Pressure

Transcript

8. PRESSURE MEASUREMENT Measurement tasks 1. Calibrate the semiconductor pressure sensor from 0 to 20 kPa. Record the pressure waveform of the pressure resistance test. 2. Calibrate the 1MPa pressure sensor with the pressure calibrator DM 603. 3. Check the function of the differential capacitor pressure sensor for low-pressure measurement. I. Dynamic pressure measurement Measurement procedure 1. Turn on the power supply of the pressure sensor TMK 4282S. Turn on the computer and run the program with the icon "Dynamic pressure measurement" on the desktop of the Windows. 2. Execute the static calibration of the measurement system by setting the required pressure (i.e. 0 and 20kPa). When calibrating the 20kPa pressure, block the open end of the measurement system and afterwards set the required pressure value with the filler of medical tonometer (check the value with the tonometer scale in kPa). 3. Learn the controls of the program. Block the open end of the system with your finger, change the pressure value and measure the time waveform of the pressure. Set the parameter No. of Samples to the value 20 and the parameter Frequency to 1000 Hz. Observe the noise level of the waveform. Change the parameter No. of Samples and observe the noise level of the waveform. Explain the difference. 4. Put the tested object on the opened end of the system and fasten it with the screw on the clip. 5. Start the measurement and increase the pressure in the system until the tested object is destroyed. Automatic level triggering can also be used for this measurement. 6. Record the destruction pressure of the tested object. Record the pressure pulse created by one pressing of the tonometer filler. Print the acquired waveform. II. 0-1 MPa Pressure Measurement Measurement procedure 1. Learn how to use the pressure calibrator DPI 603 before the beginning of the measurement. Especially take care not to switch the Pressure/Vacuum switch when the pressure is not zero (danger of damaging the instrument!). 2. Measure the output voltage of the pressure sensor “Si TT” as a function of pressure. The pressure sensor is supplied from the current supply (Fig. 8.1). Determine the transfer constant of the sensor. Measure the supply current of the sensor. Do not exceed the 1MPa pressure. p Rs1 I = konst = 10mA Ra Rb Rc Rd V A 5V 500Ω Rs2 Pressure sensor Fig.8.1 III. Low Pressure and Flow Measurement Measurement procedure Sensitivity test of the differential Capacity/Voltage Transducer This measurement is performed with zero pressure difference (fan switched off). 1. Measure the capacity of the left capacitor (left electrode against the membrane in the middle connected with the frame of the unit) CL and right capacitor CR with the LCR meter. Disconnect the differential C/U transducer while measuring capacity with LCR meter. 2. Disconnect the LCR meter cables from the unit and connect all three electrodes with the C/U transducer unit. 3. Check the connection of the differential C/U transducer to the sensor unit – see the labels of the cable terminals on the transducer board. 4. Check the supply cables connecting the differential C/U transducer to the terminals of the power supply. Connect the multimeter to the output terminals of the differential C/U transducer. 5. Turn on the power supply. Adjust the voltage of the driving generator so that the output voltage is not distorted by saturation (e.g. near to 1V). 6. Measure the voltages UR (corresponding to CR), UL and UL-R on the output of the transducer and their dependence on applied pressure. For measuring the voltages UR, UL disconnect the opposite input (electrode). 7. Analyse the sensitivity of the differential C/U transducer output voltage on the values of CR, CL and on the excitation voltage from generator UG (physical unit [V/pF]). Pressure Sensor Sensitivity Measurement Measure the changes of the CL and CR capacity (and of the voltage UL-P) according to the pressure p measured by the ethanol differential manometer. Pressure p is dependent on the supply voltage of the fan supplied by the control transformer. The fan engine starts to work at 40 Volts, maximum allowed voltage is 110V. Measure the airflow also with the flow meter (“float rotameter”). Results Processing a) Calculate the max. displacement x [mm] and stiffness k [N/m] of the sensor membrane. b) Plot the dependence of CL, CR, CL-CR as a function of pressure p. c) Plot the dependence of UL-P on the capacity difference CL-CR. IV. Units and Instruments Description Pressure Difference Supply Pressure difference supply is modeled by the pressure difference caused by the viscous friction of airflow in the cylindrical pipe. The pressure difference in the case of laminar flow is a linear function of average speed i.e. rate of flow. This effect is often used for the rate of flow measurement. The laminarity condition is granted when the Reynolds number Re is smaller than 2300. l ventilator v D p1 flowmeter p2 h liquid manometer capacitive manometer Fig.8.2 D = 2,95 mm l = 20 cm is inner diameter of the pipe, is the distance between the pressure difference sensing branches Reynolds number for the circular pipe is defined as: Re = ρD 3 ∆p , 32lη 2 (8.1) the rate of flow when the flow is laminar is: πD 4 QV = ∆p [ m 3 s −1 ] 128lη where ρ (8.2) ... air density [kg/m3], D ... inner pipe diameter [m], D = 2,95 mm, l ... distance between the pressure difference sensing branches, l = 20 cm, η ... dynamic viscosity [Pa.s]. Dynamic air viscosity depends on temperature and in the interval from 0 to 50°C is approximated by the linear function: η = 4,639 ⋅ 10 −8 ⋅ t + 1,722 ⋅ 10 −5 [ Pa ⋅ s; C] o (8.3) Normal atmospheric pressure air density is in the temperatures 15 to 25°C: ρ = 1,2 ± 0,05 [kg / m3 ] Differential Capacity Manometer Differential Capacity Manometer transduces the applied pressure difference to the displacement of a flexible membrane separating the two chambers of the manometer. (The displacement is measured through changes of capacity.) where S ∆p = p1 − p2 (8.4) FP = ∆pS (8.5) ... area of the membrane [m2], membrane diameter is 8 cm. Displacement of the membrane causes the directive force proportional to the stiffness of the membrane to act against the pressure force: Fd = k ⋅ x where k x (8.6) ... membrane stiffness [N/m] , ... displacement of the membrane from the middle position [m]. When the position of the membrane is stable: Fd = FP → ∆p = k x S (8.7) The displacement of the membrane is proportional to the measured pressure difference. The displacement of the membrane is defined by the equation: C= where d S εS d+x [F] ... idle distance of the membrane from the electrodes [m], ... area of the membrane [m2] (membrane diameter is 8 cm). (8.8) ε ... permittivity, ε ≅ εo = 8,854.10-12 [F/m], Membrane displacement (and the pressure difference) is measured easily from the capacity difference: 1   1 ∆C = C1 − C2 = εS  −   d − x d + x (8.9) Equation (8.9) can be used when the distance d of the electrodes in comparison to the area S is small and the inhomogenity of electrostatic field on the edges can be neglected. When x << d , the equation (8.9) transforms into: ∆C = εS 2x d2 (8.10) The difference arrangement partially linearizes (for small displacements) the dependency of the capacity on the distance of the electrodes. Capacity-Voltage Transducer Cref Cm U2 G U1 Fig. 8.3 C/U transducer Fig. 8.3 shows one of the possible basic layouts of the C/U transducer. This layout uses feedback circuit with the operational amplifier. Cm is measured capacity, Cref is reference capacity of the transducer The equation for voltages U1 and U2 is: U 1 ( jω ) U ( jω ) =− 2 , 1 1 jωC m jωC ref and transformed: U 2 ( jω ) = −U 1 ( jω ) Cm , C ref (8.11) which means that the output voltage amplitude is proportional to the measured capacity. Used circuitry suppresses the influence of the capacities of the input cables; one of these capacities is connected parallel to the low impedance of the generator, the second one is on very small voltage at the OpAmp’s input (virtual zero). Complete circuitry for differential measurement of the capacity is on the fig. 8.4. The first amplifier produces two sine waves of opposite polarity exciting the two electrodes of the differential pressure sensor. In an idle state, the middle electrode is in electrical balance and thus its voltage is zero. In practice, the two capacities (C1 = CR and C2 = CL) in idle state are not exactly matched. Hence it follows: U G ( jω ) U G ( jω ) U ( jω ) − = − 2 1 1 1 jωC L jω C R jωCref U 2 ( jω ) = − U 1 ( jω ) CR − CL Cref Auxiliary negative feedback resistor 200 kΩ decreases the DC amplification so that the second amplifier does not fall into the saturation by integrating its own offset voltage. 200kΩ cca 1V, 5kHz 150pF 20kΩ C1 136pF + ∆ C Cz 124pF - ∆ C C2 20kΩ Obr. 8.4 Differential C/U transducer Ethanol Manometer Ethanol manometer can be slanted for acquiring higher sensitivity. The same height is then represented by longer bar of ethanol. When measuring, use the 1:8 or 1:4 scale of height h and length l of the bar. The manometer is filled with ethanol. The density of ethanol at 20°C is: ρ 20 = 789 kg ⋅ m −3 and ethanol volume expansion factor: , ⋅ 10 −3 K −1 β 20 = 11 The actual density at the temperature measured in lab is: ρ t = ρ 20 [1 − β 20 (t − 20)]. The pressure difference measured by ethanol manometer is: p = hρ g = l ρg , 8 (8.12) where g = 9,81 m.s-2 is the gravity acceleration and h is e.g. l/8 (corresponding to the manometer slope). When the slope of manometer is in the position 1:8 it is essential to set the exact horizontal position of the manometer. Horizontal position is adjusted by the set screws on the base of the manometer and is indicated on the bubble level. It is advisable to check the horizontal position during the measurement. Don’t forget to measure the bar level for zero pressure difference (the scale offset). Flow meter Flow meters are often used to measure rate of flow of liquids and gases. The position of the float is measured contactlessly in industrial applications. We use the laboratory flow meter (rotameter) with exchangeable pipes and floats. The range is selected by choosing the diameter of the pipe and the weight of the float. The flow meter is calibrated for air (20°C) and distilled water (15°C) in the normal pressure. The measured values must be adjusted for different conditions or media. Height h on the scale of the flow meter when using the hollow aluminum float corresponds (input pressure 101,31 kPa, temperature 20°C) with the rate of flow Q according to the following formula: Q = 0,2 + 1,328.10-2.h + 9,191.10-5.h2 - 2,504.10-7.h3 [l/min; mm] (8.13) TMK4282S Pressure Sensor TMK4282S is a product of Cressto Co. from Rožnov p. Radhošť. It is a cheap gas and liquid relative pressure sensor in the plastic casing. Measured pressure is applied with a hose on the sensor input on the casing. The sensor consists of a thin silicon layer with piezoresistive bridge applied on this silicon layer with the IC technology. The circuit is laser-trimmed for the zero offset value and its temperature drift. The most important characteristics: Range pFS 20 kPa Maximum pressure pmax 40 kPa Sensitivity S 1¸2 mV/kPa Nonlinearity < 0.5 % FS Hysterezis < 0.1 % FS Voltage offset < 1 mV Temperature offset drift TCZS < 10 Pa/K Supply voltage 5V Input resistance 5 kΩ Output resistance 2.3 kΩ Temperature range -25 .. 