Watt Balance Research Articles

A novel magnet system—which enables uniformity of radial flux density by means of a parabolic yoke—applied in the Planck-Balance

Abstract A uniform magnetic flux density that is effective in the movement range of the coil is essential for accurate Kibble balance experiments. By utilizing Hopkinson’s law and Kirchhoff’s circuit laws, basic formulas have been derived, providing a method to calculate the magnetic flux density distribution in the airgap of a cylindrical magnet system. A parabolic outer contour of the inner yoke has been found to be a suitable solution to achieve uniformity. Experiments show, that this approach results in a relative change of magnetic flux density in the order of 3 ⋅ 10 − 4 per 8 mm movement range, using a magnet system with a mass of only 2.3 kg. Therefore, the system will be integrated into the upgraded version of PTB’s Planck-Balance—a compact variant of a Kibble balance—aiming for sub 1 ⋅ 10 − 6 accuracy level determination of the geometric factor. The solution described provides a comparatively easy means to design a cylindrical magnet system, using only one permanent magnet disc, without the use of complex simulation software.

Flexures for Kibble balances: minimizing the effects of anelastic relaxation

We studied the anelastic aftereffect of a flexure being used in a Kibble balance, where the flexure is subjected to a large excursion in velocity mode after which a high-precision force comparison is performed. We investigated the effect of a constant and a sinusoidal excursion on the force comparison. We explored theoretically and experimentally a simple erasing procedure, i.e. bending the flexure in the opposite direction for a given amplitude and time. We found that the erasing procedure reduced the time-dependent force by about 30%. The investigation was performed with an analytical model and verified experimentally with our new Kibble balance at the National Institute of Standards and Technology employing flexures made from precipitation-hardened Copper Beryllium alloy C17200. Our experimental determination of the modulus defect of the flexure yields 1.2×10−4 . This result is about a factor of two higher than previously reported from experiments. We additionally found a static shift of the flexure’s internal equilibrium after a change in the stress and strain state. These static shifts, although measurable, are small and deemed uncritical for our Kibble balance application at present. During this investigation, we discovered magic flexures that promise to have very little anelastic relaxation. In these magic flexures, the mechanism causing anelastic relaxation is compensated for by properly shaping and loading a flexure with a non-constant cross-section in the region of bending.

Preliminary characterization of anelastic effects in the flexure mechanism for a new Kibble balance at NIST

A new Kibble balance is being built at the National Institute of Standards and Technology (NIST). For the first time in one of the highly accurate versions of this type of balance, a single passive flexure mechanism is used for both modes of operation: the weighing mode and the velocity mode. The mechanism is at the core of the new balance design as it represents a paradigm shift for NIST away from using knife edge-based balance mechanisms, which exhibit hysteresis in the measurement procedure of the weighing mode. Mechanical hysteresis may be a limiting factor in the performance of highly accurate Kibble balances approaching single digit nanonewton repeatability on a nominal 100g mass, as targeted in this work. Flexure-based mechanisms are known to have very good static hysteresis when used as a null detector. However, for larger and especially longer lasting deformations, flexures are known to exhibit anelastic drift. We seek to characterize, and ideally compensate for, this anelastic behavior after deflections during the velocity mode to enable a 10−8 accurate Kibble balance-measurement on a nominal 100g mass artifact with a single flexure-based balance mechanism. A measurement of the anelastic after-effect after static excitation hints that the apparatus produced a result for anelastic relaxation comparable to previously published work. Furthermore, a series of oscillatory displacements similar to those occurring in a velocity mode of a Kibble balance measurement are imposed upon the flexure mechanism and show a significant anelastic relaxation torque resulting in multiple micronewton of force relaxation. The amplitude of this force relaxation could be reduced by counterbending the flexures before performing a force measurement.

High-accuracy determination of the beam divergence error in free-fall absolute gravimeters

We investigate the bias due to the beam divergence of the collimator in a free-fall absolute gravimeter of type FG5X. First, we measure the beam parameters with a Shack-Hartmann sensor. Then, we use the parameters to simulate the relative gravitational acceleration error of an FG5X gravimeter, which employs an unbalanced Mach-Zehnder laser interferometer. This investigation we do with four different commercial collimators, providing different divergence angles. We compare the results to real gravity measurements using the same collimators. The larger the divergence angle, and the bigger the relative length error, the bigger is the bias in the gravity measurements. A good agreement between theory and experiment is found, resulting in a relative bias of −2.77(24)⋅10−9 ( −2.72(24) μGal) for our standard collimator of type Thorlabs TC25APC, which is usually used for free-fall acceleration determinations. The outcome is also important for the realization of the SI unit kilogram via Kibble balance experiments that, on one side, employ laser interferometers for velocity measurements, and, on the other side, require accurate values of the gravitational acceleration. For example, if this divergence error is not corrected in the Kibble balance, then the mass determination would be biased by 2.77(24) μg kg−1 (numbers are valid only for our gravimeter with our collimator and fiber).

