Lab 3 Manual

Engineering 100 – Bright Ideas

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Laboratory 3 Rotational Motion

1. PRE-‐LAB • Read and understand this document • Answer the following questions on a separate sheet of paper and submit at the

beginning of your lab period:

1. Consider a bicycle with front and rear gears both 4 inches in diameter. a. If we replace the rear gear with one that is 3 inches in diameter, how does the

speed of the bike change in relation to the base case? (Assume that the pedals are rotated the same number of times in both cases). Would it be “harder” or “easier” to pedal?

b. Now, suppose the rear gear is 4 inches in diameter again. If we replace the front gear with one that is 2 inches in diameter, how does the speed of the bike change in relation to the base case? Would it be “harder” or “easier” to pedal?

2. What is the relationship between rotational speed and torque? What is the relationship between rotational speed and power?

3. If you were designing a system to lift/pull a physically heavy load, would you want to maximize rotational speed, torque, or neither? Why?

2. OBJECTIVES This laboratory provides an introduction to rotational motion, torque, and the operation of electric motors. After completing this lab, you should (1) understand the concept of a “gear ratio”, (2) understand the relationship between rotational speed and torque for electric motors, and (3) have a general understanding of motor operation. You will later apply these concepts to your class project.

3. EQUIPMENT 4 Pre-‐Made Gear Blocks with Different Gear Ratios Low Voltage DC Electric Motors Power Supply and Electrical Cables Dynamometer with Roller and Magnetic Rotation Sensor SimpleDyno© Computer Software Caliper


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4. BACKGROUND

Gears Gears or rotating parts are used in simple machines to change the speed or magnitude of a power source. Using two or more gears in tandem can change the speed of rotation or the torque (turning force) of a rotating system. An example that you are likely familiar with is a bicycle with a gear-‐shifting system. There is one set of gears connected to the pedals and another set of gears connected to the rear wheel. A chain connects the front and rear gears. If the front and rear gears have the same diameter (Figure 1, Combo 1), the rotational speed and torque will be the same for both the front gear and the rear gear. If the front gear has a diameter that is four times larger than the rear gear (Figure 1, Combo 3), each rotation of the front gear will result in four rotations of the rear gear, since the circumference of the front gear is four times larger than the rear gear. Your bicycle will therefore travel four times faster in Combo 3 in comparison to Combo 1 for the same number of pedal rotations. However, since the radius of the rear gear is smaller in Combo 3 in comparison to Combo 1, a greater force is required to produce the equivalent torque to propel the bicycle. In summary, Combo 3 will allow your bicycle to go four times faster, but you will need to exert four times the force at the pedals to get equivalent torque.

Figure 1: Illustration of a gear system for a bicycle with three different gear ratios.

Electric Motors An electric motor converts electrical energy into mechanical energy in the form of a rotating axle. The speed of the motor will be proportional to the applied voltage for the same load. The torque of the motor will be proportional to the applied current. For a fixed voltage on the motor, the speed and torque of the motor will depend on the load attached to the motor. Without a load, the motor will rotate at maximum speed, called the no-‐load speed. Under loading, the motor speed will decrease with increasing load. At some point of increasing load, the motor will no longer have sufficient torque to rotate. This point is called the stall torque. The relationship between torque and speed is typically linear as shown in Figure 2(a). The mechanical power is given by the product of speed and torque. The relationship between


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power and speed (or power and torque) is a quadratic relation that has a point where the power is a maximum, as shown in Figure 2(b). It is desirable to choose appropriate gearing ratios for a mechanical system to operate the motor at this maximum power point.

Figure 2: The (a) linear relationship between torque and speed for an electric motor and (b) corresponding quadratic relationship between power and speed needed to find the maximum power for the motor.

Dynamometer A dynamometer (often called a “dyno”) is a device that measures force, torque, or power. The power produced by a motor can be determined using a dyno by simultaneously measuring the torque and rotational speed. In this laboratory, you will be using a dyno that consists of a roller that interfaces with a motor. The rotational speed is measured using a magnetic sensor, and the torque is determined by assuming values for the rolling resistance (drag) of the dyno roller. A dyno can be used to construct the torque versus speed and power versus speed curves in Figure 2. Dynos are used often in real-‐world applications, particularly in the automotive field. In this lab, you will use a dyno to measure characteristics of a system powered by an electrical motor.

