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Calibration of Bourdon Gauge Lingzi Pan Team 5 · Abstract The Bourdon gauge can measure both pneumatic pressure and hydraulic pressure. There is a transparent dial on the gauge to view the readings. In this experiment, to fill the cylinder when the piston is removed, the water is poured into the cylinder until it is full. The air in the tube should be cleared by controlling the appropriate valve. After eliminating the air in the tube, add the piston the cylinder. At each increment of the piston, each pressure gauge reading is recorded. This simple experiment gives a glimpse into the fundamental method that can be utilized to determine the fluid statics. Also, to calibrate the pressure measurement system, the output has to be compared with a standard input, which is known. In this experiment, the error is obviously larger than expectation. And the accuracy is too low. Many factors, like air bubble that has not been eliminated, the friction of the water in the transparent pipe and static friction between the piston and cylinder, will influence the data we tested. · Introduction Many types of gauge are available for measurement of pressure. Bourdon gauge (aka Bourdon tube gauge) is one of the apparatus that used to measure the pressure in various applications. Boyes (2008) also states that Eugene Bourdon patented his gauge in France in 1849, and it was widely adopted because of its superior sensitivity, linearity, and accuracy; Edward Ashcroft purchased Bourdon's American patent rights in 1852 and became a major manufacturer of gauges. Pressure measure is important for many reasons. Pressure measuring devices can allow operating pressure to be monitored. As

the Bourdon tube gauge is used extensively, but calibration is necessary to give correct pressure readings. Calibration refers to the process of comparing the reading of the device that is used to measure the pressure, with primary reference standard. Baber (1996) mentioned that the words "calibrate" and "calibration" entered the English language as recent as the American Civil War, in descriptions of artillery. Some of the earliest known systems of measurement and calibration seem to have been created between the ancient civilizations of Egypt, Mesopotamia and the Indus Valley, with excavations revealing the use of angular gradations for construction. The calibration device that will be used in the experiment is called “Dead weight Pressure Calibration System”. · Objective 1. Introducing the pressure measuring devices 2. Learning how to calibrate a Bourdon Gauge · Materials and Methods. Device Dead weight Pressure Calibration System: Picture 1. Dead weight Pressure Calibration System (By taking photo)

The dead weight pressure calibration system consists of a piston and a cylinder. There are some valves to eliminate the air in the transparent tube. The weights will be added to the upper end of the piston rod. A Bourdon gauge is supplied for calibration. In the Bourdon tube gauge, it consists of a tube of elliptical cross-section, bent into circular arc. When the pressure applied, the tube tend to be straight out, thus the pointer will show the readings. Experimental method In this experiment, the pressure is relative to the mass of cylinder and piston, the surface area of piston and the gravitational acceleration through the following equation: F 𝑚𝑔 ① Where: F – the normal force exerted by cylinder (N) m – the mass of cylinder (Kg) g – Gravitational acceleration (N/Kg) P ! ! ② Where: P – Pressure (Pa) F – the normal force exerted by cylinder (N) A – Cross-section area of the surface of the piston (m2) Absolute error 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑖𝑛 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟 𝐺𝑎𝑢𝑔𝑒 𝑟𝑒𝑎𝑑𝑖𝑛𝑔 %Relative error !"" !"# %&'( !""#" !"# %&'( !"# %"# ③ ④ In calculation of this experiment, the unit on the gauge is bar, so need

transfer bar to kPa. The unit of the mass of the cylinder and piston is g, also need to transfer g to kg: 1 bar 100 kPa 1000g 1Kg Also, the area of surface of the piston is known, A 244.8 10-6 m2 And the Gravitational acceleration is equal to 9.81 N/Kg. · Result and Discussion Calculation and Table In the experiment, team 5 obtained two groups gauge pressure. I used these two group data to obtain the average gauge pressure, and list in Table 1. Table.1 the test data Mass (Kg) 1 2 3 Gauge Gauge Average Gauge Mass added Total Mass Pressure pressure pressure (Kg) (Kg) (kPa) (kPa) (kPa) 0 0.329 0 0 0 0.17 0.499 10 15 12.5 0.5 0.999 25 33 29 1 1.999 70 55 62.5 2.5 4.499 150 150 150 2 6.499 215 240 227.5 -2 4.499 150 160 155 -2.5 1.999 60 70 65 -1 0.999 30 30 30 -0.5 0.499 12 20 16 For table 1, I think there is an inappropriate procedure in my team in this experiment. In my opinion, the weight of the piston, added to the cylinder, should progressively increase. After adding 1Kg piston, I think

