EP4030243A1 - Method for monitoring and manufacturing timepiece hairsprings - Google Patents

Abstract

Process for testing a hairspring or a blank hairspring arranged to form a hairspring, the hairspring having to exhibit at least one predetermined resonance frequency, the testing process comprising the following steps: a. applying to the hairspring or to the hairspring blank a vibratory excitation that varies over time to cover a predetermined frequency range,b. identifying at least one characteristic of a resonance frequency, such as a resonance peak, of the hairspring or of the hairspring blank during vibratory excitation over the predetermined frequency range,c. subjecting the resonance frequency characteristic identified in step b to a prediction machine. to determine a stiffness of the hairspring or of the hairspring blank and/or to determine whether a dimensional correction of the hairspring or of the hairspring blank is necessary to obtain the predetermined resonance frequency.

Description

Technical area

The present invention relates to the field of control and manufacture of parts for watchmaking. The invention relates more particularly to a method for checking and manufacturing clockwork spiral springs, otherwise known as resonators.

State of the art

The movements of mechanical watches are regulated by means of a mechanical regulator comprising a resonator, that is to say an elastically deformable component whose oscillations determine the rate of the watch. Many watches include, for example, a regulator comprising a hairspring as a resonator, mounted on the axis of a balance wheel and set in oscillation by means of an escapement. The natural frequency of the balance-spring couple makes it possible to regulate the watch and depends in particular on the stiffness of the balance-spring.
Indeed, the frequency f of the regulating organ formed by the balance spring 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 vibratory characteristics, such as the natural frequency and the resonance frequencies. In the present application, the natural frequency of an elastic system (a single resonator or a resonator-pendulum couple) is the frequency at which this system oscillates when it is in free evolution, that is to say without exciting force. . Moreover, a resonance frequency of an elastic system subjected to an exciting force is a frequency at which one can measure a local maximum of displacement amplitude for a given point. of the elastic system. 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 afterwards, in all point that 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 shows 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 : $$M=\frac{E\left(\frac{e^{3}h}{12}\phi \right)}{L}$$
  
  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, as well as its dimensions and in particular the thickness (that is to say the width) of its turns along its bar. The stiffness is given more specifically by: $$R=\frac{M}{\phi }$$

with :

• ϕ , the torsion 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: $$M=\frac{E\left(\frac{e^{3}h}{12}\phi \right)}{L}$$
  
  with :
  • E , the Young's modulus of the material used for the bar,
  • L , the length of the bar,
  • h , the height of the rung, and
  • e, the thickness or width of the bar.

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

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

Very advantageously, several hundred silicon hairsprings can be manufactured on a single wafer using micro-fabrication technologies. It is in particular known to produce a plurality of silicon resonators with very high precision by 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 crystalline class m3m whose coefficient of thermal expansion (alpha) is isotropic.

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 according to the temperature. In order to at least partially compensate for this drawback, 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 variations in temperature of the 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 having a positive thermoelastic coefficient .

When hairsprings are produced in silicon or in another material by mass production 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 on the plate.

However, the micro-manufacturing 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 of the same wafer, and therefore 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 the manufacturing yield, it is therefore of interest to center the mean of the Gaussian distribution on a value of nominal stiffness and also to reduce the standard deviation of this Gaussian.

In addition, the dispersion of stiffness is even greater between hairsprings of two wafers engraved at different times according to the same process specifications. This phenomenon is shown in figure 1 where the stiffness dispersion curves Rd1, Rd2 and Rd3 for hairsprings on three different pads are shown. In general, for each wafer the distribution of the stiffnesses R (relative to the number of hairsprings N with this stiffness) follows the normal or Gaussian law, each dispersion curve being centered on its respective mean 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 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 with 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 equipped with a predetermined inertia, by calculating the thickness of material to be added to obtain the dimensions necessary for obtaining the hairspring with the predetermined stiffness, and by adding this thickness of material to the hairspring.

In this way, as demonstrated by the figure 2 , notwithstanding the mean stiffness Rm1, Rm2, etc. stiffnesses on a given insert, the stiffness dispersion curve Rd1, Rd2, etc. can be recentered with respect 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 pendulum of predetermined inertia, or by the assembly carried out. A step of calculating the thickness to be removed must then be carried out in order, again, to remove the calculated thickness with great precision. In addition, it can be noted that the coupling of the hairspring with the balance equipped with a predetermined inertia requires meticulous operations and requiring a long preparation time. Finally, it can also be noted that any assembly operation on parts or blanks still present on a wafer significantly increases the risk of pollution (for example the presence of fine silicon particles (debris) produced during handling).

The aim of the present invention is 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, and therefore a more individualized correction of the hairsprings of the insert.

Disclosure of 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 résonnance, telle qu'un pic de résonnance, du spiral ou de l'ébauche de spiral lors de l'excitation vibratoire sur la plage fréquentielle prédéterminée,
3. c. soumettre à une machine de prédiction la caractéristique de fréquence de résonnance identifiée à l'étape b. pour déterminer une raideur du spiral ou de l'ébauche de spiral et/ou déterminer si une correction dimensionnelle du spiral ou de l'ébauche de spiral est nécessaire pour obtenir la fréquence de résonnance prédéterminée.