A Bi-polar Current Source with High Short-term Stability for Tsinghua Tabletop Kibble Balance

A Bi-polar Current Source with High Short-term Stability for Tsinghua Tabletop Kibble Balance

A simple Kibble balance approach for principle demonstration at Inmetro

This work shows the results obtained by Inmetro’s mass lab implementation of a simple Kibble balance approach for demonstration of its mass measurement principle based on the Planck’s constant. It is based on some modifications of Mimimal Watt Balance work reducing the required electrical measurements by using two loudspeakers mechanically coupled so that one of them acts as a linear actuator in order to perform BL measurements in the moving phase. The mean BL value obtained in weighing phase was 2.66 N/A and in moving phase 2.67 N/A. The maximum error of mass values measured for standard weights in the range from 5 g to 50 g was lower than 5%.

A method for evaluating the force factor in oscillating Kibble balances with application to the Planck-Balance

The Planck-Balance is a table-top version of a Kibble balance, developed in a collaboration between the PTB and TU Ilmenau. In contrast to most Kibble balances, where the motion range is of up to several centimeters in the velocity mode, in the Planck-Balance it is below 100 μm. For a reliable determination of the force factor, the voice coil is set into harmonic oscillation, resulting in an induced AC voltage. The amplitude of the first harmonic is then taken to determine the force factor. However, due to the non-linear magnetic field across the motion range, the first harmonic is subject to a bias, and higher harmonics are excited. Those higher harmonics contain the information about the relative magnitude of the bias in the first harmonic, and can be used for a correction. In this paper we present an analytical model and show its application with real measurements. The estimated relative bias amounts to , with a residual relative uncertainty of , for an oscillation amplitude of 20 μm. This method is especially of importance for Kibble balances with short motion range and working with harmonic oscillation. After such a correction is applied, a table-top version of a Kibble balance can be used as a conventional balance calibrated by means of E2 mass standards in the whole E2 class mass range.

Comparison of fiber interferometric sensor with a commercial interferometer for a Kibble balance velocity calibration

This article presents a fiber interferometric sensor (FIS) for measuring the velocity amplitude of an oscillatory vibrating object, with a focus on velocity mode measurement in applications using the Kibble balance principle. The sensor uses the range-resolved interferometry method to measure the displacement of the moving object and employs a multi-harmonic sine-fit algorithm to estimate the displacement amplitude and frequency, thereby determining the velocity amplitude. This article provides a comprehensive explanation of the experimental setup and the measurement techniques employed, as well as a detailed analysis of the uncertainty budget, with the performance validation of the FIS benchmarked against a commercial interferometer within a Kibble balance setup. The velocity amplitude of a coil of the Kibble balance, oscillating with an approx. amplitude of 20 μm and a frequency of 0.25 Hz, was measured using the sensor and found to be 31.282 31 μm s−1 with a relative deviation of −1.9 ppm compared to a commercial interferometer. The high performance of the FIS, especially with regard to non-linearity errors, and the small size of the measuring head enable universality of integration into a wide variety of measurement systems, also including the use as general-purpose vibration and displacement sensor.

The Planck constant of action and the Kibble balance

It has been shown previously (P. R. Bunker and Per Jensen, J. Quant. Spectrosc. Radiat. Transf., 243 (2020) 106835) that if we choose angles to have dimension, we have to distinguish between the Planck constant h, having the dimension of actionangle−1, and the Planck constant of action hA, having the dimension of action. In the present paper, we show that a further implication that results from choosing angles to have dimension is that the Kibble balance equation relating the mass weighed to the Planck constant has to involve both of the distinct fundamental constants h and hA. We derive that new equation here and show how it compares to the equation that is obtained if one chooses angles to be dimensionless as required in SI.