85 0C +Us 10max 1 RS1 Ra Rb 4 2 Rc +Uout 20max ∅5,2 13,25 -Uout 16,25 Rd 1 2 3 4 7max RS2 GND 2,5 3 Fig.8.5 Dynamic Pressure Measurement Program The program is able to record the pressure values waveforms. The program was created in the LabView development environment. The output voltage of the TMK4282S sensor is measured by the National Instruments PCI measurement card PCI-MIO-16XE-50. The calibration starts automatically after the program starts. The voltage values for 0 and 20kPa are saved as calibration constants. These values are used for computation of the pressure values from the voltage output values of the sensor. The program presumes that the dependence of the voltage on the pressure is linear. The program is ready for measurement after the calibration. There are two ways how to trigger the measurement. Either you can choose to start the measurement immediately after pushing the button "Start" on the front panel of the program or after the pressure level reaches preset triggering level ("Level Triggering ON"). Measurement in both modes can be stopped with the "Stop" button. The measurement in the level triggering mode stops also automatically after the pressure drops under the triggering level. It is possible to print the waveform after the measurement with the "Print" button. The "Exit" button stops the execution of the program. It is essential for the correct operation of the program to understand the way the program samples the pressure waveform. The program acquires selected number of samples ("Samples" (see Fig.8.6)) with the sampling rate "Frequency". The average value from these samples forms one point in the graph. Therefore the actual sampling rate is the ratio "Frequency/Samples". This way of measurement is used to reject the power line frequency 50Hz. The averaging causes the measurement to react slowly on the pressure change. This means that in all cases the actual sampling rate should be above 10Hz (minimum 1Hz!). To enable smooth program operation it is necessary to meet these conditions. When the program stops responding it is possible to stop it by pressing Ctrl+Alt+Del keys, selecting the LabView process and closing the program with "End Task" button (in Czech Windows "Konec úkolu"). Controls Description Controls layout is on the Fig. 8.6. Samples - Number of samples acquired in one sampling period. After averaging these values form one point in the graph. Frequency – sampling rate [Hz] Pressure - instant value of the pressure 20kPaVoltage, p=0kPa Voltage - Calibration voltage values for 20kPa and 0kPa Start - Measurement start Stop - Measurement stop Level Triggering - Switching between the level triggering and button triggering. Measurement in Progress - Indication of the measurement in progress (green color) Print - printing of the graph Exit - press to exit the program Graph Clear - clearing the graph Fig. 8.6 Front panel of the program Graph Controls The acquired data are stored in the memory and at the same time displayed in the graph. The data memory can hold up to 2048 samples. In case of filling all the memory the oldest data are deleted. The graph can display any cutout of the acquired data. The graph controls enable to zoom the displayed area manually or automatically. Do not operate the graph controls during the measurement due to interference with the data acquisition. The controls are displayed on the Fig.8.7. Due to the speed of the program it is not advisable to set autoscale option. Autoscale Axes parameters (do not use) Fig. 8.7 Graph controls Pressure Calibrator Fig. 8.8 shows the picture of the DM 603 pressure calibrator with the controls description. The calibrator is designated for calibration of pressure sensors with the use of internal pressure source "Handpump". The calibrator can also be used for measurement of pressure from the external source. The maximum safe pressure of the calibrator is 2500 kPa. This value mustn't be exceeded due to possible instrument destruction. The "Pressure/Vacuum" switch mustn't be switched in the nonzero pressure value state of the calibrator due to possible instrument damage! The step-by-step guide for getting the desired pressure value: • • • • • Open the "Release Valve", make sure that the "Pressure/Vacuum Switch" is in the pressure position, execute the zero pressure correction by pressing the ”Zero” and ”P” buttons at the same time Close the "Release Valve" Pump up the pressure c. 20kPa higher than the desired value Use the "Volume Adjuster" to adjust the pressure to the desired value Don't forget to release the air with "Release Valve" after you finish the measurement Fig. 8.8