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Development of a high-accuracy 500 kg mass comparator for improved weight calibration capability
Measurement 95 (2017) 418–423
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Development of a high-accuracy 500 kg mass comparator for improved weight calibration capability Jianxin Sun ⇑, Masaaki Ueki, Kazunaga Ueda National Metrology Institute of Japan (NMIJ), National Institute of Advanced Industrial Science and Technology (AIST), Japan
a r t i c l e
i n f o
Article history: Received 21 April 2016 Received in revised form 29 July 2016 Accepted 12 October 2016 Available online 13 October 2016 Keywords: Large weight Mass comparator Knife-edge
a b s t r a c t A high-accuracy 500 kg mass comparator with a readability of 0.01 g has been developed at the NMIJ/AIST in order to improve calibration capabilities for large weights from 100 kg to 500 kg. This newly developed mass comparator uses a high-accuracy electronic balance as the sensor and a high-sensitivity two-stage lever system with knife-edges to expand the maximum weighing capacity. This design made it possible to reduce the calibration uncertainties of large weights by 34–45%. This paper reports the basic design of the mass comparator and the improved results for large weight calibrations at the NMIJ. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction
2. Sources of uncertainty in large weight calibrations
The reliabilities of mass measurements are ensured by their traceability to the national mass metrology standards, and also influence the measurement reliabilities of mass-related quantities such as force, pressure, torque, flow, density, or amount of substance. The National Metrology Institute of Japan (NMIJ), a division of the National Institute of Advanced Industrial Science and Technology (AIST), promotes the improvement of national mass standards and traceability systems for large masses in the range from 50 kg to 5000 kg, in response to advancements in various metrological activities related to these quantities. Traceability to the mass standards is realized by the calibration of weights using mass comparators. The performance of the mass comparator is the dominant source of uncertainty in the weight calibrations, especially for large masses. For weight calibrations beyond 2000 kg, the NMIJ developed a 5000 kg high-accuracy mass comparator superior to the best commercially available comparators, and was thereby able to improve the calibration capability for weights from 2000 kg to 5000 kg by more than two times [1]. In a series of further improvements to the national standards for large masses, the NMIJ has developed a high-accuracy 500 kg mass comparator in order to reduce the uncertainty in the calibration of weights of 500 kg or less. This paper describes the development of this new comparator and highlights its improved calibration capabilities.
For the weight calibration of large masses, the conventional mass is generally used. This is obtained via the measurement of the mass difference between the calibration weight and a reference weight of known mass performed using a mass comparator [2]. The following is a summary of the calculation of the mass difference and its uncertainty given in the international recommendation [2]. Mass comparisons are made between the reference and calibration weights, denoted by mcr and mct respectively, by alternately loading and unloading them n times onto a mass comparator. The mass difference in the ith mass comparison, Dmc ; is given by Eqs. (1) and (2).
⇑ Corresponding author. E-mail address: [email protected] (J. Sun). http://dx.doi.org/10.1016/j.measurement.2016.10.036 0263-2241/Ó 2016 Elsevier Ltd. All rights reserved.
Dmc ¼ mct mcr ;
ð1Þ
Dmci ¼ DIi þ mcr C i ;
ð2Þ
where
C i ¼ ðqai q0 Þ
1
qt
1
qr
:
ð3Þ
Here, I is the indicator value of the comparator, mcr C i is the correction term for air buoyancy, mcr is the conventional mass of the reference weight, qai is the air density, q0 is the reference air density of 1.2 kg/m3, and qt and qr are the densities of the calibration and reference weights, respectively. The conventional mass of the calibration weight, mct , is then calculated using Eq. (4).
mct ¼ mcr þ Dmc ;
ð4Þ
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where Dmc is the mean value of the observed conventional mass difference from n repeated measurements. The calibration uncertainty for large weights has four significant sources, as described below. The standard uncertainty in the mass comparison process, uw ðDmc Þ, is given in terms of the standard deviation sðDmc Þ and the number n of repeated mass comparisons by Eqs. (5) and (6).
sðDmc Þ pffiffiffi ; n
uw ðDmc Þ ¼
s2 ðDmc Þ ¼
ð5Þ
n 2 1 X Dmci Dmc : n 1 i¼1
ð6Þ
If only a few mass comparisons are made, the estimate of sðDmc Þ can be unreliable. A pooled estimate, using earlier mass comparisons made under similar conditions, should be used. The standard uncertainty in the reference weight, uðmcr Þ, is given by Eq. (7).
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 U uðmcr Þ ¼ þ u2inst ðmcr Þ: k
ð7Þ
Here, U is the expanded uncertainty in the calibration value of the reference weight, k is the coverage factor, and uinst ðmcr Þ is the uncertainty due to the instability of the mass of the reference weight, as estimated from variations in the mass observed during multiple past calibrations. The standard uncertainty in the air-buoyancy correction, ub ; is given by Eq. (8).
2 ðq qt Þ u2 ðqt Þ u2b ¼ mcr r uðqa Þ þ ½mcr ðqa q0 Þ2 4
qr qt
þ
m2cr ð
qa q0 Þ½ðqa q0 Þ 2ðqal q0 Þ
qt
u2 ðqr Þ
q4r
:
ð8Þ
Here, qal is the air density from the previous calibration of the reference weight against a reference standard weight of higher rank, uðqa Þ is the standard uncertainty in the air density, and uðqt Þ and uðqr Þ are the uncertainties in the densities of the calibration and reference weights, respectively. The standard uncertainty of the mass comparator, uba , is given by Eq. (9).
uba ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u2s þ u2d þ u2E þ u2ma :
ð9Þ
Here, us , ud , and uE are the standard uncertainties in the sensitivity, the readability, and the off-centred loading of the mass comparator, respectively, and uma is the standard uncertainty in the weight caused by its magnetic properties. The sensitivity of the mass comparator can be evaluated using a sensitivity weight of mass ms and uncertainty uðms Þ; the standard uncertainty due to the sensitivity, us ; is then given by Eq. (10).
