Here you will find the lab manuals for all experiments that will take place this semester. Navigate to the appropriate experiment on the left-hand menu. You can export each experiment as a PDF if you want a copy for your records, or to print as a hard copy. Also, bookmark this page on your smartphone or tablet as well as your PC/laptop as a handy guide during your lab session.

Note that this semester is the first-time we are rolling out Gitbook to deliver the manuals, so please let your TA or Instructor know if there are any typos, or suggested improvements...

Best of luck for the semester!

Importing Data

Manually importing data

One of the quickest ways to get data into MATLAB is to simply copy and paste it in from your external source. We most often save data in text (.txt) files or spreadsheet files (.csv, .xls, .xlsx), so we consider manual import methods for those two types of file here.

Consider the data obtained from a drone motor electronic speed controller (ESC) opened in Notepad as shown above (it has 505 seconds of data in total). Since Notepad doesn't allow you to select columns, and indeed doesn't even know the data it contains is actually arranged into columns, we must copy it all into MATLAB in one go. Follow the steps as follows:

1. Since MATLAB doesn't allow a mixture of text and numbers in arrays, first temporarily delete the header row in Notepad

2. Copy all data in the file by selecting all then copying(Ctrl+A then Ctrl+C)

5. Select the top right cell and paste in your data using Ctrl+C. You don't have to save the variable, it does so automatically.

6. Return to Notepad and undo your changes to the header or close the file without saving so you don't accidentally modify it forever.

8. Unless you want to keep the full ESC array variable for any reason, delete it by right clicking on it in the Workspace and hitting Delete.

The process for spreadsheets is very similar, but since spreadsheet software allows you to select columns, you can repeat Steps 3-5 above for each column and omit the array column naming in Step 7.

Using the MATLAB Import Data tool

MATLAB also has a powerful Import Data tool which gives you a lot more options for how to import the table, whether to include headers or not, etc. This can certainly be used, too, but has a few more options to know about compared to the Manual method. If you do go this route, to get the same kind of data type as above, use 'Numeric Matrix' as the Output Type. An advanced, but highly powerful, Output Type is the 'table' which has a lot of benefits that are not needed for this simple data reduction.

Write scripts

It is tempting to write your code in the command line, but this can quickly lead to a mess of variables and forgotten discoveries. Furthermore, it is very difficult to execute loops and other multi-line statements. Instead, start a script and modify that as you go a long, thus keeping an ongoing record of what you've need.

A really cool feature in MATLAB is the 'Live Script' - this is a script that also enables you to insert and format text, equations, images, etc. Moreover... it can be exported to a PDF so it shows all your code and the output plots without you having to format anything. One final nice touch is that you can set up variables as interactive inputs, so you don't have to re-run the script to change parameters... it just automatically updates.

Reducing time series data

Sometimes we will continuously gather data over a long time period, when only certain periods are of interest. Take for example the ESC data from the Importing Data for MATLAB section... this was a power consumption test of a drone propeller where only the power during periods of static throttle are of interest, not the transient periods. Below you will find a PDF of a simple Live Script used to perform such a time series reduction. The Live Script and data are also included for you to play with if desired.

Reducing binned data

Sometimes we won't collect data over time, instead gathering it in a discrete bin or category. If there are a large number of bins it can take a long time to separate and perform calculations on this data. But fear not... MATLAB eats this sort of problem for breakfast thanks to logical indexing and the ability to loop. In this example, a data set containing noisy atmospheric pressure measurements gathered by 50 weather balloons is binned by altitude. Open the Live Script-exported PDF below to show how to deal with this sort of problem. The data and files are also included for you to explore:

Objective

The primary objective of this experiment is to familiarize the student with digital data acquisition of time-varying signals. This lab covers concepts in frequency analysis of time varying signals and sampling theory. It also provides an introduction to computer-based data acquisition systems. In this experiment, you will use a computer data acquisition system to sample signals produced by waveforms stored in mp3 formats and converted to analog electrical signals by the computer’s audio system. You will explore issues in sampling, including the Nyquist limit and aliasing, and the use of analog filters. This will help prepare you for future experiments in this laboratory course that employ computerized data acquisition and involve frequency based interpretation of measured data.

Background

Most experimental measurements involve the dimension of time. Experimental data is acquired over the course of some time, and during this time the signal can change. In some cases, the actual physical parameter of interest (the measurand) may change with time. For example, the velocity in a wind tunnel generally varies with time due to turbulence or variations in the speed of the fan blades used to drive the tunnel. Even when the measurand is nominally constant in time, other parameters that influence the measurement may vary, for example drifts in the measurement device. Thus, the experimenter is often interested in measuring a variable that could be described by the general function (or waveform),

(1)

Waveforms, Frequency Content and Discrete Sampling

Fourier Series

One of the simplest time-dependent functions we encounter is the sine (or cosine*),

(2)

More general periodic waveforms, which repeat themselves with a period T and thus have a frequency f=1/T, can be written as a linear combination of simple harmonic modes. There is the basic, fundamental mode (with frequency f ), and harmonics of the fundamental mode, with integer multiples of its frequency (2f, 3f, …). For example, we could describe the vibrations of a tuning fork or the acoustic oscillations in a pipe this way. Mathematically, this linear combination of modes is expressed as a Fourier series expansion,

(3)

Figure 1. A waveform composed of a fundamental mode (at 50 Hz) and its 9th harmonic (at 10 times the fundamental frequency, or 500 Hz). The waveform also has a DC, or time-averaged, component of 4 mV. Specifically, the signal (in millivolts) is 4+sin(100πt)+2sin(1000πt), or equivalently, based on cosines, 4+cos(100πt-π/2)+2cos(1000πt-π/2), which simply represents a phase shift of -π/2.

For example, Figure 1 shows a simple waveform composed of two frequencies, a fundamental mode at 50 Hz and its 9th harmonic (at 500 Hz). Thus the complete waveform is repeated every 20 ms (=1/fundamental frequency =1/50 s). The waveform shown in the figure also has a DC component. In other words, the signal has a nonzero value when averaged over its period. In general, we can write the DC amplitude as

(4)

The other coefficients of the Fourier expansion are given by

(5)

(6)

The power, P, contained in single mode is given by the square of the amplitude

(7)

(8)

A second example that shows the ability of a combination of sine waves to create an arbitrary periodic function is shown in Fig. 2. Five sine waves and a DC component (see Fig. 3) were combined to create a function approaching a square wave. While the constructed function resembles a square wave, it is clear that more sine waves would be needed to produce a sharp square wave.

Figure 2. Partial reconstruction of a square wave using five sine waves, each with a different amplitude, frequency and phase, and a separate DC component. The individual waves are shown in Fig. 3.

Figure 3. The five sine waves and constant function used to construct the square wave shown in Fig. 2.

Fourier Transforms

(9)

(10)

For example, Figure 4 graphically shows the Fourier transforms of various functions, including sine and cosine waves, a rectangle function (Π), a triangle function (Λ) and a constant, or DC, function. The sine, cosine and DC waveforms result in Fourier transforms that are nonzero at a single frequency**;

Figure 4. Fourier transforms of various functions (left and right pairs). The arrows represent impulse functions (i.e., delta functions), which extend infinitesimally along the x-axis, but have a integrated area corresponding to the height indicated by the arrow. The dashed regions indicate imaginary values.

(11)

where it is sufficient to consider only 0<f<∞ since the PSD of a real function is symmetric about f=0.**

Extensions of the Fourier Transform method have been developed for non-continuous functions, specifically for signals that have been discretely sampled by a computer, data acquisition system, or produced by digital means. These are generally known as Discrete Fourier Transforms. In addition, methods to quickly compute the Fourier Transform have also been developed, e.g., the Fast Fourier Transform. These concepts are described in detail in references 2 and 4. The computer data acquisition system you will use employs these techniques to compute the power and phase spectra of the signals that are sampled in this lab.

Discrete Sampling

As a simple example, consider a single sine wave. If we know we are dealing with a single frequency sine wave, it takes at least two measurements per period to determine its frequency, which means we must sample at twice the sine wave’s frequency. If we sample any slower, we actually infer a lower frequency than the actual frequency of the sine wave (you will see this in the lab). This process, by which information at a higher frequency shows up at a lower frequency is known as aliasing.

Computer Data Acquisition System

Data will be acquired with an board in a computer, utilizing a LabView™ interface. The computer data acquisition board, which measures the voltage of the input signal, essentially consists of a multiplexer, a sample-and-hold device, an analog-to-digital converter, a memory buffer, an interface to the computer’s memory, a master clock, and controller (see Figure 5).

Figure 5. Schematic of multiplexed, sequential sampling, computer data acquisition board and its connection to the computer.

The multiplexer (MUX) is a switch that connects one of a number of input channels (usually numbered starting at 0) to the sample-and-hold (S/H). The input voltage on the channel switched by the MUX “charges up” the sample-and-hold during some time interval, which is a fraction of the sampling period (the time between samples). This circuit is then disconnected from the input voltage, and some of the stored charge is drained from it. From this charge, the original voltage value connected to the S/H is determined, and the result is converted to a digital value by the analog-to-digital converter (ADC). The digital value (sometimes referred to as a “word” of data depends on the input voltage, the voltage range of the ADC (the minimum and maximum voltages it reads, e.g., 0-5 V), and its digital dynamic range (number of “bits” = N). The relation between the digitizer output and the voltage input is given by

(12)

Multiple signal inputs are recorded by using the MUX to cycle through each of the input channels at a rate that must be faster than the overall sampling rate (how often a given channel is read) times the number of input channels being read. In the sequential sampling system illustrated in Fig. 5 (and which is representative of the system you will be using), note that the channels are not read at exactly the same time. There is a time delay (skew) between when one channel and the next is read. The skew determined by the maximum switching and reading rates of the MUX, S/H and ADC. This is illustrated in Fig. 6. Simultaneous data acquisition systems, which have negligible skew, typically employ multiple, synchronized S/H systems just upstream of the MUX (see Fig. 7).

Figure 6. Time delay (skew) between successive channels in sequential sampling system.

Figure 7. Schematic of simultaneous sampling, computer data acquisition system.

