Physikalisch-Technische Bundesanstalt

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1 Physikalisch-Technische Bundesanstalt Thermodynamik und Explosionsschutz PTB-Bericht ThEx-12 Dimensional Measurements and Calculation of the Effective Area. Phase A1 of the CCM Key Comparison in the Pressure Range 0,05 to 1 MPa (gas medium, gauge mode) von G. F. Molinar 1, B. Rebaglia 1, A. Sacconi 1, J. C. Legras 2, G. P. Vailleau 2, J. W. Schmidt 3, J. Stoup 3, D. R. Flack 4, W. Sabuga 5, O. Jusko 5 1 CNR, Istituto di Metrologia G. Colonnetti, Italy 2 BNM, Laboratoire National d Essais, France 3 National Institute of Standards and Technology, USA 4 National Physical Laboratory, UK 5 Physikalisch-Technische Bundesanstalt, Germany PTB-ThEx-12 Braunschweig, December 2000

2 - 1 - Abstract This report summarises the results obtained by five laboratories in the determination of the effective areas of two piston-cylinder assemblies from dimensional measurements carried out as part of a key comparison in the pressure range 0,05 MPa to 1 MPa under the auspices of the CCM. It analyses the results of the dimensional measurements performed by the laboratories as well as the methods they used to calculate the effective area from the dimensional data. Twenty -five of the 34 values reported by the laboratories deviate from the reference values by no more than the standard uncertainties of these deviations. All the results agree with the reference values within the expanded uncertainties with a coverage factor k = 2. In three of 30 pairs of compared results, the discrepancies are larger than the expanded uncertainties with a coverage factor k = 2. Zusammenfassung Dieser Bericht fasst Ergebnisse von fünf Instituten bei der Bestimmung der wirksamen Querschnittsflächen von zwei Kolben-Zylinder-Systemen aus dimensionellen Messungen zusammen, die als Teil eines CCM Schlüsselvergleichs im Druckbereich 0,05 MPa bis 1 MPa durchgeführt wurden. Der Bericht analysiert sowohl die Ergebnisse der von den Laboratorien durchgeführten dimensionellen Messungen als auch deren Methoden zur Berechnung der wirksamen Querschnittsfläche aus den dimensionellen Daten. Fünfundzwanzig der 34 von Laboratorien berichteten Werte weichen vom Referenzwert um weniger als die Standardunsicherheiten dieser Abweichungen ab. Alle Ergebnisse stimmen mit den Referenzwerten innerhalb der erweiterten Unsicherheiten mit dem Deckungsfaktor k = 2 überein. Bei drei der 30 Paare der verglichenen Ergebnisse sind die Differenzen größer als die erweiterten Unsicherheiten mit dem Deckungsfaktor k = 2.

3 Introduction In 1995, international comparison experiments in the pressure range 0,05 to 1 MPa were started as proposed by the High Pressure Working Group of the Comité Consultatif pour la Masse et les Grandeurs Apparentées (CCM). The experiments comprised two phases, A1 and A2. In phase A2, the participants had to determine the effective areas (A 0 ) of piston-cylinder assemblies of pressure balances with nominal effective areas of 9,8 cm 2 from pressure measurements with their own primary pressure standards. The measurement results obtained in phase A2 are presented in a separate report [1]. The present report describes the results obtained by the participants in phase A1. In this phase, the effective areas of the same piston-cylinder assemblies had to be calculated by each of the participating laboratories from the dimensional measurements performed at their institute. This phase has been necessary because the calculation of the effective area of piston-cylinder units, used as primary pressure standards in the pressure range from about 0,05 MPa to 1 MPa, from the dimensional characteristics of piston and cylinder is the method most frequently applied by the independent national metrology institutes. The effective areas determined in this way usually provide a basis for the entire national pressure scales, because the pressure standards operating at lower or higher pressures are traceable to the primary pressure standards by stepping-down or stepping-up procedures. Therefore, the discrepancies observed for national pressure scales in previous international comparisons might have had their origin in the differences of the dimensional measurement techniques and/or the methods applied at the national metrology institutes for calculating effective areas. The complete list of laboratories and the names of the colleagues who took part in the comparison are: 1. Consiglio Nazionale delle Ricerche, Istituto di Metrologia G. Colonnetti (CNR-IMGC), Italy: R. Bellotti, M. Pometto, B. I. Rebaglia, A. Sacconi - for dimensional measurements, G. F. Molinar - for effective area calculations; 2. Bureau National de Métrologie, Laboratoire National d Essais (BNM-LNE), France: J. Le Guinio, P. Otal, G. P. Vailleau - for dimensional measurements, J.C. Legras - for effective area calculations; 3. National Institute of Standards and Technology (NIST), USA: H. Harary, J. Stoup - for dimensional measurements, J. W. Schmidt, S. Tison - for effective area calculations; 4. National Physical Laboratory (NPL), UK: D.R. Flack, A. Hart, M.R. Sutherland, B.D. Shipp - for dimensional measurements; 5. Physikalisch-Technische Bundesanstalt (PTB), Germany: H. Bosse, O. Jusko, F. Lüdicke - for dimensional measurements, W. Sabuga, J. Jäger - for effective area calculations.

