Chapter V. Calibration
Calibration of the Model Piles
Background
Since the strain gages were mounted on the inside surface of the piles and placement could not be absolutely controlled, some minor mounting errors probably were made. These errors could be misplacement of the gages on either side of the planned gage position, misalignment of the gages so they were not perfectly straight with respect to the axis of the pile, or they could have been mounted in a rotated position, as in the case of the Red 8 and Black 8 gages in Pile 1, which were rotated about 30 degrees from the position of the rest of the gages.
All of the construction flaws have the potential of inducing errors in the strain data when the piles are loaded because the gages will be strained differently than expected. To overcome the unknowns, it was necessary to calibrate every strain gage in each pile under controlled conditions so that a correction factor could be determined and implemented when the piles were used in an actual lateral loading test.
To avoid damaging piles during a lateral load test, the piles were loaded to a maximum of 65 percent of the yield strength of the 6061-T6 aluminum pipe from which they were made. Calibration was done to 70 percent of the yield strength so that an envelope could be established in which reaction of the piles to loading would be documented. Seventy percent of the aluminum's yield strength was equal to a stress of 180.9 MPa (25900 lb/in.2) in the piles, and a corresponding allowable moment of 388.6 N-m (3440 lb-in.) using the equation: M=(σ)(I)/c, with I=3.635x10-8 m4 (0.08734 in4), and c=0.0167 m (0.6576 in.).
Calibration was accomplished by placing the piles horizontally on supports and loading them as simple beams using two loading configurations, subjecting the gages to tension and compression by turning the pile 180 degrees after the first set of loadings was completed and repeating with the other side up, thus reversing the stress state. Figure 12 shows the two calibration configurations. The first configuration used a concentrated load centered between the supports. This set-up provided a different moment value for each strain gage location at each load increment according to the equation: M=Px/2, where P is the load and x is the distance from the support to the strain gage.
The second configuration used two equal concentrated loads symmetrically spaced with respect to the supports. Loading in this manner gave different moment values for the gages between the supports and the loads according to the beam equation: M=Px, again with P as the load magnitude and with x as the distance from the support to the strain gage. Between the symmetrically spaced loads, the moment would be a constant value as given by the equation: M=Pa, where a is the distance from the support to the position of the load.
Using the two calibration configurations gave not only more data points with which to compute a calibration factor, but also allowed diagnosis to be done in the event that a strain gage was giving output much different than expected, based on theoretical calculations. If a strain gage was out of position on either side of its assumed location, it consistently would give moment values much different than expected. These values could be compared with theoretical moment values and the gage's actual location could be determined. This new location would then be used for all testing involving that pile.
The magnitude of the maximum possible calibration load, while staying under the moment limit of 388.6 N-m (3440 lb-in.), was determined by the number of weights available for calibration, the length of piles, and location of the strain gages with respect to the placement of the supports and loads. Based on the number of calibration weights available, it was decided to let the maximum load be 1112 N (250 lb.). Since the maximum moment (M) was 388.6 N-m (3440 lb-in.), and with the maximum load (P) set at 1112 N (250 lb.), the distance between the supports and spacing of the symmetric loads was determined by equating the beam equations: M=PL/4 for the centrally placed single load where L is the distance between the supports, and M=Pa for the symmetrically placed double loads, where a is the distance from the support to the load. The result was L/4=a. Using this equation, and the locations of the strain gages, distance between the supports was determined and positions of the loads were fixed. Care was taken to keep the gages at least 19 mm (0.75 in.) away from supports and loads so that Saint Venant's effects would not be read by the gages.
Equipment
Calibration equipment consisted of frames to support the piles, calibration weights and the means to hang them from the piles, a pile alignment or orientation device, and the data acquisition system and computer.
Heavy steel A-frames were used to support the piles during calibration. Because of the height of the stacked calibration weights, the A-frames had to be set on lengths of 2x4 boards to elevate piles so the weights cleared the floor at all times during calibration.
The 48 weights used for calibration were slotted, steel plates used in the USU soils lab for consolidation tests. Prior to calibration, the mass of each of the weights was checked on a scale. To have pairs of matched weights for use in the double load configuration, regular masking tape was used to add a small amount of mass to certain weights to raise them to equal the mass of other weights. The mass of each of the weights ranged from 4.000 kg (8.818 lb) to 4.945 kg (10.902 lb).