u2s
¼ ðDmc Þ
2
! u2 ðms Þ u2 ðDIs Þ : þ m2s DI2s
ð10Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Uðmct Þ ¼ kuc ðmct Þ ¼ k u2w ðDmc Þ þ u2 ðmcr Þ þ u2b þ u2ba :
ð12Þ
In the case where the standard uncertainty in the mass comparison process was evaluated using a pooled standard deviation having a sufficiently large degree of freedom, the coverage factor, k, can be taken as two. Using the national mass standards at the NMIJ for 50–500 kg, two 50 kg weights were nominated as reference weights and calibrated via mass comparison with five 10 kg reference weights which are traceable to the Japanese kilogram prototype. This was done using an AX64004 mass comparator (Mettler-Toledo International Inc.) with a maximum weighing capacity of 64 kg and a readability of 0.1 mg. The expanded uncertainty in these calibrations is 3.5 mg with a coverage factor of k = 2, which corresponds to a level of confidence of 95%. Next, five 100 kg reference weights were calibrated using these two 50 kg reference weights (as shown in Fig. 1); 200 kg and 500 kg reference weights are then calibrated using combinations of the 100 kg reference weights. This group of reference weights, ranging from 50 kg to 500 kg, is used for the calibration of weights in general use. A 100 kg mass comparator with a readability of 0.05 g and a 500 kg mass comparator with a readability of 0.1 g, both of which are commercially available, are currently used for 100 kg weight calibrations and for 200–500 kg weight calibrations, respectively. The standard deviations in the mass comparisons have been estimated to be 0.12 g for 100 kg, 0.26 g for 200 kg, and 0.46 g for 500 kg. Table 1 shows the readability and standard deviation values for commercially available, ‘state-of-the-art’ mass comparators taken from the latest manufacturer’s catalogue [3]. These standard deviation values are then used to evaluate the standard uncertainties in the mass comparison process to show the best values for the weight calibration uncertainties that could be obtained by using the commercially available mass comparators. However, the uncertainty values from sources other than the mass comparison process were evaluated based on the actual calibrations of the reference weights performed with these current mass comparators at the NMIJ, evaluated over six repeated measurements. Details of the uncertainty estimation are discussed later in Section 5; however, Table 2 summarizes the results for the standard uncertainties in the mass comparison process, uw ðDmc Þ, standard uncertainties in the readability, ud , and expanded uncertainties of the calibrations, Uðmct Þ, with a coverage factor of k = 2. It can be seen that the expanded uncertainties depend primarily on the uncertainties in the mass comparison process and in the readabilities of the mass comparators. In addition, it should be noted that these two uncertainty sources also had a significant influence on the uncertainties in the mass values of the 200 kg and 500 kg reference weights. Consequently, it is concluded that a higher-accuracy mass comparator is required to improve the mass comparison capabilities and reduce the uncertainty in large weight calibrations.
50 kg U = 3.5 mg (k = 2) S_No.1 to S_No.2
The uncertainty in the readability d of the comparator, ud ; is given by Eq. (11).
pffiffiffi d=2 pffiffiffi 2: 3
100 kg ð11Þ
S_No.1 to S_No.5
The combined standard uncertainty for a large weight calibration, uc ðmct Þ, is thus obtained from the uncertainty components mentioned above. Its expanded uncertainty Uðmct Þ is determined by Eq. (12), using a coverage factor of k with a level of confidence of 95%.
200 kg and 500 kg
ud ¼
Fig. 1. Flow chart for the calibration of reference weights from 100 kg to 500 kg.
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Table 1 Readabilities and standard deviations of current, commercially available mass comparators [3]. Nominal value
Readability d
Standard deviation sðDmc Þ
100 kg 200 kg 500 kg
0.05 g 0.1 g 0.1 g
0.102 g 0.14 g 0.19 g
Load
Sources of uncertainty Mass comparison process, uw ðDmc Þ Reference weight, uðmcr Þ Air buoyancy correction, ub Mass comparator, uba Coverage factor k Expanded uncertainty Uðmct Þ
100 kg 0.0416 g
200 kg 0.057 g
500 kg 0.078 g
0.0035 g 0.0008 g 0.0204 g 2 0.093 g
0.093 g 0.002 g 0.041 g 2 0.24 g
0.233 g 0.004 g 0.041 g 2 0.50 g
3. Development of a high-accuracy 500 kg mass comparator A 500 kg high-accuracy mass comparator, aimed at reducing the standard uncertainty in the mass comparison process and the readability as described above, is described in this work. A high-accuracy electronic balance with a small weighing capacity acts as the sensor for the mass comparator. The weighing capacity is magnified to 500 kg by means of a lever mechanism with a magnification ratio of 10, chosen to optimize the performance of the balance while maintaining a smaller ratio. In order for the readability of the mass comparator to be less than 20 mg, that of the electronic balance must be less than 2 mg. A CCE60K3 (Sartorius AG) electronic balance satisfying these requirements is used. This balance has been modified by the manufacturer to have a readability of 1 mg, at the authors’ request, in anticipation of the possible expansion of the capability of the comparator in the future. The specifications of the electronic balance [4] are shown in Table 3. The dimensions of the mass comparator are within 100 cm in width, 100 cm in depth, and 35 cm in height, taking into account the limited space in the calibration room at the NMIJ available for placing the mass comparator and handling the weights. The lever mechanism for the magnification of the weighing capacity makes use of a system of second-order levers (Fig. 2). When a large load is applied to the lever at the point of load, a smaller balancing force generated by the sensor is applied at the point of force in order to maintain equilibrium. The mass comparator is constructed such that the lever mechanism can be exchanged easily to increase the magnification ratio from 10 to 20, to allow for the possible expansion of the weighing capacity from 500 kg to 1000 kg in the future. In addition, we desire that the distance between the fulcrum and the load point be as long as possible in order to attain high sensitivity and reduce the error arising from small changes in the lever ratio. As shown in Fig. 3, the lever mechanism consists of two lever systems combined at right angles to each other. This arrangement allows the
Table 3 Specifications of CCE60K3 [4]. Max. weighing capacity Readability Repeatability Weighing pan size (W D) Weighing system dimension (W D H) a
Improved from 2 mg by the manufacturer.
Fig. 2. Second-order lever.
full dimensions of the mass comparator to be utilized effectively in order to attain higher accuracy mass measurements. Four fulcrums of the first lever and two fulcrums of the second lever are fixed on the base plate of the mass comparator. The weighing pan is supported at the four load points of the first lever. A weight load is applied to these load points and transmitted through two force points of the first lever to the two load points of the second lever. The load is then applied to the sensor, i.e. the electronic balance, through the force points of the second lever, and the mass is measured. The equilibrium state of the lever mechanism is maintained by the compensating force from the electronic balance. The magnification ratios of the first and second levers are set to 4.63 and 2.16, respectively, in order to obtain an overall ratio of 10 for the combined lever mechanism. To increase the ratio to 20, only the second lever need be exchanged, for a lever with a ratio of 4.32. The distance between the fulcrum and the load point for the second lever changes from 235 mm to 82 mm; all other dimensional parameters are the same. Two kinds of fulcrum bearings are equipped on the base plate, allowing for the easy exchange of the second lever. The fulcrums, the points of load, and the force of the levers used for large mass measurements are usually made using two types of
Fulcrum
Point of force
Point of load Sensor
L 2b
L 2a2 L 2a1
1st lever
L 1a 61 kg 1 mga 7 mg 40 cm 30 cm 40 cm 30 cm 12 cm
Force
Point of load
Fulcrum Table 2 Uncertainties in the calibrations of the reference weights using current, commercially available mass comparators over six repeated comparisons.
Point of force
2nd lever Fulcrum
L 1b
L 1a = 82 mm, L 1b = 298 mm L 2a1 = 235 mm, L 2a2 = 82 mm, L 2b = 272 mm Fig. 3. Schematic diagram of the lever mechanism.
