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

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

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

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

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

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

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

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

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

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

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