Method for monitoring and manufacturing timepiece hairsprings

Abstract

The invention relates to a method for testing a balance spring or a balance-spring blank arranged to form a balance spring, comprising the following steps: a. applying, to the balance spring or the balance-spring blank, a vibratory excitation that varies over time so as to cover a predetermined frequency range; b. identifying at least one characteristic of a resonant frequency of the balance spring or balance-spring blank, such as a resonant peak, during or in response to the vibratory excitation over the predetermined frequency range; c. submitting the resonant-frequency characteristic identified in step b. to a machine for predicting temperature coefficient in order to determine a temperature coefficient of the Young's modulus (CTE) of the balance spring and / or a temperature coefficient (CT) of a timepiece system comprising the balance spring.

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 means of a regulator or mechanical oscillator that includes a resonator, a component that can be elastically deformed and whose oscillations determine the watch's accuracy. Many watches, for example, feature an oscillator 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 spring and hairspring assembly regulates the watch's accuracy and depends on several parameters, including the stiffness of the hair spring and the operating temperature.

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

[0004] The stiffness of the balance spring also defines its intrinsic vibrational characteristics, such as its natural frequency and resonance frequencies. In this application, the natural frequency of an elastic system (a single resonator or a resonator-balance spring pair) is the frequency at which this system oscillates when it is in free motion, i.e., without an excitatory force. Furthermore, a resonance frequency of an elastic system (e.g., the single resonator) subjected to an excitatory force is a frequency at which a local maximum of 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.

[0005] The stiffness of a spiral-type resonator typically depends on the characteristics of the material from which it is made, 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 angle of torsion of the spring, 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 where: E is the Young's modulus of the material used for the bar, L is the length of the bar, h, the height of the bar, and e, the thickness or width of the bar.

[0006] As will be explained in more detail below, the operating temperature is a parameter that influences the operation of the regulating device; we can derive equation 1 with respect to temperature T, and we find: 1 F dF dT = 1 2 1 E T 0 dE dT + 3 α S − 2 α B With : T, the current temperature, T0, a reference temperature, α S , the coefficient of thermal expansion of the spiral α B , the coefficient of thermal expansion of the balance serge.

[0007] Equation 4 can be rewritten as follows: CT = 1 2 CTE + 3 α S − 2 α B With : CT: the thermal coefficient of the oscillator (seconds per day per degree), CTE: the thermal coefficient of Young's modulus (K -1< ), or otherwise called the thermo-elastic coefficient.

[0008] The natural frequency of the regulating organ formed by the balance spring with stiffness R coupled to a balance wheel with inertia I 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.

[0009] The importance of magnetic fields in the modern environment has led watchmakers to use silicon balance springs in recent years, which are less sensitive to magnetic disturbances than metallic balance springs.

[0010] 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).

[0011] It is very important that the characteristics of the oscillator are as stable as possible, in order to have a stable running of the watch, with in particular the least possible differences in running depending on the operating temperature (summer-winter, wristwatch worn or not worn).

[0012] 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.As shown in Equation 5 above, temperature variations can lead to variations in rate, with the thermal coefficient CT depending in particular on the Young's modulus thermal coefficient, the thermal expansion coefficient of the balance spring, and the thermal expansion coefficient of the balance rim. Silicon balance springs and their thermal compensation therefore allow the terms of Equation 5 relating to the balance spring to be adjusted to obtain a thermal coefficient CT for the oscillator. By extension, the CT of a more extensive watchmaking system, which includes the balance spring, can also be characterized, even down to the CT of a complete caliber, by determining the thermal drift of the caliber, including that of the escapement, the gear train, and the influence of lubrication. From this perspective, the balance spring is considered the sole variable for adjusting the CT of the watchmaking system that incorporates it, to obtain the lowest possible CT.

[0013] 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.

[0014] 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.

[0015] 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.

[0016] 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.

[0017] 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.

[0018] 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).

[0019] Documents JP6486697B2, CN103105769A, EP3845770A1 and CH281496A present frequency control methods.

[0020] 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 of the thermal coefficient of the Young's modulus (CTE) of the balance spring and / or the thermal coefficient (CT) of a watchmaking system including the balance spring, and therefore a more individualized correction of the balance springs of the plate to obtain watchmaking systems whose operation is little or not disturbed by temperature variations. Disclosure of the invention

[0021] More specifically, a first aspect of the invention relates to a method for inspecting a spiral or a spiral blank arranged to form a spiral, the inspection method comprising the following steps: a. apply to the balance spring or balance spring blank a time-varying vibratory excitation to cover a predetermined frequency range, b. identify at least one feature of a resonance frequency of the balance spring or balance spring blank, such as a resonance peak, during or in response to the vibratory excitation over the predetermined frequency range, c. submit to a thermal coefficient prediction machine the resonance frequency feature identified in step b. (and preferably said at least one feature of a resonance frequency of the balance spring or balance spring blank, such as a resonance peak identified in step b.), to determine a thermal coefficient of the Young's modulus (CTE) of the balance spring and / or a thermal coefficient (CT) of a watchmaking system including the balance spring.