Weights were set on two hangers borrowed from the USU soils lab's consolidation equipment. Short lengths of one-eighth inch stainless steel wire rope were cut and bound into loops with wire rope clips, trapping short lengths of long link chain cut to the proper length and slid onto the piles. The hangers were hung from these to give clearance between the stacked weights and the pile.
During calibration, a pile must be positioned with the strain gages oriented parallel to the axis of loading so they experience only tension or compression without any bending. To facilitate proper orienting of the pile, a device was specially designed and constructed. It is shown in Figure 13. This device was a small oak board 15 inches long that had been machined straight and sized to fit snugly into the pile crown slot, where it could be pinned by means of a hole drilled in one end. A small mirror, which was cut to fit the device was glued to the other end. Proper pile orientation was accomplished by sighting across the string from a plumb bob suspended from an eye bolt in the board and aligning it with reference lines drawn on the centerline of the board. The pile could be considered properly oriented when the lines and a single image of the string were aligned.
Input Board Connections
To facilitate the data reduction process and to lower the overall complexity of the pile-to-data acquisition system hookup because the number of strain gages per pile did not directly correlate to the number of channels on an input board, the piles were allotted two input boards each. One input board was dedicated to the red gages, all which are on one side of the pile, and one input board was dedicated to the black gages, on the other side of the pile. The boards were then referred to as the red and black boards accordingly. This left two channels unused on each board.
All input boards were hooked up in the same manner, with wires from gage number one clamped into the terminal block at channel number one and finishing with wires from gage number 14 clamped into the terminal block at channel number 14. Due to the small diameter of the strain gage lead wires, some of the connections were loose. When this problem was encountered, an extra amount of solder was melted onto the wire lead, thus increasing the diameter of the wire and improving connection.
Calibration Setup and Procedure
The calibration setup and procedure was the same for all piles, so only a detailed description of the steps taken to calibrate Pile 1 will be given. Any variances and anomalies peculiar to other piles will be noted at the appropriate place.
Once the pile was properly hooked up to the red and black input boards, the Wheatstone bridges for each gage had to be balanced. The pile was placed on the loading supports during this procedure. This was only for convenience as pile position was not critical.
Due to the close spacing of the card edge connectors on the interface bus, there was no room for accessing the potentiometers on the red board if the black board was also plugged in; therefore work could be done only on one board at a time. For Pile 1, the red board was plugged into slot 1 on the interface bus. The data acquisition box was turned on and the bridge zeroing program, ZERO.VI, was called up on the computer. This program was written by specifically for balancing the strain gage Wheatstone bridges using LabVIEW software. Figure 14 shows the ZERO.VI program control panel. A real-time display of bridge voltage output was the main feature on the control panel of this program. There also was a user input display for entering the number of the input board to be read, as well as a user input display for selecting the strain gage channel that was to be balanced. To balance the first bridge on red board, Pile 1, the board designator and the strain gage designator were set at zero because this program starts all counting from zero instead of one, and thus all boards and gages must be designated by the number one less than their respective positions. With all settings properly made, the program was started.
In the first attempt to balance a bridge, a hardware malfunction was discovered that persisted throughout the calibration process for every pile and has yet to be rectified. The problem was that when first starting the system, the voltage readout for not only the gage that was being balanced, but for all gages on that board went immediately to -2.5 volts and remained stuck there no matter how much the potentiometer for that bridge was turned. It was found by trial and error, that by unplugging the board or by leaving the board unplugged while turning on the system and then plugging it in, this problem could be sidestepped and bridge balancing could proceed.
