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

Abstract

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 centimetres 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 magntitude 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 −6.3·10−6, with a residual relative uncertainty of 6.3 · 10−7, 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.

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

“…with c denoting the quadratic coefficient of the magnetic profile function (considering the magnetic profile as a parabola) and A denoting the oscillation amplitude [14]. Removing the yoke turned out to be quite easy.…”

B6.4 - A Vertically Positionable Permanent Magnet System for the Planck-Balance

“…A scale on the adjusting ring allows the magnet to be positioned with a resolution of 20 µm, which is sufficient for our application. Since the position-dependent Bl can also lead to other errors, such as higher order harmonics in the induction voltage signal [4], an improvement in performance is expected.…”