Table of contents

The time is fast approaching when the SI unit of mass will cease to be based on a single material artefact and will instead be based upon the defined value of a fundamental constant—the Planck constant—h . This change requires that techniques exist both to determine the appropriate value to be assigned to the constant, and to measure mass in terms of the redefined unit. It is important to ensure that these techniques are accurate and reliable to allow full advantage to be taken of the stability and universality provided by the new definition and to guarantee the continuity of the world's mass measurements, which can affect the measurement of many other quantities such as energy and force.

Up to now, efforts to provide the basis for such a redefinition of the kilogram were mainly concerned with resolving the discrepancies between individual implementations of the two principal techniques: the x-ray crystal density (XRCD) method [1] and the watt and joule balance methods which are the subject of this special issue. The first three papers report results from the NRC and NIST watt balance groups and the NIM joule balance group. The result from the NRC (formerly the NPL Mk II) watt balance is the first to be reported with a relative standard uncertainty below 2 × 10⁻⁸ and the NIST result has a relative standard uncertainty below 5 × 10⁻⁸. Both results are shown in figure 1 along with some previous results; the result from the NIM group is not shown on the plot but has a relative uncertainty of 8.9 × 10⁻⁶ and is consistent with all the results shown. The Consultative Committee for Mass and Related Quantities (CCM) in its meeting in 2013 produced a resolution [2] which set out the requirements for the number, type and quality of results intended to support the redefinition of the kilogram and required that there should be agreement between them. These results from NRC, NIST and the IAC may be considered to meet these requirements and are likely to be widely debated prior to a decision on redefinition. The CCM had already recognized that agreement was close and has set in place a process whereby redefinition can take place by 2018. The final decision will be in the hands of the Conférence Générale des Poids et Mesures (CGPM) but the results reported here should aid a positive decision.

Figure 1. Results from recent measurements of the Planck constant. The reference for the results h₉₀ is derived from the conventional values of the Josephson constant K_J−90 and the von Klitzing constant R_K−90. The factor of ten improvement in uncertainty of the NRC watt balance result, over that achieved by the same apparatus at NPL a few years earlier, can be understood as a factor of five improvement arising from the elimination of an effect discovered at NPL that could not be eliminated before shipment to Canada and a factor of two arising from the considerable improvements made by NRC.

Once the kilogram has been redefined, the watt and joule balances will complete their transitions from instruments that are primarily of interest to the electrical community for determining the SI electrical units from the mechanical units, to the principal methods by which an individual National Measurement Institute (NMI) can make an independent determination of the SI unit of mass and thereby contribute to the maintenance of national and international mass scales.

This special issue gives an introduction to the diversity of techniques which are required for the operation of watt and joule balances. However it does not contain a review of existing balances; this was a deliberate decision, as a number of such review papers have been published in the past five years [3–7] and it was felt that it was not yet time for another.

The first technique considered is that of gravimetry; the watt balance measures the weight Mg of a mass M , and to convert the measured weight into a mass, the value of the acceleration due to gravity g must be known, at the time of the weighing and at the centre of gravity of the mass. The paper by Liard and his co-authors at NRC describes how they have made this essential measurement.

The accuracy of the watt balance may also depend on the alignment of the apparatus. Two papers deal with this important issue. The first, by Sanchez and his co-authors at NRC, shows that their balance is insensitive to a range of alignments and concentrates on the essential alignments that contribute directly to the overall uncertainty of the apparatus. Thomas and his co-authors at LNE describe their technique for reducing uncertainties in their watt balance by aligning its coil in the field of the magnet to minimize both horizontal forces and torques about horizontal axes.

The search for discrepancies between the results from watt balances has encouraged researchers to consider possible error mechanisms arising from the secondary electrical interactions between the coil of a watt balance and other parts of the apparatus. Researchers from INRIM have two such papers: one considering magnetic interactions and the other considering electrostatic interactions. It is essential that such investigations are carried out: both to prove that the problems are understood and for the guidance of those building the next generation of watt and joule balances.

The next four papers describe aspects of the construction of watt balances.

