THE PURPOSE AND IMPLEMENTATION OF A MULTI-PISTON PRESSURE CALIBRATION CHAIN

Transcription

1 Presented 1989 JUL 1989 NCSL WORKSHOP AND SYMPOSIUM Denver CO - USA THE PURPOSE AND IMPLEMENTATION OF A MULTI-PISTON PRESSURE CALIBRATION CHAIN Martin Girard Michael Bridge Pierre Delajoud DH Instruments, Inc East Beautiful Lane Phoenix AZ USA dhi@dhinstruments.com 1989 JUL ABSTRACT Fundamental research in the field of very high accuracy pressure standards tends to concentrate on the characterization of a single or group of piston gauges or manometers. For the results of this work to be available to and easily exploited by the high accuracy pressure measurement community, methods must exist that efficiently transfer values vertically to lower and higher pressure ranges and horizontally to a large number of other standards with as little degradation in accuracy as possible. The multi-piston pressure calibration chain offers an extremely efficient method of making the necessary transfers. A six level calibration chain covering the range of 0.01 to 500 MPa (1.5 to psi) was implemented by DH Instruments, Inc. (DHI) in the early 1980s and has been used intensively since then as a means of maintain a coherent internal standard and as a reliable and efficient tool for the calibration and recalibration of hundreds of high accuracy piston gauges and other precision pressure measuring devices. PURPOSE OF THE CALIBRATION CHAIN Fundamental research in the field of very high accuracy pressure standards tends to concentrate on the characterization of a single or small group of piston gauges or manometers to study a specific, limited pressure range with the objective of reducing as far as possible the uncertainties on the pressures defined. This leads to the local production of discreet, high quality measurements and improvements in the fundamental definition of the derived unit of pressure in a limited part of the derived unit of pressure in a limited part of the pressure range. Ideally, the coherence of the values obtained with those used over the rest of the pressure range are then verified. Once the ability to make the measurements has been established, the overriding problem becomes the widespread dissemination of the reference values obtained to the high accuracy pressure measurement community at large. The very low ratio that exists today between the accuracy available at the highest levels and the accuracy needed on a very broad basis by the pressure measurement community make it important that the transfer be able to be made to a large number of instruments with as little degradation in accuracy as possible. However, the standards used for the fundamental research are usually custom designed for that purpose, not to facilitate the calibration of other instruments. Their operation tends to be labor intensive and to require very highly qualified personnel. Also, the national metrology laboratories, which in most countries develop and maintain the fundamental standards, develop and maintain the fundamental standards, are normally chartered and funded to perform that research, not to operate a high volume calibration service. The pressure calibration chain, which this paper discusses, was developed in this context with certain very specific objectives: 1. To accomplish, at a reasonable cost, the reliable transfer of the best reference values available directly to a large volume of commercial instrumentation with as little degradation as possible.. To offer a unified and coherent standard covering the range of pressure from less than 10 kpa to 500 MPa (1.5 to psi). 3. To create a standard that allows the multidirectional verification of effective area values and the application of statistical techniques to reduce uncertainties in effective are transfer. 4. To provide a system that assures that when aberrant or faulty measurements occur, their source can be identified and isolated quickly and systematically without having to refer to an outside source DH Instruments, Inc.