[0022] The process, as implemented above, comprises a step of vibratory excitation of the balance spring or balance wheel blank and the measurement of a characteristic resonance frequency. From this, a thermal coefficient of Young's modulus (TCM) of the balance spring and / or a thermal coefficient (TCM) of a watchmaking system including the balance spring are then deduced by prediction. There is no assembly with a balance wheel or other component, which saves time. Furthermore, the measurement is performed on the balance springs or balance wheels 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 wheel blank is tested in isolation. The vibratory excitation is applied to the individual component or balance wheel 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).

[0023] It should be noted that determining the thermal coefficient of Young's modulus (TCM) of the spiral or spiral blank by the method according to the invention is well suited for oxidized parts for which the thickness of the oxide layer is not precisely known at this stage of the manufacturing process. With the present invention, the thermal coefficient of Young's modulus (TCM) of the oxidized spiral or spiral blank, which are essentially composite parts (silicon core or core with a silicon oxide shell), can easily be obtained.

[0024] In one embodiment, vibrational excitation can be performed using a shock device that applies an excitation to the part under test for a relatively short time. In other words, a displacement or acceleration can be imposed on the parts under test for a very short period (less than one second, less than 500 ms, less than 100 ms, less than 10 ms). Specifically, the shock device can apply a shock to the spiral or its support to cause the parts to vibrate. An impact hammer or any device with a moving mass can be used. In the case of parts attached to a plate, the shock can be applied to the plate itself or to a fixture supporting the plate. Depending on the part under test and its position on the plate, the shock can be applied to a specific location on the plate and / or in a specific direction.The parts begin to vibrate and the vibrational response can be recorded over time, in order to extract from this measurement resonance peaks and their frequencies, for example with a Fourier transform.

[0025] According to one embodiment, the watchmaking system including the balance spring may comprise: the balance spring, and a balance wheel, the balance spring, a balance wheel, and an escapement device, such as an anchor escapement, the balance spring, a balance wheel, an escapement device, and a gear train, such as a finishing gear train, the entire movement of the watch, including the balance spring. In all the above cases, it is possible to know in advance the thermal coefficient of the parts other than the balance spring, or at least their contribution to the thermal coefficient of the watchmaking system. In practice, these values ​​are standard and known in advance based on the chosen references or components, and in the case of a silicon balance spring, it is possible to adjust the contribution of the spiral in equation 5 above to obtain a thermal coefficient of the watchmaking system which will be in a range of values ​​and / or in a desired tolerance(s).

[0026] 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 reference frame (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. In other words, the vibrational excitation is applied to the spiral alone or to the spiral blank alone.

[0027] It can also be noted that if it is determined that dimensional correction and / or additional treatment is required 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, it is possible to apply oxidation directly to a silicon part immediately after testing). Therefore, it is possible to add or remove material from the individual part(s), or to apply doping to modify intrinsic values ​​(stiffness, Young's modulus thermal conductivity (TMC) of the spiral). In other words, the dimensional correction and / or additional treatment are performed on the individual part(s).

[0028] 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) and / or additional treatments are then possible. The process described above is equally suitable for testing finished balance springs, for example, to classify them by stiffness increments or to ensure compatibility with a specific balance wheel.

[0029] According to one embodiment, Step b. may include: b1. a first identification step which may include the identification of a first characteristic of a first resonance frequency such as a first resonance peak, b2. a second identification step which may include the identification of a second characteristic of a second resonance frequency such as a second resonance peak, the second resonance frequency being different from the first resonance frequency, and step c. may include: c1. a first prediction step which may consist of submitting to another prediction machine the first characteristic of the first resonance frequency to determine a parameter different from the thermal coefficient of the Young's modulus (CTE) of the balance spring and / or the thermal coefficient (CT) of a watchmaking system including the balance spring, such as a stiffness or defect of the balance spring or balance spring blank, c2.a second prediction step which may consist of submitting to the thermal coefficient prediction machine the second characteristic of the second resonance frequency to determine the thermal coefficient of the Young's modulus (CTE) of the balance spring and / or the thermal coefficient (CT) of a watchmaking system including the balance spring.

