Strain and Force Measurement

Transcription

1 NORTHEASTERN UNIVERSITY DEPARTMENT OF MECHANICAL, INDUSTRIAL AND MANUFACTURING ENGINEERING MIMU 0-MEASUREMENT AND ANALYSIS Strain and Force Measurement OBJECTIVES The primary objective of this experiment is to use resistance strain gauges and associated electronics to measure strain in a cantilevered beam. Data are collected using a computer-based measurement system that will be constructed in the LabVIEW environment. The effect of using a Wheatstone Bridge circuit as a signal conditioner for strain gauges is also investigated. Strain measurements are recorded for a number of force inputs to the beam. The beam/strain gauge system is then calibrated for use as a force measuring device. BACKGROUND The measurement of strain is typically accomplished using resistance strain gauges. These transducers employ a segment of thin wire that is subjected to the strain to be measured. If the gauge is appropriately bonded to the structure being measured, the strain in the structure is transmitted to the wire, which in turn produces a change in the resistance of the wire. This resistance change is a small fraction of the nominal resistance of the wire segment, frequently less than 1/0 th of a percent, which can be difficult to measure. Because of this a special electronic circuit, the Wheatstone Bridge, is employed. The bridge provides a number of benefits, including conversion of the resistance change of the wire to a voltage change, reducing the dynamic range of the measurement, creating a strain sensitivity that is easily scaled, and allowing multiple gauges to be used together to account for thermal expansion errors, and to differentiate between axial and bending loading. In this experiment, we will measure strain using a number of active and dummy gauges that are placed in half and full Wheatstone Bridge circuits. The output voltage from the circuit is measured using a computer-based data acquisition system, which is controlled using the LabVIEW application. The first step in setting up the experiment, setting up the data acquisition hardware, is already done for you. The acquisition hardware and drivers are installed on your work station, along with LabVIEW and all of the necessary components to collect and process the strain data. Your work station has a National Instruments Model SC-234 signal conditioner, pictured below, attached to the data acquisition board in the computer.

2 SC-234 Figure 1. The SC-234 Input Signal Conditioning Chassis The SC-234 contains a number of modules that are designed to provide inputs to and accept outputs from, the apparatus being measured. For this lab, the SC-234 is equipped with modules to support measurement of strain for both half- and full-bridge Wheatstone Bridge circuits. Both of the modules generate a 2. Volt DC input, or Excitation signal to the bridge, and have a voltage input to accept the output, or Sense, voltage from the bridge. For the half-bridge case, two gauges are plugged into the External Wheatstone Bridge Circuit Board, and the voltage output from the bridge is input to the half-bridge module in the SC-234. With the full-bridge module, four gauges are plugged into the Wheatstone Bridge Circuit Board, with the output of the board fed to that module. The circuit diagrams for these to configurations appear below.

3 Figure 2. Schematic Diagrams for the Half and Full Wheatstone Bridge Circuits, Including the NI Module CONSTRUCTING THE VIRTUAL INSTRUMENT IN LABVIEW The first step is to power up the computer and log onto it. The login name is lab, and the password is lab. Double click National Instruments shortcut on the desktop. Click Cancel on the registration form, then click OK, then click Continue. You are building a new VI, so click new, then, under VI From Template, subcategory DAQ, select Data Acquisition with NI-DAQmx.vi. A DAQ Express Sub VI within a While loop will be displayed on the block diagram of your new VI. To Build the VI, Double-click the DAQ Express SubVI to configure it. It will launch a wizard that helps set up the data acquisition hardware. Once in the Wizard, select Analog Input, then Strain. The My Physical Channels window will then appear on the lower right of the screen. This window maps the SC-234 signal conditioning chassis to the DAQ board in the computer, channel by channel. Dev1 (PCI-6036E) is the PCI Data Acquisition Board in the PC. Listed below it should appear (as a minimum):

