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Design Innovation Paper

Gravity insensitive flexure pivot oscillators

[+] Author and Article Information
Mohammad Hussein Kahrobaiyan

École Polytechnique Fédé rale de Lausanne (EPFL), Instant-Lab, Microcity, Rue le la Maladière 71b, CH-2000 Neuchâtel, Switzerland
mohammad.kahrobaiyan@epfl.ch

Etienne Thalmann

École Polytechnique Fédé rale de Lausanne (EPFL), Instant-Lab, Microcity, Rue le la Maladière 71b, CH-2000 Neuchâtel, Switzerland
etienne.thalmann@epfl.ch

Lennart Rubbert

INSA de Strasbourg, Université de Strasbourg, Strasbourg, Alsace, France
lennart.rubbert@insa-strasbourg.fr

Ilan Vardi

École Polytechnique Fédé rale de Lausanne (EPFL), Instant-Lab, Microcity, Rue le la Maladière 71b, CH-2000 Neuchâtel, Switzerland
ilan.vardi@epfl.ch

Simon Henein

École Polytechnique Fédé rale de Lausanne (EPFL), Instant-Lab, Microcity, Rue le la Maladière 71b, CH-2000 Neuchâtel, Switzerland
simon.henein@epfl.ch

1Corresponding author.

ASME doi:10.1115/1.4039887 History: Received June 09, 2017; Revised March 28, 2018

Abstract

Classical mechanical watch plain bearing pivots have frictional losses limiting the quality factor of the hairspring-balance wheel oscillator. Replacement by flexure pivots leads to drastic friction reduction and an order of magnitude increase of the quality factor. However, flexure pivots have drawbacks including gravity sensitivity, nonlinearity and limited stroke. This paper analyses these issues in the case of the cross-spring flexure pivot and presents an improved version addressing them. We first show that the cross-spring pivot cannot be simultaneously linear, insensitive to gravity and have long stroke: the 10 ppm accuracy required for mechanical watches holds independently of the orientation with respect to gravity only when the leaf springs cross at 12.7% of their length. But, in this case the pivot is nonlinear and the stroke is only 31% of the symmetrical (50% crossing) cross-spring pivot’s stroke. The symmetrical pivot is also unsatisfactory as its gravity sensitivity is of order 10^4 ppm. This paper introduces the co-differential concept which we show is gravity insensitive. It is used to construct a long stroke gravity insensitive flexure pivot consisting of a main rigid body, two co-differentials and a torsional beam. We show that this novel pivot achieves linearity or the maximum stroke of symmetrical pivots while retaining gravity insensitivity.

Copyright (c) 2018 by ASME
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