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J. Sun et al. / Measurement 95 (2017) 418–423
bearings: knife-edge bearings and flexible bearings. Each type has both strong and weak points, in terms of the stability of the lever ratio, ease of manufacturing and installation, sensitivity, durability against large loads, ease of combining multiple levers, and so on. Good repeatability can be achieved with the flexible bearings as the fulcrums are fixed, and thus changes in the lever ratios are suppressed; this effect is most prominent when a thin flexible bearing is utilized. Flexible bearings are also easy to manufacture and install. On the other hand, they have a high risk of breaking off, especially under heavy loads. In contrast, the knife-edge bearings exhibit high sensitivity with little risk of breaking off under large loads. In addition, multiple levers can be easily and compactly connected to each other, as with the right-angle linkage. However, they have the disadvantage that the lever ratio may show large variations, if the equilibrium state of the lever mechanism is broken and the knife-edge is detached from its bearing during loading and unloading. Knife-edge bearings also require careful handling, and skilled technicians are required in their production, fine adjustment, and maintenance. Taking the respective characteristics of these two kinds of bearings into account, we design the fulcrums of the levers and the load points of the first lever supporting the weighing pan to use knifeedge bearings as large loads are applied at these points. For the right-angle connecting link between the force points of the first lever and the load points of the second, knife-edge bearings are also used. On the other hand, a flexible bearing is used for the connecting link between the electronic balance and the force point of the second lever, because the loads being applied here are the smallest, and variations in the position of the force point due to any shock arising from loading or unloading of the weights should be avoided. This lever mechanism is kept in equilibrium by the compensating force from the electronic balance, even during the loading or unloading of weights. The fulcrums, the points of load, and the force of the knife-edge bearings are in continuous contact. We thereby achieve high sensitivity in the lever mechanism, and the fulcrums are kept fixed. A photograph of the lever mechanism is shown in Fig. 4. The levers themselves are strongly constructed from SS400 structural steel plates of either 12 mm or 16 mm in depth and 90 mm or 75 mm in width, firmly fixed in parallel with a separation of 54 mm or 32 mm, so that the influence of any bending of the levers is negligible. A photograph of the knife-edge bearing used for the fulcrum of the first lever is shown in Fig. 5. The knife-edges are all V–shaped, with an angle of 75°, so as to attain both high sensitivity and high durability. Their bearings are also V-shaped, with a notch angle of 120°. The knife-edges and bearings are made of a
1st lever
2nd lever
Fig. 5. Knife-edge and knife-edge bearing used as the fulcrum of the first lever.
2nd lever CCE60K3
Flexur
Fig. 6. Connection between the second lever and the electronic balance CCE60K3.
super hard alloy with a hardness of HRA 92.0, as well as high strength and good wear resistivity. The connecting link between the force point of the second lever and the electronic balance is uses a flexible bearing in the form of a flexible spring, as shown in Fig. 6. The spring is made of a stainless steel band SUS304-CSP 3/4H of 0.2 mm in thickness and 18 mm in width. In order to connect to the weighing pan of the electronic balance, the upper surface of the pan is covered by a 6.5 mm thick aluminium alloy plate. In addition, two hexagonal supporting pillars with a two-face width of 17 mm are fixed to the pan surface. Preliminary experiments have determined that the contact area of the supporting pillars with the pan surface should be as small as possible, in order to obtain better measurement repeatability. It is presumed that the mechanical parts of the lever mechanism could not be machined and assembled perfectly in the desired geometry, that the geometrical imperfections inevitably caused some undesirable parasitic moments, and that a comparatively small contact area should mitigate the transmission of the parasitic moments to the electronic balance (the sensing unit of the mass comparator), improving the repeatability of the measurements. 4. Evaluation of the mass comparator performance
CCE60K3
Fig. 4. Lever mechanism of the 500 kg mass comparator.
A photograph of the completed mass comparator is shown in Fig. 7. The mass comparator is set on a natural-stone base plate of 100 cm in width, 100 cm in depth, and 15 cm in height. To avoid
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J. Sun et al. / Measurement 95 (2017) 418–423
Fig. 7. Mass measurement of a 500 kg weight.
any variations in the readings of the mass comparator resulting from the influence of air flow in the large mass calibration room, a protective wind cover (W 160 cm D 140 cm H 160 cm) is used, as shown in Fig. 7. The cover is made from electrificationpreventing vinyl sheets, and opens on one side to allow for the loading of weights. The magnification ratio of the lever mechanism is 10, so the readability of the mass comparator becomes 0.01 g. Repeated comparison measurements of weights from 100 kg to 500 kg have been made in order to determine the standard deviation and evaluate the repeatability. Both the procedure for the mass comparisons and the ambient conditions followed the OIML recommendations for the weights [2]. The ABA method, in which ‘A’ refers to the mass measurement of a reference weight and ‘B’ to that of a calibration weight, was adopted in order to reduce the influence of drift on the mass comparator. Mass comparisons using the ABA method were repeated eight times as one series each for the 100 kg, 200 kg, and 500 kg weights. The eight ABA cycles were repeated on different measurement days. It should be noted that the eight ABA cycles were carried out only in the evaluation phase of the mass comparator, while six and three ABA cycles, respectively, were adopted for the calibrations of the reference weights and general-use weights. The results obtained are shown in Fig. 8, in which each data point represents the mean value of eight ABA cycles. The mean values for the observed mass differences of the 100 kg, 200 kg, and 500 kg weights are 0.405 g, 0.406 g, and 0.013 g, with standard deviations of 0.035 g, 0.046 g, and 0.092 g, respectively. The pooled standard deviations, estimated from several series of mass comparisons carried out on different measurement days 0.6
200 kg weights Mass difference / g
0.4 0.2
500 kg weights
0 -0.2
for the same nominal weight values, and the values for the readability of the mass comparator are summarized in Table 4. It should be noted that each of these pooled standard deviations has a sufficiently large degree of freedom, i.e. of 28 or more. By comparing with the data obtained from the best commercially available mass comparator, shown in Table 1, we can confirm that the standard deviation in the mass comparisons, sðDmc Þ, is reduced in all cases of 100 kg, 200 kg and 500 kg weight calibrations, by up to 41%, and the readabilities d are down to one fifth or less. The new mass comparator thus shows greatly improved performance. In addition, the sensitivity of the mass comparator was confirmed by adding F1 class 2 g and 5 g weights, for measurements of weights from 100 kg to 500 kg. For mass differences resulting from the addition of these weights, the observed deviations in the sensitivity were less than the readability of ±0.01 g; this confirms that the contribution to the uncertainty caused by the sensitivity is negligibly small. The standard deviations in the mass comparisons as well as the comparator sensitivity for every measurement performed by the new comparator in a three-year period after its development; the long-term stability of the comparator was thus confirmed. 5. Improvements in the weight calibration uncertainty The uncertainties in the weight calibrations obtained from the newly-developed mass comparator are estimated as follows. The standard uncertainty in the mass comparison process, uw ðDmc Þ, is calculated from Eq. (5), based on the number of repetitions of the measurement and on the pooled standard deviations shown in Table 4. Since each of these pooled standard deviations has a sufficiently large degree of freedom of 28 or more, a coverage factor of k = 2 can be adopted when calculating the expanded uncertainty, corresponding to a level of confidence of 95%. The repetition number is six for the reference weight calibrations and three for the general weight calibrations. The former case will be discussed here. Observations of the mass variation in the reference weights observed by three calibrations over the course of 15 years confirm that the uncertainty caused by the mass instability is negligibly small. The uncertainty in the sensitivity, us ; is also negligible in its contribution, as discussed above. The readability d of the comparator is 0.01 g, such that its standard uncertainty, ud , becomes 0.0041 g. By using a commercially available centring pan (LevelMatic 1000 supplied by Mettler-Toledo International Inc.), the uncertainty arising from the off-centred loading, uE , can be significantly reduced. In addition, we note that any remaining uncertainty due to off-centred loading is already reflected in the uncertainty in the mass comparison process, uw ðDmc Þ. Thus, the uncertainty arising from off-centred loading can be neglected [2]. As for the uncertainty due to the magnetism of the weights, uma , we ensure that weight calibrations with certain levels of small uncertainty are made only when the measured values for the magnetization and susceptibility of the weights are within the limits specified by the international recommendation [2]. Thus, this uncertainty can be neglected as well in our mass comparisons [2]. Consequently, only the standard uncertainty caused by the readability d should
100 kg weights -0.4
Table 4 Readability and standard deviation of the newly developed 500 kg mass comparator.