You will also use an analog, electronic filter manufactured by Krohn-Hite. It actually contains two filters, which separately can be switched to be either low pass or high pass filters. The cutoff-frequency of each is also adjustable, using a combination of a dial and multiplier setting. You will be examining the effects of the filters on the following time-dependent signals:

Procedure

1. Take a tour of the equipment with the TAs. In particular you will look discuss:

   • The MP3 player

   • The Krohn-Hite filter

   • Our LabView VI

   • The National Instruments DAQ (data acquisition) device

   • The Tektronix oscilloscope

   • Miscellaneous cables and connectors

2. Prepare the cables/connections:

   • Using the 3.5mm-to-BNC cable, connect the MP3 player's audio output to the BNC T-connector

   • Plug the T-connector into channel AI0 (Analog Input 0) on the DAQ with the toggle set to FS (floating source)

   • Using a coaxial jumper cable, connect the T-connector to Channel 1 on the oscilloscope.

   • Note: cables can go bad, especially BNC connectors. If you experience signal dropouts or unexpected noise, have the TA check your cables.

3. Prepare the LabView VI:

   • Open DigitalSampling.VI if not already open. It is located in D:\AE3610\<SemesterYear>\1. Digital Sampling\Execution Files

   • Hit the Run button

   • Set the sampling rate to 22,000 Samples per second, the number of samples recorded to 6000, and the averaging level to 1.

4. Prepare the MP3 player:

   • Power on the MP3 player and ensure it is not connected to power (this will introduce noise into the audio output)

   • Set the output (volume) level to 32

   • Enable track repeat

5. Prepare the oscilloscope:

   • Power it on using the push button on the lower left

   • With the help of the TAs, ensure that all key switches/dials are in the correct position

6. Commence waveform identification and characterization:

   • There are 11 audio tracks loaded onto both the MP3 player and the PC's hard drive. Each audio track contains a different periodic signal. These signals include: single sine waves, a sum of three sine waves, a product of two sine waves, and periodic waveforms that are not sine waves: square waves, triangle waves, and ramps. Some tracks also have “noisy” signals.

     • Beware: for compounded signals, power spectrum frequencies only decompose the waveform as if it is a sum of sines!!!

   • As you analyze each track, simultaneously pull up the same track on the PC and play it through the speakers using media player software, for auditory context.

   • View the output of each track on the oscilloscope, the VI time plot, and the VI power spectrum, having adjusted their display parameters to best see the waveforms. For each track, take notes/data that best describe the waveforms. These notes should include waveform shape/description, and the approximate frequency of any/all peaks in the power spectrum. If you wish, you could also take screenshots/photos of each display for future reference.

     • Tip: With the waveform displayed as you like, toggle the Continuous/Hold switch to the Hold position so that it is "frozen" in the frame. Drag the markers in the power spectrum to help you identify specific numbers.

7. Gather data to understand Nyquist sampling theory and aliasing:

   • In this step we will determine how aliasing, brought on by sampling rates below the Nyquist frequency, affects our ability to accurately reconstruct/analyze a signal.

   • Disconnect the T-connector and connect the 3.5mm-to-BNC cable directly to the DAQ's AI0 port. Turn off the oscilloscope.

   • Find and play the track containing the 1 kHz sine wave.

   • With a sampling rate of 2500 S/s and record length of 2500 S, acquire a power spectrum. Record at what frequency in the spectrum the peak occurs (i.e. the frequency with the maximum power).

   • Repeat the above step for the following seven sampling rates: 2000, 1500, 1200, 1000, 800, 675 and 665 S/s, in each case setting the record length value to the sampling rate value (i.e. capture X samples at X S/s).

   • From the 8 observed frequencies, identify at which sampling rate(s) aliasing is occurring.

   • For at least two additional sampling rates of your choice (below 650 S/s, with a matching record length as before), first predict whether aliasing will occur. If you believe aliasing will occur, predict the specific aliasing frequency, then acquire data to verify experimentally.

8. Gather data to explore the effects of varying record length and sampling rate:

   • Some important terms:

     • Sample = a single measurement captured by the DAQ

     • Record = a batch of samples collected by the DAQ before downloading to the VI

     • Record length = the number of samples in a record

     • Record time = the period over which the record was captured

     • Sampling time = the period between successive samples

     • Sampling rate = the number of samples acquired in a given period of time

     • Frequency resolution = the frequency spacing between two points in the power spectrum

   • Again play the track containing the 1 kHz sine wave.
9. Explore the implementation of a low pass filter to remove unwanted noise:

   • Reconfigure the cables/connectors:

     • Remove the BNC cable from AI0 and replace the T-connector back into AI0.

     • Connect the 3.5mm-to-BNC cable from the MP3 player to the T-connector.

     • Connect the remaining open port on the T-connector to either input of the Krohn-Hite filter using a coaxial jumper cable.

     • Connect the corresponding output from the Krohn-Hite filter to AI1 on the DAQ, ensuring the switch is set to FS (floating source), with a coaxial jumper cable.

   • Power on the filter and set it to LOW PASS x100 mode

   • Locate and play the track containing the sum of three sine waves at three frequencies on the MP3 player.

   • Set the following VI parameters:

     • Sampling rate = 22 kS/s

     • Record length = 1000 S

     • Number of averages = 1

     • Display Settings

       • Window = None (Uniform) | Vrms | Linear

       • Plot = Amplitude | Radians

     • In both time plots, turn off x-axis autoscale and set the limits from 0 to 0.005 s (will round up to 0.1 after hitting enter)

   • In this step, the sum of sines represents a fictional scenario whereby a signal with two low frequency components of interest (e.g. vibration data from a structures experiment) are subject to a high frequency noise component. Your goal is to remove the high frequency noise without altering the two low frequency components of the signal of interest. This is a very common scenario for signal processing in engineering and science.

   • Paying attention to the time history and power spectrum of both filtered and unfiltered signals, adjust the cutoff frequency dial of the low pass filter until you obtain a cleaned up filtered signal. When you are happy with your results, take a screenshot of the VI for your report and note down the cutoff frequency on the filter.

10. Explore the ramification of low pass filtering on signal phase

    • Continue playing the previous track (sum of three sine waves).

    • Set the Krohn-Hite filter to a cutoff frequency of 10 kHz

    • Set the following VI settings:

      • Sampling rate = 22 kS/s

      • Record length = 1000 S

      • Number of averages = 1

      • Display Settings

        • Window = None (Uniform) | Vrms | dB

        • Plot = Phase | Radians

    • Set the VI to CONTINUOUS and press HOLD to freeze the plots after a few seconds, once new records have downloaded.

    • Successively zoom in to the 3 frequencies of interest in each phase plot by adjusting the x-axis limits.

    • Record the phase of the unfiltered and filtered signals at each frequency. Have the TAs check your data.

11. Gather data to determine the transfer function of the low pass filter at 800 Hz

    • Locate and play the repetitive sweeping track on the MP3 player

    • Set the following VI settings:

      • Sampling rate = 6000 S/s

      • Record length = 3000 S

      • Number of averages = 1

      • Display Settings

        • Window = None (Uniform) | Vrms | Linear

        • Plot = Amplitude | Radians

    • Set the Krohn-Hite cutoff frequency dial to 800 Hz.

    • With data acquiring, click HOLD and then TAKE NEXT as many times as needed to display a relatively flat and noise-free power spectrum. The TAs will help you achieve this.

    • When you are happy, click SAVE and choose a useful filename, being sure to add .xls as an extension (this can be added in Windows Explorer afterwards if this step is forgotten).

    • Change Number of averages to 10, repeating the previous 2 steps to acquire a new data set.

12. Explore the implementation of a band pass filter to remove all frequency content except for one frequency of interest:

    • Locate and play the excessively noisy single sine wave track on the MP3 player. Ensure that the MP3 player volume is set to 32.

    • Set the following VI settings:

      • Sampling rate = 22000 S/s

      • Record length = 5000 S

      • Number of averages = 1

      • Display Settings

        • Window = None (Uniform) | Vrms | dB

        • Plot = Amplitude | Radians

    • Remove the output of the lowpass filter from DAQ AI1 and instead connect it to input of the currently unused channel of Krohn-Hite filter.

    • Connect the output of this channel to DAQ AI1 using a further coaxial jumper cable.

    • Set the second filter channel to HIGH PASS x1 mode and set the cutoff frequency dial such that the frequency is as low as possible (around 20 Hz).

    • Change the original low pass filter to x100 and set the cutoff frequency dial such that the frequency is much higher than the frequency we are trying to preserve (around 20 kHz).

    • On both of the filtered and unfiltered time history plots:

      • Turn off x-axis auto-scale and set the x-axis limits between 0 and 0.01 s.

      • Turn off y-axis auto-scale and set the y-axis limits between -0.1 and 0.1 V.

    • On both power spectrum plots:

      • Turn off x-axis auto-scale and set the x-axis limits between 0 and 11 kHz.

      • Turn off y-axis auto-scale and set the y-axis limits between -130 and -30 dBVrms (-30 on the top-most limit).

    • Take a screenshot of the VI for future reference.

    • Gain a high-level perspective of how both filters affect the power spectrum:

      • Whilst watching the filtered power spectrum and the time history plots, slowly reduce the low-pass filter cutoff frequency to 2000 Hz. Observe how both plots change.

      • Zoom closer into the frequency of interest by adjusting the x-axis limits of both power spectra to between 0 and 2000 Hz.

      • Whilst watching the filtered power spectrum, slowly increase the high-pass filter cutoff frequency to 200 Hz. Observe how the power spectrum and the time history plots change.

      • On each power spectrum, drag marker "m1" until it snaps onto the peak of the frequency of interest. The y-axis readout (in orange below the x-axis) for each marker tells you the dBVrms of each marker, filtered and unfiltered, and thus the magnitude of the signal at that frequency. If the above steps have been followed correctly, you should see almost identical dB values at these points; have the TA check your setup if this is not the case.

      • Note down the dBVrms of each peak.

    • Dial in the cut-off frequencies to complete your band-pass filter design:

      • Keeping the low pass cutoff frequency at 2000 Hz, adjust LOW PASS mode to x10.

      • Keeping the high pass cutoff frequency at 200 Hz, adjust HIGH PASS mode to x10.

      • Successively adjusting both dials until the filtered power spectrum has as much unwanted frequency content removed as possible, without exceeding a 3 dBVrms drop at the frequency of interest. The final filter cutoff frequencies should be evenly spaced around the frequency of interest (i.e. 1000 +/- X Hz).

