Primary Pressure Standards Research Articles

Analytical solutions of some model cases of piston-cylinder assemblies

Pressure balances are an important part of the sets of primary pressure standards in many national metrology institutes. The most critical factor determining their accuracy is the effective area of their piston-cylinder assemblies (PCAs). This can be determined (for PCAs with undistorted pressure) by applying a numerical procedure based on a theory by Dadson while knowing a gapprofile (of an axisymmetric PCA approximation). The pressure balances are also a basis for the primary pressure scale of the Czech Metrology Institute. Hence, we wanted to test our programme by computing the effective area from the geometrical data. Therefore, we solved the analytical formulae of Dadson et al (1982) The Pressure Balance—Theory and Practice (London: Her Majesty’s Stationery Office) for several simple geometries with a constant gap width, which are easy to calculate analytically. It is shown that the analytical results always agreed perfectly with the results of our programme. This success confirmed the correctness of our programme. However, it also pointed out a problem of discretization which can be non-negligible, even in the case of relatively simple geometries. We assume that the analytical formulae obtained can be of practical use for any other pressure metrology laboratory requiring an independent way to confirm their own PCA-modelling software.

Validation of a PTB force-balanced piston gauge primary pressure standard

Experimental methods using different pressure standards were applied to verify theoretical results obtained for the effective area of the piston-cylinder assembly (PCA) and for pressures measured with a force-balanced piston gauge (FPG). The theoretical effective area was based on the PCA’s dimensional properties defined via diameter, straightness and roundness measurements of the piston and cylinder, derived by gas-flow modelling using principles of the rarefied gas dynamics, and presented as two values: one obtained for absolute and the other for gauge pressure operation mode. Both values have a relative standard uncertainty of 5×10<sup>-6</sup>. The experimental methods chosen were designed to cover the entire operating pressure range of the FPG from 3 Pa to 15 kPa. Comparisons of the FPG with three different PTB pressure standards operated in different pressure ranges – a pressure balance, a mercury manometer and a static expansion system – were performed using the cross-float method and by a direct comparison of the generated pressures. For the theoretical and experimental effective area, as well as for pressures generated by the FPG and the reference standards, all the results demonstrated full agreement within the expanded uncertainties of the standards.

Establishment of air piston gauge as primary pressure standard at CSIR-National Physical Laboratory INDIA

The air piston gauge (APG) was established at CSIR-National Physical Laboratory, India (NPLI) since 2000. Later the same piston- cylinder(p-c) assembly was calibrated in NIST USA; however, it was never published for metrology communities. As per international protocol, the establishment of the APG as a primary standard, the effective area of p-c assembly, and masses must be directly traceable to SI units. The first time we have calculated the effective area and associated uncertainty of p-c assembly using dimension and mass metrology, traceability to the SI units, i.e., meter and kilogram. To realize the APG as primary pressure standards, we have calculated the effective area of p-c assembly of APG directly from dimension metrology, which is further supported by various other methods. The effective area values obtained in the pressure range of 6.5 – 360 kPa lie in the range of 3.356729 – 3.357248 cm² due to uncertainty limitation in the measurement of dimension of internal diameter of cylinder. The expected values of the effective area which are also measured from cross-float technique against ultrasonic interferometer manometer (UIM), primary pressure standards. The accuracy in effective area measurement is possible only when the resolution in the internal radius of the cylinder should at least be up to 5th decimal order and the uncertainty is 80 nm. The expanded uncertainty was measured nearly 11 ppm at <em>k</em> = 2 by considering the uncertainty in internal radii of cylinder and radii of piston around 80 nm.

Progress in development of an interferometric oil manometer

At PTB, a new interferometric oil manometer for the measurement of pressures below 2 kPa, is in development. This paper describes how the main quantities, length and liquid density, are determined, both in-situ, the latter for the first time in a primary pressure standard. The key features of both methods are presented.

In-situ measurement of mirror deformation using dual Fabry–Pérot cavities for optical pressure standard

An optical pressure measurement system using Fabry–Pérot (FP) cavities are being developed in several national metrology institutes as a future pressure standard. One of the challenges in these research endeavors is the deformation of the FP cavity. The purpose of this study is to evaluate mirror deformation in FP cavities constructed using different materials for the spacer and mirrors, both by simulation and experiment. Experimental and finite element method (FEM) simulation results are in broad agreement. The mirror deformation amount can be determined using the dual cavity method without using the nominal values of material and without depending on conventional pressure standards. Our results suggest that the dual cavity method as well as FEM simulation should be adopted for situations in which the mirror deformation is large and/or high accuracy is required. The results of this study contribute to the development of the primary pressure standard using FP cavities.