[0030] According to the embodiment described above, the first resonance frequency is used to determine a parameter other than the Young's modulus thermal coefficient (TMC) of the balance spring and / or the thermal coefficient (TC) of a timekeeping system including the balance spring, such as the stiffness or a defect of the balance spring or the balance spring blank. The second resonance frequency is used to determine the Young's modulus thermal coefficient (TMC) of the balance spring and / or the thermal coefficient (TC) of a timekeeping system including the balance spring. In other words, two different frequencies are selected or identified to predict or calculate two distinct parameters (stiffness or the presence of a defect on the one hand, and the Young's modulus thermal coefficient (TMC) of the balance spring and / or the thermal coefficient (TC) of a timekeeping system on the other).

[0031] In one embodiment, another predictive machine may be provided to identify a defect requiring rework or rejection of the part in question. According to this implementation, the spiral with the identified defect cannot be used at all, or cannot be used without physical modification of its geometry and / or composition and / or material. In other words, if a defect is identified or determined, a step can be taken to isolate and / or set aside the part for physical rework (modification or rejection). The part then follows a manufacturing path dedicated to non-conforming parts, which includes a rework or rejection step.

[0032] According to one embodiment, steps b1 and b2 may be separated by a thermal compensation step such as an oxidation step, and step a may include: a1. a first step of vibratory excitation, which can be carried out before step b1. and which consists of applying to the spiral or the spiral blank a first vibratory excitation which varies over time to cover a first predetermined frequency range, a2. a second step of vibratory excitation, which can be carried out before step b2. and which consists of applying to the oxidized spiral or the oxidized spiral blank a second vibratory excitation which varies over time to cover the first predetermined frequency range or a second predetermined frequency range.

[0033] According to the implementation described above, the first vibration excitation step determines stiffness or the presence of a defect, and the second vibration excitation step determines the Young's modulus thermal coefficient (TMC) of the balance spring and / or the thermal coefficient (TC) of a watchmaking system. Different vibration excitations can be applied between steps a1 and a2.

[0034] According to one embodiment, Step a can be implemented after an oxidation step, and steps b1 and b2 can take into account, or be based on, the same vibrational response of the spiral or spiral blank. In other words, a first part of the vibrational response is used to identify the first resonant frequency, and a second part of the same vibrational response is used to identify the second resonant frequency.

[0035] According to one embodiment: the first resonance frequency can be chosen to be a resonance frequency of a planar resonance mode, preferably for high resonance frequencies, for example above 40 kHz, or above 60 kHz, and / or the second resonance frequency can be chosen to be a resonance frequency of an out-of-plane resonance mode.

[0036] According to the implementation described above, a planar resonance mode can be considered one in which the different parts of the spiral or spiral blank move primarily in the plane of the part at rest. If this plane is defined by the X and Y directions, with the Z direction normal to the plane, then the displacements in X or Y are greater than or equal to the displacements in Z. In an out-of-plane resonance mode, the displacements in Z are greater than or equal to the displacements in X or Y, and preferably the displacements in Z are two to three times greater than the displacements in X or Y. The applicant has observed that an oxidized part can exhibit significantly different out-of-plane resonance mode frequencies compared to the same parts without oxidation.Consequently, to accurately predict a Young's modulus thermal coefficient (CTE) of the balance spring and / or a thermal coefficient (CT) of a watchmaking system including the balance spring, it may be preferable to consider an out-of-plane resonance mode.

[0037] According to one embodiment, the first resonant frequency may be lower than the second resonant frequency and / or: The first resonance frequency can be chosen from a range of values ​​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, and / or the second resonance frequency can be chosen from a range of values ​​from 0 Hz to 300 kHz, preferably from 50 kHz to 250 kHz, more preferably from 60 kHz to 200 kHz, and most preferably from 100 kHz to 200 kHz. The applicant has observed that an oxidized part can exhibit significantly different resonance mode frequencies compared to the same parts without oxidation for resonance frequencies above 40 kHz, preferably above 50 kHz, and most preferably above 60 kHz.Consequently, to accurately predict a Young's modulus thermal coefficient (CTE) of the balance spring and / or a thermal coefficient (CT) of a watchmaking system including the balance spring, it may be preferable to consider resonance modes with high resonance frequencies.

[0038] According to one embodiment, step b. may consist of identifying a characteristic of a resonance frequency sensitive to the thermal coefficient of the spiral or spiral blank.

[0039] 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.

[0040] 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.

[0041] 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.