4 - 3 - The comparison started in summer 1995 and ended in summer 1998 using two transfer standards - piston-cylinder assemblies one of which had been manufactured by Desgranges et Huot, France (DH) and the other one by DH Instruments, USA (DHI), and was performed in the following order: DH transfer standard PTB summer 1995 NPL autumn 1995 CNR-IMGC spring 1996 NIST autumn 1996 BNM-LNE spring 1997 PTB autumn 1997 DHI transfer standard BNM-LNE summer 1995 NIST winter 1995 CNR-IMGC spring 1996 PTB autumn 1996 BNM-LNE spring 1997 NPL summer 1998 With the exception of the NPL all laboratories performed the dimensional measurements and calculated the effective area. The NPL only determined dimensional characteristics of the transfer standards. The results obtained by the laboratories are presented in reports [2-17]. 2. The transfer standards The main dimensional and material properties of the transfer standards are given below. The DH transfer standard, with piston and cylinder, both identified by the number 6594: Piston Cylinder Nominal length 58,5 mm 40 mm Nominal diameter 35,333 mm 35,334 mm Material tungsten carbide tungsten carbide with cobalt with cobalt Young s modulus 6, Pa 6, Pa Poisson s coefficient 0,218 0,218 Linear thermal expansion coefficient 4, K -1 4, K -1 In the working position of the piston in the cylinder, the lower piston end is 8 mm below the cylinder base. The DHI transfer standard with piston and cylinder identified by numbers P0107 and C0107, respectively: Piston Cylinder Nominal length 58,5 mm 40 mm Nominal diameter 35,333 mm 35,334 mm Material Ceramic Coors tungsten carbide AD 995 with nickel Young s modulus 3, Pa 6, Pa

5 - 4 - Poisson s coefficient 0,22 0,218 Linear thermal expansion coefficient 5, K -1 4, K -1 In the working position of the piston in the cylinder, the lower piston end is 9 mm below the cylinder base. A comprehensive description of the two transfer standards is given in the measurement instructions for phase A2 drafted by the BNM-LNE in its capacity as the pilot laboratory for phase A2 [1]. To check the stability of the transfer standards, their dimensional properties had to be determined at the beginning and at the end of the comparison at the same laboratory: for the DH piston-cylinder assembly at the PTB and for the DHI at the BNM-LNE. 3. Dimensional measurements and procedures for effective area calculation Dimensional measurement procedures are described in detail in the Guideline for Phase A1 which were prepared by the PTB in its capacity as the pilot laboratory for phase A1 and accepted by the participating laboratories (see Annex 1). As obligatory measurements, the determinations of two pairs of orthogonal diameters in two horizontal planes, of roundness profiles in five equidistant horizontal sections and of eight generatrices separated by 45 for each piston and cylinder were defined. Straightness measurements on the cylinder were agreed to be performed in the height range from - 19,5 mm to 19,5 mm, assuming the gap between piston and cylinder beyond this height range to be much greater than within this range. The task of the BNM-LNE and the PTB which were the first to measure the transfer standards was to confirm this assumption. The generatrices of the DHI and DH piston-cylinder assemblies measured by the BNM-LNE and the PTB in 1995 are presented in Figs. 1 and 2. The piston and cylinder of the two assemblies are characterised by good cylindricity and form a rather wide gap below -19,5 mm and above 19,5 mm so that only the shape of the clearance between these marks had to be determined. It was free for each participating laboratory to perform additional dimensional measurements and to choose a method for the calculation of the effective area. As an option it was proposed, starting from the diameters, roundness and straightness shape deviations, to create three-dimensional data sets describing the shapes of the transfer standards and to calculate the effective area by the theory by R.S.Dadson, S.L.Lewis and G.N.Peggs [18]. To correctly treat the results reported by the participants and to distinguish the effects by differences of the dimensional data obtained and of the calculation methods for the effective area applied by the participants, it was decided that the PTB should calculate the effective area using the same calculating method on the basis of dimensional data sets supplied by the participating laboratories. 3.1 CNR-IMGC measurements and calculation methods In addition to the obligatory dimensional measurements described in the Guideline for Phase A1, the following results were reported by the CNR-IMGC [2-7]: diameters at heights -2L/5, 0 and 2L/5, each in two azimuthal directions of 0 and 90, straightness measurement results with a height step of 0,25 mm.

6 - 5 - For the piston of the DHI transfer standard, the generatrices were investigated only for the angles 0, 90, 180 and 270. From the diameters, straightness and roundness deviations, three-dimensional data sets describing the shapes of piston and cylinder for both transfer standards were created in accordance with the Guideline for Phase A1. The calculation of the effective area of each transfer standard was undertaken in several steps. In a first step, the diameters of piston and cylinder were used to calculate the average diameters, the cross-sectional areas and the mean area as the effective area of the assembly. The uncertainty estimation for the effective area included the uncertainties of the diameter measurements and the standard deviations of the average piston and cylinder diameters. The restricted reliability of such a calculation was stressed, because it would have been suitable only for piston-cylinder units with a constant radial clearance between piston and cylinder. In a second step, a restricted number of generatrix line radii were selected from the threedimensional data sets to form diameters and to calculate the effective area again as the mean of the average cross sections of piston and cylinder. In the estimation of the effective area, the uncertainties of the radial values and the standard deviations of the average piston and cylinder diameters were taken into account. The results of this calculation were evaluated as more realistic than that obtained in the first step. In a third step, all radial values available for the generatrices and circles were used to determine the average piston and cylinder diameters and, as in the previous steps, to calculate the mean of the piston and cylinder cross sections. The uncertainty estimation was similar to that in the second step. In a fourth step, the effective area was calculated using the formula L / 2 2 h0 1 A0 = π r [ u( z) + U ( z) ] d z, (1) r0 r0 L L / 2 which corresponds to the model of a constant pressure gradient along the clearance between piston and cylinder, with r 0 - piston radius and h 0 - radial clearance at z = -L/2, u(z) and U(z) - piston and cylinder radial displacements from radii at z = -L/2. The uncertainty was calculated taking into account uncertainties of the diameter measurements and of the determination of piston and cylinder shape. In a fifth step, the effective area was determined with the formula L / 2 L / 2 2 h A0 = π r [ u( z) + U ( z) ] h( z) d z h( z) d z, (2) r0 r0 L / 2 L / 2 a particular case of the general formula by Dadson et al. when the applied gauge pressure tends to zero or when the pressure-transmitting medium is incompressible. The uncertainty here was estimated in the same way as in the fourth step. This method of determining the effective area was regarded as the most realistic one and was reported as a final result for both transfer standards.