the piston added to the cylinder should be 2Kg rather than 2.5Kg. And the last one added to the cylinder should be 2.5Kg. Not just for increment, but degression as well. I have signed these improper data of added masses of table 1 in red. By using the data from table 1 and the equation①②③④, I calculate the data listed in table 2: Table 2. The calculated data of calibration Gauge Pressure in Absolute % Relative cylinder (kPa) error (kPa) error 0 13.18419118 13.18419118 100 12.5 19.99669118 7.496691176 37.48965822 29 40.03345588 11.03345588 27.56058811 62.5 80.10698529 17.60698529 21.97933829 150 180.2908088 30.29080882 16.80108322 227.5 260.4378676 32.93786765 12.64711155 155 180.2908088 25.29080882 14.02778599 65 80.10698529 15.10698529 18.85851182 30 40.03345588 10.03345588 25.06267736 16 19.99669118 3.996691176 19.98676252 pressure (kPa) Table 3. The data of average overall gauge reading and standard deviation Cylinder pressure Average overall gauge reading Standard deviation 13.18419118 0 9.322630985 19.99669118 14.25 4.0635243 40.03345588 29.5 7.448278084 80.10698529 63.75 11.56613522 180.2908088 152.5 19.65106937 260.4378676 227.5 23.29058957

Figure and result discussion 1. Gauge reading versus pressure in cylinder when pressure is increasing. Gauge reading (kPa) 300 250 200 150 100 50 0 0 50 100 150 200 250 Pressure in cylinder (kPa) Figure 1. Gauge reading versus pressure in cylinder when pressure is increasing Gauge reading (kPa) 300 250 200 150 100 50 0 0 50 100 150 200 250 Pressure in cylinder (kPa) Figure 2. Gauge reading versus pressure in cylinder when pressure is decreasing According to the Figure 1 and Figure 2, the gauge pressure is the actual pressure, and the pressure in cylinder is the true pressure. In the Figure 1, when the pressure in cylinder is increasing, the gauge reading increases as well. And the increasing trend almost is a straight line and the proportion of the line is nearly linearly. It proves

that there is no variable in the experiment except the weight of the cylinder, which can cause the variable in the pressure of the cylinder. And the first point is not at the origin because there are more other outside factor to influence the first point, but not our operation. In the Figure 2, the situation is same as the Figure 1. The trendline approximately is a straight line and linearly proportional. In terms of these two figures, the gauge readings tend to be lower values when the pressure is increasing than the pressure is decreasing. 2.The absolute error versus cylinder pressure. Absolute error (kPa) 35 30 25 20 15 10 5 0 0 50 100 150 200 250 300 Cylinder pressure (kPa) Figure 3. The absolute error versus cylinder pressure when the pressure was being increased Absolute error (kPa) 35 30 25 20 15 10 5 0 0 50 100 150 200 250 300 Cylinder pressure (kPa) Figure 4. The absolute error versus cylinder pressure when the pressure was being decreased

