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## MAE156a Lab 3: Friction Characterization

Friction is often the biggest unknown in a mechanical system and it can easily be the difference between success and failure. Friction is so important that that someone even came up with a specific name - Tribology: the study of friction, wear, and lubrication. In lab 3, students will become tribologists and attempt to characterize the friction of two stage mechanical timing belt system.

Introduction: Motivation and tools required

Learning Objectives:
1. Understand the three main types of friction: Stiction, Coulomb, Viscous
2. Understand that in the real world, friction can be extremely unpredictable and difficult to model
3. Understand that the effect of gear ratios on friction and inertia

This code runs the motor in open loop for XXX seconds, reads the encoder using interrupts (48CPR), and outputs to the terminal window characters to be saved as a .CSV (comma separated variable). Copy and paste the text from the terminal window into notepad, and save as a .CSV file.

Format: [time (ms), ticks (s), velocity (rad/s)]

### Motor Theory:

For the propose of this lab, we will use the following motor values:

I_motor = 1 e-6 Kgm^2
R = 11.3 ohms

Recall that a simple DC motor and Inertial system can be modeled as:

$\dpi{150} I\ddot{\omega }(t) = \frac{KV_a}{R}-\frac{K^2+Rc_v}{R}\omega(t) - \tau_fsign(\omega(t))$

Solving the ODE, we obtain:

$\dpi{150} \omega(t)= \omega_{ss}(1-e^{-\lambda t})\left\{\begin{matrix} \omega_{ss} = \frac{KV_a-\tau_fR}{C_vR+K^2} \\ \lambda=\frac{CvR+K^2}{IR} \end{matrix}\right.$

Friction Theory:

Coulomb Friction: A constant friction value, independent of speed. Also known as dry friction. Examples: block sliding across a surface, ball bearings, ...

Stiction: Also known as static friction. This friction only occurs at zero or low speeds. This friction is very difficult to characterize and model.

Viscous Friction: Friction that is proportional to speed. Examples: heavily greased bearings, drag, ...

In reality, friction is very difficult to measure and model. Friction is never a simple combination of these models, and it can be a function of temperature, vibration, direction, and change over time. For the simplicity of this lab, we will assume that the viscous friction is small compared to the coulomb friction, so we can ignore it.

Part 0: Measuring Mass and Estimating Inertia

Measure the mass, radius, and estimate the inertia of the following parts:
Acrylic Flywheel
Brass Weights
Calculate the Inertia of the flywheel. Recall that the moment of inertia of a solid cylinder is:

$\dpi{150} I = m\frac{r^2}{2}$

Part I: Cantilevered Mass

Click image to enlarge

Configure the ball bearings such that A = 15cm and B = 5cmAttach the flywheel with xxxg of radially symmetric mass onto the first shaft (no timing belt needed). Apply 12v (255) and record data for the 30 secondsUse the arduino code above to output and save data.

1. Save data as: "motor_flywheel.csv"
2. Plot velocity with respect to time
3. Determine the terminal velocity
4. Graphically determine the rise time (time to 68%).
5. From those values estimate: friction torque and effective inertia
6. Remove the flywheel and repeat this experiment for shaft only. Apply voltage for only 2 seconds
Example:

Part II: Dual Shaft Setup
Click image to enlarge

Build the dual shaft setup as shown. It is not super critical so try your best to assemble such that A = 15cm and B = 5cm for both shafts. Connect the 10t pulley to the 42t pulley with the timing belt. Attach the flywheel to the end of the 2nd shaft. Repeat the 6 steps in part I
1.  Repeat the 6 steps in part I for the Flywheel on Second shaft for 8 seconds

### Part III: Predictions & Results

Before analyzing the data, make some predictions of the new friction torque and effective inertia.

 Motor + Flywheel 2x Shaft + Flywheel (Prediction) 2x Shaft + Flywheel (Experimental) Friction Torque Effective Inertia

### Part IV: It all adds up (or does it?)

Conclusions:
• What assumption did we make? Is this a good assumption?
• What phenomenon did you observe when conducing the tests?
• What is better? The theoretical vs experimental friction?
• What is better? The theoretical vs experimental inertia?

ċ
MotorEnc.ino
(4k)
Daniel Yang,
Jan 22, 2018, 12:20 AM