Time stability characterization of quadrupole mass spectrometers

• Time stability of eight QMSs was investigated over 2-years period. • Stability of sensitivity of Faraday cup detector and SEM gain for He and N 2 . • Stability of peak position and peak width of He and N 2 . • Stability of minimum detectable partial pressure for He. • Measurements were carried out according to ISO TS 20175:2018. This study focuses on the time stability of different metrological characteristics of quadrupole mass spectrometers (QMSs). Investigated parameters were the sensitivity, when using a Faraday cup as a detector, the peak position, the peak width, the gain of a secondary electron multiplier, and the minimum detectable partial pressure. Eight different commercial QMSs were investigated at seven national metrology institutes under three different nominal calibration pressures of 5 × 10 −6 Pa, 5 × 10 −5 Pa, and 5 × 10 −4 Pa for N 2 and He. The measurements were carried out using a periodicity of approximately 3 months for a total duration of 2 years. Sensitivity calibrations were conducted either through a comparison method using calibrated ionization gauges or by applying a primary vacuum calibration system. In the case of ionization gauges, they were periodically recalibrated to ensure their stability and traceability to a primary pressure standard.

Final report on key comparison EURAMET.M.P-K1.c in the range 0.7 MPa to 7.0 MPa of gas gauge pressure

A EURAMET key comparison of the national pressure standards in the range 0.7 MPa to 7.0 MPa of gas gauge pressure was carried out. The circulation of the transfer standard began in November 2011 and lasted until November 2016.The measurand of the comparison was the effective area of the piston-cylinder assembly determined by gauge pressure measurements in the range from 0.7 MPa to 7.0 MPa.As the comparison reference value, the weighted mean of the results of the laboratories with primary pressure standards was used.With this reference value, all the participants who delivered the results demonstrated equivalence respective to the reference value within expanded uncertainties (k = 2) on all the range.The results of this comparison were linked to CCM key comparison CCM.P-K1.c. Also in relation to the reference values of CCM.P-K1.c, all participants demonstrated agreement within expanded uncertainties (k = 2) at all pressure points.Main textTo reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/.The final report has been peer-reviewed and approved for publication by the CCM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

Uncertainty evaluation and phase variation of ultrasonic interferometer manometer: A primary pressure and vacuum standard

The ultrasonic interferometer manometer (UIM) is an apex level primary pressure standard for Pascal realization established at National Physical Laboratory India (NPLI). The performance of UIM has been evaluated from time to time by participation in key comparisons, calibration and measurement capabilities (CMC) and publications in reputed international metrology journals. The pressure is measured using time of flight technique at 44 different frequencies in ultrasonic range and the phase measurement. The phase measurement combined with the time of flight measurement using the exact fractional algorithm provides highly accurate column length hence respective pressure values. The combined process helps in lowering the uncertainty in real experimental conditions. Recently, we have also changed UIM software from tbasic to window based program with the same algorithm which provides a column length measurement study. A detailed study was carried out for variation of fringe counts or oscillations with varying pressure. Experimental and theoretical calculation for both resolution and pressure dependent part has been carried out for uncertainties involves the physical parameters. The uncertainties in lower pressure range, i.e., between 1 Pa and 1000 Pa were varying equal or sometimes higher than the theoretical resolution value 0.0092 Pa (k = 2) because of environmental conditions like vibration, temperature, atmospheric pressure, and humidity whereas for higher pressure range, i.e., 1000 Pa to 130 kPa the uncertainties were either close or smaller than the pressure dependent theoretical uncertainty value, i.e. 7.2 × 10−6 of the reading.

Computation of the effective area and associated uncertainties of non-rotating piston gauges FPG and FRS

The effective areas of three force-balanced piston gauges (FPGs) and two Furness Rosenberg standards (FRS) in the operating pressure range of each device varying for 1 Pa–15 kPa have been accurately computed both in the gauge and absolute modes. Geometrical data for the non-rotating piston-cylinder assemblies (PCAs) have been provided by the National Metrology Institutes (NMIs) of PTB, RISE, INRiM and CMI. Since the flow is in a wide range of the Knudsen number, simulations have been based on the Batnagar–Gross–Krook (BGK) kinetic model equation, while the typical Dadson and CFD approaches have been complimentary applied only in the viscous regime. Furthermore, an uncertainty analysis has been performed. The effective area is strongly affected by the PCA geometry and the flow conditions, while its dependency on pressure may be different even for devices of the same type. The main source of uncertainty is the dimensional measurements of the piston and the cylinder, followed by the accommodation coefficient characterizing the gas-surface interaction, while the effect of other flow and modeling parameters is negligible. The total relative standard uncertainty of the effective area has been always found to be less than 1 · 10−5 indicating that pressure measurements of high accuracy can be ensured. Since the effective area is estimated based solely on computations the FPG and the FRS assemblies may be characterized as primary pressure standards.

