The Planck Balance Using A Fixed Value Of H To Calibrate E1-e2 Weights.pdf

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The Planck-Balance—using a fixed value of the Planck constant to calibrate E1/E2-weights To cite this article: C Rothleitner et al 2018 Meas. Sci. Technol. 29 074003

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- The watt or Kibble balance: a technique for implementing the new SI definition of the unit of mass Ian A Robinson and Stephan Schlamminger - Watt balance experiments for the determination of the Planck constant and the redefinition of the kilogram M Stock - Maintaining and disseminating the kilogram following its redefinition M Stock, S Davidson, H Fang et al.

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Measurement Science and Technology Meas. Sci. Technol. 29 (2018) 074003 (9pp)

https://doi.org/10.1088/1361-6501/aabc9e

The Planck-Balance—using a fixed value of the Planck constant to calibrate E1/E2-weights C Rothleitner1 , J Schleichert2 , N Rogge2 , L Günther1 , S Vasilyan2 , F Hilbrunner2, D Knopf1 , T Fröhlich2 and F Härtig1 1

  Physikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, 38116 Braunschweig, Germany   Institute of Process Measurement and Sensor Technology, Technische Universität Ilmenau, 98684 Ilmenau, Germany 2

E-mail: [email protected] Received 7 February 2018, revised 23 March 2018 Accepted for publication 9 April 2018 Published 22 May 2018 Abstract

A balance is proposed, which allows the calibration of weights in a continuous range from 1 mg to 1 kg using a fixed value of the Planck constant, h. This so-called Planck-Balance (PB) uses the physical approach of Kibble balances that allow the Planck constant to be derived from the mass. Using the PB no calibrated mass standards are required during weighing processes any longer, because all measurements are traceable via the electrical quantities to the Planck constant, and to the meter and the second. This allows a new approach of balance types after the expected redefinition of the SI-units by the end of 2018. In contrast to many scientific oriented developments, the PB is focused on robust and daily use. Therefore, two balances will be developed, PB2 and PB1, which will allow relative measurement uncertainties comparable to the accuracies of class E2 and E1 weights, respectively, as specified in OIML R 111-1. The balances will be developed in a cooperation of the Physikalisch-Technische Bundesanstalt (PTB) and the Technische Universität Ilmenau in a project funded by the German Federal Ministry of Education and Research. Keywords: Kibble balance, EMFC load cell, mass standards, dissemination of the unit mass (Some figures may appear in colour only in the online journal)

1. Introduction

measurement uncertainty, the smallest relative measurement uncertainty can be reached for a one kilogram mass value. For lower or higher mass values the relative measurement uncertainty will increase due to further comparison steps necessary to derive these mass values. The German National Prototype of the Kilogram (NPK), which is made of the same Pt-Ir alloy as the IPK, for example, has an estimated relative measurement uncertainty of 2.3 × 10−9 , or 6 × 10−9 [2] when considering the drift rate. Kilogram Prototypes made of stainless steel, on the other side, already have a relative measurement uncertainty that is by a factor 6.5 higher than that of the NPK, mainly due to air buoyancy effects. In November of 2018 the General Conference on Weights and Measures (CGPM) will, on its 26th conference, decide the new SI, including the redefinition of the kilogram. The

The kilogram, which was originally defined as the weight of a litre (cubic centimetre) of water at the freezing point, is the last SI unit that is defined by a material artefact [1]. Today, a small cylinder with a height and diameter of about 39 mm, made of a platinum-iridium alloy defines the primary standard of mass. This artefact, called the ‘International Prototype of the Kilogram (IPK)’, is at the summit of the calibration hierarchy of masses. All other mass standards must be traceable to the IPK. In order to trace a mass to the IPK a chain of mass comparisons is necessary. Each comparison goes along with a measurement uncertainty, so that the measurement uncertainty of a mass under test is increasing with decreasing hierarchical order. As the IPK defines exactly 1 kg, with zero 1361-6501/18/074003+9$33.00