2 Though some of the fundamental concepts of the calibration chain such as the redundancy of standards to allow local verification of reference values are applicable to any laboratory intending to maintain the highest quality control standards, the calibration chain described in this paper is not meant for all pressure calibration laboratories. In fact, the only ones to have the volume of piston gauge calibrations and range and accuracy requirements that can justify such a chain are probably a couple of piston gauge manufacturers and NIST, and in principal NIST is not in business to run a high volume calibration service. Figure 1 Calibration Chain Three levels of the calibration chain are used to obtain absolute reference values from NIST and other sources by crossfloat and dimensional measurement. These levels are at Kn = 0.01, 0. and MPa/kg. The first pressure calibration chain was conceived, designed and implemented by Desgranges et Huot, a French manufacturer of piston gauges, in the mid 1970s to transfer values from the French national standards to their piston gauge and calibration service users. The calibration chain was not required by any external quality assurance requirements and presented a considerable cost for a start up company be we believed that the impact it would have on the quality of our measurements and thus on our ability to meet our commitment to our customers would make its implementation well worthwhile. STRUCTURE OF THE CALIBRATION CHAIN The core of the calibration chain consists of six pairs of piston-cylinders (See Figures 1 and ) with nominal mass to pressure conversion coefficients, Kn, of 0.01, 0., 0.5, 1, and 5 MPa/kg (rough 1.5, 9, 7.5, 145, 90 and 75 psi/kg). The operating ranges of the piston-cylinders are 0.01 to 1, 0. to 0, 0.5 to 50, 1 to 100, to 00 and 5 to 500 MPa (1.5 to 145, 9 to 900, 7.5 to 7 50, 145 to , 90 to and 75 to psi). Not represented here is the 10:1 multiplier used to extend the chain to psi DH Instruments, Inc. Page Figure Calibration Chain Also part of the calibration chain are an unlimited number of working standard piston-cylinders that are linked directly to the calibration chain core and used to transfer values from the chain to other piston gauges and instruments. The number and definition of the working standards can vary based upon the measurement systems that are being supported. For example, several working standards may be maintained in ranges that are especially in demand to support satellite labs or if additional standards are needed to leave the lab for on-site work. CALIBRATION CHAIN STANDARDS AND SUPPORT EQUIPMENT Mass The maintenance of the level of accuracy needed on mass (currently ± 10 ppm for the best commercial accuracy) is a relatively easy task compared to what is

3 necessary for piston-cylinder effective area. Also, the crossfloat technique used for calibration chain crossfloats effectively eliminates the contribution of systematic uncertainties on mass values in effective area transfers. The calibration chain includes several 100 kg mass sets made up of a series of masses whose values are in progression from 10 mg to 5 kg. All the masses of 100 g and above are made of 304L non-magnetic stainless steel and their accuracy tolerance. Mass standards of the same shape, material and nominal value as the masses used on the piston gauges are maintained and calibrated at regular intervals by NIST. These are used to calibrate other masses using electronic balances and traditional weighting by double substitution techniques. The mass standards are regularly intercompared amongst themselves to assure measurement integrity between NIST calibrations. of the pistons and cylinders allows a very small annular space to be used so that the improved response time and sensitivity offered by a low viscosity oil can be exploited over the complete 0. to 500 MPa range without encountering excessive drop rates. All pistons and cylinders are made of tungsten carbide except the Kn = 5 MPa/kg piston which is made of a special tool steel. All piston-cylinders are mounted in a common simple free deformation mounting post except the Kn = 0. MPa/kg that requires a slightly larger O-ring assembly to allow passage of its 8 mm piston through its cylinder which is the preferred configuration. Piston-Cylinders The piston-cylinders of the calibration chain are identical to those used in commercial models of DHI piston gauges. The lowest level of the calibration chain is made up of a pair of Kn = 0.01 MPa/kg piston-cylinders with nominal piston diameter of mm. These piston-cylinders are operated pneumatically. Gas is used as both the pressure transmitting fluid and as the piston-cylinder lubricant. Both piston and cylinder are mode of tungsten carbide. The piston, to reduces its mass, is tubular shaped. The piston-cylinder is mounted in a simple free deformation mounting post (See Figure 3) where no pressure is applied to the outside of the cylinder and both piston and cylinder are allowed to deform freely with pressure. Figure 3 Mounting System Detail With a few minor exceptions, the Kn = 0. to Kn = 5 MPa/kg