Method for monitoring and manufacturing timepiece hairsprings

Abstract

Method for testing a spiral spring or a spiral spring blank arranged to form a spiral spring, the spiral spring being required to have at least one predetermined resonance frequency, the testing method comprising the following steps: a. applying, to the spiral spring or the spiral spring 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 spiral spring or the spiral spring blank upon vibratory excitation over the predetermined frequency range, c. subjecting the resonance frequency characteristic identified in step b to a prediction machine to determine the stiffness of the spiral spring or the spiral spring blank and / or to determine whether dimensional correction of the spiral spring or the spiral spring blank is required to obtain the predetermined resonance frequency.

Description

technical field

[0001] The present invention relates to the field of control and manufacture of watch parts. The invention relates more particularly to a method for controlling and manufacturing watch spiral springs, otherwise known as resonators. State of the art

[0002] Mechanical watch movements are regulated by a mechanical regulator that includes a resonator, a component that can be elastically deformed and whose oscillations determine the watch's accuracy. Many watches, for example, feature a regulator with a balance spring acting as a resonator, mounted on the balance staff and set in motion by an escapement. The natural frequency of the balance wheel and balance spring assembly regulates the watch and depends, in particular, on the stiffness of the balance spring.

[0003] Indeed, the frequency f of the regulating organ formed by the spiral of stiffness R coupled to a balance wheel of inertia l is given by the formula: f = 1 2 π R I

[0004] The stiffness of the spiral also defines its intrinsic vibrational characteristics, such as the natural frequency and resonance frequencies.

[0005] In this application, the natural frequency of an elastic system (a single resonator or a resonator-pendulum pair) is the frequency at which the system oscillates when it is freely moving, that is, without an excitatory force. Furthermore, the resonance frequency of an elastic system subjected to an excitatory force is the frequency at which a local maximum displacement amplitude can be measured for a given point of the elastic system. In other words, if the elastic system is excited with an excitation source of frequency that varies over time, the displacement amplitude follows an upward slope before this resonance frequency and a downward slope afterward, at any point that does not correspond to a node of vibration.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 that is associated with or characterizes the resonance frequency.

[0006] The stiffness of a spiral-type resonator typically depends on the material characteristics, as well as its dimensions, and in particular the thickness (i.e., the width) of its turns along its bar. The stiffness is given more specifically by: R = M φ with : ϕ , the spring's torsion angle, and M , the restoring torque of the spiral spring, where M, for a bar of constant cross-section made of a specific material, is given by: M = E e 3 h 12 φ 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.

[0007] The natural frequency of the regulating organ formed by the balance spring of stiffness R coupled to a balance wheel of inertia l is, in particular, proportional to the square root of the balance spring's stiffness. The main specification of a balance spring is its stiffness, which must fall within a well-defined range to be matched with a balance wheel, which forms the inertial element of the oscillator. This matching operation is essential for precisely regulating the frequency of a mechanical oscillator.

[0008] It is very important that the oscillator's characteristics be as stable as possible to ensure a stable watch time. The prevalence of magnetic fields in the modern environment has led watchmakers to use silicon balance springs in recent years, which are less susceptible to magnetic interference than metallic ones.

[0009] Highly advantageous, several hundred silicon spirals can be fabricated on a single wafer using microfabrication technologies. It is well known that multiple silicon resonators can be produced with very high precision using photolithography and machining / etching processes within a silicon wafer. The fabrication processes for these mechanical resonators generally use single-crystal silicon wafers, but wafers made of other materials are also suitable, for example, polycrystalline or amorphous silicon, other semiconductor materials, glass, ceramics, carbon, carbon nanotubes, or a composite of these materials. Single-crystal silicon belongs to the cubic m3m crystal class, which has an isotropic coefficient of thermal expansion (alpha).

[0010] Silicon exhibits a very negative first thermoelastic coefficient, and consequently, the stiffness of a silicon resonator, and therefore its natural frequency, varies significantly with temperature. To at least partially compensate for this drawback, documents EP1422436, EP2215531, and WO2016128694 describe a spiral-type mechanical resonator made from a single-crystal silicon core (or two cores in the case of WO2016128694). Temperature variations in the Young's modulus are compensated by a layer of amorphous silicon dioxide (SiO2) surrounding the core(s), silicon being one of the few materials with a positive thermoelastic coefficient.

[0011] When spirals are made of silicon or another material by collective manufacturing on a wafer, the final functional efficiency will be given by the number of spirals whose stiffness corresponds to the pairing interval, divided by the total number of spirals on the wafer.

[0012] However, the microfabrication steps, and more specifically the engraving process, used in manufacturing balance springs on a wafer typically result in significant geometric variation between the dimensions of the springs on the same wafer, and therefore significant variation between their stiffnesses, even though the engraving pattern is the same for each spring. The measured stiffness variation normally follows a Gaussian distribution. To optimize manufacturing efficiency, the aim is to center the mean of the Gaussian distribution on a nominal stiffness value and also to reduce the standard deviation of this Gaussian distribution.

[0013] Furthermore, the dispersion of stiffness is even greater between spirals of two wafers etched at different times according to the same process specifications. This phenomenon is shown in the figure 1 where the dispersion curves of the stiffness Rd1, Rd2 and Rd3 for the spirals on three different plates are illustrated. In general, for each plate the distribution of the stiffnesses R (relative to the number of spirals N with this stiffness) follows the normal or Gaussian distribution, each dispersion curve being centered on its respective average value Rm1, Rm2 and Rm3.

[0014] Documents WO2015113973 and EP3181938 propose to remedy this problem by forming a spiral with dimensions greater than the dimensions required to obtain a spiral with a predetermined stiffness, by measuring the stiffness of this spiral formed by coupling it with a balance wheel with a predetermined inertia, by calculating the thickness of material to be removed to obtain the dimensions required to obtain the spiral with the predetermined stiffness, and by removing this thickness from the spiral.Similarly, document EP3181939 proposes to remedy this same problem by forming a spiral with dimensions smaller than those required to obtain a spiral with a predetermined stiffness, by determining the stiffness of this spiral formed by coupling it with a balance wheel with a predetermined inertia, by calculating the thickness of material to be added to obtain the dimensions required to obtain the spiral with the predetermined stiffness, and by adding this thickness of material to the spiral.

[0015] In this way, as demonstrated by the figure 2 , notwithstanding the average stiffness Rm1, Rm2, etc. of the stiffnesses on a given plate, the dispersion curve of stiffnesses Rd1, Rd2, etc. can be recentered with respect to a nominal stiffness value Rnom.

[0016] This approach requires highly precise measurement of the balance spring's frequency to determine its stiffness. In particular, measurement errors can be caused by the balance wheel with a predetermined inertia, or by the assembly itself. A subsequent step is required to calculate the thickness to be removed, and then, again, to remove that calculated thickness with high precision. Furthermore, coupling the balance spring to the balance wheel with a predetermined inertia requires meticulous operations and significant preparation time. Finally, any assembly operation on parts or blanks still present on a blank significantly increases the risk of contamination (for example, the presence of fine silicon particles (debris) produced during handling).

