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Free-cylinder, strain-gauge, pressure transducers up to 2 GPa
Physica B 265 (1999) 239—245
Free-cylinder, strain-gauge, pressure transducers up to 2 GPa G. Molinar *, R. Maghenzani , R. Wis´ niewski Consiglio Nazionale delle Ricerche, Istituto di Metrologia **G. Colonnetti++, Strada delle Cacce 73, 10135 Torino, Italy Warsaw University of Technology, Institute of Physics, Koszykowa 75, 00662 Warsaw, Poland
Abstract A review of the main metrological characteristics obtained with a large family of free-cylinder and free-rod pressure transducers using different materials (hard tool steels, tungsten carbide and ceramics), different shapes of active elements and different pressure ranges up to 2 GPa is presented. In general, they have a resolution better than 1;10. Repeatability of measurements depends on pressure and typically it is of the order of few parts in 10 up to 0.5 GPa, approaching 1;10 for pressure range up to 2 GPa. Their pressure sensitivity is always of the order of few parts in 10 up to 0.5 GPa and of the order of few parts in 10 for higher pressures up to 2 GPa. Linearity of the calibration factor is of the order of some percent, so it is always necessary to use appropriate polynomial fitting to express the output signal of the pressure transducers versus the measuring pressure. The main limiting factor is hysteresis that can be of the order of few parts in 10 for some of the pressure transducers (for pressures not generally exceeding 0.5 GPa) but it can reach values of some parts in 10 for pressures from 0.5 to 1 GPa and of some percent from 1 to 2 GPa. 1999 Elsevier Science B.V. All rights reserved. Keywords: Metrology; Pressure; Sensors; Transducer
1. Introduction Since a long time pressure transducers with cylindrical elastic elements have been widely used in many applications. Some of them, extending their pressure range up to 1.4 GPa, are commercially available. Generally these transducers use an elastic element realized as a hollow cylinder, made with different materials (typically alloy steels) depending on the pressure range of their use. They have
* Corresponding author. Tel.: 0039-011-3977-306; fax: 0039011-346761; e-mail: [email protected].
a blind end on one side and, on the opposite side, the cylinder is rigidly fixed (through an appropriate mechanical fitting) to the apparatus where pressure has to be measured. In this condition it is difficult to achieve a very high accuracy of pressure measurements because of the indefinite state of stress at both ends. Deformations of the elastic element, although proportional to the applied internal pressure, are normally influenced by state of stresses imposed on the transducer (e.g. the torque applied on the pressure fitting) and the effects of deformation versus applied pressure can only be roughly predicted by analytical calculations. The idea of using a free-dilating-cylinder was developed with the purpose of improving as much
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as possible the repeatability of stresses which have to depend uniquely on the applied pressure, reducing hysteresis effects by minimizing stress effects that seals impose on the elastic element. The illustrated sensors represent an attempt to obtain improved metrological performances for a large family of free-cylinder and free-rod pressure transducers developed in the last six years, using different materials (hard tool steels, tungsten-carbide and ceramics), different shapes of active elements and different pressure ranges. In Fig. 1 the main types of pressure transducers realized are schematically given. The main realized pressure transducers are of the following models: E free-cylindrical active element with pressure applied on the internal part (1, 1a in Fig. 1) and on the open ends (2, 2a, 2b, 2c in Fig. 1) of the cylinder, for pressure ranges up to about 500 MPa [1—4];
E free-rod active element with pressure applied only on its open ends (3, 4, 4a in Fig. 1), for pressure ranges up to about 1 GPa [5—7]; E free-cylindrical active element with pressure applied on all the external part of the sensor (5, 5a in Fig. 1), (frequently this configuration is called “bulk compression cylinder” [8,9]), for pressure ranges up to about 2 GPa. In all the above configurations a combination of circumferential and longitudinal stresses is applied to the elastic element. All active elements are equipped with strain gauges (mainly of the miniaturized types) selected for the specific design of the elastic elements and used to measure strain and deformations; in some cases (e.g. bulk compression cylinder) LVDT or capacitance sensors have also been used to measure displacements of the active elements. This review also considers more recent results obtained with a pressure transducer (improvement of the patented version [10]) where the active cylinder has hexagonal shape and it is contained within two concentric cups [11]. The main metrological characteristics of some selected pressure transducers will be reviewed in this paper and critically analyzed.
2. Free-cylinder pressure transducers with pressure applied inside and on the open ends of their active element
Fig. 1. Schematic diagram of the family of pressure transducers realised. (- - - - applied pressure; ——— strain gauges).
Pressure transducers using a large diameter cylinder as active element were realized in 1992 [1]. As an improvement of this solution another transducer was designed, tested and patented [10]. Fig. 2 shows the schematic diagram of this new transducer, where: (1) is the main cylindrical vessel where the active sensor is installed, (4) are the strain gauges, (5) is a closing nut (left and right screws), (6) is also a part of the main vessel with fitting for pressure connection, (7) is a volume spacer, (9) is a coupling device and (10) is a hole allowing the access from the outside to the active cylinder (this is useful to measure, for example, temperature of the active cylinder and it may also be used to measure strain and distortion of it by optical methods from outside).