7 BNM-LNE measurements and calculation methods The BNM-LNE performed dimensional measurements as specified as obligatory in the Guideline for Phase A1 [8, 9]. For each piston and cylinder, from four reference diameters at heights -L/5 and L/5 each for two azimuthal directions 0 and 90 (D ref ), from straightness and roundness deviations (S(z,ϕ) and R(z,ϕ)), diameters D(z,ϕ) for each height (z) and each azimuth (ϕ) were created using the formulas below. Along two pairs of generatrices and , ϕ = 0, 90, z = -20 mm to 20 mm: D(z, ϕ) = D ref (z ref, ϕ) - S(z ref, ϕ) - S(z ref, ϕ+180) + S(z, ϕ) + S(z, ϕ+180). (3) Along another two pairs of generatrices and , ϕ = 45, 135, z = -20 mm to 20 mm: D(z, ϕ) = D * ref(z ref, ϕ) - S(z ref, ϕ) - S(z ref, ϕ+180) + S(z, ϕ) + S(z, ϕ+180), (3 ) where D * ref(z ref, ϕ), which were not directly measured, had to be determined using roundness deviation data according to D * ref(z ref, ϕ) = D ref (z ref, ϕ ref ) - R(z ref, ϕ ref ) - R(z ref, ϕ ref +180) + R(z ref, ϕ) + R(z ref, ϕ+180). Along five circle traces, z = -2L/5, -L/5, 0, L/5 and 2L/5, ϕ = 1 to 359 : D(z, ϕ) = D ref (z, ϕ ref ) - R(z, ϕ ref ) - R(z, ϕ ref +180) + R(z, ϕ) + R(z, ϕ+180), (4) with D ref (z, ϕ ref ) = D ref (z ref, ϕ ref ) if z = z ref (z = -L/5 or L/5) or with D ref (z, ϕ ref ) = D(z, ϕ ref ), the latter being calculated according to Eq. (3), if z z ref (z = -2L/5, 0 or 2L/5). In all the formulas given above, the reference height and the reference azimuth can be chosen at z ref = -L/5 or L/5 and ϕ ref = 0 or 90. With four different reference diameters, four diameters could be calculated for the same specific point (z, ϕ). The effective area was calculated using three approaches. First, all diameters for piston and cylinder lying on the generatrices calculated with Eq. (3) and (3') were averaged and the mean of the piston and cylinder cross-sectional areas was taken as the effective area. Second, the effective area was calculated from diameters along generatrices using the theory by Dadson et al. The numerical integration was carried out in 150 steps. The effective area was calculated for four pressure ratios p(-l/2)/p(l/2) = 1, 2, 5 and 10. Thirdly, the effective area was calculated as the mean of the piston and cylinder cross-sectional areas obtained by averaging all diameters lying at circle traces as defined by formula (4). The uncertainty was estimated for the effective areas calculated by the first and third methods. It included the uncertainty of the diameter measurements and the standard deviation of the diameters used to calculate the mean diameter. The values of the effective area calculated by the first and second methods were judged to be more reliable than that determined by the third method.

8 NPL dimensional measurements The NPL determined diameters at heights -L/5 and L/5 each for two azimuthal directions 0 and 90 and maximal roundness deviations at heights -2L/5, -L/5, 0, L/5 and 2L/5 for the piston and cylinder of the DH and DHI transfer standards [14, 15]. 3.4 NIST measurements and calculation methods In addition to the obligatory dimensional measurements described in the Guideline for Phase A1, the midway diameters (z = 0) for piston and cylinder were measured at the NIST [10-13]. From the diameters, straightness and roundness deviations three-dimensional data sets describing the shapes of piston and cylinder in an absolute co-ordinate system were constructed. The effective area was calculated in three steps. In a first step, six diameters available for each piston and cylinder were averaged and the average of the mean cross sections of piston and cylinder was calculated. The uncertainty of the diameter measurements and the standard deviation of the average diameters were accounted for in the effective area uncertainty budget. In a second step, the cross-sectional areas of piston and cylinder were found using all radial values representing the piston and cylinder jacket surfaces along eight vertical lines and five horizontal circles. The effective area was then calculated as a mean of the cross-sectional areas. In a third step, the dimensional measurements related to an absolute co-ordinate system were fitted by cylindrical harmonics to obtain an analytical function for the piston and cylinder radii r p (z, ϕ) and r c (z, ϕ). The effective area was then calculated using the theory by Dadson et al., separately analysing the components of the effective area arising from the force acting on the piston base (A b ), the force due to the pressure in the clearance acting on inclined piston surface elements (A s, shape contribution) and the viscous force in the clearance (A f, flow contribution): A 0 = A b + A s + A f, (5) π 1 2 ( / 2, ϕ) dϕ 2 A b = p 2 r L, (6) 0 2π L / 2 2π 1 p d rp ( z, ϕ) As = [ ( ) ( )] + ( ) rp L / 2, ϕ rp L / 2, ϕ dϕ d z p( z) rp z, ϕ dϕ, (7) p1 p0 2 d z 0 L / 2 0 2π L / 2 A 1 1 d p( z, ϕ) f = ( ) ( ) dϕ rp z, ϕ h z, ϕ d z p1 p0 2 d z, (8) 0 L / 2 where p 0 and p 1 are the ambient and absolute measured pressure, and p(z) is the pressure distribution in the clearance: p 1 z L / d z' d z' ( z) = p1 ( p1 p0 ) 3 3 / 2 ( ', ) L h z ϕ L / 2 h( z', ϕ). (9)