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kilogram will then be defined by fixing the numerical value of the Planck constant h, with zero uncertainty. From then the definition will probably sound as follows [3]: “The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.626 070 15 × 10−34 when expressed in the unit J s, which is equal to kg m2 s−1, where the metre and the second are defined in terms of c and ∆νCs .” The value of the Planck constant that is given in the quotation is the truncated and rounded CODATA 2017 value [4]. This value was determined to lowest measurement uncertainty via two experiments, the x-ray crystal density (XRCD) method [5] and the Kibble balance [6, 7]. While until now this experiment uses a well calibrated (traceable to the IPK) mass artefact to determine h, after the redefinition the same experiment can be used to determine the mass value of an artefact from the Planck constant. The Kibble balance will describe a primary method of realizing the new kilogram [8]. The redefinition offers a new way to calibrate mass standards, as, by means of a Kibble balance, masses of any value are traceable to the Planck constant. Strictly thinking, there is no need to establish a mass scale beginning from a nominal value of 1 kg. In this article the basic concept of a weighing instrument will be presented, which follows the principle of a Kibble balance. The instrument is named Planck-Balance (PB), as it uses the future definition of the kilogram via the Planck constant. In the next section 2 the principle of the Kibble balance will be explained. In section 3 the reasons and status of the redefinition of the SI unit mass will be briefly explained, which makes it possible to calibrate in the future a balance via the electrical quantities, rather than by calibrated mass standards. In the following section 4 then the concept and the aimed performance of the PB will be explained in detail, before the article will end with a summary and outlook.

Figure 1.  Principle of a load cell with electromagnetic force compensation. 1—weighing pan, 2—parallel guide, 3—coil, 4—magnet, 5—resistor, 6—position indicator, 7—voltmeter.

will describe the current I as a function of the load, where the current is measured as a voltage drop (7) at a resistor (5). By interpolation mass values different from those that have been used for calibration can be measured, i.e. the balance is able to measure the weight in a continuous mass range. The step towards the Kibble balance is the introduction of a second mode in the weighing process, in order to eliminate the calibration step with weights. Kibble proposed to determine the so-called ‘geometrical factor’ Bl by moving the coil (3) in the magnetic field of the permanent magnet (4) with a velocity v. This induces a voltage V in the coil that can be measured to high accuracy. By the law of induction, the induced voltage V is a function of the velocity v and the Bl as V = v · (Bl). (2)

By combining equations (1) and (2) the Bl drops out, which finally leads to

mgv = VI. (3)

Equation (3) shows a virtual equality of mechanical and electrical power—the reason why the Kibble balance formerly was called Watt balance. All remaining parameters can be measured to high accuracy. The mass m by mass comparison with a calibrated standard, the local acceleration due to gravity g by means of a (free-fall) absolute gravimeter, the velocity v by means of a length measurement via a laser interferometer, and time measurement via a frequency standard (clock). The voltage can be accurately measured by means of the Josephson effect. Finally, the current I can be measured to high accuracy via Ohm’s law, I = V/R, using high-precision resistors traceable to a quantum Hall resistor. The measurement of the electrical quantities voltage and resistance establish the link between the mass and the Planck constant. After the redefinition of the kilogram, i.e. after fixing the value of h to 6.626 070 15 × 10−34 J s, the same equation and the same measurement principle can be used to determine the mass of a weight. This Kibble balance principle is one of two suggestions in the Mise en Pratique [8] for a future realization of the kilogram (the second one is via the XRCD). As a consequence, each experiment that follows this principle of comparing virtual mechanical and electrical power is a

2.  The Kibble balance, an experiment to determine the Planck constant h The principle of the Kibble balance, as it is used today, was first proposed by Bryan Kibble in 1976 [6]. A possible route to describe its principle is via the load cell with electro­magnetic force compensation (EMFC), as depicted in figure 1. An EMFC is the state-of-the-art in high-precision weighing technology. Here, the weight of a mass that is placed on the weighing pan (1) will be compensated by an electromagnetic force. This electromagnetic force is produced by a coil-magnet system (3–4). The measurement equation for this set-up (neglecting air buoyancy effects) is mg = I · (Bl), (1)

where m denotes the mass of the weight, g the local acceleration due to gravity, B the magnetic flux density, l the length of the coil, and I the electrical current. The calibration of the instrument is done by loading the weighing pan (1) with calibrated mass standards that must be traceable to the IPK. This 2

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primary method for realizing the unit kilogram. Moreover, the link between the mass and the Planck constant is valid for any mass value, not only for 1 kg. EMFC load cells usually cover several decades of mass values. By calibrating Bl as proposed by Kibble the EMFC can be used as a primary realisation of the kilogram for any mass value within its mass range.