piston-cylinders use identical technology (See Figure 4). All of the piston-cylinders are operated hydraulically using Di--Ethyl Hexyl Sebacate as the lubricating and pressure transmitting fluid. The near perfect geometry Figure 4 Mounting System Detail Though the calibration chain is used to support piston gauges with mounting systems other than free deformation, the simple free deformation mounting system is used throughout the chain due to its superior metrological performance. Thanks to the free deformation mounting system and the good geometry of the piston-cylinders, the calibration chain piston-cylinders have pressure deformation coefficients that are readily calculable using the property of materials and mechanical and elastic deformation theory. The deformation is linear with pressure and repeatable from run to run and unit to unit. Since improvements in piston-cylinder technology have made the use of free deformation mounting systems possible even at very high pressures without excessive drop rates, the free deformation system has replaced the re-entrant mounting system as the mounting system of choice for high performance piston gauges. The design of all the piston-cylinders is such that the mass load is applied directly to the measuring piston. Intermediary pistons are avoided because they can add extraneous, unquantifiable forces that interfere with the determination of pure piston-cylinder effective area ratio by crossfloat. The piston-cylinders work with identical 100 kg mass sets which can be interchanged, without limitation, onto all the piston-cylinders and piston gauges.. Page DH Instruments, Inc

4 Other Calibration Chain Equipment All of the calibration chain piston-cylinders are operated in commercially available Type 5000 piston gauges. These are quipped with a system for electronic detection of piston position and displacement. In a crossfloat, special dual piston position read out modules display a highly amplified indication of each piston s individual movement and a third display gives directly an amplified indication of the movement of the pistons relative one to another. Platinum resistance thermometers are mounted in all the mounting posts as close as possible to the piston-cylinder. The PRTs are calibrated with a triple point of water cell. At each increment of the crossfloat process, a programmable multimeter is used to read the PRT of each piston gauge in comparison with a 100 Ohm standard resistor. The PRTs and standard resistor are all of the four wire type. The complete crossfloat process is monitored by personal computers that read the PRTs, prompt the operators through the equipment manipulation and data entry of the crossfloat routine and reduce the data once the sequence is complete. CLOSING THE CALIBRATION CHAIN The objective in closing the calibration chain is to know as well as possible the ratio of the effective areas of its individual piston-cylinders and of each level with the level above and below it. Once the ratios are known, the chain can be used as a tool to transfer values vertically and horizontally. This allows the result of successful fundamental work in one part of the pressure range, for example improvements in effective are determination at low pressure by direct comparisons with manometers, to be transferred to and exploited in the rest of the range. Also, data from different parts of the pressure range that cannot be compared directly, for example from a controlled clearance gauge at the high end and manometer at the low end, can be checked for coherence through the chain. Finally, the chain s multiple and overlapping levels facilitate transfers to other piston gauges and instruments and optimize the transfer to DHI piston gauges since the transfer is one to one to piston-cylinders of the same nominal sizes and ranges. The Ratio Based Crossfloat The ratio of the effective areas of the piston-cylinders is determined experimentally by a hydraulic comparison called a crossfloat. The ratio based crossfloat used varies slightly from the traditional crossfloat because it is designed to arrive as directly as possible at the pure ratio of the two piston-cylinder effective areas. A comparison of two piston-cylinders A and B consists of a comparison of their effective areas, Ae, and is express as a ration K B/A. K B / A = AeB AeA Because effective area changes as a function of pressure, the comparison is made at two different pressures P 1 and P with corresponding mass loads of M 1 and M. These tow points are called first add and second add. Before and after each add, a base equilibrium is defined. The base equilibrium is performed at a low nominal mass value M 0. The base equilibrium effectively zeros the system so that the first and second adds will reflect the pure ratio of effective areas unaffected by extraneous effects such as differences in level between the two instruments or defects in piston mass adjustment. Each point is defined by creating a stable equilibrium with small masses after the nominal mass is loaded. Since all the piston-cylinders have nominal whole number effective are