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measurements of 0.25 MPa which is a good result particularly for pressure higher than 200—300 MPa; E this device is “calculable” in terms of strains and distortions, as a function of the applied pressure, at the level of knowledge (some percent) of the elastic constants of the used materials, applying the formula *»/»"K(1#k)[1#2/(¼!1)]P/2E,
Fig. 2. Cross-section of a strain-gauge pressure transducer for pressure measurements up to 0.5 GPa (Italian Patent Number RM93A 000620).
The mechanical design of these transducers is oriented to reduce the anomalous stress distribution due to pressure sealing (2) by the use of double cylindrical cups (8) in which the active cylinder (3) is mounted. The main advantages of this version of pressure transducers are: E easy possibility of changing the active free cylinder (different dimensions and materials) in order to fulfil the best possible metrological requirements as a function of an appropriately selected pressure full scale. For example, it can be used with active cylinders made in hard tool steel material (internal diameter from 7 to 2 mm) to obtain sensors with full scale pressure values of 100, 200 and 300 MPa (in all cases with maximum longitudinal and radial strains on the outer surface of the active cylinder close to 1000 le 1 le"1 lm/m); when tungsten carbide material is used, pressure sensors working up to 500 MPa can be realized; E for a system operative up to 500 MPa, with an active cylinder in tungsten carbide, we obtained sensitivity to pressure changes as high as 0.02 (mV/V)/MPa (large sensitivity if compared with other transducers), stability better than 1;10\, resolution of 2;10\, hysteresis lower than 5;10\. All these metrological characteristics allow to estimate an overall uncertainty of
where *»/» is the electrical bridge signal variation, K is the gauge factor of the strain gauges, E is Young’s modulus, l is Poisson’s coefficient of the active element material, ¼ is the ratio of outer to inner diameter of the cylinder and P is the applied pressure; E this device exhibited a reduced thermal coefficient (0.006 le MPa\ K\) and it can work in dynamic conditions up to some kHz. The simple design of the transducer, the possibility of adapting and easily changing its active element, the good metrological characteristics obtained, allow to use this instrument to measure pressures up to about 500 MPa; this design does not allow to extend the pressure range to higher pressures because if more rigid sealing is used, metrological characteristics will deteriorate, mostly hysteresis.
3. Small size free-cylinder pressure transducers with pressure applied inside and on the open ends of their active element This pressure transducer has been an evolution of the previous ones [10] with the intention of simplifying their design. The first simplification was aimed to have a single external vessel body instead of three; second, to reduce its size and third in order to have all parts of the same material (hard maraging steel). Mechanical tolerances have been calculated in order to avoid friction between the different parts. Fig. 3 gives the schematic cross-section of this pressure transducer. The active element (4) is pressurized at its ends and in its internal part. It is inserted into cups (2) and (3) and all is contained in
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Fig. 3. Cross-section of a free-cylinder, hexagonal type, straingauge pressure transducer for pressure measurements up to 0.6 GPa. (1) External vessel; (2), & (3) coupling cups; (4) active cylinder, hexagonal in its central part; (5), & (6) sealing plugs; (7), & (8) longitudinal and circumferential strain gauges.
the main vessel (1). Six different configurations of this sensor were tested in order to verify the effect of sealing (using O-rings of different hardness), of the O-ring position, of different clearances and for two ¼ values. It is important to note that essential points of the design are E pre-compressed O-rings mounted into appropriately designed grooves; E clearance between active cylinder and coupling cups reduced to less than 30 lm; E all mechanical parts carefully machined and lapped (for example the grooves into which O-rings are mounted have to be without cutting edges, otherwise O-ring may be cut or damaged during the sensor mounting). The main metrological characteristics of these transducers are of interest (resolution from 1.7 to 6;10\ of full scale, stability of 1.5;10\, repeatability of 4;10\ including zero shift and creep at maximum pressure, sensitivity of 10 kPa), the main limitation being again hysteresis (maximum value was 2.9;10\ at the pressure of 100 MPa). Hysteresis was investigated, its behavior is dominated by the effects of friction between the mechanical parts and of sealing, the last playing a significant role. The agreement between calculated and experimental strains is typically below 5% if a mathematical model adapted to the hexagonal structure of the active element is considered.
A multi-parameter analysis, based on the six available sensors, showed that the characteristics of hysteresis are mainly related to the non-linear and time-dependent elasticity of the sealing material, to the properties (stiffness) of the elastomer and also to dimensions of the area where the elastomer material extrudes when pressure is applied (a wider clearance can reduce positive hysteresis and increase the negative one). Other parameters, like an appropriate choice of the ratio ¼ and position of O-rings, do not change significantly hysteresis behavior. The sensor configurations that produced the best results in terms of small hysteresis were the ones where high stiffness O-rings (polyurethane) were used. A similar design of pressure sensor can be used for transducers even of higher resolution than those presented here, and covering a pressure range up to 0.7 GPa.