[0017] Document CH281496A discloses a control and regulation system for the oscillation frequency of a balance-spring system in which, in particular, the active length of the spring is regulated automatically by a motor device, based on a measurement of the oscillation frequency.

[0018] The present invention aims to propose an approach free from the above disadvantages, which allows a faster production flow and / or with less risk of pollution(s), and / or a larger sampling, and / or a more precise measurement, and therefore a more individualized correction of the spirals of the plate. Disclosure of the invention

[0019] More specifically, the invention relates to a method for controlling a spiral or a spiral blank arranged to form a spiral, the spiral having to exhibit at least one predetermined resonance frequency, comprising the following steps: a. apply to the spiral alone or to the spiral blank alone a time-varying vibratory excitation to cover a predetermined frequency range, b. identify at least one resonance frequency characteristic, such as a resonance peak, of the spiral or spiral blank during the vibratory excitation over the predetermined frequency range, c. submit to a prediction machine the resonance frequency characteristic identified in step b. to determine a stiffness of the spiral or spiral blank and / or determine if a dimensional correction of the spiral alone or the spiral blank alone is necessary to obtain the predetermined resonance frequency.

[0020] The process, as implemented above, includes a step of vibratory excitation of the balance spring or balance blank and the measurement of a characteristic at a resonance frequency. From this, the stiffness is then predicted, and whether dimensional correction is necessary. There is no assembly with a balance wheel or other component, which saves time. Furthermore, the measurement is performed on the balance spring or balance blank alone, thus limiting errors induced by other components or their assembly, as well as any potential contamination. Measurement accuracy is improved because there are fewer sources of variability due to other components or contamination. In other words, the balance spring or balance blank is tested in isolation. The vibratory excitation is applied to the individual component or balance blank, not coupled to any balance wheel, weight, or oscillating system.The process allows for the control of individual and free parts (i.e., with at least one free end, not attached to any mechanism or balancer), which brings at least the advantages of productivity gains (no assembly with an oscillating system), quality gains (no contamination of parts, no breakage, and more parts can be tested in the same budget), and precision gains (no error related to other components of an oscillating system).

[0021] In one embodiment, vibrational excitation is applied to the spiral or spiral blank, which has one free end (typically the central ferrule) and another end fixed to the plate or a gripper. From a mechanical point of view, it can be schematically considered that the vibrational excitation is applied to a mass (located at the center of gravity of the spiral) connected to a frame of reference (a gripper for a single spiral, or the remainder of a substrate or plate for a blank, for example, made of silicon and not detached) by a spring (the elastic part of the spiral). The vibrational excitation sets the suspended mass in motion.

[0022] It can also be noted that if it is determined that a dimensional correction is necessary for the tested part (or for all the individual parts attached to the same wafer, or for the individual parts attached to a zone of a wafer, including or not the tested part), this can be done on the individual part(s) without disassembling anything (for example, one could plan to apply oxidation directly to a silicon part immediately after testing). It is therefore possible to add or remove material from the individual part(s) to vary its intrinsic stiffness. In other words, the dimensional correction is performed on the individual part(s) by changing its dimensions (typically the width and / or thickness of the bar forming the elastic part of the spiral).

[0023] The process described above allows for testing unfinished balance springs during manufacturing, minimizing the risk of contamination or assembly errors. Dimensional corrections (of cross-section, height, and / or thickness) are then possible. The process also allows for testing finished balance springs, for example, to rank them by stiffness increments to ensure proper pairing with a specific balance wheel.

[0024] Of course, the frequency range of the obtained spectrum depends not only on the source of vibrational 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 to which the oscillation amplitude measuring instrument (vibrometer or other) is sensitive. However, the excitation frequency range will be chosen so as to include at least one resonance frequency of the spiral or blank being tested.

[0025] The predetermined resonant frequency that the spiral must exhibit once finished can be a target natural frequency or a target resonant frequency, or a range of target natural frequencies, or a range of target resonant frequencies defined by a tolerance around a target value.

[0026] The dimensional correction predicted by the prediction machine can typically be a correction of the section of the flexible bar forming the spiral or spiral outline, i.e. a correction of either the height, or the thickness, or both.

[0027] In the above method, the characteristic of a resonance frequency is a characteristic of the oscillatory response measured over a predetermined frequency range, including at least one resonance frequency. Such a characteristic is typically identified after processing a raw measurement signal (e.g., measuring the amplitudes, velocities, or accelerations of displacement at certain points of the spiral or spiral blank). This processing may include, for example, a Fourier transform to identify resonance peaks and thus resonance frequencies.

[0028] It should be noted that the process can determine a stiffness value for classifying the part, and / or to then calculate / deduce a level of dimensional correction to apply to obtain a target stiffness. However, it is also possible to consider only the identified resonance frequency to directly calculate / deduce a level of dimensional correction to apply to obtain a target stiffness.

[0029] According to one embodiment, in step a, the frequency range is applied simultaneously to a plurality of spirals or spiral blanks. Speed ​​is improved because the vibrational excitation can typically be imposed on a plate supporting several hundred spiral blanks, which would, for example, still be attached to the plate.

[0030] According to one embodiment, the frequency range is predetermined to encompass at least one range of frequencies: centered on the predetermined resonant frequency, and with a range of at least 30% of the predetermined resonant frequency, that is, ±15% of the predetermined resonant frequency. For example, if the predetermined resonant frequency is 1 kHz, then the frequency range will be from 850 Hz to 1150 Hz.

[0031] In one embodiment, the spiral exhibits at least two predetermined resonant frequencies, and the frequency range is predetermined to cover at least these two predetermined resonant frequencies. By covering or sweeping a wide frequency range, several resonant peaks (or resonant frequencies) can be measured, which can provide greater accuracy.

[0032] According to one embodiment, step a includes the use of a source, such as a piezoelectric source, to induce or impose an acoustic excitation on a slice of a wafer supporting the spiral blank, or preferably on, or even under, the spiral or spiral blank to be specifically excited.

[0033] In one embodiment, the acoustic source can be coupled to an excitation cone chosen to excite at least one spiral or spiral 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 some, and preferably all, of the spiral blanks.

[0034] According to one embodiment, the acoustic source can be chosen and / or adjusted to generate the time-varying vibratory excitation to cover the predetermined frequency range: with sufficient amplitude to generate vibrations of the spiral or spiral outline of sufficient amplitude to be detected by means of amplitude measurement or velocity or acceleration of displacement of at least one point of the spiral or spiral outline and / or for a sufficient duration to deduce vibrational spectra of the spiral or spiral outline.

[0035] According to one embodiment, step b includes the use of an optical measuring means, such as a laser Doppler vibrometer.

[0036] According to one embodiment, step b is based on a measurement over time of an amplitude or a velocity, or even an acceleration of displacement of at least one point of the spiral or the spiral blank, preferably carried out at least partially during step a.

[0037] According to one embodiment, step b comprises: A step of identifying a resonance frequency of the spiral or spiral blank as a function of an operational or modal deformation of at least one point of the spiral or spiral blank. An operational or modal deformation is typically defined by an amplitude or velocity of displacement, or an acceleration, and a direction of oscillation (outside or within a particular plane) as a function of the excitation frequency.