[0042] It should be noted that the process can determine a Young's modulus thermal coefficient (CTE) of the balance spring and / or a thermal coefficient (TC) of a watchmaking system including the balance spring. This can be used to classify the component, and / or to determine its compatibility with other specific components, and / or to subsequently calculate / deduce a dimensional correction and / or additional treatment(s) to be applied to obtain a target Young's modulus thermal coefficient (CTE) of the balance spring and / or a target thermal coefficient (TC) of a watchmaking system including the balance spring. However, it is also possible to consider only the identified resonance frequency to directly calculate / deduce a dimensional correction and / or additional treatment(s) to be applied to obtain a target Young's modulus thermal coefficient (CTE) of the balance spring and / or a target thermal coefficient (TC) of a watchmaking system including the balance spring.

[0043] 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.

[0044] 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.

[0045] In one embodiment, the spiral can exhibit at least two predetermined expected resonant frequencies, and the frequency range is predetermined to cover at least these two predetermined expected resonant frequencies. By covering or sweeping a wide frequency range, several resonant peaks (or resonant frequencies) can be measured, which can provide greater accuracy.

[0046] 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.

[0047] 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.

[0048] 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.

[0049] According to one embodiment, step b includes the use of an optical measuring means, such as a laser Doppler vibrometer.

[0050] According to one embodiment, step b can be based on a time-based measurement of the amplitude, velocity, or acceleration of displacement of at least one point of the spiral or spiral blank, preferably carried out at least partially during step a.

[0051] 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.

[0052] According to one embodiment, the spiral or spiral blank may be contained within a base plane, and step b may include: 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 blank 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 blank along a direction contained in the base plane.

[0053] Measuring displacements or speeds in multiple directions allows for better identification of resonance peaks and frequencies.

[0054] According to one embodiment, step b. may include: 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.

[0055] In one embodiment, the resonance frequency characteristic can be identified based on the width of the resonance peak, half the maximum value of the resonance peak. This processing method limits calculation errors that could occur if the method relied solely on identifying the frequency position of the peak defined by its maximum value.

[0056] 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.

[0057] In one embodiment, the thermal coefficient prediction machine can be a computing machine for predicting or calculating, from frequency characteristics, the thermal coefficient of the Young's modulus (TCM) of the balance spring and / or the thermal coefficient (TC) of a watchmaking system including the balance spring. In other words, the prediction machine is not a regulated, self-regulating, or feedback-loop system for adjusting a resonant frequency in response to a measurement and comparison with a target value.

[0058] In other words, the prediction machine is a computing machine, which may be a computing unit designed to implement one or more mathematical formulas to predict a Young's modulus thermal coefficient (CTE) value of the balance spring and / or a thermal coefficient (CT) value of a watchmaking system including the balance spring, when it receives as input a value of a physical characteristic measured on the balance spring or balance spring blank.

[0059] According to one implementation, the prediction machine, for example the computing unit, can be designed to implement one or more mathematical formulas (for example with a polynomial law) constructed by linear regression from experimental or simulation data.

[0060] According to one implementation, the prediction machine, for example the computing unit, can be a prediction machine using artificial intelligence software.

[0061] According to one implementation, the prediction machine, for example the computing unit, may be a prediction machine using at least one neural network designed to receive as input values ​​or graphs taken from vibration measurement spectra and designed to give as output a thermal coefficient of the Young's modulus (CTE) of the balance spring and / or a thermal coefficient (CT) of a watchmaking system including the balance spring.

[0062] According to one embodiment, the thermal coefficient prediction machine can implement a classification carried out for example by a neural network to predict the thermal coefficient of the Young's modulus (CTE) of the balance spring and / or the thermal coefficient (CT) of a watchmaking system including the balance spring.

[0063] According to one embodiment, the thermal coefficient prediction machine can implement a regression method, for example linear regression to predict the thermal coefficient of the Young's modulus (CTE) of the balance spring and / or the thermal coefficient (CT) of a watchmaking system including the balance spring.

[0064] According to one embodiment, the thermal coefficient prediction machine can implement a classification based on a k-means or k-median partitioning to predict the thermal coefficient of the Young's modulus (CTE) of the balance spring and / or the thermal coefficient (CT) of a watchmaking system including the balance spring.

[0065] According to one embodiment, the control process may include 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.

[0066] According to one embodiment, if step c. determines that the thermal coefficient of the Young's modulus (CTE) of the balance spring and / or the thermal coefficient (CT) of a watchmaking system including the balance spring is outside a range of expected values, then the process may include at least one step of identifying or isolating or retouching or discarding the balance spring or balance spring blank.