      • Note down your final band-pass filter frequencies, the final dBVrms values of each peak (unfiltered and filtered).

      • Take a screenshot of the LabView VI at its current zoom level.

      • Set both power spectrum x-axis limits between 0 and 11 kHz before taking another screenshot of the LabView VI.

13. Lab shutdown procedure

    1. Plug the MP3 player in to charge

    2. Unplug all coaxial cables and arrange neatly on the desk

    3. Turn off filter, oscilloscope, and DAQ

    4. Have the TA upload your data/files to Canvas

Data to be Taken

1. The waveform shape/description and peak frequency(s) for each of the 11 tracks.

2. For the 1 kHz waveform:

   • The peak frequency from the power spectrum for the 10 different sampling rate/record length combinations.

   • The predicted and measured peak frequency for the 2 selected sampling rate/record length combinations.

   • A note saying which, if any, of the frequencies are aliased frequencies.

3. For the 1 kHz waveform at the 9 different sampling rate/record length combinations:

   • Record time.

   • Power spectrum x-axis range.

   • Power spectrum frequency resolution.

   • The number of points in the power spectrum.

4. For the sum of 3 sines waveform:

   • The cutoff frequency of the low-pass filter design and a screenshot of the LabView VI with the lowpass filter set at the cutoff frequency.

5. For the sum of 3 sines waveform run through a lowpass filter set at 10 kHz:

   • The phase of the filtered and unfiltered signal at all 3 frequencies of interest (6 values total).

6. For the sweeping sine waveform run through a lowpass filter set at 800 Hz:

   • Two excel documents, one containing unfiltered and filtered power spectrum data from the single record run, and one for the average of 10 records run.

7. For the excessively noise sine waveform:

   • Designed bandpass filter range.

   • dBVrms values of both peaks before and after filtering.

   • All three screenshots taken of the LabView VI.

​Data Reduction

1. From your data taken in step 3 of the Data to be Taken section, come up with rules for:

   1. The number of points in the power spectrum as a function of record length

   2. The power spectrum frequency resolution as a function of record time

   3. The power spectrum frequency resolution as a function of sampling rate and record length

   4. The power spectrum x-axis limit as a function of the sampling rate.

2. From your data taken in step 5 of the Data to be Taken section, calculate the phase difference between the unfiltered and filtered signals at all 3 frequencies of interest.

3. Calculate the ratio of the power spectra for the filtered data (i.e., the output from the filter) and unfiltered data (i.e., the input to the filter) recorded in step 6 of the Data to be Taken section. Find the Transfer Function of the filter as a function of frequency. Do this for both the single record run and the average of 10 records run.

​Results Needed for Data Report

Note: This is a Data Report, so you must follow instructions on how to prepare the Data Report (not the FORMAL report) on the Canvas course page. Also, be sure to answer any supplemental questions listed on Canvas for this lab.

1. A table describing of each of the 11 tracks including all relevant characteristics (Step 1 of Data to be Taken).

2. A table containing the data from Step 2 of the Data to be Taken section.

3. A table containing the data from Step 3 of the Data to be Taken section.

4. All 4 equations for Step 1 of the Data Reduction section.

5. A table containing the design cutoff frequency of the lowpass filter (step 4 of Data to be Taken section).

6. A figure of the lowpass filtered and unfiltered time history and power spectra from step 4 of the Data to be Taken section.

7. A table containing the data from step 5 of the Data to be Taken Section and Step 2 of the Data Reduction section.

8. Plots of the single and average power spectra, filtered and unfiltered, for the waveform with the rapidly sweeping frequency (step 6 of the Data to be Taken section)

9. Plots of the filter transfer function described in step 3 of the Data Reduction, one based on 1 record and another based on the 10-record average results.

10. For the bandpass filter design (Step 7 of Data to be Taken):

    1. A table containing:

       • The final bandpass filter design cutoff frequencies.

       • Unfiltered/filtered peak dbVrms values prior to finalizing the filter design.

       • Unfiltered/filtered peak dbVrms values after finalizing the filter design.

    2. Three screenshots of the LabView VI during filter development

Further Reading

1. R. V. Churchill and J. W. Brown, Fourier Series and Boundary Value Problems, 3rd ed., McGraw-Hill, 1978.

   ​

2. R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed., McGraw-Hill, 1978.

   ​

3. T. G. Beckwith, R. D. Marangoni and J. H. Lienhard V, Mechanical Measurements, 5th ed., Addison-Wesley, 1995.

   ​

4. W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flanner, Numerical Recipes - The Art of Scientific Computing, 2nd ed., Cambridge University Press, 1992.

​

Objective

The primary objective of this experiment is to familiarize the student with the measurement of static and stagnation pressures, and (indirectly) velocity, in a subsonic wind tunnel. Static taps and stagnation (Pitot) probes will be used to measure pressures on the surface of a 2D airfoil, in the wake region behind the airfoil and in a boundary layer next to the wind tunnel wall.

Background

The Aerodynamic Problems

i) Airfoil Surface Pressure Distribution

When a 2D airfoil is placed in a uniform subsonic freestream, the flow velocity near the airfoil is modified and, as evidenced by the Bernoulli equation, so is the local static pressure. The resulting chordwise pressure distribution on the surface of the airfoil may be calculated by various methods using an inviscid fluid model.* At moderate angles of attack, the flow accelerates over the upper surface of the airfoil, the surface static pressure is less than freestream over most of the chord, and the pressure coefficient, which is defined as

along the airfoil upper surface has mostly negative values. Normally, there is a large suction peak (large negative value of ) very near the leading edge on the upper surface, followed by a region of increasing static pressure (adverse pressure gradient) from there to the trailing edge. On the lower surface of the airfoil, there is a stagnation point near the leading edge, where = 1.0, and the flow accelerates thereafter. When the two pressure coefficient distributions are plotted versus chordwise location, (x/c), the area between the two curves is a measure of the normal force coefficient on the airfoil and hence of the airfoil lift coefficient.

As the angle of attack is increased, the suction peak on the upper surface grows larger and the adverse pressure gradient becomes larger as well. At some value of angle of attack, the adverse pressure gradient on the airfoil upper surface becomes strong enough that the boundary layer separates from that surface. At a sufficiently high angle of attack, the oncoming freestream flow perceives a radically modified airfoil shape. The resulting effect is termed airfoil (or wing) stall, and the included area between the upper and lower pressure distribution curves collapses. The presence of stall was evident in the force measurements on the airfoil that were conducted in a previous laboratory.

The airfoil used in this experiment (see Figure 1) has an NACA 64212 section. The chord is 14 inches and it has a thickness ratio of 14%. The airfoil extends from one side wall of the wind tunnel to the other. Therefore, it should behave like a 2D airfoil.

Figure 1. Two-dimensional wing showing pressure tap locations (light colored line at centerline of airfoil), red tufts used to visualize separation and tubing used to connect pressure taps to Scanivalve.

ii) Velocity Profiles in a Boundary Layer and Wake

In the flow of a viscous fluid such as air, the flow velocity right at a solid surface is zero; i.e., the fluid can be thought of as adhering to the surface (the no slip condition). Within a small interval above the surface, the flow velocity increases rapidly from zero to a value that is of the order of the freestream velocity. The result is a velocity profile which exhibits a large velocity gradient in the direction normal to the surface. This velocity gradient gives rise to significant shear stresses, and the region within which this takes place is termed a boundary layer. Using boundary layer theory** one may show that the static pressure is constant through the boundary layer in a direction normal to the surface and that the boundary layer is a region of rotational flow so that the stagnation pressure is not constant everywhere. However, the Bernoulli equation may be used locally to find the dynamic pressure distribution within the boundary layer and hence the velocity profile if the flow is incompressible.

In the case of viscous flow over an airfoil at a moderate angle of attack, the attached boundary layers on the upper and lower surfaces join at the trailing edge. The resulting viscous-dominated flow region downstream of the trailing edge is termed a wake, within which there is a velocity deficit compared to the freestream. This deficit is a result of the flow being retarded in the airfoil boundary layers.

Measuring Devices

i) Pressure Taps and Probes

The surface pressure distribution on an airfoil will be measured by means of 24 static pressure taps. These are small holes on the surface of the model that are connected to stainless steel tubes within the model and thence to plastic tubing, which are ultimately connected to a pressure transducer. The pressure taps on the airfoil are located on the upper and lower surfaces in the chordwise direction at mid-span, according to the following chord-normalized horizontal positions:

Table 1: "Tap map" showing the chord-normalized positions of each airfoil static tap

The local velocity in the boundary layer on the ceiling of the wind tunnel and in the wake behind the airfoil will be measured indirectly by traversing a Pitot* tube through the region so as to measure local stagnation pressure; the velocity follows directly because the flow is incompressible. Since the static pressure is constant throughout the ceiling boundary layer, a single static tap on the ceiling (ideally at the measurement station) will yield the local static pressure anywhere in the boundary layer at that station. In the wake region, the local static pressure will be approximately constant through the wake and will be equal to the freestream static pressure. This is because the wake measurement station is located sufficiently far downstream of the airfoil that the pressure disturbance due to the airfoil is negligible.

The end of the Pitot probe is made of thin stainless steel tubing with a 0.063 inch outer diameter (OD) and a small orifice, so that the Pitot pressure data is a local measurement compared to most other dimensions. Generally Pitot probes such as ours may be oriented a few degrees (say 5-10 degrees) away from the local flow direction without any appreciable change in the measured pressure, hence a precise alignment of the probe with the local flow direction is not required. A Pitot-static probe (a Pitot tube with a downstream static pressure tap oriented normal to the stagnation hole) located upstream of the airfoil will be used to measure freestream dynamic pressure.

ii) Pressure Transducers

We can categorize this type of pressure transducer by the way the deformation of the structural element is transformed into an electrical signal. The two most common approaches are strain gage and capacitance type transducers. A strain gage pressure transducer consists of a thin circular diaphragm on the bottom of which are bonded tiny strain gages wired as a Wheatstone bridge. When the diaphragm experiences a pressure on its exposed upper surface that is different from the pressure in a small cavity under the diaphragm it deflects, and the resulting bridge imbalance is a measure of the deflection. Calibration provides the constant of proportionality between bridge imbalance (interpreted as a voltage) and applied pressure. The voltage output of this type of transducer is usually in the millivolt (mV) range and requires amplification prior to measurement. Relatively inexpensive transducers can be made by using semiconductor materials. In this case, the semiconductor resistors are “written” as a bridge circuit directly onto a substrate (e.g., silicon) that acts as the diaphragm. The strain on the semiconductor results in a change in semiconductor resistance; this is known as the piezoresistive effect. The change in semiconductor resistance is analogous to the change in metal resistors, except in for metal resistors, the change in resistance is primarily due to the change in the resistor’s cross-sectional area as it is strained. For semiconductor materials, the resistance change is related to other changes in the internal structure of the semiconductor.

