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By means of novel packaged-structure design, a temperature independent differential pressure sensor based on fiber Bragg gratings with high sensitivity is experimentally demonstrated. The differential pressure sensitivity of the sensor can reach to 821.87nm/MPa. This device can also be used for simultaneous measurement of temperature and differential pressure, which is suitable for applications involving measurement of liquid level, liquid density or specific gravity detection.
©2008 Optical Society of America
1. Introduction
Recently the sensitivity of fiber Bragg grating pressure sensors are greatly enhanced by using several different design methods [1–6]. For further extending their applications, fiber grating pressure sensors are also applied in liquid level or water-depth measurement [7, 8]. Differential pressure (DP) measuring mechanisms for high pressure and liquid-flowing-rate detection are also applied in fiber Bragg grating pressure sensors [9, 10]. For air pressure and temperature control of cabin in airplane, submarine and laboratory or for production room in a pharmaceutical and electronic factory, the measurement sensitivity of differential pressure and temperature sensing device is important factor for providing a comfortable and safe working place. In this paper, a new designed differential pressure fiber sensor based on FBGs has been demonstrated, and in which two identical FBGs are packaged in a temperature compensated metal structure. In this paper, the differential pressure sensor based on fiber Bragg gratings is firstly experimentally demonstrated to have the maximum sensitivity of 821.87nm/MPa for our knowledge. Therefore, by means of this simple packaging construction, high-sensitivity temperature-independent differential pressure sensor can be achieved with a nice linearity for applying in the measurement of liquid level, liquid density or specific gravity detection.
2. Principle
The sensor has a metal cage composed of two metal cylinders, in which a diaphragm consists of a silicone rubber sandwiched between two metal plates located in the middle of sensor structure. Thus, this sensor includes two symmetrical pressure cavities separated by the diaphragm as shown in Fig. 1.
There is a pressure inlet hole on each pressure cavity. Two identical FBGs with the grating length of 1 cm and the separation of 0.8cm are fabricated in a SMF-28 fiber by phase-mask writing techniques. They are glued axially through the center of diaphragm at each pressure cavity with sufficient pre-strain (εs) to accommodate the wavelength shift induced by differential pressure. Surrounding temperature variation would cause a thermo-expansion of metal drum which induces the strain of εT=M×ΔT that is identical for both FBGs, where M is the thermal-expansion coefficient of metal, T is the temperature. When a liquid or an air with different pressure comes into the sensor through two pressure inlet holes respectively, a net pressure will act on the surface of round plate and diaphragm. This net pressure will induce an axial tension force to the FBG in the higher pressure cavity and an axial compress strain in the lower pressure cavity. A strain of FBG induced in a pressurized cavity with a diaphragm-hardcore is given by [11]
where , P is the pressure in the sensor, R is the diaphragm radius, t is the diaphragm thickness, r is the round plate radius, af is the fiber cross-section, E f is the Young’s modulus of fiber, E and µ are the Young’s modulus and the Poisson’s ratio of diaphragm respectively.
In our proposed sensor, the total strain of FBG in the higher pressure cavity can be expressed as
where εp,H is the strain induced only by the pressure in the higher pressure cavity. The total strain of FBG in the lower pressure cavity is given as
where εp,L is the strain induced only by the pressure in the lower pressure cavity. The Bragg wavelength shift caused simultaneously by strain and temperature variation can be expressed as [12]
where Pe is the effective photo-elastic constant of fiber. The center wavelength separation between two FBGs caused only by differential pressure (ΔP) are expressed as
where ΔλB,H and ΔλB,L are the reflected central wavelength of the gratings in the higher and lower pressure cavities respectively. The shift of the center-wavelength average-value of two FBGs caused by the temperature variation of ΔT is obtained as
From Eq. (5), the differential pressure to be measured is proportional to the separation of the central wavelengths of two FBGs. From Eq. (6), the temperature can be determined by the average value of both reflected central wavelength shifts in the sensor. Therefore, this sensor has the capability to measure differential pressure and temperature simultaneously.
3. Experimental results and discussion
The physical configuration of the sensor is made of aluminum. The reflected central wavelengths of both FBGs in the sensor are equally located in 1558.74 nm at 15°C with a little bit different reflectivity. Thus, the FBG in each cavity can be identified in the sensor. They are pre-strained for the reflected central wavelength to be shifted to 1561.76nm and the reflective peaks are kept in overlap condition during the fabricating process. Hence there is only one reflective peak shown on optical spectrum analyzer before the sensor is pressurized. All structural parameters of the sensor are shown in table 1. The experimental setup is shown in Fig. 2. The shift of the reflected central wavelength corresponding to the variation of differential pressure is monitored with an optical spectrum analyzer. The pressure air is supplied by a piston type pump which can easily provide a positive and negative pressure in the sensing device. A U-type manometer is connected to the air pressure loop for pressure measurement. Air with different pressure is applied to one pressure inlet of the sensor then which is put in a temperature controlled oven for monitoring the reflected central wavelengths shift with temperature variation. Hence different pressure can be applied to this sensor at any temperature for confirming the pressure and temperature measurement simultaneously.
