ECEN 2270

Robot DC Motor Characteristics and Speed Measurement

Lab #2

[Date]

ECEN 2270 Lab #2

Introduction and ObjectivesSection should include a brief description of the lab, and a summary of the lab objectives. What are the goals of the lab experiments? What are you trying to find out, or what are you trying to accomplish?

This is a lab to introduce the basics of DC motor operations. There are two parts to this lab. In Part A, the objectives are:

• Measure a DC motor characteristics.• Develop an LTSpice circuit model for the DC motor and determine model parameters based on

experiments.• Validate the model: compare experimental and simulation results.

In Part B, the objectives are:• Use DC motor LTSpice model to design a speed sensor (tachometer) circuit that outputs voltage

proportional to wheel speed.• Build, test and demo the speed sensor circuit.

The goal of this lab is to better understand the DC motor and its speed sensing circuit so as to continue building up our knowledge of the robot that will eventually be run by this motor. We will also be learning how to take careful experimental data and hopefully use digital schematics to validate that data.

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ECEN 2270 Lab #2

Methods and Results Section is the main part of the lab report. The experiments should be described in sufficient detail so that another engineer reading the report would be able to repeat your work. Specifically, for each Task in the laboratory include all of the components that apply to the Task: (a) Reference to the Lab Task, e.g. “Lab 1, part A.1.1. Square Wave” (b) All relevant analysis and simulation results (c) Detailed circuit diagrams of experimental circuits annotated with relevant signal names, component names and values. You may use LTspice schematic editor to produce circuit diagrams. (d) Relevant equipment setup data: a brief description of which piece of equipment was used and how. (e) Experimental results:

a. Scope waveforms (screenshots) should be annotated with signal names matching the signal names in the schematics, and scales (volts/div, and seconds/div), as well as measured important features of the waveform (such as peak value, peak-to-peak value, time delay, etc.)

b. Numerical results (you may use Excel) should be presented in graphical format, with clearly labeled axes and important features of the plots. A table of measurement data tables should be included in an Appendix at the end of the report.

c. Calculations, data analysis, comparisons to simulation results, and comments related to the experimental results.Each plot or graph in the report should have a title or caption that clearly specifies what is shown in the figure. It is not sufficient to give references to parts of the lab procedure. For example, do not just say “Lab 1, part A.1.1”; give a full caption: “Square-wave voltage waveform generated by Agilent 33521A waveform generator: minimum value is Vmin = 0 V, maximum value is Vmax = 2 V, frequency f = 1 kHz, duty-cycle D = 50%”

Experimental setupThe robot platform was placed on a stand off box‐

to allow the wheels to rotate freely. An Agilent E3631 bench power supply was then set up as a variable voltage VDC and current IDC, limited to provide 10 V and 1 A. This was the power supply and its limit for the entirety of the lab. The optical encoder was supplied from ±25 V connection terminals, again limited to 10V, while the motor was supplied from the 0-6 V terminals.

A model Agilent DSO1024A oscilloscope voltage probe, set to 1x amplification, was used to observe one of the encoder outputs, output A, and to measure the pulse frequency fenc. This was found to be 1.28 kHz with 10VDC.

Part A.1: determine RM

In a simple DC motor, a coil of wire in the form of a loop is placed between two stationary magnetic poles, with either end of the wire connected to a DC voltage supply. The result is current flowing through the loop as seen in Fig. 1.

By running DC current through the wire, a magnetic field is created according to Ampere’s Law (1).

F=iDC l x BB = magnetic flux density vector

l = vector aligned with conductor of length l in the direction of current

(1)

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Fig. 1. Simple DC motor rotor showing flow of current from DC source voltage (http://www.wisc-online.com)

ECEN 2270 Lab #2

τ=k IDCk = motor constant [Nm/A]

(2)

Additionally, by placing this loop of wire in a separate magnetic field (created by the stationary magnetic poles), a force will be generated between the two fields. This force will act upon the loop of current, creating a torque that will work to rotate the loop with a strength set by (2). When the loop reaches a position perpendicular to the main field, there is no interaction between the flux lines to cause the loop to rotate (the neutral plane), but the loop continues to rotate due to inertia. In order to maintain continuous rotation of the rotor, a commutator switches the current flow through the loops every 180°. Together, the commutator and wire loop are known as the motor’s armature.

Being a loop of wire, the armature forms a natural inductive effect. Being a long wire, there is also a resistive effect. And according to Faraday’s Law (3), the time-varying magnetic field of the wire will also generate an electromotive force VEMF, which can be modeled as a dependent voltage source. Fig. 2 shows the DC motor equivalent armature circuit model with these considerations, resulting in (4).

V EMF=−d Φdt

=k ω (3)

V DC=RM IDC+LMd IDCdt

+V EMF

(4)

Using this understanding of the DC motor, armature resistance RM can be found from a locked‐rotor experiment: with the motor being powered from the bench power supply, current runs through the motor and the end result is the wheel freely spinning. By holding the wheel so that the speed of rotation is zero, all terms in (4) go to zero but forRM I DC. Measuring VDC and IDC, RM can be solved for using Ohm’s Law (5)

RM=V DCIDC

(5)

An Agilent 34401A multimeter was used to measure VDC and IDC. There were found to be: Locked-wheel VDC: V Locked-wheel IDC: A

From our measurements, RM was found to be Ω

Part A.2: determine k, B, Tint

As for the mechanical model of the DC motor, the torque generated by (2) can also be calculated by (6). The load torque is the combined internal gear and load torque, shown in (7).

