Modeling of Magnetic Field Perturbations on the Balance Spring of a Mechanical Watch

A magnetic field is a major enemy of a mechanical watch. Such field modifies the structure of the balance spring that gives rhythm to the watch and thus changes its resonance frequency. Consequently, the watch loses its accuracy. The aim of this paper is to quantify the impact of the magnetic field on the structure and the resonance of the balance spring using a finite-element approach. This coupled magnetomechanical problem implies magnetic force computation, including both magnetostatic forces and magnetostriction effect, while accounting for a large rotation of the spring. An algorithm, including a dynamic mechanical time-stepping scheme, is proposed to quantify the change of the resonance frequency.