Technical Briefs

Correction to Design Equation for Spring Diametral Growth Upon Compression

[+] Author and Article Information
T. S. Bockwoldt

Naval Reactors,
1240 Isaac Hull Avenue,
Washington, DC 20376
e-mail: Bockwoldt@cox.net

G. A. Munsick

Bettis Atomic Power Laboratory,
814 Pittsburgh McKeesport Boulevard,
West Mifflin, PA 15122
e-mail: Greg_Munsick@hotmail.com

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received December 23, 2012; final manuscript received July 15, 2013; published online September 18, 2013. Assoc. Editor: Chintien Huang.

J. Mech. Des 135(12), 124503 (Sep 18, 2013) (4 pages) Paper No: MD-12-1622; doi: 10.1115/1.4025195 History: Received December 23, 2012; Revised July 15, 2013

In the textbook by Wahl (1963, Mechanical Springs, 2nd ed., McGraw-Hill, New York, Chap. 20), he derived an equation predicting the diametral growth of a helical spring as the spring is compressed from free to solid height, and the spring's ends are free to rotate. A recent comparison with test data for growth of compression springs revealed that the calculated growth predicted by the Wahl formula did not agree well with measured values. Review of the Wahl derivation uncovered an arithmetic error that, when corrected, brought the calculated and measured diameters into closer agreement. The corrected diametral growth equation presented herein bounds the original data provided by Wahl, better matches an alternate growth equation derived by Ancker and Goodier for most springs evaluated, predicts larger growth than the original Wahl equation, and is a better fit to recent measured data.

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Wahl, A. M., 1963, Mechanical Springs, 2nd ed., McGraw-Hill, New York, Chap. 20.
Watanabe, K., Yamamoto, H., Ito, Y., and Isobe, H., 2007, “Simplified Stress Calculation Method for Helical Spring,” Proceedings of Advanced Spring Technology JSSE (Japan Society of Spring Engineers) 60th Anniversary International Symposium, Paper 4.
Ancker, C. J., Jr., and Goodier, J. N., 1958, “Pitch and Curvature Corrections for Helical Springs,” J. Appl. Mech., 25(4), p. 468.
Wahl, A. M., 1953, “Diametral Expansion of Helical Compression Springs During Deflection,” J. Appl. Mech., 20(4), pp. 565–566.
Love, A. E. H., 1944, A Treatise on the Mathematical Theory of Elasticity, 4th ed., Dover, New York, pp. 414–415.
Wahl, A. M., 1959, “Pitch and Curvature Corrections for Helical Springs,” J. Appl. Mech., 26(2), pp. 312–313.
Zubek, L., ed., 2007, SMI Handbook of Spring Design, Spring Manufacturers Institute, Oak Brook, IL, p. 37.


Grahic Jump Location
Fig. 2

Spring diametral growth versus (p − d) tan α0



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