4. Free-rod pressure transducers with pressure applied only on their open ends In order to extend the pressure range to values higher than 0.5 GPa, a free-rod sensor was designed and tested [3] in which pressure is applied only on the opposite ends of the rod structure. This solution has the advantage of a simple strain calculation as, for example, the bridge signal *»/» is equal to K(1#l)P/2E. Thin elastic foils provide the sealing between the active rod and the cups. This requires extremely careful lapping of both mechanical parts. The metrological results obtained with this system are described in Ref. [3], for a rod made in hard steel, tested up to 1 GPa, and they can be briefly summarized as follows: E zero shift lower than 0.2 MPa and repeatability always lower than 3.2;10\ (equivalent to 0.32 MPa at 1 GPa); E creep at 1 GPa lower than 0.2 MPa, but relatively large hysteresis (1 MPa up to 0.4 GPa and inside 3 MPa close to 1 GPa). Also in this case it has been demonstrated that the material and size of the sealing significantly contribute to increasing hysteresis, the best result being obtained using a PVC disk of 0.7 mm thickness or copper—beryllium disks.
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Fig. 4. Cross-section of a free-rod pressure transducer for pressure measurements up to 1.0 GPa.
E the maximum deformation, when a hard steel rod is used, is too high; if tungsten carbide rod is used, the maximum deformation at 1 GPa is close to 2000 le, but hysteresis does not improve significantly. In order to improve the metrological characteristics and simplify the transducer design, being able also to test other materials (like alumina) another design was made. Its schematic is given in Fig. 4. In this case the active rod is loaded by the pressure applied on its opposite ends and it essentially works under pure compression. This aspect is important because the same-instrumented rod, used as pressure sensor, can be as well investigated under pure compression applied by a force standard machine. In the case of Fig. 4 the active element free-rod is 10 mm in diameter. Tests have been performed using hard steel, tungsten carbide and alumina rod materials and pre-stressed PVC flat thin disks used as sealing. With an alumina free-rod transducer a maximum output signal of 3.3 mV/V was obtained at 1 GPa. The metrological characteristics are similar to those obtained by metallic rod. It is proved again that the main limitation is hysteresis, of the order of 1;10\ for pressures higher than 0.5 GPa. For this configuration a challenge, as well as a risk, is the fact that, due to the fragility of alumina, full hydrostatic compression is essential on both opposite ends of the rod and that reaction forces due to constraints on the ends of the rod, have to be extremely small. The alumina rod was also tested under compression forces using a primary force standard machine up to 50 kN (pressure to force equivalence for this sensor is
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12.73 MPa/kN). Extremely good metrological characteristics have been obtained (repeatability below 3;10\, hysteresis below 5;10\, linearity inside 5;10\) by force calibration for all tested materials showing that the best results are obtained with tungsten carbide and alumina. This result means that sealing is largely responsible for hysteresis values and behaviors. Description of the results obtained with these pressure transducers are given in Refs. [6,7]. Attempt has been made to use alumina with sputtered thin films, but unsuccessfully, partially due to its porosity and fragility. Using sapphire, the problem of thin film deposition can be solved, but unfortunately not the too high risk of rupture under pressure application due to the non-perfect compression of the rod by effect of sealing.
5. Bulk compression pressure transducers with pressure applied outside the active element Bulk-modulus pressure transducers, where pressure is applied externally to the tubular structure which is contracted by pressure application, are old instruments. With the purpose of extending the pressure range to 2 GPa, two possible solutions of pressure transducers have been designed and tested: E a bulk-modulus pressure transducer as a free cylinder (pressure applied externally) with an internal stem. The pressure measurement is related to the measurement of the stem displacement with a resolution of 50 nm. E a bulk-modulus pressure transducer where miniaturized strain gauges are bonded in the internal part of the free-cylindrical structure (diameter of the inner active cylinder of only 8 mm and an external diameter of 12 mm). For both configurations the main improvement of the metrological characteristics, compared to the already existing versions, is due to the fact that the free-active cylindrical elements are separated by the other cylindrical components of the sensors, univocally assuring that the stress state of the active structure is not influenced by reaction forces.
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Details for construction and metrological results of bulk-modulus sensors are given in Ref. [8] for the strain gauge type and in Ref. [9] for the bulkmodulus type with stem displacement measurement. For the bulk-modulus pressure transducer used with stem, a decrease of its measuring length *l is equal to P (0.294) lm MPa\ (a displacement of 588 lm at the pressure of 2 GPa). This transducer was tested only up to 1 GPa and it has an estimated uncertainty of 0.1% up to 1 GPa. From 1 to 2 GPa, the determination of its measuring characteristics can be made only by calculation of *l versus P using the Lame` theory; this procedure does not allow an estimated uncertainty better than 2% (mainly due to the large uncertainty of elastic constants of the material and on the unknown hysteresis behavior). It is rather interesting to note that in this case hysteresis error was small (inside 0.06%) and of random type. Mounting this pressure transducer requires a lot of care, for its vertical alignment, for all appropriate preliminary tests and controls connected with the use of the distance sensor to measure the stem displacement at each applied pressure. Concerning the bulk-modulus pressure transducer equipped with miniaturized strain gauges, a relatively high value of hysteresis was confirmed (up to about 1.5 MPa), while all other metrological characteristics were satisfactory. This pressure transducer can also be calibrated using a primary standard force machine up to 0.5 MN.
