EP4310598A1 - Method for monitoring and manufacturing timepiece hairsprings - Google Patents

Abstract

Method for controlling a hairspring or a hairspring blank arranged to form a hairspring, the control method comprising the following steps: a. apply to the hairspring or the hairspring blank a vibrational excitation which varies over time to cover a predetermined frequency range,b. identify at least one characteristic of a resonance frequency of the hairspring or the hairspring blank, such as a resonance peak, during or in response to the vibrational excitation over the predetermined frequency range,c. submitting to a thermal coefficient prediction machine the resonant frequency characteristic identified in step b. to determine a thermal coefficient of the Young's modulus (CTE) of the hairspring and/or a thermal coefficient (CT) of a watch system comprising the hairspring.

Description

Technical area

The present invention relates to the field of control and manufacturing of parts for watchmaking. The invention relates more particularly to a method for controlling and manufacturing watch spiral springs, otherwise called resonators.

State of the art

The movements of mechanical watches are regulated by means of a mechanical regulator or oscillator comprising a resonator, that is to say an elastically deformable component whose oscillations determine the running of the watch. Many watches include, for example, an oscillator comprising a hairspring as a resonator, mounted on the axis of a balance wheel and set into oscillation thanks to an escapement. The natural frequency of the balance-spring couple makes it possible to regulate the movement of the watch and depends on several parameters, in particular the stiffness of the balance-spring and the operating temperature.

Indeed, the frequency f of the regulating member formed by the spiral of stiffness R coupled to a balance wheel of inertia I is given by the formula: $$F=\frac{1}{2\pi }\sqrt{\frac{R}{I}}$$

The stiffness of the hairspring also defines its intrinsic vibrational characteristics, such as the natural frequency and resonance frequencies. In the present application, the natural frequency of an elastic system (a single resonator or a resonator - balance wheel pair) is the frequency at which this system oscillates when it is in free evolution, that is to say without an exciting force. . Furthermore, a resonance frequency of an elastic system (for example the resonator alone) subjected to an exciting force is a frequency at which a local maximum of displacement amplitude can be measured for a given point of the system elastic. In other words, if the elastic system is excited with an excitation source of variable frequency over time, the displacement amplitude follows an upward slope before this resonance frequency, and follows a downward slope after, in all point which does not correspond to a vibration node. Typically, during such a test, the recording of the displacement amplitude as a function of the excitation frequency presents a displacement amplitude peak or resonance peak which is associated with or which characterizes the resonance frequency.

avec :

• ϕ, l'angle de torsion du ressort, et
• M, le couple de rappel du ressort spiral,
• où M, pour un barreau de section constante constitué d'un matériau spécifique, est donné par : $$M=\frac{E\left(\frac{e^3\mathrm{<figure-callout\; id="12"\; label="h"\; filenames="imgf0008.png"\; state="\{\{state\}\}">h</figure-callout>}}{12}\varphi \right)}{L}$$
  
  avec :
  • E, le module d'Young du matériau employé pour le barreau,
  • L, la longueur du barreau,
  • h, la hauteur du barreau, et
  • e, l'épaisseur ou la largeur du barreau.

The stiffness of a spiral type resonator typically depends on the characteristics of the material in which it is made, as well as its dimensions and in particular the thickness (i.e. the width) of its turns along of his bar. The stiffness is given more specifically by: $$R=\frac{M}{\varphi }$$

with :

• ϕ , the twist angle of the spring, and
• M, the return torque of the spiral spring,
• where M, for a bar of constant section made of a specific material, is given by: $$M=\frac{E\left(\frac{e^3\mathrm{<figure-callout\; id="12"\; label="h"\; filenames="imgf0008.png"\; state="\{\{state\}\}">h</figure-callout>}}{12}\varphi \right)}{L}$$
  
  with :
  • E , the Young's modulus of the material used for the bar,
  • L , the length of the bar,
  • h, the height of the bar, and
  • e, the thickness or width of the bar.

Avec :

• T, la température courante,
• T₀, une température de référence,
• α_S, le coefficient de dilatation thermique du spiral
• α_B , le coefficient de dilatation thermique de la serge de balancier.

As will be explained in more detail below, the operating temperature is an influential parameter on the operation of the regulating organ, we can derive equation 1 with respect to the temperature T, and we find: $$\frac{1}{F}\frac{\mathit{dF}}{\mathit{dT}}=\frac{1}{2}\left(\frac{1}{\mathrm{<figure-callout\; id="0"\; label="E\; T"\; filenames="imgf0006.png,imgf0007.png"\; state="\{\{state\}\}">E</figure-callout>}\left(T_{}\right)\left({}_0\right)}\frac{\mathit{of}}{\mathit{dT}}+3{\alpha }_S-2{\alpha }_B\right)$$

With :

• T , the current temperature,
• T ₀ , a reference temperature,
• α _S , the coefficient of thermal expansion of the hairspring
• α _B , the coefficient of thermal expansion of the balance rim.

Avec :

• CT : le coefficient thermique de l'oscillateur (secondes par jour et par degré),
• CTE : le coefficient thermique de module de Young (K^-1), ou autrement appelé coefficient thermo-élastique.

We can rewrite this equation 4 as below: $$\mathit{CT}=\frac{1}{2}\left(\mathit{CTE}+3{\alpha }_S-2{\alpha }_B\right)$$

With :

• CT: the thermal coefficient of the oscillator (seconds per day and per degree),
• CTE: Young's thermal modulus coefficient (K ^-1 ), or otherwise called thermo-elastic coefficient.

The natural frequency of the regulating member formed by the hairspring of stiffness R coupled to a balance wheel of inertia I is in particular proportional to the square root of the stiffness of the hairspring. The main specification of a spiral spring is its stiffness, which must be within a well-defined interval to be able to be paired with a balance wheel, which forms the inertial element of the oscillator. This pairing operation is essential to precisely adjust the frequency of a mechanical oscillator.

The importance of magnetic fields in the modern environment has pushed watchmakers to use silicon hairsprings in recent years, which are less sensitive to magnetic disturbances than metal hairsprings.

Very advantageously, several hundred silicon spirals can be manufactured on a single wafer using micro-manufacturing technologies. It is particularly known to produce a plurality of silicon resonators with very high precision using photolithography and machining/etching processes in a silicon wafer. The methods for producing these mechanical resonators generally use monocrystalline silicon wafers, but wafers made of other materials can also be used, for example polycrystalline or amorphous silicon, other semiconductor materials, glass, ceramic, carbon, carbon nanotubes or a composite comprising these materials. For its part, monocrystalline silicon belongs to the cubic crystal class m3m whose thermal expansion coefficient (alpha) is isotropic.

It is very important that the characteristics of the oscillator are as stable as possible, in order to have a rate of the watch which is also stable, with in particular as few differences in rate as possible depending on the operating temperature (summer -winter, wristwatch worn or not worn).

Silicon has a very negative value of the first thermoelastic coefficient, and consequently, the stiffness of a silicon resonator, and therefore its natural frequency, varies greatly depending on the temperature. In order to at least partially compensate for this disadvantage, the documents EP1422436 , EP2215531 And WO2016128694 describe a spiral type mechanical resonator made from a core (or two cores in the case of WO2016128694 ) in monocrystalline silicon and whose temperature variations in Young's modulus are compensated by a layer of amorphous silicon oxide (SiO2) surrounding the core (or cores), the latter being one of the rare materials presenting a positive thermoelastic coefficient . As shown in equation 5 above, temperature variations can lead to variations in rate with the thermal coefficient CT which depends in particular on the thermal coefficient of Young's modulus, the thermal coefficient of expansion of the hairspring and the thermal coefficient of expansion of the balance wheel. The silicon hairsprings and their thermo-compensation therefore make it possible to adjust the terms of equation 5 relating to the hairspring to obtain a thermal coefficient CT of the oscillator. By extension, we can also characterize the CT of a more extensive watchmaking system, which integrates the hairspring, going up to the CT of a complete caliber, by determining the thermal drift of the caliber integrating that of the escapement, the gear train , including the influence of lubrication. From this perspective, the hairspring is considered to be the only adjustment variable to obtain the lowest possible CT of the watchmaking system that integrates it.

When hairsprings are made from silicon or another material by collective manufacturing on a wafer, the final functional yield will be given by the number of hairsprings whose stiffness corresponds to the pairing interval, divided by the total number of hairsprings. spirals on the plate.

However, the micro-fabrication and more particularly etching steps used in the manufacture of hairsprings on a wafer typically result in a significant geometric dispersion between the dimensions of the hairsprings on the same wafer, and therefore in a significant dispersion between their stiffness, notwithstanding that the engraving pattern is the same for each hairspring. The measured stiffness dispersion normally follows a Gaussian distribution. In order to optimize manufacturing yield, we are therefore interested in centering the average of the Gaussian distribution on a nominal stiffness value and also in reducing the standard deviation of this Gaussian.

In addition, the dispersion of stiffness is even greater between hairsprings of two plates engraved at different times following the same process specifications. This phenomenon is shown in figure 1 where the stiffness dispersion curves Rd1, Rd2 and Rd3 for the hairsprings on three different plates are illustrated. Generally speaking, for each plate the distribution of stiffness R (in relation to the number of spirals N with this stiffness) follows the normal or Gaussian law, each dispersion curve being centered on its respective average value Rm1, Rm2 and Rm3.

The documents WO2015113973 And EP3181938 propose to remedy this problem by forming a hairspring with dimensions greater than the dimensions necessary to obtain a hairspring of a predetermined stiffness, by measuring the stiffness of this hairspring formed by coupling it with a balance wheel equipped with a predetermined inertia, by calculating the thickness of material to be removed to obtain the dimensions necessary to obtain the hairspring with the predetermined stiffness, and by removing this thickness from the hairspring. Similarly, the document EP3181939 proposes to remedy this same problem by forming a hairspring according to dimensions smaller than the dimensions necessary to obtain a hairspring of a predetermined stiffness, by determining the stiffness of this hairspring formed by coupling it with a balance wheel equipped with a predetermined inertia, by calculating the thickness of material to be added to obtain the dimensions necessary to obtain the hairspring with the predetermined stiffness, and by adding this thickness of material to the hairspring.

In this way, as demonstrated by figure 2 , notwithstanding the average stiffness Rm1, Rm2, etc. stiffnesses on a given wafer, the stiffness dispersion curve Rd1, Rd2, etc. can be refocused in relation to a nominal stiffness value Rnom.

This approach requires great precision in measuring the frequency of the hairspring to determine its stiffness. In particular, measurement errors can be caused by the balance of predetermined inertia, or by the assembly carried out. We must then carry out a step of calculating the thickness to be removed in order, once again, to remove the calculated thickness with great precision. In addition, it can be noted that the coupling of the hairspring with the balance having a predetermined inertia requires careful operations requiring a lot of preparation time. Finally, we can also note that any assembly operation on parts or blanks still present on a wafer significantly increases the risk of pollution (for example presence of fine silicon particles (debris) produced during handling).

The present invention aims to propose an approach free from the above drawbacks, which allows a faster production flow and/or with less risk of pollution(s), and/or greater sampling, and/or a more precise measurement of the thermal coefficient of the Young's modulus (CTE) of the hairspring and/or of the thermal coefficient (CT) of a watch system including the hairspring, and therefore a more individualized correction of the hairsprings of the plate to obtain watch systems including walking is little or not disturbed by temperature variations.

Disclosure of the invention

1. a. appliquer au spiral ou à l'ébauche de spiral une excitation vibratoire variable au cours du temps pour couvrir une plage fréquentielle prédéterminée,
2. b. identifier au moins une caractéristique d'une fréquence de résonance du spiral ou de l'ébauche de spiral, telle qu'un pic de résonance, lors de ou en réponse à l'excitation vibratoire sur la plage fréquentielle prédéterminée,
3. c. soumettre à une machine de prédiction de coefficient thermique la caractéristique de fréquence de résonance identifiée à l'étape b. pour déterminer un coefficient thermique du module de Young (CTE) du spiral et/ou un coefficient thermique (CT) d'un système horloger comprenant le spiral.

More precisely, a first aspect of the invention relates to a method of controlling a hairspring or a hairspring blank arranged to form a hairspring, the control method comprising the following steps:

1. has. apply to the hairspring or the hairspring blank a vibrational excitation which varies over time to cover a predetermined frequency range,
2. b. identify at least one characteristic of a resonance frequency of the hairspring or the hairspring blank, such as a resonance peak, during or in response to vibrational excitation over the predetermined frequency range,
3. vs. submitting to a thermal coefficient prediction machine the resonant frequency characteristic identified in step b. to determine a thermal coefficient of the Young's modulus (CTE) of the hairspring and/or a thermal coefficient (CT) of a watch system comprising the hairspring.

