Equilibrium Equations for 3D Critical Buckling of Helical Springs

WU Xiu-gen; ZHENG Bai-lin; HE Peng-fei; LIU Shu-guang

doi:10.3879/j.issn.1000-0887.2012.08.007

Volume 33 Issue 8

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WU Xiu-gen, ZHENG Bai-lin, HE Peng-fei, LIU Shu-guang. Equilibrium Equations for 3D Critical Buckling of Helical Springs[J]. Applied Mathematics and Mechanics, 2012, 33(8): 988-996. doi: 10.3879/j.issn.1000-0887.2012.08.007

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Equilibrium Equations for 3D Critical Buckling of Helical Springs

doi: 10.3879/j.issn.1000-0887.2012.08.007

¹Department of Hydraulic Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, P.R.China;²School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, P.R.China

Received Date: 2011-12-01
Rev Recd Date: 2012-04-09
Publish Date: 2012-08-15

Abstract

Abstract

In most cases, the research on the buckling of helical spring is based on column, the spring is equivalent to column and the torsion around the axial line is ignored. The 3D helical spring model was considered,and its equilibrium equations were established by introducing two coordinate systems, named Frenet and principal axis coordinate systems, to describe the spatial deformation of center line and the torsion of cross section of spring respectively. By using small deformation assumption, the variables on deflection could be expanded by Taylor’s series and the terms of high orders were ignored. So the equations could be simplified to the functions of twist angle and arc length, which was possible to be solved in numerical method. The reaction loads of spring caused by axial load subjected at the center point were also discussed, which provided boundary conditions to gain the solution of equilibrium equations. This present work can be helpful to the continued research on the behavior of postbuckling of compressed helical spring.
- helical spring,
- buckling,
- equilibrium equation

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References(11)

References

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