[0067] According to one embodiment, if step c determines that the thermal coefficient of Young's modulus (CTE) of the balance spring and / or the thermal coefficient (CT) of a watchmaking system including the balance spring is outside a range of expected values, then the process may include at least one step consisting of defining a treatment step for the balance spring or balance spring blank, such as a thermo-compensation, oxidation, or deoxidation step, to obtain the thermal coefficient of Young's modulus (CTE) of the balance spring and / or the thermal coefficient (CT) of a watchmaking system including the balance spring within the range of expected values.

[0068] According to one embodiment, step a. is carried out for a plurality of balance springs or balance spring blanks attached to a plate, and if step c. determines that the thermal coefficient of Young's modulus (CTE) of the balance spring and / or the thermal coefficient (CT) of a watchmaking system including the balance spring is outside a range of expected values ​​for first balance springs or first balance spring blanks and within the range of expected values ​​for second balance springs or second balance spring blanks, then it may be provided that only the second balance springs or second balance spring blanks are detached and a treatment step for the first balance springs or first balance spring blanks, such as a thermo-compensation, oxidation or deoxidation step, may be provided to obtain the thermal coefficient of Young's modulus (CTE) of the balance spring and / or the thermal coefficient (CT) of a watchmaking system including the balance spring within the range of expected values.We can plan to repeat these steps, repeating steps a. and b. or not.

[0069] 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.

[0070] 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.

[0071] A second aspect of the invention relates to a method for manufacturing a spiral having at least one predetermined expected resonant frequency, comprising the steps of: A / form at least one spiral or spiral blank having dimensions within predetermined tolerances necessary to obtain the expected predetermined resonant frequency, B / inspect the spiral or spiral blank according to the inspection procedure of the first aspect.

[0072] According to one embodiment, the manufacturing process may include a step consisting of: C / identifying or isolating or retouching or discarding the spiral or spiral blank formed during step A / , if step c. determines that the thermal coefficient of the Young's modulus (CTE) of the spiral and / or the thermal coefficient (CT) of a watchmaking system including the spiral is outside a range of expected values.

[0073] According to one embodiment, the spiral blank can be formed on a plate, with a plurality of other spiral blanks.

[0074] A third aspect of the invention may relate to a method for learning a prediction machine to implement step c of the control method according to the first aspect, comprising the steps of: i- to form spirals or spiral blanks and apply a thermo-compensation step to them, ii- to apply to each of the spirals or spiral blanks a variable vibrational excitation (i.e. a variable vibrational excitation which encompasses, or preferably the same variable vibrational excitation as, that used during the control process) over time to cover a predetermined frequency range (i.e. a predetermined frequency range which encompasses, or preferably the same predetermined frequency range as, that used during the control process), iii- to identify at least one characteristic of a resonance frequency (i.e. a characteristic of a resonance frequency which encompasses, or preferably the same characteristic of a resonance frequency as, that identified during the control process),of each spiral or spiral blank during the application of the predetermined frequency range and record the temperature of the parts during step ii- and / or iii-, iv'- mount a plurality of spirals or spiral blanks in an oscillating mechanism having a predetermined inertia so as to measure for each spiral or spiral blank a sustained oscillation frequency, and / or a rate of the clockwork system formed by, or comprising, the oscillating mechanism at at least one predetermined temperature and preferably at at least two predetermined temperatures,and / or iv"- model in a simulation tool a plurality of balance springs or balance spring blanks in an oscillating mechanism exhibiting a predetermined inertia so as to calculate for each balance spring or balance spring blank a sustained oscillation frequency and / or thermal coefficient of a clockwork system including the balance spring and / or the rate of the clockwork system including the balance spring at at least one predetermined temperature and preferably at at least two predetermined temperatures, v- optionally, deduce at least one expected resonance frequency from the resonance frequency identified in step iii-,and / or the sustained oscillation frequency and / or the rate of the clockwork system measured in step iv'- and / or calculated in step iv"- vi- deduce a thermal coefficient of the Young's modulus (CTE) of the balance spring and / or the thermal coefficient (CT) of a clockwork system including the balance spring from the measurements in step iv'- and / or the calculations in step iv"- vii- provide the prediction machine, for each balance spring or balance spring blank: the characteristic of the resonance frequency identified in step iii- ; optionally, the same characteristic of the expected resonance frequency; the temperature recorded during step ii- and / or iii- ; the thermal coefficient of the Young's modulus (CTE) of the balance spring and / or the thermal coefficient (CT) of a clockwork system including the balance spring deduced in step vi-. , Brief description of the drawings

[0075] Further details of the invention will become clearer upon reading the following description, made with reference to the attached drawings in which: there figure 1 shows 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 for tested parts, the Figure 10 represents an example of a prediction model built from data extracted from the figure 9 , there figure 11 shows the influence of temperature on the resonance frequency of a particular resonance mode, the figure 12 shows the sensitivity of the resonance frequency to the oxide thickness of a silicon spiral. Method of embodying the invention

[0076] THE figures 3A-3Fare 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.

