(Solved): A schematic of a clutch-testing machine is shown. The steel shaft rotates at a constant speed ...

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 $$T=\frac{fP(D+d)}{4}$$ 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 $$S_y=800\mathrm{MPa}$$ and $$S_{ut}=1000\mathrm{MPa}$$. The theoretical stress concentration factors for the fillet are $$3.0$$ and $$1.8$$ for the axial and torsional loading, respectively. (a) 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 $$10^6$$ cycles with a factor of safety of 3 . Use the modified Goodman criterion. Determine the corresponding factor of safety guarding against yielding. (b) Suppose the shaft is not rotating, but the load $$P$$ is cycled as shown. With $$f=0.3$$, find the maximum allowable load $$P$$ so that the shaft will survive a minimum of $$10^6$$ cycles with a factor of safety of 3. Use the modified Goodman criterion. Determine the corresponding factor of safety guarding against yielding. $$\begin{array}{l}=16.1\mathrm{kN},\mathrm{N}=5.69\\ =51.4\mathrm{kN},\mathrm{N}=3.87\text{ Ans }\end{array}$$