[0038] According to one embodiment, the spiral or spiral blank is contained in a base plane, and step b comprises: a step b' of measuring an amplitude or a velocity or an acceleration of displacement of at least one point of the spiral or the spiral outline along a direction normal to the base plane, and / or a step b" of measuring an amplitude or a velocity or an acceleration of displacement of at least one point of the spiral or the spiral outline along a direction contained in the base plane.

[0039] Measuring displacements or speeds in multiple directions allows for better identification of resonance peaks and frequencies.

[0040] According to one embodiment: for a first predetermined resonance frequency, only step b' of measuring a displacement or velocity of at least one point of the spiral or spiral blank along 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 velocity of at least one point of the spiral or spiral blank along a direction contained in the base plane is carried out.

[0041] Depending on the resonance frequency, measurements can be taken in one direction or another to capture the largest possible displacements or velocities, thus minimizing measurement error. Indeed, depending on the geometry of the spiral or spiral blank, the mode of vibration (typically the direction of vibration) in response to vibrational excitation can vary.

[0042] According to one embodiment, step b includes a measurement signal processing step with, for example, a Fourier transform, to identify resonance peaks of displacement amplitude or velocity or acceleration, and / or phase, as a function of the excitation frequency.

[0043] According to one embodiment, step b comprises: a step of identifying a resonance peak of the spiral or spiral blank as a function of an amplitude or a speed of displacement of at least one point of the spiral or spiral blank.

[0044] In one embodiment, the resonance frequency is identified based on the width of the resonance or amplitude peak, at half the maximum value of the amplitude resonance peak. This processing method limits calculation errors that could occur by relying solely on identifying the frequency position of the peak defined by its maximum value.

[0045] In one embodiment, step c includes a step for calculating the stiffness of the balance spring or balance spring blank. Calculating the stiffness allows for a more precise determination of whether a dimensional correction is necessary, and if so, by what value. Furthermore, it also allows for the preliminary sizing or selection of a balance wheel to which the balance spring will be coupled once it has been finished.

[0046] According to one embodiment, if a dimensional correction is necessary, then the process includes a step: d. calculate, with the prediction machine, the dimensional modification (change in section, height and / or thickness) to be applied from the resonance frequency characteristic identified in step b.

[0047] In one embodiment, the prediction machine uses a polynomial formula to predict whether a dimensional correction is necessary. For example, linear regression modeling can be performed.

[0048] According to one embodiment, the prediction machine implements a classification carried out for example by a neural network to predict whether a dimensional correction is necessary.

[0049] According to one embodiment, the prediction machine implements a classification based on a partitioning into k-means or k-medians to predict whether a dimensional correction is necessary.

[0050] According to one embodiment, the spiral blank is formed on a plate comprising a plurality of spiral blanks distributed over several sectors of the plate, Step b includes identifying at least one resonance frequency characteristic of at least one spiral blank for each sector, and step c includes determining the stiffness of the spiral blank and / or determining whether dimensional correction is necessary for the spiral blanks in each sector. The accuracy of the dimensional correction (section, height, and / or thickness) is improved by refining the sector-by-sector analysis of the wafer.

[0051] According to one embodiment, the control process includes a calculation step, with the prediction machine, of the dimensional modification to be applied to the spiral blanks of each sector.

[0052] According to one embodiment, step a includes a step of changing a direction of vibratory excitation over time, preferably in a direction pointing towards the spiral or spiral blank whose resonance frequency characteristic is identified in step b.

[0053] According to one embodiment, the control process includes a preliminary step consisting of taking into account the material of the spiral or spiral blank, and adjusting a maximum amplitude of the vibratory excitation and / or a frequency range of the predetermined frequency range according to the material of the spiral or spiral blank.

[0054] In one embodiment, the resulting frequency range extends from 0 Hz to 100 kHz, preferably from 0 Hz to 50 kHz, more preferably from 0 Hz to 40 kHz, and most preferably from 10 kHz to 35 kHz. The applicant observed that the prediction accuracy was better for peaks or resonance frequencies located in a high frequency range. Indeed, when considering stiffness, its influence on the resonance frequency is stronger in higher frequency ranges (for example, between 10 kHz and 35 kHz), so sensitivity and accuracy are better in this particular range.

[0055] According to one embodiment, step a and step b are repeated at least several times for the same measurement point of the spiral or spiral blank.

[0056] In one embodiment, steps a and b are synchronized. Such synchronization makes it possible to detect a phase shift, attenuation, or coupling, the consideration of which can improve the accuracy of the prediction, or allow the vibration excitation source to be adjusted or recalibrated.

[0057] A second aspect of the invention relates to a method for manufacturing a spiral having at least one predetermined resonant frequency, comprising the steps of: form at least one spiral or spiral blank having dimensions within predetermined tolerances necessary to obtain the predetermined resonant frequency, check the spiral or blank according to the first aspect control procedure.

[0058] According to one embodiment, the manufacturing process includes a step consisting of: • correct at least one dimension of the spiral blank formed during step a., according to the calculation of step d. of claim 11, in order to obtain a spiral having the predetermined resonance frequency.

[0059] The dimensions (section, height and / or thickness) can be corrected by removing or adding material.

[0060] Depending on the embodiment, the spiral or spiral blank is made of silicon, glass, ceramic, metal, or carbon nanotubes. Conventional metal spirals (steel, nickel-phosphorus alloy, etc.) can be tested. In this case, the metallic spiral is clamped or referenced by a tool that positions it relative to the emission source and the displacement measurement device.

[0061] According to one embodiment, the spiral blank is formed on a plate, with a plurality of other spiral blanks.

[0062] A third aspect of the invention relates to a method for learning a prediction machine to implement step c of the method for controlling the first aspect, comprising the steps of: i- to form spirals or spiral blanks, ii- to apply to each individual spiral or spiral blank a time-varying vibratory excitation to cover a predetermined frequency range, iii- to identify at least one characteristic of a resonance frequency of each spiral or spiral blank during the vibratory excitation over the predetermined frequency range, iv'- to mount a plurality of spirals or spiral blanks in an oscillating mechanism with a predetermined inertia so as to measure for each spiral or spiral blank a free oscillation frequency or stiffness and / or iv"- to model in a simulation tool a plurality of spirals or spiral blanks in an oscillating mechanism with a predetermined inertia so as to calculate for each spiral or spiral blank a free oscillation frequency or stiffness v- to provide the prediction machine,and for each spiral or blank: the characteristic of the resonance frequency identified in step iii-; the free oscillation frequency or stiffness measured in step iv'- and / or calculated in step iv"-. ,

[0063] Preferably, it will be chosen to use a measuring instrument that is sufficiently sensitive over the chosen frequency range, and ensuring that the vibratory behavior of the spiral is usable over this chosen frequency range.

[0064] According to one embodiment, step iii- includes a preliminary phase of identifying reference measurement points with: the measurement of a displacement or a speed of displacement of a plurality of predetermined points of the spiral or the spiral blank, the identification of nodes among the plurality of predetermined points, which have at least one frequency or resonance peak a displacement amplitude of zero or less than a first threshold peak value, the selection of reference points to be measured during the control 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.

[0065] Such a step of identifying reference points makes it possible to eliminate points or areas that are nodes (i.e., stationary points) at one or more resonance frequencies.