More specifically, the invention relates to a method for testing a hairspring or a hairspring blank arranged to form a hairspring, the hairspring having to have at least one predetermined resonance frequency, comprising the following steps:

1. has. applying to the hairspring or to the hairspring blank a vibratory excitation that varies over time to cover a predetermined frequency range,
2. b. identifying at least one characteristic of a resonance frequency, such as a resonance peak, of the hairspring or of the hairspring blank during vibratory excitation over the predetermined frequency range,
3. vs. subjecting the resonance frequency characteristic identified in step b to a prediction machine. to determine a stiffness of the hairspring or of the hairspring blank and/or to determine whether a dimensional correction of the hairspring or of the hairspring blank is necessary to obtain the predetermined resonance frequency.

The method according to the implementation above comprises a step of vibratory excitation of the hairspring or of the hairspring blank and the measurement of a characteristic of a resonant frequency, in order then to deduce therefrom by prediction a stiffness and/or or if a dimensional correction is necessary. There is no assembly with a pendulum or other component, which saves time. In addition, the measurement is carried out on the hairsprings or the blanks alone, which limits the errors induced by other components or their assembly, as well as any pollution. Measurement accuracy is improved because there are fewer sources of variability due to other components or pollution.

The method according to the above implementation therefore makes it possible to test balance-spring blanks during manufacture while limiting the risks of pollution or assembly errors. A dimensional correction (of section, height and/or thickness) is then possible. The method according to the implementation above makes it possible just as well to test finished hairsprings in order for example to carry out a classification by increments of stiffness, in order to provide pairing with a particular balance wheel.

Of course, the frequency range of the spectrum obtained does not only depend on the source of vibratory 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 instrument for measuring 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 of the tested blank.

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.

The dimensional correction predicted by the prediction machine can typically be a correction of the section of the flexible bar forming the hairspring or the hairspring blank, that is to say a correction either of the height or of the thickness, or both.

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

According to one embodiment, in step a, the frequency range is applied simultaneously to a plurality of balance-springs or balance-spring blanks. The speed is improved, because the vibratory excitation can typically be imposed on a wafer supporting several hundred balance-spring blanks, which would for example still be attached to the wafer.

• centrée sur la fréquence de résonnance prédéterminée, et
• d'une étendue d'au moins 30% de la fréquence de résonnance prédéterminée, c'est-à-dire ±15% de la fréquence de résonnance prédéterminée. Par exemple, si la fréquence de résonnance 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
• of a range of at least 30% of the predetermined resonant frequency, i.e. ±15% of the predetermined resonant frequency. For example, if the predetermined resonance frequency is 1 kHz, then the frequency range will be 850 Hz to 1150 Hz.

According to one embodiment, the hairspring has at least two predetermined resonance frequencies, and the frequency range is predetermined to cover at least the two predetermined resonance frequencies. By covering or sweeping a wide range of frequencies, several resonance peaks (or resonance frequencies) can be measured, which can provide better 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 an acoustic excitation on a slice of a wafer supporting the balance-spring 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 balance spring or a balance spring blank. Preferably, if a wafer supports several balance-spring blanks, then the acoustic source can be coupled to an excitation cone chosen to excite at least some and preferably all of the balance-spring 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 the variable vibratory excitation over time to cover the predetermined frequency range:

• with sufficient amplitude 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 displacement acceleration of at least one point of the hairspring or of the balance-spring blank and/or
• for a period sufficient to deduce therefrom the vibratory spectra of the hairspring or of the hairspring blank.

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

According to one embodiment, step b is based on a measurement over time of an amplitude or a speed, or even an acceleration of displacement of at least one point of the hairspring or of the blank of hairspring, preferably performed at least partially during step a.

• une étape d'identification d'une fréquence de résonnance 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 of the hairspring blank as a function of an operational or modal deformation of at least one point of the hairspring or of the hairspring blank. An operational or modal deformation is typically defined by an amplitude or speed of displacement or else by 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 is contained in a base plane, and step b comprises:

• a step b' of measuring an amplitude or a speed or an acceleration of displacement 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 displacement of at least one point of the hairspring or of the hairspring blank in a direction contained in the base plane.

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

• pour une première fréquence de résonnance prédéterminée, seule l'étape b' de mesure d'un déplacement ou d'une vitesse d'au moins un point du spiral ou de l'ébauche de spiral selon une direction normale au plan de base est effectuée,
  et/ou
• pour une deuxième fréquence de résonnance prédéterminée, seule l'étape b" de mesure d'un déplacement ou d'une vitesse d'au moins un point du spiral ou de l'ébauche de spiral selon une direction contenue dans le plan de base est effectuée.

According to one embodiment:

• for a first predetermined resonance frequency, only step b' of measuring a displacement or a speed of at least one point of the hairspring or of the hairspring blank in a direction normal to the base plane is carried out ,
  and or
• for a second predetermined resonance frequency, only step b" of measuring a displacement or a speed of at least one point of the hairspring or of the hairspring blank in a direction contained in the base plane is carried out.

Depending on the resonance frequency, it is possible to choose to measure in one direction or another, to measure the greatest possible displacements or speeds, so as to minimize the measurement error. Indeed, depending on the geometry of the hairspring or of the hairspring blank, the mode of vibration (typically the direction of vibration) in response to vibrational excitation may vary.

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 phase, depending on the excitation frequency.