The BIPM watt balance group describe the principles behind their simultaneous measurement scheme for a watt balance. The balance that they are constructing can also be used in the conventional two-phase mode and their paper describes the relative advantages and disadvantages of the two modes of operation.

In a watt balance there are some advantages to precise vertical movement of the coil. The METAS group describe the two mechanisms that they have tested to achieve such motion and give the reasons for the choice of mechanism for use in the balance that they are constructing.

The KRISS watt balance group are in the initial phases of the design and construction of a watt balance and their paper provides valuable information on the design that they are building.

The design of the main magnet of a watt balance is critical to its successful operation, and an important assumption of watt balance operation is that the field of the magnet in moving mode is equivalent to that in weighing mode. Sutton and Clarkson from MSL describe a novel magnet which is designed to address this issue.

The international prototype of the kilogram is kept in air but, after redefinition, the best realizations of the mass unit will be in vacuum. In their paper Berry and Davidson from NPL describe progress in techniques which relate mass measured in vacuum to that measured in air. Such techniques will be essential for making the results of watt and joule balance measurements available to science and industry.

Both the NIST and NPL Mark II (NRC) watt balances use knife edges to act as the pivots for the beam. Knife edges suffer from hysteresis which can produce systematic offsets during weighing. In their paper Choi (KRISS) and Robinson (NPL) describe the analysis of this problem using both finite element (FEM) techniques and a stand-alone balance designed for testing knife edges.

The last two papers deal with the possible future of the watt balance technique.

The BIPM simultaneous measurement scheme for the watt balance was originally conceived for operation at cryogenic temperatures with a superconducting coil. In their paper de Mirandes and her co-authors describe initial work on the principles of this superconducting variant of the BIPM watt balance and concentrate on the characteristics of the superconducting coil in comparison with those of a normal coil.

The final paper is a good example of serendipity in which Kibble (Independent Consultant) was designing novel watt balances based on seismometer suspensions and Robinson (NPL) had derived a set of general expressions, which are required for a watt balance to be immune to a range of common misalignments but also lead to the design of watt balances with a range of coil motions. The combination of these techniques has led to the novel watt balance designs which are described.

Finally I would like to thank: the editor of Metrologia and the editorial staff of IOP Publishing, the referees who have responded rapidly to requests and have kept the issue on schedule, and the authors who have taken the time to provide a range of papers showing the breadth of the work required to build and operate watt or joule balances.

References

[1] Andreas B et al 2011 Determination of the Avogadro constant by counting the atoms in a 28Si crystal Phys. Rev. Lett.106 030801

[2] BIPM 2013 Report of the 14th Meeting of the CCM Sèvres pp 34–7

[3] Steiner R 2013 History and progress on accurate measurements of the Planck constant Rep. Prog. Phys.76 016101

[4] Stock M 2013 Watt balance experiments for the determination of the Planck constant and the redefinition of the kilogram Metrologia50 R1–16

[5] Li S, Han B, Li Z and Lan J 2012 Precisely measuring the Planck constant by electromechanical balances Measurement45 1–13

[6] Eichenberger A, Genevès G and Gournay P 2009 Determination of the Planck constant by means of a watt balance Eur. Phys. J. Spec. Top.172 363–83

[7] Robinson I A 2009 Toward the redefinition of the kilogram: measurements of Planck's constant using watt balances IEEE Trans. Instrum. Meas.58 942–8

We have measured Planck's constant and have obtained a value of 6.626 070 34(12) × 10⁻³⁴ J s. To our knowledge this measurement of h has the lowest uncertainty reported to date. This result has been obtained from measurements of four masses of different material and nominal values varying from 1 kg to 250 g. The experimental procedures and the measurement uncertainties are described in detail.

For the past two years, measurements have been performed with a watt balance at the National Institute of Standards and Technology (NIST) to determine the Planck constant. A detailed analysis of these measurements and their uncertainties has led to the value h = 6.626 069 79(30) × 10⁻³⁴ J s. The relative standard uncertainty is 45 × 10⁻⁹. This result is 141 × 10⁻⁹ fractionally higher than h₉₀. Here h₉₀ is the conventional value of the Planck constant given by $h_{90}\equiv 4 /( K_{{\rm J\mbox{-}90}}^2R_{{\rm K\mbox{-}90}})$, where K_J-90 and R_K-90 denote the conventional values of the Josephson and von Klitzing constants, respectively.

