Page 62 - Mechanical Engineer's Data Handbook

STRENGTHS OF MATERIALS 51

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1.9 Contact stresses

When a ball is in contact with a flat, concave or convex rectangular contact area of very small width. The
surface, a small contact area is formed, the size of the following gives the size of these areas and the maxi-
area depending on the load and materials. In the case mum stress for several common cases. The theory is of
of a roller, a line contact is obtained, giving a great importance in the design of rolling bearings.

I .9. I Contact stresses for balls and
rollers

Symbols used:
E,, E,=Young’s moduli
F = load
r, , r2 =radii
vl, v2 = Poisson’s ratio
Two balls in contact
Contact area radius a = t w

Contact stress a, = 3F/2na2

Ball on frat surface, same material: r2=co, rl=r

Two balls in contact, same material: E, =E2, v1 = v2