ratios, their nominal mass load ratios are also whole numbers at each point and only a small amount of mass, ε, is required on one piston or the other to arrive at equilibrium. At first and second add, the amount of trim mass, ε, is determined relative to the trim mass, ε 0, of the preceding and following base equilibria by averaging. An equilibrium is considered to have been achieved when a small mass, µ, placed on one load will bread the equilibrium in one direction and µ, subsequently placed on the other load, breaks the equilibrium in the other direction. In most cases, the value of m is less than 1 ppm of the load. Additional manipulations are performed at each add to reduce the contribution of mass uncertainty to the uncertainty on the ratio, K B/A. The main mass load is exchanged between the instruments and another equilibrium is created. In the case where the pistoncylinders being compared do not have 1:1 nominal effective areas, more permutations are required. Where the ratio is 1:, one piston will have two units of mass loaded for every unit loaded on the other. Three equilibria must be made in order for each unit of mass to be loaded at least once on each instrument. The first base - first add - second base - second add - third base sequence is called a run. Following the first run, a thorough data analysis is done to look for anomalies, particularly excessive disagreement between the theoretical difference between the two piston-cylinders deformation coefficients and the measured difference found in the run DH Instruments, Inc. Page 4

5 A second complete run is performed. Whenever possible, the piston-cylinders are swapped in their mounting posts between the first and second run. The second run is used to reduce possible systematic effects of the test system on the effective area ratio determination. After the second run, the data is analyzed and the relative difference between the ratio determined in the first run and the ratio determined in the second run is examined. If the difference is inside of a defined limit, the data from the two runs is averaged and the result is assigned as the piston-cylinder effective area ratio. If the difference exceeds the limit, the cause must be identified and the difference between runs brought inside the limits before the crossfloat can be considered completed and an effective area ratio assigned. Checking The Loops The relationship between two contiguous piston-cylinders in the calibration chain is called a link. The group of four piston-cylinders that makes up two contiguous levels is called a loop (See Figure 5). Figure 5 Loop The values obtained for each link by crossfloat are checked against values determined indirectly by calculation. For example, the value of K A1/B1 determined by the direct comparison of the two piston-cylinders can be compared to the value calculated through the loop as: K A1/B1 = (K A1/A )(K A/B1 ) And the same relationship can be verified as: K A1/B1 = (K A1/B )(K B/B1 ) Comparing values measured directly with values obtained indirectly from several directions allows defective links to be identified and corrected and establishes the overall coherence of the chain with a very high level of confidence. The looping technique is used systematically in closing the calibration chain. Also, between calibration chain maintenance cycles, when measurements using links between the chain and a working piston gauge under test appear abnormal, the looping techniques is used as a rapid means of isolating the source of the problem by isolating the rest of the chain. This quickly and definitively isolates an aberrant measurement. The Kn = 0.01 to 0. MPa/kg Loop The loop consisting of the Kn = 0.01 and 0. MPa/kg piston-cylinders is different from the other loops in that there is a 0:1 ratio between the levels and that one level operates in gas and the other operates in oil. The 0:1 comparison is made like any other nominal whole number ratio comparison but is relatively time consuming due to the number of permutations requires so that all of the mass will have been loaded on both pistons. The overlap between the two ranges is limited but this is not much of a handicap since the deformation coefficient of the piston-cylinders is very small and the operating pressures are low. To directly compare an oil operated piston-cylinder with a gas operated piston-cylinder, at some point gas and oil have to be interfaced. To accomplish this, a visible level interface is used in which gas and oil come in direct contact at a reference point in a vessel with a sight glass. A large amount of work with the visible level interface has established that an experienced operator can set and maintain the interface point to within about ± 0.1 mm which at the 1 MPa (150 psi) full scale pressure of the crossfloat represents about ± 1 ppm. The results obtained in the closing of the 0.01 to 0. MPa loop, on which more is said below, are excellent despite the high nominal effective are ratio and the use of the oil/gas interface. Some might have expected deterioration in performance of the gas operated piston-cylinders due to the