• une étape d'identification d'un pic de résonnance 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 comprises:

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

According to one embodiment, the resonance frequency is identified based on the width of the resonance or amplitude peak, halfway up the maximum value of the amplitude resonance peak. This processing method makes it possible to limit the calculation errors which 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 c comprises a step of calculating a stiffness of the hairspring or of the hairspring blank. The calculation of the stiffness makes it possible to determine with improved precision whether a dimensional correction is necessary, and of what value this correction must be. In addition, this also makes it possible to pre-dimension or choose a balance wheel to couple the hairspring once it is finished manufacturing.

According to one embodiment, if a dimensional correction is necessary, then the method comprises a step:
d. calculating, with the prediction machine, the dimensional modification (modification of section, height and/or thickness) to be applied from the resonance frequency characteristic identified in step b.

According to one embodiment, the prediction machine implements a polynomial formula to predict whether a dimensional correction is necessary. One can for example carry out a modeling by linear regression.

According to one embodiment, the prediction machine implements a classification performed for example by a neural network to predict whether a dimensional correction is necessary.

According to one embodiment, the prediction machine implements a classification based on a partitioning into k-means or into k-medians to predict whether a dimensional correction is necessary.

According to one embodiment, the hairspring blank being formed on a wafer comprising a plurality of hairspring blanks distributed over several sectors of the wafer,
step b comprises a step consisting in identifying at least one characteristic of a resonance frequency of at least one balance-spring blank for each sector,
and step c comprises a step consisting in determining a stiffness of the balance-spring blank and/or in determining, for the balance-spring blanks of each sector, whether a dimensional correction is necessary. The precision of the dimensional correction (section, height and/or thickness) is improved by refining the analysis by sectors of the wafer.

According to one embodiment, the control method comprises a step of calculating, with the prediction machine, the dimensional modification to be applied for the balance-spring blanks of each sector.

According to one embodiment, step a comprises a step consisting in modifying a direction of vibratory excitation over time, preferably in a direction pointing to the balance spring or the balance spring blank whose resonance frequency characteristic is identified in step b.

According to one embodiment, the control method comprises a preliminary step consisting in taking into account the material of the hairspring or of the hairspring blank, and in adjusting a maximum amplitude of the vibratory excitation and/or a frequency range of the predetermined frequency range as a function of the material of the hairspring or of the hairspring blank.

According to one embodiment, the frequency range obtained extends over a frequency range ranging 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 at 35kHz. The applicant realized that the accuracy of the prediction was better for peaks or resonance frequencies located in a high frequency range. Indeed, if we focus on the stiffness, its influence on the resonance frequency is stronger in high frequency ranges (for example between 10 kHz to 35 kHz), so that the sensitivity and precision are better on this particular beach.

According to one embodiment, step a and step b are repeated at least several times for the same measurement point of the hairspring or of 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, the consideration of which can improve the precision of the prediction, or make it possible to adjust or recalibrate the vibratory excitation source.

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

A second aspect of the invention relates to a process for manufacturing a hairspring having at least one predetermined resonance frequency comprising the steps consisting in:

• forming at least one hairspring or a hairspring blank having dimensions within predetermined tolerances necessary to obtain the predetermined resonance frequency,
• checking the hairspring or the blank according to the checking method of the first aspect.

• corriger au moins une dimension de l'ébauche de spiral formée lors de l'étape a., selon le calcul de l'étape d. de la revendication 11, afin d'obtenir un spiral présentant la fréquence de résonnance prédéterminée.

According to one embodiment, the manufacturing method comprises a step consisting in:

• correcting at least one dimension of the balance-spring blank formed during step a., according to the calculation of step d. of claim 11, in order to obtain a hairspring exhibiting the predetermined resonant frequency.

The dimensions (section, height and/or thickness) can be corrected by shrinking or adding material.

According to one embodiment, the hairspring or the hairspring blank is formed in silicon, or in glass, or in ceramic, or in metal, or in carbon nanotubes.

According to one embodiment, the hairspring blank is formed on a wafer, with a plurality of other hairspring blanks.

• i- former des spiraux ou des ébauches de spiraux,
• ii- appliquer à chacun des spiraux ou à 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 résonnance de chaque spiral ou chaque ébauche de spiral lors de l'excitation vibratoire sur la plage fréquentielle prédéterminée,
  • 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 chaque ébauche de spiral une fréquence libre d'oscillation ou une raideur
    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 chaque ébauche de spiral une fréquence libre d'oscillation ou une raideur
• v- fournir à la machine de prédiction, et pour chaque spiral ou chaque ébauche :
  • la caractéristique de la fréquence de résonnance identifiée à l'étape iii-;
  • la fréquence libre d'oscillation ou la raideur mesurée(s) à l'étape iv'- et/ou calculée(s) à l'étape iv"-.

A third aspect of the invention relates to a method for learning a prediction machine to implement step c of the method for checking the first aspect, comprising the steps consisting in:

• i- forming hairsprings or outlines of hairsprings,
• ii- apply to each of the hairsprings or to each of the hairspring blanks a variable vibratory excitation 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 during vibratory excitation over the predetermined frequency range,
  • iv'- mounting a plurality of balance-springs or balance-spring blanks in an oscillating mechanism having a predetermined inertia so as to measure for each balance-spring or each balance-spring blank a free oscillation frequency or a stiffness
    and or
  • iv"- modeling in a simulation tool a plurality of balance-springs or balance-spring blanks in an oscillating mechanism having a predetermined inertia so as to calculate for each balance-spring or each balance-spring blank a free oscillation frequency or a stiffness
• v- provide the prediction machine, and for each hairspring or each blank:
  • the characteristic of the resonance frequency identified in step iii-;
  • the free oscillation frequency or the stiffness measured in step iv′- and/or calculated in step iv″-.