Characterization of a force-balanced piston gauge as a primary pressure standard

This work characterizes a force-balanced piston gauge (FPG), model FPG8601, as a primary pressure standard over its whole operation range from 1 Pa to 15 kPa. To date, FPGs have been handled as secondary standards that are usually calibrated against pressure balances at pressures above 5 kPa. Starting from dimensional measurements on the FPG piston-cylinder assembly (PCA), 3-dimensional data sets were created that presented the radius of the piston and the cylinder bore along the selected circle and generatrix traces with uncertainties of about 50 nm for the piston and 30 nm for the cylinder. Using this dimensional data and modeling the gas flow in the PCA gap, the effective area of the PCA was determined over the whole pressure range for absolute and gauge operation modes. In the pressure distribution calculation, the methods of the rarefied gas dynamics were applied, and the effect of the change from viscous via transient to molecular flow mode on the effective area was quantified and found to have a relative value of 1.5·10−6. The theoretical effective areas are compared with the experimental areas obtained by means of a calibration against a deadweight pressure balance, and the result shows a reasonable agreement within a relative value of 8·10−6.

Development of a new UHV/XHV pressure standard (cold atom vacuum standard)

The National Institute of Standards and Technology has recently begun a program to develop a primary pressure standard that is based on ultra-cold atoms, covering a pressure range of 1 × 10−6 Pa–1 × 10−10 Pa and possibly lower. These pressures correspond to the entire ultra-high vacuum range and extend into the extreme-high vacuum. This cold-atom vacuum standard (CAVS) is both a primary standard and absolute sensor of vacuum. The CAVS is based on the loss of cold, sensor atoms (such as the alkali-metal lithium) from a magnetic trap due to collisions with the background gas (primarily H2) in the vacuum. The pressure is determined from a thermally-averaged collision cross section, which is a fundamental atomic property, and the measured loss rate. The CAVS is primary because it will use collision cross sections determined from ab initio calculations for the Li + H2 system. Primary traceability is transferred to other systems of interest using sensitivity coefficients.

An Approach to Synchronise Effective Areas of Pressure Balances

A method to synchronise effective areas of pressure balances is presented. By this method, the effective areas of piston-cylinder assemblies (PCAs) with their uncertainties determined from dimensional characteristics of the piston and the cylinder or from a calibration against reference pressure standards can be adjusted to achieve an optimal agreement with the effective area ratios determined by cross-float measurements between the PCAs. The approach is based on the weighted least squares’ method and leads to minimum discrepancies between the initial effective areas and the cross-float area ratios on one side, and the synchronised effective areas on the other side. Examples of the new method’s application to five gas-operated PCAs and five oil-operated PCAs of PTB, and to five gas-operated PCAs of NIMT, which are used as primary pressure standards in the two institutes, are presented.

Evaluation of roundness error using a new method based on a small displacement screw

In relation to industrial need and the progress of technology, LNE would like to improve the measurement of its primary pressure, spherical and flick standards. The spherical and flick standards are respectively used to calibrate the spindle motion error and the probe which equips commercial conventional cylindricity measuring machines. The primary pressure standards are obtained using pressure balances equipped with rotary pistons with an uncertainty of 5 nm for a piston diameter of 10 mm. Conventional machines are not able to reach such an uncertainty level. That is why the development of a new machine is necessary. To ensure such a level of uncertainty, both stability and performance of the machine are not sufficient, and the data processing should also be done with accuracy less than a nanometre. In this paper, a new method based on the small displacement screw (SDS) model is proposed. A first validation of this method is proposed on a theoretical dataset published by the European Community Bureau of Reference (BCR) in report no 3327. Then, an experiment is prepared in order to validate the new method on real datasets. Specific environment conditions are taken into account and many precautions are considered. The new method is applied to analyse the least-squares circle, minimum zone circle, maximum inscribed circle and minimum circumscribed circle. The results are compared to those done by the reference Chebyshev best-fit method and reveal perfect agreement. The sensibilities of the SDS and Chebyshev methodologies are investigated, and it is revealed that results remain unchanged when the value of the diameter exceeds 700 times the form error.

