Flexure Pivot Oscillator With Intrinsically Tuned Isochronism

Abstract

The most important property for accurate mechanical time bases is isochronism: the independence of period from oscillation amplitude. This paper develops a new concept in isochronism adjustment for flexure-based watch oscillators. Flexure pivot oscillators, which would advantageously replace the traditional balance wheel-spiral spring oscillator used in mechanical watches due to their significantly lower friction, exhibit nonlinear elastic properties that introduce an isochronism defect. Rather than minimizing this defect, we are interested in controlling it to compensate for external defects such as the one introduced by escapements. We show that this can be done by deriving a formula that expresses the change of frequency of the oscillator with amplitude, i.e., isochronism defect, caused by elastic nonlinearity. To adjust the isochronism, we present a new method that takes advantage of the second-order parasitic motion of flexures and embody it in a new architecture we call the co-RCC flexure pivot oscillator. In this realization, the isochronism defect of the oscillator is controlled by adjusting the stiffness of parallel flexures before fabrication through their length Lp, which has no effect on any other crucial property, including nominal frequency. We show that this method is also compatible with post-fabrication tuning by laser ablation. The advantage of our design is that isochronism tuning is an intrinsic part of the oscillator, whereas previous isochronism correctors were mechanisms added to the oscillator. The results of our previous research are also implemented in this mechanism to achieve gravity insensitivity, which is an essential property for mechanical watch time bases. We derive analytical models for the isochronism and gravity sensitivity of the oscillator and validate them by finite element simulation. We give an example of dimensioning this oscillator to reach typical practical watch specifications and show that we can tune the isochronism defect with a resolution of 1 s/day within an operating range of 10% of amplitude. We present a mock-up of the oscillator serving as a preliminary proof-of-concept.

Design of a Flexure Rotational Time Base With Varying Inertia

“…In our previous research on flexure oscillators, we developed design principles that allow to minimize gravity effects [15,22] and introduced the concept of isochronism tuning by changing second order stiffness properties of the oscillator [16]. We showed that we could compensate isochronism defects by adjusting the stiffness of flexures whose motion is of second order of the main oscillation, that is, the same order as the isochronism defect, see Eq.…”

“…(6). The fact that this is is done by changing oscillator properties without affecting any other crucial characteristic of the pivot (such as such as nominal stiffness, gravity sensitivity and parasitic center shift) is called intrinsic isochronism tuning [16] and is superior to existing solutions. Indeed, the first flexure pivot oscillator to be introduced in a watch, the 2014 "Genequand System" [9,10] used an external mechanism to tune its isochronism [23]; other oscillators based on the crossed flexure pivot [24] use special values for the point at which the leaf springs cross and the angle between them to reach isochronism [22,25,26,27,28] which, however, does not qualify as isochronism tuning since changing these parameters affects other crucial properties of the pivot [16,22,29,30].…”

“…In previous research, we noticed that the deviation of flexures from the motion of ideal linkages resulted in changes in the mass distribution of our time bases as they oscillate, thus affecting their isochronism. For instance, the "GIFP" oscillator [15,22] has a parasitic tilt of its rotation axis and the "co-RCC" [15,16,31] has an inward motion of its intermediate bodies. These effects were neglected, assuming that they were small and could be compensated by acting on the restoring torque nonlinearity of the flexures [16].…”

“…For instance, the "GIFP" oscillator [15,22] has a parasitic tilt of its rotation axis and the "co-RCC" [15,16,31] has an inward motion of its intermediate bodies. These effects were neglected, assuming that they were small and could be compensated by acting on the restoring torque nonlinearity of the flexures [16]. Similar inertia variations are also present in other existing flexure time bases, for instance in Refs.…”

“…These directly affect timekeeping accuracy. Other external factors can also affect the period such as temperature, magnetic fields and shocks; these effects which can be addressed with existing materials and techniques [15,16] are not treated in the present article.…”