Preferably, it will be chosen to use a sufficiently sensitive measuring instrument on the chosen frequency range, and ensuring that the vibratory behavior of the hairspring is exploitable on this chosen frequency range.

• la mesure d'un déplacement ou d'une vitesse de déplacement d'une pluralité de points prédéterminés du spiral ou de l'ébauche du spiral,
• l'identification de nœuds parmi la pluralité de points prédéterminés, qui présentent à au moins une fréquence ou pic de résonnance une amplitude de déplacement nulle ou inférieure à une première valeur de pic seuil,
• la sélection de points de référence à mesurer lors du contrôle parmi la pluralité de points prédéterminés, qui sont différents des nœuds identifiés, et qui de préférence présentent chacun un pic d'amplitude de déplacement supérieur à une deuxième valeur de pic seuil.

According to one embodiment, step iii- comprises a preliminary phase of identifying reference measurement points with:

• measuring a displacement or a displacement speed of a plurality of predetermined points of the hairspring or of the hairspring blank,
• the identification of nodes among the plurality of predetermined points, which have at least one frequency or resonance peak a zero displacement amplitude or less than a first threshold peak value,
• the selection of reference points to be measured during the check from among the plurality of predetermined points, which are different from the identified nodes, and which preferably each have a displacement amplitude peak greater than a second threshold peak value.

Such a step of identifying the reference points makes it possible to eliminate the points or the zones which are nodes (that is to say immobile points) at one or more resonance frequencies.

• dans une première zone à moins de 0.20 x Ra, ou
• dans une deuxième zone entre 0.05 x Ra et 0.30 x Ra, ou
• dans une troisième zone entre 0.35 x Ra et 0.65 x Ra, ou
• dans une quatrième zone entre 0.65 x Ra et 0.85 x Ra.

According to one embodiment, the hairspring or the hairspring blank has a radius Ra defined between a free central end and a recessed peripheral end, and at least two reference points, and preferably four reference points are chosen and located:

• in a first zone at less than 0.20 x Ra, or
• in a second zone between 0.05 x Ra and 0.30 x Ra, or
• in a third zone between 0.35 x Ra and 0.65 x Ra, or
• in a fourth zone between 0.65 x Ra and 0.85 x Ra.

The choice of these zones guarantees that the points whose displacements are tracked have a sufficient displacement amplitude to be measured correctly and with good precision.

Brief description of the drawings

• la figure 1 montre les 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 résonnance identifié à une fréquence particulière sur la figure 7,
• la figure 9 représente les pics de résonnance mesurés et superposés pour la fréquence particulière de la figure 8,
• la figure 10 représente un exemple modèle de prédiction construit à partir de données extraites de la figure 9.

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

• the figure 1 shows the uncorrected stiffness dispersion curves for hairsprings on three different pads,
• the figure 2 shows the centering of the average stiffness on a plate around a nominal value,
• them Figures 3A-3F are a simplified representation of a process for manufacturing a mechanical resonator, here a hairspring, on a wafer,
• the figure 4 represents a device for evaluating the torque of a hairspring,
• the figure 5 schematically represents the implementation of the evaluation of the stiffness of a hairspring by vibration analysis,
• the figure 6 represents an example of frequencies applied to a silicon wafer supporting balance-spring blanks, to impose vibratory excitation,
• the figure 7 represents an example of measurement of the displacement amplitudes of a point of a balance-spring blank, in response to the imposed frequency range of the figure 6 ,
• the figure 8 depicts in detail an identified resonance peak at a particular frequency on the figure 7 ,
• the figure 9 represents the measured and superimposed resonance peaks for the particular frequency of the figure 8 ,
• the figure 10 represents an example prediction model built from data extracted from the figure 9 .

Embodiment of 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 intended in particular to equip a regulating member of a timepiece and, according to this example, is in the form of a spiral spring 100 in silicon which is intended to equip a balance of a mechanical clock movement.

Plate 10 is illustrated in Figure 3A as an SOI (“silicon on insulator”) wafer and comprises a substrate or “handler” 20 bearing a sacrificial layer of silicon oxide (SiO ₂ ) 30 and a layer of monocrystalline silicon 40. By way of 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 figure 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. By referring to the Figure 3B , in this exemplary embodiment, the layer 40 is covered with a protective layer 50, for example 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 patterning by lithography forms the patterns for the plurality of resonators in layer 50, as illustrated in Fig. 3C .

Subsequently, in the step of 3d figure , the patterns are machined, in particular etched, to form the plurality of resonators 100 in the layer 40. The etching can be performed 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 removed.

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 of the substrate or handler 20. Smoothing (not shown) of the etched surfaces can also take place before the release step, by for example by a thermal oxidation step followed by a deoxidation step, consisting for example of wet etching based on hydrofluoric acid (HF).

At the last stage of the manufacturing process at the 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 the vibratory characteristics of the hairspring leading to obtaining a particular natural frequency. of the balance-spring couple in a given watch mechanism.

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

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

The description above relates to resonators 100 made of silicon, but it is possible to envisage making the resonators out of glass, ceramic, carbon nanotubes, or even metal.