The advantage of the joule balance over the classic watt balance is that the dynamic measurement in the watt balance is replaced by a static measurement, which makes the whole measurement procedure easier. The main problems in the joule balance are the precise measurement of mutual inductance and coil heating. These problems and recent progress in the development of the joule balance are described and discussed in this paper. The whole system is at the stage of being adjusted and improved. The principle of the joule balance has been demonstrated by a measurement of the Planck constant, h = 6.626 104(59) × 10⁻³⁴ J s with an 8.9 ppm measurement uncertainty.

In a watt balance (WB) the gravity on a known mass is used in the determination of the value of the Planck constant with a precision of <2 × 10⁻⁴¹ J s. To attain this precision the gravity value at the centre of a mass within the WB must be known with a relative uncertainty of <1 × 10⁻⁸. This necessitates laboratory gravity mapping in three dimensions, the establishment close to the WB of a gravity reference station, and modelling of the ties to the centre-of-mass location. The self-gravity of the WB must be accounted for, and since WB measurements run over several weeks, corrections for tidal, polar motion and atmospheric effects must be included. We describe the gravimetry carried out at the National Research Council of Canada WB laboratory, and include a discussion of past gravity variations in the vicinity of the WB, which suggest that seasonal variation may be of sufficient magnitude to affect results obtained with the balance.

This paper presents a comprehensive analysis of the alignment uncertainties in the NRC watt balance. We show that, due to the use of a beam balance in both phases of the experiment, some of the alignment errors of the weighing phase are correlated with errors in the moving phase, which makes our watt balance insensitive to some forms of misalignment. These correlations become inexact in the presence of parasitic forces acting on the coil former. We present evidence of such forces and estimate their effect and contribution to the various uncertainty components. Finally we describe the techniques used to align the apparatus and we give an estimate of all relevant alignment uncertainty components.

Alignments of watt balance experiments are necessary to achieve a relative uncertainty at a level of few parts in 10⁸. This paper briefly describes the LNE watt balance and concentrates on adjustments made to minimize the coil movements during weighing mode. The parasitic forces and torques involved in these movements are estimated by a mathematical model. Some of the calculated parasitic forces are compared with an evaluation done by studying the yaw movement of the beam.

In the watt-balance experiments, separate measurements of the magnetic and electromotive forces in a coil in a magnetic field enable a virtual comparison between mechanical and electric powers to be carried out, which leads to an accurate measurement of the Planck constant. This paper investigates the three-dimensional nature of the coil–field interaction and describes the balance operation by a continuous three-dimensional model.

In a watt balance, stray capacitances exist between the coil and the magnet. Since the electric current flowing in the coil creates a difference in electric potentials between the coil and magnet, their electrostatic interactions must be taken into account. This paper reports the results of a finite element analysis of the forces acting on the coil.

The International Bureau of Weights and Measures (BIPM) is developing a novel watt balance based on a simultaneous measurement scheme for the forthcoming redefinition of the kilogram. The two distinct measurement phases in a conventional watt balance are carried out in a single phase where all quantities are measured simultaneously. The main characteristics of this simultaneous measurement approach are described. An analysis of the advantages and the drawbacks is carried out.

There is a firm will in the metrology community to redefine the kilogram in the International System of units by linking it to a fundamental physical constant. The watt balance is a promising way to link the mass unit to the Planck constant h. At the Federal Institute of Metrology METAS a second watt balance experiment is under development. A decisive part of the METAS Mark II watt balance is the mechanical linear guiding system. The present paper discusses the development and the metrological characteristics of two guiding systems that were conceived by the Laboratoire de Systèmes Robotiques of EPFL and built using flexure mechanical elements. Integration in the new setup is also described.

