Gravity-Insensitive Flexure Pivot Oscillators

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 a drastic reduction in friction and an order of magnitude increase in quality factor. However, flexure pivots have drawbacks including gravity sensitivity, nonlinearity, and limited stroke. This paper analyzes these issues in the case of the cross-spring flexure pivot (CSFP) and presents an improved version addressing them. We first show that the cross-spring pivot cannot be simultaneously linear, insensitive to gravity, and have a long stroke: the 10 ppm accuracy required for mechanical watches holds independently of 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 30% of the symmetrical (50% crossing) crossspring pivot's stroke. The symmetrical pivot is also unsatisfactory as its gravity sensitivity is of order 10 4 ppm. This paper introduces the codifferential concept which we show is gravity-insensitive. It is used to construct a gravity-insensitive flexure pivot (GIFP) consisting of a main rigid body, two codifferentials, and a torsional beam. We show that this novel pivot achieves linearity or the maximum stroke of symmetrical pivots while retaining gravity insensitivity.

Flexure Pivot Oscillator With Intrinsically Tuned Isochronism

“…Following our previous research in Ref. [18], we consider a flexure to be gravity-insensitive when there is no first order effect of the load on its stiffness (assuming small loads).…”

“…The design principle used to achieve gravity insensitivity is similar to the codifferential concept that we introduced in Ref. [18]. The two concepts are compared in Sec.…”

“…In Ref. [18], we presented a pivot capable of reaching both goals since the crossing point of its flexures can be used to set the isochronism defect and its architecture is intrinsically gravity-insensitive.…”

Design of a Flexure Rotational Time Base with Varying Inertia

“…Alternatively, Di Domenico et al [6] [9] [5] use crossed flexure pivots with special values for the point at which the leaf springs cross and the angle between them to obtain the desired restoring torque characteristic. In previous work, we also presented a flexure pivot whose restoring torque nonlinearity can be modified by adjusting the crossing point of the flexures while preserving its property of minimizing the effect of gravity on the stiffness [12,17].…”

“…The loading of flexures can be influenced by gravity, which changes their stiffness and causes variations of the period of the time base. This issue is not treated in this paper but it is known that symmetry of the system reduces its sensitivity to gravity [12]. We thus assume that the rotational symmetry of the RDCO will allow it to perform well under varying gravity orientation.…”