Recent progress in high pressure metrology in Europe

Five European national metrology institutes in collaboration with a university, a research institute and five industrial companies are working on a joint research project within a framework of the European Metrology Research Programme aimed at development of 1.6 GPa primary and 1.5 GPa transfer pressure standards. Two primary pressure standards were realised as pressure-measuring multipliers, each consisting of a low pressure and a high pressure (HP) piston-cylinder assembly (PCA). A special design of the HP PCAs was developed in which a tungsten carbide cylinder is supported by two thermally shrunk steel sleeves and, additionally, by jacket pressure applied to the outside of the outer sleeve. Stress-strain finite element analysis (FEA) was performed to predict behaviour of the multipliers and a pressure generation system. With FEA, the pressure distortion coefficient was determined, taking into account irregularities of the piston-cylinder gap. Transfer pressure standards up to 1.5 GPa are developed on the basis of modern 1.5 GPa pressure transducers. This project shall solve a discrepancy between the growing needs of the industry demanding precise traceable calibrations of the high pressure transducers and the absence of adequate primary standards for pressures higher than 1 GPa in the European Union today.

Establishing a Continuous Chain of Traceability for Pressure Measurements up to 40 MPa

Abstract:An Ultrasonic Interferometer Manometer (UIM) has been in use as the primary pressure standard at the National Physical Laboratory in India (NPLI) for absolute and gauge modes up to 130 kPa since 1982. However, the primary pneumatic pressure standard in gauge mode up to 6 MPa was based on the performance of controlled clearance Piston Gauges (CCPG). The uncertainty of measurements in UIM and CCPG were of great concern in establishing the primary pneumatic pressure scale of NPLI. To bridge the gap between the high vacuum, both in absolute and gauge modes, pneumatic pressure and hydraulic pressure up to 1 GPa, a conscientious attempt has been made to establish a uniform scale in the entire pressure range from 1 × 10−4 to 1 × 109 Pa that utilizes the UIM as the primary pressure standard. This paper presents the results of this entire systematic exercise up to a pressure of 40 MPa, in terms of the characterization of the piston gauges by the method of cross floating in the overlapping pressure ranges,...

Establishment of a force balanced piston gauge for very low gauge and absolute pressure measurements at NPL, India

National Physical Laboratory, the National Metrology Institute (NMI) of India is maintaining Primary standards of pressure that cover several decades of pressure, starting from 3.0E-06 Pa to 1.0 GPa. Among which a recent addition is a Force Balanced Piston Gauge, the non-rotating piston type, having better resolution and zero stability compared to any other primary pressure standards commercially available in the range 1.0 Pa to 15.0 kPa (abs and gauge). The characterization of this FPG is done against Ultrasonic Interferometer Manometer (UIM), the National Primary pressure standard, working in the range 1.0 Pa to 130.0 kPa (abs and diff) and Air Piston Gauge (APG), a Transfer Pressure Standard, working in the range 6.5 kPa to 360 kPa (abs and gauge), in their overlapping pressure regions covering both absolute and gauge pressures. As NPL being one of the signatories to the CIPM MRA, the Calibration and Measurement Capabilities (CMC) of both the reference standards (UIM & APG), are Peer reviewed and notified in the Key Comparison Data Base (KCDB) of BIPM. The estimated mean effective area of the Piston Cylinder assembly of this FPG against UIM (980.457 mm2) and APG (980.463 mm2) are well within 4 ppm and 10 ppm agreement respectively, with the manufacturer's reported value (980.453 mm2). The expanded uncertainty of this FPG, Q(0.012 Pa, 0.0025% of reading), evaluated against UIM as reference standard, is well within the reported value of the manufacturer, Q(0.008 Pa, 0.003% of reading) at k = 2. The results of the characterization along with experimental setup & measurement conditions (for gauge and absolute pressure measurements), uncertainty budget preparation and evaluation of measurement uncertainty are discussed in detail in this paper.

