1. Contact Stress (3.19) MAE 316 – Strength of Mechanical Components
NC State University Department of Mechanical and Aerospace Engineering
Contact Stress

2. Introduction Where does contact stress occur?
Ball bearings
Railroad wheel on a track
Bowling ball on an alley
Want to find the local stress at the point (region) of contact.
This will depend on elasticity of contacting materials (E & ν), loading, and geometry.
Contact Stress

3. Spherical Contact Surfaces (3.19)
Where a = radius of circular contact area and po = pmax = maximum pressure.
Contact Stress

4. Spherical Contact Surfaces (3.19)
For spheres in contact, the contact patch is circular (radius a).
Where:
F = force pressing the two spheres together
d1 and d2 = diameters of the two solid spheres in contact
E1, ν1, E2, ν2 = respective elastic constants of the two spheres
Contact Stress

5. Spherical Contact Surfaces (3.19)
The maximum contact pressure is
The stress distribution is
Contact Stress

6. Spherical Contact Surfaces (3.19)
Figure 3-37 in the textbook shows the magnitude of the stress components below the surface as a function of pmax of contacting spheres with ν = 0.3.
Contact Stress

7. Cylindrical Contact Surfaces (3.19)2b l
Where b = half-width of rectangular contact area and po = pmax = maximum pressure.
Contact Stress

8. Cylindrical Contact Surfaces (3.19)
For cylinders in contact, the contact patch is rectangular (half-width b).
Where:
l = length of contact area
F = force pressing the two spheres together
d1 and d2 = diameters of the two solid spheres in contact
E1, ν1, E2, ν2 = respective elastic constants of the two spheres
Contact Stress

9. Cylindrical Contact Surfaces (3.19)
The maximum contact pressure is
The stress distribution is
Contact Stress

10. Cylindrical Contact Surfaces (3.19)
Figure 3-39 in the textbook shows the magnitude of the stress components below the surface as a function of pmax of contacting cylinders with ν = 0.3.
Contact Stress

11. Example
Two carbon steel balls, each 30 mm in diameter, are pressed together by a force F. Find the maximum values of the principal stress and the maximum shear stress if F = 50 N, ν = 0.3, and E = 207 GPa.
Contact Stress