presence of oil in the system but absolutely none was observed indicating that the problems of oil migration in this type of application are probably more myth than reality. RATIO DATA REDUCTION The result if closing the calibration chain is the attribution of effective area ratio values to the links of the calibration chain and the assignment of uncertainties to those values. The ratios will then be used for the vertical and horizontal transfer of reference values up, down and through the chain. For convenience and consistency, the ratio values are usually given at null pressure. In a nominal 1:1 ratio, the null pressure ratio, K 0, is calculated back using the deformation coefficient, λ, from the ratio obtained at first add, K 1. First add is used rather than second add to minimize the effect of the uncertainty on λ on the K 0 determination. In a nominal ratio other than 1:1, the null pressure ratio is calculated back from second add since first add may be as little as 1/5 of the range of the higher pressure piston-cylinder.. Page DH Instruments, Inc

6 The calculation of K 0 from K 1 is performed as follows: K 0 = K 1 [1-(λ B -λ A )P 1 ] To calculate from K, K is substituted for K 1 and P is substituted for P 1. The values used for λ are the theoretical deformation coefficients of the piston-cylinders. The reason for this as well as the uncertainties involved are explained below. RATIO UNCERTAINTY ANALYSIS Uncertainty is assigned to the ratios following the traditional uncertainty analysis techniques that separates uncertainties into systematic and random categories and then combines the variables by root sum squaring those that are independent one from the other. Random Uncertainties (Repeatability) From experience with a very large population of intercomparisons, we know that the single standard deviation of the typical complete crossfloat procedure can be held to less than ppm. Therefore, to assure that this value is not exceeded, we limit the maximum acceptable disagreement of K 0 between two runs of a complete crossfloat procedure to less than 6 ppm. Systematic Uncertainties The sources of systematic uncertainty include main mass values, ε mass values, piston-cylinder sensitivity, piston-cylinder temperature measurement, thermal expansivity of the piston-cylinder, pressure deformation of the piston-cylinder, piston mass, surface tension, fluid heads, piston verticality and mounting system inconsistencies. A. Mass values and piston-cylinder sensitivity As explained above, the nominal ratios between piston-cylinder effective areas are whole numbers. The main masses refer to the mass loads in whole numbers of kilograms that are used to apply the nominal load at each increment. The small amount of mass that is then required to establish equilibirum between the pistons is referred to as ε. At each increment, the main masses are permutated and a new equilibrium and ε are established until all the main masses have been loaded on both pistons. The average value of ε plus the nominal mass load is used to calculate the ratio. For example, in a :1 comparisons, K 1 is calculated following: K = 1 ( M1 + ε1,1 ) + ( M + ε1, ) + ( M3 + ε1,3 ) 1 ε1,1 + ε1, + ε1,3 = + ( M + ) + ( + ) + ( + ) ( + + ) 3 M M3 M1 M1 M M1 M M3 Where: K1 = ratio of effective areas at first add M1, M, M3 = main mass units in :1comparison ε I,j = trim mass used to establish equilibrium at add i and permutation j This technique eliminates the influence of the uncertainty on the main masses in the determination of K 1 leaving only the very small uncertainly on the m values. The masses used to establish the m values have absolute uncertainty of less than g which is negligible. The minimum sensitivity allowed at the base and first or second add equilibrium is 0.0 g. The uncertainty on the determination of K 1 due to uncertainty on mass and sensitivity represents less than 1 ppm on typical first add load of 50 kg. B. Piston-cylinder temperature measurement and thermal compensation All pistons and cylinders are made of tungsten carbide except the 5 MPa/kg piston which is made of steel. The linear thermal expansivity of the tungsten carbide used, a, is 4.5 ppm/ C. The value with a steel piston is slightly larger. The uncertainty on the thermal coefficient of expansion is estimated at ± 10 %. The maximum difference in temperature observed between two piston-cylinders in a crossfloat is less than 1 C which leads to a maximum uncertainty of 0.1 (ac + ap) which is less than 1 ppm. Piston-cylinder temperatures are monitored by platinum resistance thermometers built-in to the mounting posts. The accuracy of the PRTs is ± 0.1 C. The tests are run in a temperature controlled environment in which the units have been allowed to stabilize thermally prior to the measurements for at least four hours. The maximum uncertainty due to temperature measurement is 0.1 (αc + αp) which is less than 1 ppm. It should be noted that the swapping piston-cylinders between the two runs cancels out the possible systematic uncertainties on temperature measurements. C. Pressure deformation coefficient As mentioned above, all the piston-cylinders are mounted in simple free deformation mounting posts. This results in linear and repeatable deformation with pressure. It also makes it possible to predict deformation using well known properties of materials theory. the linearity and repeatability of the deformation coefficients arrived at by calculation has been confirmed by comparison with measured deformation values form national standard controlled clearance gauges in the United States, France and Japan DH Instruments, Inc. Page 6