We report the design of the KRISS watt balance, which includes a magnet, a guiding stage and a coil position measurement system. The KRISS watt balance incorporates a closed-type cylindrical permanent magnet and a motion guiding stage. For the magnet, a flux shunt is used to reduce flux changes due to temperature variations. A piston gauge is used to achieve linearity in the motion guiding stage. In the weighing mode, the residual force between the weight of the test mass and the Lorentz force generated in a coil is measured by a commercial weighing cell. In the dynamic mode, a linear motor in the motion guiding stage vertically translates the coil and the weighing cell. The in-plane motion of the coil is measured by position sensors, and the out-of-plane motion is measured by single-pass homodyne interferometers.

A novel design for the magnet system of a watt balance is presented. While primarily intended for the watt balance being developed by MSL, this design could be used for other watt balances. It has a radial magnetic field in an annular gap that is screened from external fields. The magnetic field is generated by a single ring-shaped permanent magnet and the geometry is such that the field induced in the permanent magnet by the current in the coil in the weighing mode is zero on average. Hence the magnetic field in the gap is expected to be the same for both the weighing and dynamic modes of a watt balance. From finite element modelling, the magnetic field strength can be uniform to within 40 parts in 10⁶ over more than 50 mm (50% of the gap height) and the usable working range for the coil is about 40 mm. Further, the diameter of the annular gap can be relatively small, allowing the coil and its support structure to be kept relatively stiff and light.

This paper reports work undertaken to evaluate the change in mass of platinum/iridium, stainless steel and silicon artefacts measured at atmospheric pressure and in vacuum at a range of pressures typical of those used in vacuum mass comparators and watt balances and for x-ray crystal density (XRCD) measurements. The sets of platinum/iridium, stainless steel and silicon artefacts used in this work have different surface areas and the effect of transferring them between atmospheric pressure and different levels of vacuum was evaluated by measuring the relative changes in mass between them.

Reversible variations in the mass differences between the artefacts were found over the pressure range from 0.1 Pa to 100 000 Pa (atmospheric pressure). At lower pressures (0.001 Pa to 0.1 Pa) the mass differences between all the artefacts were stable and no evidence for hysteresis over this range was found when going down in pressure compared with increasing pressure. Therefore consistent results between watt balance, XRCD measurements and vacuum mass measurements can be realized providing the measurements are performed within this pressure range.

Of the seven base units of the international system of units, the SI, only the kilogram is still defined in terms of a material artefact. The watt balance is an experimental approach which supports a new definition of the kilogram in terms of constants of nature. Some watt balances, such as the NPL Mk II watt balance, use knives and flats for the balance pivots as they have the advantages of greater robustness over flexure pivots in this particular application. However, hysteresis in the knives can produce errors in the weighing through systematic shifts in the equilibrium point of the balance and it is desirable to investigate this effect as an aid to its elimination. This paper analyses the hysteresis mechanism using both finite element techniques and direct measurement. It was found that the cause of hysteresis is not normal stress but shear stress and that the deformation of the flat, rather than that of the knife, is an important factor. Problems that could not be analysed in a two-dimensional finite element model were investigated using a simplified stand-alone balance. The combined results from the finite element analysis and the stand-alone balance suggest that material properties and tip radius are more important than friction coefficient and tip angle. At loads where knife and flat distortion are low the straightness of the knife and the roughness of the surfaces can have a significant effect.

The BIPM has built an experimental setup dedicated to the study of the physical behaviour of a superconducting coil during the dynamic phase of a watt balance experiment. We have compared it with the behaviour of a normal conducting coil. First experimental results are presented and preliminary conclusions are drawn.

It has been known for some time that the watt balance, which is based on the virtual work principle, is insensitive to some misalignments which would, at first sight, be expected to produce significant errors. In this paper we show that, in particular circumstances, this insensitivity applies to a whole range of misalignments. This effect can be exploited to design a watt balance, with a constrained coil motion, which offers advantages over conventional designs. We present three such new designs: one is based on a conventional balance and the other two are based on strip hinges, which are known to have excellent properties when measuring small force differences and with the production of precise linear movements having little motion in the other five degrees of freedom. A constrained design of this kind would have advantages for reproducing the forthcoming SI definition of mass in the range from milligrams to kilograms, whenever and wherever desired, and might well do so with improved accuracy.