[0077] 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.

[0078] A lithography stage is shown to Figures 3BAnd 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 3B In 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 .

[0079] Subsequently, in the next step of the 3D figureThe 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.

[0080] 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).

[0081] 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.

[0082] 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.

[0083] 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.

[0084] Finally, it should be noted that during manufacturing, more localized manufacturing defects may appear. For example, during the machining stage of the 3D figureSome material may remain between two adjacent turns. We may also see parts where material residue is still present between the turns or the substrate, contrary to what is shown. figure 3E Bridges of matter can also form between two adjacent turns during the oxidation process shown. figure 3F Finally, contamination can also occur with debris or particles becoming trapped between two turns or between the turns and the substrate. All these defects significantly affect vibrational behavior and cannot be corrected by adding or removing material from all the parts, as is known to be done in the prior art.

[0085] The description above relates to silicon resonators, but it is possible to fabricate resonators from glass, ceramic, carbon nanotubes, or even metal. In particular, conventional steel spirals or spirals detached from the wafer can be tested. In this case, the metal spiral or the spiral detached from the wafer is pinched or referenced by a tool that positions it opposite the emission source and the displacement measurement device.

[0086] As is known, the stiffness of the balance spring can be measured statically, that is, without oscillating the spring, but by determining its torque. For example, see document EP3654111.

[0087] An alternative to the method described in the latter document is to perform a torque measurement using a rheometer, such as those marketed by Anton Paar. A device designed for this purpose is illustrated in the figure 4Advantageously, it allows the spiral 200 to be evaluated to be placed on a fixture 202, and positioned so that it can be secured at its last turn by a holding element 204. Once the last turn is secured, the fixture 202 is moved away from the spiral 200, which is thus completely free of any elastic stress. The head of the rheometer 206 is then positioned opposite the spiral's ferrule. It has a non-circular, but smaller, counterform of the ferrule, which allows the rheometer head to engage in the ferrule with controllable precision, without contacting the spiral. The rheometer head is then rotated in the direction of spiral contraction. When the head makes contact with the ferrule, it pulls it along, and the rheometer measures the torque exerted by the elastic return of the spiral over a given angle.However, such a measure remains a unitary measure and requires significant handling time, with numerous risks of breakage and pollution.

[0088] The present invention proposes to determine at least one characteristic of a resonance frequency of a sample of 100 resonators on the plate at step 3F, to deduce a thermal coefficient of the Young's modulus (CTE) of the balance spring and / or a thermal coefficient (CT) of a watchmaking system including the balance spring, and optionally at step 3E, to deduce stiffness and / or a structural defect. In particular, the present invention proposes to identify the above parameters without disassembling the plate or taking measurements in a test subset, using a method that is more efficient than prior art methods.

[0089] 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 identification of the thermal coefficient of the Young's modulus (CTE) of the balance spring and / or the thermal coefficient (CT) of a watchmaking system including the balance spring.

[0090] 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 thermal coefficient of the Young's modulus (CTE) of the spiral and / or the thermal coefficient (CT) of a watchmaking system including the spiral at certain frequencies (natural frequency or resonance frequencies associated with a resonance peak or a full width at half maximum) specifically chosen.

[0091] Once the learning phase is complete (once the operating modes and excitation frequencies have been determined), it is possible to move to a prediction phase and use the prediction machine. This machine leverages the predictive model to control the resonators of a produced wafer, in order to predict the Young's modulus thermal coefficient (CTE) of the balance spring and / or the thermal coefficient (TC) of a watch system including the balance spring. The prediction result can be used to validate produced parts, and / or to determine additional processing to correct the Young's modulus thermal coefficient (CTE) of the balance spring and / or the thermal coefficient (TC) of a watch system including the balance spring, and / or to discard parts that do not conform to the Young's modulus thermal coefficient (CTE) of the balance spring and / or the thermal coefficient (TC) of a watch system including the balance spring.

[0092] Thus, it is possible to integrate the control process into a manufacturing process to obtain parts that are capable of achieving, maintaining, and generating a specific and predetermined natural frequency of oscillation, independent of temperature variations, once the resonators are each coupled to a balance wheel of a given watch mechanism.