After unplugging and replugging the input board, the voltage readout began to bounce around, thus showing that the bridge could be balanced. Balancing the bridge was done by turning the screw in the potentiometer whichever direction caused the readout to approach zero. The sensitivity of the 25 turn potentiometers was such that when nearing zero, just applying pressure to the screw could cause the readout to overshoot the goal. A soft touch was necessary when getting close to zero. It was not possible to balance the bridge at a perfect zero reading, but since an initial reading of all gages would be made before pile calibration as a reference, a perfectly balanced bridge was not necessary. Nevertheless, it was desirable to get as close to zero as possible so there would be no danger of going out of the voltage range of the straining gage during calibration. When a satisfactory voltage reading was attained, the program was turned off, the next strain gage bridge was selected, the program was restarted, and the process repeated until all the bridges on the red board for Pile 1 were satisfactorily balanced. The black board then was plugged in to slot two in the interface bus. At this point it also was found that plugging in another circuit board could cause the voltage readouts on a previously inserted board to jump to the value of -2.5 volts and stick. Again, trial and error showed that by unplugging and replugging the already balanced board, normal voltage readings could be regained and that previously balanced bridges were not seriously affected. The proper changes were made to the ZERO.VI panel by setting the board designator at 1 and the bridge designator at 0. This numbering scheme was confusing at times. Perhaps it can be changed in the future by reprogramming. With input designators properly set, the program was restarted and all of the bridges were balanced following the procedure used for the red board. With all of the bridges for Pile 1 balanced, the pile was ready for calibration.
To assure proper pile positioning and load placement during calibration, stripes were marked on the piles at the correct locations. Supports were situated the proper distance apart and aligned parallel to each other. The load hanging loops were slid onto the pile and the pile was positioned on supports according to the support makings and seated there with chunks of butyl rubber, which allowed enough movement for fine positioning of the pile yet held it in place when set. Every pile calibration started with the pile turned right side up. The special pile orienting device described earlier was then inserted into the pile crown slot and pinned there. A plumb bob was hung from the eye bolt in the device and the pile was twisted until the string lined up with the centering lines on the device and with its own reflection in the mirror at the end of the device. The butyl rubber then held the pile in the correct position when the pile was pushed firmly into it. This finished calibration preparations for the pile.
To prepare the computer, the calibration program GO-CAS.VI was first called up. This program also was programmed with LabVIEW software specifically for calibration purposes. GO-CAS.VI collected data from the red and black boards and stored it in separate files, which were named by means of file designators on the program control panel. Figure 15 shows the Go-CAS.VI program control panel with the associated setting designators. Since pile calibration started with the pile laying on its right side and with the single central loading configuration, the file names selected for the red and black output files were chosen as Pile1RRS and Pile1BRS, respectively, meaning Pile 1, Red gages, Right side up, Single load, and Pile 1, Black gages, Right side up, Single load. Other designators on the front panel used for instructing the computer which boards to look for and read were set at 0 and 1 for the first two positions on the interface bus. Two other user input designators told the computer how many of the channels on each board were to be read. These were set at fourteen, which would leave the fifteenth and sixteenth channels unscanned.
When all of the inputs were made, the program was started by clicking the run button on the row of icon buttons on the program control panel. This caused a virtual light on the panel to flicker, which meant that the program was ready. After checking the vertical alignment of the pile, and holding the load hanging loops up off the pile so that no load would be registered, a baseline reading was taken by clicking the GO button on the control panel. Twenty readings of each strain gage were taken after which the GO button clicked off. This took about 10 seconds during which time the virtual light froze. It then resumed flickering when the readings were finished, thus signaling that the reading phase was complete. The load hanging loop was positioned at the center load position and the weight hanger and the first load plate were hung in place. Care was taken after this and all load plates were placed on the hanger to stop the load from swinging and bouncing. The first load reading was taken by clicking the GO button and so on until the maximum load of 1115.5 N (250.8 lb) was reached in 24 load increments. Further readings were made as each of the load plates was taken off going from the maximum load back down to and finishing with another baseline reading. This gave a total of 49 load steps with 20 readings taken by each strain gage at each step. After the concluding zero load reading, the program was stopped by clicking the STOP button. To assure that no load steps were missed or no double readings were taken at the same load increment, the output files were checked to see if they contained 980 lines of data.