7 The piston-cylinder used for these comparisons is Kn = MPa/kg No with a range of to 00 MPa (90 to psi). For all the levels of the calibration chain and all other piston-cylinders, except the Kn = 5 MPa/kg level, the values used for the deformation are the theoretical values. The crossfloat procedure, rather than having to measure and assign a unique value of deformation to each piston-cylinder agrees with its predicted deformation. When measured values and predicted values disagree excessively, it is assumed that either the piston-cylinder or some aspect of the test procedure is faulty. The very wide range over which the Kn = 5 MPa/kg piston-cylinders can be compared allows a measured value of deformation inside the tolerance on the theoretical value to be determined with lower uncertainty than the uncertainty on the theoretical value. The uncertainty assigned to the value of pressure deformation is ± 10 % on piston-cylinders whose piston is tungsten carbide and uncertainty is based on the uncertainties associated with the calculation of theoretical deformation including possible inconsistencies in materials and from the uncertainties on the deformation values reported by national laboratories. For each link, the difference in the theoretical deformation coefficients, λ th, can be used to predict the evolution of the effective area ratio with pressure. For example, for two nominally identical piston-cylinders, λ th equals zero and the effective area ratio should be the same at all pressures. In the crossfloat procedure, a comparison of the ratio found at first add and the ratio found at second add results in a measured value of the difference in the deformation coefficients, λ meas. The magnitude of the difference between λ th and λ meas is used as an indicator of the quality of the piston-cylinders, the test system and the crossfloat procedure. This difference is not allowed to exceed 10 % for tungsten pistons and 0 % for steel pistons. There is no contribution of the uncertainty on the deformation coefficient λ to the uncertainty on the transfer of effective area because K 1 and K are a direct measurement of the true ratios of the effective areas of the piston-cylinders at first and second add pressures. However, λ will be used to determine the effective are of the piston-cylinder over the rest of its range and the uncertainty on λ results in additional uncertainty on effective area at points K 1 and K. Figure 6 illustrates the effect of λ on the uncertainty on effective area as you move up the chain. In the transfer of effective area from level N to level N+1, the ratio K is used. The uncertainty on the effective area of the N+1 level piston can be the root sum squared with uncertainty on the K ratio to arrive at the uncertainty on the effective area of the N+1 level piston at pressure P. However, the transfer to the N+ level from the N+1 level will occur at full pressure, P 3, of the N+1 level. The effective area of the N+1 level piston-cylinder at pressure P 3 is determined using λ. The uncertainty on the N+1 level piston-cylinder at pressure P 3 will be the uncertainty at pressure P plus the uncertainty on λ times (P 3 - P ). the uncertainty due to l, UAελP 3, can be expressed as: UAeλ P3 = ( 0.1λ )( P - P ) And the total uncertainty on the level N+1 pistoncylinder effective area, UAe P3, can be expressed as: UAe P3 = [( UAe ) + ( UAeλ ) ] 1/ P for piston-cylinder levels up to MPa/kg where λ th is used and: UAe P3 = UAe P 3 P3 + UAeλ for the transfer to the Kn = 5 MPa/kg level where λ meas is used. Figure 6 Effective Area Transfer D. Piston mass, surface tension, fluid heads Piston mass, surface tension and fluid heads are all force effects that are nulled out in the base equilibria of the crossfloat procedure. The uncertainty on these values is therefore considered insignificant in assessing the global uncertainty on the K 1 and K ratios. E. Piston verticality, mounting system inconsistencies In the crossfloat procedure, after the first run, the piston-cylinders are swapped in the piston gauges and a second run is performed. The results of the two runs are averaged which eliminates effects of piston verticality and mounting system inconsistencies. Before averaging, however, the disagreement between the two runs is compared to pre-established limits that it may not exceed. P3. Page DH Instruments, Inc

