Elsevier

Precision Engineering

Volume 72, November 2021, Pages 502-520
Precision Engineering

Shaking force balancing of a 2-DOF isotropic horological oscillator

https://doi.org/10.1016/j.precisioneng.2021.06.003Get rights and content
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Highlights

  • New mechanism design for 2-DOF flexure horological oscillator based on Watt linkages.

  • New shaking force balancing method based on the different orders of COM displacements.

  • Analytical model allowing to reach typical mechanical watch chronometric specification.

  • An eccentric masses mechanism used to tune gravity effects and eigenfrequencies.

  • Successful driving of two Wattwins prototype time bases at centimeter-scale.

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.

Keywords

Compliant mechanisms
Shaking force balancing
Dynamic balancing
2-DOF Mechanism
Mechanical oscillator
Silicon flexures

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