Preparation for the double load configuration test was begun by renaming the output file for the red board to Pile1RRD for Pile 1, Red gages, Right side up, Double load and by renaming the output file for the black board to Pile1BRD for Pile 1, Black gages, Right side up, Double load. If this was not done, the new data would be amended to the files previously mentioned. No other changes were necessary on the calibration program control panel. The pile was readied by positioning the load hanging loops on the correct marks at 13.5 inches away from each support. The pile alignment was checked for verticality and the program was restarted. A baseline reading was taken while the load loops were held in the air. Then the hangers and the first load plates were put on and the first load reading was taken. The loading order and procedure was exactly the same as with the single load, and the load plates were paired so that no discrepancy in the loading existed. At the test's conclusion, data files were checked for 980 lines of data corresponding to the 49 readings.
During the double load test, it was noticed that the pile tended to rotate out of its proper orientation as the total load increased. This was probably due to the wire rope load loops gripping the pile on one side more than the other, thus turning it slightly. By carefully watching for this problem, it was prevented from causing difficulty during the remainder of this test. Afterward, short pieces of wood were cut and sized to fit between the pile orientation device and the legs of the support, which would hold the pile in the correct position during subsequent tests without continual monitoring.
Calibration continued by turning the pile 180 degrees and repositioning it in the proper place and in the correct orientation. The double load configuration was used first with the left side of the pile turned up. New file names were chosen to reflect this.
Calibration of Pile 1 was completed with the single load test after which the calibration program was stopped and all data files were checked for the proper volume of data. If for some reason a data file had greater than 980 lines of data, the file could be scanned manually to find the redundant set or sets of 20 lines of data, which could then be deleted. It was quite easy to find this extra data because the voltage readings changed so much from load to load. If it was found that output files contained less than 980 lines of data, the whole test in that position and configuration had to be repeated to get full calibration data.
Data Reduction and Analysis
Completed calibration data files were given the suffix .prn when downloaded to a floppy disk so they could be imported into a Quattro Pro spreadsheet for data analysis. The file Pile1RRS.prn was imported into Quattro Pro and was used for development of the calibration figures. Since 20 readings of each strain gage were taken at every load increment, they had to be averaged before anything could be done to the data. The next step was to subtract the voltage value at the baseline reading from the rest of the voltage readings. Next, strain was calculated by multiplying the voltages by the constant 3.87046 x 10-3, which comes from the Wheatstone bridge strain equation, ∈=Vo(R2 + R3)2/VsSR2R3 x (amplification value), where Vo is the voltage difference, R2 is the resistance of the resistors in the bridge (160 Ohms), R3 is the resistance of the strain gage (120 Ohms), Vs is the magnitude of the supply voltage (5 volts), S is the strain gage factor (2.11), and the amplification value is 100. Stresses at each location and load were obtained by multiplying strain values by the modulus of elasticity for aluminum (E=68,950 MPa or E=10,000,000 psi). The theoretical stresses for each load increment at each strain gage location were calculated using beam theory for a simply supported beam loaded with a single concentrated load at a distance halfway between the supports. This completed the data reduction process for the file Pile1RRS and was the most difficult step of the data reduction procedure. Thereafter, this page of the spreadsheet was just copied to other pages where raw data from the seven remaining data files could be imported and the computations could be performed automatically.
After importing and processing all data for the eight Pile 1 calibration files, stress results from each file were copied onto two new pages in the spreadsheet according to the strain gage type, red or black. This was done so that results of the four different loading configurations could be used in a regression analysis of theoretical versus measured stresses for each strain gage. The regression analysis gave a factor with which the measured stresses could be corrected with multiplication to match theoretical stresses. This value then became the calibration factor for each strain gage. To complete the calibration of Pile 1, a graph was made of all the measured stresses plotted against the theoretical stresses for each strain gage.
Once this first pile calibration spreadsheet was completed, data reduction for the rest of the piles was easily accomplished by copying and renaming the whole calibration spreadsheet, importing data into the appropriate places, and changing relevant names and titles on output graphs to reflect results of the computations. It was necessary to do the regression analyses one by one because this was not an automatic operation that could be copied from file to file.
