paraphrasing
tbpl_93
lab_report_2.docx
Mohammad Albuloushi
Experiment II
The Resistance Strain Gauge
EGME 306A
Monday 8:30 – 11:15 am
Group Members: Bader Alrashidi – Christian Aguinaga – Yousef Ali
Abstract
The main objective of this experiment was to become familiar with the use of the resistance strain gauge. Then after collecting data obtained from the strain gauge, we compare them with the data also obtained from the extensometer measurements. The experiment was conducted using a machine that applies load to the sample and calculates the elongation, which helps us to calculate the strain. There was also a strain a gauge attached to the sample, which gave us a reading of the strain directly. Another objective of this experiment was to learn a new way to calculate error during the experiment by using the standard error SE method, which will be shown in the sample calculation page. It is really difficult which to decide which measurement method is most precise of most accurate. As for the analytical error for stress, the value calculated is 13.33. While for the statistical standard error SE, the value found is 71.65 for the data obtained from the extensometer, and 0.07776 for the data obtained from the strain gauge.
TABLE OF CONTENTS
Abstract………………………………………………………………………………2
Table of contents…………………………………………………………………….3
Introduction and Theory…………………………………………………………….4-5
Procedures…………………………………………………………………………..6-7
Summary of Important Results………………………………………………………8-9
Sample Calculations and Error Analysis……………………………………………10-11
Discussion and Conclusion…………………………………………………………..12
References……………………………………………………………………………13
Appendix……………………………………………………………………………..14
Introduction Theory
Measuring the strain using the resistance strain gauge is all based on the change in the electrical resistance of a thin wire when this wire deforms. The resistance (R) of the wire depends on the length (L) and area (A) of the wire. The equation used to calculate the resistance is:
(II-1)
Where is the resistivity of the wire. Since the volume of the wire is V=LA, (II-1) can also be written as:
(II-2)
If the thin wire is bonded securely to an object, which is being strained, this strain will change the length of the wire from L to . According to equation (II-2), this change in length will cause a change in resistance. Assuming the volume V does not change, and the resistivity of the material remains the same, it follows from eq. (II-2) that:
And
(II-3)
For finite, but small, changes eq. (II-3) becomes
(II-4)
And
(II-5)
Where F=2.125 is the gauge factor, since the strain is defined ε= ∆L/L. The strain from the strain gauge is directly proportional to the fractional change in resistance. The set up reads the strain directly when the gauge factor is 2, so whenever F differs from this value it is necessary to correct the strain, as follows:
(II-6)
Where,
= Corrected strain
= Strain read by the data acquisition
Procedures
First we ensured that the “Emergency Stop” is released and not activated then we turned on the PC and the power switch at the bottom panel of the MTS frame. After that we ensured that the Wedge Action Grips are installed on the MTS frame. We double clicked the TestWorks 4 icon on the PC, which is the software that operates the MTS and collects information from the extensometer. Then, we logged in under “306A lab.” We clicked on “Open Method” drop down list after that then highlighted “Exp.2 Tensile with extensometer Mod9-15-X,” the clicked OK.
After that we clicked on the “Calibrate Device” icon and highlighted the load cell serial number associated with the load cell that is installed on our MTS machine, and then clicked Calibrate. We clicked Next the waited until the process is completed then clicked Finish then OK. After that, we measured the diameter of the Aluminum bar using the calipers and recorded it. Then we used the handset on the side of the MTS machine to install the Aluminum sample simply by lowering the grips using the arrow buttons. Then, we connected the wires from the strain gauge, which is attached to the Aluminum bar, to the terminals identified as “#1 Strain” on the ADC interface box and ensured that the internal ribbon cable is installed on the right side connector of the interface box. After that we attached extensometer at narrow section of the test sample. We connected the cable of the extensometer to J1 DC Cond 1 (behind the MTS frame). We went to the computer and right clicked inside the load and the Extensometer windows then left clicked on “Zero Channel.” Then, we double clicked on the National Instruments or Measurement & Automation icon on the desktop after minimizing the TestWork 4 window and the LabView opened. After that, we clicked on the “down arrow” in the open box and clicked on the file specified by the lab manual. Then, on LabView, we clicked the run arrow then the Zero Strain box. Then we opened the windows for the “TestWorks” and “LabView” side-by-side and clicked on the “Motor Reset” button. Then we clicked on the “Green Arrow” in the TestWork 4 window when prompted type in the Aluminum bar diameter. After doing all of this we were able to collect screen data from the following sources (1) Load & length increase from TestWork 4, and (2) Strain from LabView. Then, we paused the load in an increment of 100 lb and recorded the elongation from the extensometer and the strain using the strain gauge. After reaching 1500 lb, which is below the elastic limit for Aluminum, we stopped both calculations and wrote the data down on a sheet of paper.