Measuring Planck’s Constant With Compton Scattering

Measured values of the electron mass and Compton wavelength yield a value of Planck’s constant with a relative standard
 uncertainty of 3 × 10−10. This is only slightly larger than the 1.3 × 10−10 relative standard uncertainty in measurements
 performed using the Kibble balance. Compton scattering presents an alternative pathway for improving the value of
 Planck’s constant.
 Natural units of length, mass, and time offer viable solutions for improving the values of physical constants. While
 extensive values of the Planck units lie beyond the reach of present-day instrumentation, certain product and quotient
 pairs of Planck units such as the speed of light can be measured with relatively high precision. Better measurements of
 certain unit pairs will improve the value of the gravitational constant.

Vacuum compatible vertical-laser alignment method based on an oil mirror and air-spaced doublets.

In the field of precision measurement and metrology, a vertical laser is a valuable measurement tool. Its applications include, but are not limited to, the measurement of vertical displacement and attitude in the Kibble balance and joule balance for kilogram realization. A vacuum compatible, vertical-laser alignment method based on an oil mirror and air-spaced doublets is proposed to measure and compensate the vertical deviation angle of the laser beams. Dimethyl silicone oil was selected as the natural direction reference, and the air-spaced doublets were designed as the focusing elements to make the deviation angle correspond to a distance of spots. The corresponding alignment system is vacuum compatible, nonmagnetic, and can be miniaturized. In addition to the mass traceability in the realization of a kilogram, this system can also be applied to the gravity measurements of outer space planets in the field of aerospace science. The off-axis error, which is the highly influential systematic error of the alignment system, is suppressed by replacing the plano-convex lens with a combined optical element-"air-spaced doublets+aperture." The performance of the alignment system has been investigated by experiments. The Type B uncertainty of the alignment system was evaluated to be 19.19 µrad.

Design of the Tsinghua Tabletop Kibble Balance

The Kibble balance is a precision instrument for realizing the mass unit, the kilogram, in the new international system of units (SI). In recent years, an important trend for Kibble balance experiments is to go tabletop, in which the instrument’s size is notably reduced while retaining a measurement accuracy of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-8</sup> . In this paper, we report a new design of a tabletop Kibble balance to be built at Tsinghua University. The Tsinghua Kibble balance aims to deliver a compact instrument for robust mass calibrations from 10 g to 1 kg with a targeted measurement accuracy of 50 μg or less. Some major features of the Tsinghua Kibble balance system, including the design of a new magnet, one-mode measurement scheme, the spring-compensated magnet moving mechanism, and magnetic shielding considerations, are discussed.

Establishing and characterizing a permanent magnet system for the prototype of NIS's Kibble balance

Establishing and characterizing a permanent magnet system for the prototype of NIS's Kibble balance

UME Kibble balance operating in air

The UME KB-3 operating since 2020 allows the realization of kilogram under ambient air conditions owing to its distinguishing design and operation protocol. This is possible only because the coil pair is stationary but the surrounding magnet assembly is moving. The mechanically decoupled nature of the magnet assembly allows the implementation of a local vacuum for displacement measurements rather than a vacuum covering the entire apparatus. The balance operates in single mode with simultaneous operation of weighing and moving phases instead of successive phases. A novel dynamical measurement procedure is developed in order to conform with the single phase measurements. The paper describes the apparatus and presents the measurement results for stainless steel mass artefact with a nominal value of 1 kg. The mass of the artefact is measured with a total relative uncertainty of 54 ppb.

Novel Multi-Electromagnetic-Force-Compensation Weighing Cell With Axis-Symmetric Structure

A Kibble balance for the realization of a redefined kilogram requires an ultraprecision weighing cell for measuring the difference between gravitational force and electromagnetic force. In this article, we propose a novel electromagnetic force compensation weighing cell for the Kibble balance at the Korea Research Institute of Standards and Science. To be compatible with the Kibble balance, the proposed weighing cell is designed axial symmetrically using a triple compound guide mechanism and a trilever mechanism based on a compliant mechanism. The weighing cell employs three independent mass measurement units to measure the test mass by dividing it, thereby improving the structural stability, weighing accuracy, and ground-tilt response. For a 1-kg test mass, the repeatability of the weighing cell was 0.74 mg in the air; it was improved to 0.20 mg when the zero-point drift was compensated. Finally, the experimental ground-tilt response of the weighing cell suggested that the ground-tilt angle can be estimated by observing the change in the compensating force of each mass measurement unit.