6. Conclusions The simple design of the pressure transducers described here makes it possible to reduce constraints on the different active elements, this substantially improves some of the metrological characteristics (particularly repeatability) of the transducers. Pressure transducers are in many cases “calculable” devices, if the user does not need a pressure measurement uncertainty better than few percent. Some of the pressure transducers (mainly the free-rod and bulk modulus types, which operate in compression mode) allow to perform their calibration and tests by the use of force primary stan-
dard machines. This is a particularly useful aspect as it may be used to demonstrate the effects of the sealing systems, which have to be used for pressure operations with the described sensors. Based on our experience, the following general conclusions can be drawn: E from the view point of the best possible metrological characteristics, the free-cylinder types (2 in Fig. 1) can be used up to a maximum pressure of 0.5 GPa with typical uncertainty well within 0.05%. The free-rod pressure transducers are a better choice when pressure range has to be extended to 1 GPa. Hysteresis is the main limiting factor that reduces the typical uncertainty within 0.1%. Bulk-modulus pressure transducers are a better choice when pressure range has to be extended to 2 GPa, in this case the typical uncertainty ranges between 2 and 3%; E concerning the materials for the construction of active elements, hard-tool steel is preferable for pressures lower than 0.5 GPa, whereas tungsten carbide is a better choice for pressures higher than 0.5 GPa and extending up to 2 GPa. The use of ceramic materials (e.g. alumina of high purity and low porosity) is possible for laboratory experiments or tests, but the material fragility, coupled with possible unpredictable constraints on its structure, sets practical limits for its use at industrial level; E some of the important metrological characteristics are completely satisfactory (resolution, stability of electrical signal, creeps and repeatability). Hysteresis is, generally speaking, the main limiting factor, particularly if pressure range has to be extended above 0.4—0.5 GPa. It has been demonstrated, however, that in the case of a free-cylinder transducer type and when a pure compressive force is applied to the elastic-active element, hysteresis can be maintained at the level of few parts in 10, if pressure is lower than 0.6 GPa. In the case of the free-rod pressure transducer, hysteresis is larger and generally not better than 1;10\ for a pressure range extending up to 1 GPa. Different tests on this type of pressure transducers, demonstrated that hysteresis error is strongly correlated to the sealing system, so if this aspect is improved, obtaining
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E
E
E
E
stresses univocally related to pressures, hysteresis error will decrease; the bulk-modulus pressure transducers can find important applications, for example, when a manganin pressure sensor cannot be used (too rapid pressure variations, high viscosity media, electrical conducting media,2) or coupled to system for higher pressures used for phase transition experiments; some of these pressure transducers can find useful applications in metrological laboratories when they are used as transfer standards to verify the pressure scale of participants to a pressure comparison. This is important because, for pressures higher than 1 GPa very few primary standards exist, they are complex devices and not transportable; on the contrary the pressure transducers here described, even if in many cases require care in their use, are simple low cost devices and easily transportable; these prototype pressure transducers have been studied using bonded strain gauges on the elastic active elements because of their rapid and cheaper installation on the sensors. Thin films or semiconductor structures can also be used to detect deformations of the elastic elements. Other attempts have been made also to use active element structures in systems where the axial deformation was detected by the use of birefringence optical fibres or capacitance sensors; the transducers presented here have been realised for laboratory applications. They have not been fully studied for industrial applications,
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where other problems have to be considered (e.g., thermal compensation in a wide temperature range, sealing adapted to a specific fluid or to a large thermal operative range, use under shocks and vibrations, use in electrically noisy environment, ionising radiation,2) for the specific case of pressure measurement application.
References [1] R. Wis´ niewski, G. Molinar, Rev. Sci. Instrum. 63 (8) (1992) 3983. [2] R. Wis´ niewski, G. Molinar, Metrologia 30 (6) (1994) 683. [3] G. Molinar et al., Metrologia 30 (6) (1994) 691. [4] G. Molinar, R. Wis´ niewski, High Pressure Res. 12 (1994) 279. [5] R. Wis´ niewski, G. Molinar, in: S.C. Schmidt, J.W. Shaner, G.A. Samara, M. Ross (Eds.), AIP Conf. Proc. 309, Part 2, American Institute of Physics, New York, USA, 1994, p. 1685. [6] G. Molinar, R. Wis´ niewski, Proc. XIII IMEKO World Congress, Torino, vol. 3, 5—9 September 1994, p. 1982. [7] A.J. Rostocki et al., in: J. Kamara`d, Z. Arnold, A. Kapicka (Eds.), Proc. XXXIInd EHPRG Conf. Brno, Czech Rep., 1994, p. 37. [8] G. Molinar et al., in: W.A. Trzeciakowski (Ed.), High Pressure Science and Technology, Word Scientific, Singapore, 1996, p. 90. [9] R. Wis´ niewski, G. Molinar, Rev. Sci. Instrum. 67 (5) (1996) 2020. [10] G. Molinar, R. Wis´ niewski, Italian Patent Number RM93A 000620, Rome, Italy, 14 September 1993. [11] G. Molinar et al., New measurements — challenges and visions, in: J. Halttunen (Eds.), Proc. XIV IMEKO World Congress, Tampere, Finland, vol. IXA, 1997, p. 116.