8 Uncertainty on the Ratios Uncertainties are assigned to the ratios by root sum squaring the independent variables and multiplying the result by three to establish a three sigma level of confidence. The result is uncertainties on K 1 and K that range from 6.6 to 7 ppm. This includes the Kn = 0.01 MPa/kg to Kn = 0. MPa/kg despite the potential increased uncertainties due to the use of an oil to air interface and to the inability to permutate piston-cylinders in the piston gauges. The agreement between runs in the crossfloat procedure was better than ppm and the loops verified a maximum link error of less than 6 ppm. OBTAINING AND TRANSFERRING REFERENCE VALUES Obtaining Reference Values Having established the calibration chain links and loops, the chain can be used to transfer reference values. These values are obtained through three calibration chain piston-cylinders: Kn = 0.01 MPa/kg No. 116, Kn = 0. MPa/kg No. 51 and Kn = MPa/kg No Our current Quality Assurance Program requires values be obtained from NIST every two years. Our 1988 February paper, Increasing the Accuracy of Pressure Measurements Through Improved Effective Area Determination described the assignment of an effective are value to No. 116 from repeated NIST dimensional measurements and verification by intercomparison with Japanese and French national pressure standards. The result was an effective are value with an estimated uncertainty of ± 14.4 ppm. Recently, the uncertainties available from the NIST pressure group on effective area determination by crossfloat with a piston gauge in the range of No. 116 were significantly improved. In February 1989, No. 116 was intercompared with the NIST pressure groups newly characterized piston gauges. They estimated an uncertainty of 1 ppm on a value of effective area at 100 kpa (14.5 psi) that agrees within less than 6 ppm with the value that was determined from other values obtained for No. 116 (See Table 1). These new results lend further support to the work on which we reported last year and increase our confidence in the use of No. 116 as the source of Ae for the calibration chain. Table 1 Ae 0 Values of Piston-Cylinder No. 116 Kn = MPa/kg piston-cylinder No. 063 is used as the source of measured values for deformation under pressure. As explained above, it is more exact to say that it used to confirm the theoretical deformation coefficients that we use agree with the measured values from NIST and others. Until 1985, when the 35 mm tungsten carbide piston-cylinders were introduced, Kn = 0. MPa/kg piston-cylinder No. 51 was used as the source of Ae. Though it no longer serves that purpose, we find it useful to continue sending it to NIST every two years. Having outside values for both No. 116 and No. 51 is a further means of checking the coherence of the critical 0.01 MPa to 0. MPa to 0.5 MPa loops. Also, No. 51 is a good intermediary point between No. 116 and No Table shows the value of No. 51 as determined by transfer from No. 116 and as reported by NIST in New NIST figures for No. 51 will be obtained in July Table Ae 0 Values of Piston-Cylinder No. 51 Assigning Values and Uncertainties to the Calibration Chain Piston-Cylinders Once the links and the loops of the calibration chain have been established, they can be used to transfer values of effective area from piston-cylinder No. 116 upwards. The formulae used for the transfer from a known level A to an unknown level B are: 1 AeB1= 1+K B/B1 K B1/A1 Ae +K A1 B1/A +AeA + K K B/A1 B/B1 Ae +K A1 B/A +AeA DH Instruments, Inc. Page 8

9 And: Table 3 Calibration Chain Values Ae B = K B/B1 Ae B1 Where: Ae = Effective area of the subscripted piston-cylinder A1,A = Piston-cylinders at known level B1,B = Piston-cylinders at unknown level K = Ratio of the subscripted piston-cylinders These equations use the weighted mean determination method because greater confidence is placed in the 1:1 transfer from B 1 to B and all other possible paths, such as B 1 to A 1 to B, should reflect this. For each piston-cylinder, the value of pressure deformation is also checked for agreement with the theoretical value. The uncertainty on the effective area of piston-cylinder B at the pressure of first or second add is arrived at by root sum squaring the uncertainty on the reference, A, and the uncertainty on the transfer, K. Then, the uncertainty due to λ, is added. As explained above, this uncertainty is 10 or 0 % (depending upon, if the piston is tungsten carbide or steel) of the value of λ times the range of pressure over which the effective area is calculated using λ. Given the 1: and :5 nominal ratios of the links, the uncertainty on the effective area, UAe λ, due to λ is either: or UAe UAe λ = ( 10% λ)( FullscaleP- HalfscaleP) ( 1 : ) λ = ( 10% λ)( FullscaleP- 0.4scaleP) ( : 5) The effective area of a piston-cylinder, Ae, over its operating ranges is represented using Ae0 and λ. though technically the uncertainty on Ae is lower at the transfer point K 1 or K and increases due to λ as you go up or down in pressure, we eport Ae0 and λ and assign a global uncertainty to the value of Ae. The uncertainty assigned is the maximum uncertainty on Ae which is the uncertainty at full pressure. Table 3 identifies the calibration chain piston-cylinders and gives their operating range, λ and maximum uncertainty on effective area at any point in the range. USING