Table 1.  Aimed parameters for the PBs. The aimed relative

measurement uncertainty urel results from the accuracy classes as recommended in [16]. MPE is the maximum permissible error of a weight. PB2 Mass range MPE/m(max)

1 mg … 100 g 16 × 10−7 (E2) urel = um(max) /m(max)(k = 1) 2.7 × 10−7 (E2) Environment Air (atmospheric pressure) Time / Weighing 10–120 s

3.  Redefinition of the SI-unit kilogram One of the reasons for the new definition is that the IPK is the last SI unit that is defined by an artefact. Evidence suggests that it is unstable over time. Moreover, there is always the risk that it could be damaged or lost. Fortunately, this did not happen, although there were two world wars in the meantime. Thus, metrologists and scientists intended already for about 40 years [9] to find a way to define the kilogram via a fundamental constant. Such a constant can never be damaged or lost and, furthermore, is accessible to everybody. Another property is its stability over time. Since its definition in 1889, the official copies have been calibrated four times [1] against the IPK. At its third calibration campaign in 1991 it has been observed that the weight of the IPK shows a trend with respect to the official copies. This trend amounts to about 50 µg (5 × 10−8 in relative units) over 100 years with respect to the mean value of the copies [1]. This would mean, that the trend within five years would almost amount to the measurement uncertainty that is attributed to the weighing procedure itself. In a more recent calibration campaign against the IPK in 2014, known as ‘Extraordinary Calibrations’, however, the existence of this trend could not be confirmed [10] and thus ensures a solid base for the measurement of the Planck constant. Many methods have been proposed in the past 40 years to redefine the kilogram, but only two methods reached the aimed accuracy, that was recommended by the Consultative Committee for Mass and Related Quantities (CCM) [11]. This recommendation says that there should be at least three experiments (including XRCD and the Kibble balance) yielding relative standard uncertainties of 5 × 10−8 or better, and at least one yielding 2 × 10−8 or better. One experiment is the XRCD method, which defines a route via counting the number of atoms in a highly isotopically enriched monocrystalline 28Si crystal. The latest publication shows a relative standard uncertainty of 12 × 10−9 [12]. The other route is via the Kibble balance experiments, realised by several National Metrology Institutes (NMI) world-wide. The lowest measurement uncertainties have been reached by the National Research Council of Canada (NRC) and National Institute of Standards and Technology (NIST) with 9 × 10−9 [13] and 13 × 10−9 [14], respectively. With these uncertainties a recommendation of the CCM for a redefinition was fulfilled. Another recommendation requires a consistency of the results at the 95% level. This is a somehow critical point as the latest measurements that show relative standard uncertainties equal or less than 5 parts in 108 are not statistically consistent (chi-squared test) to the desired level [15]. Nevertheless, the SI units—including the kilogram—will be redefined at the

PB1 1 mg … 1 kg 5 × 10−7 (E1) 8.4 × 10−8 (E1) High vacuum

10–120 s

26th General Conference of Weights and Measures (CGPM) in November 2018. It will finally come into force on 20 May, 2019, the World Metrology Day. 4.  Concept of the Planck-Balance Within the PB-project run time two balances will be developed and validated. A first balance will be called PB2 and a second one PB1. The reason for the numbering results from the aimed accuracies of the balances, as will be explained later in this text. Both balances will follow the principle of the Kibble balance. In this section  the general concept and parameters will be presented. 4.1.  Aimed parameters of the Planck-Balances

Table 1 summarizes the main aimed parameters of the PB. The PB1 will be equipped with a vacuum chamber with a pressure of about 1 × 10−6 mbar to mitigate influences of the ambient air on the measurement result, especially for the interferometer and the buoyancy of the weight. This will be necessary in order to reach the aimed uncertainties for the PB1. 4.2.  Use of standard components

The PB is not aimed for measuring h to high accuracy, but describes a weighing instrument for the dissemination of the unit kilogram in a range of nominal values. The requirements are a bit more relaxed than in conventional Kibble balances, as it is aimed to measure ‘only’ at the accuracy level of E2 and E1 weights that are lower than for Kibble balance experiments at NMIs. Therefore, the PB concept differs in some ways. As an example, it is aimed to use as many standard components as possible, like the commercial high-end EMFC load cell. Such a load cell is used for analytical balances in E1/E2 mass laboratories, as well as in industry. These sophisticated sensors can lay back on decades of knowledge in design and machining. Other standard components are, e.g. the interferometer, the clock, or the Josephson standard. Custom made parts should be avoided in general, but might be necessary in some exceptional cases. This is why the coil will be custom made.