9 - 8 - The uncertainty of the effective area determined by this method contained the uncertainties of radii and derivatives in formulas (6) to (9) due to the uncertainties in the dimensional measurements. The effect of the changing angular position of the piston in the cylinder, of pressure p 1 as well as of the change from the Poiseuille-flow to the molecular-flow regime on the effective area was analysed. 3.5 PTB measurements and calculation methods In addition to the obligatory program described in the Guideline for Phase A1, the following results were obtained at the PTB [16, 17]: roundness measurement data with a height step of 4 mm yielding nine circle traces for the cylinder and 11 for the piston; straightness measurement data with a height step of 0,1 mm. From the diameters, straightness and roundness deviations three-dimensional data sets describing the shapes of piston and cylinder for the two transfer standards were created in accordance with the Guideline for Phase A1. The effective area was calculated in three steps. In a first step, it was calculated as a mean of the average piston and cylinder cross sections, each determined from four diameters. The uncertainty estimation for the effective area included the uncertainties of the diameter measurements and the standard deviations of the average piston and cylinder diameters. The uncertainties in the measurements of piston and cylinder diameters were considered to be correlated. In a second step, the effective area was calculated by the method by Dadson et al. on the basis of diameters, straightness and roundness deviations. To obtain from these data diameters along the generatrix lines and circle traces, first, two pairs of generatrices at ϕ = 0, 180 and ϕ = 90, 270 were "attached" to two pairs of respective reference diameters, yielding diameters along these generatrix pairs. For each circle trace, from roundness deviations and two perpendicular diameters determined above, using an LS-procedure, absolute diameter values of circle traces were found. Choosing the diameters at ϕ = 45 and 135 on the circle traces at z = -L/5 and L/5, finally two generatrix pairs at ϕ = 45, 225 and ϕ = 135, 315 were "attached", yielding diameters along these generatrix pairs. It should be pointed out that the circle and generatrix diameters obtained by this method are not absolutely consistent. They coincide at points z = -L/5, L/5 and ϕ = 45, 135 ; the discrepancies between them are minimal at points z -L/5, L/5 and ϕ = 0, 90, but at all other intersection points they remain non-fitted and can yield major contradictions. In a third step, the effective area was calculated by the method by Dadson et al. on the basis of radial values for generatrices and circle traces prepared by the PTB Geometrical Standards Section. In contrast to the dimensional data processed in the second step, the generatrices and circles here were linked so that the sum of contradictions between their radial values was minimal at all intersection points. In the two latter steps, the effective area was calculated from straightness and roundness data taken separately for all possible azimuthal directions and piston angle positions in the cylinder, at minimal, maximal and some intermediate pressures. Before numerical integration, the straightness data, which have a high density in the vertical direction, were smoothed to avoid abrupt changes of the numerically calculated derivatives, and the missing cylinder radii in the regions near the cylinder

10 - 9 - edges were created by linear extrapolation on the basis of the points lying within 0,5 mm at the beginning and at the end of the gauge length. To have a sufficient number of integration steps, on the basis of a restricted number of straightness or roundness points, new data sets with 1000 or 100 values respectively along the assembly engagement length were prepared by a linear interpolation procedure. These numbers of integration steps were found to be great enough because their further increase no longer had an effect on the value of the effective area. The uncertainty estimation for the effective area took into account the uncertainty of diameter measurement, differences in the effective areas obtained from the straightness and roundness data, the standard deviation of values calculated for different azimuthal directions, errors due to smoothing and numerical integration procedures, change of the effective area with piston rotation and with pressure. All these contributions were considered to be uncorrelated. In its capacity as the pilot laboratory for Phase A1 of the comparison, the PTB also calculated the effective areas of the transfer standards by the methods described above, using dimensional data supplied by other participating laboratories. Where only reference diameters and shape deviation data were available, the method described in the second step was applied; if there were reference diameters and absolute radial values, both methods from the second and third steps were used. 4. Results and discussion The participants' results of diameter measurements as well as of effective area calculations are here presented and analysed in terms of their deviations from respective reference values as recommended by "Mutual recognition of national standards..." (MRA) - document [19]. All the reference values were determined as averages of values reported by the participants. Two results of the institutes which twice performed dimensional measurements on the same transfer standard in 1995 and 1997, the BNM-LNE on the DHI and the PTB on the DH standard, were averaged before a reference value was calculated so that ultimately only one value from each participant was taken into account. Considering the participants' results to be independent, the uncertainties of the reference values were calculated from the uncertainties claimed by the participants as uncertainties of means and, therefore, do not allow for a scatter of the values obtained by the participants 1). In addition, the results obtained for the effective area were analysed in terms of deviation from the median to check the effect of possible "outliers" [20] Uncertainties of the diameters, straightness and roundness measurements with indication of a correlation type, contradictions of circle and generatrix radii at intersection points and resulting uncertainties of radii describing piston and cylinder shapes are given for the DH and DHI transfer standards in Tables 1 and 2, respectively. Roundness measurements are most accurate, the main uncertainties of the radii describing the piston and cylinder shape origin from diameter Note 1) The uncertainty calculated in this way is usually used in the statistical theory to decide whether two or more measurement results of the same measurand conform with one other [21]. It cannot be considered a realistic uncertainty characterising a property of a transfer standard or demonstrating "state of the art" in its determination. Unfortunately, the MRA document [19] does not tell how the uncertainty of the reference value should be calculated. Probably, a value comprising both the standard deviation of the mean of scattered results reported by the participants and the uncertainties claimed by the participants would be a much more realistic estimation of the reference value uncertainty. However, such a value would be less suitable to verify the conformity of results.

