Hello,
I have a multiple part question:
Backgroud to Q#1& Q#2 My interest is in the full stress distribution through the cross section of a helical coil compression spring, including the effects of curvature that are often cited by Wahl, but reported only for maximum stress at the surface. The coil is simple - constant wire diameter, coil diameter, and pitch. I have been unable to come across the solution for the full stress distribution (analytical), although there are endless references to Wahl's correction factor for the maximum stress.
Q#1 Does anyone have the reference for the analytical solution to the stress distribution in the spring, not just the maximum stress and Wahl correction factor?
Q#2 Is anyone familiar with a simple finite element model approach to compare the analytical solution to FEA without having to model the entire spring, e.g. a section of the spring? I find that modeling the entire spring leads to critical issues with properly setting boundary conditions to be consistent with those of the analytical approach (e.g. I believe that the assumptions in the analytical solutions include displacement/loading of the spring along the direction of the length of the spring.)
Background to Q#3 I seek to investigate the sensitivity of the stress in the spring due to variations in the boundary conditions for ground ends, e.g. if the ground ends are not perfect (they are not perfectly perpindicular to the length of the spring), and if the spring is assembled with one end of the spring offset from the other (e.g. creating bending of the overall spring).
The task appears feasible in ABAQUS, especially with CAE's features for creating the coil geometry and cutting off the ends to simulate 'ground' ends in a 3D model. However, as is typical in FEM, boundary conditions are critical. I do not wish to seek to reinvent the wheel here. I have come up empty in seeking any similar type of study. Perhaps I have looked in the wrong place.
Q#3 Does anyone have any knowledge/references to the sensitivity to BCs? Publications, ABAQUS models, other?
Any help would be appreciated.
Stress Distributions in Helical Compression Springs
Dear mcgrete,
sorry, I came across your posting only this week.
Most likely you need
Schubspannungsverteilung im Querschnitt einer Schraubenfeder (Shear stress distribution in the cross-section of a helical spring, in German)
Author: O. Göhner
Archive of Applied Mechanics, 1929, Volume 1, Number 5, Pages 619-644
The journal is actually "Ingenieur - Archiv", but for some undisclosed reason I found it under "Archive of Applied Mechanics".
When you search for more publications of that guy - or publications that refer to him - you should try the spellings
Göhner, Gohner, Goehner.
Also check out:
1) Finite Elements in Analysis and Design 35 (2000) 363}377
A novel finite element model for helical springs
W.G. Jiang, J.L. Henshall
2) if you happen to have command of Japanese:
ONLINE ISSN : 1348-1479
PRINT ISSN : 0385-6917
Transactions of Japan Society of Spring Engineers
Vol. 2004 (2004) , No. 49
Report of Research Committee on the Analysis of Helical Spring 35
Research Committee on the Analysis of Helical Spring
Release Date: 2005/11/15
3) ON THE STRESSES IN CLOSE-COILED HELICAL SPRINGS
By W. M. SHEPHERD
Quart. Journ. Mech. and Applied Math., Vol. 3, Pt. 4 (1950)
4) Simplified Stress Calculation Method for Helical Spring
wwwsoc.nii.ac.jp/jssr/english/Proceeding/paper4.pdf
5) http://deepblue.lib.umich.edu/handle/2027.42/3310
Title: Springs : a bibliography
Authors: Associated Spring Corporation. Research Committee.
Keywords: Springs -- Bibliography.
Issue Date: 1952
Other Identifiers: UMR0127
Appears in Collections: Engineering, College of - Technical Reports
I skipped the study of springs in my research. Thus, I do not know if there is anything better now. I couldn't find anything at least in the internet. I, too, was striving to find some PhD thesis or the like that scrutinizes the formulas given by Göhner, to no avail.
If you dig out something, please let me know.
Good luck
Frank
------------------------------------------
Ruhr-University
Bochum
Germany
In reply to Stress Distributions in Helical Compression Springs by Frank Richter
You can model your structure
You can model your structure as initially twisted/curved beams. An approach commonly adopted by the helicopter and wind turbine industry is the decouple it to a cross-sectional analysis for the beam constants and a 1D beam analysis. The best cross-sectional analysis which can capture initial curvature/twist effects is VABS . It only helps get the beam constants but also recover the 3D stress. A companion 1D beam anlysis is GEBT. As for the initially curved/twisted beams, there are couplings between the fundamental deformation modes of the beams. It seems the right alterative if you don't want to use the full blown 3D fea.
In reply to You can model your structure by Wenbin Yu
Late reply...
Hello Wenbin,
Thank you for your reply as well. I will look into your suggestions.
Regards,
mcgrete
In reply to Stress Distributions in Helical Compression Springs by Frank Richter
Late Reply...
Hello Frank,
I just received your notification on another thread regarding your answer here. Thank you.
I have not pursued the subject further. If/when I do, I will be happy to share my findings.
Thank you for the references.
FYI - I don't use such internet tools often, and am reluctant to sharing personal contact information due to some unfortunate unpleasent experiences in the past. Please forgive and understand; your response is much appreciated!