Summary
This experiment is about the static calibration of a differential pressure transducer. Test measurements are done to find the range of input and output of the transducer, and to determine the “best-fit” line that models how the voltage reading would equate to the real pressure measurement. The input pressure comes from a hydraulic ram with pressure gauge. The output of the differential pressure transducer is in voltage, and is measured by a digital voltmeter. The input pressure is varied from 0 to 6 bar, and the three voltage readings are recorded for each pressure step value.
Introduction
The differential pressure transducer is statically calibrated in this experiment with the goal of determining the line of best fit to model the relationship between the pressure and the voltage readings. The method of calibration is needed for any measuring device (in this case, a pressure transducer) in order to correctly interpret the output as it is used in measuring something (in this case, measuring pressure). An input pressure range of 0 to 6 bar, with increments of 0.4 bar, is tested and measured of the corresponding voltage readings. From this, the pressure versus voltage graph is plotted and the line of best fit is estimated. The best fit line is verified of its accuracy and linearity.
In the succeeding sections, a background about the differential pressure transducer is presented, and a definition of the term static calibration. Then, the procedure of the experiment is enumerated including the experimental setup and the equipment used. In the Results and Discussion section, the results are presented in a table and graphically; then, the line of best fit is presented and analyzed. Finally, the conclusions section presents the important points achieved by the experiment. The references section enumerates the sources used in this report.
Background/Theory
The differential pressure transducer consists of two pressure inlets which act on a metal diaphragm placed centrally between two inductive coils. If the pressures from the two inlets are equal, there is no movement of the diaphragm and the inductance of the two inductive coils is the same. If there is a difference between the two pressures, the diaphragm will be deflected to one side, thus resulting in a difference between the inductances of the two coils. The difference in inductance of the coils is directly proportional to the pressure difference of the two pressure inlets. Usually a signal conditioning unit is used to convert the change in the inductance to the DC voltage which can be easily recorded by a voltmeter.
The differential pressure transducer is a type of pressure sensor that measures the difference in pressure from two pressure inlets by measuring the difference in inductance in the two coils. The varying inductance is measured in terms of voltage difference between the two coils. The difference in inductance of the two coils is designed to be directly proportional to the pressure difference of the two pressure inlets. Therefore, the relationship between the input pressure and the output voltage of the differential pressure transducer is expected to be linear.
Static calibration is a method of calibration of a sensor in which the input is varied incrementally over a defined range of input values . While varying the input, all the other factors in measurement are held constant. The goal of static calibration is to define the accuracy of the sensor, and to model transfer function or the relationship between the input (measured quantity) and the output. Thus, it is necessary that the input values are reliable because much of the accuracy of measurement would rely on them. For the input pressure, a hydraulic ram with a pressure gauge is used. In this manner, the value of the pressure is assumed accurate because standard equipment is being used. Through static calibration, a transfer equation relating input to output can be developed. Moreover, the static sensitivity of the sensor is determined. Consequently, the linearity error of the calibration line is also determined.
In this experiment, the goal of static calibration is to derive an input-output equation that can be used for further usage of the differential pressure transducer. Then, the errors are estimated in order to define the accuracy of the derived input-output equation. As mentioned above, the relationship between the input pressure and the output voltage is linear, thus a linear equation is expected to be the resulting input-output equation. Aside from the accuracy, the linearity of the equation is also analyzed.
Experimental Procedure and Equipment
The equipment used in this experiment include the following instruments: 1. Hydraulic ram with pressure gauge
2. Differential pressure transducer
3. Digital Voltmeter
The experimental setup is shown in the following figure:
Figure 1. Schematics of LABVIEW’S VI for Calibrating the Pressure Transducer
One of the pressure inlet ports of the transducer is connected to a hydraulic ram, used to exert pressure on the transducer. The other inlet port is simply exposed to the atmosphere. When the pressure from the hydraulic ram is increased (by sliding the “Ram Position” pointer upward), it causes the deflection of the diaphragm within the transducer toward one side of the inductive coils. The resultant differences in inductance of the coils is measured by a signal conditioning unit which outputs DC voltage proportional to the gauge pressure of the hydraulic ram.
The procedure followed in this experiment is as follows:
Procedure
1. Calibrate the pressure transducer from 0 to 6 bar in steps of 0.4 bar.
*These fixed step values follow the principle of static calibration. Moreover, this pressure value is the only factor being varied as the calibration is executed. In this way, it is assured that the resulting input-output equation has only one independent variable (the pressure) and one dependent variable (the output voltage reading).
