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Experimental Methods in Mechanical Engineering Calibration of Pressure Measuring Instruments 1 Introduction A deadweight tester is a commonly used pressure reference instrument, which is a standard method for calibrating pressure measuring devices. With a deadweight tester (DWT), pressure is determined from its fundamental definition of force per unit area. A diagram of a deadweight tester is shown in Figure 1 below. Pressure transducers attached to the reference port of a deadweight tester allow one to compare the pressure on the dead weight tester to that measured with the transducer. Then, using regression analysis, the calibration equation and other calibration parameters may be determined. This experiment also requires a thorough uncertainty analysis. Figure 1. Diagram of a deadweight tester showing how weights are applied to the platform to increase the pressure inside and pressure is measured at the reference port. Prior to the experiment, students are required to read the lab manual and take a pre-lab quiz. Students should also watch the video on Blackboard and ask their instructor (prior to lab) if you have questions. 2 Equipment There are four experimental lab stations in 3290 SELE and students are assigned to teams of three. The experiment requires the following equipment:  Deadweight tester  Two types of pressure transducers: • Bourdon tube pressure transducers  Low range: 0-100 psig  High range: 0-400 psig • Capacitance type pressure transducers  Low range: 0-100 psig. The transducer can measure 0 to 5 V. The output of the transducer will be in volts.  High range: 0-500 psig. The transducer can measure 0 to 5 V. The output of the transducer will be in volts.  Weights marked with its equivalent pressure on the DWT • L5 is 5 psi; quantity: 2 • L10 is 10 psi; quantity 5 • L20 is 20 psi; quantity 1  Pressure relief valve mounted to DWT  Digital multi-meter (DMM)  DC power supply  Male-male dual banana plug cable The experimental setup is shown in Figures 2 and 3 for deadweight tester apparatus and the location of the four pressure transducers. The Bordon tube pressure transducers may have a dead band where small pressures might not be detected by the instrument; this is indicated on the dial of the Bordon tube where low pressures are bracketed and the pressure gauge cannot accurately measure pressure. This should be noted when performing the experiment as it may affect low pressure measurements. Do not record any data from the instrument if it is in the dead band. Bring a USB drive to store data if you use the computers in the lab room (they have no internet). Otherwise, you are free to bring a tablet/laptop to store data in a spreadsheet. You will need to plot data during lab, so it is best to record data digitally. 3 Procedure During the experiment, be sure you are not leaning or bumping into the table or causing the table to vibrate. Do not get oil onto your hands or clothes. Caution: be careful taking data; part of your grade depends on how accurately your team can take measurements. Not having good data can affect your report grade. Come prepared to lab! Read the lab manual and watch the video on Blackboard. All the pressure transducers are tested prior to the experiment to ensure linearity in the input and output relationship. Measurements are taken sequentially: upscale and then downscale. Make two copies of all measured data-one digital copy is emailed to the TA by the end of lab. The procedure for the experiment is as follows: 1. Record the room temperature and relative humidity. This is for your own reference, should conditions change from the beginning of the experiment to the end, then you might see that the transducers are sensitive to changes in temperature and humidity and you will need to write about it. 2. Open the release valve on the deadweight tester. a) If the release valve is completely closed, turn the knob approximately two full turns counterclockwise. b) Do not fully open the release valve. This will result in the removal of the valve and the release of hydraulic oil. It will not damage the equipment, but it creates a mess. The DWT’s hydraulic oil will stain your clothing, so be careful. 3. Remove all weights from the platform. 4. Verify that the DWT displacement valve is completely closed (turn the knob clockwise). Figure 2. Front view of deadweight tester and setup used in the experiment, showing the location of the four pressure transducers. The platform must be floating the in piston assembly for valid measurements. 5. Power on DC power supply by toggling the power switch. See Figure 4 for a schematic of the power supply. 6. Connect the DWT’s banana plug to the FIXED 5V terminals of the DC power supply. a) The body of the dual banana plug has a nub indicating the ground plug. Connect the ground plug to the BLACK (-) power supply jack. b) This provides constant power to both capacitance pressure transducers. Figure 3. Back view of the deadweight tester and setup used in the experiment. Figure 4. DC power supply used in the experiment. 7. Connect the active transducer’s output jack to the to the DMM’s voltage (V) and common (COM) banana plug jacks, via the male-male dual banana plug cable. a) The body of the dual banana plug has a nub indicating the ground plug. On the DMM, the ground plug should be connected to the COM jack. On the DWT, the ground plug should be connected to the BLACK (-) output jack. b) Polarity is not crucial, but the configuration noted here is most convenient and follows the standard convention. 8. Set the DMM for DC voltage measurements, indicated by the symbol V̿ (where bottom bar is actually dashed). To begin taking data for the upscale measurements, 9. Completely close the DWT release valve (turn clockwise). There should be no weights on the piston. The piston will be sitting on top of the piston assembly and is not floating. 