The method according to the implementation above comprises a step of vibratory excitation of the hairspring or the hairspring blank and the measurement of a characteristic of a resonance frequency, to then deduce by prediction a thermal coefficient of the Young's modulus (CTE) of the hairspring and/or a thermal coefficient (CT) of a watch system including the hairspring. There is no assembly with a balancer or other component, which saves time. In addition, the measurement is carried out on the hairsprings or blanks alone, which limits errors induced by other components or their assembly, as well as possible pollution. Measurement accuracy is improved because there are fewer sources of variability due to other components or pollution. In other words, the hairspring or the hairspring blank is tested alone. The vibration excitation is applied to the part or the unitary blank, not coupled to any balance, weight or oscillating system. The process makes it possible to control unitary and free parts (that is to say with at least one free end, not attached to any mechanism or balance), which provides at least the advantages of productivity gains (no assembly with an oscillating system), gains in quality (no pollution of parts, no breakage, and more parts can be tested within the same budget), gains in precision (no errors linked to other components of 'an oscillating system).

It will be noted that the determination of the thermal coefficient of the Young's modulus (CTE) of the hairspring or of the hairspring blank by the method according to the invention is well suited for oxidized parts for which the thickness of the balance is not precisely known. oxide layer at this stage of the manufacturing process. With the present invention, one can easily obtain the thermal coefficient of the Young's modulus (CTE) of the oxidized hairspring or the oxidized hairspring blank, which are in a way composite parts (heart or soul in silicon, with a shell in silicon oxide).

According to one embodiment, the vibration excitation can be carried out with a shock device which applies excitation to the part to be tested in a relatively short time. In other words, we can plan to impose a movement or acceleration on the parts to be tested in a very short time (over a period of less than a second, less than 500 ms, less than 100 ms, less than 10 ms). In particular, the shock device can apply a shock to the balance spring or to its support to make the parts vibrate. An impact hammer or any device with a moving mass can be used. In the case of parts attached to a plate, provision can be made to apply the shock to the plate, or to a fixture supporting the plate. Depending on the part to be tested and its position on the wafer, it is possible to plan to apply the shock to a particular location on the wafer and/or in a particular direction. The parts begin to vibrate and we can record the vibration response over time, to extract resonance peaks and their frequencies from this measurement, for example with a Fourrier transform.

• le spiral, et un balancier,
• le spiral, un balancier, et un dispositif d'échappement, comme un échappement à ancre,
• le spiral, un balancier, un dispositif d'échappement, et un rouage, comme un rouage de finissage,
• l'intégralité du mouvement de la montre, y-compris le spiral.

Dans tous les cas ci-dessus, il est possible de connaître par avance la valeur du coefficient thermique des pièces autres que le spiral, ou à tout le moins leur contribution sur le coefficient thermique du système horloger. En pratique, ces valeurs sont standard et connues à l'avance en fonction des références ou composants choisis, et dans le cas d'un spiral en silicium, il est possible d'ajuster la contribution du spiral dans l'équation 5 ci-dessus pour obtenir un coefficient thermique du système horloger qui sera dans une plage de valeurs et/ou dans une tolérance désirée(s).According to one embodiment, the watch system comprising the hairspring may comprise:

• the hairspring, and a balance wheel,
• the hairspring, a balance wheel, and an escapement device, such as an anchor escapement,
• the hairspring, a balance wheel, an escapement device, and a gear train, like a finishing gear train,
• the entire movement of the watch, including the hairspring.

In all of the above cases, it is possible to know in advance the value of the thermal coefficient of the parts other than the hairspring, or at least their contribution to the thermal coefficient of the watch system. In practice, these values are standard and known in advance depending on the references or components chosen, and in the case of a silicon hairspring, it is possible to adjust the contribution of the hairspring in equation 5 above to obtain a thermal coefficient of the watch system which will be within a range of values and/or within a desired tolerance(s).

According to one embodiment, the vibration excitation is applied to the hairspring or to the hairspring blank having a free end (typically the central ferrule) and another end fixed to the plate or to a clamp. From a mechanical point of view, we can consider schematically that the vibratory excitation is applied to a mass (located at the center of gravity of the hairspring) connected to a frame of reference (a gripping pliers for a hairspring alone, or the rest of a substrate or a plate for a blank, for example made of silicon and not detached) by a spring (the elastic part of the hairspring). The vibrational excitation sets the suspended mass in motion.

It can also be noted that if it is determined that it is necessary to make a dimensional correction and/or additional treatment(s) to the part tested (or to all the unit parts attached to the same wafer, or even to the parts units attached to an area of a wafer, including or not the part tested), this can be done on the unitary part(s) without dismantling anything (for example, we can provide apply oxidation directly on a silicon part at the test output). We can therefore plan to add or remove material from the unitary part(s), to do doping to vary intrinsic values (stiffness, thermal coefficient of Young's modulus (CTE ) of the hairspring). In other words, the dimensional correction and/or additional treatment(s) are carried out on the unit part(s).

The method according to the implementation above therefore makes it possible to test spiral blanks during manufacture while limiting the risks of pollution or assembly errors. A dimensional correction (section, height and/or thickness) and/or additional treatment(s) are then possible. The method according to the implementation above also makes it possible to test completed hairsprings for example to carry out a classification by increments of stiffness, or to plan a pairing with a particular balance wheel.

• l'étape b. peut comprendre :
  • b1. une première étape d'identification pouvant comprendre l'identification d'une première caractéristique d'une première fréquence de résonance telle qu'un premier pic de résonance,
  • b2. une deuxième étape d'identification pouvant comprendre l'identification d'une deuxième caractéristique d'une deuxième fréquence de résonance telle qu'un deuxième pic de résonance, la deuxième fréquence de résonance étant différente de la première fréquence de résonance,
• et l'étape c. peut comprendre :
  • c1. une première étape de prédiction pouvant consister à soumettre à une autre machine de prédiction la première caractéristique de la première fréquence de résonance pour déterminer un paramètre différent du coefficient thermique du module de Young (CTE) du spiral et/ou du coefficient thermique (CT) d'un système horloger comprenant le spiral, tel qu'une raideur ou un défaut du spiral ou de l'ébauche de spiral,
  • c2. une deuxième étape de prédiction pouvant consister à soumettre à la machine de prédiction de coefficient thermique la deuxième caractéristique de la deuxième fréquence de résonance pour déterminer le coefficient thermique du module de Young (CTE) du spiral et/ou le coefficient thermique (CT) d'un système horloger comprenant le spiral.

According to one embodiment,

• step b. may include:
  • b1. a first identification step which may include the identification of a first characteristic of a first resonance frequency such as a first resonance peak,
  • b2. a second identification step which may include the identification of a second characteristic of a second resonance frequency such as a second resonance peak, the second resonance frequency being different from the first resonance frequency,
• and step c. may include:
  • c1. a first prediction step which may consist of submitting the first characteristic of the first resonance frequency to another prediction machine to determine a parameter different from the thermal coefficient of the Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system comprising the hairspring, such as stiffness or a defect in the hairspring or the hairspring blank,
  • c2. a second prediction step which may consist of submitting to the thermal coefficient prediction machine the second characteristic of the second resonance frequency to determine the thermal coefficient of the Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) d 'a watchmaking system including the hairspring.

According to the above embodiment, the first resonant frequency is used to determine a parameter different from the thermal coefficient of the Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system comprising the hairspring , such as for example stiffness or a defect in the hairspring or the hairspring blank. The second resonance frequency is used to determine the thermal coefficient of Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system comprising the hairspring. In other words, two different frequencies are retained or identified to predict or calculate two distinct parameters (stiffness or presence of a defect on the one hand, the thermal coefficient of Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT ) of a watchmaking system on the other hand).

• a1. une première étape d'excitation vibratoire, pouvant être effectuée avant l'étape b1. et consistant à appliquer au spiral ou à l'ébauche de spiral une première excitation vibratoire variable au cours du temps pour couvrir une première plage fréquentielle prédéterminée,
• a2. une deuxième étape d'excitation vibratoire, pouvant être effectuée avant l'étape b2. et consistant à appliquer au spiral oxydé ou à l'ébauche de spiral oxydée une deuxième excitation vibratoire variable au cours du temps pour couvrir la première plage fréquentielle prédéterminée ou une deuxième plage fréquentielle prédéterminée.

According to one embodiment, steps b1 and b2 can be separated by a thermo-compensation step such as an oxidation step, and step a. may include:

• a1. a first vibrational excitation step, which can be carried out before step b1. and consisting of applying to the hairspring or the hairspring blank a first vibrational excitation variable over time to cover a first predetermined frequency range,
• a2. a second vibrational excitation step, which can be carried out before step b2. and consisting of applying to the oxidized hairspring or to the oxidized hairspring blank a second vibrational excitation which varies over time to cover the first predetermined frequency range or a second predetermined frequency range.

According to the implementation above, the first vibrational excitation step makes it possible to determine a stiffness or the presence of a defect, and the second vibrational excitation step makes it possible to determine the thermal coefficient of the Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system. Different vibrational excitations can be imposed between stages a1 and a2.

• l'étape a. peut être mise en œuvre après une étape d'oxydation,
• et les étapes b1. et b2. peuvent prendre en compte ou peuvent se baser sur la même réponse vibratoire du spiral ou de l'ébauche de spiral. Autrement dit, une première partie de la réponse vibratoire est exploitée pour identifier la première fréquence de résonance et une deuxième partie de la même réponse vibratoire est exploitée pour identifier la deuxième fréquence de résonance.

According to one embodiment,

• step a. can be implemented after an oxidation step,
• and steps b1. and b2. can take into account or can be based on the same vibration response of the hairspring or the hairspring blank. In other words, a first part of the vibration response is used to identify the first resonance frequency and a second part of the same vibration response is used to identify the second resonance frequency.

• la première fréquence de résonance peut être choisie pour être une fréquence de résonance d'un mode de résonance plan, de préférence pour des fréquences de résonance élevées, par exemple supérieures à 40 kHz, ou supérieures à 60 kHz, et/ou
• la deuxième fréquence de résonance peut être choisie pour être une fréquence de résonance d'un mode de résonance hors plan.

According to one embodiment:

• the first resonance frequency can be chosen to be a resonance frequency of a planar resonance mode, preferably for high resonance frequencies, for example greater than 40 kHz, or greater than 60 kHz, and/or
• the second resonance frequency may be chosen to be a resonance frequency of an out-of-plane resonance mode.

According to the implementation above, we can consider that a planar resonance mode is a resonance mode in which the different parts of the hairspring or the hairspring blank move mainly in the plane of the part at rest. If this plane is defined by directions X and Y, with a direction Z normal to the plane, then the displacements in X or Y are greater than or equal to the displacements in Z. In an out-of-plane resonance mode, the displacements in Z are greater than or equal to the displacements in X or Y, and preferably the displacements in Z are two to three times greater than the displacements in It is seen that an oxidized part can present significantly different frequencies of out-of-plane resonance modes compared to the same non-oxidized parts. Consequently, to predict a thermal coefficient of Young's modulus (CTE) of the hairspring and/or a thermal coefficient (CT) of a watch system including the hairspring precisely, it may be preferable to take into account a resonance mode out of plan.

• la première fréquence de résonance peut être choisie dans une plage de valeurs allant de 0 Hz à 100 kHz, de préférence de 0 Hz à 50 kHz, plus préférentiellement de 0 Hz à 40 kHz, et très préférentiellement de 10 kHz à 35 kHz, et/ou
• la deuxième fréquence de résonance peut être choisie dans une plage de valeurs allant de 0 Hz à 300 kHz, de préférence de 50 kHz à 250 kHz, plus préférentiellement de 60 kHz à 200 kHz, et très préférentiellement de 100 kHz à 200 kHz. La demanderesse s'est aperçue qu'une pièce oxydée peut présenter des fréquences de modes de résonnance significativement différentes comparativement aux mêmes pièces non oxydées pour des fréquences de résonance supérieures à 40 kHz, de préférence supérieures à 50 kHz et très préférentiellement supérieures à 60 kHz. En conséquence, pour prédire un coefficient thermique du module de Young (CTE) du spiral et/ou un coefficient thermique (CT) d'un système horloger comprenant le spiral de manière précise, il peut être préférable de prendre en compte des modes de résonance avec des fréquences de résonnance élevées.

According to one embodiment, the first resonance frequency may be lower than the second resonance frequency and/or:

• the first resonance frequency can be chosen in a range of values going from 0 Hz to 100 kHz, preferably from 0 Hz to 50 kHz, more preferably from 0 Hz to 40 kHz, and very preferably from 10 kHz to 35 kHz, and /Or
• the second resonant frequency can be chosen in a range of values going from 0 Hz to 300 kHz, preferably from 50 kHz to 250 kHz, more preferably from 60 kHz to 200 kHz, and very preferably from 100 kHz to 200 kHz. The applicant has noticed that an oxidized part can present significantly different resonance mode frequencies compared to the same non-oxidized parts for resonance frequencies greater than 40 kHz, preferably greater than 50 kHz and very preferably greater than 60 kHz . Consequently, to predict a thermal coefficient of the Young's modulus (CTE) of the hairspring and/or a thermal coefficient (CT) of a watch system including the hairspring precisely, it may be preferable to take into account resonance modes with high resonance frequencies.

According to one embodiment, step b. may consist of identifying a characteristic of a resonance frequency sensitive to the thermal coefficient of the hairspring or the hairspring blank.