The capacitance-based pressure transducer has a stretched membrane clamped between two insulating discs, which also support capacitive electrodes. A difference in pressure across the diaphragm causes it to deflect, increasing one capacitor and decreasing the other. These capacitors are connected to an electrical, alternating-current (AC) bridge circuit, producing a high level of voltage output (usually 10 Volts full scale without amplification).

Strain gage transducers can be made small, hence they can be internally mounted in a wind tunnel model. Also, they have reasonably good frequency response because of the small mass of the diaphragm and the short distance between the pressure tap and the diaphragm face. Capacitance transducers usually are not well suited for internal mounting (too large) and such systems do not have a fast response. Both types of transducers can be calibrated using a primary pressure standard such as a dead-weight tester, which supplies a pressure of precisely known magnitude, or using another (already) calibrated pressure transducer. In this lab, you will use both capacitance type and semi-conductor strain gage transducers to measure pressure.

Baratron

Scanivalve Digital Sensor Array

FlowKinetics Manometer/Flow Speed Meter

Whereas all previous measuring devices measure only wind tunnel and/or test article pressures, the FlowKinetics 3DP1A device also measures local ambient pressure and temperature, enabling air density and thus flow speed to be calculated. As shown in Figure 5, the FlowKinetics has a selector dial for choosing the display of either pressure or velocity (with multiple options for units on each). The FlowKinetics is an independent reference in that it does not output any signals that are read during the lab; we will be using it only for a sanity check on flow speed magnitude and for the ambient pressure and temperature measurements.

iii) Traverse

The Wind Tunnel

A wind tunnel is a duct or pipe through which air is drawn or blown.* The Wright brothers designed and built a wind tunnel in 1901. The basic principle upon which the wind tunnel is based is that the forces on an airplane moving through air at a particular speed are the same as the forces on a fixed airplane with air moving past it at the same speed. Of course, the model in the wind tunnel is usually smaller than (but geometrically similar to) the full size device, so that it is necessary to know and apply the scaling laws in order to interpret the wind tunnel data in terms of a full scale vehicle. The wind tunnel used in these experiments is of the open-return type (Figure 6). Air is drawn from the room into a large settling chamber (1) fitted with a honeycomb and several screens. The honeycomb is there to remove swirl imparted to the air by the fan. The screens break down large eddies in the flow and smooth the flow before it enters the test section. Following the settling chamber, the air accelerates through a contraction cone (2) where the area reduces (continuity requires that the velocity increase). The test (working) section (3) is of constant area (42" × 40"). The test section is fitted with one movable side wall so that small adjustments may be made to the area in order to account for boundary layer growth, thus keeping the streamwise velocity and static pressure distributions constant. The air exhausts into the room and recirculates. The maximum velocity of this wind tunnel is ~35 mph, and the turbulent fluctuations in the freestream are typically less than 0.5% of the freestream velocity. Thus, it is termed a “low turbulence wind tunnel.”

Lab Procedure

This lab is broken down into 2 major parts:

1. Surface pressure distribution measurement

2. Wind tunnel boundary layer pitot traverse survey

In all experiments during this lab, the wind tunnel should be set to maximum "throttle", which should result in a wind speed of around 16 m/s (about 35.5 mph). This may vary based on the day

Familiarization and Preliminary Setup

The TAs will first give you a brief tour of the low turbulence wind tunnel and the associated equipment, paying particular attention to that outlined in the Background section above. Once complete, you will need to perform the following items:

• Ensure Scanivalves are turned on (do this ASAP so they have time to thermally stabilize)

• Power on the FlowKinetics manometer, following the steps to configure it for measuring air (without calibrating the transducer or setting a correction factor other than 1.0)

  • Press the On/Off button to turn the manometer on

  • When prompted, press the Zero button for AIR.

  • When prompted to set a Correction Factor, press the Zero button again to store C=1.0.

• Make a manual note of the ambient pressure, temperature, and air density displayed by the FlowKinetics manometer.

• Document the mapping between Scanivalve port number and pressure tap label. Note down which Wing Pressure Port (U__ and L__) is connected to which scanivalve pressure port number (this is vital information for your data reports). Check with the TAs for accuracy.

Surface Pressure Measurements

In this first part of the lab, the primary goals are: (1) to get an intuitive feel of what is happening with the airfoil with the wind on at a variety of angles of attack, and (2) to directly measure the pressure distribution over the airfoil.

Preliminary tests

1. Configure the Scanivalve software

   1. Go to D:\AE3610\<Semester Year>\Subsonic\ScanivalveDSALink (Real Time Scanner View) and open Instance 1 of the Scanivalve executable, setting the IP address to 192.168.1.72 (the top scanner)

   2. Go to D:\AE3610\<Semester Year>\Subsonic\ScanivalveDSALink (Real Time Scanner View) and open Instance 2 of the Scanivalve executable, setting the IP address to 192.168.1.73 (the bottom scanner).

   3. If either scanner won't connect, make sure all cables are properly seated and the network switch connecting the scanners is turned on

   4. For each software instance, make sure the Scan Settings are set as per the list below (for now we will have averaging of 1 to have the fastest response with no smoothing to hide anything)

      • Period: 1000 microseconds

      • Average: 1

      • Frames Per Scan: 1000000 (arbitrarily high to prevent scan ending too quickly)

      • Conversion Units: mmHg

      • Units: Engineering Units

      • Time Stamp: No Time Stamp

      • Zero Correct: ON

      • SCAN trigger: Internal

   5. Click CALZ in each software instance to zero-calibrate each scanner

   6. Click Scan to start the scan, ensuring the sensors do indeed look zeroed

2. Following the wind tunnel operating procedure and with the help of the TAs, power on the wind tunnel to full speed

3. Take turns varying the airfoil's angle of attack, paying particular attention to the scanner readings throughout, as well as how the airfoil feels in your grip across its range of motion. Be sure to look for, and beyond, the stall angle of attack

4. Once everyone has finished, have everyone return to the control room and turn off the tunnel

Pressure distribution logging tests

1. Now having some insight into the angles of interest, decide amongst your group a minimum of six angles of interest at which you will log data. They must include:

   1. Negative angle of attack (AoA)

   2. Zero degrees AoA

   3. Low AoA below critical angle

   4. High AoA below critical angle

   5. Critical AoA: the angle of attack at which lift is greatest

   6. One Angle in the Stall Region: past critical AoA

2. Make sure the airfoil is at zero degrees angle of attack

3. For each software instance:

   1. Stop the scan

   2. Change the Averaging level in Scan Settings to 100 (this will give some low-pass filtering and smaller log file sizes at the expense of speed of response)

4. Gather pressure data at your six angles of choice:

   1. !!! Thoroughly read all the sub-steps in this step so you understand what is about to happen !!!

   2. Select one member of your group to be the designated "Angle of Attack Adjuster" for the wing

   3. Hit CALZ

   4. Click Start Data File, navigate to your group's save folder, and come up with a meaningful name for each scanner so you remember for the data reduction which was which

      1. Create your groups save folder in the following location:

      2. D:\AE3610Data\<Semester Year>\<Section>

   5. Once you are comfortable with the sequence, click Scan to begin recording data to the log file and wait 10 seconds to gather some data at wind-off condition

   6. Power on the wind tunnel to maximum speed

   7. Once the wind tunnel is up to speed, wait around 10 seconds for the zero angle of attack condition to log some data

   8. Cycle through your target angles of attack. For each target AoA, make sure the actual angle is recorded from the markings on the Angle Finder (it may differ slightly from the planned angle you selected), and that the adjuster doesn't disturb the airfoil for around 10 seconds to ensure good data

   9. Once all target AoAs have been visited, return the wing to 0 degrees AoA. Wait 10 seconds, and turn off the tunnel. Wait for the fan to come to a complete stop

   10. Click Stop and Close Data File on both Scanivalve instances

5. Ensure the data saved correctly by opening the saved data files from both instances. Plot at least one of the valid pressure tap columns*. You should see a trajectory starting and ending in zero mmHg, with a ramp up/down as the fan accelerates/decelerates, and multiple plateaus representing the points at which you stopped to log. If the data hasn't saved correctly, or the plateaus are not pronounced enough, re-attempt this procedure from the beginning. You may have a TA help ensure your data is acceptable

6. Rename your data files to include the actual angles of attack at which you took data

7. Close both Scanivalve Instances

*Each spreadsheet output by the Scanivalve software has 33 columns:

• Column 1 = Data Index

• Columns 2-17 = Pressure at each of the DSA's ports (whatever unit you used during Scanivalve logging - should have been mmHg)

• Columns 18-33 = Temperature at each of the DSA's ports (degC). Note that all scanner port pressures are recorded, so you should ignore any ports that are not used by this lab.

Pitot Traverse Surveys

LabView VI and Sensor Setup

To control the traverse and acquire data, we use a LabView VI, shown below in Figure 7. The main display on the VI is the large graph in the center, which shows airspeed derived from the Baratron.

1. Open the SubsonicWindTunnel Application VI found in D:\AE3610\<Semester Year>\SubsonicWindTunnel

2. Choose the correct file location D:\AE3610Data\<Semester Year>\<Section> and give it an arbitrary filename (this file will not be saved).

3. Click "END TEST"

4. Under Traverse Position in the VI, select the VISA Resource Name dropdown and Select COM4. If COM4 is not available, ensure the peripherals are plugged in. Select the Visa Resource Name dropdown and click Refresh. Then select the dropdown again and select COM4.

5. Start the VI again by pressing the Run button (white arrow on the top left of the window) and choose the correct file location D:\AE3610Data\<Semester Year>\<Section> and give it a sensible filename (this file will be saved).