10. Record initial measurements (0 psig) from all four pressure transducers. Use the spreadsheet from Blackboard to record data; note the column headers and record data for the proper transducer in the correct column. a) The measurements from the Bourdon tube transducers are read from the needle. Note the dead band on the transducer in your notebook. Note the increments of pressure that can be recorded and what psig think you can measure accurately. Do not record any measurements if you are within the dead band of the transducer; these points cannot be used for data analysis. b) The measurements from the capacitance transducers are taken from the digital multi-meter. Depressing either side of the active transducer selection switch will result in voltage from the corresponding transducer to be displayed on the digital multi-meter. Record one and then depress the button to record the other voltage. 11. Begin pumping the handle. a) This pressurizes the hydraulic fluid inside the DWT and applies a force to the piston assembly. b) The first measurement will be of just the platform when it is floating. The platform applies a pressure of 5 psig on the piston assembly; this will be the first non-zero measurement. When we add begin to weights to the platform (platform/weight system), we must add in the 5 psig for the platform to get the total pressure in the DWT. See Table 1. 12. While pumping the handle, observe the pressure measurement from the Bourdon tube transducers. 13. Once the measurement from the Bourdon tube transducer is within the range of the applied pressure, stop pumping. 14. Gently spin the platform/weights. Spinning the platform reduces the friction between the piston and enclosing cylinder. 15. When the pressure of the hydraulic fluid is equal to that applied by the platform/weight, the platform/weight will lift slightly (it will float). c) Under-pressurization will result in the platform still remaining in contact with the piston assembly. Go to Step 16. d) Over-pressurization will result in the piston assembly reaching its maximum lift position; this will yield invalid data. Go to Step 17. e) You should ensure that the platform/weight is not in contact with the piston assembly and the piston has not reached the maximum lift (it should not be all the way at the top). It should be floating. 16. If the platform/weight is not floating, cautiously pump the handle through a small range of motion and return to Step 12. If the platform/weight floats, go to Step 18. If the platform becomes over-pressurized (platform no longer floats and shoots to the top; this is called the maximum lift position), go to Step 17. 17. For over-pressurization, the data point is invalid. Do not open the release valve to correct over-pressurization; this will invalidate all future measurements. You must skip this measurement and move on to adding the next weight on the platform. Leave a blank cell in your data collection spreadsheet for this pressure! You must take the next measurement and add a weight to the platform; continue to Step 19. 18. When the platform/weight is floating, record measurements from all four pressure transducers (see Step 10 for reading measurements). 19. Continue with taking upscale measurements by increasing the applied pressure on the platform by adding additional weight to the platform. See Table 1 and data collection spreadsheet. 20. Return to Step 12 and repeat the procedure until all weights have been applied to the platform. 21. Plot your upscale measurements in your spreadsheet, Psi. vs. equivalent DWT psi or Volts vs. equivalent DWT psi, i.e. y vs. x, for all the transducers. Ensure the trends are linear before continuing. Do not plot any data within a dead band. If not linear, contact your TA and you will need to start a new trial and re-take all measurements. Table 1. Recommendations for weight increments to be added to the platform during upscale testing. This corresponds to the data collection spreadsheet and tells you which weight to add to get the total applied pressure in the table. For downscale testing, the same weights should be used so that for each weight increment, there is an upscale and a downscale measurement. Weight Increments to Add to Platform Total Equivalent Pressure on DWT None (platform rests at bottom) 0 psig Platform (floating) 5 psig L5 10 psig L10 20 psig L10 30 psig L10 40 psig L10 50 psig L10 60 psig L20 80 psig For downscale measurements, the weights are removed in the same increments (as was added for the upscale measurements) from the platform. 22. The first downscale measurement is the same as the last upscale measurement. Record it again. Downscale measurements are required for hysteresis analysis; you must take them or lose points on data analysis in your team report. 23. Remove the top most weight from the platform/weights. The piston assembly should move into the maximum lift position (it will be at the top). 24. Carefully open the DWT release valve (see Step 2 for details). This will depressurize the hydraulic oil. 25. The platform will start to fall quickly; when it starts to float, quickly close the DWT release valve. Be careful that you are ready to close the valve quickly so the platform remains floating. 26. Caution: if the platform/weights come in contact with the piston assembly, the data point is invalid and cannot be taken (you must skip this measurement and proceed to the next measurement by removing another weight). Do not record any measurements for this DWT pressure-leave the cells blank. Do not pump the handle to “float” the platform/weights again; this will invalidate all future downscale measurements. 27. Record measurements from all four pressure transducers (see Step 10 for how to read measurements). 28. Return to Step 23 and repeat the procedure until all weights have been removed. 29. Finally, there are no more weights on the platform and we still need a measurement for the platform itself. Carefully release the pressure until the platform floats. The weight of the platform applies a pressure of 5 psig on the piston assembly. Record values of the pressure transducers. 30. Now, release all the pressure in DWT by closing the valve. The platform no longer floats and sits on top of the piston assembly. This corresponds to 0 psig. Record values of the pressure transducers. 31. Plot your downscale measurements in your spreadsheet, Psi. vs. Equivalent DWT psi or Volts vs. Equivalent DWT psi ( i.e. y vs. x) for all the transducers. Ensure the trends are linear before continuing. If not, contact your TA and you will need to start a new trial and re-take all measurements. 