Table 1. parameters of sensor structure
For temperature measurement at no differential pressure, the wavelength shift of the sensor versus temperature variation from 15 to 60 °C is shown in Fig. 3. There is only one reflective peak in the reflected central wavelengths shift profile when ambient temperature is varied.
Fig. 3. The wavelength shift versus temperature variation, (a) wavelength shift profile, (b) a nice linear curve of wavelength shift versus temperature variation.
The responsivity of reflected central wavelengths shift versus temperature is around 0.04nm/°C with a nice linearity and without obvious deviation. Thus, a symmetrical packaged structure in the higher and lower pressure cavity of the sensor is experimentally confirmed. In the sensor, the cavity with higher reflected peak FBG is denoted as A-cavity and the other is B-cavity. During differential pressure measuring experiments, A-cavity is pressurized by piston pump at different surrounding temperature and the pressure inlet of B-cavity is vented. The pressure applied to A-cavity is in the range of +50 to -50 cmH2O with a decrement of 10 cmH2O, and the surrounding temperature is 15°C to 60°C with an increment of 5°C. When differential pressure is changed at fixed surrounding temperature, reflected central wavelengths of the two FBGs in respective cavities shifted in opposite direction with an equal shifting amount. The profile of reflected central wavelengths shift with differential pressure variation at temperature 25°C and 45°C is shown as Fig. 4.
Fig. 4. The profile of the fiber Bragg gratings wavelength shift with differential pressure (cmH2O) variation at temperature (a)25 °C, PA<PB (b) 25 °C, PA>PB (c) 45 °C, PA<PB (b) 45 °C, PA>PB.
When the surrounding temperature is changed at a fixed differential pressure stage, reflected average-central wavelength shifts linearly to temperature variation. Position of two reflected wavelength peaks at differential pressure (PA-PB) of 20 and 50 cmH2O with surrounding temperature variation of 15–60°C in an increment of 5°C are shown in Fig. 5. The separation between reflected central wavelengths of both FBGs is only proportional to differential pressure without any interference of temperature perturbation. A measuring responsivity of 0.806 nm per 10 cmH2O is obtained in the experiment as shown in the curve slope of Fig. 6, corresponding to the differential pressure sensitivity of 821.87nm/MPa equivalent to the differential pressure sensitivity factor of 5.27×10-1/Mpa (normalized value with 1558.74 nm) is obtained. According to Eq. (5), the theoretical responsivity is 0.915nm per 10 cmH2O. The discrepancy between the experimental result and the theoretical value is attributed to the dimension error of each element in the sensor.
Fig. 5. Position of two wavelength peaks at pressure PA-PB=20 and 50 cmH2O with temperature variation of 15–60°C in increment of 5°C.
Fig. 6. Separations between reflected central wavelengths of FBGs versus differential pressure (PA-PB) at any temperature with a responsivity of 0.806nm/10cmH2O.
In the proposed sensor, the differential pressure measuring range is determined by the maximum allowable stretched strain of FBG located in the high pressure cavity and the prestrain of FBG located in the low pressure cavity at certain temperature. The maximum allowable stretched strain of an FBG fabricated in SMF-28 single mode fiber is around 8000 micro-strain. In the temperature range of our experiment, the maximum differential pressure measuring range can be -11.681 to +11.681 kpa (-119 to +119 cmH2O) at 59.2°, and the minimum measuring range is -7.349 to +7.349 kpa (-74.9 to +74.9 cmH2O) at 15°. For the FBGs with an appropriate pre-strain, the maximum measuring range of differential pressure can be obtained at certain required ambient or working temperature.
4. Conclusion
A simple, temperature-independent and novel grating-packaged differential pressure sensor is experimentally demonstrated with the maximum sensitivity of 821.78 nm/Mpa. Its operation mechanism is based on one of two fiber Bragg gratings to be compressed and the other to be extended by a diaphragm. This sensor has a potential application in a simultaneous differential pressure and temperature control system and is expected to be used in liquid density or specific gravity measurement system.
Acknowledgment
The authors would like to thank the National Science Council of Republic of China, Taiwan, for financially supporting this research under contract No. NSC 97-2221-E-013-001-MY2 and NSC 97-2221-E-035-047.
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