(Solution) - A schematic of a clutch testing machine is shown The steel -(2025 Original AI-Free Solution)

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A schematic of a clutch-testing machine is shown. The steel shaft rotates at a constant speed ?. An axial load is applied to the shaft and is cycled from zero to P. The torque T induced by the clutch face onto the shaft is given by
T = f P(D + d)/4
Where D and d are defined in the figure and f is the coefficient of friction of the clutch face. The shaft is machined with Sy = 120 kpsi and Sut = 145 kpsi. The theoretical stress-concentration factors for the fillet are 3.0 and 1.8 for the axial and torsional loading, respectively. Assume the load variation P is synchronous with shaft rotation. With f = 0.3, find the maximum allowable load P such that the shaft will survive a minimum of 106 cycles with a factor of safety of 3. Use the modified Goodman criterion.