[0066] According to one embodiment, the spiral or spiral blank has a defined radius Ra between a free central end and a fixed peripheral end, and at least two reference points, and preferably four reference points, are chosen and located: in a first zone 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 ensures that the points whose displacements are tracked have a sufficient amplitude of displacement to be measured correctly and with good accuracy.

[0067] Alternatively, one can plan to measure the displacements / movements / vibrations only at a specific point, preferably located on a large area of ​​the component that does not deform (or deforms only marginally compared to the deformations caused by the balance spring's oscillations). In particular, one can plan to focus the measurement on a point on the balance spring's ferrule or the balance spring blank. Indeed, on the one hand, the ferrule is large compared to the coils (a coil typically has a width of 20 µm to 40 µm, while the ferrule can have dimensions of at least 110 µm), which makes aiming the measuring tool easier, and on the other hand, the ferrule can be considered undeformable during vibrational excitation, and all points on the ferrule exhibit similar displacements / movements / vibrations.Consequently, aiming the measurement point (4 µm in size for a laser sensor, for example) on the ferrule will be easier, and / or a small error in locating the measurement point on the ferrule will have little impact on the final result. Furthermore, by choosing a specific measurement point on the part, a particular frequency range can be identified and selected to perform the stiffness prediction.

[0068] According to an embodiment in which several parts, still attached to a substrate or tooling, are to be tested in series, the following can be envisaged: An image capture step of the parts to be tested, an image analysis step to, for example, identify each part type and / or the position and / or orientation of each part, a selection step of one or more points to be measured for each part, and / or the selection of a vibrational excitation spectrum to be applied to each part and / or each selected point, for each part to be tested, a positioning step of the substrate or tooling supporting the parts to be tested in a vibrational excitation and measurement device. According to this implementation, excitation and measurement can be automated in the case of a wafer that still bears the spiral blanks: one or more images of the wafer are taken, an automatic image analysis is performed to determine at least the XY position of each part (part type or model identification can also be performed).Depending on the position, orientation, and / or type of part recognized, specific pre-established measurement points are identified or selected (for example, on the ferrule). A specific excitation cycle can also be selected based on the part type or a particular point. For example, with a tooling that holds the insert and includes a moving XY table, each spiral blank is automatically positioned successively opposite the excitation source and the measuring device to be tested by targeting the correct measurement point and applying the correct excitation specification. Optionally, an autofocus step can be performed, i.e., an adjustment of the relative position along the z-axis of the vibrometer head, allowing for the sharpest possible image of the observed part. The laser beam is thus focused precisely on the surface of the part.provided that the focal planes of the laser beam and the observation camera coincide, or that their offset is known and systematically compensated.

[0069] In one embodiment, depending on the measurement point selected on the part to be tested and / or the excitation frequency, and / or the model of the part to be tested, a step can be included to give a specific orientation to the excitation direction and / or the measurement direction. For this purpose, an excitation direction (or an axial direction of the excitation source) perpendicular to the part to be tested can be chosen to maximize displacements perpendicular to the plane formed by the part at rest. Alternatively, an excitation direction (or an axial direction of the excitation source) inclined relative to the part to be tested can be chosen to maximize displacements contained within the plane formed by the part at rest.Regarding measurement, one can choose a measurement direction (or an axial direction of a laser beam from the measuring device) perpendicular to the part being tested to maximize the measurement accuracy of displacements perpendicular to the plane formed by the part at rest. One can choose a measurement direction (or an axial direction of a laser beam from the measuring device) inclined relative to the part being tested to maximize the measurement accuracy of displacements contained within the plane formed by the part at rest.In the case of a measurement along an inclined axis, a suitable receiving sensor can be provided to receive the reflected signal, depending on the roughness of the parts: for "mirror" parts with low roughness, a receiving sensor with a large collection cone (preferably covering at least twice the angle of inclination), or offset, can be provided, while for "rough" parts, the receiving sensor can be combined with the light emission source.

[0070] In an embodiment where several parts are attached to a substrate such as a wafer, sampling can be performed by detaching one or a few parts for individual testing. This allows for the deduction of a specific excitation frequency to be applied, a specific measurement point to be used, and / or a specific region of the vibration spectrum to be considered in order to determine the desired resonance frequency characteristic. In other words, this preliminary sampling allows for testing individual parts under optimal conditions (measurement errors and interference are limited) to select the best test conditions for the parts remaining attached to the substrate. When exciting parts attached to a substrate, the substrate's response can be excited and measured to identify and subsequently exclude the spectral ranges in which it vibrates. Brief description of the drawings

[0071] Further details of the invention will become clearer upon reading the following description, made with reference to the attached drawing in which: there figure 1 shows the uncorrected stiffness dispersion curves for spirals on three different plates, the 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 manufacturing process for a mechanical resonator, here a spiral, on a plate, the figure 4 represents a device allowing the evaluation of the torque of a spiral, the figure 5 schematically represents the implementation of the evaluation of the stiffness of a spiral by vibration analysis, the figure 6 represents an example of frequencies applied to a silicon wafer supporting spiral blanks, to impose a vibrational excitation, the figure 7represents an example of measuring the displacement amplitudes of a point on a spiral outline, in response to the imposed frequency range of the figure 6 , there figure 8 represents 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 , there Figure 10 represents a model example of prediction built from data extracted from the figure 9 . Method of embodying the invention

[0072] THE figures 3A-3F are a simplified representation of a manufacturing process for a mechanical resonator 100 on a plate 10. The resonator is intended in particular to equip a regulating organ of a timepiece and, according to this example, is in the form of a spiral spring 100 made of silicon which is intended to equip a balance wheel of a mechanical timepiece movement.

[0073] Plate 10 is illustrated at the figure 3A as a SOI (silicon-on-insulator) wafer and comprises a substrate or handler 20 bearing a sacrificial silicon oxide (SiO₂) layer 30 and a single-crystal silicon layer 40. By way of example, the substrate 20 may have a thickness of 500 µm, the sacrificial layer 30 may have a thickness of 2 µm, and the silicon layer 40 may have a thickness of 120 µm. The single-crystal silicon layer 40 may have any crystal orientation.

[0074] A lithography stage is shown to Figures 3B And 3C By "lithography," we mean all the operations involved in transferring an image or design onto or above the plate 10. Referring to the figure 3BIn this exemplary embodiment, layer 40 is covered with a protective layer 50, for example, a polymerizable resin. This layer 50 is structured, typically by a photolithography step using an ultraviolet light source and, for example, a photomask (or other type of exposure mask) or a stepper and reticle system. This lithographic structuring forms the patterns for the plurality of resonators in layer 50, as illustrated in the figure 3C .

[0075] Subsequently, in the next step of the 3D figure The patterns are machined, specifically engraved, to form the plurality of 100 resonators in layer 40. The etching can be performed using a deep reactive ion etching technique (also known as DRIE for "Deep Reactive Ion Etching"). After etching, the remaining portion of the protective layer 50 is subsequently removed.

[0076] 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, for example by a thermal oxidation step followed by a deoxidation step, consisting for example of wet etching with hydrofluoric acid (HF).