To center the average stiffness of the resonators on different pads with respect to a nominal stiffness value as shown in picture 2 , the resonators obtained in step 3E on the wafer 10 in question can be deliberately formed with dimensions d which are different from the dimensions necessary (for example greater) for obtaining a nominal or target stiffness. Thus, it is possible to set up a control method intended to estimate the vibratory characteristics of the resonators (natural frequency and/or resonance frequencies) to deduce therefrom the stiffness and/or the real dimensions of the resonators 100 to correct the dimensions thereof. , which will lead to obtaining the natural frequency of the desired resonator-balancer couple.

The present invention proposes to determine from at least one characteristic of a resonance frequency of a sample of resonators 100 on the wafer in step 3E and whether a geometric correction of the resonators is necessary. If so, the present invention proposes to precisely calculate the thickness of material to be modified (to be removed or added), around each turn, to obtain the dimensions leading to obtain the vibratory characteristics of the resonators (natural frequency and/or resonance frequencies, and/or stiffness) corresponding to target values, 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 measuring vibration and apply a predictive method (for example a numerical model or a classification or categorization method) to link the result of said vibration measurement to the necessary geometric correction.

The modal properties of the hairspring attached to the wafer are thus exploited. 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 dimensions (in particular the thickness) and/or the stiffness at certain frequencies (natural frequency or resonance frequencies associated with a resonance peak or a width at mid-height) specifically chosen.

Once the learning phase is complete (once the modes to be exploited 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 whether a correction of the dimensions is necessary, and if necessary, calculate or predict the exact correction to be made to the dimensions of the resonators (by shrinkage if the blank is produced with dimensions greater than the final dimensions required, or by adding material if the blank is made with dimensions smaller than the final dimensions required, for example).

Thus, it is possible to integrate the control method into a manufacturing process to correct, if necessary, the vibratory characteristics of the resonators (natural frequency and/or resonance frequencies, and/or stiffness) to obtain a particular natural oscillation frequency. and predetermined, once the resonators are each coupled to a balance wheel of a given watch mechanism.

Vibration 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 100 kHz, de préférence de 0 à 75 kHz, de préférence de 0 à 50 kHz, de préférence de 5kHz à 50 kHz, et de préférence de 10 à 35 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.

The measurement of the vibratory 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, one must first impose a vibratory excitation on the wafer. Several options are available:

1. has. Measurements in the frequency domain:
   1. 1- using a piezoelectric source (or any other source making it possible to induce or impose an acoustic excitation) on the edge of the wafer, on, or under the blank of the hairspring 200 to be excited specifically (preferred) which excites at a particular frequency f ₀ (continuous mono-frequency excitation). In this variant, the excitement is maintained.
   2. 2- As a variant, one 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 excited specifically ( preferential) which excites at a variable frequency over time to cover a predetermined frequency range, ranging for example from 0 to 100 kHz, preferably from 0 to 75 kHz, preferably from 0 to 50 kHz, preferably from 5 kHz to 50 kHz , and preferably from 10 to 35 kHz. The entire frequency range can be swept or covered in a time interval that can range from a fraction of a second to a few seconds. For example, provision may be made to sweep 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 making it possible to induce an acoustic impulse) on the edge of the wafer, on, or under the hairspring to be excited specifically (preferred) which gives an acoustic impulse as short as possible (multi-frequency pulse excitation). In this variant, the excitation is punctual and not maintained.

Furthermore, the measurements can be performed by 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, it is possible to choose a signal sampling frequency of at least 100 kHz if the frequency range extends up to 50 kHz for example.

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 according to one or more axial direction (s) ), and make this or these direction(s) evolve over time). In the case where a wafer comprising a plurality of resonators is excited, provision may be made to adjust the direction of the vibrations so as to point to one or the other of the resonators, depending on the displacement amplitude measurements described below. below.

Finally, provision may be made 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 vibratory excitation of the resonator(s) and having an amplitude sufficient to be detected and measured accurately by the chosen measuring instruments.

Measurement of amplitude or velocity, or displacement acceleration

• 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, 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) are recorded via a suitable measuring device. of the specifically excited hairspring. In a non-limiting way, we can cite the following possible means of measurement:

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

The figure 5 schematically represents a silicon wafer 25 on which are formed a plurality of balance-spring blanks 200. A vibratory excitation source 400 is coupled to the wafer 25, so as to be able to impose a vibratory excitation. Consequently, each hairspring blank 200 will begin to vibrate, and a laser vibrometer 300, here focused on a point of the hairspring blank 200 on the right, will be able to measure the vibration amplitudes of the measurement point over time. Provision can be made to measure the displacements in a direction normal to the plane of the wafer 25, but it is just as possible to measure the displacements in one or more directions contained in the plane of the wafer 25.

Once a particular point has been studied, the laser vibrometer 300 can be moved to another measurement point of the hairspring blank 200, or move on to another hairspring blank 200 of the wafer 25. Of course, one can alternatively move the draft of hairspring 200 with respect to the laser vibrometer.

The figure 6 represents an example of vibratory excitation over time. In the example given, the excitation frequency varies over time, between 0 Hz and 50 kHz, and a succession of rising edges can be imposed, each spaced by a rest period without excitation. For each measurement point on the balance spring blank 200, a plurality of rising edges can be imposed (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

With regard to the displacement amplitude measurement, during the learning phase, a step can be provided consisting in identifying points of the resonator for which the vibratory response is significant. Indeed, in the case of a hairspring on which a vibration is imposed, especially if the frequency varies over time, the vibratory response will cause nodes to appear on the hairspring, that is to say particular points of the hairspring whose displacement amplitude is low or zero. If a displacement measurement is performed on a point of the hairspring which turns out to be a knot at one or more particular frequency(ies), the identification of resonant frequency characteristics will be adversely 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 predetermined points. Provision can be made to select the predetermined points arranged on an X-Y orthonormal reference mark in the plane of the hairspring.