6. Input ambient pressure and temperature from FlowKinetics into the Air Density Calculation part of the VI, which should yield a realistic air density (note that the graph will not input until this is done, otherwise it will be trying (unsuccessfully) to plot NaNs)

7. Zero the Baratron voltage by clicking Tare on the VI. Make sure you do this with the wind tunnel off, and check that the airspeed reading is centered around 0 m/s. If not, hit Tare again.

8. Take a screenshot of the VI (like below, but with values populated) to remember your settings and have the image as a reference for future use.

Traverse Setup

Since the Arduino and stepper motor are not synchronized (that is to say there is no feedback of the actual stepper position, only a running tally of the number of pulses sent to it which translates to linear position), it is crucial to initially synchronize the two. To do this, the Arduino commands the stepper downwards until it hits the bottom limit switch, at which point it moves slightly up to de-activate the switch and sets its current position to home.

1. Initial power on and zero:

   1. Check the position of the traverse carriage. If it is clear of the bottom limit switch, no action is necessary.

   2. If it is touching the limit switch, have a TA turn off power to the stepper motor using the E-STOP and manually twist the aluminum shaft coupler until the carriage is clear of the bottom limit switch. Turn the power back on once the carriage is clear by pressing the GREEN E-STOP button.

      1. Have a TA power cycle the Arduino by pressing its reset button (top-most of the two small black buttons on the circuit board). Alternatively, you can unplug it from the USB hub under the wind tunnel and plug it back in.

   3. Press the GREEN E-STOP button if you have not already done so.

   4. Prep the LabView VI for serial communications with the Arduino:

      1. Stop the VI running if it isn't already stopped by clicking "END TEST"

      2. Under Traverse Position in the VI, select the VISA Resource Name dropdown and click Refresh. Select the correct device in the list (COM4) and run the VI. Ensure you are in your group save folder and select an arbitrary file name. Successful communication is known to have occurred if the Arduino Motion Status and Arduino Time start outputting legible values.

         • As of 8/24/2023 the correct device is COM4.

         • Note that the VI only polls the VISA Resource Name once on initialization... changing the dropdown mid-experiment will not change anything. To make changes, you must stop the VI, change the dropdown, and then re-initialize the VI.

         • Occasionally, nothing can be done within the VI to get the serial communication going. In this event, fully shut down LabView (including the shortcut window that comes up when you close the VI) and open up the VI again, whilst simultaneously having a TA power cycle the Arduino.

   5. Click "Go Home" - the traverse will move down slowly until it hits the bottom limit switch, then goes up a couple of millimeters before setting this position as Home.

2. Re-synchronization procedure - If at any point the Arduino and stepper motor become unsynchronized, repeat the procedure outlined in Step 1 above.

3. Traverse reset procedure - Since there is no software stop command in the LabView VI, and the traverse sequence takes a good period of time, you can reset the traverse by pressing the Arduino's hardware reset button (top-most button of the two small black buttons on the circuit board) or power cycling it by unplugging and re-plugging the USB. You may also want to restart the VI to get a new, clean, log file.

Boundary Layer Survey

1. Prep the probe for the boundary layer survey:

   1. Run the VI and select an arbitrary file name in your group's data save folder

   2. Click on "Go Home"

   3. Have a TA install a plug over the wake stagnation hole if it is not already there

2. Re-zero the Baratron in the VI

3. Following the wind tunnel operating procedure, turn on the wind tunnel and set it to maximum speed

4. Once the wind tunnel is at maximum speed, click Initiate Boundary Layer Traverse at which point the hard-coded survey sequence will commence as follows:

   1. Return home

   2. Set Motion Status to LOGGING for "X" seconds

      • Note: The LabView VI will automatically log when it sees the Motion Status LOGGING flag

   3. Traverse "Y" inches to the next logging position, during which time the Motion Status will read RUNNING

   4. Repeat until the final position is logged

   5. Return home

5. After the probe returns Home, stop the VI and power down the wind tunnel

6. Open the log file in Notepad, copy and paste its contents into a new MS Excel spreadsheet, and save the file with a meaningful file name into your groups data folder

7. Make a quick plot to sanity check the data is all there, if not you will need to re-run the experiment. The file format is as follows: Column 1 = Time (s), Column 2 = Traverse Position (inches), Column 3 = Baratron Output (Volts).

Note (As of 1/16/2024): --The boundary layer stagnation probe is positioned just outside the sidewall of the tunnel at the start of the boundary layer survey. It traverses sideways 4 inches during the test.

Shutdown Procedure and Final Steps

Once you have verified all data has been successfully acquired:

1. Follow the wind tunnel operating procedure to power down the tunnel

2. Unplug both power cables in the control room; peripherals and e-stop

3. Close the VI without saving

4. Have your TA upload your data files from the Wind Tunnel PC to Canvas

5. Make a tubing schematic of all the probes/taps/instruments in the experiment. Peruse the "Results Needed for Report" section below to see what exact information is expected for your schematics. You may run your schematic by the TAs to ensure it is correct.

   1. Be VERY CAREFUL not to pull the tubes out of the ports!!

Data to be Taken

1. A tubing schematic showing how the pitot-static probe, the ceiling static tap, and the traverse probe are connected to the Baratron, FlowKinetics, and the Scanivalves

2. A diagram or table documenting the Scanivalve port numbers and pressure tap labels

3. Two CSV files, one per Scanivalve instance, containing the surface pressure of the wing at a minimum of 6 different angle of attacks

4. A screenshot of the LabView VI containing the ambient temperature and pressure conditions you obtained from FlowKinetics

5. A LabView log file and corresponding excel spreadsheet containing the boundary layer traverse data

Data Reduction

2. Boundary Layer Survey

   1. Convert the recorded Baratron voltage into wind speed (u) using the Baratron pressure scaling factor, the Bernoulli Equation, and the ambient atmospheric conditions recorded in the LabView VI

   2. 1. δ is defined as the height above the wind tunnel floor where the velocity becomes essentially the same as freestream velocity (>99%)

Results Needed for Report

1. Make a tubing schematic figure showing all connections necessary for the measurement of (a) the airfoil static pressures and (b) the boundary layer velocity profile. Indicate what each tube is connected to at both of its ends and label each tube as to what pressure it contains. Note: you only need one figure since the tubing setup does not change during this experiment.

2. A screenshot of the LabView VI containing information about the ambient temperature, pressure, and calculated density.

3. 1. On one figure, plot the pressure distribution at zero angle of attack as a standard and also plot the pressure distribution at the negative AoA, low AoA, and high (before critical angle) AoA for which you recorded data.

   2. On a second figure, plot the pressure distribution at zero angle of attack as a standard and also plot the pressure distribution at the high (before critical angle) AoA, critical AoA, and stall AoA

   3. Plot data points only; do NOT draw lines or smooth curves between them. Furthermore, average the multiple data points recorded for each static port so you are plotting one point for each static port at a given angle of attack.

   4. On all plots, make sure to plot the lower and upper surface data on the same figure! You should have a total of 2 figures.

Objective

This experiment will allow you to investigate hoop and axial stress/strain relations for a pressurized thin-walled cylinder. This is an opportunity to examine a system with a biaxial state of stress, as opposed to the primarily uniaxial stress systems of earlier labs. Furthermore, you will be analyzing transient (as well as steady-state) strain readings from a rosette strain gauge in response to a dynamic event. Finally, you will be able to determine the internal pressure within the vessel from your wall stress measurements and cylindrical pressure vessel relations.

Background

Many components of aerospace vehicles have an internal pressure higher than the surrounding pressure. Perhaps the most obvious examples are the fuselages of manned aircraft and the crew-compartments of spacecraft, which maintain internal pressures close to one atmosphere in low pressure environments. In other applications, the internal pressure can be significantly higher than 1 atm. For example, pressurized structures are required for many gas and liquid storage systems, e.g., propellant tanks in spacecraft, and for the propulsion engines used in aircraft and spacecraft.

We can characterize many of these structures as thin-wall pressure vessels, where the wall is essentially a membrane because its thickness is much less than other characteristic dimensions of the vessel, such as its length or radius. In an ideal thin-wall pressure vessel, the stresses are uniform across the thin wall and the bending stresses are negligible over much of the structure. The vast majority of thin-wall pressure vessels are nearly spherical or cylindrical in shape (or composed of combinations of these two geometries). A sphere provides the advantage of minimizing stresses for a given volume and storage pressure compared to other shapes, i.e., it is structurally efficient. While cylinders are not as efficient and have larger stresses at the ends, which require additional structural reinforcement, they often have significant manufacturing and implementation advantages compared to spheres (imagine the drag induced by a spherical aircraft fuselage).

Wall Stress and Pressure Relations

Ignoring the ends, we can calculate the hoop stress by considering the top half of the cylinder (a section of this is shown in Figure 2). We can use a free body diagram to get the necessary relationships for a cylinder of length L, radius R and wall thickness t. First, from the definition of stress, we have

(1)

The wall must support the difference in (vertical) forces on the inner and outer sides of the wall due to the pressure difference, so

(2)

Combining (1) and (2), gives us a relation between the hoop stress and the gauge pressure.

(3)

A similar process looking at a cross-sectional cut normal to the longitudinal axis (Figure 3), where the longitudinal force in the wall must balance the pressure difference across the end of the cylinder, gives

(4)

Solving (4) for the longitudinal stress gives

(5)

Stress-Strain Relations

As you will be measuring strains in our thin-wall vessel, you will need to convert them to stresses. As usual, this relationship is provided by Hooke’s Law for strain, e.g.,

(7)

(8)

(9)

Transients

Experimental Equipment

The equipment used in this lab are pictured in Figure 5. The pressure vessel you will investigate is the common soda can. You will mount on the can either a rectangular rosette strain gauge, which measures strain along three directions, or a T-rosette gauge, which measures the strain along two perpendicular directions. You will use the Vishay 7000 acquisition system to record the reading from the strain gauge. Care must be exercised when handling the soda can. Be careful not to indent or drop the can or shake it so as not to increase the internal pressure. Be sure not to excessively strain the lead wires connected to the T-rosette gauges.

At Home Before the Lab

Procedure

1. Measure the diameter of the can using digital calipers. Zero the calipers with the jaws in the fully closed position. Measure the diameter of the can by laying the calipers over the top of the can with the can standing upright. Carefully close the caliper jaws around the can being sure not to squeeze the can. Iterate between locating the diameter and allowing the jaws to contact the walls of the can. Conduct a total of 3 diameter measurements and record these values.