Simultaneous sound velocity and density measurements of NaCl at high temperatures and pressures: Application as a primary pressure standard

The elastic compressional (P) and shear (S) wave velocities in NaCl were measured up to 12 GPa at 300 K, and up to 8 GPa at 473 and 673 K, by combining ultrasonic interferometry, in situ synchrotron X-ray diffraction, and X-ray radiographic techniques in a large-volume Kawai-type multi-anvil apparatus. The simultaneously measured sound velocity and density data at 300 K and high pressures up to 12 GPa were corrected to transform the adiabatic values to isothermal values and then used to estimate the 300 K equation of state (EOS) by a least-squares fit to the fourth-order Birch-Murnaghan finite strain equation, without pressure data. For a fixed isothermal bulk modulus K T0 of 23.7 GPa at 0 GPa and 300 K, we obtained the first and the second pressure derivatives of K T0, K ′T0 = 5.14 ± 0.05 and K ″T0 = −0.392 ± 0.021 GPa−1, respectively. A high-temperature and high-pressure EOS of NaCl was then developed using the Mie-Gruneisen relation and the Debye thermal model. To accomplish this, the simultaneously measured sound velocities and densities up to 8 GPa at both 473 and 673 K, as well as previously reported volume thermal expansion data of NaCl at 0 GPa were included in the fit. This resulted in a q parameter of 0.96, while holding the Gruneisen parameter and the Debye temperature, both at 0 GPa and 300 K, fixed at 1.56 and 279 K, respectively. Our EOS model accurately modeled not only the present measured K T data at pressures up to 12 GPa and temperatures between 300 and 673 K, but also the previously reported volume thermal expansion and the temperature dependence of K T, both at 0 GPa. The new temperature-pressure-volume EOS for NaCl, presented here, provides a pressure-independent primary pressure standard at high temperatures and high pressures.

Concept and architecture of a new apparatus for cylindrical form measurement with a nanometric level of accuracy

In relation to the industrial need and to the progress of technology, Laboratoire National de Métrologie et d’Essais (LNE) would like to improve the measurement of its primary pressure standards, spherical and flick standards. The spherical and flick standards are, respectively, used to calibrate the spindle motion error and the probe, which equip commercial conventional cylindricity-measuring machines. The primary pressure standards are obtained using pressure balances equipped with rotary pistons. To reach a relative uncertainty of 10−6 in the pressure measurement, it is necessary to know the diameters of both the piston and the cylinder with an uncertainty of 5 nm for a piston diameter of 10 mm. Conventional machines are not able to reach such an uncertainty level. That is why the development of a new machine is necessary. The purpose of this paper is to present the concepts and the architecture adopted in the development of the new equipment dedicated to cylindricity measurement at a nanometric level of a accuracy. The choice of these concepts is based on the analysis of the uncertainty sources encountered in conventional architectures. The architecture of the new ultra-high equipment as well as the associated calibration procedures will be described and detailed.

Final report on key comparison CCM.P-K13 in the range 50 MPa to 500 MPa of hydraulic gauge pressure

This report describes a CCM key comparison of hydraulic pressure standards of seven National Metrology Institutes, listed in the chronological order of their measurements, that was carried out in the period from December 2008 to March 2010 in order to determine their degrees of equivalence in the range 50 MPa to 500 MPa of gauge pressure. The pilot laboratory was PTB. The primary pressure standards were pressure balances of different design equipped with piston–cylinder assemblies operated in free-deformation, controlled-clearance or re-entrant operation mode. The transfer standard was a piston–cylinder assembly in a pressure balance. The pressure-dependent effective areas of the transfer standard at specified pressures were reported by the participants and led to the reference values calculated as medians. Results of all participants excepting NIM agree with the reference values and with each other within the expanded uncertainties calculated with a coverage factor 2, most of them even within their standard uncertainties. In addition, the results were analysed in terms of the zero pressure effective area and the pressure distortion coefficient. Also for them agreement within expanded uncertainties (k = 2) is observed. The results of the comparison demonstrate equivalence of the laboratory standards and of the Calibration and Measurement Capabilities currently presented in the BIPM key comparison database.Main text.To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/.The final report has been peer-reviewed and approved for publication by the CCM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

Use of a higher order Heydemann–Welch model to characterize a controlled clearance piston gauge

We present a new method for characterizing a controlled-clearance piston gauge as a primary pressure standard. This method requires operating the piston gauge to jacket pressures of over 80% of the system pressure. We present measurements on a hydraulic piston gauge with a 290MPa maximum pressure and a nominal piston diameter of 3.27mm. Measurements showed that the cylinder becomes stiffer as the jacket pressure increases, and that non-linear models of the Heydemann–Welch parameters improve the determination of the effective area. The relative standard uncertainty in the effective area of the piston gauge ranges from 16.0×10−6 to 17.6×10−6, and the agreement to the present NIST pressure scale is within the standard uncertainty.