9 Contact Stresses
9 Contact Stresses
9 Contact Stresses
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TABLE 9-2 Formulas for <strong>Contact</strong> <strong>Stresses</strong> 439<br />
TABLE 9-2 FORMULAS FOR CONTACT STRESSES, DIMENSIONS, AND CONTACT AREAS, AND RIGID-BODY<br />
APPROACHES a<br />
Notation<br />
γ = (1 − ν 2 1 )/E1 + (1 − ν 2 2 )/E2<br />
a, b = semimajor axis and semiminor axis of contact ellipse, respectively<br />
d = rigid distance of approach of contacting bodies or surface deformation<br />
Ei = modulus of elasticity of object i, i = 1or2<br />
F = force<br />
p = pressure<br />
q = distributed line load<br />
σc = maximum compressive stress of contact area, = (σc)max<br />
νi = Poisson’s ratio of object i, i = 1or2<br />
τ = shear stress<br />
Case Formulas<br />
1a.<br />
Sphere on sphere<br />
K = D1 D2<br />
D1+D2<br />
a = b = 0.721(FKγ) 1/3<br />
σc = 0.918[F/(K 2 γ 2 )] 1/3<br />
d = 1.040(F 2 γ 2 /K ) 1/3<br />
Spheres
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