11 measurements or from inconsistency between roundness and straightness measurements. The individual diameters reported by the institutes for each piston and cylinder of the two transfer standards at heights -L/5 and L/5 in the directions 0 and 90 are given in Table 3 in terms of deviations from the respective reference diameters. For the reference diameters the following standard uncertainties were calculated (see Note 1) on page 9): DH standard, piston 24 nm DH standard, cylinder 23 nm DH standard, piston 34 nm DH standard, cylinder 26 nm. The deviations of the diameters obtained by the laboratories from mean piston-cylinder diameters for the two transfer standards are presented in Figs The diameters measured at the same place by different institutes differ by up to 366 nm; it is greater than the typical uncertainties of the diameter measurements claimed by the institutes by an order of magnitude. Although all the diameter uncertainties with the exception of those obtained by the CNR-IMGC for the DHI unit are similar in magnitude, ratios of uncertainty contributions of types A and B reported by the participants are very different. Depending on this ratio, the diameters measured at different positions on piston and cylinder were considered by the participants to be correlated or uncorrelated, and as a result, the respective diameter uncertainties were arithmetically or geometrically added when the uncertainty of the effective area was estimated. Nevertheless, the results graphically represented in Figs. 3 to 6 show an obvious correlation between diameters measured at the same laboratory: a laboratory that measured a smallest diameter for a particular cylinder position, as a rule, also determined smallest diameters for other cylinder positions and for all piston positions. For this reason, the diameter uncertainties reported by the participants were all considered to be correlated when the effective area was calculated at the PTB and its uncertainty was estimated. For each transfer standard the participants reported several values of the effective area calculated by different methods described above. From them, only the one indicated by the laboratory as the most reliable was used in calculating the reference value: CNR-IMGC - calculated with Dadson's equation for limiting case of zero gage pressure (2), BNM-LNE - calculated as average from diameters along the generatrices (3) and (3'), NIST - calculated by Dadson's theory in the Poiseuille-flow regime, Eqs. (5)-(9), NPL - average from directly measured diameters, calculated by the PTB, PTB - calculated by Dadson's theory using radii of generatrices and circle traces. From the effective area values and their uncertainties reported by the laboratories, the following effective area reference values with the standard uncertainties were determined (see Note 1) on page 9) for the transfer standards: DH No 6594 assembly A 0ref = 9,80**** (1 ± 2, ) cm 2, DHI No 107 assembly A 0ref = 9, (1 ± 2, ) cm 2. 2) Note 2) The exact effective area of assembly DH 6594 is not reported because the assembly is currently being used as a transfer standard in a EUROMET comparison.

12 The relative deviations of the effective areas obtained by the laboratories from these reference values together with the expanded relative uncertainties of these deviations with a coverage factor k = 2 are presented in Table 4. An analysis of these results in accordance with the recommendation [19] allows conclusions about high degree of equivalence of the participants' measurement standards to be drown. The median of the effective area values reported for the DH transfer standard coincides with the result of NIST, that of the DHI piston-cylinder assembly with the result of CNR-IMGC. They are herewith by 1, and 0, in relative units larger than the effective area's reference values for the DH and DHI transfer standards, respectively. According to [20], the relative uncertainties of the medians corresponding to standard uncertainties of the normal distribution are 3, for the DH and 4, for DHI standards. These values do not comprise information about the uncertainties claimed by the participants but only reflect the scatter of the values reported. For both transfer standards, they, multiplied by a coverage factor 2, are larger than the deviation of any participant from the medians. They are, probably, better estimators for the uncertainties of the reference values but are not very expedient to be used for a check of the agreement between the laboratories. The latter are automatically in agreement with the reference values independently of how large their own uncertainties are. All the laboratory results of the effective area calculations are summarised for the DH and DHI piston-cylinder units in Tables 5 and 6 in terms of deviations from the reference values determined above. These tables contain two parts: first, with the results reported by the participating institutes and, second, with the effective areas calculated at the PTB from the dimensional data supplied by the participants using the same calculation procedure. For the DH piston-cylinder unit (Table 5), the effective areas calculated by the participants from the average piston and cylinder diameters agree within 8, in relative units,- this is a fairly good agreement although this difference is larger than the uncertainties claimed by the most institutes by approximately three times. Considering a flow in the gap according to the theory by Dadson et al., the relative difference between the institutes becomes 11, If the effective areas are calculated only from four piston and four cylinder diameters (PTB calculation), their maximum relative difference is equal to 10, and again is larger than the estimated uncertainties. A difference of 8, was obtained when Dadson's theory was applied using the diametrical values and straightness and roundness deviations (PTB calculation). A relatively small difference of 1, was achieved when the effective area was calculated from piston and cylinder radial values, because only two participants supplied three-dimensional data sets for piston and cylinder and could be compared here. The last column of the table contains the maximum difference between the effective areas calculated by the different methods from the geometrical data of the same institute. It should be kept in mind that these relatively large differences up to 6, certainly are not attributable to the methods, e.g. diameter averaging vs. Dadson's theory, but are rather due to very different amounts of input information, when, e.g., first, only four reference diameters are used and, second, the whole assembly shape is described. Indeed, if the effective area is calculated by averaging all diameters along the generatrices and circle traces and then by Dadson's theory, e.g., CNR-IMGC results denoted by 3) and 5), the relative difference will be equal to only 1, For the DHI piston-cylinder unit (Table 6), the effective areas calculated from average piston and cylinder diameters differ in relative terms by 13, ; this again is much more than the uncertainties reported by most laboratories. The agreement is better when Dadson's theory is

