9 Contact Stresses

9.2 HERTZIAN CONTACT STRESSES 431
cient of friction was 0.1 or greater, the point of maximum shear stress occurs on the
contact surface rather than below it.
Example 9.4 Contact Stress in Cylinders with Friction Consider two steel
cylinders each 80 mm in diameter and 150 mm long mounted on parallel shafts
and loaded by a force F = 80 kN (Fig. 9-7). The two cylinders (E = 200 GPa
and ν = 0.29) are rotated at slightly different speeds so that the cylinder surfaces
slide across each other. If the coefficient of sliding friction is µ = 1 3 , determine the
maximum compressive principal stress σc, the maximum shear stress τmax, andthe
maximum octahedral shear stress τoct.
The value of the required quantities are obtained from Table 9-5 for µ = 1 3 ,
(σc)max =−1.40(b/) (1)
τmax = 0.435(b/) (2)
τoct = 0.368(b/) (3)
where b and are given by Eqs. (9.18a) and (9.18b) with with q = F/ℓ:
1 − ν2
= 2R
E = 2(0.040)(1 − 0.292 )
200 × 109 = 3.664 × 10 −13 m 3 /N (4)
1/2 2F 2(80 × 10
b =
=
ℓπ
3 )(3.664 × 10−13 )
= 0.3527 × 10
0.150π
−3 m
= 0.3527 mm (5)
b/ = 962.6MPa (6)
Figure 9-7: Example 9.4.