Summary of Important Results
Figure II-1 Stress vs. Strain Using the Strain Gauge Reading
Figure II-2 Stress vs. Strain Using the Extensometer Readings
In every graph, by convention, strain is always plotted on the horizontal axis and stress on the vertical axis. The slope of the curve on the graph is known as Young’s Modulus or the modulus of elasticity. For the first graph, we used the data obtained from the resistance strain gauge to plot the graph. The slope of it, which is the modulus of elasticity turned out to equal 999,991.52 (psig). While for the other graph, we used the data obtained from the extensometer and the Young’s modulus equals 10,740,785.28 (psig).
SAMPLE CALCULATION AND ERROR ANALYSIS
Calculating Stress:
Calculating Strain:
Standard Error from strain gauge:
=
Standard Error from extensometer:
Modulus of Elasticity:
Analytical Error:
The uncertainty of the strain gauge method of measurement is that the wires are not attached properly or the wires are old which will not give us accurate results. While, the uncertainty of the extensometer method could be wrong calculation, or the extensometer is not installed properly on the middle of the sample.
Discussion and Conclusion
After successfully conducting the experiment, gathering the data, and plotting the graphs, in my opinion, the resistance strain gauge method is more convenient and faster. As plugging in the data on excel helps you a lot with the calculations. In the strain gauge method, we got a modulus of elasticity of 999,991.52 (psig). Meanwhile, we got 10,740,785.28 (psig) for the Young’s Modulus in using the data from the extensometer. The published value of the modulus of elasticity for the Aluminum sample is 10x106 (psig). The standard error for the strain gauge was calculated to be 0.07776 and on the other hand, for the extensometer, the standard error is calculated to be 71.6523, which makes the resistance strain gauge more accurate.
Reference
[1] CSUF EGME 306A Lab Manual.
[2] Modulus of Elasticity – Young Modulus for Some Common Materials
http://www.engineeringtoolbox.com/young-modulus-d_417.html
Appendix
|
Stress (psig) |
Strain (extensometer) (in/in) |
|
|
|
|
962.3422562 |
0.00015 |
|
1999.780188 |
0.000245 |
|
2806.680365 |
0.00031 |
|
3771.338462 |
0.0004 |
|
4757.882162 |
0.00049 |
|
5722.865198 |
0.000575 |
|
6702.48005 |
0.000665 |
|
7933.406604 |
0.0008 |
|
8879.7152 |
0.00087 |
|
9540.125197 |
0.000935 |
|
10511.22473 |
0.00103 |
|
11379.96846 |
0.00111 |
|
12400.01911 |
0.00121 |
|
13286.39557 |
0.00129 |
|
14339.74292 |
0.00139 |
|
Stress (psig) |
Strain Gauge (in/in) |
|
|
|
|
962.3422562 |
0.00096202 |
|
1999.780188 |
0.00199978 |
|
2806.680365 |
0.00280668 |
|
3771.338462 |
0.003771338 |
|
4757.882162 |
0.004757882 |
|
5722.865198 |
0.005722865 |
|
6702.48005 |
0.00670248 |
|
7933.406604 |
0.007933407 |
|
8879.7152 |
0.008879715 |
|
9540.125197 |
0.009540125 |
|
10511.22473 |
0.010511225 |
|
11379.96846 |
0.011379968 |
|
12400.01911 |
0.012400019 |
|
13286.39557 |
0.013286396 |
|
14339.74292 |
0.014339743 |
|
Approximate Stress (Gauge) (psig) |
Approximate Stress (Extensometer) (psig) |
|
|
|
|
962.1021985 |
1064.322792 |
|
1999.85323 |
2084.687894 |
|
2806.746564 |
2782.832437 |
|
3771.396481 |
3749.494112 |
|
4757.931815 |
4716.155787 |
|
5722.906668 |
5629.114036 |
|
6702.513213 |
6595.775711 |
|
7933.429329 |
8045.768224 |
|
8879.7299 |
8797.616194 |
|
9540.134297 |
9495.760737 |
|
10511.2256 |
10516.12584 |
|
11379.96196 |
11375.38066 |
|
12400.00396 |
12449.44919 |
|
13286.3729 |
13308.70401 |
|
14339.71131 |
14382.77254 |
17