Of course, the frequency range of the spectrum obtained does not only depend on the source of vibration excitation but also on the sensor of the measuring instrument used. Thus, the frequency range is linked both to the excitation frequency range and to the frequency range over which the measurement instrument the amplitude of oscillation (vibrometer or other) is sensitive. However, the excitation frequency range will be chosen so as to include at least one resonance frequency of the hairspring or blank tested.

The predetermined resonance frequency that the hairspring must present once finished can be a target natural frequency or a target resonance frequency, or a target natural frequency range, or a target resonance frequency range defined by a tolerance around a target value.

In the above method, the characteristic of a resonance frequency is a characteristic of the oscillatory response measured over a predetermined frequency range, comprising at least one resonance frequency. Such a characteristic is typically identified after processing a raw measurement signal (for example measurement of the amplitudes or speeds or accelerations of movement of certain points of the hairspring or of the hairspring blank), the processing being able to include for example a transform of Fourier to identify resonance peaks and therefore resonance frequencies.

It can be noted that the method can determine a thermal coefficient of the Young's modulus (CTE) of the hairspring and/or a thermal coefficient (CT) of a watch system comprising the hairspring to classify the part, and/or to predict a pairing with other particular components and/or to then calculate/deduce a dimensional correction and/or additional treatment(s) to be applied to obtain a thermal coefficient of the target Young's modulus (CTE) of the hairspring and/or a coefficient thermal (CT) target of a watch system including the hairspring. However, we can only take into account the identified resonance frequency to directly calculate/deduce a dimensional correction and/or additional treatment(s) to be applied to obtain a thermal coefficient of Young's modulus (CTE) target for the hairspring and/or a target thermal coefficient (CT) of a watch system including the hairspring.

According to one embodiment, in step a, the frequency range is applied simultaneously to a plurality of hairsprings or hairspring blanks. The speed is improved, because it is typically possible to impose the vibrational excitation on a plate supporting several hundred hairspring blanks, which would for example still be attached to the plate.

• centrée sur la fréquence de résonance prédéterminée, et
• d'une étendue d'au moins 30% de la fréquence de résonance prédéterminée, c'est-à-dire ±15% de la fréquence de résonance prédéterminée. Par exemple, si la fréquence de résonance prédéterminée est de 1 kHz, alors la plage fréquentielle ira de 850 Hz à 1150 Hz.

According to one embodiment, the frequency range is predetermined to encompass at least one frequency range:

• centered on the predetermined resonance frequency, and
• with an extent of at least 30% of the predetermined resonance frequency, that is to say ±15% of the predetermined resonance frequency. For example, if the predetermined resonance frequency is 1 kHz, then the frequency range will be from 850 Hz to 1150 Hz.

According to one embodiment, the hairspring can have at least two expected predetermined resonance frequencies, and the frequency range is predetermined to cover at least the two expected predetermined resonance frequencies. By covering or sweeping a wide frequency range, multiple resonance peaks (or resonant frequencies) can be measured, which can provide greater accuracy.

According to one embodiment, step a comprises the use of a source, such as a piezoelectric source, making it possible to induce or impose acoustic excitation on a edge of a plate supporting the spiral blank , or preferably on, or even under the hairspring or the hairspring blank to be specifically excited.

According to one embodiment, the acoustic source can be coupled to an excitation cone chosen to excite at least one hairspring or a hairspring blank. Preferably, if a plate supports several spiral blanks, then the acoustic source can be coupled to an excitation cone chosen to excite at least part and preferably all of the spiral blanks.

• avec une amplitude suffisante pour générer des vibrations du spiral ou de l'ébauche de spiral d'amplitude suffisante pour être détectées par le moyen de mesure d'amplitude ou de vitesse ou d'accélération de déplacement d'au moins un point du spiral ou de l'ébauche de spiral et/ou
• pendant une durée suffisante pour en déduire des spectres vibratoires du spiral ou de l'ébauche de spiral.

According to one embodiment, the acoustic source can be chosen and/or adjusted to generate vibrational excitation which varies over time to cover the predetermined frequency range:

• with an amplitude sufficient to generate vibrations of the hairspring or of the hairspring blank of sufficient amplitude to be detected by the means for measuring the amplitude or speed or acceleration of movement of at least one point of the hairspring or of the spiral blank and/or
• for a sufficient duration to deduce vibrational spectra of the hairspring or the hairspring blank.

According to one embodiment, step b comprises the use of an optical measuring means, such as a laser Doppler effect vibrometer.

According to one embodiment, step b can be based on a measurement over time of an amplitude or a speed or an acceleration of movement of at least one point of the balance spring or of the blank of spiral, preferably carried out at least partially during step a.

• une étape d'identification d'une fréquence de résonance du spiral ou de l'ébauche de spiral en fonction d'une déformée opérationnelle ou modale d'au moins un point du spiral ou de l'ébauche de spiral. Une déformée opérationnelle ou modale est typiquement définie par une amplitude ou vitesse de déplacement ou encore d'une accélération et une direction d'oscillation (hors ou dans un plan particulier) en fonction de la fréquence d'excitation.

According to one embodiment, step b comprises:

• a step of identifying a resonance frequency of the hairspring or the hairspring blank as a function of an operational or modal deformation of at least one point of the hairspring or the hairspring blank. An operational or modal shape is typically defined by an amplitude or speed of movement or even an acceleration and a direction of oscillation (outside or in a particular plane) as a function of the excitation frequency.

• une étape b" de mesure d'une amplitude ou d'une vitesse ou d'une accélération de déplacement d'au moins un point du spiral ou de l'ébauche de spiral selon une direction normale au plan de base, et/ou
• une étape b'" de mesure d'une amplitude ou d'une vitesse ou d'une accélération de déplacement d'au moins un point du spiral ou de l'ébauche de spiral selon une direction contenue dans le plan de base.

According to one embodiment, the hairspring or the hairspring blank may be contained in a base plane, and step b may include:

• a step b" of measuring an amplitude or a speed or an acceleration of movement of at least one point of the hairspring or of the hairspring blank in a direction normal to the base plane, and/or
• a step b'" of measuring an amplitude or a speed or an acceleration of movement of at least one point of the hairspring or of the hairspring blank in a direction contained in the base plane.

Measurements of displacement or speed in several directions make it possible to better identify resonance peaks and frequencies.

• une étape d'identification d'un pic de résonance du spiral ou de l'ébauche de spiral en fonction d'une amplitude ou d'une vitesse de déplacement d'au moins un point du spiral ou de l'ébauche de spiral.

According to one embodiment, step b. may include:

• a step of identifying a resonance peak of the hairspring or the hairspring blank as a function of an amplitude or a speed of movement of at least one point of the hairspring or the hairspring blank.

According to one embodiment, the characteristic of the resonant frequency can be identified based on the width of the resonance peak, at half height of the maximum value of the resonance peak. This processing method makes it possible to limit calculation errors that could be made based solely on the identification of the frequency position of the peak defined by its maximum value.

According to one embodiment, step b comprises a step of processing the measurement signal with for example a Fourier transform, to identify resonance peaks of displacement amplitude or speed or acceleration, and/or of phase, depending on the excitation frequency.

According to one embodiment, the thermal coefficient prediction machine can be a calculation machine for predicting or calculating from the frequency characteristics the thermal coefficient of the Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system including the hairspring. In other words, the prediction machine is not a regulated or self-regulated or feedback loop system for adjusting a resonant frequency in response to measurement and comparison with a target value.

According to one embodiment, the thermal coefficient prediction machine can implement a classification carried out for example by a neural network to predict the thermal coefficient of the Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system including the hairspring.

According to one embodiment, the thermal coefficient prediction machine can implement a regression method, for example a linear regression to predict the thermal coefficient of the Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system including the hairspring.

According to one embodiment, the thermal coefficient prediction machine can implement a classification based on partitioning into k-means or k-medians to predict the thermal coefficient of the Young's modulus (CTE) of the hairspring and/or or the thermal coefficient (CT) of a watch system including the hairspring.

According to one embodiment, the control method may comprise a preliminary step consisting of taking into account the material of the hairspring or the hairspring blank, and of adjusting a maximum amplitude of the vibrational excitation and/or a frequency range of the predetermined frequency range depending on the material of the hairspring or the hairspring blank.

According to one embodiment, if step c. determines that the thermal coefficient of the Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system comprising the hairspring is outside a range of expected values, then the method may comprise at least one step consisting of identifying or isolating or retouching or discarding the hairspring or the hairspring blank.

According to one embodiment, if step c. determines that the thermal coefficient of the Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system comprising the hairspring is outside a range of expected values, then the method may comprise at least one step consisting of defining a step of processing the hairspring or the hairspring blank, such as a thermo-compensation, oxidation or deoxidation step, to obtain the thermal coefficient of the Young's modulus (CTE) of the hairspring and /or the thermal coefficient (CT) of a watch system including the hairspring in the range of expected values

According to one embodiment, step a. is carried out for a plurality of hairsprings or hairspring blanks attached to a plate, and if step c. determines that the thermal coefficient of Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system comprising the hairspring is outside a range of expected values for first hairsprings or first blanks of hairsprings and included in the range of expected values for second hairsprings or second hairspring blanks, then we can plan to detach only the second hairsprings or second hairspring blanks and provide a step of processing the first hairsprings or first hairsprings of hairspring blanks, such as a thermo-compensation, oxidation or deoxidation step, to obtain the thermal coefficient of Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a system watchmaker including the hairspring within the range of expected values. We can plan to repeat these steps, repeating steps a or not. and B.

According to one embodiment, step a and step b are repeated at least several times for the same measuring point of the hairspring or the hairspring blank.

According to one embodiment, step a and step b are synchronized. Such synchronization provides the possibility of detecting a phase shift, or an attenuation, or a coupling whose taking into account can improve the precision of the prediction, or make it possible to adjust or realign the source of vibration excitation.

• A/ former au moins un spiral ou une ébauche de spiral ayant des dimensions comprises dans des tolérances prédéterminées nécessaires pour obtenir la fréquence de résonance prédéterminée attendue,
• B/ contrôler le spiral ou l'ébauche de spiral selon le procédé de contrôle du premier aspect.

A second aspect of the invention may relate to a method of manufacturing a hairspring having at least one expected predetermined resonance frequency comprising the steps consisting of:

• A/ form at least one hairspring or a hairspring blank having dimensions within predetermined tolerances necessary to obtain the expected predetermined resonance frequency,
• B/ check the hairspring or the hairspring blank according to the first aspect control method.

According to one embodiment, the manufacturing process may comprise a step consisting of:
C/ identify or isolate or retouch or discard the hairspring or the hairspring blank formed during step A/, if step c. determines that the thermal coefficient of Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system including the hairspring is outside a range of expected values.

According to one embodiment, the hairspring blank can be formed on a plate, with a plurality of other hairspring blanks.

• i- former des spiraux ou des ébauches de spiraux et leur appliquer une étape de thermo-compensation,
• ii- appliquer à chacun des spiraux ou chacune des ébauches de spiral une excitation vibratoire variable au cours du temps pour couvrir une plage fréquentielle prédéterminée,
• iii- identifier au moins une caractéristique d'une fréquence de résonance de chaque spiral ou chaque ébauche de spiral lors de l'application de la plage fréquentielle prédéterminée et enregistrer la température des pièces lors de l'étape ii- et/ou iii-,
  • iv'- monter une pluralité de spiraux ou d'ébauches de spiral dans un mécanisme oscillant présentant une inertie prédéterminée de sorte à mesurer pour chaque spiral ou ébauche de spiral une fréquence entretenue d'oscillation, et/ou une marche du système horloger formé par, ou comprenant, le mécanisme oscillant à au moins une température prédéterminée et de préférence à au moins deux températures prédéterminées,
    et/ou
  • iv"- modéliser dans un outil de simulation une pluralité de spiraux ou d'ébauches de spiral dans un mécanisme oscillant présentant une inertie prédéterminée de sorte à calculer pour chaque spiral ou ébauche de spiral une fréquence entretenue d'oscillation et/ou coefficient thermique d'un système horloger comprenant le spiral et/ou la marche du système horloger comprenant le spiral à au moins une température prédéterminée et de préférence à au moins deux températures prédéterminées,
• v- optionnellement, déduire au moins une fréquence de résonance attendue de la fréquence de résonance identifiée à l'étape iii-, et/ou de la fréquence entretenue d'oscillation et/ou de la marche du système horloger mesurée à l'étape iv'- et/ou calculée à l'étape iv"-
• vi- déduire un coefficient thermique du module de Young (CTE) du spiral et/ou le coefficient thermique (CT) d'un système horloger comprenant le spiral à partir des mesures de l'étape iv'- et/ou des calculs de l'étape iv"-
• vii- fournir à la machine de prédiction, et pour chaque spiral ou ébauche de spiral :
  • la caractéristique de la fréquence de résonance identifiée à l'étape iii- ;
  • optionnellement, la même caractéristique de la fréquence de résonance attendue ;
  • la température enregistrée lors de l'étape ii- et/ou iii- ;
  • le coefficient thermique du module de Young (CTE) du spiral et/ou le coefficient thermique (CT) d'un système horloger comprenant le spiral déduit à l'étape vi-.

