Research Papers

Consistent Derivations of Spring Rates for Helical Springs

[+] Author and Article Information
Clive L. Dym

Department of Engineering, Harvey Mudd College, 301 Platt Boulevard, Claremont, CA 91711clive_dym@hmc.edu

J. Mech. Des 131(7), 071004 (Jun 04, 2009) (5 pages) doi:10.1115/1.3125888 History: Received October 27, 2008; Revised March 31, 2009; Published June 04, 2009

The spring rates of a coiled helical spring under an axial force and an axially directed torque are derived by a consistent application of Castigliano’s second theorem, and it is shown that the coupling between the two loads may not always be neglected. The spring rate of an extensional spring is derived for the first time through the use of the displacement based principle of minimum total potential energy. The present results are also compared with available derivations of and expressions for the stiffness of a coiled spring.

Copyright © 2009 by American Society of Mechanical Engineers
Topics: Springs , Force , Stress
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Grahic Jump Location
Figure 1

(a) An axially loaded helical spring and (b) the coordinate systems for the spring and a face at a point P along the centerline of the coil. The pitch of the spring coil is given by p=2πR tan α.

Grahic Jump Location
Figure 2

The dominant part of the extension δext=(f110+fshear)F≅f110F of a helical extensional spring is due to the twist φ of a section of a rod that results from the downward force F that creates the torque FD/2



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