Lab4_Strain_Gauge_100322

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University of Massachusetts, Lowell *

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3020

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Mechanical Engineering

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Dec 6, 2023

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MECH.3020 - Strain Gage Measurement Lab 1 Rev 100322 MECH3020 - Experiment 3 Strain Gauge Measurements Introduction The design of components for many engineering systems is based on the application of theoretical models. The accuracy of these models can be verified through testing. One way of validating a math model is to use a strain gage measurement system to measure the strain at the surface of a structure. The sensor used to transfer a mechanical strain to a quantifiable output is the strain gage. The strain gage has a resistance which changes as a function of mechanical strain. Although the change in resistance can be quantified using an ohm meter, signal conditioning is used to convert the change in resistance to a voltage. The voltage may then be amplified, thus reducing quantization errors. The relationship between the input strain and the output voltage may be determined using the system sensitivity. The objective of this assignment is to experimentally determine the system sensitivity and compare it to the ideal sensitivity of a strain gage measurement system. The actual system sensitivity will then be used to determine the modulus of elasticity of a cantilever beam. Pre-Lab Assignment Pre-Lab assignments are to be done in your lab notebook following normal lab notebook documentation procedures. The Pre-Labs are not to be handed in but will be checked in the lab to assure that they have been completed. 1. Determine the ideal system sensitivity of a strain gage system expressed in millivolts per microstrain, given the following: Sg = 2.130, Ei = 1.5 Vdc, G = 500. Also, determine the ideal slope of the calibration equation in microstrain per millivolt. 2. Using a Excel spreadsheet, calculate the deflection required to produce 100, 200, 300, 400, 500, 600, 700, 800, and 900 microstrain at a strain gage mounted to a cantilever beam. The geometry of the beam and location of the gage is as follows: b = 1.0" (beam width) t = 0.125" (beam thickness) L = 11.5" (length of cantilever beam) x = 10.0" (distance from the strain gage to the micrometer) Copy your results to your logbook. Save your spreadsheet in your USB drive and bring it to the lab .

MECH.3020 - Strain Gage Measurement Lab 2 Rev 100322 3. Determine ten different beam loading values that will be used in lab to end load a cantilever beam using weights. Load values should increase by 100 gram intervals with an initial load of approximately 200 grams. Calculate the stress levels generated at the strain gage location for each load. Copy your results to your logbook. Save your spreadsheet in your USB drive and bring it to the lab . 4. Read Section 8.1 and 8.6 in Wheeler & Gangi text 2 nd edition. 5. Review the additional notes appended at the end of this document or on the webpage (Old Writeup), (These are critically important to understand every part of this lab assignment). Assignment 1: Equipment Configuration & Initialization Procedure 1. Install the cantilever beam into the Flexor if not already assembled. The beam should be placed with the strain gage on the upper surface closest to the clamp. Adjust the free end of the beam so that motion is not impeded by the sides of the Flexor. 2. Measure and record the following cantilever beam dimensions: x - distance from the center of the strain gage to the micrometer load point. L - distance from the clamped end of the beam to the micrometer load point. b - beam width t - beam thickness 3. Compare the measured values with dimensions used in the pre-lab assignment. If the values of x, b, and t differ, pre-lab calculations must be recalculated using your excel spreadsheet. 4. Connect the lead wires of the strain gage to P3 Strain Indicator’s Channel 1 as shown in Figure 1.

MECH.3020 - Strain Gage Measurement Lab 3 Rev 100322 Figure 1 – Quarter Bridge Connections – P+ (Red), S- (White) and D 350 (Black) 5. Turn on the P3 Strain Indicator. 6. Press the BAL button to bring the Balance menu up. Press BAL again to initialize the Balancing algorithm. Finally, press the RECORD button to save the balance parameters. 7. The Gage factor has to be updated to 2.130 . In order to do so, press the GF/SCALING button, then select Gage Factor using the arrows located around the MENU button. Once the change is made, press MENU to go back to the main screen. 8. Using a BNC cable, connect the Strain Indicator output to the multimeter. Remember, the signal generated by the P3 is a DC signal. 9. Press the MENU button, select “Options” and press MENU. Then, select “Outputs”. Here turn the “Analog Out” to “Chan 1”. Then, set the “Out Range” to “Normal”. Finally, press MENU. The P3 will display the level of strain while the multimeter a constant voltage. This will be the initial voltage. Record both values. 10. Press down on the beam. Note the change in output voltage on the multimeter as well as strain on the Strain Indicator display. As the strain gage is mechanically strained, the change in resistance is sensed by the wheatstone bridge and a resultant output voltage is generated which is automatically converted to strain by the Strain Indicator