A third aspect of the invention may relate to a method of learning a prediction machine to implement step c. of the control method according to the first aspect, comprising the steps consisting of:

• i- form hairsprings or blanks of hairsprings and apply a thermo-compensation step to them,
• ii- apply to each of the hairsprings or each of the hairspring blanks a vibrational excitation which varies over time to cover a predetermined frequency range,
• iii- identify at least one characteristic of a resonant frequency of each hairspring or each hairspring blank when applying the predetermined frequency range and record the temperature of the parts during step ii- and/or iii-,
  • iv'- mount a plurality of hairsprings or hairspring blanks in an oscillating mechanism having a predetermined inertia so as to measure for each hairspring or hairspring blank a sustained oscillation frequency, and/or a rate of the watch system formed by , or comprising, the mechanism oscillating at at least one predetermined temperature and preferably at at least two predetermined temperatures,
    and or
  • iv"- model in a simulation tool a plurality of hairsprings or hairspring blanks in an oscillating mechanism having a predetermined inertia so as to calculate for each hairspring or hairspring blank a sustained oscillation frequency and/or thermal coefficient d 'a watch system comprising the hairspring and/or the operation of the watch system comprising the hairspring at at least one predetermined temperature and preferably at at least two predetermined temperatures,
• v- optionally, deduce at least one expected resonance frequency from the resonance frequency identified in step iii-, and/or from the sustained oscillation frequency and/or from the operation of the watch system measured in step iv '- and/or calculated in step iv"-
• vi- deduce a thermal coefficient of the Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system including the hairspring from the measurements of step iv'- and/or the calculations of the 'step iv'-
• vii- provide the prediction machine, and for each hairspring or hairspring blank:
  • the characteristic of the resonance frequency identified in step iii-;
  • optionally, the same characteristic of the expected resonance frequency;
  • the temperature recorded during step ii- and/or iii-;
  • the thermal coefficient of the Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system comprising the hairspring deduced in step vi-.

Brief description of the drawings

• la figure 1 montre des courbes de dispersion de raideurs non corrigées pour les spiraux sur trois plaquettes différentes,
• la figure 2 montre le centrage de la moyenne des raideurs sur une plaquette autour d'une valeur nominale,
• les figures 3A-3F sont une représentation simplifiée d'un procédé de fabrication d'un résonateur mécanique, ici un spiral, sur une plaquette,
• la figure 4 représente un dispositif permettant l'évaluation du couple d'un spiral,
• la figure 5 représente schématiquement la mise en œuvre de l'évaluation de la raideur d'un spiral par analyse vibratoire,
• la figure 6 représente un exemple de fréquences appliquées à une plaquette de silicium supportant des ébauches de spiral, pour imposer une excitation vibratoire,
• la figure 7 représente un exemple de mesure des amplitudes de déplacement d'un point d'une ébauche de spiral, en réponse à la plage fréquentielle imposée de la figure 6,
• la figure 8 représente en détail un pic de résonance identifié à une fréquence particulière sur la figure 7,
• la figure 9 représente les pics de résonance mesurés et superposés pour la fréquence particulière de la figure 8 pour des pièces testées,
• la figure 10 représente un exemple de modèle de prédiction construit à partir de données extraites de la figure 9,
• la figure 11 montre l'influence de la température sur la fréquence de résonance d'un mode de résonance particulier,
• la figure 12 montre la sensibilité de la fréquence de résonance à l'épaisseur d'oxyde d'un spiral en silicium.

Other details of the invention will appear more clearly on reading the description which follows, made with reference to the appended drawings in which:

• there figure 1 shows uncorrected stiffness dispersion curves for the hairsprings on three different plates,
• there figure 2 shows the centering of the average stiffness on a plate around a nominal value,
• THE figures 3A-3F are a simplified representation of a process for manufacturing a mechanical resonator, here a hairspring, on a wafer,
• there Figure 4 represents a device allowing the evaluation of the torque of a hairspring,
• there figure 5 schematically represents the implementation of the evaluation of the stiffness of a hairspring by vibration analysis,
• there Figure 6 represents an example of frequencies applied to a silicon wafer supporting balance spring blanks, to impose vibrational excitation,
• there Figure 7 represents an example of measuring the amplitudes of displacement of a point of a spiral blank, in response to the imposed frequency range of the Figure 6 ,
• there figure 8 depicts in detail a resonance peak identified at a particular frequency on the Figure 7 ,
• there Figure 9 represents the measured and superimposed resonance peaks for the particular frequency of the figure 8 for tested parts,
• there Figure 10 represents an example of a prediction model built from data extracted from the Figure 9 ,
• there Figure 11 shows the influence of temperature on the resonance frequency of a particular resonance mode,
• there Figure 12 shows the sensitivity of the resonance frequency to the oxide thickness of a silicon hairspring.

Mode of carrying out the invention

THE figures 3A-3F are a simplified representation of a method of manufacturing a mechanical resonator 100 on a plate 10. The resonator is in particular intended to equip a regulating member of a timepiece and, according to this example, is in the shape of a silicon spiral spring 100 which is intended to equip a balance wheel with a mechanical watch movement.

Plate 10 is illustrated in Figure 3A as an SOI wafer (“silicon on insulator”) and comprises a substrate or “handler” 20 carrying a sacrificial layer of silicon oxide (SiO ₂ ) 30 and a layer of monocrystalline silicon 40. For example, the substrate 20 may have a thickness of 500 µm, sacrificial layer 30 may have a thickness of 2 µm and silicon layer 40 may have a thickness of 120 µm. The monocrystalline silicon layer 40 can have any crystalline orientation.

A lithography step is shown to figures 3B And 3C . By “lithography” we mean all the operations making it possible to transfer an image or pattern on or above the wafer 10 to the latter. Referring to the Figure 3B , in this exemplary embodiment, the layer 40 is covered with a protective layer 50, for example made of a polymerizable resin. This layer 50 is structured, typically by a photolithography step using an ultraviolet light source as well as, for example, a photo mask (or another type of exposure mask) or a stepper and reticle system. This structuring by lithography forms the patterns for the plurality of resonators in layer 50, as illustrated in Figure 3C .

Subsequently, in the stage of 3D figure , the patterns are machined, in particular engraved, to form the plurality of resonators 100 in the layer 40. The etching can be carried out by a deep reactive ion etching technique (also known by the acronym DRIE for “Deep Reactive Ion Etching”). . After etching, the remaining part of the protective layer 50 is subsequently eliminated.

To the Figure 3E , the resonators are released from the substrate 20 by locally removing the sacrificial layer 30 or even by etching all or part of the silicon from the substrate or handler 20. Smoothing (not illustrated) of the etched surfaces can also take place before the release step, for example example by one step thermal oxidation followed by a deoxidation step, consisting for example of wet etching based on hydrofluoric acid (HF).

At the last stage of the manufacturing process Figure 3F , the turns 110 of the silicon resonator 100 are covered with a layer 120 of silicon oxide (SiO2), typically by a thermal oxidation step to produce a thermo-compensated resonator. The formation of this layer 120, which generally has a thickness of 2-5 µm, also affects the final stiffness of the resonator and therefore must be taken into account during the previous steps to obtain vibrational characteristics of the hairspring leading to obtaining a particular natural frequency of the hairspring-balance couple in a given watch mechanism.

As indicated above, at the stage preceding the production of the thermo-compensation layer, the different resonators formed in the wafer generally have a significant geometric dispersion between them and therefore a significant dispersion between their stiffnesses, notwithstanding that the stages of formation of the patterns and the machining/engraving through these patterns are the same for all resonators.

Furthermore, this dispersion of stiffness is even greater between the hairsprings of two plates engraved at different times even if the same process specifications are used.

Finally, it should be noted that during manufacturing, more specific manufacturing defects may appear. For example, during the machining stage of the 3D figure , material can remain between two adjacent turns. We can also see parts for which material residues are still present between the turns or the substrate, contrary to what is represented Figure 3E . We can also form bridges of material between two adjacent turns during the oxidation shown Figure 3F . Finally, pollution can also occur with debris or particles that get stuck between two turns or the turns and the substrate. All these defects strongly affect the vibration behavior and cannot be corrected by adding or removing material from all of the parts as is known to do in the prior art.

The above description relates to silicon resonators 100, but we can consider making the resonators in glass, ceramic, carbon nanotubes, or even metal. We can in particular test hairsprings conventional steel or detached from the plate. In this case, the metal hairspring or detached from the plate is pinched or taken as a reference by a tool which positions it opposite the emission source and the displacement measuring device.

In known manner, the stiffness of the hairspring can be measured in a so-called static manner, that is to say without putting the hairspring into oscillation, but by determining its torque. We can for example refer to the document EP3654111 .

An alternative to the method described in this last document consists of carrying out a torque measurement using a rheometer, as marketed by the company Anton Paar. A device provided for this purpose is illustrated on the Figure 4 . Advantageously, it makes it possible to arrange the spring 200 to be evaluated on a mounting 202, and to position it so that it can be fixed at the level of its last turn by a holding member 204. Once the last turn fixed, the installation 202 is distant from the hairspring 200 which is thus completely free from any elastic constraint. The head of the rheometer 206 is then positioned opposite the ferrule of the hairspring. It presents a counter-shape of the ferrule, not circular, but with a reduced size, which allows engagement of the head of the rheometer in the ferrule, with controllable precision, without coming into contact with the hairspring. The head of the rheometer is then rotated, in a direction of contraction of the hairspring. When the head comes into contact with the ferrule, it drives it and the rheometer measures the torque exerted by the elastic return of the hairspring, over a given angle. However, such a measurement remains a unitary measurement and requires significant handling time, with numerous risks of breakage, pollution, etc.

The present invention proposes to determine at least one characteristic of a resonance frequency of a sample of resonators 100 on the wafer in step 3F, to deduce a thermal coefficient of the Young's modulus (CTE) of the hairspring and/or a thermal coefficient (CT) of a watch system comprising the hairspring and possibly in step 3E, to deduce a stiffness and/or a structural defect. In particular, the present invention proposes to identify the above parameters without dismantling the wafer or measuring in a test subset, according to a more efficient method than the methods of the prior art.

Thus, the invention proposes to determine at least one characteristic of a resonance frequency of a sample of resonators by vibration measurement and apply a predictive method (for example a digital model or a classification or categorization method) to connect the result of said vibration measurement to the identification of the thermal coefficient of the Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system comprising the hairspring.

We thus exploit the modal properties of the hairspring attached to the plate. During a learning phase, and through an analytical and numerical approach, it is possible to set up a prediction machine by establishing a predictive model linking the thermal coefficient of the Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system comprising the hairspring at certain frequencies (natural frequency or resonance frequencies associated with a resonance peak or a width at half height) specifically chosen.

Once the learning phase is completed (once the modes to be used as well as the excitation frequencies have been determined), it is possible to move on to a prediction phase and use the prediction machine by exploiting the predictive model to control the resonators of a wafer produced, in order to predict the thermal coefficient of Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system comprising the hairspring. The result of the prediction can be used to validate produced parts, and/or decide on additional processing to correct the thermal coefficient of Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system comprising the hairspring and/or scrapping non-compliant parts in terms of thermal coefficient of Young's modulus (CTE) of the hairspring and/or thermal coefficient (CT) of a watch system including the hairspring.

Thus, it is possible to integrate the control process into a manufacturing process to obtain parts capable of reaching, maintaining, generating a particular and predetermined natural oscillation frequency and independent of temperature variations, once the resonators are each coupled to a balance wheel of a given watch mechanism.

• se base sur un modèle mathématique (par exemple une loi polynomiale reliant une ou plusieurs fréquences de résonance au coefficient thermique du module de Young (CTE) du spiral et/ou au coefficient thermique (CT) d'un système horloger comprenant le spiral),
• utilise un réseau de neurones pour recevoir en entrée des valeurs ou des graphes tirés des spectres de mesures vibratoires pour donner en sortie un coefficient thermique du module de Young (CTE) du spiral et/ou un coefficient thermique (CT) d'un système horloger comprenant le spiral,
• mette en œuvre un système utilisant de l'intelligence artificielle.

It should be noted that the prediction machine is a device which makes it possible to predict, therefore to give or calculate in advance, from one or more measured resonance frequencies, thermal coefficient values of Young's modulus (CTE) of the hairspring and/or thermal coefficient (CT) of a watch system including the hairspring, without coupling the hairspring to a balance wheel, and without carrying out tests at several temperatures. We can predict that the prediction machine:

• is based on a mathematical model (for example a polynomial law linking one or more resonant frequencies to the thermal coefficient of the Young's modulus (CTE) of the hairspring and/or to the thermal coefficient (CT) of a watch system including the hairspring),
• uses a neural network to receive as input values or graphs taken from vibration measurement spectra to output a thermal coefficient of the Young's modulus (CTE) of the hairspring and/or a thermal coefficient (CT) of a watch system including the hairspring,
• implements a system using artificial intelligence.