5. PROCEDURE 5.1 Measuring Gear Ratios Each lab setup will have a specific gear ratio. Note the number of the station you are working at (1-‐4). Your instructor will give you the theoretical gear ratios at the beginning of your lab. All tables should be included in your Post-‐Lab. First, examine the set of gears in your lab setup, and make a note of which gear ratio you are currently working with. You should notice that the system's overall gear ratio is a cascade of three separate gear ratios. The first gear system on the apparatus consists of the gear connected directly to the motor and a gear immediately below it. We will call this gear ratio R1. Your first task is to measure R1. You may either measure the diameter of the gears or count the teeth. Use these measurements to find the gear ratio. Note: See Figure 3 to determine whether the gear is referred to as Gear A (driver) or Gear B (driven) in this lab. It is important

Torque

(τ)

Speed (ω)

stall torqueτS

ωn

no-‐loadspeed

Power (P)

Speed (ω) ωn

no-‐loadspeed

P = ωτ = -‐(τs/ωn)ω2 + τsω

τ = τs -‐ ωτs/ωn

(a) (b)


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to get this correct and to remain consistent as any discrepancy can result in incorrect answers for the post-‐lab questions.

Figure 3: Labeling Convention for Gear Ratios, R1

R1

Station Gear A diameter (cm) or (teeth)

Gear B diameter (cm) or (teeth)

Measured Gear Ratio (B:A)

Theoretical Gear Ratio (B:A)

1 2 3 4

The next gear ratio in the system, R2, consists of the gears on the outside of the upper block as shown in figure 4.

Figure 4: Labeling Convention for Gear Ratios, R2

Gear B

Gear A

Gear B

Gear A


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Taking Gear A as the driver and Gear B as the driven gear (shown in Figure 4), measure and compute R2 at each station.

R2

Station Gear A diameter (cm) or (teeth)

Gear B diameter (cm) or (teeth)

Measured Gear Ratio (B:A)


1 2 3 4

The final gear ratio in the system consists of the white pulley and the roller, where the pulley is the driver (A), and the roller is driven (B). Measure these components of the system using a caliper and find the gear ratio, R3. R3 will remain the same for stations 1-‐3. Although the thickness of the roller in station 4 is not of uniform thickness, we will measure the diameter of the thickest part in order to approximate and differentiate the overall gear ratio from the other setups.

R3 Station Pulley (A)

diameter (cm Roller (B)

diameter (cm) Measured Gear Ratio (B:A)


1-‐3 4

The overall gear ratio RTotal for each system can be calculated by multiplying the chain of gear ratios together as such:

𝑅!"#$% = 𝑅! ∗ 𝑅! ∗ 𝑅! Use this equation to calculate the overall system gear ration for each station.

RTotal

Station Measured Gear Ratio (B:A)


1 2 3 4

Be sure to include all tables in your Post-‐Lab.


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5.2 Measuring Speed, Torque, and Power To facilitate the torque, speed, and power measurements for this lab, we will be using a dynamometer. To automate the measurement of the dynamometer, we are using a software package called SimpleDyno®. The software measures the rotational rate of the dynamometer and extracts torque and power information from the data. In order to measure the rotational rate of the dynamometer, a strip of magnets is placed on the roller, and a solenoid is connected to Line In port on your lab station computer. The changing magnetic field created by the moving magnets is detected by the solenoid and fed into the computer as electric pulses. These pulses, illustrated by “Signal 1” in Figure 5, can be seen in the waveform viewer at the bottom of the SimpleDyno® Software. Figure 5: Electric Pulses from Solenoid (used to determine speed of rotation) There are four lab stations that each lab group will rotate through. You and your teammates will have to switch stations after each experiment. Each gear station contains a gear block, four gears, axles, a motor, a power supply, and a dynamometer. Each station will have a different fixed gear ratio. See Figure 6 for the correct setup for the gear stations. You will use the DC power supply to run the motor at a voltage of 1.75, 2.25, and 2.75V. For each measurement, make sure the current output of the DC power supply is limited to 2 A.

Figure 6: Gear Station Setup

Signal 1 (waveform of interest) Threshold Trigger for Signal 1

Signal 2 (not used in this lab) Threshold Trigger for Signal 2


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Setting Up the SimpleDyno® Software The SimpleDyno® program is not installed on your computer by default. However, you can download it easily from the link provided by your instructor. Once you have the software downloaded, you can open the program (If prompted by Windows, click “Run”). The SimpleDyno® software consists of a “Main,” “Dyno,” and “Analysis” tab. You will be using the “Main” and the “Dyno” tabs during the lab experiment. The “Main” tab displays the real time signal input from the solenoid along with several calculated parameters including the rotational rate of the roller. The “Dyno” screen characterizes the dynamometer (dyno) with inputs of size, mass, and input signal type. It is very important that you fill in these inputs yourself as they are used in the calculations of speed, torque, and power. The following values in Figure 7 correspond to our current lab setup.