τ=J dωdt

+Bω+τ load

J = moment of inertia B = friction coefficient

(6)

τ load=τ∫¿+τ ext ¿(7)

A circuit equivalent model is shown in Fig. 3. The moment of inertia J is the property that resists change in angular velocity, similar to a circuit capacitor’s resistance to change in the circuit’s voltage. It can be symbolized in parallel with the generated torque. The generated torque itself is modeled after a dependent current source, as it will depend on how much current is flowing through the DC motor. As with any real physical motion, there is a friction element to consider which is shown as a resistor in Fig. 3. The resulting angular velocity ω is modeled in Fig. 3 as a current.

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Fig. 2. DC Motor equivalent armature circuit model

ECEN 2270 Lab #2

Angular velocity can be found by using the optical encoder. There are 12 output pulses per motor shaft rotation coming from the optical encoder. The optical encoder is also connected through a motor shaft to a 64:1 gear box, which then turns the wheel shaft turning the wheel itself. The encoder’s output pulses, measured as the encoder frequency fenc, are proportional to the speed of the motor according to (8). The angular velocity can be found using (9).

f enc=12∗64∗n60

n = wheel speed, rpm

(8)

ω=2πn60

=2π f enc12∗64

(9)

Motor constant k, friction coefficient B, and internal motor torque τ∫¿¿can be estimated from an unloaded motor experiment: while letting the wheel rotate freely, VDC is varied from 0 to 10 V, with IDC and fenc measured at each point. With the wheel rotating freely, there would be no external load on the motor, driving τ extto zero and leaving the motor’s total load torque equal to the internal motor torque in (7). At each point, measuring only after the system has reached steady-state behavior would also mean that there is no change in angular velocity ω, driving its derivative term in (6) to zero as well.

For VDC between 0 and 6 V, the separate 0 6V terminals were used, while keeping encoder ‐ VCC = +10V. For VDC between 7.5 V and 10V, both VDC and VCC together from the same supply voltage.

The measured current IDC could be used with (4) to measure the VEMF. The encoder frequency fenc could be used to calculate angular velocity ω. Together, these could be used with (3) to estimate the motor constant k, which would then be used with (2) to calculate the generated torque τ. • In the report, include measured data and explain how you determined k, B, and Tint . You may use an Excel spreadsheet to enter data and perform calculations

Part A.3: determine JThe moment of inertia J can be estimated from a motor turn off transient in an unloaded motor ‐

experiment: Turn on the motor at +10 V and let the wheel rotate freely at constant +10 V input. Then, turn off the motor supply voltage (using the supply output on/off button) to bring the supply current to zero. A probe connected to an Agilent DSO1024A oscilloscope was used to measure VDC during the transient.

As stated earlier, J is the property that resists a change in angular velocity and can be seen in Fig. 4, the screenshot of what was seen using the oscilloscope probe.• In the report, include measured scope screenshots and any data measured on the scope, and explain how you determined J

Part A.4: Validate the modelAn LTspice model for the motor was provided from the Lab 2 website. We updated the model

parameters based on our results determining RM, k, B, τ∫¿¿, and J. The resulting circuit can be seen in Fig. 5.

The equivalent of a locked rotor experiment was setup and run to compare the model to the measurements taken in Part A.1. This was accomplished by . The resulting waveform can be seen in Fig. 6.

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Fig. 3. Simple DC motor equivalent mechanical circuit model

ECEN 2270 Lab #2

Afterwards, the equivalent of an unloaded motor experiment was setup in simulation and run to compare the model to the measurements taken in Part A.2 We were able to verify the expected VDC, IDC, and fenc. The resulting waveform can be seen in Fig. 7.

Finally, we simulated the equivalent of Part A.3, letting the speed settle at a given input VDC, then “turn off” the supply, meaning bring the supply current to zero. ‐ The resulting waveform can be seen in Fig. 8.• In the report, include recorded LTSpice results and simulation waveforms.Compare the simulation results to the experimental results and comment on the behavior of the model

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ECEN 2270 Lab #2

Discussion and ConclusionsSection should be a brief summary of the lab results. Have the lab objectives been met? What conclusions can you draw? What are the limitations of the experiments? What have you learned from the lab? Give suggestions on how the lab could be improved or what other experiments could follow.

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ECEN 2270 Lab #2

AppendixDC Motor power supply set-up: powered using an Agilent E3631 bench power supply configured to provide VLIMIT = 10V and ILIMIT = 1A. Measurements for current and voltage taken using an Agilent 34401A multimeter. Measurements for frequency taken using an Agilent DSO1024A oscilloscope with probes set to 1x attenuation.

Part A.1: Determine RM

Measurements

MeasurementLocked wheel VDC VLocked wheel IDC A

RM = VDC/IDC = Ω

Part A.2: determine k, B, Tint

Voltage Sweep Measurements

Measured (a) (b) (c) (d)

ω k τVDC IDC fenc RM VEMF

(a) VEMF = VDC - RMIDC

(b) ω = 2π*fenc/(12*64)(c) k = VEMF/ω(d) τ = kIDC

(e)

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