Vibrational excitation

1. a. Mesures dans le domaine fréquentiel :
   1. 1- utiliser une source piézo-électrique (ou toute autre source permettant d'induire ou imposer une excitation acoustique) sur la tranche de la plaquette, sur, ou sous l'ébauche de spiral 200 à exciter spécifiquement (préférentiel) qui excite à une fréquence particulière f₀ (excitation mono-fréquentielle continue). Dans cette variante, l'excitation est entretenue.
   2. 2- En variante, on peut aussi utiliser la source piézo-électrique (ou toute autre source permettant d'induire ou imposer une excitation acoustique) sur la tranche de la plaquette, sur, ou sous l'ébauche de spiral 200 à exciter spécifiquement (préférentiel) qui excite à une fréquence variable dans le temps pour couvrir une plage fréquentielle prédéterminée, allant par exemple de 0 à 300 kHz, de préférence de 0 à 275 kHz, de préférence de 0 à 250 kHz, de préférence de 5kHz à 250 kHz, et de préférence de 10 à 235 kHz. La totalité de la plage fréquentielle peut être balayée ou couverte dans un intervalle de temps pouvant aller d'une fraction de seconde à quelques secondes. Par exemple, on peut prévoir de balayer ou couvrir la plage de fréquences de la plage fréquentielle en moins de 0.5 s, moins de 1 s, ou moins de 1.5 s. Dans cette variante, la fréquence d'excitation change de manière continue.
2. b. Mesures dans le domaine temporel : utiliser un marteau d'excitation (ou toute autre source permettant d'induire une excitation acoustique impulsionnelle) sur la tranche de la plaquette, sur, ou sous le spiral à exciter spécifiquement (préférentiel) qui donne une impulsion acoustique la plus courte possible (excitation impulsionnelle multi-fréquentielle). Dans cette variante, l'excitation est ponctuelle et non entretenue.

Measuring the vibration response of the resonators makes it possible to deduce at least one characteristic of a resonance frequency, such as for example a value of a resonance frequency. In detail, we must first impose a vibrational excitation on the wafer. Several options are offered:

1. has. Frequency domain measurements:
   1. 1- use a piezoelectric source (or any other source making it possible to induce or impose acoustic excitation) on the edge of the wafer, on, or under the balance spring blank 200 to be specifically excited (preferential) which excites at a particular frequency f ₀ (continuous single-frequency excitation). In this variation, the excitement is maintained.
   2. 2- Alternatively, we can also use the piezoelectric source (or any other source making it possible to induce or impose acoustic excitation) on the edge of the wafer, on, or under the balance spring blank 200 to be specifically excited ( preferential) which excites at a frequency variable over time to cover a predetermined frequency range, for example going from 0 to 300 kHz, preferably from 0 to 275 kHz, preferably from 0 to 250 kHz, preferably from 5kHz to 250 kHz , and preferably from 10 to 235 kHz. The entire frequency range can be scanned or covered in a time interval ranging from a fraction of a second to a few seconds. For example, we can plan to scan or cover the frequency range of the frequency range in less than 0.5 s, less than 1 s, or less than 1.5 s. In this variant, the excitation frequency changes continuously.
2. b. Measurements in the time domain: use an excitation hammer (or any other source allowing pulsed acoustic excitation to be induced) on the edge of the wafer, on or under the hairspring to be specifically excited (preferential) which gives an acoustic pulse as short as possible (multi-frequency pulse excitation). In this variant, the excitement is punctual and not sustained.

Furthermore, the measurements can be carried out following a particular sampling, for example according to a sampling range of 4, 2 or 1 Hz. Indeed, the resolution for processing the acquisition data according to for example a Fourier transform depends directly from the duration of this acquisition.

Furthermore, we can choose a signal sampling frequency of at least 600 kHz if the frequency range extends up to 300 kHz for example. We can generally follow Shannon's theorem which advises choosing a sampling frequency greater than twice the maximum frequency present in the measured signal.

In general, we can finally plan to change the direction of excitation, that is to say the direction of the movements imposed by the source (we can impose vibrations in one or more axial direction(s). ), and make this or these direction(s) evolve over time). In the case where a plate comprising a plurality of resonators is excited, it is possible to adjust the direction of the vibrations so as to point towards one or the other of the resonators, depending on the displacement amplitude measurements described below. below.

Finally, it is possible to couple the acoustic source to a divergent cone directed towards the resonators to be excited, and to adjust the acoustic source to emit an excitation signal with sufficient amplitude to impose vibrational excitation of the resonator(s) and having sufficient amplitude to be detected and measured precisely by the chosen measuring instruments.

Measurement of amplitude or speed, or acceleration of movement

• Méthodes optiques par interférométrie :
  1. a. Par effet Doppler 3D (vibromètre laser par effet Doppler),
  2. b. Holographique,
• Méthodes optiques stroboscopiques,
• Profilométrie confocale chromatique haute résolution temporelle,
• Réflectométrie optique :
  1. a. Analyse de vibration par déflection de faisceau sur détecteur multi-cadrans ou caméra,
  2. b. Analyse par analyse temporelle type TCSPC,
• Méthodes acoustiques par ultrason par effet Doppler.

During excitation, we record, via a suitable measuring means, the amplitude and phase (relative to the exciting source) of oscillation in the 3 directions X, Y (in the plane) and Z (out of plane) of the hairspring excited specifically. In a non-limiting manner, the following possible means of measurement can be cited:

• Optical methods by interferometry:
  1. has. By 3D Doppler effect (laser vibrometer by Doppler effect),
  2. b. Holographic,
• Stroboscopic optical methods,
• High temporal resolution chromatic confocal profilometry,
• Optical reflectometry:
  1. has. Vibration analysis by beam deflection on a multi-dial detector or camera,
  2. b. Analysis by TCSPC type temporal analysis,
• Acoustic methods using ultrasound using the Doppler effect.

There Figure 5 schematically represents a silicon wafer 25 on which a plurality of spiral blanks 200 are formed. A source of vibration excitation 400 is coupled to the wafer 25, so as to be able to impose vibration excitation. Consequently, each hairspring blank 200 will begin to vibrate, and a laser vibrometer 300, here focused on a point of the right-hand hairspring blank 200, will be able to measure the vibration amplitudes of the measuring point over time. We can plan to measure the displacements in a direction normal to the plane of the plate 25, but we can just as easily measure the movements in one or more directions contained in the plane of the plate 25.

Once a particular point has been studied, the laser vibrometer 300 can be moved to another measuring point on the balance spring blank 200, or move to another balance spring blank 200 on the plate 25. Of course, one can alternatively move the balance spring blank 200. 'spring blank 200 compared to the laser vibrometer.

There Figure 6 represents an example of vibrational excitation over time. In the example given, the excitation frequency varies over time, between 0 Hz and 50 kHz (but we can plan to go up to 300 kHz), and we can impose a succession of rising edges, each spaced of a period of rest without excitement. For each measurement point on the spiral blank 200, we can impose a plurality of rising edges (between 2 rising edges and 60 rising edges), each lasting between 0.5 s and 2 s for example.

Selection of reference points to measure

Concerning the measurement of displacement amplitude, during the learning phase, a step can be provided consisting of identifying points of the resonator for which the vibration response is significant. Indeed, in the case of a hairspring to which a vibration is imposed, especially if the frequency varies over time, the vibration response will cause nodes to appear on the hairspring, that is to say particular points of the hairspring whose amplitude of movement is small or zero. If a displacement measurement is made at a point on the hairspring that turns out to be a node at a particular frequency(ies), the identification of resonant frequency characteristics will be negatively affected.

Thus, it is advantageous to provide a preliminary step of measuring displacement on a plurality of predetermined points of the hairspring, for example at least ten predetermined points, preferably at least twenty predetermined points, and very preferably at least thirty of predetermined points. We can plan to select the predetermined points arranged on an orthonormal X-Y reference frame in the plane of the hairspring.

At the end of this preliminary step of measuring amplitude on the predetermined points, we can plan to identify resonance frequencies for each measurement point, and then a step of selecting reference points for which the measurement of amplitude of displacement during excitation shows that they are not nodes at these resonant frequencies. In other words, the identified nodes present, at at least one resonant frequency, a displacement amplitude of zero or less than a first threshold peak value, and these points forming nodes are separated from the reference points to be considered for subsequent measurements. It can also be noted that the reference points are different depending on the position of the balance spring blank 200 on the plate 25.

• dans une première zone à moins de 0.20 × Ra (par exemple sur la virole centrale), ou
• dans une deuxième zone entre 0.05 × Ra et 0.30 × Ra (par exemple sur la deuxième spire en partant de la virole), ou
• dans une troisième zone entre 0.35 × Ra et 0.65 × Ra (par exemple sur une spire située au milieu du spiral), ou
• dans une quatrième zone entre 0.65 × Ra et 0.85 × Ra (par exemple sur une spire située aux trois quarts du spiral).
  Ainsi, les points de référence sont éloignés de la partie ancrée sur la plaquette et présentent naturellement une capacité de déplacement oscillatoire importante, ce qui assure une meilleure précision de la mesure de déplacement.

Typically, it can be assumed that at least two reference points will be selected, and preferably at least four reference points will be selected. In the case where the resonator has a radius Ra and is anchored or embedded on the plate by its external eyebolt end, we can preferably select four chosen and located reference points:

• in a first zone less than 0.20 × Ra (for example on the central shell), or
• in a second zone between 0.05 × Ra and 0.30 × Ra (for example on the second turn starting from the shell), or
• in a third zone between 0.35 × Ra and 0.65 × Ra (for example on a turn located in the middle of the hairspring), or
• in a fourth zone between 0.65 × Ra and 0.85 × Ra (for example on a turn located three-quarters of the hairspring).
  Thus, the reference points are far from the part anchored on the plate and naturally have a significant oscillatory displacement capacity, which ensures better precision of the displacement measurement.

Furthermore, it is also possible to measure the displacements of a point of the body of the wafer, and/or of a point of the excitation source, to identify or measure for example a phase shift or a vibrational attenuation, or even a resonance resulting from a vibrational coupling or from the plate. These additional measurements make it possible to ensure that the peaks identified are indeed those of the hairspring alone. It is also possible to synchronize the measurement of displacement amplitude and the vibration excitation.

Alternatively, we can plan to measure the displacements/movements/vibrations only on a particular point preferably located in an area of the part which does not deform. In particular, it is possible to plan to point the measurement at a point on the ferrule of the hairspring or of the hairspring blank. Indeed, the ferrule can be considered non-deformable during vibrational excitation and all the points of the ferrule exhibit similar displacements/movements/vibrations. Consequently, a small error in locating the measuring point on the ferrule will have little impact on the final result. Furthermore, by having chosen a particular measurement point on the part, we can identify and choose a particular frequency range to conduct the stiffness prediction.

• une étape de capture d'image des pièces à tester,
• une étape d'analyse de l'image pour par exemple reconnaître chaque type de pièce, et/ou la position de chaque pièce,
• une étape de sélection d'un ou plusieurs points à mesurer pour chaque pièce, et/ou de sélection d'un spectre vibratoire d'excitation à imposer pour chaque pièce et/ou chaque point sélectionné,
• pour chaque pièce à tester, une étape de mise en position du substrat ou de l'outillage supportant les pièces à tester dans un appareil d'excitation vibratoire et de mesure. Selon cette mise en œuvre, on peut automatiser l'excitation et la mesure dans le cas d'une plaquette qui porte encore les ébauches de spiraux :
• une ou plusieurs images de la plaquette sont prises,
• une analyse automatique d'image est effectuée pour connaitre au moins la position X-Y de chaque pièce (on peut aussi faire une reconnaissance du type ou modèle de pièce),
• en fonction de la position et/ou du type de pièce reconnues, des points particuliers de mesure préétablis sont identifiés ou sélectionnés (par exemple sur la virole), on peut aussi sélectionner un cycle d'excitation particulier en fonction du type de pièce ou d'un point particulier,
• avec par exemple un outillage qui porte la plaquette et qui comprend une table mobile en X-Y, chaque ébauche de spiral est successivement placée automatiquement en regard de la source d'excitation et de l'appareil de mesure pour être testée en visant le bon point de mesure et en appliquant la bonne spécification d'excitation.

According to an embodiment in which several parts still attached to a substrate or to a tool are to be tested in series, we can provide:

• a step of image capture of the parts to be tested,
• a step of analyzing the image to, for example, recognize each type of part, and/or the position of each part,
• a step of selecting one or more points to measure for each part, and/or selecting a vibrational excitation spectrum to impose for each part and/or each selected point,
• for each part to be tested, a step of positioning the substrate or the tooling supporting the parts to be tested in a vibration excitation and measuring device. According to this implementation, we can automate the excitation and the measurement in the case of a plate which still carries the hairspring blanks:
• one or more images of the plate are taken,
• an automatic image analysis is carried out to know at least the XY position of each part (we can also recognize the type or model of the part),
• depending on the position and/or type of part recognized, particular pre-established measurement points are identified or selected (for example on the ferrule), it is also possible to select a particular excitation cycle depending on the type of part or 'a particular point,
• with for example a tool which carries the wafer and which includes a movable table in XY, each balance spring blank is successively automatically placed opposite the excitation source and the measuring device to be tested by aiming at the right point of measurement and applying the correct excitation specification.