Results of the calibration of Pile 1 showed that the Red 8 and Black 8 gages inadvertently had been mounted backward so that the red gage was on the black side of the pile and vice versa. This also was the case with Pile 3 gages Red 6 and Black 6 and Pile 4 gages Red 3, Black 3, Red 5, and Black 5. This problem was easily rectified in all cases by simply switching wires for the gages from one board to the other. All the gages in Pile 6 were reading the opposite of what was expected, so it was determined that the pile crown must have been installed backward. It must be remembered when Pile 6 is used that this is the case and the input boards installed accordingly, or all output data will be reversed.
Calibration also revealed that several gages, their connections, or lead wires were defective. These gages were Pile 1, Black 11, Pile 2, Red 2, and Pile 3, Red 1. These gages gave random output data, shown on their calibration graphs. Figure 16 shows the random output from a defective gage. The Black 14 gage in Pile 2 had a short circuit before calibration was started and was not even hooked up to its input board for calibration.
Several trends were noticed when comparing calibration graphs from all of the piles. One of these was how the gages near the pile's center measured stresses closer to theoretical than the gages at the ends of the piles. This was probably because the gages in the pile's center were subjected to a much larger range of stresses by the nature of the loading configurations than were the end gages. It also was noticed that in general, one side of the pile had higher calibration factors than the other side. Red or black, it did not matter, but it was a fairly consistant phenomenon.
The overall performance of the gages was quite good, with the average calibration factor being 1.126, meaning that theoretical stresses were on the average 1.126 times greater than the measured stresses. Most of the calibration factors were off by less than 20 percent of the theoretical value, with one gage off by only 0.03 percent. Figure 17 shows the typical calibration output from a functioning strain gage. The four gages at the ends of the piles had an average calibration factor of 1.28. This could probably be improved if the piles were calibrated in an additional configuration where the piles were loaded as a cantilever beam. This would be especially important for the top end of the pile, since that is where the loading takes place under testing conditions. For comparison sake, Pile 1 was recalibrated to see how much change in calibration factor might occur from its initial calibration. None of the calibration factors from the second trial agreed exactly with those from the first trial, but the average difference for all gages was only 0.525 percent. This concluded the pile calibration.
Calibration of the Load Rod and Load Cells
Instrument Description
The load rod was designed and fabricated from 6061-T6 aluminum so that it could not only transfer the load to all the piles in the group, but it also would act as four load cells to measure loads that were transferred to each pile. The load cells were fabricated from 6061-T6 aluminum so that the same strain gages that were used in the piles and load rod could be used.
The load rod was designed to allow maximum pile head movement with a minimum of interference, but this resulted in the axis through which the load rod pins would act being below the centroidal axis of the aluminum strap material between the pin connections. Bending stresses could then be induced from the moment created by loading along the unaligned axes. Therefore, it was essential that all the gages on the load rod be functioning so that bending stresses could be eliminated from total stresses by averaging output readings from gages on opposite sides of the load rod.
As in the piles, the eight strain gages on the load rod and the two strain gages on each of the load cells had to be calibrated before being used in a pile group test to account for possible alignment errors and mounting defects.
Input Board Connections
Connecting the load rod and load cell strain gages to the input board was done starting with Red gage number 1 as designated on the load rod. Its wires were clamped into the terminal block at channel number one. Black gage 1 was then clamped into the terminal block at channel number two and so on until all gages were thus connected with the last gage, Black gage 4, clamped into channel number eight.
The red and black gages from load cell A were connected to the circuit board at channels nine and 10, respectively, with the red and black gages from load cell B going into channels 11 and 12.
Although the absolute order probably does not matter, to assure consistency, improve data acquisition speed, and reduce software complexity, the input board dedicated to the load rod and load cells was plugged into the interface bus at slot number 13, where it was during the pile group lateral load tests.
Calibration Apparatus, Setup, and Procedure
Upon completion of the hookup, it was necessary to balance the Wheatstone bridges in each strain gage channel. The LabVIEW program ZERO.VI was called up on the computer, and the proper input board number was entered to tell the computer where to look for the gages to be balanced. The program was started and each of the 12 bridges were balanced individually by turning the screw on the bridge's potentiometer until the readout was as close as possible to zero. This required turning the screw through about eight complete revolutions before the readout started to change from its initial reading, which was always -2.5 volts. Once the readout started to change, it continued to change rapidly with only slight pressure to the potentiometer screw. All bridges were rechecked and readjusted as necessary before calibration was begun.
