9 Contact Stresses

424
The maximum compressive stress becomes
σc = 0.579nc
F/(K 2 γ 2 1/3 )
40 000
= 0.579 × 0.9964
0.39382 × 9.1592 × 10−24 1/3 The rigid approach of the two bodies is given as
d = 0.825nd(F 2 γ 2 /K ) 1/3
40 000
= 0.825(0.9964)
2 × 9.1592 × 10−24 1/3 0.3938
CONTACT STRESSES
= 838.8 MPa (16)
= 0.05742 mm (17)
Example 9.2 Ball Bearing At the contact region of the ball bearing system
shown in Fig. 9-6, find the maximum principal stress, the maximum shearing stress,
the maximum octahedral shearing stress, the dimensions of the area of contact,
and the distance from the point of contact to the point along the force direction
where the stresses occur. Assume that E = 200 GN/m 2 and ν = 0.3.
Figure 9-6: Single-row ball bearing system: r = 20 mm; d0 = 38 mm; c denotes the center
of curvature for r.