THE CALIBRATION CHAIN Working standards are connected directly to the core of the calibration chain in the same manner that the calibration chain piston-cylinders are interconnected. The working standards are used to perform day to day calibrations and include duplicates of most of the calibration chain elements as well as liquid lubricated gas operated piston-cylinders and piston-cylinders whose Kn are in psi. Calibration of DHI Piston-Cylinders The Ae 0 and λ of DHI piston-cylinders used in a re-entrant mounting system, for example, gas operated, liquid lubricated piston-cylinders, Dλ meas is used to find a measured value of l and the measured value is assigned. Once Ae 0 and λ have been assigned, a verification of operating characteristics (VOC) is performed. The objective of the VOC is an independent check in an actual pressure measurement situation of the values that have been assigned. A working standard of the calibration chain is used to apply pressure to the piston-cylinder that has just been calibrated. A minimum of four points, normally six, including that defined by a 1 kg load and full scale, are verified. At each point, the mass load is adjusted until an equilibrium is established. The traditional pressure equation is used to calculate the pressure defined by both the piston-cylinder under test and the working standard. The uncertainty on the pressure defined by the standard and the test instrument must be less than the tolerance on the test instrument or the VOC is considered failed and the piston-cylinder and its calibration cannot be released. To the extent it is possible, the VOC is run using the same piston gauge and mass set that the test piston-cylinder normally work with. Other Calibrations The calibration chain is the foundation of the DHI pressure calibration service which, in addition to DHI piston gauges, calibrates other makes of high accuracy piston gauges and deadweight testers as well as other types of pressure measuring and controlling devices.. Page DH Instruments, Inc

10 CONCLUSION The objective of this paper has been to give a good overall understanding of the principals of the calibration chain and how it is used as a tool for the maintenance of reference values of effective area and pressure. In so doing we have tried to avoid overloading the reader with technical information and have summarized at certain points when we felt that too much detail would make the paper lengthier than necessary and would not contribute materially to an understanding of the chain. If, however, you would like more information on a specific technical point, please do not hesitate to contact the authors. As stated at the outset of this paper, we are not suggesting that the calibration chain is for everyone. The equipment costs alone could into be justified by most labs not to mention the minimum of man hours required just to perform the crossfloats necessary for the biennial chain closing process. In our application, we have found it to be a worthwhile investment for several reasons that relate to our large volume of high accuracy calibration work and the very wide range of pressure we cover. The first is, that in our day to day operations, we save time compared to traditional techniques, particularly in the highest accuracy work. These time savings alone make up for the time expended in calibration chain maintenance. The second is that the chain gives us a high degree of metrological independence. We are able to independently track precisely the evolution of our standards over time and quickly and definitively identify aberrant measurements internally or aberrant values coming from outside. Third, the chain provides us with a level of confidence in our measurements that we do not believe we could match with traditional pressure standard maintenance techniques. Improvements in the calibration chain can be anticipated for the future with improvements in crossfloating techniques, in particular with the use of automation and with improvements in the performance of piston-cylinders and the systems in which they are used. However, at this time, without further improvement, the calibration chain could effectively exploit improved reference values. On-going work at NIST and other laboratories is expected to provide those improvements. With the calibration chain, the tool necessary to assure that the improvements will be disseminated efficiently, is in place. REFERENCES [1] Cross, J.L., "Reduction of Data for Piston Gauge Pressure Measurements", NBS Monograph 65, 1963 June. [] Dadson, R.S., Lewis, S.L., Peggs, G.N., "The Pressure Balance, Monograph of the National Physical Laboratory, U.K., 198. [3] Delajoud, P., Girard, M., Increasing the Accuracy of Pressure Measurements Through Improved Piston Gauge Effective Area Determination, Proceedings of the 33rd International Instrumentation Symposium, Albuquerque, NM, 1988 May. [4] Huot, A., Delajoud, P., Methodes et Moyens de Transfert de Pressions Comprises Entre 0.1 at MPa. (Methods and Means for Transfer of Pressure in the 0.1 to MPa Range), BNM Bulletin, 1977 April DH Instruments, Inc. Page 10