The apparatus necessary for calibration included the data acquisition system, a C- clamp from which everything would be suspended, chains of various lengths, clevises for connecting the components, S hooks and lengths of rope for hanging the weights, and the calibration weights themselves.
The load rod and load cells were calibrated using the same procedure and so only the procedure for calibrating the load rod will be explained in detail. Any step specific or peculiar to the load cell calibration will be highlighted at the proper time.
Calibration was done in the basement of the USU engineering building where the necessary apparatus could be suspended from a floor joist I-beam of the first floor. A C-clamp was fastened to the flange of the I-beam and a three-foot length of long link chain was hung from the clamp to allow for convenient vertical positioning of the load rod and the calibration weights. The load rod was connected to the chain by means of a specially ordered stainless steel twisted clevis with a threaded pin. The dimensions of the clevis were such that it barely fit over the end of the load rod. The threaded pin fit through the hole in the end of the load rod so that little relative movement was allowed. Another clevis of the same type was pinned in the other end of the load rod, and a 22-inch length of chain was hung from it. Calibration weights were then suspended from this chain by means of S-hooks put into the individual chain links, with two-foot pieces of rope connecting the weights to the S-hooks. Fifteen weights were borrowed from the Utah Water Research Laboratory for the calibration. Fourteen of the weights weighed 222.4 N (50 lb.) each and one weighed 111.2 N (25 lb.).
The calibration procedure was begun by calling up the LabVIEW calibration program, GO-CAS.VI, naming the output files, and adjusting the settings so the proper interface bus slots and the correct number of strain gages were read. For the load rod calibration, the number of strain gages to be read was set at eight, since the load cells could not be calibrated at that same time. This allowed the program to run faster and also eliminated extraneous data that would be collected from the load cells. Later in the calibration of the load cells, the number of strain gages to be read would be increased to pick up the load cell channels, but the eight channels of extraneous data collected from the load rod strain gages would have to be discarded in the data reduction process. With all of the settings initialized, the program was begun.
The load rod was calibrated using load increments of 111.2 N (25 lb.), beginning with a zero-load baseline reading, increasing to a maximum of 3225 N (725 lb.), and then decreasing to a final zero-load reading. This was accomplished by hanging the 111.2 N (25 lb.) weight from the chain attached to the load rod, taking a reading, removing this load and putting on a 222.4 N (50 lb.) weight, and taking a reading. The 111.2 N (25 lb.) weight was again hung from the load rod and a reading was taken. It was removed and another 222.4 N (50 lb.) weight was added and a reading taken. This procedure produced 59 data points with which to calculate a calibration factor for each gage pair on the load rod. The initial and final zero load readings on all eight of the load rod strain gages were compared at the end to determine if any yielding of the rod had occurred. Output file names were changed when the load cells were calibrated, but the procedure was the same in all cases.
Data Reduction and Results
Before downloading the load rod and load cell calibration data files, the .prn suffix was added to their file names so they could be imported into the calibration spreadsheet. They were then copied to a backup disk for protection.
The load rod data file was imported directly into the calibration spreadsheet, but as was mentioned earlier, the load cell data files had to be imported into an intermediate spreadsheet where data from the load rod the load cell not being calibrated was deleted. Once this was done, the load cell files were imported to the calibration spreadsheet.
When properly imported, the 20 voltage values taken at each load increment for each strain gage were averaged automatically. The initial baseline reading for each gage served as the basis from which all other readings were referenced. Differences between the voltage at the baseline reading and the voltages at each of the loadings were calculated. Using the strain equation cited above and the voltage differences, the strain induced by each load was calculated. Stress at each load increment was calculated by multiplying the strain value by the modulus of elasticity for aluminum. All of the calculations could have been accomplished in a single step, but by using this method intermediate results could be examined and printed out, and errors could be more easily found. At this point in the data reduction, affects of the bending stresses on the calibration output could be readily seen. Gages opposite each other on the load rod showed stress levels that were vastly different. When these opposing gage stresses were averaged, the bending stresses were eliminated according to theory, and the resultant stress was compared to the theoretical normal stress by a regression analysis to determine a calibration factor for each gage pair. Although there should not have been any bending stress in the load cells, their measured stresses also were averaged before doing the regression analysis.