According to one embodiment, depending on the measurement point selected on the part to be tested and/or depending on the excitation frequency, and/or depending on the model of the part to be tested, a step can be provided consisting of giving a particular orientation to the direction of excitation and/or the direction of measurement. For this purpose, we can choose an excitation direction (or an axial direction of the excitation source) perpendicular to the part to be tested to maximize the movements perpendicular to the plane formed by the part at rest. We can choose an excitation direction (or an axial direction of the excitation source) inclined relative to the part to be tested to maximize displacements contained in the plane formed by the part at rest. Regarding the measurement, we can choose a measurement direction (or an axial direction of a laser beam from the measuring device) perpendicular to the part to be tested to maximize the precision of measurement of displacements perpendicular to the plane formed by the part at rest. We can choose a measurement direction (or an axial direction of a laser beam from the measuring device) inclined relative to the part to be tested to maximize the precision of measuring the displacements contained in the plane formed by the part at rest. .

According to an embodiment in which several parts are attached to a substrate such as a wafer, it is possible to carry out sampling by detaching one or a few parts to test them individually, and to deduce a particular excitation frequency. to apply, and/or a particular measurement point to use, and/or a particular area of the vibration spectrum to take into account. In other words, this preliminary sampling makes it possible to test single parts in good conditions (measurement errors and interference are limited) to choose the best test conditions for the parts that remain attached to the substrate.

Determination of vibration characteristics

1. a. Mesures dans le domaine fréquentiel
   1. 1- variante avec excitation entretenue :
      1. i. Intégrer temporellement l'amplitude et la phase d'oscillation suffisamment longtemps pour avoir une bonne résolution spectrale à la fréquence d'excitation f₀,
      2. ii. Décaler la fréquence d'oscillation de delta f pour exciter à la fréquence f₀ + Δ f et répéter l'étape i d'intégration,
      3. iii. Reconstruire les spectres d'amplitude et de phase d'oscillation en fonction de la fréquence d'excitation (possiblement avec plusieurs pics à plusieurs fréquences).
   2. 2- variante avec excitation dont la fréquence varie au cours du temps :
      1. i. Enregistrer temporellement l'amplitude et la phase d'oscillation au cours du balayage fréquentiel de la plage fréquentielle,
      2. ii. Réitérer l'étape i- au moins une fois, de préférence au moins trois fois,
      3. iii. Reconstruire les spectres d'amplitude et de phase d'oscillation en fonction de la fréquence d'excitation (possiblement avec plusieurs pics à plusieurs fréquences).
2. b. Mesures dans le domaine temporel :
   1. i. Enregistrer le déplacement temporel de la spire selon X, Y et Z sur une durée suffisamment longue de manière à obtenir un signal suffisamment représentatif, comme par exemple quelques secondes.
   2. ii. On peut choisir d'enregistrer le signal pour en faire un signal de référence à comparer avec d'autres signaux mesurés sur d'autres pièces. On peut aussi choisir de faire un traitement du signal de type transformée de Fourier pour identifier des fréquences de résonance dans le signal enregistré.

We then have several scenarios depending on the domain previously chosen for excitation:

1. has. Frequency domain measurements
   1. 1- variant with maintained excitation:
      1. i. Integrate temporally the amplitude and the phase of oscillation long enough to have a good spectral resolution at the excitation frequency f ₀ ,
      2. ii. Shift the oscillation frequency by delta f to excite at frequency f ₀ + Δ f and repeat integration step i,
      3. iii. Reconstruct the oscillation amplitude and phase spectra as a function of the excitation frequency (possibly with multiple peaks at multiple frequencies).
   2. 2- variant with excitation whose frequency varies over time:
      1. i. Temporally record the amplitude and phase of oscillation during the frequency sweep of the frequency range,
      2. ii. Repeat step i- at least once, preferably at least three times,
      3. iii. Reconstruct the oscillation amplitude and phase spectra as a function of the excitation frequency (possibly with multiple peaks at multiple frequencies).
2. b. Time domain measurements:
   1. i. Record the temporal movement of the turn along X, Y and Z over a sufficiently long period so as to obtain a sufficiently representative signal, such as a few seconds for example.
   2. ii. You can choose to record the signal to make it a reference signal to compare with other signals measured on other parts. We can also choose to carry out Fourier transform type signal processing to identify resonant frequencies in the recorded signal.

As a result, one can identify at least one resonance peak for each excited resonator, and it is proposed to determine the resonance frequency not on the basis of the top of the resonance peak, i.e. on the amplitude maximum, but rather on an area of the curve located between 25% and 75% of the maximum amplitude value of the resonance peak, for example from its width at half height. Indeed, this processing method which focuses on a part of the curve between 25% and 75% of the maximum amplitude value of the resonance peak makes it possible to limit errors due to the singularity of the maximum amplitude point and to the approximation calculations to reconstruct the summit part of the resonance peak. The area of the curve located between 25% and 75% of the maximum amplitude value of the resonance peak has better precision than the part above 75% (typically the peak), which offers better precision on the exact frequency of determined resonance. For example, we can take the middle of the segment connecting the two points halfway up the resonance peak to determine the resonance frequency associated with the peak in question.

There Figure 7 represents an example of a vibration spectrum for a point of a balance spring 200 of the Figure 5 free of defects, reconstructed from measurements of the displacement amplitude of the measuring point considered in response to the vibratory excitation of the Figure 6 , between 10 kHz and 15 kHz. We can note the presence of three amplitude peaks, at approximately 11 kHz, 12.3 kHz, and 13.7 kHz. Although not shown, between 10 and 250 amplitude peaks can typically be identified if the vibrational excitation sweeps over a frequency range between 0 Hz and 300 kHz. Each peak amplitude has a resonant frequency, and peak amplitudes vary greatly.

There figure 8 represents in detail the processing that can be done on an amplitude peak for a part free of defects, that at 11 kHz for example. THE The goal is to find the resonant frequency and give it as precise a value as possible. Instead of basing this treatment on the maximum value of the peak, the applicant realized that better precision could be achieved by determining the length of the segment connecting the rising part and the falling part of the curve, halfway up the peak. The resonant frequency typically being the value in the middle of this segment. However, we can perform an interpolation on points in the vicinity of the resonance peak to improve the precision, and shift the chosen point on the segment, which will not be the middle, in particular if the real position of the resonance peak is shifted by example due to the chosen sampling frequency.

There Figure 9 represents, for the example of an amplitude peak at approximately 10 kHz, the amplitude peaks constructed for around ten hairspring blanks 200 tested. It can be noted that from one spiral blank to another, the frequency position of the amplitude peak varies (from approximately 9.8 kHz to 10.02 kHz), and that the maximum displacement amplitude varies in a ratio of 1 to 5 approximately. Since the tops of amplitude peaks are not truly symmetrical, it may be wise to determine the resonant frequency based on the width of the peak at half height. We can also use the width of the peak at half height to determine damping, and compare this damping to a reference value.

For these tests of the Figure 9 , we were able to deduce the following resonance frequencies: Spiral no. Resonant frequency (Hz) 2 9824 9 9824 3 9840 8 9840 7 9848 4 9863 10 10020 5 10121 1 10129 6 10148

With reference to the manufacturing process described in figures 3A-3F , an optional first measurement can be carried out on the parts described Figure 3E to estimate the stiffness of non-oxidized parts, to determine whether dimensional correction is required or not. We could also consider making the first optional measurement after an oxidation step adding a predetermined thickness of oxide, from which any dimensional corrections are made. Once the parts have been oxidized (that is to say with a thermo-compensation treatment), the invention proposes to make a second measurement to determine a thermal coefficient of the Young's modulus (CTE) of the hairspring and/or a coefficient thermal (CT) of a watch system including the hairspring.

Consequently, we will first describe the steps implemented to determine the stiffness of the parts.

Determination of the stiffness and/or real dimensions of the bar of the resonators tested

To establish a prediction model that can receive the vibration characteristics as input (typically a resonant frequency) and output a stiffness and/or a dimensional correction, it is necessary, during the learning phase, to provide the data relating to the actual stiffness and/or bar dimensions of the resonators tested. To this end, we can plan to concretely measure a natural frequency of a spiral-balance system in an environment similar to that of a particular watch mechanism.

Two alternatives can be implemented. According to a first alternative, we can couple a predetermined balance directly to the resonator still attached to the plate, and measure a natural frequency of oscillation of the resonator - balance wheel couple to compare this natural frequency with an expected natural frequency and above all calculate the real stiffness or actual dimensions based on equations 1 to 3 above. According to a second alternative, we can finish manufacturing the resonators tested, in order to mount or couple them with a balance wheel individually to measure here again a natural frequency of oscillation of the resonator - balance wheel couple.

In the two alternatives above, we can go through an intermediate step of determining the stiffness of each resonator, and then determine the real dimensions of the bar of the resonators tested. In other words, it is possible to determine the natural frequency or a resonance frequency and then the stiffness or the dimensions of the resonator bar by analyzing the free oscillations of a hairspring coupled to a reference balance wheel. In this approach, a laser pointed at the balance arms or at the hairspring holder records the passage times of the balance arms or a key. We then deduce an estimate of the period, then the frequency and finally the stiffness. The data collected are essentially point clouds of passage times.

Indeed, to evaluate the stiffness of a spiral on the wafer, several solutions are offered, as notably described by M. Vermot et al, in the Treatise on Watch Construction (2011) on pages 178-179 . For example, we can carry out a dynamic evaluation, by coupling the hairspring to a reference balance wheel whose inertia is known. Measuring the frequency of the assembly makes it possible to deduce the stiffness of the balance spring precisely. This assessment can be carried out on the wafer or by detaching the spiral from the wafer. The references and prior art given above provide details on this method.

Analogously, the stiffness can also be deduced from a measurement of reaction torque at the shell using a rheometer. The acquired signal represents the evolution of the torque as a function of the amplitude. Analysis of the slope of this curve for low amplitudes (linear part) makes it possible to deduce the stiffness, and then the dimensions of the resonator bar. We can then determine the dimensions of the hairspring bar.

On the other hand, it is possible to estimate by simulation a natural frequency and/or a resonance frequency and/or the stiffness for each resonator tested on the wafer. To this end, dimensional measurements can be taken of each resonator tested to reconstruct the resonator by digital modeling in order to simulate by numerical calculation its vibrational response to the imposed spectrum, and to also find the stiffness of the resonator.

A high-resolution 3D X-ray tomography approach would make it possible to extract point clouds giving the 3D material density of the hairsprings, and, through appropriate image reconstruction, a map of the hairspring section. These different types of data make it possible to deduce the dimensions of the bar from the bar and to estimate the stiffness of the hairspring using a geometric approach.

Another approach consists of analyzing the forced oscillations of a hairspring on a reference balance wheel with an escapement. A laser measurement of the passage times of the balance arms (point clouds), as presented above, makes it possible to measure the frequency and deduce the stiffness. An alternative can be considered based on an acoustic acquisition (Witschi type microphone) which records the shocks of the different operating phases of the escapement/anchor system. The measured data are either point clouds of the moments of passage of the balance arms, or the temporal evolution of the sound pressure level. These types of experimental data make it possible to deduce the period, then the frequency, then the stiffness and finally the dimensions of the resonator bar.

Returning to the tests discussed above at the Figure 9 , a measurement of the stiffness was carried out by coupling each balance spring 200 to a reference balance, and the stiffnesses below could be deduced: Spiral no. Measured stiffness (10 ^-7 N.mm) 2 3.89 9 3.88 3 3.92 8 3.90 7 3.91 4 3.95 10 4.111 5 4.135 1 4.119 6 4.196

Establishing the prediction model

To be able to predict the stiffness, reference data must first be established or constructed, such as a reference spectrum. During the learning phase, oscillation amplitude measurements are carried out on physical resonators, and resonance frequencies are identified. In order to subsequently be able to relate the resonance frequencies measured on resonators to stiffnesses and/or dimensional (thickness) corrections to be made, it is necessary to provide a correlation phase during which a predictive model is constructed.

The operations described above (vibration measurements, identification of resonance peaks, bandwidth at half height and its midpoint or corrected value, determination of the stiffness and/or dimensions of the bar of the bar) make it possible to supply a base data that can relate the position of the balance spring to the wafer, spectra or periods of oscillation or bandwidth at half height and its midpoint value or corrected with the stiffnesses and/or dimensions of the effective bar of the hairspring. As seen above, this database can be constructed from numerical simulations on a finite element model of a hairspring. These simulations make it possible to generate reference spectra or oscillation periods associated with stiffnesses. This database can also be supplemented by experimental measurements by measuring vibration spectra, oscillation periods and the positions of hairsprings on the plate as well as their associated stiffnesses. One of the advantages of this approach lies in the fact that the training database is enriched as the tests are carried out. This can make it possible to have an adaptive model depending on the plates and hairsprings and contributes to the reduction of the standard deviation in stiffness on the plates.

