Coefficient of Restitution Interpreted as Damping in Vibroimpact

[+] Author and Article Information
K. H. Hunt

Monash University, Clayton, Victoria, Australia

F. R. E. Crossley

Department of Mechanical Engineering, University of Massachusetts, Amherst, Mass.

J. Appl. Mech 42(2), 440-445 (Jun 01, 1975) (6 pages) doi:10.1115/1.3423596 History: Received May 01, 1974; Revised August 01, 1974; Online July 12, 2010


During impact the relative motion of two bodies is often taken to be simply represented as half of a damped sine wave, according to the Kelvin-Voigt model. This is shown to be logically untenable, for it indicates that the bodies must exert tension on one another just before separating. Furthermore, it denotes that the damping energy loss is proportional to the square of the impacting velocity, instead of to its cube, as can be deduced from Goldsmith’s work. A damping term λxn ẋ is here introduced; for a sphere impacting a plate Hertz gives n = 3/2. The Kelvin-Voigt model is shown to be approximated as a special case deducible from this law, and applicable when impacts are absent. Physical experiments have confirmed this postulate.

Copyright © 1975 by ASME
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