In all cases, the averaged, measured stresses turned out to be quite close to theoretical stresses for the many loadings, with calibration factors close to 1 and output data plots showing straight lines indicating linear measurements. Figures 18 and 19 show calibration output for a pair of strain gages on the load rod and a load cell. The results of these calibrations show that the load rod and load cells can be used with confidence in the capacities for which they were designed.
Calibration of the LVDTs
Equipment
Two LVDTs used were purchased from RDP Electrosense Inc. of Pottstown, Penn., and are of the type LDC 3000C. They were identical in appearance and so were distinguished by marking them with red and blue tape. They will hereafter be referred to as the blue or red LVDT. The LVDTs have a linear range of three inches on either side of the zero point with a linearity of 0.12 percent. They were calibrated at the factory and have a sensitivity of 0.76 volts/inch for the red LVDT and 0.768 volts/inch for the blue.
Input Board Connections
The LVDTs arrived form the manufacturer with seven colored wires extending from their connecting cables. An accompanying wiring diagram showed the connection details for the proper hookup. The LVDTs had the capability of being powered by a 12- volt power supply, so it was decided to modify one of the input boards so the power could be supplied to the LVDTs while taking advantage of the multiplexing, filtering, and amplifying capabilities already built into the circuit board. Channels 15 and 16 on board number 16 were chosen as hookup points for the LVDTs so that if, at a future time, expansion of the strain gage monitoring capabilities of the system is desired, the LVDT monitoring capabilities could be retained without encountering undue difficulties.
Before the actual hookup, the LVDTs were tested with a digital volt meter to measure voltage at the extremes of slider position. Limits of the linear range were found to occur at just over ± 3 inches of travel with corresponding voltage outputs of ± 2.35 volts.
A voltage dividing circuit was used for connecting LVDTs to the data acquisition system, and because a standard strain gage circuit board was used, the output signal gain had to be reduced by a factor of 100, since it would have to be processed through the board's amplifier, which would amplify it by a factor of 100 and thus bring it back to its original magnitude. Power was supplied by a jumper wire from the power input trace of the interface bus. All LVDT wires were hooked up as specified by the LVDT connection details sheet with soldered connections.
After connecting the LVDTs, it was found that when the sliders were moved to points where the output reached approximately ± 2 volts, a sudden jump in output occurred to ± 2.5 volts where it remained constant no matter how much movement was made with the slider, until the slider was returned to positions where the output was approximately ± 1.8 volts, after which the output returned to normal. The cause of this problem is unknown, but to avoid it, sensitivity of the LVDTs was reduced so that at the extremes of slider travel, the output would never go beyond ± 1.75 volts.
To accomplish this, 270-ohm resistors were added in parallel to the 100-ohm grounding resistors in the voltage divider circuit. This procedure limited voltage output to ± 1.75 volts and succeeded in eliminating the problem, but since this also changed the sensitivity of the LVDTs, it was necessary to recalibrate the LVDTs to determine their new sensitivities.
Calibration Apparatus, Setup, and Procedure
The calibration apparatus included a dial gauge with a mounting bracket, a C-clamp, and a 24-inch ruler. The dial gauge used was an ELE International brand, model LC 10, graduated to read 0.001 inch movement over a two-inch span. The mounting bracket fastened to the dial gauge with a thumb screw and allowed for fixing the position of the dial gauge to a table top with the C-clamp. The ruler was taped to the table top and used as a coarse reference for placement of the dial gauge during the calibration process.
The program, GO-CAS.VI, was used for calibration. The Red Board and Black Board settings were initialized at 14 and 15 and the number of channels to be read was set at 16 so that the whole board would get read, and thus pick up the LVDT data from the last two channels on the board. A random name was given to the Output File Red file designator for the fourteenth board, since no data would be collected from that slot and would therefore be less confusing when locating data files in the computer directory. For the data recorded from the fifteenth board, a name corresponding to the LVDT being calibrated was used and sent through the Output File Black file designator. When the blue LVDT was calibrated, the file name BLUELVDT was used, and for the red LVDT, the file name was REDLVDT.