32. Steps 9-31 compose a single trial, i.e. this is called Trial 1. Repeat Steps 9-31 an additional time to produce the second data trial (upscale + downscale). 33. Plot the upscale and downscale measurements for Trial 2 and ensure they are linear before leaving lab. 34. Repeat Steps 9-31 an additional time to produce the third trial (upscale + downscale). You should have time to complete three Trials this during lab if you are careful and wellprepared for the experiment. 35. Plot the upscale and downscale measurements for Trial 3 and ensure they are linear before leaving lab. 36. Record the temperature and relative humidity in the room. Ensure that conditions have remained stable during your experiment. 37. Save your data collection spreadsheet on USB if using computers in the room. Include your team number in the file name. Email a digital copy of your data to the TA by the end of lab. 4 Results Determine the linear calibration equations for each instrument tested. Report all uncertainties as percentages of the pressure transducer’s output span. You must use consistent units to get a percentage (no units), so the Bourdon tube and Capacitance transducers will have different units; do not convert any units. Each pressure transducer must be analyzed separately. For the low Bourdon tube transducer, determine the uncertainties associated with: 1. Hysteresis Uncertainty. Perform a hysteresis analysis for each of the three trials separately. Assume each trial is its own experiment (it is). Determine the maximum uncertainty due to hysteresis (uH%) for each trial. Report these values. Then, note the maximum hysteresis uncertainty of these three values. You will use this max value (%) over all three trials to determine the total uncertainty. Report as percentages of the output span. 2. Linearity Uncertainty. To do the linearity analysis, combine all of your data together and generate a scatter plot (all 3 trials). Then, fit a linear regression curve to all the data. If you have measurements in the dead band of the transducer, ensure they are removed from being included in a curve fit. You should discuss the dead band when presenting your calibration plot in the report so we don’t think you skipped the measurements on purpose. On the figure, you should show the equation of the curve fit and the coefficient of determination R2 on the figure. Edit the figure so it looks professional (recall the Excel workshop and your report template). Then, determine the maximum linearity uncertainty (uL%). Report value as percentage of the output span. Include the figure in the Results section. 3. Repeatability. You have taken repeated measurements as you did 3 trials. For example, you have weight on the platform corresponding to (total) equivalent DWT pressure of 10 psi. How many times did you measure 10 psi of equivalent DWT pressure during the experiment? 6! (If you were careful, Trial 1 should have 1 upscale and 1 downscale measurement; Trial 2 also has 2; Trial 3 also has 2). For each equivalent DWT pressure, do a repeatability analysis for the pressure transducer. Determine the maximum repeatability uncertainty and then report value as percentage of the output span (uR%). 4. Determine the total uncertainty which is composed of hysteresis, linearity, and repeatability uncertainties. Report the value as percentage of the output span for the transducer (u%). Which contributes the most to the total uncertainty? 5. Determine the standard error of the linear curve fit. It has units! 6. Determine the precision estimates of the slopes and zero-intercepts of the linear curve fit. They have units! 7. Estimate the confidence interval for 95% confidence. You will report this as a range of values (with units). 8. Make a table which show values from 1-7 for the Bourdon tube low range transducer. Use appropriate significant figures. All numbers should be in percentages. 9. Repeat 1-7 for the Bourdon tube high range transducer. 10. Repeat 1-7 for the Capacitance transducer low range transducer. 11. Repeat 1-7 for the Capacitance transducer high range transducer. 12. You should have 4 different tables; one for each transducer. Refer to the 341 Report Template on Blackboard for table formatting. 5 Discussion The Discussion section of your report should answer the following questions: 1. Give a quantitative discussion on the accuracy, precision, range, hysteresis, and repeatability of the measurements for each transducer. Note that small, large, etc. are not quantitative, so you must discuss as percentages. 2. Discuss the possible sources of errors in your experiment. 3. Compare the performances of the Bourdon tube low transducer and high transducer. 4. Compare the performances of the Capacitance transducer low and high transducer. 5. Compare the performances of the Bourdon tube to the Capacitance transducer.

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In engineering, there are several types of devices which measures pressure. For example, Bourdon Tube Low Range Tube High Range, Capacitance Low Range, Capacitance High Range. The main goal is using these devices to see if there are any changes in pressure. If we are not careful using these devices, then there are more possibilities that we may collect more errors which can guide to pick up wrong data for readings. To ignore these errors, the sensors should be calibrated to its primary identification.
Often time in engineering industry, Deadweight testers are used in a large scale. Deadweight testers also known as calibrating pressure measuring devices. The main objective for these testers to use is how to determine pressure, which is taken out as force per unit area. A deadweight tester is made up of the piston, when it comes to measurement all weights are loaded on the very top of the piston. The only time force happens to see is when the hydraulic press raised up the objectives. Diameter and the length of area of the cylindrical piston is helping to find the area. When there are no errors at all that’s when we find the most precise pressure. But in engineering...
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