2. Measure the thickness of the soda can Aluminum material from the provided cutout sheet. Be careful not to close the calipers too tightly and deform the material plastically. Collect a total of 3 thickness measurements and record these values.

Transient Can Opening Test

1. Mount the strain gauge on your soda can.

2. If you are using a T-rosette gauge, it should be bonded so that one grid is aligned with the longitudinal axis of the can and the other grid is aligned with the hoop direction. It is best to scribe perpendicular lines on the sanded region of the can to facilitate the alignment of the gauge with the axial and radial directions.

4. Properly connect the strain gauge wires to the strain gauge card in the Vishay 7000.

5. Configure the Vishay 7000/Strain smart software interface. Be sure to supply the appropriate values for the strain gauge and transverse sensitivity factors - assign the correct values for the appropriate strain gauge grid. Set the data sampling rate to the maximum possible value (2048 samples/second). The fast sampling rate will allow you to capture some data points associated with the early, sharply rising portion of the strain gauge record when the pressure suddenly changes.

6. The individual strain gauges will already be configured to their respective 1/4-bridge circuits. Zero each 1/4-bridge circuit and perform standard shunt calibrations.

7. Shake the can carefully, being sure not to accidentally damage the strain gauge, or the lead wires.

8. WITHOUT OPENING THE CAN, carefully and gently pry up the soda can tab just a bit so that you will be able to easily get your finger underneath when you are ready to crack open the can.

10. Be sure to note down which strain gauge grid corresponds to each recorded strain gauge signal. This is especially important in the case of the 3-element rectangular rosette gauge if that is the type of gauge you are using in your experiment.

Data to be Taken

1. Can diameter and can wall material thickness.

3. Strain gauge outputs for the transient can opening test.

4. Displacement rate and the digital sampling rates for the Vishay system

5. Axial loads and bending strains for loading and unloading runs for short beam-column.

Data Reduction

1. If you used a rectangular rosette for the transient can experiment (and misaligned it as you were supposed to), then you need to transform the measured strains to the principal strains (maximum and minimum) and corresponding principal strain angles using a similar approach to that used in the cantilever beam bending lab. The principal strains should turn out to be the hoop and longitudinal strains.

2. Determine the rise times for the hoop and longitudinal strain (magnitudes) that occurred as the can was first opened.

4. Use the value of the Poisson ratio that you found from the material database in the at home exercise and estimate the radial strain in the can wall. Combine with the measured can wall thickness to estimate the change in wall thickness when the can was pressurized.

5. From you hoop and axial strain versus time profiles, identify the steady state portions of each curve (before opening the can and afterwards where the strain finally levels out to a nearly constant value). Use data from each steady state portion to estimate the overall change in hoop and longitudinal strains experienced by the can.

Results Needed for Report

1. Table of can dimensions.

2. Table of gauge factors and transverse sensitivity factors for each of the strain gauge.

3. Combined plot of measured strains (in microstrain) as function of time (in seconds) for the can-opening experiment.

1. Combined plot of hoop and axial strains (in microstrain) as a function of time (in seconds). You may truncate your plots in time as required – but be sure to clearly display the transient and steady state of your data.

3. Table of overall changes in hoop and longitudinal strains and stresses (reported in MPa) from the initial can state to the final state. Provide stress results using both the full (Equations (8)) and simplified (Equations (9)) Hooke’s Law relations.

Objective

One object of this experiment is to explore the displacement and strain behavior of structures using the digital image correlation technique. In addition, you will explore the interesting response of polypropylene, a material that exhibits different moduli in tension and compression. The experiment consists of two tests: 1) a four point bending test of a polypropylene specimen from which you will estimate the elastic moduli of polypropylene; and 2) a tension test of a second polypropylene specimen with a hole cut in it, from which you can determine the strain and stress concentrations caused by the hole. The loading for both tests will be accomplished using an Instron load frame.

Background

Digital Image Correlation

In the context of structural testing, Digital Image Correlation (DIC) is a method for tracking the point-wise displacements of a structure (typically a surface of the structure) using a series of images of the structure undergoing deformation. DIC is a non-intrusive measurement technique since nothing has to be mounted to the specimen directly. Furthermore, DIC can measure real structural component geometries in real world conditions. The DIC measurements are primarily limited by image resolution, such that higher resolution images produce more accurate results. Alternatively, a higher-resolution displacement field can be captured by zooming the camera’s field of view to a smaller portion of the specimen of interest. To use DIC, it is usually necessary to prepare the specimen by painting a high-contrast speckle pattern on the surface so that subsequent pre- and post-deformation images can be analyzed to accurately determine the displacement field on the structural surface.

There are some requirements and rules-of-thumb for producing good speckle patterns. First, the pattern should be “random”; a highly organized and repeatable pattern would produce ambiguity in the displacement measurement. Second, the size of the speckles (or high contrast objects) should be roughly the same as (or slightly larger than) a 3x3 pixel region on the digital image for optimal tracking of the displacement. If the speckles are smaller than this, the image magnification can be changed to meet this criterion. Finally, the “density” of speckle features should be sufficient to have an average of 3-4 such features in a 10x10 pixel region. DIC does not rely on correlating a single speckle features, but rather multiple features to get an average displacement in a (multi-pixel) sub-region of the image.

DIC has its origin in speckle imaging approaches used in solid mechanics, and correlation-based analysis methods developed in the 1980’s for object tracking in image processing applications and particle-based velocimetry measurements in fluid mechanics. In fact, DIC is very similar to a common velocity-field measurement approach used in fluid mechanics, Particle Image Velocimetry (PIV). In both DIC and PIV, the individual displacements of many small subregions of an imaged area are obtained by comparing images before and after the displacement has occurred. For each subregion, the “before” (pre) and “after” (post) images are cross-correlated, sometimes using Fast Fourier Transform (FFT) algorithms. The displacement for that subregion is the one that provides the best correlation between the two images. In DIC, the displacement is the desired quantity. In PIV, this displacement is divided by the (short) time between the two images to obtain the local velocity.

This analysis process is typically performed after recording a sequence of images. In DIC, after the displacement field is calculated, the strain field can be determined. The two-dimensional surface displacement field is characterized as u(x,y) and v(x,y), where u and v are the displacements in the x and y directions for a point originally at location (x,y). With u and v determined, we can obtain the surface strain field using the strain-displacement relationships

(1)

Note that differentiating the displacement data amplifies the noise in the data; so advanced analysis software like the package used here$^1$ employ additional processing approaches such as sophisticated smoothing to find the strain field from the displacement data.$^2$

Figure 1. The 3D DIC imaging systems, with two cameras mounted in a stereoscopic configurations and two light sources.

DIC (and PIV) systems come in different flavors. For example, the measured displacements of a thin region can be two-dimensional (2D) or three-dimensional (3D). In this lab, we will use a 3D DIC system (shown in Figure 1) that enables us to capture displacements in all three coordinate directions, including out-of-plane deformations. A 3D system provides more information than the more common 2D systems by adding an additional measurement. The 2D system requires only one camera (or equivalently, only camera imaging view point). To capture out-of-plane deflections, the 3D DIC system uses two cameras in a stereoscopic configuration. It is important to reiterate that 3D DIC (and PIV) systems provide three components of displacement (or velocity) from a surface (or thin planar region). There are also volumetric DIC and PIV approaches that provide 3D results for each location within a three-dimensional volume.

Our 3D DIC system, which employs two 5-megapixel cameras, will measure the displacements within a test volume that is centered on the test specimen. While the 3D DIC system provides accurate 3D displacement fields, it requires additional calibration effort compared to a simple, single-camera 2D system. The cameras are calibrated by orienting a thermally balanced plate with calibrated markings on it within the test volume.$^3$

Four-Point Flexure Testing

The four-point flexure or bending test is designed to test the flexural response of a slender beam. The goal of the four point bending test is to create a state of pure bending. Pure bending is a stress state where the bending moment is constant and the shear resultant is zero everywhere. The diagram on the left in Figure 2 illustrates a pure bending condition in which only opposing bending moments are applied to either end of the beam. Unfortunately, it is difficult to generate a pure bending moment in a real experiment. Instead, we will use opposing off-set point loads that generate a couple at either end of a beam. This configuration is shown on the right diagram in Figure 2. The advantage of this loading condition is that over the central span there are no shear loads and the beam is subject only to a bending moment.

Figure 2. Idealized pure bending load (left); four point bending test load (right).

Figure 3 illustrates the setup of the test apparatus for the four point bending test. The test specimen is placed on rollers which are placed below and above the specimen. The load frame applies a compressive load to the experimental apparatus which transmits point loads to the top and bottom of the beam. Rollers are used to ensure that simple support conditions are imposed.

Figure 3. Apparatus schematic for a four point bending test

Under ideal conditions in pure bending, the strain in the beam should be linear through the thickness:

(2)

Furthermore, if the material is linear elastic and isotropic, then Hooke's law applies and the bending moment can be calculated as follows:

(3)

where I is the second moment of area of the beam, which is given as

(4)

In Eq. (4), w is the width of the beam, and h is its depth. Therefore, if we impose M through a four point bending test, and can estimate from the digital image correlation results, we can infer the elastic modulus from

(5)

Polypropylene, however, exhibits different elastic moduli under tension and compression. As a result, the neutral surface is not at the geometric centroid of the cross-section and we have to use a composite beam analysis technique to find the elastic modulus under tension and compression. The measured strain will be offset from the geometric centroid, i.e., Eq. (2) has to be modified as follows:

(6)

where b is a strain offset.

The through-thickness stress distribution is shown in Figure 5. The y-location of the neutral surface can be found as $y_N=-b/\kappa$. The bending moment can be found by a similar integration as that in Eq. (3), except using Eq. (6) for the strain and integrating separately on either side of the neutral surface, i.e.,

(7)

Integrating Eq. (7) yields

(8)

Substituting our expression for $y_N$in (8) and simplifying gives

(9)

Next, we know from equilibrium that there cannot be an internal axial load in the beam. Therefore, the axial resultant (N) must be zero:

(10)

Integrating Eq. (10) and replacing $y_N$ with $-b/\kappa$ yields

(11)

Now combining Eq. (11) and Eq. (9) for the bending moment, eliminating __$E_C$ and using our expression for the 2nd moment of area, Eq. (4), results in

(12)

Eq. (12) can be solved for the modulus under tension, giving

(13)

Inserting this into Eq. (11) provides an expression for the compressive modulus

(14)

Stress Concentrations

Stresses around defects and sudden changes in a structure can be significantly higher than the average stress in the structure. These sharp increases in stress are called stress concentrations. A good example of a stress concentration is the behavior of the stress near a circular hole in a structure subject to uniform tension or compression. For an infinite plate loaded in-plane, the tangential stress around the edge of the hole has an analytic solution

(15)

where the coordinate θ runs circumferentially around the circular hole and $\sigma_{av}$ is the average stress in the specimen far away from the hole. The direction θ=0 is aligned with the loading direction, or the x-axis in our geometry. The maximum value of the stress (due to the hole) normalized by $\sigma_{av}$ is known as the stress concentration factor.

