section of second part, which studies mechanical problems arising during the manufacturing of helical springs.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
go back to reference Ali, A.R.M.: Plastic deformation and springback of pre-loaded rod under subsequent torsion. J. Inst. Eng (India): Mech. Eng. Div. 86, 26–30 (2005) Ali, A.R.M.: Plastic deformation and springback of pre-loaded rod under subsequent torsion. J. Inst. Eng (India): Mech. Eng. Div. 86, 26–30 (2005)
go back to reference Allen, A.J., Hutchings, M.T., Windsor, C.G., Andreani, C.: Neutron diffraction methods for the study of residual stress fields. Adv. Phys. 34, 445–473 (1985)CrossRef Allen, A.J., Hutchings, M.T., Windsor, C.G., Andreani, C.: Neutron diffraction methods for the study of residual stress fields. Adv. Phys. 34, 445–473 (1985)CrossRef
go back to reference Baragetti, S.: A theoretical study on nonlinear bending of wires. Meccanica 41, 443–458 (2006)CrossRef Baragetti, S.: A theoretical study on nonlinear bending of wires. Meccanica 41, 443–458 (2006)CrossRef
go back to reference Brooks, D.S.: The elasto-plastic behaviour of a circular bar loaded by axial force and torque in the strain hardening range. Int. J. Mech. Sci. 11, 75–85 (1969)CrossRef Brooks, D.S.: The elasto-plastic behaviour of a circular bar loaded by axial force and torque in the strain hardening range. Int. J. Mech. Sci. 11, 75–85 (1969)CrossRef
go back to reference Eisenhart, L.P.: Introduction to Differential Geometry with use of the Tensor Calculus. Princeton, Princeton University Press (1940)MATH Eisenhart, L.P.: Introduction to Differential Geometry with use of the Tensor Calculus. Princeton, Princeton University Press (1940)MATH
go back to reference Gaydon, F.A.: On the combined torsion and tension of a partly plastic circular cylinder. Quart. J. Mech. Appl. Math. 5(1), 29–41 (1952) Gaydon, F.A.: On the combined torsion and tension of a partly plastic circular cylinder. Quart. J. Mech. Appl. Math. 5(1), 29–41 (1952)
go back to reference Gaydon, F.A., Nuttal, H.: On the combined bending and twisting of beams of various sections. J. Mech. Phys. Solids 6, 17–26 (1957)CrossRef Gaydon, F.A., Nuttal, H.: On the combined bending and twisting of beams of various sections. J. Mech. Phys. Solids 6, 17–26 (1957)CrossRef
go back to reference Handelman, G.H.: A variational principle for a state of combined plastic stress. Quart. Appl. Math. 1, 351–353 (1944)MathSciNetCrossRef Handelman, G.H.: A variational principle for a state of combined plastic stress. Quart. Appl. Math. 1, 351–353 (1944)MathSciNetCrossRef
go back to reference Hill, R., Siebel, M.P.L.: On the plastic distortion of solid bars by combined bending and twisting. J. Mech. Phys. Solids 1, 207–214 (1953)CrossRef Hill, R., Siebel, M.P.L.: On the plastic distortion of solid bars by combined bending and twisting. J. Mech. Phys. Solids 1, 207–214 (1953)CrossRef
go back to reference Imegwu, E.O.: Plastic flexure and torsion. J. Mech. Phys. Solids 8(2), 141–146 (1960) Imegwu, E.O.: Plastic flexure and torsion. J. Mech. Phys. Solids 8(2), 141–146 (1960)
go back to reference Ishikawa, H.: Elasto-plastic stress analysis of prismatic bar under combined bending and torsion. ZAMM 68, 17–30 (1973)CrossRef Ishikawa, H.: Elasto-plastic stress analysis of prismatic bar under combined bending and torsion. ZAMM 68, 17–30 (1973)CrossRef
go back to reference Jones, R.M.: Deformation Theory of Plasticity. Bull Ridge Publishing, Blacksburg, VA (2009) Jones, R.M.: Deformation Theory of Plasticity. Bull Ridge Publishing, Blacksburg, VA (2009)
go back to reference Kobelev, V.: Elastoplastic stress analysis and residual stresses in cylindrical bar under combined bending and torsion. ASME J. Manuf. Sci. Eng. 133(4), 044502 (2011) Kobelev, V.: Elastoplastic stress analysis and residual stresses in cylindrical bar under combined bending and torsion. ASME J. Manuf. Sci. Eng. 133(4), 044502 (2011)
go back to reference Matejicek, J., Brand, P.C., Drews, A.R., Krause, A., Lowe-Ma, C.: Residual stresses in cold-coiled helical compression springs for automotive suspensions measured by neutron diffraction. Mater. Sci. Eng. A 367, 306–311 (2004)CrossRef Matejicek, J., Brand, P.C., Drews, A.R., Krause, A., Lowe-Ma, C.: Residual stresses in cold-coiled helical compression springs for automotive suspensions measured by neutron diffraction. Mater. Sci. Eng. A 367, 306–311 (2004)CrossRef
go back to reference Neuber, H.: Theory of stress concentration for shear-strained prismatical bodies with arbitrary nonlinear stress–strain law. J. Appl. Mech. 28, 544–550 (1961a) Neuber, H.: Theory of stress concentration for shear-strained prismatical bodies with arbitrary nonlinear stress–strain law. J. Appl. Mech. 28, 544–550 (1961a)
go back to reference Neuber, H.: Theory of notch stresses: principles for exact calculation of strength with reference to structural form and material. United States Atomic Energy Commission, US Office of Technical Services, Oak Ridge, TN (1961b) Neuber, H.: Theory of notch stresses: principles for exact calculation of strength with reference to structural form and material. United States Atomic Energy Commission, US Office of Technical Services, Oak Ridge, TN (1961b)
go back to reference SAE AE-22 (1997) SAE fatigue design handbook. SAE International, Warrendale SAE AE-22 (1997) SAE fatigue design handbook. SAE International, Warrendale
go back to reference Sankaranarayanan, R., Hodge, P.G.: On the use of linearized yield conditions for combined stresses in beams. J. Mech. Phys. Solids 7, 22–36 (1958)MathSciNetCrossRef Sankaranarayanan, R., Hodge, P.G.: On the use of linearized yield conditions for combined stresses in beams. J. Mech. Phys. Solids 7, 22–36 (1958)MathSciNetCrossRef
go back to reference Steele, M.C.: The plastic bending and twisting of square section members. J. Mech. Phys. Solids (1954). 8188-166 Steele, M.C.: The plastic bending and twisting of square section members. J. Mech. Phys. Solids (1954). 8188-166
go back to reference Życzkowski, M.: Combined loadings in the theory of plasticity. Int. J. Non-Linear Mech. 173–205 (1967) Życzkowski, M.: Combined loadings in the theory of plasticity. Int. J. Non-Linear Mech. 173–205 (1967)
go back to reference Życzkowski, M.: Combined Loadings in the Theory of Plasticity. Springer (1981) Życzkowski, M.: Combined Loadings in the Theory of Plasticity. Springer (1981)
Metadata
Title
Coiling of Helical Springs
Author
Vladimir Kobelev
Copyright Year
2021
DOI
https://doi.org/10.1007/978-3-030-59253-0_6

Premium Partner