Figure 7:”Dyno” Tab Critical Parameters

NOTE: Due to the altered state of the roller at Station 4, Roller Mass (g) = 494 and Roller Diameter (mm) = 37.5 at Station 4 only. All other parameters should remain the same. Be sure to change these two parameters back to the Roller Mass and Roller Diameter values shown above after you have completed Station 4. Amplifying and Detecting the Solenoid Signal In order for the software to detect the electric pulses from the solenoid, we must manually configure the signal threshold and amplitude. In “Main” of the SimpleDyno® software, the signal threshold level (Channel 1, green line) must be set below the peaks of the signal. A revolution of the roller is detected when the signal peak intersects the threshold line.


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If your signal does not resemble the “Good” or “Better” examples in Figure 8, go to “Control Panel”à“Hardware and Sounds”à”Manage Audio Devices”. Right click on “Line In” and click “Properties”. Set the Line In level to approximately 30%.

o Bad example:

o Good example:

o Better example:

Figure 8: Solenoid Input Signal Examples

Connecting the Power Supply to the Motor Because of the method that the SimpleDyno©software uses for determining speed, torque, and power, it is important that the motor receive a “step” input of voltage. In other words, it is important that the power to the motor is applied quickly and at full voltage. To facilitate this, there is an inline electrical switch to the motor. Before turning on the power supply, ensure that the switch is in the off position. Adjust the Power Supply Voltage to either 1.75, 2.25, or 2.75V using the tuning knobs on the front panel of the DC power supply. Once you are satisfied with your voltage adjustment, click the “Turn on Sensor” button in the “Main” tab of the software. Next, click the “Power Run” button and provide a descriptive name for the measurement you are about to perform. (Make sure you remember where you save the files, as you will need them for your lab report.) Approximately 2 seconds after you click “Save” in the dialog window you can throw the switch to apply power to the motor. Watch the display graph of RPM vs. time as the motor speed increases and then reaches a steady-‐state value. Once your motor has reached steady state,

Microphone at 5% Boost at +20dB Power supply: 2V



Does not detect


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wait a few seconds, and then throw the switch to the off position. At this point, the software will take a few seconds to calculate the power and torque curves for your motor. The “Power Run” button will display “Done” when the calculations are complete. To quickly view your results, there is a radio button on the bottom left of the “Main” tab that reads “Power Curve.” By clicking on this button you should see a rough graph of your data (note that you cannot use a screen shot of this for your lab report). Before you leave the lab, make sure that everyone has a copy of the saved data files from the Power Runs. You should have three saved data files per station. Without these files, you will be unable to complete the lab report.

6. ANALYSIS

Summary of Collected Data Using the following table as a guide, create a table that summarizes the important values that you found from your lab experiment.

Voltage (V)

Theoretical Gear Ratio

No Load Speed (rpm)

Stall Torque (N*m)

Stead State Speed (rpm)

Max Power (W)

xx xx xx xx xx xx

Determine the Relationship of Torque and Gear Ratio On the same set of axes, plot two torque curves taken at the same input voltage but with two different gear ratios (you can choose which two).

• How does the gear ratio affect the torque? • How does the gear ratio affect the speed? • In a designed to pull a heavy load, what should the gear ratio be with reference to B:A?

In other words, should A or B be larger (recall that B is attached to the wheels)? Determine the Relationship of Power and Speed For two different voltages at the same gear ratio (pick one), plot the power vs. rotational speed curves on the same graph and compare.

• Does the speed at which the motor produces maximum power change? If so, why? (Hint: 𝑃 = − !!

!!𝜔! + 𝑇!𝜔 where 𝑇! is stall torque and 𝜔! is no load rotational speed)

For all plots, use a spreadsheet or mathematical software program (e.g., Excel, Matlab, etc.; consult with instructors if you have questions on this). Comprehension Questions

1. If the wheel that touches the roller is spinning at an angular velocity of 150 rpm, what is the angular velocity of the motor (Assume that R1 and R2 both equal 4:3, and use your measurements for R3 to determine RTotal)?


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2. If the wheel that touches the roller is spinning with a torque of 1 N*m, what is the torque applied by the motor (assume the same setup as Question 1)?

7. REPORT REQUIREMENTS The analysis for this lab will consist of a standard lab report. Include the following in your report:

• Tables o Gear ratios o Results

• Plots o Torque curves at different gear ratios (same graph) o Power curves at different voltages (same graph)

• Answer analysis questions • Answer comprehension questions

Lab 3 Manual

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