-0.6 1
2
3
4
5
6
7
8
Number of sequences Fig. 8. Measured mass differences using the 500 kg mass comparator (each data point represents the mean value of eight ABA cycles).
Nominal value
Readability d
Standard deviation sðDmc Þ
100 kg 200 kg 500 kg
0.01 g 0.01 g 0.01 g
0.060 g 0.10 g 0.18 g
J. Sun et al. / Measurement 95 (2017) 418–423 Table 5 Uncertainty in the calibration for the reference weights using the 500 kg mass comparator with six repeated comparisons. Sources of uncertainty Mass comparison process, uw ðDmc Þ Reference weight, uðmcr Þ Air buoyancy correction, ub Mass comparator, uba Coverage factor k Expanded uncertainty Uðmct Þ
100 kg 0.0245 g
200 kg 0.041 g
500 kg 0.073 g
0.0035 g 0.0008 g 0.0041 g 2 0.050 g
0.050 g 0.002 g 0.004 g 2 0.13 g
0.125 g 0.004 g 0.004 g 2 0.29 g
Table 6 Expanded uncertainty for the calibration of weights from 100 kg to 500 kg with three repeated comparisons. Nominal value
Commercially available mass comparators
New 500 kg mass comparator
100 kg 200 kg 500 kg
0.16 g 0.31 g 0.56 g
0.088 g 0.18 g 0.37 g
be taken into account in evaluating the standard uncertainty of the mass comparator, uba . The authors prescribe environmental conditions for the NMIJ calibration room to be within the ranges of 985 hPa to 1025 hPa for the atmospheric pressure, 20–26 °C for the room temperature, and 40–60% for the relative humidity, in accordance with the OIML R111 [2]; these conditions are maintained by air-conditioning the room year round. Consequently, the combined standard uncertainty in the air-buoyancy correction, ub, is evaluated to be less than 0.0025 kg/m3, when the air density qa is calculated from measured values of these ambient conditions, using the international equation for CIPM (2007) [5]. The density of the reference weights, which were made of nonmagnetic stainless steel, was determined beforehand by measuring the density of a sample cut from the same material; its combined standard uncertainty was estimated to be 10 kg/m3 or less. The densities of the calibration weights are specified in the information from the weight suppliers, and in the case where those are unknown, the recommended density values [2] are applied. For calibration weights made of stainless steel, the relative standard uncertainty in the air-buoyancy correction is estimated to be 8 108 or less. Using the new 500 kg mass comparator, mass comparisons for the calibration of 100 kg, 200 kg, and 500 kg reference weights have been carried out based on six repeated measurements. The uncertainties in the calibrations are summarized in Table 5; the expanded uncertainties, due to the calibrations with a coverage factor k = 2, and corresponding to a level of confidence of 95%, are also shown. By comparing these expanded uncertainties with those in Table 2 (Section 2), it can be seen that the uncertainties
423
in the calibrations have been greatly improved. The new comparator gives uncertainty values of 0.050 g, 0.13 g, and 0.29 g for the 100 kg, 200 kg, and 500 kg weights, respectively, showing a reduction to 58% or less of their previous values. For reference, the uncertainties in the calibrations for generaluse weights from 100 kg to 500 kg, based on three repeated comparisons, are given in Table 6. In these weight calibrations, the calibration uncertainties have also been reduced by 34–45%, and its relative expanded uncertainty, due to any weight has become less than 1 106. 6. Conclusions In this work, a high-accuracy 500 kg mass comparator with a readability of 0.01 g has been developed in order to improve the national measurement standards for large masses. The mass comparator is equipped with a highly accurate sensor and a highsensitivity magnifying lever mechanism. The readability of this new comparator has been reduced to one-tenth of that of the best 500 kg commercially available mass comparator, and the repeatability has been reduced slightly to 95%. Compared to the best 100 kg commercially available mass comparator, reductions to one-fifth and to 59% of the current values were observed, respectively. As a result, the uncertainties in the weight calibrations for 100 kg to 500 kg weights have been reduced by 34–45%. For the calibration of weights for general use, the relative expanded uncertainties have also been reduced to less than 1 106. This newly developed mass comparator will contribute to the further improvement of national measurement standards, not only for large masses, but also for mass-related quantities such as force or liquid flow. Acknowledgement The authors would like to thank Kubota Keisou ltd. Co. and Miyamoto Scale for their cooperation in manufacturing the 500 kg high-accuracy mass comparator. References [1] J. Sun, M. Ueki, K. Ueda, Improvement of the calibration and measurement capability of large weights in NMIJ (In the range from 2000 kg to 5000 kg), in: Proc. 24th Sensing Forum, Sendai, Japan, 2007, pp. 158–161 (in Japanese). [2] OIML R 111, Weights of classes E1, E2, F1, F2, M1, M1–2, M2, M2–3, M3 – Part 1: Metrological and Technical Requirements, International Organization of Legal Metrology, 2004. [3] Brochure, Comparator Balances Catalog, Mettler-Toledo International Inc., 2015. [4] Operating Instructions – Sartorius CCE Series, Electronic Mass Comparators, Sartorius AG, 2007. [5] A. Picard, R.S. Davis, M. Glӓser, K. Fujii, Revised formula for the density of moist air (CIPM-2007), Metrologia 45 (2008) 149–155.
