Read each question carefully. Remember to explain your solution as you go since design problems can be solved in a number of ways. It is acceptable to look things up in your textbook or on line, but be sure to provide a reference to any information that you use. Remember to state any assumptions that you make and provide a rationale for making them.

1. Shown below is a drum sander that both rotates and oscillates to provide a smooth sanding motion. This particular sander has a spindle speed of 1725 rpm and is rated at ½ hp.

The spindle oscillates vertically at a rate of 30 strokes per minute and travels +/- 1.0" for each stroke. The spindle is machined from 1018 steel and is secured by screwing the threaded end into the drive shaft and tightening it with a wrench, providing a solid connection. A 3" diameter 200 grit sanding drum is installed over the spindle (kinetic coefficient of friction of 0.75). The drums transmit loads to the spindle, but they do not provide additional strength.

If the user pushes the wood against the drum with a force of 5.0 lbf centered in the middle of the 6" spindle length (if it wasn't oscillating), answer the following:

A. Draw a free body diagram, shear and moment diagrams, and graph the loads on the spindle for a few sanding cycles. Label the maximum and minimum values.

B. Determine if the spindle has infinite fatigue life. If not, determine the number of cycles to failure. Also determine the safety factor for first cycle yield.

2. Shown in the drawing below is the drive system for a cast removal saw, a shaft machined from 1018 steel and supported by two bearings.

This type of saw cuts using a circular blade that oscillates in a small arc at approximately 5,000 strokes per minute rather than one that spins continuously.

This motion is created using a mechanism that inputs an oscillating torque onto the end of the shaft. Cutting a cast produces an alternating force, F, at the blade's outer edge, as shown in the diagram.

If the oscillating force F = +/- 5 lbf acts in the direction shown, answer the following:

A. Draw a free body diagram, shear and moment diagrams, and graph the loads on the shaft for a few oscillations. Label the maximum and minimum values.

B. Determine if the shaft has infinite fatigue life. If not, determine the number of cycles to failure. Also determine the safety factor for first cycle yield.