Position control for the MSL Kibble balance coil using a syringe pump

The position of the coil in a Kibble balance must be finely controlled. In weighing mode, the coil remains stationary to maintain a constant magnetic field. In calibration mode, the coil is moved in the magnetic field to induce a voltage. The MSL Kibble balance design is based on a twin pressure balance where the coil is attached to the piston of one of the pressure balances. Here we investigate how the piston (and therefore coil) position may be controlled through careful manipulation of the gas column under the piston. We demonstrate the use of a syringe pump as a programmable volume regulator which can provide fall rate compensation as well as controlled motion of the piston. We show that the damped harmonic oscillator response of the pressure balance must be considered when moving the coil. From this initial investigation, we discuss the implications for use in the MSL Kibble balance.

A ‘Dynamic Kibble’ mass balance for the undergraduate physics teaching laboratory

Originally envisaged in 1975 to realise the SI unit of electrical current, the Ampere, the Kibble balance has since developed into a powerhouse of modern scientific measurement. By combining theoretical simplicity with precision of measurement, it has enabled the redefinition of Planck’s constant, and subsequently a practical method of defining the kilogram in terms of fundamental constants. This article introduces a novel version of this classic apparatus, the ‘Dynamic Kibble’ Balance. Dynamic in this case because the magnet velocity is now 3 orders of magnitude higher than the original, but the same theory applies. The apparatus is simple in approach, robust, easy to set up, and capable of a high level of precision using only electrical measurements (plus length and time). The importance of this measurement to metrology re-enforces the link between what is measured in the laboratory via calibration, measurement standards, and traceability. Using the apparatus and measurements described in this paper, the mass of the magnet assembly was measured as 19.4 ± 0.3 g, which lies within one SEM of the known value. This paper describes an uncomplicated method with a clear focus on the key physics and theory required. This experiment is intended for use in a first-year undergraduate physics laboratory. Further potential for both more advanced theory demonstration and experimental work is discussed.

Accurate graphene quantum Hall arrays for the new International System of Units

Graphene quantum Hall effect (QHE) resistance standards have the potential to provide superior realizations of three key units in the new International System of Units (SI): the ohm, the ampere, and the kilogram (Kibble Balance). However, these prospects require different resistance values than practically achievable in single graphene devices (~12.9 kΩ), and they need bias currents two orders of magnitude higher than typical breakdown currents IC ~ 100 μA. Here we present experiments on quantization accuracy of a 236-element quantum Hall array (QHA), demonstrating RK/236 ≈ 109 Ω with 0.2 part-per-billion (nΩ/Ω) accuracy with IC ≥ 5 mA (~1 nΩ/Ω accuracy for IC = 8.5 mA), using epitaxial graphene on silicon carbide (epigraphene). The array accuracy, comparable to the most precise universality tests of QHE, together with the scalability and reliability of this approach, pave the road for wider use of graphene in the new SI and beyond.

Development of a novel dynamic torque generation machine based on the principle of a Kibble balance

This paper presents a novel dynamic torque generator based on the principle of a Kibble balance. A generator is developed to dynamically calibrate torque-measuring devices (TMDs) for the measurement of dynamic torque. Unlike conventional gravity-based deadweight torque standards, this method uses electromagnetic force to generate a dynamic torque traceable to the International System of Units. Dynamic torque is generated by dynamically changing the electric current supplied to the coil. Consequently, dynamic torque is generated up to 100 Hz. Furthermore, a system is developed to simultaneously measure the electric current and output of a TMD to verify the evaluation method of the dynamic characteristics of the TMD.

Deploying the high-power pulsed lasers in precision force metrology – Towards SI traceable and practical force quantization by photon momentum

Abstract Design and operational performance of table-top measurement apparatus is presented towards direct Planck constant traceable high accuracy and high precision small forces and optical power measurements within the SI unit system. Electromagnetic force compensation weighing balances, highly reflective mirrors and high-energy pulsed laser unit (static average power 20 W) are tailored together with a specially developed opto-electro-mechanical measurement infrastructure for cross-mapping the scale-systems of two different precision small force measurement methods. One of these methods obtains the force measurements by a state-of-the-art classical kinematic system employing the partial use of Kibble balance principle in the range of 10 nN to 4000 nN to be compared with forces generated due to quantum-mechanical effect namely the transfer of the momentum of photons from a macroscopic object. Detailed overview of the adapted measurement methodology, the static and the limits of dynamic measurement, the metrological traceability routes of the measurement parameters, quantities and their measurement uncertainties, parametric estimation of up (down)-scaling perspectives of the measurements are presented with respect to the state-of-the-art measurement principles and standard procedures within the newly redefined International System of Units (SI).