2. At each step, record the pressure reading displayed on the gauge indicator of the hydraulic ram and the corresponding voltage readings from the digital voltmeter.
*In each pressure step value, 3 voltage readings are recorded.
The results and analysis are presented in the succeeding sections. The following questions need to be answered:
1. What is the input and output range in the calibration exercise?
2. Plot graph of Voltage against Pressure in Excel.
3. Determine the equation of best-fit line passing through the data points and hence the static sensitivity of the pressure transducer.
4. Determine the maximum deviation (ignore the sign) of the actual measurements from the calibration line and hence calculate the maximum linearity error in the calibration (expressed in % FSR).
The other pressure inlet is exposed to the atmosphere. This static calibration experiment assumes that the ambient air pressure in the course of the execution remains constant. In this sense, the pressure from the hydraulic ram is measured by the differential pressure transducer using the ambient air pressure as a reference point. Therefore, if the resulting calibration line is to be used in conjunction with the differential pressure transducer, the assumption that ambient air pressure is constant should be established initially. The calibration line may yield erroneous results if the ambient air pressure is varying.
Results and Discussion
The experimental setup of figure 1 is implemented. Each pressure variation is done very carefully to minimize human error in the measurements. Each voltage reading is finalized when the output value displayed by the digital voltmeter is relatively fixed. The following table shows the pressure step values and the measured voltages from the digital voltmeter.
Preliminary observation of the results suggests that for every pressure step, the output voltage readings do not vary significantly from one another. The deviations are maintained to a very small percentage of the values. This observation would attest to the precision of the differential pressure transducer and the minimization of errors in terms of the experimental setup and the experiment runs.
The input varies from 0 to 6 bar for a corresponding output variation of 0.009 to 7.836 V. These values are considered the input and output ranges of the calibration. As expected, the relationship between the input and the output is a direct proportionality (as pressure increases, the voltage also increases). Going forward, the next relationship to be verified is the linearity between the pressure input and the voltage output.
The plot of voltage against pressure is in figure 2.
Figure 2. Voltage Versus Pressure
The graph very easily displays the linear relationship between voltage and pressure. The three data points (three voltage readings) for each pressure step value seem to overlap. This further shows visually that the measured data have achieved high precision. With the imposition of the best-fit line, the linear relationship is verified visually.
The equation of the best-fit line is:
y=1.3089x-0.0135
The calculated R-parameter is 0.9999≈1. This signifies that the relationship between voltage and pressure is nearly perfect linear, and the linear equation is an excellent and accurate fit for the relationship. At this point, not only did the linearity been proven visually, but it has also been proven using linear estimation method of Excel.
The best-fit equation can be rearranged in order to make it a transfer equation with voltage as input and pressure value as output. The x-coordinate corresponds to the pressure values, and the y-coordinate corresponds to the voltage values. If voltage is V, and pressure is P, the input-output equation of voltage-pressure is:
V=1.3089×P-0.0135→P=V+0.01351.3089→P=0.764V+0.0103
P=0.764×2.567+0.0103=1.97→2.0 bar
The conversion is accurate, assuming the ambient air pressure remained constant. Given this calibration line, the static sensitivity of the pressure transducer is simply the slope of the line, which is equal to 0.764. The intercept is a very small value of 0.0103 (very close to zero), also adds up to the reliability of the calibration line estimate. Ideally, the measured voltage should be equal to zero if the pressure input is also equal to zero.
% Max. Linearity Error=0.0354.0×100%=0.875%
This error is very small; the experiment achieved highly accurate results. This linearity error guarantees that all the measurements done using the derived input-output equation will have less than 1% error.
Conclusions
The application of static calibration on the differential pressure transducer was successful. The experiment produced a highly accurate input-output equation (P=0.764V+0.0103) that can be used for further pressure measurements. The linearity error achieved is a significantly low value of 0.875% (less than 1%), and the linearity of the best-fit line is almost perfectly linear (R≈1). The static sensitivity of the differential pressure transducer in this experiment is 0.764. These factors assure the accuracy of the pressure transducer itself, and also the accuracy of the derived best-fit line equation.
References
Hitchcox, Alan. "Fundamentals of Pressure Transducers." 17 September 2013. Hydraulics and Pneumatics. 17 January 2016 <http://hydraulicspneumatics.com/200/FPE/Sensors/Article/False/6439/FPE-Sensors>.
"Static Calibration/Static Performance." 2013. 17 January 2016 <http://www.meteor.iastate.edu/classes/mt432/lectures/mteor432_staticcalibration_spring2013.pdf>.