4 SCC1Mod1 (SCC-SG04) Full Bridge Strain Gauge SCC1Mod2 (SCC-SG03) Half Bridge Strain Gauge Click the + in front of SCC1Mod1 (SCC-SG04) Full Bridge Strain Gauge Then click on ai0 below it, and then click Finish. The next step is to enter and/or modify the strain gauge parameters, using the dialog box that appears. These include the resistance and Gauge Factor of the strain gauges. These are as follows: Gauge Factor = 2.11 (Dimensionless) Gauge Resistance = 120 (Ohms) Initial Voltage 0 is used to Zero the Strain Gauge output voltage from the bridge for the zero strain condition. Leave this set at zero. We will be doing this manually in the data acquisition module, as this produces better results for our measurements. Next configure the additional parameters: Vex Source = Internal Vex Value = 2. (Volts) Strain Configure = Full Bridge I Lead Resistance = 0 Acquire Continuously = SET TO MEASURE 0 SAMPLES AT 0 HZ When you have set the parameters correctly, click OK. The DAQ is now set up with the input parameters set for a full Wheatstone Bridge circuit with four strain gauges having a resistance of 120 Ohms and Gauge Factors of The unstrained output of the bridge will be set to 0 Volts. The input or excite voltage, the DC voltage supplied to the bridge, is set to be created by the module ( internal ), at a level of 2. Volts. The lead resistance is small, so is set at 0 Ohms, and the DAQ is set to sample the voltage at a rate of 0 cycles per second (0 Hz) for 0 samples. The way that the data acquisition modules work in LabVIEW, half bridge data is divided by two, and full bridge data is divided by four. As we wish to make comparisons between configurations, it is necessary to remove these factors. To do this, add a Scaling and Mapping Express VI to your VI. DO this by going to the Mathematics/Comparison palette under the Functions palette. Select the VI and place it to the right of the DAQ VI. Once placed, a dialog box appears. Select Linear from the menu, and set the slope to 4 and the Y intercept to 0. Then click OK. Wire the output of the DAQ VI to the input of the Scaling and Mapping VI.

5 Now, we must create the ability to change from full bridge to half bridge mode. To do this we will use a Case Structure. The Case Structure allows for two different configurations to be run, depending on the value of a Boolean. To set this up, right click the block diagram, go to Execution Control and select Case Structure. Place the structure on the block diagram, around the DAQ Express VI and the Scaling and Mapping VI. Once in position, the structure loop will appear grey, with a dialog box at the top, and a small green box on the left that contains a question mark. The value in the box at the top should be True. If the box is clicked, the value changes to False. You now notice that there no contents in the False loop. To place circuitry there, go back to the True structure, and select its contents, and select Copy on the edit menu. Next, move back to the False box, and paste the contents of the buffer inside it. It now has the same contents as the true box. To modify the contents of the False box for use in collecting half bridge data, right click on the DAQ VI. Click the - to remove the SCC1Mod1 (SCC-SG04) Full Bridge Strain Gauge from the configuration, and then click the + in front of the SCC1Mod2 (SCC-SG03) Half Bridge Strain Gauge. Then click ai0. The only other parameter that must be changed is the Strain Configure, which should be set to Half Bridge II. Click Finish to reconfigure the DAQ. Now double click the Scaling and Mapping VI, and change the slope to 2. The False box is now ready. To control the Case Structure, right click the left hand terminal on the green question mark on the Case Structure box. Select Create and Control from the menus that appear. A Boolean control is wired to the box. Label it True: Full Bridge, False: Half Bridge. This controls the state of the instrument, allowing you to select between a full bridge (True) and half bridge (False) configuration. Now, create a waveform graph to display the strain gauge data. On the Front Panel of your instrument, place Graph Indicator to create the display. A waveform graph should appear on your Front Panel. You can modify the axis labels and scales to suit your measurements. The X-Axis scale (time) should be set to be 1 second, which is the length of the total data acquisition segment. Write your data to a file using the Express Write LVM VI located on the Output palette. Place it on the block diagram near the graph icon. Double click into it. Leave the path statement blank. Under Action, select: Save to One File, Ask User to Choose File, and Ask Each Iteration. Under If a File Already Exists, select Rename Existing File. Under Segment Headers, select: One Header Per Segment. Under X Value Columns, select: One Column Only. And under Delimiter, select: Tab. Click OK and then wire this Sub VI to the output of the DAQ Sub VI through the Case Structure box wall. Finally, create a routine to determine the mean and standard deviation of each sample of 0 data points. Do this by right clicking the Block Diagram and selecting the