[0077] At the final stage of the manufacturing process at the figure 3FThe 110 turns of the silicon resonator 100 are coated with a 120 layer of silicon dioxide (SiO2), typically through a thermal oxidation step to produce a thermo-compensated resonator. The formation of this 120 layer, which is generally 2–5 µm thick, also affects the final stiffness of the resonator and therefore must be taken into account in the preceding steps to obtain the vibrational characteristics of the balance spring, leading to a specific natural frequency of the balance spring couple in a given watch mechanism.

[0078] As indicated above, at the stage prior to the creation of the thermo-compensation layer, the different resonators formed in the wafer generally exhibit a significant geometric dispersion between them and therefore a significant dispersion between their stiffnesses, notwithstanding that the pattern formation steps and the machining / engraving through these patterns are the same for all resonators.

[0079] Moreover, this dispersion of stiffness is even greater between the spirals of two plates etched at different times even if the same process specifications are used.

[0080] The above description relates to 100 silicon resonators, but it is possible to consider making the resonators from glass, ceramic, carbon nanotubes, or even metal.

[0081] To center the average stiffness of the resonators on different plates relative to a nominal stiffness value as illustrated in the figure 2 The resonators obtained in step 3E on the plate 10 in question can be deliberately formed with dimensions d that differ from the dimensions required (for example, larger) to obtain a nominal or target stiffness. Thus, it is possible to implement a control method to estimate the vibrational characteristics of the resonators (natural frequency and / or resonance frequencies) in order to deduce the stiffness and / or the actual dimensions of the resonators 100 and correct their dimensions, which will lead to obtaining the desired natural frequency of the resonator-balancer pair.

[0082] The present invention proposes to determine, from at least one characteristic of a resonance frequency of a sample of 100 resonators on the wafer in step 3E, whether a geometric correction of the resonators is necessary. If so, the present invention proposes to calculate precisely the thickness of material to be modified (removed or added) around each turn to obtain the dimensions leading to the vibrational characteristics of the resonators (natural frequency and / or resonance frequencies, and / or stiffness) corresponding to target values, according to a method more efficient than the methods of the prior art.

[0083] Thus, the invention proposes to determine at least one characteristic of a resonance frequency of a sample of resonators by vibration measurement and to 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.

[0084] This exploits the modal properties of the spiral 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 dimensions (in particular the thickness) and / or the stiffness to certain frequencies (natural frequency or resonance frequencies associated with a resonance peak or a full width at half maximum) specifically chosen.

[0085] Once the learning phase is complete (once the modes to be exploited and the excitation frequencies have been determined), it is possible to move to a prediction phase and use the prediction machine by exploiting the predictive model to control the resonators of a produced wafer, in order to predict if a correction of the dimensions is necessary, and if so, calculate or predict the exact correction to be made to the dimensions of the resonators (by removal if the rough is made with dimensions greater than the final dimensions required, or by adding material if the rough is made with dimensions less than the final dimensions required, for example).

[0086] Thus, it is possible to integrate the control process into a manufacturing process to correct, if necessary, the vibrational characteristics of the resonators (natural frequency and / or resonance frequencies, and / or stiffness) to obtain a particular and predetermined natural frequency of oscillation, once the resonators are each coupled to a balance wheel of a given watch mechanism. Vibratory excitation

[0087] Measuring the vibrational response of resonators allows us to deduce at least one characteristic of a resonant frequency, such as a resonant frequency value. Specifically, we must first apply a vibrational excitation to the plate. Several options are available: a. Frequency domain measurements: 1- Use a piezoelectric source (or any other source capable of inducing or imposing acoustic excitation) on the edge of the wafer, on or under the spiral blank 200 to be specifically excited (preferred), which excites at a particular frequency f0 (continuous single-frequency excitation). In this variant, the excitation is sustained. 2- Alternatively, the piezoelectric source (or any other source allowing to induce or impose an acoustic excitation) can also be used on the edge of the wafer, on, or under the spiral blank 200 to be specifically excited (preferred) which excites at a frequency variable in time to cover a predetermined frequency range, going for example from 0 to 100 kHz, preferably from 0 to 75 kHz, preferably from 0 to 50 kHz, preferably from 5kHz to 50 kHz, and preferably from 10 to 35 kHz.The entire frequency range can be swept or covered within a time interval ranging from a fraction of a second to a few seconds. For example, the frequency range can be swept or covered in less than 0.5 s, less than 1 s, or less than 1.5 s. In this variant, the excitation frequency changes continuously. b. Time-domain measurements: use an excitation hammer (or any other source capable of inducing impulsive acoustic excitation) on the edge of the wafer, on, or under the spiral to be specifically excited (preferred), which provides the shortest possible acoustic pulse (multi-frequency impulsive excitation). In this variant, the excitation is instantaneous and not sustained.

[0088] Furthermore, measurements can be performed using a specific sampling method, for example, a sampling range of 4, 2, or 1 Hz. Indeed, the resolution required to process the acquired data, for example using a Fourier transform, depends directly on the duration of the acquisition.

[0089] Furthermore, a signal sampling frequency of at least 100 kHz can be chosen if the frequency range extends up to 50 kHz, for example.

[0090] In general, it is possible to change the direction of excitation, that is, the direction of the movements imposed by the source (vibrations can be imposed along one or more axial directions, and this direction or these directions can be changed over time). In the case where a plate containing multiple resonators is excited, the direction of the vibrations can be adjusted to point at one or another of the resonators, depending on the displacement amplitude measurements described below.

[0091] Finally, it is possible to couple the acoustic source to a diverging cone directed towards the resonators to be excited, and to adjust the acoustic source to emit an excitation signal with an amplitude sufficient to impose a 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 speed, or acceleration of movement

[0092] During excitation, the amplitude and phase (relative to the excitation source) of oscillation in the three directions X, Y (in the plane) and Z (out of the plane) of the specifically excited spiral are recorded using a suitable measuring instrument. The following are examples of possible measuring instruments, but are not limited to: Optical methods by interferometry: a. By 3D Doppler effect (laser vibrometer by Doppler effect), b. Holographic, Stroboscopic optical methods, High temporal resolution chromatic confocal profilometry, Optical reflectometry: a. Vibration analysis by beam deflection on multi-dial detector or camera, b. Analysis by time analysis type TCSPC, Acoustic methods by ultrasound by Doppler effect.

[0093] There figure 5Figure 25 schematically represents a silicon wafer on which a plurality of spiral blanks 200 are formed. A vibrational excitation source 400 is coupled to the wafer 25, so as to impose vibrational excitation. Consequently, each spiral blank 200 will vibrate, and a laser vibrometer 300, here focused on a point of the right-hand spiral blank 200, will measure the vibration amplitudes of the measurement point over time. It is possible to measure the displacements along a direction normal to the plane of the wafer 25, but it is equally possible to measure the displacements along one or more directions contained within the plane of the wafer 25.

[0094] Once a particular point has been studied, the laser vibrometer 300 can be moved to another measurement point of the spiral blank 200, or it can be moved to another spiral blank 200 of the plate 25. Of course, the spiral blank 200 can alternatively be moved relative to the laser vibrometer.