The stresses in planar cylindrical coordinates (i.e., $\sigma_{rr}$, $\sigma_{\theta\theta}$, and $\sigma_{r\theta}$) can be calculated from Cartesian stresses (i.e., $\sigma_{x}$, $\sigma_{y}$ and $\gamma_{xy}$) using standard coordinate transformations, for example

(16)

(17)

In this lab, you will measure displacements and strains in a polypropylene test specimen (Figure 6) with a circular cutout subject to tension. The DIC system will enable us to visualize the distribution of strains around the hole and observe the stress and strain concentration.

Figure 4. Photograph of test specimen with hole.

Procedure

Specimen Preparation

A critically important step for a DIC experiment is to prepare the specimen's surface and to apply a speckle pattern that the software can interpret and transform into a strain field. Various resources such as Trilion's FAQ and Correlated Solution's technical article detail how best to do this. For this lab, the specimens have already been prepared, so the steps below are for your enlightenment.

Printed label method

If your specimen has a flat surface and good adhesion, self-adhesive labels with pre-printed speckle patterns can be directly applied to the specimen. The following process was followed to generate speckles for this lab:

1. Download the Correlated Solutions Speckle Generator software.

3. Convert the PDF to a high-resolution image using Adobe Acrobat Online or similar. This file can also be found below this list.

4. Open Dymo Connect, set up the Extra Large shipping label in portrait, and import the image from the previous step, scaling it up to full size.

5. Print labels.

6. Remove any previous labels and/or any large residues or deposits on the specimen surface.

7. Degrease the specimen's surface.

8. Carefully apply the label in the region of interest without folding the edges, and applying firm pressure to aid its adhesion.

9. Use a sharp knife to trim away the excess label, taking care to not cut away any from the region of interest.

Paint-and-toothbrush method

For certain surfaces, such as those that aren't flat, speckling paint directly onto the specimen is the preferred approach. One such paint application method is using a toothbrush as follows:

• Lightly sand and deburr the specimen to remove any manufacturing artifacts. Wipe clean the specimen to remove any oils/residues that may prevent paint adhesion.

• Apply a matte white paint base layer to the specimen to remove any reflectivity it inherently has. Do this using spray paint, shaking the can well and applying in multiple thin layers with ample time for each layer to dry before applying the next.

• Dip a toothbrush into black paint, tapping off any excess. Having determined the appropriate distance away from the specimen to get the desired particle size beforehand, flick the brush's bristles to create a distribution of speckles over the base layer that will give good results. Consult the DIC manual for recommended particle size and coverage.

DIC System Hardware Setup

1. Take a look at the tripod and ensure the legs are resting on the 3 X's marked on the floor

2. Visually inspect the camera and ensure it is facing the Instron machine with no yaw or pitch offset. This is VERY important since this is a 2D DIC system which cannot characterize out-of-plane displacements!

3. Ensure that the LED light power cord is plugged into the power strip.

4. Plug the USB cable from the Camera into the USB 3.0 port on the front of the computer. A small green light will illuminate on the back of the camera once you plug this cable in.

5. !! IF ANYTHING IS AWRY, DO NOT FIX IT YOURSELF. ASK YOUR TA FOR HELP !!

   1. TA Note: Ask the Lab Manager or Head TA for assistance if necessary.

6. !! BE VERY CAREFUL NOT TO BUMP OR KNOCK THE CAMERA OR TRIPOD AROUND !!

   1. It is best to load all specimens into the Instron machine from BEHIND the Instron machine.

7. Turn on the Instron Machine and the Instron PC if it is not already turned on.

8. Open Bluehill Universal and ensure the Software connects to the Machine.

Four-Point Bending Test

Table 1. Four-point loading parameters to be used in experiment (defined in Figure 2)

1. Prepare the specimen:

   1. Rotate the Instron grips such that it is facing forward if necessary. You will need 2 people to do this and make sure a TA is supervising this process!

   2. Locate the square beam specimen that has a self-adhesive speckle pattern label applied.

   3. Measure the specimen's thickness, width, and length.

   4. Place the 4 point bending fixture into the Instron grips. You will need 2 people to do this and make sure a TA is supervising this process!

      1. Grip the bending fixture such that the grip section on the fixture is flush to the back of the clamps. If done correctly, there should be a gap in the front.

      2. It should also be gripped ~3mm below where the grip starts to diverge. See the image below for reference.
   5. Locate the beam specimen that has a self-adhesive speckle pattern label applied.

   6. Measure the thickness and width of the beam specimen being careful not to touch the speckle pattern with your fingers

   7. With the help of a TA, ensure that there is no folding, fading, or any other damage to the speckle pattern. If there is, apply a new speckle pattern sticker to the specimen.

   8. With the help of a TA, position the beam in the test fixture using a 12-inch lower support length and a 4-inch upper support length.

      1. Place the rollers in locations to produce the four-point bending parameters listed in Table 1. There are arrows on the fixture itself to depict where the rollers must be placed

      2. Ensure the bottom rollers are on placed below the beam. These 2 rollers are labeled with a "B"

      3. Ensure the top rollers are placed above the beam. These 2 rollers are labeled with a "T"
   9. TA Note: If this line starts to become faded, redraw it with the sharpie in the green toolbox at the end of the lab.

   10. Jog the Instron Crosshead down until there is very little play in the top rollers.

       1. You should use the fine adjustment wheel once you get very close to ensure you are not accidentally loading the specimen.

       2. BE CAREFUL NOT TO PINCH YOUR FINGERS DURING THIS PROCESS!!!!

       3. A good way to do this is to zero the load and stop and scroll the fine adjustment wheel back up AS SOON as you see a load being applied.

       4. Another option is to use your fingers but again, be careful not to pinch your fingers.

   11. Zero the load and displacement on the Instron software.

2. Verify LED Illumination:

   1. Switch on the left side LED light by flipping the switch. Check to make sure it is illuminating the area of interest.

   2. Switch off the left side LED.

   3. Switch on the right side LED light by flipping the switch. Check to make sure it is illuminating the area of interest.

   4. If both LEDs are pointing in the right direction, turn on both lights and keep them on.

   5. !! IF ANYTHING IS AWRY, DO NOT FIX IT YOURSELF. ASK YOUR TA FOR HELP !!

      1. TA Note: Ask the Lab Manager or Head TA for assistance if necessary.

3. Perform the experiment:

   1. Open Vic-Snap 10 from the Start Menu

   2. Under Project Path, select a save location that is convenient and easy to access.

   3. Under Speckle prefix, type in "4pt" and under Calibration prefix, type in "4pt-cal"

   4. Click OK. The software will open to the main screen.

   5. You should now see the specimen on your screen.

   6. If needed, HAVE A TA raise or lower the tripod with the hand crank.

   7. On the bottom of the screen, you should see a slide rule where you can change the exposure time of the photograph. Slide this back and forth until you see no overexposure on the picture.

      1. You can see overexposure when you see red dots on the image.

      2. Your goal is to get as much exposure as possible without ANY overexposure ANYWHERE on the image.

   8. When you are satisfied, click the "Focus" button on the top of the toolbar.

      1. Verify that the predicted noise is below 0.05.

      2. The camera has already been focused for you. If any changes are necessary, have your TA call the Lab Manager or Head TA for assistance.

      3. Unclick the "Focus" button.

      4. You are now ready to begin taking images.

   9. Under Project on the left side of the screen, select the "Calibration" radio button.

      1. This is the radio button directly underneath "Speckle"

      2. Be sure not to select the Calibration tab!

   10. Click the "Capture" button from the top toolbar.

   11. Under Project and Under System on the left side of the screen, switch back to the "Images" tab. You should now see a number 1 next to Calibration indicating you have taken you calibration photograph

   12. Select the "Speckle" radio button.

   13. Take a reference image of the specimen WITHOUT any loading by clicking "Capture" from the top toolbar. Your count of Speckle photographs should now read 1.

   14. Jog the Instron down using the fine adjustment wheel until you've applied a bending load of 150 lbf.

   15. Click "Capture" from the top toolbar. Your count of Speckle photographs should now read 2.

   16. Unload the specimen

4. Upload Images to Vic-2D:

   1. Without, closing the Vic-Snap Software, open the Vic-2D 7 software from the start menu.

   2. From the Home page, select the "Calibration images" button.

   3. Locate the folder in which you have saved your images, and select the "4pt-cal" TIF file you captured earlier

   4. Select "Speckle Images" button from the top toolbar (4th from the left)

   5. Select and upload the Reference image and Loaded image TIF files you took earlier using Vic-Snap

   6. On the left hand side under Project, you should now have 2 speckle images and one calibration image

   7. Ensure that the proper image is selected as your reference image. It will have a red arrow next to the image.

      1. If you are unsure which of your speckle images was the reference image, you can double click the image and see which one is under loading.

5. Calibrate the Scale

   1. In this step, we will be using the calibration image to understand the dimensions of the specimen. We will draw a line across the dimension of the specimen that we know. Using this information, the software will be able to calculate strain in the dimensions we are interested in rather than pixels.

   2. Click the "Calibrate Scale" button from the top toolbar (6th from the left)

      1. Scroll in as best you can to zoom into the picture and pan to the required area. You can also resize the entire window if needed.

      2. Once you are satisfied with how far you are zoomed in, select the "Manually Select" button under Tools (2nd from the left)

      3. Holding the left click button on the mouse, drag a line across the entire width of the specimen

         1. HINT: this line needs to be perpendicular to the length of the specimen. Think of the best way you can make this line as close to perpendicular as you can!