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Figure 2.  Overview of the components and the measurement scheme of the PB2 with a weight to be calibrated (1), EMFC balance (2), Interferometer (3) and combined magnet system from three single magnet systems (4). The width of the housing is 200 mm.

have approximately the same dimensions as a commercial analytical balance, as an identical load cell is used. Large components will only be the high precision measurement devices, such as the Josephson standard, the voltmeters, and the laser interferometer. In order to avoid a large magnet, it is intended to use 3 magnet-coil systems in a row, as depicted in figure 2. The size will thus increase in height, but not in width. Figure  2 shows a technical drawing of the PB2 design. For PB1 there will additionally be a vacuum chamber, which will significantly size up the system.

4.3.  Modular design

Besides the use of commercially available standard comp­ onents the balances will have a modular design. This means that both balances (PB1 and PB2) will contain as many similar components as possible. Only those components that are necessary to reach the desired specifications (measurement uncertainty for the desired mass range), will be replaced by other adequate standard components. As an example, PB1 will have the same interferometer type and frequency standard as PB2, but the load cell might be different.

5.  Projected performance of the system

4.4.  Weights handling and measurement procedure

In this section it will be discussed how the different measurement systems will be traceable to their primary standards. Then, the magnet-coil system will be described, before a short presentation about motion deviations of the EMFC load cell follows. Finally, the so-called Virtual Planck-Balance will be presented, which is a virtual twin of the PB.

For commodity and better repeatability the balances will be equipped with an automatic mass exchanger. This will automate the measurement procedure based on an ABBA-like weighing cycle. The calibration cycle here is the dynamic mode (A) of the Kibble balance principle, whereas the static mode (B) corresponds to the conventional weighing mode. During the weighing phase, the weight will be raised several times by means of the automatic mass exchanger, meaning that several weighings will take place with and without the weight. As the balance is aimed for routine calibration, the weighing should be much faster than high precision determinations of h by means of Kibble balances.

5.1.  Traceability of measurement devices

The PB allows a primary realization of the unit kilogram. To this end, the electrical quantities (i.e. voltage and resist­ ance) must be traceable to their quantum standards. In addition, the velocity measurement of the coil within the magnetic field must be traceable to length and time standards. Finally, there is the local gravity that must be accurately known at the site and time of measurement. Figure 3 shows how the traceability of these quantities will be realised. For the voltage, a

4.5.  Size of the instrument

Another important aim is to have a compact and user friendly weighing instrument. In principle, the final balance could 4

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Table 2.  Parameters of one magnet-coil system as will be used for

the PB2.

Material

SmCo

Temperature coefficient Diameter Br Bl Number of turns, N

300 ppm K−1 40 mm 0.5 T 500 Tm 5000

Figure 3.  The different quantities of the measurement equation must finally be traced to primary standards. (The subscripts FM and VM denote the force mode and the velocity mode of the experiment, respectively.)

commercial digital voltmeter will be used that is calibrated to a Josephson standard. The electrical current will be measured via the voltage drop at a temperature controlled precision resistor. Thus, the resistor must be calibrated to a quantum hall resistance. The velocity is measured with a laser interferometer and a frequency standard, both of which are traceable to primary standards. The local gravity is measured by means of a free-fall gravimeter, which consists of a laser interferometer and a frequency standard, similar to the velocity measurement in the velocity mode. In order to get a more accurate gravity value at the weighing pan, an additional gravity gradient determination is necessary in the laboratory with a relative gravimeter. This gradient has a magnitude of about 3 µ m s−2 m−1 or 3 × 10−7 m−1 in relative units. Thus, for reaching a relative measurement uncertainty in gravity to one part in 108 the gravity value must be known within a range of 3 cm. The relative gravimeter, in turn, can be calibrated to an absolute gravimeter. All quantities can be measured to better than one part in 108.