This database can be used to build a prediction model, and several solutions are offered.

We can construct a digital model, for example polynomial, to calculate, as a function of a resonant frequency value, a real thickness, a dimensional correction or a real stiffness.

We can also carry out a categorization by carrying out a k-means partitioning of the input data (the results of the vibration measurements, typically the frequency of the resonance peaks) and the output data (the stiffness, and/or the dimensions of the bar of the resonator) and connect them together to establish a correspondence.

It is also possible to process the images of the resonance peaks by a neural network, for example a perceptron, to carry out a classification according to stiffness or dimensions of the bar, the classes being able to be defined by increments of values.

In summary, the learning phase includes a test phase (excitation of resonators with measurement of vibration characteristics to reconstruct a vibration spectrum and identify resonance frequencies). A phase of measuring the stiffness and/or dimensions of the resonator bar is also carried out. Once the input data (the resonance frequencies) and the output data (the stiffness and/or the dimensions of the bar) for a significant sample available, the construction phase of the prediction model can be carried out.

• R pour la raideur en 10^-7 N.mm
• F pour la fréquence de résonance en Hz.

La raideur peut donc être prédite et comparée avec la raideur réelle mesurée comme le montre le tableau ci-dessous, avec pour les six premières lignes les données utilisées pour bâtir ou entraîner la régression linéaire, et pour les quatre dernières lignes, une prédiction uniquement : N° F (Hz) R (10^-7 N.mm) mesurée R (10^-7 N.mm) prédite écart 2 9824 3.89 3.84 -1.20% 9 9824 3.88 3.84 -1.10% 3 9840 3.92 3.87 -1.40% 8 9840 3.9 3.87 -0.90% 7 9848 3.91 3.88 -0.70% 4 9863 3.95 3.9 -1.20% Test 10 10020 4.111 4.136 0.60% 5 10121 4.135 4.288 3.70% 1 10129 4.119 4.3 4.40% 6 10148 4.196 4.328 3.20% Une erreur maximale de 4.40% a pu être mesurée, et la figure 10 représente la droite de régression linéaire pour les valeurs des six premières lignes.To return to the example treated and described in relation to the Figure 9 , the data collected is as follows: Spiral no. Resonant frequency (Hz) Measured stiffness (10 ^-7 N.mm) 2 9824 3.89 9 9824 3.88 3 9840 3.92 8 9840 3.90 7 9848 3.91 4 9863 3.95 10 10020 4.111 5 10121 4.135 1 10129 4.119 6 10148 4.196 Linear regression modeling was performed on the above data for the first six rows, and the relationship below could be established:
R = 0.0015 F - 10.894,
With

• R for stiffness in 10 ^-7 N.mm
• F for the resonant frequency in Hz.

The stiffness can therefore be predicted and compared with the actual measured stiffness as shown in the table below, with for the first six lines the data used to build or train the linear regression, and for the last four lines, a prediction only: No. F (Hz) R (10 ^-7 N.mm) measured R (10 ^-7 N.mm) predicted gap 2 9824 3.89 3.84 -1.20% 9 9824 3.88 3.84 -1.10% 3 9840 3.92 3.87 -1.40% 8 9840 3.9 3.87 -0.90% 7 9848 3.91 3.88 -0.70% 4 9863 3.95 3.9 -1.20% Test 10 10020 4.111 4.136 0.60% 5 10121 4.135 4,288 3.70% 1 10129 4.119 4.3 4.40% 6 10148 4.196 4.328 3.20% A maximum error of 4.40% could be measured, and the Figure 10 represents the linear regression line for the values of the first six rows.

It can be noted that it is advantageous to verify that the established prediction model has good sensitivity, that is to say that for two different input values, the model gives two distinct output values. The applicant noticed that the sensitivity of the prediction model was not the same for all the resonance peaks. In particular, if we refer to the prediction formula established and represented Figure 10 , the slope coefficient is 0.0015 10 ^-7 N.mm/Hz. On the one hand, the applicant noticed that the leading coefficient could be larger for high resonance frequencies, which provides better prediction sensitivity, to predict distinct stiffness or dimensional correction values, even from close resonance frequency values. It is advantageous to provide, during the learning phase, a step of comparing the sensitivity of the prediction to verify/confirm that it is preferable to consider and choose certain resonance peaks at high frequencies (for example beyond of 5 kHz) to then predict as precisely as possible a stiffness and/or a dimensional correction based on the measured vibration response.

On the other hand, the applicant also noticed that even for close resonance frequencies, the resonance modes (in particular the modes of deformation and/or movement of the resonators) could differ significantly, which can also affect the sensitivity of the prediction of stiffness and/or dimensional correction. It is advantageous to provide, during the learning phase, a step of comparing the sensitivity of the prediction to choose to subsequently consider this or that resonance frequency and not another to predict as precisely as possible a stiffness and /or a dimensional correction depending on the vibration response.

From the above remarks relating to the study of the sensitivity of the prediction, we can plan, during the learning phase, to classify the different resonance peaks identified according to the sensitivity of prediction of the stiffness and/or the dimensional correction. We can then plan to define the excitation frequency range (which will be applied during a pure prediction phase) to include at least one or more peaks or resonance frequencies which give(s) the best sensitivity. Thus, imposing a variable vibrational excitation on the frequency range thus predetermined will guarantee being able to make a precise prediction for the identified resonance peak or predictions for each of the identified resonance peaks, which overlap or reinforce each other.

Generally speaking, the learning phase makes it possible to choose either resonance peaks at high frequencies and/or resonance peaks which correspond to particular resonance modes making it possible to predict precise and reliable values, and the frequency range will be predetermined. to include at least one resonance peak and preferably several, to be able to make either a a single prediction as precise as possible, or several predictions (one per resonance peak deemed interesting) to then carry out cross-checking, averages or even adjustments of the predicted values.

We can for example plan to predict several values of stiffness or dimensional corrections from several peaks or resonance frequencies, and then calculate a final value, by carrying out, from the predicted values, a weighted average by assigning weights to each predicted value, each weight being determined based on the sensitivity identified for each corresponding peak or resonance frequency.

Alternatively and preferably, we can plan to have only one model which takes all the peaks or resonant frequencies as input and which returns the stiffness or the dimensional correction, the learning phase of the model serving precisely to calculate the weightings on the peaks or input resonance frequencies.

Prediction phase

Once the learning phase is completed, we can move on to a prediction phase, for example during a resonator control process. The control process can typically be carried out on hairspring blanks made on a plate and still attached to this plate, so as to estimate the stiffness and/or the dimensions of the bar of the hairsprings of the sample, in order to determine whether a correction dimension is to be provided.

1. 1) Repérage de la position du spiral sur le wafer, mesure vibratoire des spectres ou période d'oscillation (comme décrit plus haut),
2. 2) Prédiction de la raideur et/ou des dimensions du barreau du spiral par application du modèle prédictif,
3. 3) Déterminer si une correction dimensionnelle est nécessaire pour atteindre la fréquence propre ou raideur cible.

Once the model has been trained, the control procedure to deploy can be as follows:

1. 1) Identification of the position of the hairspring on the wafer, vibration measurement of the spectra or oscillation period (as described above),
2. 2) Prediction of the stiffness and/or dimensions of the hairspring bar by application of the predictive model,
3. 3) Determine if a dimensional correction is necessary to achieve the target natural frequency or stiffness.

1. 1) Connaissant la raideur effective du spiral estimée(s) selon le modèle et la raideur cible et/ou les dimensions du barreau cibles : appliquer la dose de correction nécessaire.
   Réitérer l'étape 1) et l'étape 2) du procédé de contrôle pour contrôler la raideur / les dimensions du spiral et confirmer que les valeurs cibles sont atteintes, à un seuil de tolérance près, ou répéter ces étapes et la correction dimensionnelle jusqu'à ce que la raideur/dimension prédite par le modèle atteigne les valeurs cibles.

During the control process, it is also possible to quantify the exact correction to be made, so that the manufacturing process can include, in addition to the above control:

1. 1) Knowing the effective stiffness of the hairspring estimated(s) according to the model and the target stiffness and/or the dimensions of the target bar: apply the necessary correction dose.
   Repeat step 1) and step 2) of the control process to check the spring stiffness/dimensions and confirm that the target values are reached, within a tolerance threshold, or repeat these steps and the dimensional correction until until the stiffness/dimension predicted by the model reaches the target values.

Sampling

We know that several hundred spirals are made on a wafer and that the dimensions of the bar of the spirals produced can vary depending on the regions of the wafer. If the stiffness evaluation can be carried out on a single hairspring, in practice, it will be carried out on a sample of hairsprings, distributed over the plate.

From the evaluations carried out, corrections can be made for the entire plate in a homogeneous manner, or differentiated by region, if the results obtained vary from one spiral to another. We can thus reduce the standard deviation of the dispersion of stiffnesses. Furthermore, if we know the stiffness of all the hairsprings by applying the model, we can determine the optimal correction to reduce the overall dispersion.

We can even consider going as far as evaluating all the spirals of the plate, in particular with a vibration evaluation, because this is very quick to carry out and can allow automation of the process.

Although the examples above have been given mainly on the basis of manufacturing hairsprings having initial bar dimensions larger than the target bar dimensions, it is also possible to plan to produce hairsprings having initial bar dimensions larger smaller than the dimensions of the target bar. The correction step then consists of adding material, as for example described in the document EP3181939 aforementioned.

The method, consisting of identifying resonant frequencies by imposing vibratory excitation on the hairspring blanks alone, makes it possible to quickly obtain measurement data, without having to, for example, carry out assembly operations on a balance wheel, while limiting measurement errors. measure because only the hairspring blank is tested (there are no errors that could be linked to the balance, such as its mass, its mounting position, etc.).

Prediction of the thermal coefficient of Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system including the hairspring

• Étape 1 : mesures ou calculs des fréquences propres ou de résonance sur plaquette à plusieurs températures T (par exemple 8°C, 23°C et 38°C) ;
• Etape 2 : détacher les spiraux, les assembler avec un balancier et les monter dans des mouvements ;
• Etape 3 : mesurer les coefficients thermiques (CT) en mouvement selon la procédure du Contrôle officiel suisse des chronomètres (COSC) par exemple (24h à 8°C, 24h à 23°C et 24h à 38°C) ;
• Etape 4 : construire un modèle de prédiction entre les fréquences propres ou de résonance mesurées à l'étape 1 et les coefficients thermiques (CT) du mouvement mesurés à l'étape 4.

For the part relating to the prediction of the thermal coefficient of the Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system including the hairspring, we can proceed as follows:

• Step 1: measurements or calculations of the natural or resonance frequencies on the wafer at several temperatures T (for example 8°C, 23°C and 38°C);
• Step 2: detach the hairsprings, assemble them with a balance wheel and mount them in movements;
• Step 3: measure the thermal coefficients (CT) in motion according to the Swiss Official Chronometer Control (COSC) procedure for example (24 hours at 8°C, 24 hours at 23°C and 24 hours at 38°C);
• Step 4: build a prediction model between the natural or resonance frequencies measured in step 1 and the thermal coefficients (CT) of the movement measured in step 4.

• Construire un modèle par éléments finis de spiral avec une couche d'oxyde de silicium ;
• Attribuer les paramètres matières pertinents et leurs évolutions avec la température ;
• Faire une analyse modale sur l'intervalle de température [8°C 38 °C] ;
• Tracer l'évolution des fréquences propres ou de résonance en fonction de la température et pour différentes épaisseurs de couche d'oxyde.

In step 1, it may be difficult to make the vibration measurement for several temperatures. We can consider carrying out the vibration measurement for a single temperature (for example 23°C, clean room temperature) then building a digital model capable of estimating the evolution of the natural frequencies with the temperature according to the following procedure:

• Construct a finite element model of a hairspring with a layer of silicon oxide;
• Assign the relevant material parameters and their evolution with temperature;
• Carry out a modal analysis on the temperature interval [8°C 38°C];
• Trace the evolution of natural or resonance frequencies as a function of temperature and for different oxide layer thicknesses.

With these laws of evolution, it becomes possible to predict the desired natural frequencies from a single experimental vibration measurement carried out at 23°C. However, we could imagine different heating systems in an oven or by conduction to identify these laws experimentally.

The result of such a prediction can be observed Figure 11 , where the resonance frequencies of the same resonance mode (the number x among for example 240 identified resonance modes) are represented for three distinct temperatures T1, T2, T3. We can see a difference in the value of the frequency of the resonance peak between the three temperatures.

Furthermore, the applicant noticed that the resonant frequency was significantly affected by different oxidation values (implying variations in the thermal coefficient of the Young's modulus (CTE) of the hairspring and therefore variations in the thermal coefficient (CT) of a watch system including the hairspring) for certain resonance modes only.

