Research Papers: Design Automation

Enhanced Formulae for Determining Both Free Length and Rate of Cylindrical Compression Springs

[+] Author and Article Information
Manuel Paredes

Institut Clément Ader (ICA),
Université de Toulouse,
CNRS FRE 3687,
135, avenue de Rangueil,
Toulouse F-31077, France
e-mail: manuel.paredes@insa-toulouse.fr

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received July 29, 2015; final manuscript received November 10, 2015; published online December 16, 2015. Assoc. Editor: Massimiliano Gobbi.

J. Mech. Des 138(2), 021404 (Dec 16, 2015) (6 pages) Paper No: MD-15-1537; doi: 10.1115/1.4032094 History: Received July 29, 2015; Revised November 10, 2015

Cylindrical compression springs have been commonly exploited in mechanical systems for years and their behavior is considered as well identified. Nevertheless, it appears that, even though old research studies suggest correcting the rate formula, the main industrial software dedicated to spring design exploits the uncorrected one. In order to evaluate the accuracy of the analytical formulae for spring behavior, an experimental study was performed, which tried to cover the common design space. This study was done using the two common coil ends: closed and ground ends, and closed and not ground ends. Moreover, the accuracy of the load–length relation was investigated whereas older studies focused only on the spring rate. It appears that the common uncorrected formulae give satisfactory results only when large numbers of coils are involved. We also highlight, for the first time, that it is interesting to correct not only the spring rate but also the free length of the spring.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.


Xie, L. , and Cai, M. , 2015, “ Development of a Suspended Backpack for Harvesting Biomechanical Energy,” ASME J. Mech. Des., 137(5), p. 054503. [CrossRef]
Vazquez-Gonzalez, B. , and Silva-Navarro, G. , 2008, “ Evaluation of the Autoparametric Pendulum Vibration Absorber for a Duffing System,” Shock Vib., 15(3–4), pp. 355–368. [CrossRef]
Wu, Y.-S. , and Lan, C.-C. , 2014, “ Linear Variable-Stiffness Mechanisms Based on Preloaded Curved Beams,” ASME J. Mech. Des., 136(12), p. 122302. [CrossRef]
Bukowski, J. V. , Gross, R. E. , and Goble, W. M. , 2014, “ Investigation of Adhesion Formation in New Stainless Steel Trim Spring Operated Pressure Relief Valves,” ASME J. Mech. Des., 136(6), p. 061602.
“  The Spring Manufacturing Institute,” Spring Manufacturers Institute, Inc., Oak Brook, IL, www.smihq.org
The Institute of Spring Technology, Sheffield, UK, www.ist.org.uk/index.html
Lee Spring Company, “  Customizable Online Spring Calculators,” http://www.planetspring.com
Spring-I-pediA, “ Counting Coils,” http://springipedia.com/compression-counting-coils.asp
Wahl, A. M. , 1963, Mechanical Springs, McGraw-Hill, New York.
Rodriguez, E. , Paredes, M. , and Sartor, M. , 2006, “ Analytical Behavior Law for a Constant Pitch Conical Compression Spring,” ASME J. Mech. Des., 129, pp. 1352–1356. [CrossRef]
Paredes, M. , 2013, “ Analytical and Experimental Study of Conical Telescoping Springs With Nonconstant Pitch,” ASME J. Mech. Des., 135(9), p. 094502. [CrossRef]
Pearson, D. , 1982, “ The Transfer Matrix Method for the Vibration of Compressed Helical Springs,” J. Mech. Eng. Sci., 24(4), pp. 163–171. [CrossRef]
Yildirim, V. , 1999, “ An Efficient Numerical Method for Predicting the Natural Frequencies of Cylindrical Helical Springs,” Int. J. Mech. Sci., 41(8), pp. 919–939. [CrossRef]
Dym, C. , 2009, “ Consistent Derivations of Spring Rates for Helical Springs,” ASME J. Mech. Des., 131(7), p. 071004. [CrossRef]
Lee Spring Company, 2010, “ An Introduction to Compression Springs,” https://www.youtube.com/watch?v=5xYk7_YwbEg
Vogt, R. F. , 1934, Number of Active Coils in Helical Springs, ASME, New York, pp. 467–476.
Pletta, D. H. , Smith, S. C. , and Harrison, N. W. , 1936, “ The Effect of Overstrain on Closely Coiled Helical Springs and the Variation of the Number of Active Coils With Load,” Bull. Va. Polytech. Inst., 29(8), pp. 13–29.
Keysor, H. C. , 1940, “ Calculation of the Elastic Curve of a Helical Compression Spring,” Trans. ASME, 62(4), pp. 319–326.
European Standard NF EN 13906-1, 2013, “Cylindrical Helical Springs Made From Round Wire and Bar—Calculation and Design—Part 1: Compression Springs,” pp. 14–15.
Andilog Technologies, “ Manual Spring Tester: Springtest 1,” http://www.andilog.com/springtest-manual-spring-tester.html?category_id=14


Grahic Jump Location
Fig. 1

Compression springs with nf = 9 and nT = 11

Grahic Jump Location
Fig. 2

Experimental and analytical load–length relations for compression springs

Grahic Jump Location
Fig. 3

Details of the experimental setup and measuring system

Grahic Jump Location
Fig. 4

Details on the lengths and loads used to evaluate the individual error, e, related to configuration CG9

Grahic Jump Location
Fig. 5

Individual errors, e, obtained with the common formulae

Grahic Jump Location
Fig. 6

Individual errors, e, obtained with rate correction

Grahic Jump Location
Fig. 12

Individual errors, e, obtained with bilinear correction

Grahic Jump Location
Fig. 10

Individual errors, e, obtained with rate and length correction

Grahic Jump Location
Fig. 9

Individual errors, e, obtained with rate correction

Grahic Jump Location
Fig. 8

Individual errors, e, obtained with common formulae

Grahic Jump Location
Fig. 7

Individual errors, e, obtained with rate and length correction

Grahic Jump Location
Fig. 11

Experimental load–length curves for reference CNG1



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In