1. Context of the Experiment

One of the most important parts of everyday systems are electrical motors - they have a great impact on every aspect of modern living. Household appliances like refrigerators, vacuum cleaners, air conditioners, fans, computer hard drives as well as electric cars and multitudes of industrial machines and devices use electric motors to convert electrical energy into useful mechanical energy. Energy is one of the highest cost items in a plant or facility, and motors often contribute to a high percentage of the power demand, so making sure motors are operating optimally is vital. Accurate power measurements can help to reduce overall energy consumption, as the measurement is always the first step towards better performance and can also help extend the life of a motor. Power is the rate of doing work, i.e., the amount of energy consumed per unit of time. The aim of this experiment is to measure motor power.

2. Learning Goals of this Experiment

• knowledge: basic understanding of an electric motor characteristic, electric motor mechanical and electrical power, stall torque, no-load speed

• abilities: running a motor; changing the series resistance; measuring voltage, current and power of the motor

• understanding: the impact of resistance on motor currents; how to work with a motor

3. Literature

[1]. Erickson, Robert W., and Dragan Maksimovic. Fundamentals of Power Electronics. Springer Science & Business Media, 2007.

[2]. Binder, Andreas. "Elektrische Maschinen und Antriebe." (2012): 678-691.

[3]. Thorsten A. Kern, Hatzfeld, Christian, and Alireza Abbasimoshaei. Engineering Haptic Devices. Springer London Limited, 2022.

[4]. Measurement Technology lecture slides

4. Basics / Fundamentals

Electrical motors

An electrical motor is a device that converts electrical energy into mechanical energy (typically in form of a rotation). Electrical current flows through coils, generating a rotating electromagnetic field. Through a variety of physical principles like magnetic reluctance or eddy currents and Lorentz forces, the electromagnetic energy is converted into mechanical torque acting on the motor's rotor.

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Figure 4.1: Different principles of torque generation in electrical motors (left: Lorentz force, right: magnetic reluctance)

Resistors

A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element.

Selecting the proper resistor

When selecting the appropriate resistor, you have to consider the wanted voltage drop across the resistor, the current flowing through it and the maximum power rating. The resistance R is given in Ohm .

For the resistance R, the following physical law for the relationship between voltage V and current I applies:

Using the power equation , the power dissipated by a resistor is or .

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Figure 4.2: Different types of resistors
_{David Ludovino, CC BY-SA 3.0 via Wikimedia Commons}

Resulting resistance of series and parallel connections

If n resistors are connected in series, the equivalent resistance is .

If n resistors are connected in parallel, the equivalent resistance can be calculated with.

Mechanical power

Mechanical power is the amount of work performed over a specific amount of time. The mechanical motor power can be calculated by multiplying the rotor’s torque (T in Newton meters, [Nm]) by its rotational speed (ω in radians per second, [rad/s]):

Electrical power

The motor electrical power is defined by the following formula:

Efficiency

For electric motors, the electrical power is considered as the input power and the mechanical power as the output power. The efficiency is defined as the ratio of output mechanical power per input electrical power:

Maximum mechanical power

For the given permanent magnet DC motor, torque and rotational speed are inversely correlated. At no rotor speed, maximum torque called “stall torque” is exerted. At no load on the rotor, the entire mechanical power is used to accelerate the rotor’s inertia to an equilibrium speed called “no-load speed”. As the mechanical power is proportional to torque and rotational speed, the maximum power is at half of the motor’s no-load speed, as can be seen in Figure 4 below.

The maximum mechanical power is:

By considering the relation between angular rotational velocity ω and rotational frequency f, the motor efficiency at maximum mechanical power results in:

5. Technical Basics & Preparations

Before measuring, these aspects of measuring should be considered and thought through:

• What is supposed to be measured? What values are necessary for the calculations?

• What measuring devices are appropriate for the measurements? How do you need to arrange the devices (e.g. multimeter in series or parallel)?

• What are the possible (systemic) errors and external limitations that exist in the setup?

Preparations

A multimeter ususally has four different inputs:

6. Experiment Procedure

The experiment parts 6.1, 6.2 and 6.3 will take place at the seat that you booked. For the last part 6.4, you do not need your experiment boxes anymore - this part will take place at one of the five teststands.

6.1 Measuring the no-load voltage of the motor

a) Mount your motor to the motor plate so that the bottom part of the metal casing is fully covered by the motor holders. Put your slotted disk onto the rotor and carefully tighten the setscrew so it does not slide anymore. Make sure that the slotted disk does not rub against the motor. When holding the forked photoelectric sensor next to it, it should not collide with the slotted disk.

b) Connect your multimeter, the motor and the power supply to measure the voltage of the motor. Adjust the power supply voltage to 24V and set the current limitation to the maximum of 3.2A and check all cable connections while the power supply output is still turned off.

c) Turn on the power supply output and measure the voltage. Turn off the output afterwards.

For the following experiments 6.2 and 6.3, you will measure the no-load current and no-load speed of the motor in three different configurations:

• with no resistors in series to the motor

• with one resistor in series to the motor

• with four parallel resistors in series to the motor.

Use a breadboard and wires to connect the resistors to the rest of your setup. It is recommended that you first measure the no-load current and then the no-load speed for all three configurations, respectively, by simply reconnecting the resistors according to each configuration.

6.2 Measuring the no-load current of the motor

Connect your multimeter, the motor and the power supply to measure the current of the motor. Turn on the power supply output and measure the current. Turn off the output afterwards. Repeat for each of the above mentioned configurations.

