A configuration of a power distribution shaft is shown in Figure 1. The main shaft with a stepped configuration will be machined with AISI 1020CD rod stock. During normal operation, the shaft will rotate at 200 rpm. Pulley A receives 10 hp from below. Gear C delivers 6 hp to the mating gear below it. Chain sprocket D delivers 4 hp to a shaft above. It is known that the force in the high tension side of the flat belt on pulley A is about 3 times the force in the low- tension side. The force in the low tension side of the chain on the sprocket D is close to zero. Roller bearing D₁ DE Roller bearing P₁=3P2 D 20 in dia. Jflat-belt pulley 10 in dia. spur gear 20°FD -6 in dia. chain sprocket S=0 S 41 C driven by Q P₂ Figure 1. Configuration of power distribution shaft¹. Interaction force between Gear C and D is shown in Figure 2. The force exerted on the gear tooth makes a 20 degree angle (Pressure Angle) with the tangential direction of the gear. 2 of 2 Gear C Gear C 20° Ө 20° Fca Gear Q Gear Q Design Analysis Tasks: Figure 2. Interaction force between Gear C and Q. Analysis should be conducted to determine the appropriate diameters D1 and D2, and fillet radius for all steps. Detailed analysis should be provided to show that shaft is safe against yielding and fatigue failure (infinite life using Modified Goodman criteria). Use a factor-of- safety value of 2 for both yielding and fatigue analysis. Check deflection of shaft: the defection at point C should less than 0.01 inch; the slope at roller bearing locations (B and E) should be less than 0.002 radian. The diameters should be adjusted if the deflection requirement is not satisfied. Assume gear C and sprocket D are coupled to the shaft via key. Size the size using the factor of safety of 1.5. Estimate the critical speed of the shaft/gear assembly. Assume A, C, D weigh 20, 10, and 5 lbs, respectively.