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Development of a high-accuracy 500 kg mass comparator for improved weight calibration capability Jianxin Sun ⇑, Masaaki Ueki, Kazunaga Ueda National Metrology Institute of Japan (NMIJ), National Institute of Advanced Industrial Science and Technology (AIST), Japan
a r t i c l e
i n f o
Article history: Received 21 April 2016 Received in revised form 29 July 2016 Accepted 12 October 2016 Available online 13 October 2016 Keywords: Large weight Mass comparator Knife-edge
a b s t r a c t A high-accuracy 500 kg mass comparator with a readability of 0.01 g has been developed at the NMIJ/AIST in order to improve calibration capabilities for large weights from 100 kg to 500 kg. This newly developed mass comparator uses a high-accuracy electronic balance as the sensor and a high-sensitivity two-stage lever system with knife-edges to expand the maximum weighing capacity. This design made it possible to reduce the calibration uncertainties of large weights by 34–45%. This paper reports the basic design of the mass comparator and the improved results for large weight calibrations at the NMIJ. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction
2. Sources of uncertainty in large weight calibrations
The reliabilities of mass measurements are ensured by their traceability to the national mass metrology standards, and also influence the measurement reliabilities of mass-related quantities such as force, pressure, torque, flow, density, or amount of substance. The National Metrology Institute of Japan (NMIJ), a division of the National Institute of Advanced Industrial Science and Technology (AIST), promotes the improvement of national mass standards and traceability systems for large masses in the range from 50 kg to 5000 kg, in response to advancements in various metrological activities related to these quantities. Traceability to the mass standards is realized by the calibration of weights using mass comparators. The performance of the mass comparator is the dominant source of uncertainty in the weight calibrations, especially for large masses. For weight calibrations beyond 2000 kg, the NMIJ developed a 5000 kg high-accuracy mass comparator superior to the best commercially available comparators, and was thereby able to improve the calibration capability for weights from 2000 kg to 5000 kg by more than two times [1]. In a series of further improvements to the national standards for large masses, the NMIJ has developed a high-accuracy 500 kg mass comparator in order to reduce the uncertainty in the calibration of weights of 500 kg or less. This paper describes the development of this new comparator and highlights its improved calibration capabilities.
For the weight calibration of large masses, the conventional mass is generally used. This is obtained via the measurement of the mass difference between the calibration weight and a reference weight of known mass performed using a mass comparator [2]. The following is a summary of the calculation of the mass difference and its uncertainty given in the international recommendation [2]. Mass comparisons are made between the reference and calibration weights, denoted by mcr and mct respectively, by alternately loading and unloading them n times onto a mass comparator. The mass difference in the ith mass comparison, Dmc ; is given by Eqs. (1) and (2).
⇑ Corresponding author. E-mail address: [email protected] (J. Sun). http://dx.doi.org/10.1016/j.measurement.2016.10.036 0263-2241/Ó 2016 Elsevier Ltd. All rights reserved.
Dmc ¼ mct mcr ;
ð1Þ
Dmci ¼ DIi þ mcr C i ;
ð2Þ
where
C i ¼ ðqai q0 Þ
1
qt
1
qr
:
ð3Þ
Here, I is the indicator value of the comparator, mcr C i is the correction term for air buoyancy, mcr is the conventional mass of the reference weight, qai is the air density, q0 is the reference air density of 1.2 kg/m3, and qt and qr are the densities of the calibration and reference weights, respectively. The conventional mass of the calibration weight, mct , is then calculated using Eq. (4).
mct ¼ mcr þ Dmc ;
ð4Þ
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where Dmc is the mean value of the observed conventional mass difference from n repeated measurements. The calibration uncertainty for large weights has four significant sources, as described below. The standard uncertainty in the mass comparison process, uw ðDmc Þ, is given in terms of the standard deviation sðDmc Þ and the number n of repeated mass comparisons by Eqs. (5) and (6).
sðDmc Þ pffiffiffi ; n
uw ðDmc Þ ¼
s2 ðDmc Þ ¼
ð5Þ
n 2 1 X Dmci Dmc : n 1 i¼1
ð6Þ
If only a few mass comparisons are made, the estimate of sðDmc Þ can be unreliable. A pooled estimate, using earlier mass comparisons made under similar conditions, should be used. The standard uncertainty in the reference weight, uðmcr Þ, is given by Eq. (7).
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 U uðmcr Þ ¼ þ u2inst ðmcr Þ: k
ð7Þ
Here, U is the expanded uncertainty in the calibration value of the reference weight, k is the coverage factor, and uinst ðmcr Þ is the uncertainty due to the instability of the mass of the reference weight, as estimated from variations in the mass observed during multiple past calibrations. The standard uncertainty in the air-buoyancy correction, ub ; is given by Eq. (8).
2 ðq qt Þ u2 ðqt Þ u2b ¼ mcr r uðqa Þ þ ½mcr ðqa q0 Þ2 4
qr qt
þ
m2cr ð
qa q0 Þ½ðqa q0 Þ 2ðqal q0 Þ
qt
u2 ðqr Þ
q4r
:
ð8Þ
Here, qal is the air density from the previous calibration of the reference weight against a reference standard weight of higher rank, uðqa Þ is the standard uncertainty in the air density, and uðqt Þ and uðqr Þ are the uncertainties in the densities of the calibration and reference weights, respectively. The standard uncertainty of the mass comparator, uba , is given by Eq. (9).
uba ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u2s þ u2d þ u2E þ u2ma :
ð9Þ
Here, us , ud , and uE are the standard uncertainties in the sensitivity, the readability, and the off-centred loading of the mass comparator, respectively, and uma is the standard uncertainty in the weight caused by its magnetic properties. The sensitivity of the mass comparator can be evaluated using a sensitivity weight of mass ms and uncertainty uðms Þ; the standard uncertainty due to the sensitivity, us ; is then given by Eq. (10).
