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.

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Fig. 1

Compression springs with nf = 9 and nT = 11

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Fig. 2

Experimental and analytical load–length relations for compression springs

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Fig. 3

Details of the experimental setup and measuring system

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Fig. 4

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

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Fig. 5

Individual errors, e, obtained with the common formulae

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Fig. 6

Individual errors, e, obtained with rate correction

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Fig. 7

Individual errors, e, obtained with rate and length correction

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Fig. 8

Individual errors, e, obtained with common formulae

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Fig. 9

Individual errors, e, obtained with rate correction

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Fig. 10

Individual errors, e, obtained with rate and length correction

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Fig. 11

Experimental load–length curves for reference CNG1

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Fig. 12

Individual errors, e, obtained with bilinear correction




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