The absolute error refers to the difference between the value and the approximation value. In this experiment, the pressure in cylinder is the true value, and the gauge reading is the approximation value. The absolute error reflect the degree of diverge of the measured valued from the true value. Absolute error has same unit as the measured value. In this experiment, the unit of absolute error is kPa. According to the Figure 3, the absolute error is increasing in general, with increasing cylinder pressure. For Figure 4, the absolute error decrease with the decreasing pressure of cylinder. But In Figure 3, the first point does not follow this principle, because the absolute error equals pressure in cylinder minus the gauge reading. At the first point in Figure 3, the gauge reading is equal to 0, because the piston has not been put on the cylinder. And the gauge is not so sensitive to test the small pressure applied by the piston (329g). So the absolute error of the first point is higher than the 2nd and 3rd point in Figure 3. And the first point obeys the general trend. But the absolute error cannot completely reflect how accurate test value is. So we need the relative error to measure it. According the absolute error, the accuracy of meter can be calculated. The accuracy of meter (The maximum value of absolute error / span of meter) 100%. In the Figure 3 and Figure 4, the Maximum value of the absolute error is 32.938 kPa, and the span of the meter is equal to 2.5bar, 25bar is 250kPa. The accuracy of meter (32.938kPa / 250kPa) 100% 13.18% So the accuracy of this gauge is 13.2%.

3. The %relative error versus cylinder pressure 120 %relative error 100 80 60 40 20 0 0 50 100 150 200 250 300 Cylinder pressure (kPa) Figure 5. The % relative error versus cylinder pressure when the pressure was being increased 30 %relative error 25 20 15 10 5 0 0 50 100 150 200 250 300 Cylinder pressure (kPa) Figure 6. The % relative error versus cylinder pressure when the pressure was being decreased The relative error always is used to compare the measured values in different size. The relative error of measured value is more comparable than the absolute error. For Figure 5, the relative error of the first point is 100%, the reason why the relative error of the first point is so high is that the value of the cylinder pressure is equal to the value of the absolute value. Because the gauge pressure at the first point is 0. Possibly because the Bourdon gauge is not so sensitive to measure the small pressure

applied by the piston, which weight 329g. Also it might be influenced by other factors, like friction in the tube or the elasticity of the tube in the Bourdon gauge. 4. The average overall gauge reading versus cylinder pressure and Average overall gauge reading (kPa) the standard deviation. 300 y 0.899x - 7.7605 R² 0.99903 250 200 150 100 Trendline 50 0 -50 0 100 200 300 Cylinder pressure (kPa) Figure 7. The average overall gauge reading versus cylinder pressure According to the Figure 7, the equation that appropriately relates the average overall gauge reading and cylinder pressure is y 0.899x-7.7605. This equation is calculated by the trendline in the Excel. The R2 of the trendline is 0.99903, it approximately approach 1. It means that the trendline is infinitely approach the actual line of these points in the Figure 7. So the equation is reliable. The standard deviation is shown on the Figure 7. The standard deviation refers to the degree of the deviation between tested value and average value. The small value of the standard deviation represent that the tested value has less difference with the average value. And vice versa. In Figure 7, the first four points have small deviation value. But the standard deviation of the 5th and 6th point is bigger. This result represent that the difference between the two-group test values will increase, when the weight is increasing. It

shows that with the weight and time increasing, there is more factors influence the result. · Conclusion The analysis of the collected data from calibration of Bourdon Gauge in this experiment allowed for a sufficient overview of the calibration measurement. According to analysis the data we obtained from the Bourdon gauge, I found calibration is important for meter. In this experiment, the data in my team is not so accurate. Friction, backlash and The absolute error and the relative error are higher than expectation. The accuracy is lower than the standard. And with the increasing time, the standard deviation increases as well. So calibration is indispensable for the accurate data. · Reference Boyes, Walt (2008). Instrumentation Reference Book (Fourth ed.). Butterworth-Heinemann. p. 1312. Baber, Zaheer (1996). The Science of Empire: Scientific Knowledge, Civilization, and Colonial Rule in India. SUNY Press. pp. 23–24. ISBN 978-0-7914-2919-8.

In the experiment, team 5 obtained two groups gauge pressure. I used these two group data to obtain the average gauge pressure, and list in Table 1. Table.1 the test data Mass (Kg) 1 2 3 Mass added (Kg) Total Mass (Kg) Gauge Pressure (kPa) Gauge pressure (kPa) Average Gauge pressure (kPa) 0 0.329 0 0 0 0.17 0.499 10 15 12.5

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