Results available in the literature for the problem of two contacting bodies, suffering Hertzian contact and with an assumed proportional shear, are reviewed. The general case of the problem, when the axes of the contact patch are unequal, is studied, and the resulting stresses deduced in their most convenient and closed form. An example of the use of these results, in deducing the elastic limit, is given.
Get full access to this article
View all access options for this article.
References
1.
SackfieldA.HillsD. A.Some useful results in the classic Hertz problem’, J. Strain Analysis, 1983, 18, 101–105 (This issue).
2.
CattaneoC.‘Sul contatto di due corpi elastic’, Accad. Lincei, Rendi conti, 1938, 27 (Ser. 6), 342–348, 434–436, 474–478.
3.
DeresiewiczH.‘Oblique contact of nonspherical elastic bodies’, J. appl. Mech, 1957, 79, 623–624.
4.
JohnsonK. L.‘The effect of a tangential contact force upon the rolling motion of an elastic sphere on a plane’, J. appl. Mech., 1958, 80, 334–346.
5.
HainesD. J.OllertonE.‘Contact stress distributions on elliptical contact surfaces subjected to radial and tangential forces’, Proc. Instn mech. Engrs, 1963, 177, 95–114.
6.
PoritskyH.‘Stress and deflexions of cylindrical bodies in contact with application to contact of gears and of locomotive wheels’, J. appl. Mech., 1950, 72, 191–201.
7.
SmithJ. O.LiuC. K.‘Stresses due to tangential and normal loads on an elastic solid with application to some contact stress problems’, J. appl. Mech., 1953, 75, 157–166.
8.
JohnsonK. L.JefferisJ. A.‘Plastic flow and residual stresses in rolling and sliding contact’ inSymposium on Fatigue Rolling Contact, 1963 (IMechE, London) pp. 54–65.
9.
HamiltonG. M.GoodmanL. E.‘The stress field created by a circular sliding contact’, J. appl. Mech., 1966, 33, 371–376.
10.
HillsD. A.AshelbyD. W.‘The influence of residual stresses on contact load bearing capacity’, Wear, 1982, 75, 221–240.
11.
VermeulenP. J.JohnsonK. L.‘Contact of nonspherical elastic bodies transmitting tangential forces’, J. appl. Mech., 1964, 86, 338–340.
12.
LoveA. E. H.The mathematical theory of elasticity (4th edition) 1952 (Cambridge University Press).
