22.302 Experiment 5 Strain Gage 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 1. Determine the ideal system sensitivity of a strain gage system expressed in millivolts per microstrain, given the following: Sg = 2.085, Ei = 2 Vdc, G = 1000. Also, determine the ideal slope of the calibration equation in microstrain per millivolt. 2. 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" t = 0.125" L = 10.0" x = 9.0" (beam width) (beam thickness) (length of cantilever beam) (distance from the strain gage to the micrometer) 3. Determine ten different beam loading values that will be used in lab to end load a cantilever beam using a platform and weights. Load values should increase by 100 gram intervals with an initial load of approximately 173 grams. Calculate the stress levels generated at the strain gage location for each load. The weights available are as follows: 1-173 gram platform 1-100 gram weight 2-200 gram weights1-500 gram weight 4. Read Section 8.1 and 8.6 in text. ME 22.302 Strain Gage Measurement Lab 1 Rev 010505
Assignment 1: Equipment Configuration & Initialization Prior to calibrating the strain gage measurement system, the signal conditioning module must be connected to the strain gage and initialized. The four major components of the 2311 Signal Conditioner Amplifier are the variable DC power supply, wheatstone bridge, low pass filter, and amplifier. The power supply is used to excite the wheatstone bridge which converts a change in the strain gage resistance to a corresponding change in voltage. The amplifier is used to amplify the output signal from the wheatstone bridge reducing possible quantization errors. The lowpass filter is used to filter out undesired frequencies associated with background noise. Procedure 1. Install the cantilever beam into the Flexor. 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. Connect the lead wires of the strain gage to the binding posts of the Flexor as shown in figure 1. Connect leads numbered 1, 2, and 3 of the Flexor to the input cable of the 2311 Signal Conditioning Amplifier at points "S-", "D-120", and "P+" respectively. 3. 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 Figure 1 - Strain Gage System Initialization 4. Compare the measured values with dimensions used in the pre-lab assignment. Adjust the length of the cantilever beam so that it coincides with the pre-lab value used. If the values of x, b, and t differ, pre-lab calculations must be recalculated. ME 22.302 Strain Gage Measurement Lab 2 Rev 010505
5. Check that the power to the 2311 Signal Conditioner is shut off. Plug the power cord from the bottom rear of the 2311 into the bench power strip. 6. Connect the Bendix connector attached to the wire junction to the rear of the 2311. The +/- 10 volt BNC output on the top rear of the 2311 should be connected to the oscilloscope and digital multimeter. 7. Set the LOW PASS FILTER to 10 Hz. Shut the EXCITATION switch to OFF. 8. Turn the 2311 on using the POWER button at the bottom of the module. 9. Balance the power amplifier by setting the gain to X100. Check that the dial to the left of the gain buttons is set to 1. Adjustment will result in a fractional value of the set gain. 10. Examine the two lights at the top of the front panel. If either is lit, turn the AMP BAL adjustment screw located below the EXCITATION toggle switch so that both lamps are fully extinguished. 11. Balance the internal wheatstone bridge by first setting the EXCITATION voltage to 2 Vdc. Turn the EXCITATION switch to ON. One of the two output lamps at the top of the module should light indicating that the wheatstone bridge is out of balance. Press the AUTO BAL switch to the RESET position for a second then release. After a few seconds the lamps should extinguish indicating the bridge is balanced. 12. Set the amplifier GAIN to X1000. If either of the output lamps are lit, turn the TRIM knob until the lamps are extinguished. The multimeter should be reading zero volts. The strain gage system is now initialized and ready to make measurements. 13. Manually load the beam. Note the change in output voltage on the multimeter as well as the two output lamps on the front of the 2311. As the strain gage is mechanically strained, the change in resistance is sensed by the wheatstone bridge and a resultant output voltage is generated. Figure 2 shows the major components of the 2311 Signal Conditioning Amplifier used to convert the input resistance to an output voltage. ME 22.302 Strain Gage Measurement Lab 3 Rev 010505
Figure 2-2311 Signal Conditioning Amplifier 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. Procedure 1. With the wheatstone bridge balanced, an output voltage of 0 Volts DC should be displayed on the multimeter. Adjust the TRIM knob if necessary. 2. Adjust the micrometer on the Flexor so that the tip is just touching the cantilever beam. The multimeter and output lamps can be used to determine when contact occurs. Record the reading on the micrometer and the multimeter as the initial displacement and corresponding output voltage for the undeflected beam. 3. Using the micrometer, deflect the beam an amount that will produce a strain of 100 microstrain at the strain gage. Record the ideal strain level, the micrometer setting, and the output voltage indicated by the multimeter. 4. 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 ideal strain level, beam deflection, and output voltage from the system. 5. Unload the beam and record the final output voltage. The output should return to ME 22.302 Strain Gage Measurement Lab 4 Rev 010505
the initial value with no load on the beam. If the two values do not coincide, contact the instructor. 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 2311 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. Procedure 1. Initialize the 2311 Signal Conditioning Amplifier. 2. After weighing the platform, hang the hook and platform from the end of the cantilever beam as seen in figure #3. Record the platform weight and output voltage from the strain gage system. 3. Add the weight necessary to produce the 2 nd stress level calculated in the pre-lab assignment question #3. Record the weight including the weight of the platform and the corresponding output voltage. Repeat this process for a total of ten loading values calculated in the pre-lab. 4. Unload the beam at the same increments and record the output voltage to verify that significant hysteresis errors have not occurred. Figure 3 - Young's Modulus Determination ME 22.302 Strain Gage Measurement Lab 5 Rev 010505
Post-lab Analysis 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. Plot the strain produced at the strain gage and the corresponding output voltage from the 2311 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. Plot 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 to methods of increasing the strain gage system sensitivity. Why would the strain gage measurement system sensitivity be increased. ME 22.302 Strain Gage Measurement Lab 6 Rev 010505
Strain Gage Experiment #5 for ME Lab I (scanned document) 8 Department of Mechanical Engineering
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