In detail, a sensitivity analysis of the resonance frequency to the oxidation value was carried out for approximately 240 resonance modes identified with the equation below: $$S=\frac{\mathit{Var}\left[E\left[Y|\mathit{Xi}\right]\right]}{\mathit{Var}\left[Y\right]}$$

There Figure 12 shows that the sensitivity of the resonance frequency to the thickness of the oxide layer to predict the thermal coefficient of Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system including the hairspring ( CT curve) increases for certain resonance modes from approximately the ^100th resonance mode identified. It can be concluded that it is advantageous to take into account resonance modes that have high resonance frequencies to predict the thermal coefficient of Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a system watchmaker including the hairspring. On the other hand, the same Figure 12 shows that the sensitivity of the resonance frequency to the thickness of the oxide layer and/or to the ratio of thickness of the silicon core vs. thickness of silicon oxide, to predict the stiffness (R curve) decreases for certain modes resonance from approximately the ^100th resonance mode identified. We can conclude that it is advantageous to take into account the modes of resonance which have low resonance frequencies to predict the stiffness of the hairspring.

Furthermore, the applicant has noticed that for resonance modes having a high frequency, the sensitivity of the resonance frequency is particularly high for so-called "out-of-plane" resonance modes, while so-called "plane" resonance modes » do not present any particular sensitivity. We can conclude that it is advantageous to take into account “out-of-plane” resonance modes which have high resonance frequencies to predict the thermal coefficient of Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT ) of a watchmaking system including the hairspring. Conversely, it is advantageous to consider the “plane” resonance modes to predict the stiffness of the parts.

Step 3 can be carried out by detaching the parts measured in step 1 and mounting them in a reference movement, and the progress of these movements can be measured according to the three temperatures 8°C, 23°C, 38° vs.

To establish a thermal coefficient prediction model which can receive the vibration characteristics as input and give as output the thermal coefficient of the Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system including the hairspring , we can therefore use the resonance frequency data identified at the three temperatures for the parts taken into account, and the operating data at the three temperatures for these same parts.

Once the thermal coefficient prediction model is established, a thermal coefficient prediction machine can use it to predict, for example from resonance frequency data for an out-of-plane resonance mode having a high resonance frequency, the thermal coefficient of Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system including the hairspring. Of course, when it comes to predicting the thermal coefficient (CT) of a watch system including the hairspring, the thermal coefficient prediction machine can receive as input the reference of the watch device in question, or its value or contribution to the thermal coefficient. We can in fact consider that for a given caliber reference, the different parameters which intervene in the CT of the movement (sensitivity to the temperature of the balance, of the cog, bearings, lubricants, etc.) are constant and do not constitute adjustment variables.

There is no longer any need to assemble movements to measure the thermal coefficient (CT) of a watch system including the hairspring; this time-consuming step and source of variability can be eliminated.

There would be the possibility of carrying out iterative processing on parts of the same wafer: after predicting the thermal coefficient of the Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system including the hairspring , we could detach only the parts having the desired performances, and apply a new thermo-compensation step (oxidation and/or deoxidation) to the parts which are identified as not compatible or not conforming to the desired performances.

• en appliquant une excitation vibratoire particulière à des pièces oxydées,
• en fournissant la réponse vibratoire ou des fréquences de résonance ou des pics de résonance ou des données extraites de la réponse vibratoire à une machine de prédiction de coefficient thermique. Avec ce procédé, on peut vérifier simplement si les pièces ont une thermo-compensation adaptée au mouvement dans lequel elles seront montées.

On peut retenir que l'on peut aussi, de manière optionnelle, à une étape précédente de fabrication (avant thermo-compensation ou oxydation par exemple) effectuer une excitation vibratoire particulière et soumettre la réponse vibratoire ou des fréquences de résonance ou des pics de résonance ou des données extraites de la réponse vibratoire à une machine de prédiction de raideur ou de présence de défaut structurels comme par exemple :

• une ou plusieurs spires collée(s) ou pontée(s) à une spire adjacente, au reste de la plaquette, comme par exemple le support isolant,
• une porosité, locale ou non, du matériau ou de l'oxyde,
• une interface entre une âme en silicium et une couche d'oxyde avec un vide, un décollement, des irrégularités...,
• une épaisseur d'oxyde irrégulière ou interrompue...,
• un défaut ou manque local de matière, comme par exemple un défaut d'infiltration,
• un surplus de matière, lié par exemple à un défaut de masquage,
• une hétérogénéité de la matière (le silicium, l'oxyde de silicium),
• un défaut de planéité (lissage) des tranches latérales du barreau formant le spiral,
• un défaut de verticalité des tranches latérales du barreau formant le spiral (une dépouille ou une contre dépouille des faces),
• des spires déformées, ondulées ou décentrées par rapport à la position théorique...

In summary, the invention makes it possible to simplify the manufacturing and control processes of silicon resonators to manufacture movements having little or no sensitivity to temperature variations:

• by applying a particular vibratory excitation to oxidized parts,
• by providing the vibration response or resonance frequencies or resonance peaks or data extracted from the vibration response to a thermal coefficient prediction machine. With this process, we can simply check whether the parts have thermo-compensation adapted to the movement in which they will be mounted.

We can remember that we can also, optionally, at a previous manufacturing stage (before thermo-compensation or oxidation for example) carry out a particular vibrational excitation and submit the vibrational response or resonance frequencies or resonance peaks or data extracted from the vibration response to a machine for predicting stiffness or the presence of structural defects, such as:

• one or more turns glued or bridged to an adjacent turn, to the rest of the plate, such as for example the insulating support,
• porosity, local or not, of the material or oxide,
• an interface between a silicon core and an oxide layer with a void, separation, irregularities, etc.
• an irregular or interrupted oxide thickness...,
• a local defect or lack of material, such as for example an infiltration defect,
• a surplus of material, linked for example to a masking defect,
• heterogeneity of matter (silicon, silicon oxide),
• a lack of flatness (smoothing) of the lateral edges of the bar forming the hairspring,
• a lack of verticality of the lateral edges of the bar forming the hairspring (an undercut or an undercut of the faces),
• deformed, wavy or off-centered turns compared to the theoretical position...

However, it can be noted that the data taken from the vibration response and used for these predictions of stiffness or presence of defects are not necessarily the same as those for the prediction of thermal coefficient and we can even consider that in a preferred manner, the data taken from the vibration response and used are different and distinct from those for the prediction of the thermal coefficient.

Claims (16)

Method for controlling a hairspring or a hairspring blank arranged to form a hairspring, the control method comprising the following steps: has. apply to the hairspring or the hairspring blank a vibrational excitation which varies over time to cover a predetermined frequency range, b. identify at least one characteristic of a resonance frequency of the hairspring or the hairspring blank, such as a resonance peak, during or in response to vibrational excitation over the predetermined frequency range, vs. submitting to a thermal coefficient prediction machine the resonant frequency characteristic identified in step b. to determine a thermal coefficient of the Young's modulus (CTE) of the hairspring and/or a thermal coefficient (CT) of a watch system comprising the hairspring. Control method according to claim 1, in which step b. understand : b1. a first identification step comprising the identification of a first characteristic of a first resonance frequency such as a first resonance peak, b2. a second identification step comprising the identification of a second characteristic of a second resonance frequency such as a second resonance peak, the second resonance frequency being different from the first resonance frequency, and in which step c. understand : c1. a first prediction step consisting of submitting to another prediction machine the first characteristic of the first resonance frequency to determine a parameter different from the thermal coefficient of the Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) d 'a watchmaking system comprising the hairspring, such as a stiffness or defect of the hairspring or the hairspring blank, c2. a second prediction step consisting of submitting to the thermal coefficient prediction machine the second characteristic of the second resonance frequency to determine the thermal coefficient of Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system including the hairspring. Control method according to claim 2, in which steps b1 and b2 are separated by an oxidation step, and in which step a. understand : a1. a first vibrational excitation step, carried out before step b1. and consisting of applying to the hairspring or the hairspring blank a first vibrational excitation which varies over time to cover a first predetermined frequency range, a2. a second vibrational excitation step, carried out before step b2. and consisting of applying to the oxidized hairspring or to the oxidized hairspring blank a second vibrational excitation which varies over time to cover the first predetermined frequency range or a second predetermined frequency range. Control method according to claim 2, in which step a. is implemented after an oxidation step, and in which steps b1. and b2. take into account the same vibration response of the hairspring or the hairspring blank. Control method according to one of claims 2 to 4, in which: - the first resonance frequency is chosen to be a resonance frequency of a plane resonance mode, and/or - the second resonance frequency is chosen to be a resonance frequency of an out-of-plane resonance mode. Control method according to one of claims 2 to 5, in which the first resonance frequency is lower than the second resonance frequency and/or: - the first resonance frequency is chosen in a range of values going from 0 Hz to 100 kHz, preferably from 0 Hz to 50 kHz, more preferably from 0 Hz to 40 kHz, and very preferably from 10 kHz to 35 kHz, and /Or - the second resonance frequency is chosen in a range of values going from 0 Hz to 300 kHz, preferably from 50 kHz to 250 kHz, more preferably from 60 kHz to 200 kHz, and very preferably from 100 kHz to 200 kHz. Control method according to one of claims 1 to 6, the hairspring having at least two expected predetermined resonance frequencies, in which the frequency range is predetermined to cover at least the two expected predetermined resonance frequencies. Control method according to one of claims 1 to 7, in which step b is based on a measurement over time of an amplitude or a speed or an acceleration of movement of at least one point of the hairspring or the hairspring blank, preferably carried out at least partially during step a. Control method according to one of claims 1 to 8, the hairspring or the hairspring blank being contained in a base plane, in which step b comprises: - a step b" of measuring an amplitude or a speed or an acceleration of movement of at least one point of the hairspring or of the hairspring blank in a direction normal to the base plane, and/or - a step b'" of measuring an amplitude or a speed or an acceleration of movement of at least one point of the hairspring or of the hairspring blank in a direction contained in the base plane. Control method according to one of claims 8 or 9, in which step b. understand : - a step of identifying a resonance peak of the hairspring or the hairspring blank as a function of an amplitude or a speed of movement of at least one point of the hairspring or the hairspring blank. A monitoring method according to claim 10, wherein the characteristic of the resonance frequency is identified based on the width of the resonance peak, at half the maximum value of the resonance peak. Control method according to one of claims 1 to 11, in which the thermal coefficient prediction machine implements a regression method, for example a linear regression, to predict the thermal coefficient of the Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system including the hairspring. Control method according to one of claims 1 to 11, comprising a preliminary step consisting of taking into account the material of the hairspring or the hairspring blank, and of adjusting a maximum amplitude of the vibratory excitation and/or a range frequency of the predetermined frequency range depending on the material of the hairspring or the hairspring blank. Control method according to one of claims 1 to 13, in which, if step c. determines that the thermal coefficient of the Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system comprising the hairspring is outside a range of expected values, then the method comprises at least one step consisting of identifying or isolating or retouching or discarding the hairspring or the hairspring blank. Control method according to one of claims 1 to 13, in which, if step c. determines that the thermal coefficient of the Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system comprising the hairspring is outside a range of expected values, then the method comprises at least one step consisting of defining a processing step of the hairspring or the hairspring blank, such as a thermo-compensation, oxidation or deoxidation step, to obtain the thermal coefficient of the Young's modulus (CTE) of the hairspring and/or or the thermal coefficient (CT) of a watch system including the hairspring within the range of expected values Method for learning a prediction machine to implement step c. of the control method of one of claims 1 to 15, comprising the steps consisting of: i- form hairsprings or blanks of hairsprings and apply a thermo-compensation step to them, ii- apply to each of the hairsprings or each of the hairspring blanks a vibrational excitation which varies over time to cover a predetermined frequency range, iii- identify at least one characteristic of a resonance frequency of each hairspring or each hairspring blank when applying the predetermined frequency range and record the temperature of the parts during step ii- and/or iii-, iv'- mount a plurality of hairsprings or hairspring blanks in an oscillating mechanism having a predetermined inertia so as to measure for each hairspring or hairspring blank a sustained frequency of oscillation or a rate of the watch system formed by, or comprising , the mechanism oscillating at at least one predetermined temperature and preferably at at least two predetermined temperatures,
and or iv"- model in a simulation tool a plurality of hairsprings or hairspring blanks in an oscillating mechanism having a predetermined inertia so as to calculate for each hairspring or hairspring blank a sustained oscillation frequency and/or a thermal coefficient of a watch system comprising the hairspring and/or the running of the watch system comprising the hairspring at at least one predetermined temperature and preferably at at least two predetermined temperatures, v- optionally, deduce at least one expected resonance frequency from the resonance frequency identified in step iii-, and/or from the sustained oscillation frequency and/or from the operation of the watch system measured in step iv '- and/or calculated in step iv"- vi- deduce a thermal coefficient of the Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system including the hairspring from the measurements of step iv'- and/or the calculations of the 'step iv'- vii- provide the prediction machine, and for each hairspring or hairspring blank: - the characteristic of the resonance frequency identified in step iii-; - optionally, the same characteristic of the expected resonance frequency; - the temperature recorded during step ii- and/or iii-; - the thermal coefficient of the Young's modulus (CTE) of the hairspring and/or the thermal coefficient (CT) of a watch system comprising the hairspring deduced in step vi-.

Images