Free-cylinder, strain-gauge, pressure transducers up to 2 GPa G. Molinar *, R. Maghenzani , R. Wis´ niewski Consiglio Nazionale delle Ricerche, Istituto di Metrologia **G. Colonnetti++, Strada delle Cacce 73, 10135 Torino, Italy Warsaw University of Technology, Institute of Physics, Koszykowa 75, 00662 Warsaw, Poland
Abstract A review of the main metrological characteristics obtained with a large family of free-cylinder and free-rod pressure transducers using different materials (hard tool steels, tungsten carbide and ceramics), different shapes of active elements and different pressure ranges up to 2 GPa is presented. In general, they have a resolution better than 1;10. Repeatability of measurements depends on pressure and typically it is of the order of few parts in 10 up to 0.5 GPa, approaching 1;10 for pressure range up to 2 GPa. Their pressure sensitivity is always of the order of few parts in 10 up to 0.5 GPa and of the order of few parts in 10 for higher pressures up to 2 GPa. Linearity of the calibration factor is of the order of some percent, so it is always necessary to use appropriate polynomial fitting to express the output signal of the pressure transducers versus the measuring pressure. The main limiting factor is hysteresis that can be of the order of few parts in 10 for some of the pressure transducers (for pressures not generally exceeding 0.5 GPa) but it can reach values of some parts in 10 for pressures from 0.5 to 1 GPa and of some percent from 1 to 2 GPa. 1999 Elsevier Science B.V. All rights reserved. Keywords: Metrology; Pressure; Sensors; Transducer
1. Introduction Since a long time pressure transducers with cylindrical elastic elements have been widely used in many applications. Some of them, extending their pressure range up to 1.4 GPa, are commercially available. Generally these transducers use an elastic element realized as a hollow cylinder, made with different materials (typically alloy steels) depending on the pressure range of their use. They have
* Corresponding author. Tel.: 0039-011-3977-306; fax: 0039011-346761; e-mail: [email protected].
a blind end on one side and, on the opposite side, the cylinder is rigidly fixed (through an appropriate mechanical fitting) to the apparatus where pressure has to be measured. In this condition it is difficult to achieve a very high accuracy of pressure measurements because of the indefinite state of stress at both ends. Deformations of the elastic element, although proportional to the applied internal pressure, are normally influenced by state of stresses imposed on the transducer (e.g. the torque applied on the pressure fitting) and the effects of deformation versus applied pressure can only be roughly predicted by analytical calculations. The idea of using a free-dilating-cylinder was developed with the purpose of improving as much
0921-4526/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 1 3 8 4 - 2
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G. Molinar et al. / Physica B 265 (1999) 239—245
as possible the repeatability of stresses which have to depend uniquely on the applied pressure, reducing hysteresis effects by minimizing stress effects that seals impose on the elastic element. The illustrated sensors represent an attempt to obtain improved metrological performances for a large family of free-cylinder and free-rod pressure transducers developed in the last six years, using different materials (hard tool steels, tungsten-carbide and ceramics), different shapes of active elements and different pressure ranges. In Fig. 1 the main types of pressure transducers realized are schematically given. The main realized pressure transducers are of the following models: E free-cylindrical active element with pressure applied on the internal part (1, 1a in Fig. 1) and on the open ends (2, 2a, 2b, 2c in Fig. 1) of the cylinder, for pressure ranges up to about 500 MPa [1—4];
E free-rod active element with pressure applied only on its open ends (3, 4, 4a in Fig. 1), for pressure ranges up to about 1 GPa [5—7]; E free-cylindrical active element with pressure applied on all the external part of the sensor (5, 5a in Fig. 1), (frequently this configuration is called “bulk compression cylinder” [8,9]), for pressure ranges up to about 2 GPa. In all the above configurations a combination of circumferential and longitudinal stresses is applied to the elastic element. All active elements are equipped with strain gauges (mainly of the miniaturized types) selected for the specific design of the elastic elements and used to measure strain and deformations; in some cases (e.g. bulk compression cylinder) LVDT or capacitance sensors have also been used to measure displacements of the active elements. This review also considers more recent results obtained with a pressure transducer (improvement of the patented version [10]) where the active cylinder has hexagonal shape and it is contained within two concentric cups [11]. The main metrological characteristics of some selected pressure transducers will be reviewed in this paper and critically analyzed.
2. Free-cylinder pressure transducers with pressure applied inside and on the open ends of their active element
Fig. 1. Schematic diagram of the family of pressure transducers realised. (- - - - applied pressure; ——— strain gauges).
Pressure transducers using a large diameter cylinder as active element were realized in 1992 [1]. As an improvement of this solution another transducer was designed, tested and patented [10]. Fig. 2 shows the schematic diagram of this new transducer, where: (1) is the main cylindrical vessel where the active sensor is installed, (4) are the strain gauges, (5) is a closing nut (left and right screws), (6) is also a part of the main vessel with fitting for pressure connection, (7) is a volume spacer, (9) is a coupling device and (10) is a hole allowing the access from the outside to the active cylinder (this is useful to measure, for example, temperature of the active cylinder and it may also be used to measure strain and distortion of it by optical methods from outside).
