A helical spring that is constrained to no rotation has a compliance that is typically more than 95% of the compliance of springs constrained to free rotation when restricted to symmetric wires made from materials with Poisson’s ratio between 0 and 1/2. It is shown that the shape of the spring wire can be designed so the spring will not twist when it is extended nor extend when it is twisted. The constrained spring versus a freely rotating spring with the helix angle equal to has the largest reduction in compliance in the limits of beam theory. Spring compliances for torsion and extension with quite complex helical spring geometries are found to be related by a dimensionless ratio of compliances in a very simple equation that only depends on Poisson’s ratio and the helical, spring angle, . Springs made from materials with negative Poisson’s ratio, however, can have a very substantial reduction in compliance; the no rotation compliance is zero when Poisson’s ratio is −1. There are large changes in spring compliances for springs with geometric coils that are elongated rectangles or flattened ellipses.
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November 2011
Research Papers
The Relation Between Helical Spring Compliances With Free and Fixed End Rotations
S. J. Burns
S. J. Burns
Department of Mechanical Engineering, Materials Science Program, Hajim School of Engineering and Applied Sciences,
e-mail: burns@me.rochester.edu
University of Rochester
, Rochester, NY 14627-0133
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S. J. Burns
Department of Mechanical Engineering, Materials Science Program, Hajim School of Engineering and Applied Sciences,
University of Rochester
, Rochester, NY 14627-0133e-mail: burns@me.rochester.edu
J. Appl. Mech. Nov 2011, 78(6): 061005 (5 pages)
Published Online: August 24, 2011
Article history
Received:
June 24, 2010
Revised:
February 28, 2011
Published:
August 24, 2011
Citation
Burns, S. J. (August 24, 2011). "The Relation Between Helical Spring Compliances With Free and Fixed End Rotations." ASME. J. Appl. Mech. November 2011; 78(6): 061005. https://doi.org/10.1115/1.4003739
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