6 Analysis palette. Select the Statistics Express VI, and drag this onto the block diagram outside the Case Structure box. The Configure Statistics window will appear. Check the Arithmetic Mean and Standard Deviation check boxes, then click OK. Wire the Express VI into the output of the DAQ. Next, create two Numeric Indicators to display the average and standard deviation for the measurement. To do this, right click the Front Panel. Select Numerical Indicators from the controls palette. Then select a simple numeric indicator, drag it onto the Front Panel, and repeat this step. You may need to grow the numeric display to display the entire output strain. Label the indicators appropriately and wire them into the output of the DAQ through the box wall. Save the VI you have created to the desktop. You will also need to save the VI and data files to a storage device at some time before leaving the lab, in case you wish to examine your data at a later time. Now, run the VI you have created, and verify that it works. BALANCING AND TESTING In either configuration, the bridge circuit must be balanced to account for the resistance of the lead wires, and the signal produced by the weight of the beam and of the weight hanger. To do this, double click the DAQ Assistant VI. At the top of the dialog box, there is a green triangle labeled Test. Select this, and another window appears. It contains a graph that is being continuously updated of the output of your VI. Observe the data for evidence of random behavior about a mean value. Then under Display select Waveform Values. Now the numeric values are displayed. With no added weight, the Strain window should read zero. If it does not, use the screwdriver supplied to you to adjust the correct input module on the SC-234. The top module is the SG04 Full Bridge module, and the module next to the top is the SG03 Half Bridge. Adjust the potentiometer labeled X. MAKE SURE YOU ARE ADJUSTING THE PROPER MODULE AND POT! As you adjust, note the changes in the value on the test window. You should adjust the pot so that the Strain output is less than 1 x -6. This adjustment must be performed each time you change bridge wiring and configuration.

7 GENERAL DATA REDUCTION The VI you have just created records 0 samples for each bridge measurement, based on the measurement configuration below. You must record the average and standard deviation displayed on the Front Panel after reach measurement. You must also save data to files, and store these on floppy for possible later use. STRAIN MEASUREMENT PROCEDURES 1. Measure the dimensions of the beam: the cross sectional dimensions of the beam, and the distance from the center of the orange and yellow strain gauges to the applied force. Assume that the black and red gauges are directly under the yellow and orange gauges, respectively. Make a sketch of the color and location of the strain gauges on the beam. 2. Configure your acquisition system for Half Bridge data collection. 3. Wire the orange gauge (leads) to position on the wiring board, and the grey gauge to 4. Balance the system. Place the lb. weight on the beam and measure and record the strain (Avg and STD) and the raw data. 6. Repeat with lbs. total load 7. Repeat 3 and 6 with the Yellow gauge attached to 8. Repeat 3 and 6 with the Black gauge attached to 9. Repeat 3 and 6 with the Red gauge attached to. Repeat 3 and 6 with the Yellow gauge attached to and the Orange gauge attached to 11. Convert to Full Bridge configuration 12. Connect the Orange gauge to, the Grey to, the Yellow to R3, and White to R4 13. Balance the system 14. Place the lb. weight on the beam and measure and record the strain (Avg and STD) and the raw data. 1. Repeat with lbs. total load 16. Repeat steps and 11 with the Orange gauge attached to, the Yellow to, the Red to R3, and the Black to R4

8 Results: 1. Construct a table that summarizes the strain measurements made using the different bridge configurations described in the Procedures section above (Use the attached data sheet). Use this table to answer the remaining questions. 2. Compare the strain values obtained in Procedure () with the algebraic differences of the individual readings for steps (-7). How should the results compare? What are the primary differences between these two configurations, and how will this affect the data? 3. Compare the strain values measured in the steps (11-1) with the algebraic sum of the strains measured with the individual gauges in steps (-7). How should the results compare? 4. Compare the values of the strains measured in step (16) with those measured in steps (-9). Use the following relationship: ε T = ε1 ε 2 ε 3 + ε 4 where ε 1, ε 2, ε 3, ε 4 are the strain data from the Orange, Red, Black, and Yellow strain gauges, respectively. Discuss the results. Is temperature compensated for in step 16?. The upper fiber strain at the center of the strain gauge can be calculated from the beam theory. ε = 6P( l a) Ebh2 where: ε = upper fiber strain P = applied force h = thickness of the beam b = width of the beam l = length of the beam from the support to the applied force a = length of the beam fro the support to the center of the strain gauge E = Young s modulus Assume that: E =,000,000 psi Calculate the expected strain for the two loading conditions at each of the four locations on the beam. 6. Estimate the precision interval of this measurement using the recorded standard deviation data for each of the measurement locations and load conditions. Do the strain values calculated fall within the precision interval? Are the measured values of strain consistent with the above beam theory? Discuss your results with reference to the potential experimental errors in the procedures you used. 7. Explain how the temperature of the laboratory affects the results of this experiment.

9 Beam Dimensions 3 bh I=, h= 2c 12 Width, b Height, h Distance to Load: Distance to Strain Gauges Orange Yellow Black Red Beam Dimensions

10 STRAIN DATA TABLE Procedure Bridge Circuit Bridge Load (lbs) Color Gage Wire / Conn Strain (µε) STD Deviation (µε) -9 Half Orange Grey Yellow Grey Black Grey Red Grey Half Orange Yellow 11-1 R3 R4 Full Orange Gray, Yellow White R4 R3 16 R3 R4 Full Orange Red Black Yellow R3 R4