Figure 4.  Dual magnet system used in the Planck-balance consisting of a ferromagnetic flux guide (1), a coil (2) and two permanent magnets (3) which are generating a radial magnetic field (4) in the air gap. Sizes: Outer coil radius, rla = 16.5 mm, inner coil radius, rli = 13.5 mm, 1/2 height of air gap, hp  =  6  mm, height of one magnet, hm  =  6 mm, inner magnet diameter, rmi = 5 mm, outer magnet diameter, rma = 13 mm.

Figure 4 shows a sketch of one of the three magnet-coil systems for the PB2. It can be seen that the magnet systems that will be used in the PB2 have a similar magnet configuration as the magnet systems of Kibble balances [18, 19]. They are made of two permanent magnets with opposing magnetization, indicated by the yellow arrows. This design amplifies the magn­etic flux density in the air gap and reduces stray fields [18]. A ferromagnetic flux guide is used to focus the flux in the area of the coil and shield the magnets from external influences. Figure 5(a) shows a simulation of the Bl as a function of the axial coil position for a coil motion range of  ±3 mm. Actually, the load cell that will be used in the PB2 has a motion range of only  ±40 μm around the zero position, which will be defined by the alignment of the coil to the magnet. Through the magnetic field generated by the current in the coil, the magnetic field of the permanent magnets is distorted. Because the Bl is measured in the velocity mode without a current through the coil this can lead to a deviation of Bl between the force- and the velocity modes. For a coil, which is ideally centred in the magnetic field during the force mode, the deviation is zero. If the coil is generating one third of the force required to compensate the mass of 100 g (≈0.33 N) it needs to be aligned to within 0.5 µ m to the ideal coil position

5.2.  Magnet-coil system

Earlier in this text it was mentioned that the magnet-coil system is one of the few parts that will be custom made. Moreover, it has been mentioned that a combination of three magnet-coil systems will be used in order to carry a mass of 100 g for PB2 (see figure 2). A reason for a custom design is the fact that commercial voice coils usually have a low Bl at reasonable size and cost. With those systems a high current is necessary to produce a high force. Another reason is the way of how the velocity mode in the PB works. The coil will be moved sinusoidally within the field of permanent magnet. This excitation will have a frequency of about 4 Hz. Commercial voice coils are often wound around a metal carrier (hollow cylinder). When moving the coil in the magnetic field, eddy currents will damp the system, which signifies a loss of power [17]. For PB2 the coils will not be on a carrier but will be baked together in order to avoid damping by eddy currents in the coil carrier. The design for the PB1-magnet-coil system is under development. Table 2 summarizes the main parameters of the magnet-coil system, as it will be used for the PB2. 5

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Figure 5.  (a) Simulation of the normalized Bl as a function of the axial coil position. (b) Close-up for the range from  −300 μm to  

+300 μm.

Figure 6.  (a) Measurement set-up (horizontal configuration): 1—Interferometer, 2—holder for mass piece, 3—mirror, 4—EMFC balance, 5—load carrier. (b) Schematic sketch of the measurement of the motion deviation in the horizontal and vertical configuration.

if a relative deviation below 0.1 ppm is required. The ideal coil position can be identified during the velocity mode and used in the position control of the force mode for adjustment of the coil position. In order to check the results of the numerical simulations, measurements of the Bl factor were done on a real magnet system. The measurement was performed by changing the axial position of the coil while compensating a constant force and measuring the coil current. The measurement results in figure 5(b) show a good agreement of the numerical simulation with the measurement. The required axial positioning uncertainty of the coil that is necessary in order to reach a 0.1 ppm maximum deviation of the coil position, is 0.13 µ m. This positioning uncertainty can be achieved by the position control loop in the force mode if the interferometer signal is used as an input signal. It is noteworthy that in principle the leverage ratio of the load cell could be used, as described by Hilbrunner et al [17]. The magnet-coil system would significantly be reduced in size, depending on the leverage ratio. It is not necessary to know the exact leverage ratio, as in the final measurement equation  this ratio drops out. In the PB2, however, the load cell is used mainly as a mechanical guide, and the weight will be compensated directly.

