# Section 3

**Equipment (per team of 2 people):**

2x bearing mounts

1x 12” by ¼” shaft

Two flywheels (DO NOT REMOVE FROM 311)

1x motor mount

3x right angle mounts

1x 80-20

1x flywheel hub

Assorted nuts and bolts

8-32 nuts and bolts

2 calipers (1 per person)

**Part 1 -- Calculations and free body diagram:**

Using the masses provided for your flywheel, hub, and shaft, compute the equivalent inertia of your total motor and shaft assembly.

Compute the time constant to reach steady state speed.

Draw a free body diagram of your motor and bearing assembly. Let’s assume that the shaft coupler is perfectly aligned and does not generate any radial forces on the shaft.

Clearly label the bearing to bearing spacing as L_BD, and the distance from the base bearing to the flywheel as L_tot.

Using the equations for static equilibrium (sum of forces and sum of moments = 0) write an equation that solves for the bearing forces as a function of system parameters.

Write an equation for the frictional torque from the bearings assuming a coefficient of friction . (Don’t forget the shaft radius is needed for the frictional torque).

Write the equation relating steady state speed and friction.

Make a copy of the spreadsheet template provided here.

Fill in the necessary values for your kit on the

*Hardware parameters*tab.In the part 1 tab, implement a formula that computes the coefficient of friction (as derived in step 6) as a function of the provided sample data and your motor parameters. You should compare your calculated coefficient with the real coefficient in the adjacent column and verify your calculation is the same.

**Part 2 -- Kit Assembly:**

Build the bearing and shaft assembly. On a single piece of 80-20 mount three right angle brackets (with the face of the long side mounted to the 80-20).

Mount two bearing mounts to the middle and right side angle bracket. Mount the motor mount to the left side angle bracket.

Insert the motor in the motor mount and tighten in place with a nut and bolt.

Mount the shaft coupler to the motor. Do your best to align the coupler so that it is co-aligned with the motor shaft. Tighten the set screw to fix to motor.

Insert the shaft into the two bearings and into the shaft coupler. Tighten the coupler set screw.

Place the flywheel hub onto TWO flywheels and insert four screws loosely, do not tighten yet.

Place the flywheel and hub onto the end of the shaft and tighten the flywheel hub set screw prior to tightening the four mounting screws.

Wire up your Arduino and motor driver with the following connections:

**Part 3 -- Steady-state speed measurements for varied bearing spacing:**

Download the provided Arduino code here and upload it to your Arduino with a motor value of 0.

This code runs your motor at the designated PWM duty cycle and then prints the average

**counts/s**every 1 second.

In this section we will only be moving the right side bearing that is closest to the flywheel. Keep the motor position and the left bearing fixed.

Perform a series of measurements of steady state speed at different bearing spacings for a constant PWM duty factor (choose 75 to keep vibrations low). Be sure to use the specified bearing distances in the spreadsheet.

Using your equation that relates coefficient of friction, steady state speed, and system parameters, solve for the coefficient of friction in these measurements.

Plot friction coefficient versus bearing spacing.

Discuss with your partner your results.

Does this make sense? We’re the results what you expected?

How could you potentially improve these measurements?

Pllot of friction coefficient versus steady state speed.

Does this make sense?

**Part 4 -- Friction coefficient measurements at varied voltage with the double flywheel:**

Reconfigure the bearings to be maximally spaced out, which should have the lowest friction torque.

Using your Arduino program measure the steady state speed at 8 different PWM values as noted in the spreadsheet part_3 tab.

Plot friction coefficient versus steady state speed.

Do your results make sense?

Hey What do you notice about the coefficient of friction?

**Part 5 -- Friction coefficient measurements at varied voltage with nuts and bolts flywheel:**

Using a single flywheel add 12x 8-32 x 1.5” long nuts and bolts to the outer holes making the mass approximately equal to the previous double flywheel assembly.

Repeat part 4 to measure steady state speed and friction coefficient versus for increasing values of motor PWM duty cycle.

Plot friction coefficient versus steady state speed. Compare this plot with the experiment from part 4. It may help to use Matlab to overlay the two graphs

How does coefficient of friction for the flywheel with nuts and bolts differ from the smooth flywheel?

Why do these results differ?

**Part 6 -- Final analysis:**

The friction coefficient should not have a speed dependence. If we fit a line to the friction coefficient data versus speed from part 3, the y-intercept of this fit should give an estimate of our true Couloumb friction coefficient. Perform this plot and provide your estimate for coefficient of friction. Why does this provide an estimate for the friction coefficient?

Extra credit: How could you estimate the drag coefficients of your flywheel and your flywheel + nuts assembly? Provide a written solution and an estimate from data of this coefficient for extra credit.