[0095] There figure 6 This represents an example of vibrational excitation over time. In the given example, the excitation frequency varies over time, between 0 Hz and 50 kHz, and a succession of rising edges can be imposed, each separated by a period of rest without excitation. For each measurement point on the spiral 200 blank, a plurality of rising edges can be imposed (between 2 and 60 rising edges), each lasting between 0.5 s and 2 s, for example. Selection of reference points to measure

[0096] Regarding displacement amplitude measurement, during the learning phase, a step can be planned to identify points on the resonator where the vibrational response is significant. Indeed, in the case of a spiral subjected to vibration, especially if the frequency varies over time, the vibrational response will create nodes on the spiral—that is, specific points on the spiral with a small or zero displacement amplitude. If a displacement measurement is taken at a point on the spiral that turns out to be a node at one or more specific frequencies, the identification of resonance frequency characteristics will be negatively affected.

[0097] Therefore, it is advantageous to include a preliminary step of measuring displacement at a plurality of predetermined points on the spiral, for example, at least ten predetermined points, preferably at least twenty predetermined points, and most preferably at least thirty predetermined points. It is possible to select the predetermined points arranged on an orthonormal XY coordinate system in the plane of the spiral.

[0098] Following this preliminary amplitude measurement step at predetermined points, it is possible to identify resonance frequencies for each measurement point. Subsequently, a step is taken to select reference points for which the displacement amplitude measurement during excitation shows that they are not nodes at these resonance frequencies. In other words, the identified nodes exhibit, at at least one resonance frequency, a displacement amplitude of zero or less than a first threshold peak value, and these node-forming points are excluded from the reference points to be considered for subsequent measurements. It should also be noted that the reference points differ depending on the position of the spiral blank 200 on the plate 25.

[0099] Typically, at least two reference points will be selected, and preferably at least four. If the resonator has a radius Ra and is anchored or embedded in the plate by its outer end of the mounting hole, four chosen and located reference points are preferable: in a first zone less than 0.20 x Ra (for example on the central ferrule), or in a second zone between 0.05 x Ra and 0.30 x Ra (for example on the second turn from the ferrule), or in a third zone between 0.35 x Ra and 0.65 x Ra (for example on a turn located in the middle of the spiral), or in a fourth zone between 0.65 x Ra and 0.85 x Ra (for example on a turn located three-quarters of the way around the spiral). Thus, the reference points are far from the part anchored on the plate and naturally exhibit a significant oscillatory displacement capacity, which ensures better accuracy of displacement measurement.

[0100] Furthermore, the displacements of a point on the wafer body, and / or a point on the excitation source, can also be measured to identify or measure, for example, a phase shift, vibrational attenuation, or resonance resulting from vibrational coupling or from the wafer itself. These additional measurements ensure that the identified peaks are indeed those of the spiral alone. The displacement amplitude measurement can also be synchronized with the vibrational excitation. Determination of vibrational characteristics

[0101] We then have several scenarios depending on the domain previously chosen for the arousal: a. Frequency-domain measurements 1- Variant with sustained excitation: i. Time-integrate the amplitude and phase of oscillation long enough to obtain good spectral resolution at the excitation frequency fa, ii. Shift the oscillation frequency by Δf to excite at the frequency f₀ + Δf and repeat integration step i, iii. Reconstruct the amplitude and phase spectra of oscillation as a function of the excitation frequency (possibly with several peaks at multiple frequencies). 2- Variant with excitation whose frequency varies over time: i. Time-record the amplitude and phase of oscillation during the frequency sweep of the frequency range, ii. Repeat step i at least once, preferably at least three times, iii. Reconstruct the amplitude and phase spectra of oscillation as a function of the excitation frequency (possibly with several peaks at multiple frequencies). b.Time-domain measurements: i. Record the temporal displacement of the coil along X, Y, and Z over a sufficiently long period to obtain a representative signal, such as a few seconds. ii. The signal can be recorded as a reference signal for comparison with other signals measured on other parts. Alternatively, the signal can be processed using a Fourier transform to identify resonance frequencies in the recorded signal.

[0102] Consequently, at least one resonance peak can be identified for each excited resonator, and it is proposed to determine the resonance frequency not based on the peak's apex (i.e., the maximum amplitude), but rather on a region of the curve located between 25% and 75% of the peak's maximum amplitude, for example, using its full width at half maximum (FWHM). This processing method, which focuses on a portion of the curve between 25% and 75% of the peak's maximum amplitude, helps to limit errors due to the singularity of the maximum amplitude point and the approximation calculations required to reconstruct the peak's apex.The area of ​​the curve between 25% and 75% of the maximum amplitude of the resonance peak exhibits greater accuracy than the portion above 75% (typically the peak itself), thus providing a more precise determination of the exact resonance frequency. For example, the midpoint of the segment connecting the two points at the midpoint of the resonance peak can be used to determine the resonance frequency associated with that peak.

[0103] There figure 7 represents an example of a vibration spectrum for a point on a 200 spiral blank of the figure 5 reconstructed from the amplitude measurements of the displacement of the measurement point considered in response to the vibratory excitation of the figure 6between 10 kHz and 15 kHz. Three amplitude peaks can be observed, at approximately 11 kHz, 12.3 kHz, and 13.7 kHz. Although not shown, between 10 and 30 amplitude peaks can typically be identified if the vibrational excitation sweeps across a frequency range between 0 Hz and 50 kHz. Each amplitude peak has a resonant frequency, and the maximum amplitudes vary considerably.

[0104] There figure 8This document details the processing that can be performed on an amplitude peak, such as the one at 11 kHz. The goal is to find the resonance frequency and assign it the most precise value possible. Instead of basing this processing on the peak's maximum value, the applicant discovered that greater accuracy could be achieved by determining the length of the segment connecting the rising and falling parts of the curve, at the midpoint of the peak. The resonance frequency is typically the value at the midpoint of this segment. However, interpolation can be performed at points near the resonance peak to improve accuracy, and the chosen point on the segment can be shifted, which will not be the midpoint, particularly if the actual position of the resonance peak is shifted, for example, due to the chosen sampling frequency.

[0105] There figure 9This represents, for example, an amplitude peak at approximately 10 kHz, the amplitude peaks constructed for about ten tested spiral 200 blanks. 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 by a ratio of approximately 1 to 5. Since the peak apexes are not perfectly symmetrical, it seems judicious to determine the resonance frequency based on the full width at half maximum (FWHM).

[0106] For these trials of the figure 9 The following resonance frequencies could be deduced: Spiral 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 actual dimensions of the tested resonator bar

[0107] To establish a predictive model that can take vibrational characteristics (typically a resonance frequency) as input and output a stiffness and / or dimensional correction, it is necessary, during the training phase, to provide data relating to the actual stiffness and / or dimensions of the bars of the resonators being tested. For this purpose, one could plan to measure the natural frequency of a balance spring system in an environment similar to that of a particular watch mechanism.

[0108] Two alternatives can be implemented. The first alternative involves coupling a predetermined pendulum directly to the resonator while it is still attached to the plate, and measuring the natural frequency of oscillation of the resonator-pendulum pair. This natural frequency can then be compared with an expected natural frequency, and, more importantly, the actual stiffness or dimensions can be calculated based on equations 1 to 3 above. The second alternative involves finishing the fabrication of the tested resonators, so that they can be mounted or coupled individually with a pendulum pair to again measure the natural frequency of oscillation of the resonator-pendulum pair.