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measurements of 0.25 MPa which is a good result particularly for pressure higher than 200—300 MPa; E this device is “calculable” in terms of strains and distortions, as a function of the applied pressure, at the level of knowledge (some percent) of the elastic constants of the used materials, applying the formula *»/»"K(1#k)[1#2/(¼!1)]P/2E,
Fig. 2. Cross-section of a strain-gauge pressure transducer for pressure measurements up to 0.5 GPa (Italian Patent Number RM93A 000620).
The mechanical design of these transducers is oriented to reduce the anomalous stress distribution due to pressure sealing (2) by the use of double cylindrical cups (8) in which the active cylinder (3) is mounted. The main advantages of this version of pressure transducers are: E easy possibility of changing the active free cylinder (different dimensions and materials) in order to fulfil the best possible metrological requirements as a function of an appropriately selected pressure full scale. For example, it can be used with active cylinders made in hard tool steel material (internal diameter from 7 to 2 mm) to obtain sensors with full scale pressure values of 100, 200 and 300 MPa (in all cases with maximum longitudinal and radial strains on the outer surface of the active cylinder close to 1000 le 1 le"1 lm/m); when tungsten carbide material is used, pressure sensors working up to 500 MPa can be realized; E for a system operative up to 500 MPa, with an active cylinder in tungsten carbide, we obtained sensitivity to pressure changes as high as 0.02 (mV/V)/MPa (large sensitivity if compared with other transducers), stability better than 1;10\, resolution of 2;10\, hysteresis lower than 5;10\. All these metrological characteristics allow to estimate an overall uncertainty of
where *»/» is the electrical bridge signal variation, K is the gauge factor of the strain gauges, E is Young’s modulus, l is Poisson’s coefficient of the active element material, ¼ is the ratio of outer to inner diameter of the cylinder and P is the applied pressure; E this device exhibited a reduced thermal coefficient (0.006 le MPa\ K\) and it can work in dynamic conditions up to some kHz. The simple design of the transducer, the possibility of adapting and easily changing its active element, the good metrological characteristics obtained, allow to use this instrument to measure pressures up to about 500 MPa; this design does not allow to extend the pressure range to higher pressures because if more rigid sealing is used, metrological characteristics will deteriorate, mostly hysteresis.
3. Small size free-cylinder pressure transducers with pressure applied inside and on the open ends of their active element This pressure transducer has been an evolution of the previous ones [10] with the intention of simplifying their design. The first simplification was aimed to have a single external vessel body instead of three; second, to reduce its size and third in order to have all parts of the same material (hard maraging steel). Mechanical tolerances have been calculated in order to avoid friction between the different parts. Fig. 3 gives the schematic cross-section of this pressure transducer. The active element (4) is pressurized at its ends and in its internal part. It is inserted into cups (2) and (3) and all is contained in
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Fig. 3. Cross-section of a free-cylinder, hexagonal type, straingauge pressure transducer for pressure measurements up to 0.6 GPa. (1) External vessel; (2), & (3) coupling cups; (4) active cylinder, hexagonal in its central part; (5), & (6) sealing plugs; (7), & (8) longitudinal and circumferential strain gauges.
the main vessel (1). Six different configurations of this sensor were tested in order to verify the effect of sealing (using O-rings of different hardness), of the O-ring position, of different clearances and for two ¼ values. It is important to note that essential points of the design are E pre-compressed O-rings mounted into appropriately designed grooves; E clearance between active cylinder and coupling cups reduced to less than 30 lm; E all mechanical parts carefully machined and lapped (for example the grooves into which O-rings are mounted have to be without cutting edges, otherwise O-ring may be cut or damaged during the sensor mounting). The main metrological characteristics of these transducers are of interest (resolution from 1.7 to 6;10\ of full scale, stability of 1.5;10\, repeatability of 4;10\ including zero shift and creep at maximum pressure, sensitivity of 10 kPa), the main limitation being again hysteresis (maximum value was 2.9;10\ at the pressure of 100 MPa). Hysteresis was investigated, its behavior is dominated by the effects of friction between the mechanical parts and of sealing, the last playing a significant role. The agreement between calculated and experimental strains is typically below 5% if a mathematical model adapted to the hexagonal structure of the active element is considered.
A multi-parameter analysis, based on the six available sensors, showed that the characteristics of hysteresis are mainly related to the non-linear and time-dependent elasticity of the sealing material, to the properties (stiffness) of the elastomer and also to dimensions of the area where the elastomer material extrudes when pressure is applied (a wider clearance can reduce positive hysteresis and increase the negative one). Other parameters, like an appropriate choice of the ratio ¼ and position of O-rings, do not change significantly hysteresis behavior. The sensor configurations that produced the best results in terms of small hysteresis were the ones where high stiffness O-rings (polyurethane) were used. A similar design of pressure sensor can be used for transducers even of higher resolution than those presented here, and covering a pressure range up to 0.7 GPa.