Before calibration, the total travel distance of each LVDT slider was measured with a measuring tape. This distance was necessary for planning the calibration process and for data reduction.
To begin the calibration procedure, the LVDT was positioned parallel to the reference ruler with the stationary end butted against a rigid stop. It was then taped to the table to prevent movement. The slider of the LVDT was pushed in completely and the dial gauge was positioned so that its plunger touched and was aligned with the end fitting on the LVDT slider. The dial gauge was then clamped in place with the C-clamp once it had been properly oriented to give the dial a reading of zero. After final alignment checks were made, the calibration program, GO-CAS.VI, was brought up on the computer and all of the settings were checked and the program was started. A reading was taken with the LVDT slider completely pushed in and the dial gauge reading 0. The LVDT slider was then extended 0.1 inches as measured by the dial gauge and held in place by hand while another reading was taken. The slider was moved another 0.1 inches and a reading was taken. This procedure was followed until the slider had been extended the full two-inch travel of the dial gauge plunger, and resulted in the taking of 21 readings. At this point, the calibration program was stopped while the dial gauge was moved. The initial position of the dial gauge, with respect to the ruler taped to the table, was recorded, and then the dial gauge was moved approximately 1-7/8 inches farther away from the LVDT and reclamped to the table. The dial gauge was not moved a full 2-inch distance from the LVDT so that some data overlap would be assured and thus preserve the continuity of the calibration data. After alignment between the dial gauge and the LVDT was corrected and the dial gauge reading was zeroed, the calibration program was restarted and another set of 21 readings was taken over the two-inch travel distance of the dial gauge.
This same procedure was followed for a third group of readings, after which the dial gauge was repositioned so that the next set of data would be taken with the LVDT slider starting at its fully extended position and moving back in. This was done to read from the known boundary of the full extension of the LVDT slider and thus the limits of LVDT voltage output could be correlated to the known distance of travel. The procedure used in collecting this set of data was the same used for the other three sets, with the only difference being that the 21 data points were reversed in order from the rest of the data because of the different direction of slider travel. The four sets of data resulting from this calibration covered the full range of LVDT slider travel with enough overlap to guarantee that no portion escaped calibration.
Data Reduction and Results
As with all calibration data, the LVDT data files were given the .prn suffix when downloaded to a floppy disk so they could be imported directly into a Quattro Pro spreadsheet. The LVDT calibration data as, gathered by the acquisition, system contained 16 columns of numbers corresponding to the 16 channels that had to be read to include the 15th and 16th channels to which the LVDTs were connected.
The raw data first were imported into an intermediate spreadsheet where the 15 columns of extraneous data were deleted. The remaining data were then copied into the calibration spreadsheet where the 20 values from each reading were averaged. Once the averages were obtained, groups of data from the four separate calibration steps could be recognized by looking for overlapping numbers or for the numbers gathered at the extremes of LVDT slider travel. The 21 readings from the fourth calibration step were located easily because of their reverse order caused by readings taken as the slider was moved into the LVDT and not out as with the other three steps. These values were manually reversed so that all of the data would be consistent. Graphs of voltage versus extended distance were made using the data and total possible travel distance, as measured before the calibration was begun. From these graphs, the linear range of the LVDTs was readily determined, as was extent of the linear range, which remained at six inches as given by the manufacturer's specifications. Figure 20 shows the calibration output for the blue LVDT.
The sensitivity of each LVDT was determined next. Four groups of readings were separated and the difference in voltage between each data point in each group was calculated. By using the graphs of voltage versus extended distance, the voltage differences corresponding to the readings that fell in the nonlinear regions were thrown out and the average of all of the remaining values was figured. The resulting sensitivities were calculated as 0.5196 volts/inch for the blue LVDT and 0.5195 volts/inch for the red LVDT where their respective sensitivities had been 0.768 volts/inch and 0.76 volts/inch when received from the manufacturer.
The close agreement between the two recalibrated sensitivities is a verification of the process used to change the sensitivities to a range compatible with the data acquisition system and lends confidence to the overall calibration procedure.