u2s
¼ ðDmc Þ
2
! u2 ðms Þ u2 ðDIs Þ : þ m2s DI2s
ð10Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Uðmct Þ ¼ kuc ðmct Þ ¼ k u2w ðDmc Þ þ u2 ðmcr Þ þ u2b þ u2ba :
ð12Þ
In the case where the standard uncertainty in the mass comparison process was evaluated using a pooled standard deviation having a sufficiently large degree of freedom, the coverage factor, k, can be taken as two. Using the national mass standards at the NMIJ for 50–500 kg, two 50 kg weights were nominated as reference weights and calibrated via mass comparison with five 10 kg reference weights which are traceable to the Japanese kilogram prototype. This was done using an AX64004 mass comparator (Mettler-Toledo International Inc.) with a maximum weighing capacity of 64 kg and a readability of 0.1 mg. The expanded uncertainty in these calibrations is 3.5 mg with a coverage factor of k = 2, which corresponds to a level of confidence of 95%. Next, five 100 kg reference weights were calibrated using these two 50 kg reference weights (as shown in Fig. 1); 200 kg and 500 kg reference weights are then calibrated using combinations of the 100 kg reference weights. This group of reference weights, ranging from 50 kg to 500 kg, is used for the calibration of weights in general use. A 100 kg mass comparator with a readability of 0.05 g and a 500 kg mass comparator with a readability of 0.1 g, both of which are commercially available, are currently used for 100 kg weight calibrations and for 200–500 kg weight calibrations, respectively. The standard deviations in the mass comparisons have been estimated to be 0.12 g for 100 kg, 0.26 g for 200 kg, and 0.46 g for 500 kg. Table 1 shows the readability and standard deviation values for commercially available, ‘state-of-the-art’ mass comparators taken from the latest manufacturer’s catalogue [3]. These standard deviation values are then used to evaluate the standard uncertainties in the mass comparison process to show the best values for the weight calibration uncertainties that could be obtained by using the commercially available mass comparators. However, the uncertainty values from sources other than the mass comparison process were evaluated based on the actual calibrations of the reference weights performed with these current mass comparators at the NMIJ, evaluated over six repeated measurements. Details of the uncertainty estimation are discussed later in Section 5; however, Table 2 summarizes the results for the standard uncertainties in the mass comparison process, uw ðDmc Þ, standard uncertainties in the readability, ud , and expanded uncertainties of the calibrations, Uðmct Þ, with a coverage factor of k = 2. It can be seen that the expanded uncertainties depend primarily on the uncertainties in the mass comparison process and in the readabilities of the mass comparators. In addition, it should be noted that these two uncertainty sources also had a significant influence on the uncertainties in the mass values of the 200 kg and 500 kg reference weights. Consequently, it is concluded that a higher-accuracy mass comparator is required to improve the mass comparison capabilities and reduce the uncertainty in large weight calibrations.
50 kg U = 3.5 mg (k = 2) S_No.1 to S_No.2
The uncertainty in the readability d of the comparator, ud ; is given by Eq. (11).
pffiffiffi d=2 pffiffiffi 2: 3
100 kg ð11Þ
S_No.1 to S_No.5
The combined standard uncertainty for a large weight calibration, uc ðmct Þ, is thus obtained from the uncertainty components mentioned above. Its expanded uncertainty Uðmct Þ is determined by Eq. (12), using a coverage factor of k with a level of confidence of 95%.
200 kg and 500 kg
ud ¼
Fig. 1. Flow chart for the calibration of reference weights from 100 kg to 500 kg.
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Table 1 Readabilities and standard deviations of current, commercially available mass comparators [3]. Nominal value
Readability d
Standard deviation sðDmc Þ
100 kg 200 kg 500 kg
0.05 g 0.1 g 0.1 g
0.102 g 0.14 g 0.19 g
Load
Sources of uncertainty Mass comparison process, uw ðDmc Þ Reference weight, uðmcr Þ Air buoyancy correction, ub Mass comparator, uba Coverage factor k Expanded uncertainty Uðmct Þ
100 kg 0.0416 g
200 kg 0.057 g
500 kg 0.078 g
0.0035 g 0.0008 g 0.0204 g 2 0.093 g
0.093 g 0.002 g 0.041 g 2 0.24 g
0.233 g 0.004 g 0.041 g 2 0.50 g
3. Development of a high-accuracy 500 kg mass comparator A 500 kg high-accuracy mass comparator, aimed at reducing the standard uncertainty in the mass comparison process and the readability as described above, is described in this work. A high-accuracy electronic balance with a small weighing capacity acts as the sensor for the mass comparator. The weighing capacity is magnified to 500 kg by means of a lever mechanism with a magnification ratio of 10, chosen to optimize the performance of the balance while maintaining a smaller ratio. In order for the readability of the mass comparator to be less than 20 mg, that of the electronic balance must be less than 2 mg. A CCE60K3 (Sartorius AG) electronic balance satisfying these requirements is used. This balance has been modified by the manufacturer to have a readability of 1 mg, at the authors’ request, in anticipation of the possible expansion of the capability of the comparator in the future. The specifications of the electronic balance [4] are shown in Table 3. The dimensions of the mass comparator are within 100 cm in width, 100 cm in depth, and 35 cm in height, taking into account the limited space in the calibration room at the NMIJ available for placing the mass comparator and handling the weights. The lever mechanism for the magnification of the weighing capacity makes use of a system of second-order levers (Fig. 2). When a large load is applied to the lever at the point of load, a smaller balancing force generated by the sensor is applied at the point of force in order to maintain equilibrium. The mass comparator is constructed such that the lever mechanism can be exchanged easily to increase the magnification ratio from 10 to 20, to allow for the possible expansion of the weighing capacity from 500 kg to 1000 kg in the future. In addition, we desire that the distance between the fulcrum and the load point be as long as possible in order to attain high sensitivity and reduce the error arising from small changes in the lever ratio. As shown in Fig. 3, the lever mechanism consists of two lever systems combined at right angles to each other. This arrangement allows the
Table 3 Specifications of CCE60K3 [4]. Max. weighing capacity Readability Repeatability Weighing pan size (W D) Weighing system dimension (W D H) a
Improved from 2 mg by the manufacturer.
Fig. 2. Second-order lever.
full dimensions of the mass comparator to be utilized effectively in order to attain higher accuracy mass measurements. Four fulcrums of the first lever and two fulcrums of the second lever are fixed on the base plate of the mass comparator. The weighing pan is supported at the four load points of the first lever. A weight load is applied to these load points and transmitted through two force points of the first lever to the two load points of the second lever. The load is then applied to the sensor, i.e. the electronic balance, through the force points of the second lever, and the mass is measured. The equilibrium state of the lever mechanism is maintained by the compensating force from the electronic balance. The magnification ratios of the first and second levers are set to 4.63 and 2.16, respectively, in order to obtain an overall ratio of 10 for the combined lever mechanism. To increase the ratio to 20, only the second lever need be exchanged, for a lever with a ratio of 4.32. The distance between the fulcrum and the load point for the second lever changes from 235 mm to 82 mm; all other dimensional parameters are the same. Two kinds of fulcrum bearings are equipped on the base plate, allowing for the easy exchange of the second lever. The fulcrums, the points of load, and the force of the levers used for large mass measurements are usually made using two types of
Fulcrum
Point of force
Point of load Sensor
L 2b
L 2a2 L 2a1
1st lever
L 1a 61 kg 1 mga 7 mg 40 cm 30 cm 40 cm 30 cm 12 cm
Force
Point of load
Fulcrum Table 2 Uncertainties in the calibrations of the reference weights using current, commercially available mass comparators over six repeated comparisons.
Point of force
2nd lever Fulcrum
L 1b
L 1a = 82 mm, L 1b = 298 mm L 2a1 = 235 mm, L 2a2 = 82 mm, L 2b = 272 mm Fig. 3. Schematic diagram of the lever mechanism.
