Abstract
Despite centuries of research and significant advances, the escapement mechanism used to count and maintain oscillations of mechanical time bases remains a complex mechanism and a major source of energy losses. We showed in previous work that, instead of the widely used rotational one degree-of-freedom (DOF) oscillators, 2-DOF flexure oscillators have the potential of revolutionizing mechanical watchmaking by eliminating the traditional escapement, replacing it by a simple crank driving a pin. Additionally, using flexures increases the quality factor of the time base, leading to further potential improvements in timekeeping accuracy and energy consumption. However, a significant challenge of these new time bases is their balancing such that the influence of external accelerations on their frequency is minimized, a necessary condition for accurate timekeeping in portable applications. This article presents a novel 2-DOF planar flexure oscillator called Wattwins and demonstrates how it can be made insensitive to linear accelerations such as gravity. For this purpose, a new approach to shaking force balancing is developed based on the decomposition of perturbations into effects corresponding to different orders of center of mass displacement. A full analytical model for frequency tuning and shaking force balancing of the 2-DOF oscillator is derived using a pseudo-rigid-body model and assuming that it can be decomposed into two independent 1-DOF oscillators. The results are validated by the finite element method and show that practical mechanical watch specifications can theoretically be reached. A physical prototype was also constructed and preliminary experimental results confirm the theory as well as the simulations.
Highlights
We introduced the Wattwins horological time base, a novel 2-DOF flexure oscillator based on the parallel coupling of two 1DOF Watt oscillators
For this time base to be compatible with a time keeper, we showed that we were able to tune independently and match its two eigenfrequencies, as well as make them insensitive to linear ac celerations such as gravity, a major source of perturbation for portable timekeepers
This was achieved by developing a new approach to shaking force balancing based on the decomposition of perturbations into effects corresponding to different orders of center of mass (COM) displacement
Summary
The recent developments of silicon flexure oscillators have allowed to significantly increase the quality factor of the time base in comparison to traditional balance wheel and hairspring oscillator [1,2] This paves the way to significant improvements in ac curacy and efficiency since the quality factor quantifies the energy losses of the time base and is considered to be a direct indicator of timekeeping accuracy [3]. The step in increasing mechanical watch efficiency is to address the efficiency of the escapement mechanism, which does not exceed 40% for the lever escapement used in most mechanical watches This significant power loss results from shocks and friction between parts during the stop-and-go motion of this mechanism, see Fig. 1 [4]
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