Modeling of magnetic field perturbations on the balance-spring of a mechanical watch

Abstract : A magnetic field is a major enemy of a mechanical watch. This field may modify the structure of the balance-spring and change its resonance frequency. As a consequence, the watch loses its accuracy. The aim of this work is to quantify the impact of the magnetic field to the balance-spring resonance using a finite element approach. This coupled magneto-mechanical problem implies magnetic forces computation while accounting for a large rotation of the spring. An original algorithm including a dynamic mechanical time-stepping scheme is proposed to quantify the change of the resonance frequency. Index Terms-Mechanical watch, resonance frequency, coupled magneto-mechanic problem.