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bearings: knife-edge bearings and flexible bearings. Each type has both strong and weak points, in terms of the stability of the lever ratio, ease of manufacturing and installation, sensitivity, durability against large loads, ease of combining multiple levers, and so on. Good repeatability can be achieved with the flexible bearings as the fulcrums are fixed, and thus changes in the lever ratios are suppressed; this effect is most prominent when a thin flexible bearing is utilized. Flexible bearings are also easy to manufacture and install. On the other hand, they have a high risk of breaking off, especially under heavy loads. In contrast, the knife-edge bearings exhibit high sensitivity with little risk of breaking off under large loads. In addition, multiple levers can be easily and compactly connected to each other, as with the right-angle linkage. However, they have the disadvantage that the lever ratio may show large variations, if the equilibrium state of the lever mechanism is broken and the knife-edge is detached from its bearing during loading and unloading. Knife-edge bearings also require careful handling, and skilled technicians are required in their production, fine adjustment, and maintenance. Taking the respective characteristics of these two kinds of bearings into account, we design the fulcrums of the levers and the load points of the first lever supporting the weighing pan to use knifeedge bearings as large loads are applied at these points. For the right-angle connecting link between the force points of the first lever and the load points of the second, knife-edge bearings are also used. On the other hand, a flexible bearing is used for the connecting link between the electronic balance and the force point of the second lever, because the loads being applied here are the smallest, and variations in the position of the force point due to any shock arising from loading or unloading of the weights should be avoided. This lever mechanism is kept in equilibrium by the compensating force from the electronic balance, even during the loading or unloading of weights. The fulcrums, the points of load, and the force of the knife-edge bearings are in continuous contact. We thereby achieve high sensitivity in the lever mechanism, and the fulcrums are kept fixed. A photograph of the lever mechanism is shown in Fig. 4. The levers themselves are strongly constructed from SS400 structural steel plates of either 12 mm or 16 mm in depth and 90 mm or 75 mm in width, firmly fixed in parallel with a separation of 54 mm or 32 mm, so that the influence of any bending of the levers is negligible. A photograph of the knife-edge bearing used for the fulcrum of the first lever is shown in Fig. 5. The knife-edges are all V–shaped, with an angle of 75°, so as to attain both high sensitivity and high durability. Their bearings are also V-shaped, with a notch angle of 120°. The knife-edges and bearings are made of a
1st lever
2nd lever
Fig. 5. Knife-edge and knife-edge bearing used as the fulcrum of the first lever.
2nd lever CCE60K3
Flexur
Fig. 6. Connection between the second lever and the electronic balance CCE60K3.
super hard alloy with a hardness of HRA 92.0, as well as high strength and good wear resistivity. The connecting link between the force point of the second lever and the electronic balance is uses a flexible bearing in the form of a flexible spring, as shown in Fig. 6. The spring is made of a stainless steel band SUS304-CSP 3/4H of 0.2 mm in thickness and 18 mm in width. In order to connect to the weighing pan of the electronic balance, the upper surface of the pan is covered by a 6.5 mm thick aluminium alloy plate. In addition, two hexagonal supporting pillars with a two-face width of 17 mm are fixed to the pan surface. Preliminary experiments have determined that the contact area of the supporting pillars with the pan surface should be as small as possible, in order to obtain better measurement repeatability. It is presumed that the mechanical parts of the lever mechanism could not be machined and assembled perfectly in the desired geometry, that the geometrical imperfections inevitably caused some undesirable parasitic moments, and that a comparatively small contact area should mitigate the transmission of the parasitic moments to the electronic balance (the sensing unit of the mass comparator), improving the repeatability of the measurements. 4. Evaluation of the mass comparator performance
CCE60K3
Fig. 4. Lever mechanism of the 500 kg mass comparator.
A photograph of the completed mass comparator is shown in Fig. 7. The mass comparator is set on a natural-stone base plate of 100 cm in width, 100 cm in depth, and 15 cm in height. To avoid
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Fig. 7. Mass measurement of a 500 kg weight.
any variations in the readings of the mass comparator resulting from the influence of air flow in the large mass calibration room, a protective wind cover (W 160 cm D 140 cm H 160 cm) is used, as shown in Fig. 7. The cover is made from electrificationpreventing vinyl sheets, and opens on one side to allow for the loading of weights. The magnification ratio of the lever mechanism is 10, so the readability of the mass comparator becomes 0.01 g. Repeated comparison measurements of weights from 100 kg to 500 kg have been made in order to determine the standard deviation and evaluate the repeatability. Both the procedure for the mass comparisons and the ambient conditions followed the OIML recommendations for the weights [2]. The ABA method, in which ‘A’ refers to the mass measurement of a reference weight and ‘B’ to that of a calibration weight, was adopted in order to reduce the influence of drift on the mass comparator. Mass comparisons using the ABA method were repeated eight times as one series each for the 100 kg, 200 kg, and 500 kg weights. The eight ABA cycles were repeated on different measurement days. It should be noted that the eight ABA cycles were carried out only in the evaluation phase of the mass comparator, while six and three ABA cycles, respectively, were adopted for the calibrations of the reference weights and general-use weights. The results obtained are shown in Fig. 8, in which each data point represents the mean value of eight ABA cycles. The mean values for the observed mass differences of the 100 kg, 200 kg, and 500 kg weights are 0.405 g, 0.406 g, and 0.013 g, with standard deviations of 0.035 g, 0.046 g, and 0.092 g, respectively. The pooled standard deviations, estimated from several series of mass comparisons carried out on different measurement days 0.6
200 kg weights Mass difference / g
0.4 0.2
500 kg weights
0 -0.2
for the same nominal weight values, and the values for the readability of the mass comparator are summarized in Table 4. It should be noted that each of these pooled standard deviations has a sufficiently large degree of freedom, i.e. of 28 or more. By comparing with the data obtained from the best commercially available mass comparator, shown in Table 1, we can confirm that the standard deviation in the mass comparisons, sðDmc Þ, is reduced in all cases of 100 kg, 200 kg and 500 kg weight calibrations, by up to 41%, and the readabilities d are down to one fifth or less. The new mass comparator thus shows greatly improved performance. In addition, the sensitivity of the mass comparator was confirmed by adding F1 class 2 g and 5 g weights, for measurements of weights from 100 kg to 500 kg. For mass differences resulting from the addition of these weights, the observed deviations in the sensitivity were less than the readability of ±0.01 g; this confirms that the contribution to the uncertainty caused by the sensitivity is negligibly small. The standard deviations in the mass comparisons as well as the comparator sensitivity for every measurement performed by the new comparator in a three-year period after its development; the long-term stability of the comparator was thus confirmed. 5. Improvements in the weight calibration uncertainty The uncertainties in the weight calibrations obtained from the newly-developed mass comparator are estimated as follows. The standard uncertainty in the mass comparison process, uw ðDmc Þ, is calculated from Eq. (5), based on the number of repetitions of the measurement and on the pooled standard deviations shown in Table 4. Since each of these pooled standard deviations has a sufficiently large degree of freedom of 28 or more, a coverage factor of k = 2 can be adopted when calculating the expanded uncertainty, corresponding to a level of confidence of 95%. The repetition number is six for the reference weight calibrations and three for the general weight calibrations. The former case will be discussed here. Observations of the mass variation in the reference weights observed by three calibrations over the course of 15 years confirm that the uncertainty caused by the mass instability is negligibly small. The uncertainty in the sensitivity, us ; is also negligible in its contribution, as discussed above. The readability d of the comparator is 0.01 g, such that its standard uncertainty, ud , becomes 0.0041 g. By using a commercially available centring pan (LevelMatic 1000 supplied by Mettler-Toledo International Inc.), the uncertainty arising from the off-centred loading, uE , can be significantly reduced. In addition, we note that any remaining uncertainty due to off-centred loading is already reflected in the uncertainty in the mass comparison process, uw ðDmc Þ. Thus, the uncertainty arising from off-centred loading can be neglected [2]. As for the uncertainty due to the magnetism of the weights, uma , we ensure that weight calibrations with certain levels of small uncertainty are made only when the measured values for the magnetization and susceptibility of the weights are within the limits specified by the international recommendation [2]. Thus, this uncertainty can be neglected as well in our mass comparisons [2]. Consequently, only the standard uncertainty caused by the readability d should
100 kg weights -0.4
Table 4 Readability and standard deviation of the newly developed 500 kg mass comparator.