4. Free-rod pressure transducers with pressure applied only on their open ends In order to extend the pressure range to values higher than 0.5 GPa, a free-rod sensor was designed and tested [3] in which pressure is applied only on the opposite ends of the rod structure. This solution has the advantage of a simple strain calculation as, for example, the bridge signal *»/» is equal to K(1#l)P/2E. Thin elastic foils provide the sealing between the active rod and the cups. This requires extremely careful lapping of both mechanical parts. The metrological results obtained with this system are described in Ref. [3], for a rod made in hard steel, tested up to 1 GPa, and they can be briefly summarized as follows: E zero shift lower than 0.2 MPa and repeatability always lower than 3.2;10\ (equivalent to 0.32 MPa at 1 GPa); E creep at 1 GPa lower than 0.2 MPa, but relatively large hysteresis (1 MPa up to 0.4 GPa and inside 3 MPa close to 1 GPa). Also in this case it has been demonstrated that the material and size of the sealing significantly contribute to increasing hysteresis, the best result being obtained using a PVC disk of 0.7 mm thickness or copper—beryllium disks.
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Fig. 4. Cross-section of a free-rod pressure transducer for pressure measurements up to 1.0 GPa.
E the maximum deformation, when a hard steel rod is used, is too high; if tungsten carbide rod is used, the maximum deformation at 1 GPa is close to 2000 le, but hysteresis does not improve significantly. In order to improve the metrological characteristics and simplify the transducer design, being able also to test other materials (like alumina) another design was made. Its schematic is given in Fig. 4. In this case the active rod is loaded by the pressure applied on its opposite ends and it essentially works under pure compression. This aspect is important because the same-instrumented rod, used as pressure sensor, can be as well investigated under pure compression applied by a force standard machine. In the case of Fig. 4 the active element free-rod is 10 mm in diameter. Tests have been performed using hard steel, tungsten carbide and alumina rod materials and pre-stressed PVC flat thin disks used as sealing. With an alumina free-rod transducer a maximum output signal of 3.3 mV/V was obtained at 1 GPa. The metrological characteristics are similar to those obtained by metallic rod. It is proved again that the main limitation is hysteresis, of the order of 1;10\ for pressures higher than 0.5 GPa. For this configuration a challenge, as well as a risk, is the fact that, due to the fragility of alumina, full hydrostatic compression is essential on both opposite ends of the rod and that reaction forces due to constraints on the ends of the rod, have to be extremely small. The alumina rod was also tested under compression forces using a primary force standard machine up to 50 kN (pressure to force equivalence for this sensor is
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12.73 MPa/kN). Extremely good metrological characteristics have been obtained (repeatability below 3;10\, hysteresis below 5;10\, linearity inside 5;10\) by force calibration for all tested materials showing that the best results are obtained with tungsten carbide and alumina. This result means that sealing is largely responsible for hysteresis values and behaviors. Description of the results obtained with these pressure transducers are given in Refs. [6,7]. Attempt has been made to use alumina with sputtered thin films, but unsuccessfully, partially due to its porosity and fragility. Using sapphire, the problem of thin film deposition can be solved, but unfortunately not the too high risk of rupture under pressure application due to the non-perfect compression of the rod by effect of sealing.
5. Bulk compression pressure transducers with pressure applied outside the active element Bulk-modulus pressure transducers, where pressure is applied externally to the tubular structure which is contracted by pressure application, are old instruments. With the purpose of extending the pressure range to 2 GPa, two possible solutions of pressure transducers have been designed and tested: E a bulk-modulus pressure transducer as a free cylinder (pressure applied externally) with an internal stem. The pressure measurement is related to the measurement of the stem displacement with a resolution of 50 nm. E a bulk-modulus pressure transducer where miniaturized strain gauges are bonded in the internal part of the free-cylindrical structure (diameter of the inner active cylinder of only 8 mm and an external diameter of 12 mm). For both configurations the main improvement of the metrological characteristics, compared to the already existing versions, is due to the fact that the free-active cylindrical elements are separated by the other cylindrical components of the sensors, univocally assuring that the stress state of the active structure is not influenced by reaction forces.
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Details for construction and metrological results of bulk-modulus sensors are given in Ref. [8] for the strain gauge type and in Ref. [9] for the bulkmodulus type with stem displacement measurement. For the bulk-modulus pressure transducer used with stem, a decrease of its measuring length *l is equal to P (0.294) lm MPa\ (a displacement of 588 lm at the pressure of 2 GPa). This transducer was tested only up to 1 GPa and it has an estimated uncertainty of 0.1% up to 1 GPa. From 1 to 2 GPa, the determination of its measuring characteristics can be made only by calculation of *l versus P using the Lame` theory; this procedure does not allow an estimated uncertainty better than 2% (mainly due to the large uncertainty of elastic constants of the material and on the unknown hysteresis behavior). It is rather interesting to note that in this case hysteresis error was small (inside 0.06%) and of random type. Mounting this pressure transducer requires a lot of care, for its vertical alignment, for all appropriate preliminary tests and controls connected with the use of the distance sensor to measure the stem displacement at each applied pressure. Concerning the bulk-modulus pressure transducer equipped with miniaturized strain gauges, a relatively high value of hysteresis was confirmed (up to about 1.5 MPa), while all other metrological characteristics were satisfactory. This pressure transducer can also be calibrated using a primary standard force machine up to 0.5 MN.