At the end of this preliminary step of amplitude measurement on the predetermined points, provision can be made to identify resonance frequencies for each measurement point, and then a step of selecting reference points for which the measurement of displacement amplitude during excitation shows that they are not nodes at these resonant frequencies. In other words, the identified nodes have, at at least one resonance frequency, a zero displacement amplitude 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 spiral blank 200 on the wafer 25.

• dans une première zone à moins de 0.20 x Ra (par exemple sur la virole centrale), ou
• dans une deuxième zone entre 0.05 x Ra et 0.30 x Ra (par exemple sur la deuxième spire en partant de la virole), ou
• dans une troisième zone entre 0.35 x Ra et 0.65 x Ra (par exemple sur une spire située au milieu du spiral), ou
• dans une quatrième zone entre 0.65 x Ra et 0.85 x 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 considered 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 outer end of the stud, it is possible to preferably select four chosen and located reference points:

• in a first zone at less than 0.20 x Ra (for example on the central shroud), or
• in a second zone between 0.05 x Ra and 0.30 x Ra (for example on the second turn starting from the ferrule), or
• in a third zone between 0.35 x Ra and 0.65 x Ra (for example on a coil located in the middle of the hairspring), or
• in a fourth zone between 0.65 x Ra and 0.85 x Ra (for example on a turn located at three quarters of the hairspring).

Thus, the reference points are far from the part anchored on the wafer and naturally have a high capacity for oscillatory displacement, 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 vibration attenuation, or even a resonance resulting from a vibratory coupling or from the wafer. 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 displacement amplitude measurement and the vibratory excitation.

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 résonnance dans le signal enregistré.

There are then several scenarios depending on the domain chosen beforehand for the excitation:

1. has. Frequency Domain Measurements
   1. 1- variant with sustained excitation:
      1. i. Temporally integrate 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 oscillation amplitude and phase spectra as a function of 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 oscillation amplitude and phase spectra as a function of excitation frequency (possibly with multiple peaks at multiple frequencies).
2. b. Time domain measurements:
   1. i. Record the temporal displacement of the turn along X, Y and Z over a sufficiently long period so as to obtain a sufficiently representative signal, such as for example a few seconds.
   2. ii. It is possible to choose to record the signal to make it a reference signal to be compared with other signals measured on other parts. It is also possible to choose to process the signal of the Fourier transform type to identify resonance frequencies in the recorded signal.

Consequently, 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 a zone of the curve situated between 25% and 75% of the maximum amplitude value of the resonance peak, for example from its width at mid-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 the errors due to the singularity of the point of maximum amplitude and to the approximation calculations to reconstruct the top 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 accuracy than the part above 75% (typically the peak), which offers better accuracy on the exact frequency of determined resonance. One can take for example the middle of the segment connecting the two points at mid-height of the resonance peak to determine the resonance frequency associated with the peak in question.

The figure 7 shows an example of a vibration spectrum for a point on a 200 balance-spring blank from the figure 5 , reconstructed from the displacement amplitude measurements of the measurement point considered in response to the vibratory excitation of the figure 6 , between 10 kHz and 15 kHz. One can note the presence of three amplitude peaks, at approximately 11 kHz, 12.3 kHz, and 13.7 kHz. Although not shown, one can typically identify between 10 and 30 amplitude peaks if the vibrational excitation sweeps a frequency range between 0 Hz and 50 kHz. Each amplitude peak has a resonance frequency, and the maximum amplitudes vary greatly.

The figure 8 shows in detail the processing that can be done on an amplitude peak, the one at 11 kHz for example. The goal is to find the resonance frequency and give it as precise a value as possible. Instead of basing this processing on the maximum value of the peak, the applicant noticed that better accuracy could be achieved by determining the length of the segment connecting the rising part and the falling part of the curve, at mid-height of the peak. The resonance frequency being typically the value in the middle of this segment. However, one can perform an interpolation on points in the vicinity of the resonance peak to improve accuracy, and shift the point chosen 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 sample rate chosen.

The figure 9 represents, for the example of an amplitude peak at around 10 kHz, the amplitude peaks constructed for ten or so balance-spring blanks 200 tested. It can be noted that from one balance-spring 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 approx. The tops of amplitude peaks not being really symmetrical, it seems judicious to determine the resonance frequency on the basis of the width of the peak at mid-height.

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

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

To establish a prediction model which can receive as input the vibratory characteristics (typically a resonance frequency) and give as 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 tested resonators. To this end, provision can be made to concretely measure a natural frequency of a balance-spring system in an environment similar to that of a particular watch mechanism.

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

In the two alternatives above, it is possible to go through an intermediate step of determining the stiffness of each resonator, and then to determine the actual 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 bar of the resonator by analyzing the free oscillations of a hairspring coupled to a reference balance wheel. In this approach, a laser pointed at the arms of the balance wheel or on the balance-spring holder records the passage times of the arms of the balance wheel or of a polarizer. We then deduce an estimate of the period, then of the frequency and finally of the stiffness. The data collected are essentially scatter plots of passage times.

