9 Contact Stresses

TABLE 9-1 SUMMARY OF GENERAL FORMULAS FOR CONTACT
STRESSES
A = 1
1R1 4 + 1 R2
B = 1 4
Notation
Ri, R ′ i = minimum and maximum radii of curvature
of two contacting surfaces i = 1, 2
F = applied force
θ = angle between planes containing principal radii
of curvature
1
+
R ′ +
1
1
R ′
2
1R1
1
−
R ′
1R2
1
+ −
1
R ′ 2
1R1
1
− 4 −
2
R ′
1R2
1
−
1
R ′
sin
2
2 1/2 θ
1
+
R ′ +
1
1
R ′
2
1R1
1
−
R ′
1R2
1
+ −
1
R ′ 2
1R1
1
− 4 −
2
R ′
1R2
1
−
1
R ′
sin
2
2 1/2 θ
− 1 4
1R1 + 1 R2
+ 1 4
Compute B/A and obtain coefficients Cb, k, Cσ , Cτ , Coct, Cz, Cd from plots of Figs. 9-3
or 9-4. Then
Semiminor axis:
Semimajor axis:
Maximum compressive stress:
Maximum shear stress:
γ = 1−ν2 1
E1 + 1−ν2 2
E2
= γ 1
A+B
Formulas for Stresses and Deformation
b = Cb(F) 1/3
a = b/k
(σc)max =−Cσ (b/)
τmax = Cτ (b/)
Maximum octahedral shear stress:
(τoct)max = Coct(b/)
Distance from contact area to location of maximum shear stress:
Zs = Czb
Distance of approach of contacting bodies:
d = Cd F π A+B
b/
438 TABLE 9-1 Summary of General Formulas for Contact Stresses