[0093] It should be noted that the prediction machine is a device that allows for the prediction, and therefore the calculation or provision, in advance, of the Young's modulus thermal coefficient (TMC) values ​​of the balance spring and / or the thermal coefficient (TC) of a watchmaking system including the balance spring, based on one or more measured resonance frequencies, without coupling the balance spring to a balance wheel and without performing tests at various temperatures. It can be predicted that the prediction machine: is based on a mathematical model (for example a polynomial law relating one or more resonance frequencies to the thermal coefficient of Young's modulus (CTE) of the balance spring and / or to the thermal coefficient (CT) of a watchmaking system including the balance spring), uses a neural network to receive as input values ​​or graphs taken from vibration measurement spectra to give as output a thermal coefficient of Young's modulus (CTE) of the balance spring and / or a thermal coefficient (CT) of a watchmaking system including the balance spring, implements a system using artificial intelligence. Vibrational excitation

[0094] 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, for example from 0 to 300 kHz, preferably from 0 to 275 kHz, preferably from 0 to 250 kHz, preferably from 5kHz to 250 kHz, and preferably from 10 to 235 kHz.The entire frequency range can be 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.

[0095] 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.

[0096] Furthermore, a signal sampling frequency of at least 600 kHz can be chosen if the frequency range extends up to 300 kHz, for example. Generally, Shannon's theorem can be followed, which advises choosing a sampling frequency greater than twice the maximum frequency present in the measured signal.

[0097] 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.

[0098] 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

[0099] 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.

[0100] 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.

[0101] 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.

[0102] 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 (but can be extended up to 300 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 200 spiral 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

[0103] 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.

[0104] 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. The predetermined points can be selected and arranged on an orthonormal XY coordinate system in the plane of the spiral.

[0105] 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.

[0106] 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).

[0107] 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.

[0108] 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.

[0109] Alternatively, one can plan to measure displacements / movements / vibrations only at a specific point, preferably located in a non-deforming area of ​​the part. Specifically, one can plan to target a point on the spiral shell or spiral blank. Indeed, the shell can be considered rigid during vibrational excitation, and all points on the shell exhibit similar displacements / movements / vibrations. Consequently, a small error in locating the measurement point on the shell will have little impact on the final result. Furthermore, by choosing a specific measurement point on the part, one can identify and select a particular frequency range for predicting stiffness.

[0110] 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, recognize each type of part, and / or the position of each part, a step of selecting one or more points to be measured for each part, and / or of selecting a vibrational excitation spectrum to be imposed for each part and / or each selected point, for each part to be tested, a step of positioning the substrate or the tooling supporting the parts to be tested in a vibrational excitation and measurement device.According to this implementation, excitation and measurement can be automated in the case of a wafer that still carries the spiral blanks: one or more images of the wafer are taken, an automatic image analysis is performed to know at least the XY position of each part (it is also possible to recognize the type or model of the part), depending on the position and / or type of part recognized, specific pre-established measurement points are identified or selected (for example on the ferrule), it is also possible to select a specific excitation cycle depending on the type of part or a specific point, with for example a tooling that carries the wafer and which includes a moving table in XY, each spiral blank is successively automatically placed opposite the excitation source and the measuring device to be tested by aiming at the correct measurement point and applying the correct excitation specification.

[0111] 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, a measurement direction (or an axial direction of a laser beam from the measuring device) perpendicular to the part being tested can be chosen to maximize the measurement accuracy of displacements perpendicular to the plane formed by the part at rest. A measurement direction (or an axial direction of a laser beam from the measuring device) inclined relative to the part being tested can be chosen to maximize the measurement accuracy of displacements contained within the plane formed by the part at rest.

[0112] 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 other words, this preliminary sampling enables the testing of individual parts under optimal conditions (measurement errors and interference are limited) in order to select the best test conditions for the parts remaining attached to the substrate. Determination of vibrational characteristics

[0113] 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 f₀, 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 multiple peaks at several 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 multiple peaks at several 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.

[0114] 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.

[0115] There figure 7 represents an example of a vibration spectrum for a point on a 200 spiral blank of the figure 5 free from defects, 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 250 amplitude peaks can typically be identified if the vibrational excitation sweeps across a frequency range between 0 Hz and 300 kHz. Each amplitude peak has a resonant frequency, and the maximum amplitudes vary considerably.

[0116] There figure 8This document details the processing that can be performed on an amplitude peak for a defect-free part, 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.

[0117] 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 can be useful to determine the resonant frequency based on the full width at half maximum (FWHM). The FWHM can also be used to determine damping and compare this damping to a reference value.

