In the fatigue testing machine of Problem 17.9, the same cylinder is used, but the toroid is replaced by a second toroid, where R1 = ∞, R'1 = 32 mm, R2 = 12.8 mm, and R'2 = 32 mm. Use the same steel properties as in Problem 17.9.
a. Determine σmax for fatigue failure at approximately N = 109 cycles. Neglect size effects and assume that fatigue failure is governed by the maximum range 2τ0 of the orthogonal shear stress.
b. Determine the required load P. Since α = 0 and R'1 and R'2 lie in the x-z plane (see Figure 17.5), a (the major semiaxis of the ellipse) lies in the direction of rolling.
A fatigue testing machine used to determine fatigue life under rolling contact consists of a steel toroid (body 2) rolling on a steel cylinder (body 1), where R1 = 32 mm, R'1 = ∞, R2 = 32 mm, and R'2 = 20 mm. For steel, E = 200 GPa and v = 0.29.
a. Determine an expression for σmax in terms of P.
b. Fatigue test results indicate that fatigue failure occurs at approximately N = 109 cycles with σmax = −2758 MPa. Determine the applied load P. Since α = 0 and R1, and R2 lie in the x-z plane (see Figure 17.5), b (the minor semiaxis of the contact eclipse) is in the direction of rolling.
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