Indeed, to evaluate the stiffness of a hairspring on the wafer, several solutions are available, as described in particular by M. Vermot et al, in the Watch Construction Treaty (2011) on pages 178-179 . For example, a dynamic evaluation can be carried out 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 hairspring precisely. This evaluation can be performed on the wafer or by detaching the hairspring from the wafer. The references and prior art given above, provide details on this method.

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

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, it is possible to carry out dimensional measurements of each resonator tested in order to reconstruct the resonator by digital modeling in order to simulate by digital calculation its vibratory response to the imposed spectrum, and moreover to find the stiffness of the resonator.

A high-resolution 3D X-ray tomography approach would make it possible to extract clouds of points giving the 3D material density of the balance-springs, and, subject to appropriate image reconstruction, a cartography of the section of the balance-spring. 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 in analyzing the forced oscillations of a hairspring on a reference balance wheel with an escapement. A laser measurement of the passage times of the arms of the balance wheel (clouds of points), as presented above, makes it possible to measure the frequency and to deduce the stiffness therefrom. An alternative can be envisaged from an acoustic acquisition (Witschi type microphone) which records the shocks of the different operating phases of the escapement/anchor system. The data measured are either scatter plots of the passage times of the arms of the balance wheel, 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 bar of the resonator.

Returning to the trials discussed above at the figure 9 , a measurement of the stiffness was carried out by coupling each spiral blank 200 to a reference balance wheel, and the stiffnesses below could be deduced: Hairspring 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

Establishment of the prediction model

During the learning phase, oscillation amplitude measurements are performed on physical resonators, and resonance frequencies are identified. In order to be able subsequently to link the resonance frequencies measured on resonators to stiffnesses and/or dimensional (thickness) corrections to be made, a correlation phase must be provided during which a predictive model is constructed.

The operations described above (vibration measurements, identification of resonance peaks, bandwidth at mid-height and its middle 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 hairspring on the wafer, spectra or periods of oscillation or band width at mid-height and its mid-value or corrected with the stiffnesses and/or dimensions of the effective bar of the hairspring. As seen above, this database can be built from numerical simulations on a finite element model of hairspring. These simulations make it possible to generate spectra or reference oscillation periods associated with the stiffnesses. This database can also be supplemented by experimental measurements by measuring vibration spectra, oscillation periods and the positions of hairsprings on the wafer as well as their associated stiffnesses. One of the advantages of this approach lies in the fact that the learning database is enriched as the trials progress. This can make it possible to have an adaptive model according to the pads and the hairsprings and contributes to the reduction of the standard deviation in stiffness on the pads.

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

A digital model, for example polynomial, can be constructed to calculate, as a function of a resonance frequency value, a real thickness, a dimensional correction or a real stiffness.

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

Provision can also be made to process the images of the resonance peaks by a neural network, for example a perceptron, to perform a classification according to stiffnesses or dimensions of the bar, the classes possibly being defined by value increments.

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

Avec

• R pour la raideur en 10^-7 N.mm
• F pour la fréquence de résonnance 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 discussed and described in connection with the figure 9 , the data collected are as follows: Hairspring no. Resonance 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: $$\mathrm{R}=\mathrm{0.0015}\mathrm{F}-\mathrm{10.894},$$

With

• R for the 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 difference 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 may 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 direction coefficient is 0.0015 10 ^-7 N.mm/Hz. On the one hand, the applicant has noticed that the guiding coefficient could be larger for high resonance frequencies, which provides better prediction sensitivity, for predicting distinct dimensional stiffness or correction values, even from resonance frequency values relatives. It is advantageous to provide, during the learning phase, a step of comparing the sensitivity of the prediction to check / 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 accurately as possible a stiffness and/or a dimensional correction according to the measured vibration response.

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

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

In general, 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 single prediction as precise as possible, or several predictions (one per resonance peak deemed interesting) to then carry out cross-checks, averages or even readjustments of the predicted values.

For example, it is possible 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 as a function of the sensitivity identified for each corresponding peak or resonance frequency.

Alternatively and preferably, it is possible to have only one model which takes all the peaks or resonance frequencies as input and which returns the stiffness or the dimensional correction, the learning phase of the model being used precisely to calculate the weightings on the input resonance peaks or frequencies.

Prediction phase

Once the learning phase is complete, it is possible to move on to a prediction phase, for example during a resonator control method. The control process can typically be carried out on hairspring blanks made on a wafer and still attached to this wafer, 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 brought.

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 be deployed is as follows:

1. 1) Identification of the position of the hairspring on the wafer, vibration measurement of the spectra or period of oscillation (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 reach 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 control above:

1. 1) Knowing the effective stiffness of the hairspring estimated 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 checking process to check the stiffness / dimensions of the hairspring 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

It is known that several hundred hairsprings are produced on a wafer and that the dimensions of the bar of the hairsprings produced can vary according to the regions of the wafer. Although the stiffness evaluation can be performed on a single hairspring, in practice, it will be performed on a sample of hairsprings, distributed over the wafer.

Based on the evaluations carried out, corrections can be made for the entire wafer in a homogeneous manner, or differentiated by region, if the results obtained vary from one hairspring to another. It is thus possible to reduce the standard deviation of the dispersion of the stiffnesses. Moreover, if the stiffnesses of all the hairsprings are known by applying the model, it is possible to determine the optimum correction making it possible to reduce the overall dispersion.

