Analysis of lateral vibrations of the axially loaded helical spring

• Autorzy: Michalczyk K.

Identyfikatory

DOI

10.15632/jtam-pl.53.3.745

• Języki publikacji: EN

Abstrakty

EN

It is shown in this paper that the proposed concept by Krużelecki and Życzkowski (1990) of the equivalent rod can be applied in calculations of natural lateral vibrations of springs and that the obtained results will be nearer FEM results than the standard model based on the Timoshenko equivalent beam. The model, created on this base, allows one to calculate natural frequencies of the clamped-clamped spring. It is also shown that models based on the equivalent beam concept, which are easier to apply than the models treating the spring as the spatially curved rod, have only a slightly smaller accuracy. It is also indicated that in the most common practice making of manufacturing end coils of springs, the natural frequencies differ significantly from the frequencies calculated by means of all tested methods. The performed simulations show that differences between the first and the second as well as the third and the fourth natural frequency of the spring are small and, therefore, the axially symmetrical equivalent beam model can be used without a large error. The diagram allowing one to determine whether the desired frequencies are lower or higher than the cut-off frequency is developed for the presented model.

Słowa kluczowe

EN

helical spring vibrations; axially loaded spring; coil spring; Timoshenko equivalent beam

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2015
• Tom: Vol. 53 nr 3
• Strony: 745—755
• Opis fizyczny: Bibliogr. 25 poz., rys., tab.

Twórcy

autor

Michalczyk K.

• AGH University of Science and Technology, Faculty of Mechanical Engineering and Robotics, Kraków, Poland

Bibliografia

• 1. Becker L. E., Chassie G. G., Cleghorn W. L., 2002, On the natural frequencies of helical compression springs, International Journal of Mechanical Sciences, 44, 825-841
• 2. Della Pietra L., Della Valle S., 1982, On the dynamic behavior of axially excited helical springs, Meccanica, 17, 31-43
• 3. Guido A.R., Della Pietra L., Della Valle S., 1978, Transverse vibrations of helical springs, Meccanica, 13, 2, 90-108
• 4. Haringx J.A., 1948, On highly compressible helical springs and rubber rods, and their application for vibration-free mountings, I, Philips Research Reports, 3, 401-449
• 5. Haringx J. A., 1949, On highly compressible helical springs and rubber rods, and their application for vibration-free mountings, II, Philips Research Reports, 4, 49-80
• 6. Jiang W., Jones W.K., Wang T.L., Wu K.H., 1991, Free vibrations of helical springsm, Transactions of ASME, 58, 222-228
• 7. Kobelev V., 2014, Effect of static axial compression on the natural frequencies of helical springs, MMMS, issue 3
• 8. Krużelecki J., Życzkowski M., 1990, On the concept of an equivalent column in the problem of stability of compressed helical springs, Ingenieur-Archiv, 60, 367-377
• 9. Lee J., 2007, Free vibration analysis of cylindrical helical springs by the pseudospectral method, Journal of Sound and Vibration, 302, 185-196
• 10. Lee J., Thompson D. J., 2001, Dynamic stiffness formulation, free vibration and wave motion of helical springs, Journal of Sound and Vibration, 239, 297-320
• 11. Love A.E.M., 1899, The propagation of waves of elastic displacement along a helical wire, Transactions of the Cambridge Philosophical Society, 18, 364-374
• 12. Majkut L., 2009, Free and forced vibrations of Timoshenko beams described by single difference equation, Journal of Theoretical and Applied Mechanics, 47, 1,193-210
• 13. Michalczyk K., 2009, Analysis of helical compression spring support influence on its deformation, The Archive of Mechanical Engineering, 56, 4, 349-362
• 14. Michalczyk K., 2014, Influence of the elastomeric coating on parameters of steady state vibrations of coil springs in the resonance and outside it, Journal of Theoretical and Applied Mechanics, 52, 2, 507-518
• 15. Mottershead J.E., 1980, Finite elements for dynamical analysis of helical rods, International Journal of Mechanical Sciences, 22, 267-283
• 16. Nagaya K., Takeda S., Nakata Y., 1986, Free vibration of coil springs of arbitrary shape, International Journal for Numerical Methods in Engineering, 23, 1081-1099
• 17. Pearson D., 1982, The transfer matrix method for the vibration of compressed helical springs, Journal of Mechanical Engineering Sciences, 24, 163-171
• 18. Pearson D., Wittrick W.H., 1986, An exact solution for the vibration of helical springs using a Bernoulli-Euler model, International Journal of Mechanical Sciences, 28, 83-96
• 19. Stander N., Du Preez R.J., 1992, Vibration analysis of coil springs by means of isoparametric curved beam finie elements, Communications in Applied Numerical Methods, 8, 373-383
• 20. Stephen N.G., Puchegger S., 2006, On the valid frequency range of Timoshenko beam theory, Journal of Sound and Vibration, 297, 1082-1087
• 21. Taktak M., Dammak F., Abid S., Haddar M., 2008, A finite element for dynamic analysis of a cylindrical isotropic helical spring, Journal of Materials and Structures, 3, 641-658
• 22. Timoshenko S., Gere J.M., 1961, Theory of Elastic Stability, New York and London: McGraw Hill, p. 140
• 23. Wittrick W.H., 1966, On elastic wave propagation in helical springs. International, Journal of Mechanical Sciences, 8, 25-47
• 24. Yildrim V., 1999, An efficient numerical method for predicting the natural frequencies of cylindrical helical springs, International Journal of Mechanical Sciences, 41, 919-939
• 25. Yu A.M., Yang C.J., 2010, Formulation and evaluation of an analytical study for cylindrical helical springs, Acta Mechanica Solida Sinica, 23, 1, 85-94