The Differential Geometry of the General Helix as Applied to Mechanical Springs

[+] Author and Article Information
Yuyi Lin, Albert P. Pisano

Mechanical Engineering Department, University of California, Berkeley, CA 94720

J. Appl. Mech 55(4), 831-836 (Dec 01, 1988) (6 pages) doi:10.1115/1.3173729 History: Received January 01, 1988; Revised April 29, 1988; Online July 21, 2009


In order to improve the performance of helical springs, such as increasing the fatigue life and suppressing resonance, variable pitch angle and variable helix radius may be incorporated into the helical spring geometry. Employing the tool of differential geometry, new and complete formulae of curvature, torsion, and spring force are derived. It is shown that these formulae are more general and accurate than Kelvin’s curvature and torsion formulae, than commonly used force formulae (Wahl, 1963). Possible simplifications to the complete formulae and the corresponding errors introduced are both discussed and compared with experimental data.

Copyright © 1988 by ASME
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