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MECH.3020 - Strain Gage Measurement Lab 4 Rev 100322 Assignment 2: Determine the System Sensitivity The system sensitivity of the strain gage measurement system can be determined by displacing the free end of the cantilever beam a known distance and recording the output voltage generated by the signal conditioning module. The strain induced in the beam at the strain gage location is determined using the following equation: where is the strain at the surface of the beam at the gage location, is the deflection at the free end of the beam, is the beam's thickness, is the distance from the strain gage to the point where the load is applied, and is the cantilever beam length ( Note: this L is different from the one of Assignment 1 ). Procedure 1. Adjust the micrometer on the Flexor so that the tip is just touching the cantilever beam. Record the reading on the micrometer, Strain Indicator and the multimeter as the initial displacement and corresponding output voltage for the undeflected beam. 2. Using the micrometer, deflect the beam an amount that will produce a strain of 100 microstrain at the strain gage. Record the strain level, the micrometer setting, and the output voltage indicated by the multimeter. 3. Deflect the beam an amount that will produce strain levels of 200, 300, 400, 500, 600, 700, 800, and 900 microstrain at the strain gage. Record the strain level, beam deflection, and output voltage from the system. 4. Unload the beam and record the final output voltage. The output should return to the initial value with no load on the beam. If the two values do not coincide, record the final value. Why do you think this may have occurred?

MECH.3020 - Strain Gage Measurement Lab 5 Rev 100322 Assignment 3: Young's Modulus Determination The Modulus of Elasticity of the cantilever beam can be determined by hanging known weights from the free end of the beam and recording the corresponding output voltage from the signal conditioning amplifier. The flexure formula can be used to calculate the stress level at the gage, while the strain gage system sensitivity is used to quantify the strain. Plotting stress and strain data and performing a regression analysis on the linear elastic range will result in the determination of the Modulus of Elasticity of the beam. NOTE: Make sure you check your units! Procedure 1. Add the weight necessary to produce the first stress level calculated in the pre-lab assignment question #3. Now, the weight will be placed at the tip of the beam. Update your Excel spreadsheet with the new values of x and L. 2. Note that the weights can be "piggy-backed" to achieve the desired weight, as shown in Figure 2. Record the weight and the corresponding output voltage and corresponding strain. Repeat this process for a total of ten loading values calculated in the pre-lab. 3. Unload the beam and record the final output voltage. The output should return to the initial value with no load on the beam. If the two values do not coincide, record the final value. Why do you think this may have occurred? Document your observations on your logbook. Weights Figure 2 - Young's Modulus Determination

MECH.3020 - Strain Gage Measurement Lab 6 Rev 100322 Post-lab Analysis NOTE: Be brief, concise and to the point in all responses. Provide clear, concise answers to questions. Lengthy responses that ramble will not be graded and may lose additional points. 1. Determine the strain gage system sensitivity. Compare the actual system sensitivity to the ideal value determined from the pre-lab assignment. Discuss possible sources of error. 2. Make a proper engineering plot of the strain produced at the strain gage and the corresponding output voltage from the signal conditioning amplifier. Properly distinguish experimental data from curve fit data. 3. Using the calibrated system sensitivity, determine the strain produced at the strain gage in Assignment #3. 4. Compare the ten values of strain obtained while loading the beam to those obtained during unloading. Discuss why differences may have occurred. Are these differences acceptable? 5. Calculate the stress levels generated from end loading the cantilever beam in Assignment #3. 6. Make a proper engineering plot of the stress vs. strain from Assignment #3. Perform a regression analysis on the data to determine Young's Modulus. 7. What type of material is the beam made of? Support conclusions with theoretical and experimental proof as well as listing any publications referenced. 8. Explain two methods of increasing the strain gage system sensitivity. Why would the strain gage measurement system sensitivity need to be increased?

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