13 applied. No improvement of the agreement could be achieved by calculating the effective areas by the PTB procedures from the participants' dimensional data. When the effective area is calculated from radial values a somewhat better agreement (7, ) can probably only be explained by the fact that three results instead of five were available for the comparison. As in the case of the DH unit, the application of the different calculation methods does not influence the effective area as strongly as dimensional data. The uncertainty budget for the effective area calculation from the dimensional data of the participants which was performed at the PTB on the basis of Dadson's theory is presented in Tables 7 and 8 for the DH and DHI transfer standards. The main uncertainties of the effective area arise from the uncertainties of the dimensional data, irregularities of the piston and cylinder shapes and, sometimes, contradictions between the straightness and roundness data. Relative deviations of the calculated effective areas from the reference value are shown for the DH and DHI transfer standards in Figs. 7 and 8. Vertical bars indicate the standard uncertainties of these deviations. Most of the participants' results deviate from the reference value by not more than the standard uncertainties of the deviations; all of them agree with the reference value within the expanded uncertainties with a coverage factor k = 2. The results of the laboratories obtained with the two transfer standards are well reproducible: the deviations of the laboratory results from the reference value observed for the DH and DHI transfer standards are very similar. In Figs. 7 and 8, positions of reference values for the effective areas determined from the cross-float experiments in Phase A2 of the comparison are indicated by dashed lines. The reference values in Phase A2 are greater than those in Phase A1 by 3, and 4, relative for the DH and DHI transfer standards, respectively. This is to some extent due to the fact that NPL took part in Phase A1 but not in Phase A2. If the Phase A1 reference values had been calculated without the NPL results, the relative differences between A 0ref (Phase A2) and A 0ref (Phase A1) would have been 2, and 2, for the DH and DHI transfer standards, respectively. These differences are smaller than their standard uncertainties. Relative differences between the effective areas of each individual pair of laboratories and relative standard uncertainties of the differences are presented in Table 9. For the DH piston-cylinder assembly, all 15 pairs of results under comparison show agreement within the expanded uncertainties with a coverage factor k=2. 12 of them even agree within their standard uncertainties. For the DHI piston-cylinder assembly, three of the 15 pairs of results differ by more than the expanded uncertainties with a coverage factor k=2 and another three by more than the standard uncertainties. An analysis of the differences between the same pair of laboratories for the two transfer standards show that for each pair of laboratories they are reproducible within ±4, relative. 5. Stability of the transfer standards For the DHI transfer standard, all cylinder and piston diameters measured by the BNM-LNE in 1997 were found to be larger than that determined in 1995 [8] (Table 1). The changes of the piston diameters lie between 0,026 µm and 0,056 µm - this is comparable with the diameter measurement uncertainties of 0,040 µm claimed by the BNM-LNE.

14 The changes of the cylinder diameters are somewhat greater - from 0,027 µm to 0,111 µm. No changes in the shape of the piston and cylinder can be stated, because the roundness deviation values obtained in 1995 and 1997 differ by only max. 0,022 µm, i.e. less than the standard uncertainty of the roundness measurement of 0,030 µm. Using the different calculation methods, the relative change of the effective area of the DHI piston-cylinder unit during the time of the comparison was found to lie between 2, and 4, For the DH transfer standard studied twice by the PTB [17], the cylinder was found to be stable during the comparison. According to the measurements performed in 1995 and 1997, the cylinder diameters increased in this period of time by 0,025 µm to 0,031 µm - these changes are very close to the diameter measurement uncertainties of 0,025 µm claimed by the PTB. As to the piston, its dimensional properties changed during the comparison. The first indication of unusually large roundness deviations of the upper piston sections was communicated by the CNR-IMGC in February To verify this change, the roundness of the piston was again studied at the PTB in March 1996, and the change in the piston shape was confirmed. Nevertheless, as no changes could be detected in the behaviour of the transfer standard when performing pressure measurements - the sensitivity, the free rotation time and the fall rate were the same as measured by the pilot laboratory (BNM-LNE) at the beginning of the comparison -, it was decided to continue the comparison using this transfer standard. The roundness deviations of five piston sections as found in the roundness measurement by different laboratories are given in Fig. 9 versus time. The roundness profiles of section z = +2L/5 as determined by the participants are presented in Fig. 10. The roundness profile of this section measured by NPL is rather similar to that determined by PTB Evidently, the main change in shape happened between September 1995 and March After March 1996, the piston shape remained relatively stable. The slight decrease of the roundness deviations in the upper part of the piston and their increase in the lower part is probably due to relaxation of stresses arising from the incident. The change in piston shape can be clearly seen from a comparison of the piston generatrices determined by the PTB in 1995 and 1997 (Figs. 2 and 11). In 1997 the clearance width between the piston and the cylinder in certain directions became so small that if the piston could drop to about 15 mm below its working position, it would probably wedge in the cylinder. When the effective areas obtained by the PTB at the beginning and at the end of the comparison are compared, it is interesting to note that the change in the piston shape described above did not lead to any significant change in the effective area calculated from the dimensional data as well as that determined from the pressure measurements [1]. The relative changes in the effective areas determined from the dimensions and pressure measurements are 0, and 1,2 10-6, respectively and therefore are substantially smaller than the relative uncertainties of these measurements which are equal to 3, and 4, Such a constancy of the effective area can be understood when analysing the diameter changes - the increase in those lying in the azimuthal section 0/180 was accompanied by an equivalent decrease of the diameters lying in the section 90 /270 (Table 1). This shows that the results obtained by the participants on the DH transfer standard are comparable in spite of the change in shape. 6. Additional measurements, corrections After distributing two draft versions of this report, additional measurements have been performed by NPL and BNM-LNE.

