By A. Sackfield, D A. Hills and D. Nowell (Auth.)
Fabrics and mechanical engineering researchers learning put on, fretting, elastic indentation trying out and different tribological techniques usually desire closed-form recommendations for varied attributes of contacts. those features comprise touch legislations, strain distribution, inner kingdom of pressure caused and the impression of friction.
fabrics and mechanical engineering researchers learning put on, fretting, elastic indentation checking out and different tribological procedures often desire closed-form options for numerous attributes of contacts. those features comprise touch legislations, strain distribution, inner country of rigidity brought on and the impression of friction. those ideas, scattered through the utilized mechanics literature, are tough to find, are offered utilizing various resolution options, and express
results in a fashion that's compatible just for specialists within the box. `Mechanics of Elastic Contacts' makes use of a constant set of recipes for the answer of all suitable difficulties, offers leads to the easiest attainable varieties, and includes summaries using
tabulated info. This reference resource will offer a transparent advisor to elastic contacts for engineering designers, fabrics scientists and tribologists regardless of their point of craftsmanship during this vital subject.
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Example text
No surface shear tractions must arise. This may be realized in one of two ways. e. the cylinders must be smooth. 18 vanishing. e. 15). In these cases we expect the pressure to fall continuously to zero at each end of the contact, and hence require a solution for p(x) which is both symmetrical and bounded (see Chapter 5). 2). 27 is given by *>--;>-«MS r ar .! V ( l - r 2 ) ( r - s ) -(T)^-«1' and the consistency equation is satisfied identically. e. p = Po\" V[1-(*/a)2]dx = ^ . 31) and '-isr <232) thereby enabling the peak contact pressure, p 0 , and the contact semi-width, a, to be found directly.
Problems where the size of the contact patch is small in comparison with bodies' surface radius of curvature, and which therefore permit the half-plane or half-space approximation to be used, are said to be non-conformal. An example of an incomplete contact where the use of a half-plane approximation is not valid is that occurring between a pin pressed radially into an almost conforming hole. In this case the contact width Essential solid mechanics 41 is not negligible in comparison with the radius of the hole (or pin), and hence it will be necessary to use a formulation appropriate to an infinite plane containing a hole, and to a disk.
Thus, all pairs of materials yielding the same values of A and ß will have the same solution to the contact problem. In particular, therefore, we may always choose one body to be rigid, without loss of generality, providing that the elastic constants of the other body are adjusted appropriately. This process may be adopted when formulating any contact problem, as it is often conceptually easier to visualize the indentation process when the deformation is accommodated entirely within one body. Plane contacts: surface tractions 53 If one body is rigid, ß will take the value in which form it appears in the work of Spence (1968, 1973), denoted by y.