         2. You can always redraw this line until you are satisfied

      4. Under Point distance, enter the width of the specimen (1 inch). Click OK to save this. If you get prompted that this is a short line, select "Yes"

6. Perform Displacement Analysis

   1. You should see a box that says "Aoi tools" near the top left of your screen. If you don't see this, select "Aoi Editor" from the "Window" drop down menu at the top of the screen

   2. Select the "Create Rectangle" button under Aoi tools (2nd from the left)

   3. Highlight your area of interest. This should be an area between the two rollers where you expect to see pure bending. You should also select a VERY small portion (a sliver) of the black area outside of the speckle pattern to ensure you are capturing the specimen edge effects!

      1. You can delete and redo this as many times as you would like until you are satisfied with the area you select

   4. Under Aoi tools, select the "Create Starting Point" button (2nd from the right)

      1. Select a point somewhere within the area of interest.

   5. Keep the default Subset value of 29 and Steps value of 7

   6. Select the Green "Start Analysis" button from the top toolbar. Verify that the proper image is selected for your reference and that the loaded image is checked in the box below.

   7. Also verify your output directory. Keep this the same as folder in which you saved your images so everything is in one place!

   8. Click "Run"

   9. You will see a preview of the analysis on the proceeding screen. Does it look like what you would expect to see? Click "Close"

   10. Now that you have run your displacement analysis, we can calculate strain using this displacement data and the calibration image we characterized earlier.

   11. Select the "Calculate Strain" button from the top toolbar (7th from the right)

   12. Ensure that both ".out" files are selected for your computation. Click "Preview"

       1. Does this look like what you would expect?

       2. Discuss!

   13. If you are satisfied with this preview and are confident that this looks like what you would expect, click "Start"

   14. Click "Close"

7. Visualize your Results

   1. Under the "Plot" drop down menu at the top of the screen, select "New Plot"

   2. Under "Plotting Tools" on the left hand side, make sure you are on the "Contour" tab

   3. Under "Project" on the left hand side, go to the "Data" tab. Double click your loaded image.

   4. Under "Plotting Tools" on the left hand side again, change the variables between xx, yy, xy, and principal strains and observe all the plots. You can and should also observe displacements in all 3 cartesian directions

      1. Discuss what you see with your labmates!

      2. Take notes in your lab notebooks!

      3. Does this all make sense?

      4. Discuss with your TA

      5. Redo any portions of the procedure if needed

   5. If you are satisfied with your results, select the "Data" drop-down menu and under "Export" select "All Data"

   6. Make sure both of your ".out" files are selected and click "Export"

      1. You may select any file format that works for you. The default is a CSV and is what we recommend.

Open-Hole Tension Test

1. Prepare the specimen:

   1. Rotate the Instron grips such that it is facing sideways if necessary. You will need 2 people to do this and make sure a TA is supervising this process!

   2. Locate the open-hole dog-bone specimen that has a self-adhesive speckle pattern label applied.

   3. Measure the specimen's thickness, width, and hole diameter.

   4. With the help of a TA, ensure that there is no folding, fading, or any other damage to the speckle pattern. If there is, apply a new speckle pattern sticker to the specimen.

   5. With the help of a TA, position the specimen in the clamping test fixture.

   6. Zero the load and displacement on the Instron software.

2. Verify LED Illumination:

   1. Switch on the left side LED light by flipping the switch. Check to make sure it is illuminating the area of interest.

   2. Switch off the left side LED.

   3. Switch on the right side LED light by flipping the switch. Check to make sure it is illuminating the area of interest.

   4. If both LEDs are pointing in the right direction, turn on both lights and keep them on.

   5. !! IF ANYTHING IS AWRY, DO NOT FIX IT YOURSELF. ASK YOUR TA FOR HELP !!

      1. TA Note: Ask the Lab Manager or Head TA for assistance if necessary.

3. Perform the experiment:

   1. Open Vic-Snap 10 from the Start Menu

   2. Under Project Path, select a save location that is convenient and easy to access.

   3. Under Speckle prefix, type in "OpenHole" and under Calibration prefix, type in "OpenHole-cal"

   4. Click OK. The software will open to the main screen.

   5. You should now see the specimen on your screen.

   6. If needed, HAVE A TA raise or lower the tripod with the hand crank.

   7. On the bottom of the screen, you should see a slide rule where you can change the exposure time of the photograph. Slide this back and forth until you see no overexposure on the picture.

      1. You can see overexposure when you see red dots on the image.

      2. Your goal is to get as much exposure as possible without ANY overexposure ANYWHERE on the image.

   8. When you are satisfied, click the "Focus" button on the top of the toolbar.

      1. Verify that the predicted noise is below 0.05.

      2. The camera has already been focused for you. If any changes are necessary, have your TA call the Lab Manager or Head TA for assistance.

      3. Unclick the "Focus" button.

      4. You are now ready to begin taking images.

   9. Under Project on the left side of the screen, select the "Calibration" radio button

      1. This is the radio button directly underneath "Speckle"

      2. Be sure not to select the Calibration tab!

   10. Click the "Capture" button from the top toolbar.

   11. Under Project and Under System on the left side of the screen, switch back to the "Images" tab. You should now see a number 1 next to Calibration indicating you have taken you calibration photograph

   12. Select the "Speckle" radio button.

   13. Take a reference image of the specimen WITHOUT any loading by clicking "Capture" from the top toolbar. Your count of Speckle photographs should now read 1.

   14. Jog the Instron crosshead up using the fine adjustment wheel until you've applied a tensile load of 2.2 kN.

   15. Click "Capture" from the top toolbar. Your count of Speckle photographs should now read 2.

   16. Unload the specimen

4. Upload Images to Vic-2D:

   1. Without, closing the Vic-Snap Software, open the Vic-2D 7 software from the start menu.

   2. From the Home page, select the "Calibration images" button.

   3. Locate the folder in which you have saved your images, and select the "OpenHole-cal" TIF file you captured earlier

   4. Select "Speckle Images" button from the top toolbar (4th from the left)

   5. Select and upload the Reference image and Loaded image TIF files you took earlier using Vic-Snap

   6. On the left hand side under Project, you should now have 2 speckle images and one calibration image

   7. Ensure that the proper image is selected as your reference image. It will have a red arrow next to the image.

      1. If you are unsure which of your speckle images was the reference image, you can double click the image and see which one is under loading.

5. Calibrate the Scale

   1. In this step, we will be using the calibration image to understand the dimensions of the specimen. We will draw a line across the dimension of the specimen that we know. Using this information, the software will be able to calculate strain in the dimensions we are interested in rather than pixels.

   2. Click the "Calibrate Scale" button from the top toolbar (6th from the left)

      1. Scroll in as best you can to zoom into the picture and pan to the required area. You can also resize the entire window if needed.

      2. Once you are satisfied with how far you are zoomed in, select the "Manually Select" button under Tools (2nd from the left)

      3. Holding the left click button on the mouse, drag a line across the entire width of the specimen

         1. HINT: this line needs to be perpendicular to the length of the specimen. Think of the best way you can make this line as close to perpendicular as you can!

         2. You can always redraw this line until you are satisfied

      4. Under Point distance, enter the width of the specimen (1.5 inches). Click OK to save this. If you get prompted that this is a short line, select "Yes"

6. Perform Displacement Analysis

   1. You should see a box that says "Aoi tools" near the top left of your screen. If you don't see this, select "Aoi Editor" from the "Window" drop down menu at the top of the screen

   2. Select the "Create Rectangle" button under Aoi tools (2nd from the left)

   3. Highlight your area of interest. You should select the area around the open hole all the way to the edge of the specimen.

      1. Select a vertical length that is about 1.5x the width of the dogbone specimen, creating a rectangle

      2. You should also select a VERY small portion (a sliver) of the black area outside of the speckle pattern to ensure you are capturing the specimen edge effects!

      3. You can delete and redo this as many times as you would like until you are satisfied with the area you select

   4. Select the "Cut Circle" button under Aoi tools (3rd from the right)

      1. Cut out dark section of the hole MAKING SURE you are not cutting out any part of the specimen itself!

   5. If necessary, select a starting point by clicking "Select Starting Point" under Aoi tools (2nd from the right).

   6. Keep the default Subset value of 29 and Steps value of 7

   7. Select the Green "Start Analysis" button from the top toolbar. Verify that the proper image is selected for your reference and that the loaded image is checked in the box below.

   8. Also verify your output directory. Keep this the same as folder in which you saved your images so everything is in one place!

   9. Click "Run"

   10. You will see a preview of the analysis on the proceeding screen. Does it look like what you would expect to see? Click "Close"

   11. Now that you have run your displacement analysis, we can calculate strain using this displacement data and the calibration image we characterized earlier.

   12. Select the "Calculate Strain" button from the top toolbar (7th from the right)

   13. Ensure that both ".out" files are selected for your computation. Click "Preview"

       1. Does this look like what you would expect?

       2. Discuss!

   14. If you are satisfied with this preview and are confident that this looks like what you would expect, click "Start"

   15. Click "Close"

7. Visualize your Results

   1. Under the "Plot" drop down menu at the top of the screen, select "New Plot"

   2. Under "Plotting Tools" on the left hand side, make sure you are on the "Contour" tab

   3. Under "Project" on the left hand side, click the "Data" tab. Double click your loaded image.

   4. Under "Plotting Tools" on the left hand side again, change the variables between xx, yy, xy, and principal strains and observe all the plots. You can and should also observe displacements in all 3 cartesian directions

      1. Discuss what you see with your labmates!

      2. Take notes in your lab notebooks!

      3. Does this all make sense?

      4. Discuss with your TA

      5. Redo any portions of the procedure if needed

   5. If you are satisfied with your results, select the "Data" drop-down menu and under "Export" select "All Data"

   6. Make sure both of your ".out" files are selected and click "Export"

      1. You may select any file format that works for you. The default is a CSV and is what we recommend.

Shutdown Procedure

1. CHECK YOUR DATA FILES. REDO ANY PORTIONS OF THE LAB YOU FEEL YOU MUST REDO

2. Close the Vic-2D and Vic-Snap softwares. You may save the project to your folder in Vic-2D if you wish but it is not necessary

3. Turn off both the LED lights by flipping the switches.

4. Remove the specimens from the Instron Machine and place them on the Table for the next groups.

5. Unplug the Camera USB cable from the front of the computer.

6. Have your TA upload your data to Canvas. It is best to zip your entire folder containing all your images, output files, and exported data files