[0109] In both alternatives described above, an intermediate step can be taken to determine the stiffness of each resonator, followed by the determination of the actual dimensions of the resonator bars. In other words, it is possible to determine the natural frequency or resonance frequency and then the stiffness or dimensions of the resonator bar by analyzing the free oscillations of a balance spring coupled to a reference balance wheel. In this approach, a laser pointed at the balance arms or the balance spring carrier records the transit times of the balance arms or a locating device. From this, an estimate of the period, then the frequency, and finally the stiffness can be deduced. The data collected are essentially point clouds of the transit times.

[0110] Indeed, several solutions exist for evaluating the stiffness of a balance spring on the wafer, as described by Vermot et al. in the *Traité de construction horlogère* (2011), pages 178-179. For example, a dynamic evaluation can be performed by coupling the balance spring to a reference balance wheel whose inertia is known. Measuring the frequency of the assembly allows for a precise determination of the balance spring's stiffness. This evaluation can be carried out on the wafer or by detaching the balance spring from the wafer. The references and precedents given above provide details on this method.

[0111] 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. Analyzing the slope of this curve for low amplitudes (linear portion) allows us to deduce the stiffness, and subsequently the dimensions of the resonator bar. The dimensions of the spiral bar can then be determined.

[0112] Furthermore, it is possible to estimate, through simulation, a natural frequency and / or a resonance frequency and / or the stiffness for each resonator tested on the plate. To this end, dimensional measurements can be taken of each tested resonator to reconstruct it using numerical modeling. This allows for the numerical simulation of its vibrational response to the imposed spectrum and, moreover, the determination of the resonator's stiffness.

[0113] A high-resolution 3D X-ray tomography approach would allow the extraction of point clouds providing the 3D material density of the spirals, and, with appropriate image reconstruction, a map of the spiral's cross-section. These different types of data make it possible to deduce the dimensions of the individual bars and to estimate the spiral's stiffness using a geometric approach.

[0114] Another approach involves analyzing the forced oscillations of a balance spring on a reference balance wheel with an escapement. Laser measurement of the balance arm transit times (point clouds), as described above, allows for the measurement of the frequency and the deduction of the stiffness. An alternative can be considered using acoustic data (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 balance arm transit times or the temporal evolution of the acoustic pressure level. These types of experimental data allow for the deduction of the period, then the frequency, then the stiffness, and finally the dimensions of the resonator bar.

[0115] Returning to the tests discussed above at the figure 9A stiffness measurement was carried out by coupling each 200 spiral blank to a reference balance wheel, and the stiffness values ​​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

[0116] During the learning phase, oscillation amplitude measurements are taken on physical resonators, and resonance frequencies are identified. In order to subsequently link the resonance frequencies measured on resonators to stiffness and / or dimensional (thickness) corrections to be applied, a correlation phase is necessary during which a predictive model is built.

[0117] The operations described above (vibration measurements, identification of resonance peaks, full width at half maximum (FWHM) and its midpoint or corrected value, determination of the stiffness and / or dimensions of the spiral bar) allow for the creation of a database that can relate the spiral's position on the wafer, oscillation spectra or periods, or FWHM and its midpoint or corrected value, to the effective stiffness and / or dimensions of the spiral bar. As mentioned above, this database can be built from numerical simulations on a finite element model of the spiral. These simulations generate reference spectra or oscillation periods associated with the stiffness values. This database can also be supplemented by experimental measurements, such as vibration spectra, oscillation periods, and the positions of spirals on the wafer, along with their associated stiffness values.One of the advantages of this approach is that the training database grows with each trial. This allows for an adaptive model that varies depending on the plates and spirals, and contributes to reducing the standard deviation in stiffness for the plates.

[0118] This database can be used to build a prediction model, and several solutions are available.

[0119] We can construct a numerical model, for example polynomial, to calculate, as a function of a resonance frequency value, an actual thickness, a dimensional correction or an actual stiffness.

[0120] One can also perform a categorization by performing 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 resonator bar) and linking them together to establish a correspondence.

[0121] It is also possible 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 being able to be defined by increments of values.

[0122] In summary, the learning phase includes a testing phase (exciting resonators and measuring their vibrational characteristics to reconstruct a vibration spectrum and identify resonance frequencies). A measurement phase of the resonator bar stiffnesses and / or dimensions is also performed. Once the input data (resonance frequencies) and output data (bar stiffnesses and / or dimensions) are available for a significant sample, the predictive model building phase can begin.

[0123] To return to the example discussed and described in relation to the figure 9 The data collected is as follows: Spiral 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

[0124] A linear regression model was performed on the above data for the first six rows, and the following relationship was established: R = 0.0015 F − 10.894 ,

[0125] With R for stiffness in 10⁻⁷ N.mm² F for resonance frequency in Hz.

[0126] The stiffness can therefore be predicted and compared with the actual measured stiffness, as shown in the table below, with the first six rows containing the data used to build or train the linear regression, and the last four rows containing only a prediction: N° 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%

[0127] A maximum error of 4.40% was measured, and the Figure 10 represents the linear regression line for the values ​​of the first six rows.

[0128] It is worth noting that it is advantageous to verify that the established prediction model exhibits good sensitivity, meaning that for two different input values, the model yields two distinct output values. The applicant observed that the sensitivity of the prediction model was not the same for all resonance peaks. In particular, when referring to the established prediction formula and its representation Figure 10The slope is 0.0015 × 10⁻⁷ N.mm / Hz. The applicant observed that the slope could be larger for higher resonance frequencies, thus providing better prediction sensitivity for predicting distinct stiffness or dimensional correction values, even from similar resonance frequencies. It is advantageous to include, during the training phase, a step to compare prediction sensitivity to verify / confirm that it is preferable to consider and select certain resonance peaks at high frequencies (e.g., above 5 kHz) to then predict, as accurately as possible, a stiffness and / or dimensional correction based on the measured vibration response.

[0129] Furthermore, the applicant also observed that even for similar resonance frequencies, the resonance modes (particularly the deformation and / or displacement modes of the resonators) could differ significantly, which can also affect the sensitivity of the stiffness and / or dimensional correction prediction. It is advantageous to include, during the training phase, a step to compare the sensitivity of the prediction in order to subsequently choose one resonance frequency over another to predict stiffness and / or dimensional correction as accurately as possible based on the vibration response.

[0130] Based on the above remarks concerning the study of prediction sensitivity, we can anticipate, during the training phase, classifying the different identified resonance peaks according to their predictive sensitivity for stiffness and / or dimensional correction. We can then 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 that provide the best sensitivity. Thus, applying variable vibrational excitation over this predetermined frequency range will ensure the ability 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.

[0131] In general, the learning phase allows the selection of either high-frequency resonance peaks and / or resonance peaks that correspond to particular resonance modes, enabling the prediction of precise and reliable values. The frequency range will be predetermined to include at least one resonance peak and preferably several, in order to make either a single prediction as precise as possible, or several predictions (one per resonance peak deemed interesting) to then perform cross-checks, averages, or recalibrations of the predicted values.