-0.6 1
2
3
4
5
6
7
8
Number of sequences Fig. 8. Measured mass differences using the 500 kg mass comparator (each data point represents the mean value of eight ABA cycles).
Nominal value
Readability d
Standard deviation sðDmc Þ
100 kg 200 kg 500 kg
0.01 g 0.01 g 0.01 g
0.060 g 0.10 g 0.18 g
J. Sun et al. / Measurement 95 (2017) 418–423 Table 5 Uncertainty in the calibration for the reference weights using the 500 kg mass comparator with six repeated comparisons. Sources of uncertainty Mass comparison process, uw ðDmc Þ Reference weight, uðmcr Þ Air buoyancy correction, ub Mass comparator, uba Coverage factor k Expanded uncertainty Uðmct Þ
100 kg 0.0245 g
200 kg 0.041 g
500 kg 0.073 g
0.0035 g 0.0008 g 0.0041 g 2 0.050 g
0.050 g 0.002 g 0.004 g 2 0.13 g
0.125 g 0.004 g 0.004 g 2 0.29 g
Table 6 Expanded uncertainty for the calibration of weights from 100 kg to 500 kg with three repeated comparisons. Nominal value
Commercially available mass comparators
New 500 kg mass comparator
100 kg 200 kg 500 kg
0.16 g 0.31 g 0.56 g
0.088 g 0.18 g 0.37 g
be taken into account in evaluating the standard uncertainty of the mass comparator, uba . The authors prescribe environmental conditions for the NMIJ calibration room to be within the ranges of 985 hPa to 1025 hPa for the atmospheric pressure, 20–26 °C for the room temperature, and 40–60% for the relative humidity, in accordance with the OIML R111 [2]; these conditions are maintained by air-conditioning the room year round. Consequently, the combined standard uncertainty in the air-buoyancy correction, ub, is evaluated to be less than 0.0025 kg/m3, when the air density qa is calculated from measured values of these ambient conditions, using the international equation for CIPM (2007) [5]. The density of the reference weights, which were made of nonmagnetic stainless steel, was determined beforehand by measuring the density of a sample cut from the same material; its combined standard uncertainty was estimated to be 10 kg/m3 or less. The densities of the calibration weights are specified in the information from the weight suppliers, and in the case where those are unknown, the recommended density values [2] are applied. For calibration weights made of stainless steel, the relative standard uncertainty in the air-buoyancy correction is estimated to be 8 108 or less. Using the new 500 kg mass comparator, mass comparisons for the calibration of 100 kg, 200 kg, and 500 kg reference weights have been carried out based on six repeated measurements. The uncertainties in the calibrations are summarized in Table 5; the expanded uncertainties, due to the calibrations with a coverage factor k = 2, and corresponding to a level of confidence of 95%, are also shown. By comparing these expanded uncertainties with those in Table 2 (Section 2), it can be seen that the uncertainties
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in the calibrations have been greatly improved. The new comparator gives uncertainty values of 0.050 g, 0.13 g, and 0.29 g for the 100 kg, 200 kg, and 500 kg weights, respectively, showing a reduction to 58% or less of their previous values. For reference, the uncertainties in the calibrations for generaluse weights from 100 kg to 500 kg, based on three repeated comparisons, are given in Table 6. In these weight calibrations, the calibration uncertainties have also been reduced by 34–45%, and its relative expanded uncertainty, due to any weight has become less than 1 106. 6. Conclusions In this work, a high-accuracy 500 kg mass comparator with a readability of 0.01 g has been developed in order to improve the national measurement standards for large masses. The mass comparator is equipped with a highly accurate sensor and a highsensitivity magnifying lever mechanism. The readability of this new comparator has been reduced to one-tenth of that of the best 500 kg commercially available mass comparator, and the repeatability has been reduced slightly to 95%. Compared to the best 100 kg commercially available mass comparator, reductions to one-fifth and to 59% of the current values were observed, respectively. As a result, the uncertainties in the weight calibrations for 100 kg to 500 kg weights have been reduced by 34–45%. For the calibration of weights for general use, the relative expanded uncertainties have also been reduced to less than 1 106. This newly developed mass comparator will contribute to the further improvement of national measurement standards, not only for large masses, but also for mass-related quantities such as force or liquid flow. Acknowledgement The authors would like to thank Kubota Keisou ltd. Co. and Miyamoto Scale for their cooperation in manufacturing the 500 kg high-accuracy mass comparator. References [1] J. Sun, M. Ueki, K. Ueda, Improvement of the calibration and measurement capability of large weights in NMIJ (In the range from 2000 kg to 5000 kg), in: Proc. 24th Sensing Forum, Sendai, Japan, 2007, pp. 158–161 (in Japanese). [2] OIML R 111, Weights of classes E1, E2, F1, F2, M1, M1–2, M2, M2–3, M3 – Part 1: Metrological and Technical Requirements, International Organization of Legal Metrology, 2004. [3] Brochure, Comparator Balances Catalog, Mettler-Toledo International Inc., 2015. [4] Operating Instructions – Sartorius CCE Series, Electronic Mass Comparators, Sartorius AG, 2007. [5] A. Picard, R.S. Davis, M. Glӓser, K. Fujii, Revised formula for the density of moist air (CIPM-2007), Metrologia 45 (2008) 149–155.