6.3 Measuring the no-load speed of the motor

Connect the forked photoelectric sensor to a 5V power source, ideally your Arduino Uno. Plug your Arduino into a USB port. If you do not have a USB port available, please ask the WorkINGLab staff for a USB power brick.

The sensor has four cables:

Connect one black cable to your Arduino’s ground (GND) pin and the red cable to the 5V pin using the Arduino’s headers. Connect the second ground cable and the signal cable to your multimeter using the measuring probes and set it to frequency measurement (Hz). Switch on the power supply’s output and carefully slide the forked photoelectric sensor into the slotted disk until you can measure a stable frequency on the multimeter. Repeat for each of the above mentioned configurations. Note the frequency measurement and the amount of slots of your slotted disk.

For the following measurement, you do not need your experiment boxes anymore. You can clean up your desk and put all parts into the box again.

6.4 Stall torque measurement

a.) To measure the stall torque of the motor, go to one of the five MATLAB PCs and start the MTApp. Enter your matriculation number and TUHH e-mail address, select Experiment 2 from the drop-down list and you will be greeted by the following screen:

The instructions for how to use the test stand are written in the “Scale Controls” panel, too. Please make yourself familiar with the process before executing the measurement.

b) Carefully remove the load cell holder and put it on the two screws for calibration. While you have access to all parts, note how many teeth the load cell holder and the pulley on the motor have (it’s printed into the plastic). Every teststand has different parts!

c) Connect the MTApp to the Arduino by clicking the “Connect” button. The button should turn green, indicating the test stand number that it is connected to. You will see the raw measurements (24-bit number) in the black scale display.

d) Tare the load cell by clicking the “Tare” button. The reading on the display of the MTApp should now read values close to 0 and the numeric input for the calibration weight should be editable now.

The calibration button will activate once the number in the calibration weight field has been edited.

e) Calibrate the load cell: Enter the weight of your calibration weight into the weight input box. Hang the calibration weight on the end of the load cell and click the “Calibrate” button. Afterwards, the display should read values close to that of the known weight in gram [g]. Remove the weight - it should read values close to 0 g now.

f) Take the load cell holder, place the belt around it and put it back onto the shaft. Align the end of the load cell with the stop block - it should be perpendicular as seen in Figure 6.4.14. Normally, this should already be properly aligned. If not, you can turn the screw to achieve this.

Measure and note the distance between the center of the load cell holder (marked on the plastic) and the center of the screw in the stop block.

g) Now, the teststand is ready for the measurement. Switch on the power supply, set it to 24V and 3.2A, keep your hands away from the teststand and hit the “Start Measurement” button! The motor will be powered for three seconds. During this time, the load cell will measure the force and plot the measurement afterwards. Determine the measurement value and enter it together with the appropriate unit into the MTApp.

7. Evaluation of Experiment Results

7.1 Torque and efficiency calculation

At the teststands that you used, the power supplies are only able to supply a current of 3.2A. The motor has a higher current demand of 7.22A at standstill (= in stall condition). However, supplying this current to the motor would destroy it within a couple of seconds (and maybe cause a fire: 24V * 7.22A = 173W - this small motor would create a lot of heat!). As such, the teststands only do a measurement with a reduced current of 3.2A, resulting in the torque .

As the torque of this DC motor type is linearly proportional to the current, a linear adjustment can be used to calculate the stall torque at 7.22A.

The stall torque at 24V and 7.22A follows the following calculation:

For questions 12 and 13, please use this adjustment to calculate the full stall torque . For the calculation of the efficiency at maximum power (cf. section 4), the current should be assumed to be 7.22A.

7.2 Questions

1. Please enter your matriculation number, so we can assign the results to you.

2. What is the no-load voltage of the motor?

unit: [V]
relevant section: 6.1

3. What is the no-load speed of the motor?

unit: [min^-1]
relevant section: 6.3

4. What is the no-load resistance of the motor?

unit: Ohm [Ω]
relevant section: 6.1 and 6.2

5. What is the total resistance of the circuit in the configuration with one resistor in series to the motor?

unit: Ohm [Ω]
relevant section: 6.1 and 6.2

6. What is the total resistance of the circuit in the configuration with four parallel resistors in series to the motor?

unit: Ohm [Ω]
relevant section: 6.1 and 6.2

7. What is the power of the circuit in the configuration with one resistor in series to the motor?

unit: [W]
relevant section: 6.1 and 6.2

8. What is the power of the circuit in the configuration with four parallel resistors in series to the motor?

unit: [W]
relevant section: 6.1 and 6.2

9. What is the unit of the measurement that the load cell measured at the teststand?

select from:

• Newton [N]

• gram [g]

• Newtonmeter [Nm]

• second [s]

relevant section: 6.4

10. Consider the following three plots of measurements that were recorded using the teststands:

Of the three measurement plots, two show incorrectly recorded measurements and only one plot shows a correctly recorded measurement. Which of the three plots (a), (b) and (c) shows the correctly recorded measurement?

11. Consider the following plot of a measurement that was correctly recorded using the teststand:

Please note that the y-axis scale is normalized to the maximum recorded weight at t = 300ms. Which of the three points (A), (B) or (C) should be used to calculate the stall torque of the motor?

12. What is the stall torque of the motor at full stall current of 7.22A?

unit: [Nm]
relevant section: 6.4 and 7.1

13. What is the efficiency of the motor at maximum mechanical power?

unit: unitless
relevant section: 6 and 7.1