15 NPL remeasured their fused silica box standard which was applied to calibrate the stylus used on the NPL internal diameter measuring machine when measuring cylinder DHI C0107 [22]. The diameter results presented in the report are based on a calibration of the silica box dated by February 1996 which furnished 9,97460 mm. The new silica box size determined in January 1999 is 9,97464 mm. With the new value the cylinder DHI C0107 diameters reported should be increased by 40 nm. This diameter change corresponds to a relative increase in effective area of the DHI piston-cylinder assembly by 1, BNM-LNE found out that the difference between the BNM-LNE diameters and the results of other laboratories could have been caused by a change in a BNM-LNE operating procedure which amplified Abbe errors due to the reversal movement (tilt and yaw) on the measuring machine (SIP 214) used. With a new operating procedure and reduced Abbe offset, the reliability of which was confirmed by control measurements on plug and ring standards, BNM-LNE repeated diameter measurements on piston and cylinder of the transfer standard DH All new diameters are larger than the old ones by: BNM-LNE: (D new - D old ) / nm -L/5, 0 -L/5, 90 L/5, 0 L/5, 90 DH unit, piston DH unit, cylinder With the new diameter values, the effective area should be by larger than that calculated from the old diameters. 7. Conclusions - The reference values for the effective areas of the DH No 6594 and DHI No 107 transfer standards determined from the dimensional measurements are: DH No 6594 assembly A 0ref = 9,80**** (1 ± 2, ) cm 2, (s. Note 2 on p. 10) DHI No 107 assembly A 0ref = 9, (1 ± 2, ) cm 2. The uncertainties stated here are the standard uncertainties calculated from the uncertainties reported by the participants. They do not allow for a scatter of the participants' results and, therefore, cannot be considered reliable. - The median effective areas are A 0med = 9,80**** (1 ± 3, ) cm 2 for the DH No 6594 assembly and A 0med = 9, (1 ± 4, ) cm 2 for DHI No 107 assembly. These uncertainties are the standard uncertainties arising from the deviations of the participants' results and does not take into account uncertainties claimed by the participants.. - The comparison showed good agreement of the participants' results, when these are compared with the reference values determined for the DH and DHI transfer standards - all differences between the laboratory and the reference values are smaller than the expanded uncertainties of these differences with a coverage factor k = 2; 25 of the 34 reported values agree with the reference values even within the standard uncertainties.

16 However, if the participants' results are compared with one other, in three of 30 pairs the results differ by more than two standard uncertainties of the differences. Another six further pairs of results differ by more than the standard uncertainties. - The relative differences between the reference values for effective areas based on the dimensional measurements and determined in cross-float experiments in Phase A2 of the comparison [1] are 3, and 4, for the DH and DHI transfer standards, respectively. When only those laboratories are considered which took part in both, Phase A1 and Phase A2, the relative differences between the reference values are equal to 2, for the DH and 2, for the DHI transfer standards. These differences are smaller than their standard uncertainties. - Differences between the reported diameters are often many times larger than the uncertainties of the diameter measurements claimed by the participants. The diameter differences have a systematic character, leading to systematic differences between the calculated effective areas. These differences correlate with the differences in effective areas between some laboratories observed in previous intercomparisons. Obviously, to improve the agreement of the national pressure scales, a harmonisation of the dimensional measurements and, first and foremost, the diameter measurements should be achieved. - The reproducibility of differences of the effective areas calculated by the institutes, when the first and then the second transfer standards are considered, is within ±4, relative. - Among the dimensional measurement and calculation methods, the following importance hierarchy was stated. Reference diameters of piston and cylinder are a dominant factor for the calculated effective area. Straightness and roundness measurement data, which are intended to transfer the absolute diameter values to any point of the piston and cylinder surfaces and to ensure completeness of the description of their shape, in most cases appear to be of sufficient accuracy and influence the effective area first of all in dependence on their numbers along generatrices and circles. The calculation methods themselves seem not to be that important: even an application of the simplest formulas in which all diameters are averaged yields a result which is very close to that calculated by the more sophisticated theories which consider the fluid flow in the piston-cylinder gap. - A cylindrical perfection of the piston and cylinder bore is very important for obtaining reliable results. Great irregularities of their surfaces make the description of the piston and cylinder shape uncertain because it is very difficult to exactly identify intersection points of generatrix and circle traces as well as the same points in diameter and shape deviation measurements.