It is even possible to consider going as far as an evaluation of all the hairsprings of the wafer, in particular with a vibration evaluation, because this is very quick to perform.

Although the examples above have been given mainly on the basis of the manufacture of hairsprings having initial bar dimensions larger than the target bar dimensions, provision can also be made to produce hairsprings having initial bar dimensions greater than the target bar dimensions. smaller than the target rung dimensions. The correction step then consists in adding material, as for example described in the document EP3181939 aforementioned.

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

Claims (18)

Process for testing a hairspring or a balance-spring blank arranged to form a hairspring, the hairspring having to exhibit at least one predetermined resonance frequency, the testing process comprising the following steps: has. applying to the hairspring or to the hairspring blank a vibratory excitation that varies over time to cover a predetermined frequency range, b. identifying at least one characteristic of a resonance frequency, such as a resonance peak, of the hairspring or of the hairspring blank during vibratory excitation over the predetermined frequency range, vs. subjecting the resonance frequency characteristic identified in step b to a prediction machine. to determine a stiffness of the hairspring or of the hairspring blank and/or to determine whether a dimensional correction of the hairspring or of the hairspring blank is necessary to obtain the predetermined resonance frequency. Control method according to claim 1, in which the frequency range is predetermined to encompass at least one frequency range: - centered on the predetermined resonance frequency, and - of a range of at least 30% of the predetermined resonance frequency. Control method according to one of Claims 1 to 2, the hairspring exhibiting at least two predetermined resonance frequencies, in which the frequency range is predetermined to cover at least the two predetermined resonance frequencies. Control method according to one of Claims 1 to 3, in which step b is based on a measurement over time of an amplitude or of a speed or of an acceleration of displacement of at least one point of the hairspring or of the hairspring blank, preferably performed at least partially during step a. Control method according to one of Claims 1 to 4, 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 displacement 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" for measuring an amplitude or a speed or an acceleration of displacement 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 4 to 5, in which step b comprises: - a step of identifying a resonance peak of the hairspring or of the hairspring blank as a function of an amplitude or of a displacement speed of at least one point of the hairspring or of the hairspring blank. A monitoring method according to claim 6, wherein the resonance frequency is identified based on the width of the resonance peak, halfway up the maximum value of the resonance peak. Control method according to one of Claims 1 to 7, in which, if a dimensional correction is necessary, then the method comprises a step:
d. calculating, with the prediction machine, the dimensional modification to be applied from the resonance characteristic identified in step b. Control method according to one of Claims 1 to 8, in which the prediction machine implements a polynomial formula to predict whether a dimensional correction is necessary. Control method according to one of Claims 1 to 9, in which the prediction machine implements a classification carried out for example by a neural network to predict whether a dimensional correction is necessary. Control method according to one of Claims 1 to 10, the hairspring blank being formed on a wafer comprising a plurality of hairspring blanks distributed over several sectors of the wafer,
in which step b comprises a step consisting in identifying at least one characteristic of a resonance frequency of at least one balance-spring blank for each sector,
and wherein step c includes a step of determining for the spring blanks of each sector a stiffness and/or if a dimensional correction is necessary. Control method according to one of Claims 1 to 11, comprising a preliminary step consisting in taking into account the material of the hairspring or of the hairspring blank, and in 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 of the hairspring blank. Control method according to one of Claims 1 to 12, in which the frequency range extends over a frequency range ranging 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. Method of manufacturing a hairspring having at least one predetermined resonance frequency comprising the steps consisting in: • form at least one hairspring or a hairspring blank having dimensions within predetermined tolerances necessary to obtain the predetermined resonance frequency, • checking the hairspring or the hairspring blank according to the checking method of one of the preceding claims. Manufacturing process according to the preceding claim, comprising a step consisting in: • correcting at least one dimension of the spiral blank formed during step a., according to the calculation of step d. of claim 8, in order to obtain a hairspring exhibiting the predetermined resonant frequency. Manufacturing process according to one of Claims 14 to 15, in which the balance-spring blank is formed on a wafer, with a plurality of other balance-spring blanks. Method for learning a prediction machine to implement step c of the control method of one of claims 1 to 13, comprising the steps consisting in: i- forming hairsprings or outlines of hairsprings, ii- apply to each of the hairsprings or each of the hairspring blanks a variable vibratory excitation 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, iv'- mounting a plurality of balance-springs or balance-spring blanks in an oscillating mechanism having a predetermined inertia so as to measure for each balance-spring or balance-spring blank a free oscillation frequency or a stiffness,
and or iv"- modeling in a simulation tool a plurality of balance-springs or balance-spring blanks in an oscillating mechanism having a predetermined inertia so as to calculate for each balance-spring or balance-spring blank a free oscillation frequency or a stiffness v- provide the prediction machine, and for each hairspring or blank: - the characteristic of the resonance frequency identified in step iii-; - the free oscillation frequency or the stiffness measured in step iv′- and/or calculated in step iv″-. Learning method according to the preceding claim, in which step iii- comprises a preliminary phase of identification of reference measurement points with: - the measurement of a displacement of a plurality of predetermined points of the balance spring or of the blank of the balance spring, - the identification of nodes among the plurality of predetermined points, which have at least one frequency or resonance peak a zero displacement amplitude or less than a first threshold peak value, - the selection of reference points to be measured during the check from among the plurality of predetermined points, which are different from the identified nodes, and which preferably each have a displacement amplitude peak greater than a second threshold peak value.

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