Geometrical and mechanical characteristics of deformed balance spring obtained by simulation study

This paper analyzes the geometrical and mechanical characteristics of balance springs, which have the most important influence on the oscillation rate of the balance wheel and, consequently, the most decisive effects on the timekeeper’s accuracy. These characteristics are obtained by a set of SolidWorks simulations of static structural studies based on the finite element model, which are performed and accomplished in a specific and original way. Our study demonstrates that the position of the balance spring center of mass and its momentum of inertia are not constant but depend on the angular displacement of the spring collet end. It also shows that the torque spring rate (the spring stiffness) varies as a function of angular displacement during the balanced spring twist. All results are presented numerically and graphically by a set of diagrams and can contribute to the better understanding of the balance spring geometrical and mechanical features and, therefore, be applied for improving a timepiece’s accuracy. Moreover, the method of simulation study disclosed and explained in this paper provides general suggestions and guidance for similar studies. The accuracy of the presented results, as well as the validity of the complete simulation-based method, is proven by the experimentally determined relationship between balance spring restoring torque, stiffness, and spring angular displacement.