17 References 1. J. Jäger, J. C. Legras, G. Molinar and J. W. Schmidt, Phase A2 of the CCM key comparison in the pressure range kpa (gas medium, gauge mode). Pressure measurements 2. G. F. Molinar, Analysis of dimensional measurements on the D.H. piston-cylinder No. 6594, tungsten carbide (used as transfer standard in the CCM comparison in gas media up to 1 MPa, Phase A1) in order to calculate its effective area A 0 at atmospheric pressure and at 20 C, Rapporto Tecnico Interno R 426, CNR-IMGC, Torino, July B. I. Rebaglia, R. Bellotti and E. Malgieri, CCM Intercomparison, Phase A1, Dimensional measurements (diameters and generating lines), IMGC Internal Report n. RT 237/L, July A. Sacconi, W. Pasin, CCM Intercomparison, Phase A1, Roundness measurements, IMGC Measurements Report, IMGC Internal Report n. RT 236/L, July B. I. Rebaglia, M. Pometto and R. Bellotti, CCM Intercomparison, Phase A1, DH Instruments pressure balance (ceramic piston), Dimensional measurements (diameters and generating lines), IMGC Internal Report n. RT 242/L, July A. Sacconi, W. Pasin, CCM Intercomparison, Phase A1, DH Instruments pressure balance (ceramic piston), Roundness measurements, IMGC Measurements Report, IMGC Internal Report n. RT 241/L, July G. F. Molinar, Analysis of dimensional measurements on the D.H. Instruments piston-cylinder, piston P0107 in ceramic and cylinder C0107 in tungsten carbide, (used as transfer standard in the CCM comparison in gas media up to 1 MPa, Phase A1) in order to calculate its effective area A 0 at atmospheric pressure and at 20 C, Rapporto Tecnico Interno R 450, CNR-IMGC, Torino, July J. C. Legras, J. Le Guinio, P. Otal and G. P. Vailleau, CCM comparison in the pressure range 0,05 to 1 MPa. Phase A1. Characterisation of the DHI transfer standard N o 107 from dimensional measurements, BNM-LNE results, Convention BNM N o C544 B15, December J. C. Legras, J. Le Guinio, P. Otal and G. P. Vailleau, CCM comparison in the pressure range 0,05 to 1 MPa. Phase A1. Characterisation of the Desgranges et Huot transfer standard N o 6594 from dimensional measurements, BNM-LNE results, Convention BNM N o C544 B15, December H. H. Harary, Report of test for (1 set) 35 mm diameter piston and cylinder DHI. Piston and cylinder - tungsten carbide. Sn: P0107, C0107, Group control No. M5211, NIST, Gaithersburg, Maryland 20899, 28 October 1996

18 S. Tison, Effective area derived from dimensional measurements (Round Robin #1). Instrument data: Manufacturer - DHI. Piston number - P0107. Cylinder number - C0107, NIST, P8574-A, 16 October H. H. Harary, Report of test for (1 set) 35 mm diameter piston and cylinder D&H. Piston and cylinder - tungsten carbide. Sn: 6594, Group control No. M5239, NIST, Gaithersburg, Maryland 20899, 22 November J. W. Schmidt, Effective area derived from dimensional measurements (Round Robin #2). Instrument data: Manufacturer - Desgranges et Huot. Model Piston number P. Cylinder number C, NIST, P-8586-B, 23 December D. Flack, G. N. Peggs, Certificate of calibration. Piston and cylinder assembly A type 5111 Desgranges et Huot piston-cylinder assembly made of tungsten carbide and having a nominal effective area of 10 cm 2, Reference: 08B071/95053/B94/01, NPL, Teddington Middlesex UK, 23 November D. Flack, G. N. Peggs, Certificate of calibration. Piston and cylinder assembly A DHI piston-cylinder assembly comprising a cylinder (tungsten carbide with nickel) and piston (ceramic Coors AD995), Reference: 08B071/98018/B94/77, NPL, Teddington Middlesex UK, 2 September W. Sabuga, O. Jusko, Effective area of the DH Instruments piston-cylinder, piston P0107 and cylinder C0107, calculated from the dimensional measurements data. Phase A1 of the CCM comparison in gas media up to 1 MPa, PTB-Bericht, PTB-ThEx-6, Braunschweig, W. Sabuga, O. Jusko, Effective area of the Desgranges et Huot piston-cylinder No calculated from the dimensional measurements data. Phase A1 of the CCM comparison in gas media up to 1 MPa, PTB-Bericht, PTB-ThEx-7, Braunschweig, R. S. Dadson. S. L. Lewis and G. N. Peggs, The pressure balance: theory and practice, HMSO, London, 1982, 290 p. 19. Mutual recognition of national standards and calibration certificates issued by national metrology institutes, Draft A of 25 February 1998 edited 15 May 1998, BIPM, PTB- Mitteilungen, 108, 3/98, p J. W. Müller, Possible advantages of a robust evaluation of comparisons, Rapport BIPM-95/2, April 1995, 7 p. 21. K. Weise, W. Wöger, Comparison of two measurement results using the Bayesian theory of measurement uncertainty, Meas. Sci. Technol., 5 (1994), p D. R. Flack, Communication MOT 3/3/342/DRF/001 of 27 April J. C. Legras, Communication of 11 May 1999