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Publication# Flexure Pivot Oscillator With Intrinsically Tuned Isochronism

Simon Nessim Henein, Mohammad Hussein Kahrobaiyan, Etienne Frédéric Gabriel Thalmann, Ilan Vardi

2020

Journal paper

2020

Journal paper

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.

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Related publications (13)

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Simon Nessim Henein, Etienne Frédéric Gabriel Thalmann

Flexure pivot oscillators have the potential to advantageously replace the traditional balance wheel-spiral spring oscillator used in mechanical watches due to their significantly lower friction. However, they have inherent nonlinear elastic properties that can introduce a variation of their frequency with amplitude called isochronism defect. Previous research has focused on controlling the elastic behavior of flexure pivot oscillators to reach isochronism. We present a new way of minimizing the isochronism defect of rotational oscillators by varying their inertia. This principle is embodied in a new family of oscillators we call rotation-dilation coupled oscillator (RDCO). Their architecture also presents a rotational symmetry that is advantageous for minimizing the effects of gravity on their period. We present a description of this new oscillator family, give conceptual tools for tuning its isochronism and show examples of physical implementations.

2019Methods based on the electron spin resonance (ESR) phenomenon are non-invasive tools adopted to investigate paramagnetic systems at temperatures ranging from above 1000 K to below 1 K. Since 2008, the group of Dr. Boero has been working on a detection technique based on the integration of ESR sensors on single chips. The proposed methodology allowed to study samples in the nanoliter scale and reach a spin sensitivity at least two orders of magnitude better than the best commercially available spectrometers.
The detection principle can be summarized as follows. An ESR sensitive sample is placed in close proximity to the planar inductor of an LC oscillator operating at microwave frequency. In presence of a suitable static magnetic field, the ESR phenomenon takes place. It causes a variation in the sample magnetization which translates to a variation of the inductance, leading to both a frequency shift of the oscillator (frequency detection) and a variation of the oscillation amplitude (amplitude detection). Consequently, the ESR phenomenon may be detected by tracking the operating point of the oscillator.
In this thesis, I investigate the application of the aforementioned detection principle in the range from 400 MHz to 360 GHz. Firstly, a semi-integrated solution operating from 400 MHz to 610 MHz is developed for an industrial application (CTI project). In such context, the originality of the work stands in the implementation of a completely standalone portable scanner for contactless inspection which may also be used for ferromagnetic (FMR) applications and zero-field measurements.
Secondly, a set of single-chip ESR detectors working from 10 GHz to 146 GHz and based on CMOS technologies are characterized from 300 K down to 10 K. Here, an ESR experiment at a frequency as high as 360 GHz can be performed thanks to the fourth harmonic signal generated by a 90 GHz detector. Conversely, the 10 GHz detector shows the best noise performance and allows to achieve the record distance resolution of 0.3 pm when used as a proximity sensor.
After that, the possibility of using integrated technologies based on HEMTs is investigated so as to overcome the main limitations of the CMOS based detectors: (1) the high power consumption which denies their use below 10 K and (2) the saturation issue due to the magnitude of the intrinsic microwave magnetic field produced by the oscillators. In this context, two HEMT oscillators working at 11 GHz and 25 GHz are realized. In particular, the former achieves the record minimum power consumption (90 uW at 300 K and 4 uW below 30 K) currently reported in the literature for oscillators working in the same frequency range. Also, the proposed sensor achieves a minimum microwave magnetic field of less than 1 uT at 300 K and less than 0.1 uT below 30 K, i.e., orders of magnitude below the values achieved with previous CMOS detectors. Furthermore, an analytical model is carried out in order to estimate the minimum achievable power consumption for an LC single-ended Colpitts oscillator based on any single FET.
Lastly, the DC characterization of a standing alone HEMT transistor is provided from 300 K down to 1.4 K, ranging from the standard Ids-Vs-Vds curves to the extraction of both the number of carriers and their effective mobility. The former comes from the analysis of the Shubnikov-de-Haas oscillations whereas the latter is calculated by means of Hall-effect based experiments.

Simon Nessim Henein, Mohammad Hussein Kahrobaiyan, Lennart Rubbert, Ilan Vardi

Classical pivots have frictional losses leading to the limited quality factor of oscillators used as time bases in mechanical watches. Flexure pivots address these issues by greatly reducing friction. However, they have drawbacks such as gravity sensitivity and limited angular stroke. This paper analyses these problems for the cross-spring flexure pivot and presents an improved version addressing these issues. We first show that the cross spring pivot cannot be both insensitive to gravity and have a long stroke. A 10 ppm sensitivity to gravity acceptable for watchmaking applications occurs only when the leaf springs cross at about 87.3 % of their length, but the stroke is only 30.88 % of the stroke of the symmetrical cross-spring pivot. For the symmetrical pivot, gravity sensitivity is of the order of 104 ppm. Our solution is to introduce the co-differential concept which we show to be gravity insensitive. We then use the co-differential to build a gravity insensitive flexure pivot with long stroke. The design consists of a main rigid body, two co-differentials and a torsional beam. We show that our pivot is gravity insensitive and achieves 100 % of the stroke of symmetrical pivots.

2016