Theoretical foundations of nonlinear electromagneto-mechanical systems: applying Finsler geometry to Kibble Balances

TL;DR

This paper introduces a differential geometric framework using Finsler geometry to analyze nonlinear electromagneto-mechanical systems like Kibble balances, providing new insights into their design and limitations.

Contribution

It develops a novel mathematical approach based on Finsler geometry to model and analyze nonlinear Kibble balances, extending existing theories to include non-linear effects.

Findings

Finsler geometry effectively models nonlinear behaviors in Kibble balances.

Numerical simulations highlight differences between linear and nonlinear analyses.

Hysteretic effects in magnetic systems are better understood through this approach.

Abstract

Kibble balances are energy-conversion devices currently employed to realize the metrological redefinition of the kilogram unit of mass. The authors, noticing that the literature lacks a fundamental mathematical description of the Kibble balance working principle, propose a differential geometric approach to study general non-linear electromagneto-mechanical systems. Based on the application of Finsler geometry, the mathematical apparatus introduced in the paper is used to analyze the limits of modern Kibble balances, with particular attention to the magnetic design. The authors review the formalism introduced by G. Kron (who proposed a unified theory of electrical machines) and extend it to non-linear systems. Numerical simulations are presented to show the difference between a linear and non-linear analysis of Kibble balance machines, with attention to the hysteretic behaviour of the permanent magnet system.