Gravity-Compensation Design Approaches for Flexure-Pivot Time Bases

While flexure time bases have gained significant traction in the watchmaking industry thanks to their high quality factor and monolithic design, maintaining a stable frequency in varying orientations of wrist watches with respect to gravity remains a significant challenge. This results from the fact that the flexures play two roles simultaneously: guiding the oscillating mass along a one-degree-of-freedom pivotal motion, and providing the oscillator’s elastic restoring force. Indeed, varying stress-stiffening effects induced by the varying direction of the weight of the oscillating mass affect the pivot angular stiffness, which impacts its oscillating frequency. In order to address this issue, two design approaches are presented which, when combined, allow to reach the strict chronometric standards of mechanical watches. Firstly, the frequency differences for all vertical positions (i.e., gravity orthogonal to the rotation axis) are mitigated by designing architectures with reduced parasitic center shift, or by offsetting the center of mass (COM) along their axis of symmetry, or both. Secondly, the frequency differences between vertical and horizontal positions (i.e., gravity parallel to the rotation axis) are reduced by offsetting the COM along the rotation axis. The implementation and effectiveness of these approaches are demonstrated by numeric simulations, as well as by experimental measurements performed on watch-scale silicon etched prototypes.