Dynamic balancing of a flexure-based Watt’s linkage horological oscillator

Abstract

Mechanical watches are generally regulated by a balance and a spring constituting a harmonic oscillator. This mechanism is intrinsically force-balanced, which makes it essentially insensitive to gravity as well as to the linear accelerations of the watch. Nevertheless, this mechanism is not dynamically balanced, i.e., its motion is affected by the angular accelerations of the watch around axes parallel to the pivoting axis of the balance. This phenomenon degrades the chronometric precision of the watch when worn on the wrist. This article presents a novel dynamically-balanced oscillator mechanism dedicated to mechanical watches, which solves this issue: a 1-DOF mechanism relying on a flexure-based Watt’s linkage equipped with two balances rotating in opposite directions. The use of flexures brings additional advantages: absence of friction, no need for lubrication, increased quality factor, and monolithic design. The mechanism is presented with its Pseudo-Rigid-Body-Model and the numerical model used to predict force and dynamic-balancing residual defects: this includes sag and frequency variations under in-plane gravitational loads and pose sensitivity to in-plane angular accelerations. Experimental results from a 2:1 scale titanium prototype, compared to a watch-scale prototype, validated both the analytical and numerical models for large force and dynamic-balancing defects. An iterative tuning method achieved a sag variation below $5\mu m$, a daily rate variation of less than 18 seconds per day for all in-plane gravity orientations, and sensitivity to angular accelerations 250 times lower than its single-balance version.