Designing a Shaft for 500 W of Power

[ganondorf29]

Homework Statement

I'm supposed to design and analyze a shaft including all features to retain the shaft in the bearings and attach the coupling and sheave and the shaft shouldn't fail in static loading or through fatigue.

Homework Equations

3

-The flexible coupling attaches your shaft to the shaft of a driving motor. The motor shaft has a diameter of 0.4997” +0.0000 / -0.0005”.
- The pillow blocks can be aligned parallel to no better than 25 micrometers.
- The sheave can be of your choosing, but should have a diameter of about 150 mm.
- The shaft rotates at 1200 RPM while transmitting approximately 500 W of power

The Attempt at a Solution

So far all I've done is found the torque.

Power = Torque * $$\omega$$

500 = T*(1200rpm*(2pi/60))
T = 3.97887 N*mI'm not exactly sure where to move from here. I attached a copy of what I think the free body diagram is. Is my FBD correct and where should I go from here?

 

[Valkarie]

Yes, your free body diagram is correct. Now that you have the torque, you can use it to determine the necessary size of the shaft. You will need to take into account the forces that will be acting on the shaft due to its rotation as well as the load that it will be transmitting. You can begin by calculating the maximum bending moment and shear force in the shaft due to the torque. The maximum bending moment is given by: M = T*r, where T is the torque and r is the radius of the shaft. The maximum shear force is given by: F = T/L, where T is the torque and L is the length of the shaft. Once you have determined the maximum bending moment and shear force, you can then calculate the minimum required diameter of the shaft. You can do this using basic beam theory and applying the equations for maximum stress and deflection. You will also need to consider the bearing loads that will be acting on the shaft due to its rotation. You can calculate the radial and thrust loads on each bearing using the equations for a uniform load. Finally, you will need to consider fatigue loading. You can do this by calculating the maximum number of cycles that the shaft will experience before it fails. This will help you determine the fatigue strength of the shaft material that you need to use.