5.3.  Motion deviation of the EMFC load cell

In a preliminary study the performance of the load cell was investigated to identify the horizontal displacement of the balance beam during the velocity mode. This is of importance as horizontal parasitic motions can induce a bias in the induced voltage. Additionally, the tilt of the weighing pan during its vertical motion was measured in order to determine the magnitude of the cosine error in the velocity mode. In order to study these effects, the vertical and horizontal motions have been measured by means of a three beams laser interferometer. The investigated load cell is a commercial EMFC load cell with a measurement range of up to 200 g and a resolution of 0.1 mg. For internal selfcalibration the balance is provided with two calibrated 100 g mass pieces, which can be applied on special holders (see figure 6) that are attached to the load carrier. When placed on these holders, the centres of gravity of the mass pieces have a distance of 50 mm along the z-axis relative to the plane of symmetry of the balance. Figure  6 shows the set-up for the measurement of the horizontal motion deviation. Due to geometric considerations, it is expected that the desired vertical movement sy of the load carrier also causes a parasitic horizontal motion sx: 6

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Figure 7.  Measured rotation of load carrier for both configurations. (ver. conf.  =  vertical configuration, hor. conf.  =  horizontal configuration).

Given the fact that a tilt of 45 μrad corresponds to a relative error on the order of 1 × 10−9, the investigations show that the expected errors due to rotation of the load carrier are negligible.

s2y (4) sx = , 2Ll

where Ll is the length of the parallel levers. For a vertical motion range, sy, of  ±40 μm, the horizontal displacement reaches a maximum of about 8 nm. Measurements show an agreement of the expected behaviour described by equation (4) to less than a nanometre. The tilt angle was measured in two configurations. In a first configuration the laser interferometer was installed horizontally. In a second configuration the same laser interferometer was installed vertically. This allowed to investigate the tilts of the load carrier about all three axes. The rotations around the x- and z-axes were measured as functions of the displacement along y (see figure 6) in the vertical configuration. The rotation around the y- and z-axes were measured in the horizontal configuration, again as a function of a vertical movement. The rotation is measured relative to the zero position and the results are presented in figure 7. The rotations measured in the vertical configuration show no significant effect depending on the displacement of the load carrier. In contrast, the rotations observed in the horizontal configuration seem to show a small but significant change along the vertical movement. However, the observed values correlate to a displacement difference of 22 nm measured by one of the three laser beams. As the utilized mirror is specified with a flatness of 63 nm, the change can be explained by the greater movement of the laser spots on the mirror surface in the horizontal configuration. This effect also explains the differences between the observations for the rotation around the z-axis within the comparison of the two configurations. Nonetheless, a rotational movement of the load carrier greater than  ±100 nrad is unlikely regarding the observed behaviour.

5.4.  Virtual Planck-Balance

The concept of the PB also includes a virtual measuring device, called Virtual Planck-Balance (VPB). The VPB is a theoretical model of the measurement system. It includes a theoretical model for the weight [20], interferometer system, load cell, magnet system, gravimeter, etc. In the ideal case it provides a complete ‘virtual copy’ of the real measurement set-up. After some initial measurement cycles of the PB, the VPB will be provided with the start parameters. The VPB then performs a Monte Carlo simulation based on the models describing the physical processes, and provides the estimated measurement uncertainty of the weighing procedure. The VPB provides several features. (1) The resulting measurement uncertainty is more realistic and more precise than a conventional uncertainty estimation based on uncertainty propagation, since the uncertainty estimation is not based on a truncated Taylor expansion of the model function, but considers the complete model function. This is important if the model function is significantly non-linear, or if the probability density function of a significant uncertainty contribution is non-Gaussian. (2) Varying environmental conditions during the weighing process can be taken into account for the measurement uncertainty estimation. (3) The module VPB can be used off-line for error prediction. The starting parameters can be varied in order to simulate different environmental conditions. This can give an idea of how much the measurement uncertainty would increase or decrease if, e.g. the temperature changes. (4) A determination of the measurement uncertainty 7

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Figure 8.  Relative measurement uncertainty urel (k = 1) = u(mmax ) /mmax as a function of the maximum nominal mass value mmax. PB2 and PB1 are intended to cover the nominal mass values from 1 mg up to 100 g, and from 1 mg up to 1 kg, respectively.

becomes difficult or impossible. The mass under test could remain on the weighing pan during the calibration (velocity) mode. Figure  8 depicts the relative measurement uncertainties that correspond to classes E1 and E2 weights. It can be noted that below 100 g the relative measurement uncertainty is increasing. One reason for this increase lies in the propagation of uncertainty when the mass scale is established. The second reason is that for lower mass values the weighing systems that are used for establishing the corresponding mass decades do not increase in their resolutions any more. Here is, where the PB can bear advantages. No mass scale is necessary and, if a balance for lower mass values is designed it can be optimized for the corresponding mass range.