[0132] For example, we can predict several stiffness values ​​or dimensional corrections from several peaks or resonance frequencies, and then calculate a final value by performing a weighted average from the predicted values, assigning weights to each predicted value, each weight being determined according to the sensitivity identified for each corresponding peak or resonance frequency.

[0133] Alternatively, and preferably, we can plan to have only one model which takes all the peaks or resonance frequencies into input and returns the stiffness or dimensional correction, the model learning phase serving precisely to calculate the weightings on the peaks or resonance frequencies into input. Prediction phase

[0134] Once the learning phase is complete, a prediction phase can be performed, for example, during a resonator control process. Typically, the control process can be carried out on spiral blanks made on a wafer and still attached to that wafer, in order to estimate the stiffness and / or dimensions of the spiral bars of the sample, and thus determine whether a dimensional correction is necessary.

[0135] Once the model is trained, the control procedure to be deployed is as follows: 1) Locating the position of the spiral on the wafer, vibrational measurement of the spectra or oscillation period (as described above), 2) Prediction of the stiffness and / or dimensions of the spiral bar by application of the predictive model, 3) Determining if a dimensional correction is necessary to reach the target natural frequency or stiffness.

[0136] During the inspection process, it is also possible to quantify the exact correction to be made, so the manufacturing process can include, in addition to the above inspection: 1) Knowing the effective stiffness of the spiral estimated according to the model and the target stiffness and / or the target bar dimensions: apply the necessary correction dose. Repeat steps 1) and 2) of the control process to check the stiffness / dimensions of the spiral and confirm that the target values ​​are met, within a tolerance threshold, or repeat these steps and the dimensional correction until the stiffness / dimension predicted by the model reaches the target values. Sampling

[0137] We know that several hundred spirals are produced on a plate and that the dimensions of the spiral bars can vary depending on the region of the plate. While stiffness evaluation can be performed on a single spiral, in practice it will be carried out on a sample of spirals distributed across the plate.

[0138] Based on the evaluations performed, corrections can be applied uniformly to the entire coil, or differentiated by region if the results vary from one spiral to another. This allows us to reduce the standard deviation of the stiffness dispersion. Furthermore, if the stiffness of all the spirals is known through application of the model, we can determine the optimal correction to reduce the overall dispersion.

[0139] We can even consider going so far as to evaluate all the spirals of the plate, in particular with a vibrational evaluation, as this is very quick to perform.

[0140] Although the examples above were primarily based on manufacturing spirals with initial bar dimensions larger than the target bar dimensions, it is also possible to produce spirals with initial bar dimensions smaller than the target bar dimensions. The correction step then consists of adding material, as described, for example, in the aforementioned EP3181939 document.

[0141] The method, which consists of identifying resonance frequencies by imposing a vibratory excitation on the spiral blanks alone, allows for the rapid acquisition of measurement data, without having to, for example, carry out the operations of assembling a balance wheel, while limiting measurement errors because only the spiral blank is tested (there is no error that can be linked to the balance wheel, such as its mass, its mounting position, etc.).

Claims

1. A method for controlling a hairspring or a hairspring blank arranged to form a hairspring, the hairspring required to have at least one predetermined resonance frequency, the control method including the following steps: a. applying to the hairspring alone or to the hairspring blank alone a vibrational excitation varying 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 the vibrational excitation over the predetermined frequency range, c. submitting to a prediction machine the resonance frequency characteristic identified in step b. to determine a stiffness of the hairspring or of the hairspring blank and / or to determine whether a dimensional correction of the hairspring alone or of the hairspring blank alone is necessary to obtain the predetermined resonance frequency.

2. The control method according to claim 1, wherein 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.

3. The control method according to any of claims 1 to 2, the hairspring having at least two predetermined resonance frequencies, wherein the frequency range is predetermined to cover at least the two predetermined resonance frequencies.

4. The control method according to any of claims 1 to 3, wherein step b is based on a measurement over time of an amplitude or a speed or an acceleration of displacement of at least one point of the hairspring or of the hairspring blank, preferably carried out at least partially during step a.

5. The control method according to any of claims 1 to 4, the hairspring or the hairspring blank being contained in a base plane, wherein 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 along 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 along a direction contained in the base plane.

6. The control method according to any of claims 4 to 5, wherein 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 a speed of displacement of at least one point of the hairspring or of the hairspring blank.

7. The control method according to claim 6, wherein the resonance frequency is identified based on the width of the resonance peak, at mid-height of the maximum value of the resonance peak.

8. The control method according to any of claims 1 to 7, wherein, if a dimensional correction is necessary, then the method comprises a step of: d. calculating, with the prediction machine, the dimensional modification to be applied from the resonance characteristic identified in step b.

9. The control method according to any of claims 1 to 8, wherein the prediction machine implements a polynomial formula to predict whether a dimensional correction is necessary.

10. The control method according to any of claims 1 to 9, wherein the prediction machine implements a classification performed for example by a neural network to predict whether a dimensional correction is necessary.

11. The control method according to any 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, wherein step b comprises a step consisting in identifying at least one characteristic of a resonance frequency of at least one hairspring blank for each sector, and wherein step c comprises a step consisting in determining for the hairspring blanks of each sector a stiffness and / or whether a dimensional correction is necessary.

12. The control method according to any 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 vibrational 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.

13. The control method according to any of claims 1 to 12, wherein the frequency range extends over a frequency range 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.

14. A method for manufacturing a hairspring having at least one predetermined resonance frequency comprising the steps consisting in: • forming at least one hairspring or one hairspring blank with dimensions comprised in predetermined tolerances necessary to obtain the predetermined resonance frequency, • controlling the hairspring or the hairspring blank according to the control method of any of the preceding claims.

15. The manufacturing method according to the preceding claim, comprising a step consisting in: • correcting at least one dimension of the hairspring blank alone formed during step a., according to the calculation of step d. of claim 8, in order to obtain a hairspring with the predetermined resonance frequency.

16. The manufacturing method according to any of claims 14 to 15, wherein the hairspring blank is formed on a wafer, with a plurality of other hairspring blanks.

17. A method for learning a prediction machine to implement step c of the control method of any of claims 1 to 13, comprising the steps consisting in: i- forming hairsprings or hairspring blanks, ii- applying to each of the hairsprings alone or each of the hairspring blanks alone a vibrational excitation that varies over time to cover a predetermined frequency range, iii- identifying at least one characteristic of a resonance frequency of each hairspring or each hairspring blank during the application of the predetermined frequency range, iv'- mounting a plurality of hairsprings or of hairspring blanks in an oscillating mechanism with a predetermined inertia so as to measure for each hairspring or each hairspring blank a free oscillation frequency or a stiffness, and / or iv"- modeling in a simulation tool a plurality of hairsprings or of hairspring blanks in an oscillating mechanism with a predetermined inertia so as to calculate for each hairspring or hairspring blank a free oscillation frequency or a stiffness, v- providing to 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"-.

18. The learning method according to the preceding claim, wherein step iii- comprises a preliminary phase of identifying reference measurement points with: - the measurement of a displacement 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 resonance frequency or peak a zero displacement amplitude or a displacement amplitude less than a first threshold peak value, - the selection of reference points to be measured during the control 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.

Images