Contact Mechanics by K. L. Johnson

By K. L. Johnson

This treatise is worried with the stresses and deformation of strong our bodies involved with one another, alongside curved surfaces which contact at first at some degree or alongside a line. Examples are a railway wheel and rail, or a couple of substances wheel the teeth. Professor Johnson first reports the advance of the speculation of touch stresses because the challenge used to be initially addressed by way of H. Hertz in 1882. subsequent he discusses the impact of friction and the topographical roughness of surfaces, and this can be included into the idea of touch mechanics. a major characteristic is the remedy of our bodies which deform plastically or viscoelastically. as well as desk bound touch, an considerable component of the booklet is anxious with our bodies that are in sliding or rolling touch, or which collide.

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Contact Mechanics

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Example text

The displacement 53 Pressure applied to a polygonal region at B due to the pressure distributed over the whole of S is thus: uz = I-V'! 19). Pressure applied to a polygonal region (a) Unifonn pressure We shall consider in this section a uniform pressure p applied to a region of the surface consisting of a straight-sided polygon, as shown in Fig. 3(a). It is required to find the depression Uz at a general point B(x, y) on the surface and the stress components at a sub3urface point A(x ,y, z), BHh BB2 • etc.

237 and are plotted in curves E, F and H in fig. 13(a and b). 61). 5 in Fig. 14, where it is compared with the pressure distribution in the absence of friction. Fig. 14. 5). 0 " A / .... 6 ,'" I / / "8 With friction (eq. 0 01 . ~ o . 0 xla Line loading of an elastic half-space 42 The punch is moving from right to left so that the effect of friction is to reduce the pressure in the front half of the punch and to increase it on the rear. In this case also it is apparent that the influence of frictional traction upon the normal pressure is relatively small.

The principal shear stress has the value p . 29) a 1r Expressed in this form it is apparent that contours of constant principal stress and constant Tl are a family of circles passing through the points 0 1 and O2 as shown in Fig. 7(a) and by the photoelastic fringes in Fig. 6(b). The principal shear stress reaches a uniform maximum value p/tr along the semi-circle Q: = tr12. The trajectories of principal stress are a family of confocal eHipses and hyperbolae with foci 0, and 0, as shown in Fig.

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