6. Conclusions The simple design of the pressure transducers described here makes it possible to reduce constraints on the different active elements, this substantially improves some of the metrological characteristics (particularly repeatability) of the transducers. Pressure transducers are in many cases “calculable” devices, if the user does not need a pressure measurement uncertainty better than few percent. Some of the pressure transducers (mainly the free-rod and bulk modulus types, which operate in compression mode) allow to perform their calibration and tests by the use of force primary stan-
dard machines. This is a particularly useful aspect as it may be used to demonstrate the effects of the sealing systems, which have to be used for pressure operations with the described sensors. Based on our experience, the following general conclusions can be drawn: E from the view point of the best possible metrological characteristics, the free-cylinder types (2 in Fig. 1) can be used up to a maximum pressure of 0.5 GPa with typical uncertainty well within 0.05%. The free-rod pressure transducers are a better choice when pressure range has to be extended to 1 GPa. Hysteresis is the main limiting factor that reduces the typical uncertainty within 0.1%. Bulk-modulus pressure transducers are a better choice when pressure range has to be extended to 2 GPa, in this case the typical uncertainty ranges between 2 and 3%; E concerning the materials for the construction of active elements, hard-tool steel is preferable for pressures lower than 0.5 GPa, whereas tungsten carbide is a better choice for pressures higher than 0.5 GPa and extending up to 2 GPa. The use of ceramic materials (e.g. alumina of high purity and low porosity) is possible for laboratory experiments or tests, but the material fragility, coupled with possible unpredictable constraints on its structure, sets practical limits for its use at industrial level; E some of the important metrological characteristics are completely satisfactory (resolution, stability of electrical signal, creeps and repeatability). Hysteresis is, generally speaking, the main limiting factor, particularly if pressure range has to be extended above 0.4—0.5 GPa. It has been demonstrated, however, that in the case of a free-cylinder transducer type and when a pure compressive force is applied to the elastic-active element, hysteresis can be maintained at the level of few parts in 10, if pressure is lower than 0.6 GPa. In the case of the free-rod pressure transducer, hysteresis is larger and generally not better than 1;10\ for a pressure range extending up to 1 GPa. Different tests on this type of pressure transducers, demonstrated that hysteresis error is strongly correlated to the sealing system, so if this aspect is improved, obtaining
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E
E
E
E
stresses univocally related to pressures, hysteresis error will decrease; the bulk-modulus pressure transducers can find important applications, for example, when a manganin pressure sensor cannot be used (too rapid pressure variations, high viscosity media, electrical conducting media,2) or coupled to system for higher pressures used for phase transition experiments; some of these pressure transducers can find useful applications in metrological laboratories when they are used as transfer standards to verify the pressure scale of participants to a pressure comparison. This is important because, for pressures higher than 1 GPa very few primary standards exist, they are complex devices and not transportable; on the contrary the pressure transducers here described, even if in many cases require care in their use, are simple low cost devices and easily transportable; these prototype pressure transducers have been studied using bonded strain gauges on the elastic active elements because of their rapid and cheaper installation on the sensors. Thin films or semiconductor structures can also be used to detect deformations of the elastic elements. Other attempts have been made also to use active element structures in systems where the axial deformation was detected by the use of birefringence optical fibres or capacitance sensors; the transducers presented here have been realised for laboratory applications. They have not been fully studied for industrial applications,
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where other problems have to be considered (e.g., thermal compensation in a wide temperature range, sealing adapted to a specific fluid or to a large thermal operative range, use under shocks and vibrations, use in electrically noisy environment, ionising radiation,2) for the specific case of pressure measurement application.
References [1] R. Wis´ niewski, G. Molinar, Rev. Sci. Instrum. 63 (8) (1992) 3983. [2] R. Wis´ niewski, G. Molinar, Metrologia 30 (6) (1994) 683. [3] G. Molinar et al., Metrologia 30 (6) (1994) 691. [4] G. Molinar, R. Wis´ niewski, High Pressure Res. 12 (1994) 279. [5] R. Wis´ niewski, G. Molinar, in: S.C. Schmidt, J.W. Shaner, G.A. Samara, M. Ross (Eds.), AIP Conf. Proc. 309, Part 2, American Institute of Physics, New York, USA, 1994, p. 1685. [6] G. Molinar, R. Wis´ niewski, Proc. XIII IMEKO World Congress, Torino, vol. 3, 5—9 September 1994, p. 1982. [7] A.J. Rostocki et al., in: J. Kamara`d, Z. Arnold, A. Kapicka (Eds.), Proc. XXXIInd EHPRG Conf. Brno, Czech Rep., 1994, p. 37. [8] G. Molinar et al., in: W.A. Trzeciakowski (Ed.), High Pressure Science and Technology, Word Scientific, Singapore, 1996, p. 90. [9] R. Wis´ niewski, G. Molinar, Rev. Sci. Instrum. 67 (5) (1996) 2020. [10] G. Molinar, R. Wis´ niewski, Italian Patent Number RM93A 000620, Rome, Italy, 14 September 1993. [11] G. Molinar et al., New measurements — challenges and visions, in: J. Halttunen (Eds.), Proc. XIV IMEKO World Congress, Tampere, Finland, vol. IXA, 1997, p. 116.