of a weighing process is easier for the scientific staff. This has positive influence on possible (calculation) errors and cost efficiency. The idea of the VPB arose from the virtual coordinate measuring machine (VCMM) [21], which has been developed at PTB and is now integrated into the products of several industrial partners. In that case, the uncertainty of a measurement by means of a coordinate measuring machine (CMM) is estimated with the VCMM. It considers the CMM, the environ­ment, the probing process, as well as the work piece. 5.5.  Aimed uncertainties, measurement ranges and environ­mental conditions

The balances are designed for industrial use or for NMIs, applications where mass standards of highest accuracies are required. Mass standards follow an international recommended classification scheme. The highest accuracies class is denoted by E1, which is followed by E2, F1, F2, and following lower accuracy classes. A detailed description can be found in the document OIML R 111-1 [16] by the International Organization of Legal Metrology (OIML). It is noteworthy that E1 mass standards are used for the calibration of E2 mass standards, whereas E2 mass standards are used for the calibration of F1 mass standards or for the calibration of weighing instruments. This fact is the reason for the aimed accuracies of the PB. The PB should be capable of calibrating E1 or E2 mass standards, or reach an accuracy that is comparable as if the balance were calibrated with an E1 (or E2) mass standard. As a result, the aimed accuracy makes it possible to weigh masses without calibrating the balance by means of calibrated mass standards. This has the significant advantage that no handling of reference masses is necessary, because especially for mass values of 1 mg and below the handling

6.  Summary and outlook A new weighing instrument, the Planck-Balance, has been presented that will be able to calibrate mass standards without comparison to other mass standards of higher acc­ uracy classes. This is possible due to the new definition of the kilogram which will relate the mass to the Planck constant. Additionally, the PB can be used as a weighing instrument with traceability to the new definition of the kilogram. It is based on the Kibble balance principle and is thus a primary method of realizing the unit kilogram, as described in the Mise en Pratique. The new instrument will be able to cover a measurement range from 1 mg up to 1 kg, with an aimed relative measurement uncertainty (k  =  1) of up to 8.4 × 10−8 (at 1 kg). This will be sufficient to calibrate E1 and E2 standard masses, and represents an attractive alternative for NMIs, for industry or legal metrology where high accuracy is required. A convincing benefit of the Planck-Balance is that artefacts of small 8

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sizes can easily be calibrated. With the conventional calibration method, where the mass under test is compared to a calibrated weight, the handling sometimes is very difficult or even impossible. The PB will be able to measure over a continuous range and will not be limited to discrete mass values. Acknowledgments The research of this project is funded via Validierung des technologischen und gesellschaftlichen Innovationspotenzials —VIP  +, a program of the German Federal Ministry of Education and Research (BMBF), and is managed by VDI/ VDE Innovation  +  Technik GmbH. We like to thank Dr. Ilko Rahneberg for all the fruitful discussions during prep­aration of the project and his valuable contributions to the first exper­ imental set-up. ORCID iDs C Rothleitner https://orcid.org/0000-0002-7757-0007 J Schleichert https://orcid.org/0000-0002-3679-686X N Rogge https://orcid.org/0000-0001-5614-3180 L Günther https://orcid.org/0000-0002-7981-3770 S Vasilyan https://orcid.org/0000-0001-9399-3504 D Knopf https://orcid.org/0000-0002-8723-7187 T Fröhlich https://orcid.org/0000-0002-6060-7248 References [1] Davis R, Barat P and Stock M 2016 A brief history of the unit of mass: continuity of successive definitions of the kilogram Metrologia 53 A12 [2] Gläser M, Borys M, Ratschko D and Schwartz R 2010 Redefinition of the kilogram and the impact on its future dissemination Metrologia 47 419 [3] BIPM Cons. Com. Units 2016 Draft of the ninth SI Brochure. www.bipm.org/utils/common/pdf/si-brochure-draft-2016b. pdf Accessed 30-January-2018 [4] Mohr P, Newell D, Taylor B and Tiesinga E 2018 Data and analysis for the CODATA 2017 special fundamental constants adjustment Metrologia 55 125 [5] Azuma Y et al 2015 Improved measurement results for the avogadro constant using a 28 Si-enriched crystal Metrologia 52 360

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