Numerical Buckling Analysis of Cylindrical Helical Coil Springs in a Dynamic Manner

Year 2009, Volume: 1 Issue: 1, 20 - 32, 01.03.2009

V. Yıldırım

Abstract

The free vibration equations of cylindrical isotropic helical springs loaded axially, developed by the author are solved numerically based on the transfer matrix method to perform buckling analysis in a dynamic manner. The axial and shear deformation effects together with the rotatory inertia effects are all considered based on the first order shear deformation theory. For the determination of the vertical tip deflection of helical springs with large pitch angles, closed-form equation obtained by the author based on Castigliano’s first theorem is used to take into account for the whole effect of the stress resultants such as axial and shearing forces, bending and torsional moments on the tip deflection. A good agreement is observed with related benchmark studies

Keywords

Linear analysis, helical spring, numeric, transfer matrix, buckling

References

• 1. Haringx J.A., On highly compressible helical springs and rubber rods, and their application for vibration-free mountings, Philips Research Reports, 4, 49–80, 1949.
• 2. Ünlüsoy Y.S., Modelling helical springs for the dynamic behavior, Middle East Technical University (METU) Journal of Applied Researches, 3(9), 45-57, 1983 (In Turkish)..
• 3. Yalçın V., Finite element mobility analysis of helical coil springs, MS Thesis in METU The Graduate School of Natural and Applied Sciences, Ankara 1984.
• 4. Haktanır V., The investigation of the statical, dynamic and buckling behavior of helical rods by the transfer and stiffness matrices methods, Ph.D. Thesis, Çukurova University, Mechanical Engineering Department, 1990 (In Turkish).
• 5. Haktanır V., Kıral E., Computation of free vibration frequencies of helical springs subjected to axial load., Journal of Engineering Faculty of Isparta of Akdeniz University, 6, 201-218, 1992.
• 6. Xiong Y., Tabarrok B., A finite element model for the vibration of spatial rods under various applied loads, International Journal of Mechanical Sciences, 34 (1), 41-51, 1992.
• 7. Becker L.E., Chassie G.G., Cleghorn W.L., On the natural frequencies of helical compression springs, International Journal of Mechanical Sciences, 44(4), 825-841, 2002.
• 8. Becker L.E., Cleghorn W.L., On the buckling of helical compression springs, Int. J. of Mech. Eng. Sci., 34(4), 275-282, 1992.
• 9. Becker L.E., Cleghorn W.L., The buckling behavior of rectangular-bar helical compression springs, Journal of Applied Mechanics, 61, 491–493, 1994.
• 10. Chassie G.G., Becker L.E., Cleghorn W.L., On the buckling of helical springs under combined compression and torsion, International Journal of Mechanical Sciences, 39(6), 697-704, 1997.
• 11. Yıldırım V., An efficient numerical method for predicting the natural frequencies of cylindrical helical springs, International Journal of Mechanical Sciences, 41/ 8, 919-939, 1999.
• 12. Ibrikçi T., Saçma S., Yıldırım V., Koca T., Application of Artificial Neural Networks to the Prediction of Critical Buckling Loads of Helical Compression Springs, Strojniski Vestnik – Journal of Mechanical Engineering (submitted for publication)
• 13. Pestel E.C., Leckie F.A., Matrix Methods in Elastomechanics, McGraw-Hill, NewYork, 1963