[0118] 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

[0119] With reference to the manufacturing process described in figures 3A-3F An initial optional measurement can be carried out on the parts described figure 3E To estimate the stiffness of unoxidized parts, in order to determine whether dimensional correction is required. Alternatively, the first optional measurement could be taken after an oxidation step adding a predetermined thickness of oxide, from which any necessary dimensional corrections are made. Once the parts are oxidized (i.e., with a thermo-compensation treatment), the invention proposes to perform a second measurement to determine a thermal coefficient of Young's modulus (TCM) of the balance spring and / or a thermal coefficient (TC) of a watchmaking system including the balance spring.

[0120] Consequently, we will first describe the steps implemented to determine the stiffness of the parts.

[0121] Determination of the stiffness and / or actual dimensions of the tested resonator bar

[0122] 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.

[0123] 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 completing the fabrication of the tested resonators, then mounting them individually or coupling them with a pendulum pair to again measure the natural frequency of oscillation of the resonator-pendulum pair.

[0124] 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.

[0125] 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.

[0126] 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.

[0127] 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.

[0128] 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.

[0129] 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.

[0130] 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 following stiffness values ​​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

[0131] To predict stiffness, reference data, such as a reference spectrum, must first be established or constructed. During the training phase, oscillation amplitude measurements are taken on physical resonators, and resonance frequencies are identified. To subsequently link these measured resonance frequencies to stiffness values ​​and / or dimensional (thickness) corrections, a correlation phase is necessary, during which a predictive model is built.

[0132] 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 correlate the spiral's position on the wafer, oscillation spectra or periods, or FWHM and its midpoint or corrected value with the effective stiffness and / or dimensions of the spiral bar. As seen 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 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.

[0133] This database can be used to build a prediction model, and several solutions are available.

[0134] 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.

[0135] 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.

[0136] 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.

[0137] 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 model building phase can begin.

[0138] 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

[0139] 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 , With R for stiffness in 10⁻⁷ N.mm² F for resonance frequency in Hz.

[0140] 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%

[0141] 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.

[0142] 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 high 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.

[0143] 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.

[0144] 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.

[0145] 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.

[0146] 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.

[0147] 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

[0148] 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.

[0149] Once the model is trained, the control procedure to be deployed can be 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.

[0150] 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.

[0151] 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

[0152] 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.

[0153] 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.

[0154] We can even consider going so far as to evaluate all the spirals of the wafer, in particular with a vibrational evaluation, because this is very quick to perform and can allow automation of the process.

[0155] 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.

[0156] The method, which involves identifying resonance frequencies by applying vibrational excitation to the balance spring blanks alone, allows for the rapid acquisition of measurement data without the need for, for example, assembling a balance wheel. It also minimizes measurement errors because only the balance spring blank is tested (eliminating errors related to the balance wheel itself, such as its mass, mounting position, etc.). This method enables the prediction of the Young's modulus thermal coefficient (TMC) of the balance spring and / or the thermal coefficient (TC) of a watchmaking system that includes the balance spring.

[0157] For the aspect relating to the prediction of the thermal coefficient of the Young's modulus (CTE) of the balance spring and / or the thermal coefficient (CT) of a watchmaking system including the balance spring, the following procedure can be used: Step 1: Measure or calculate the natural or resonant frequencies on a plate at several temperatures T (for example 8°C, 23°C and 38°C); Step 2: Detach the balance springs, assemble them with a balance wheel and mount them in movements; Step 3: Measure the thermal coefficients (TC) in motion according to the procedure of the Official Swiss Chronometer Testing Institute (COSC) for example (24h at 8°C, 24h at 23°C and 24h at 38°C); Step 4: Build a predictive model between the natural or resonant frequencies measured in step 1 and the thermal coefficients (TC) of the movement measured in step 4.

[0158] During step 1, it can be difficult to perform vibration measurements at multiple temperatures. One option is to perform vibration measurements at a single temperature (e.g., 23°C, the cleanroom temperature) and then build a numerical model capable of estimating the evolution of natural frequencies with temperature, using the following procedure: Construct a finite element model of a spiral with a silicon oxide layer; Assign the relevant material parameters and their evolution with temperature; Perform a modal analysis over the temperature range [8°C 38°C]; Plot the evolution of the natural or resonance frequencies as a function of temperature and for different oxide layer thicknesses.

[0159] With these evolution laws, it becomes possible to predict the desired natural frequencies from a single experimental vibration measurement carried out at 23°C. However, one could imagine different heating systems, such as ovens or conduction heating, to identify these laws experimentally.

[0160] The result of such a prediction can be observed figure 11 where the resonance frequencies of the same resonance mode (number x among, for example, 240 identified resonance modes) are represented for three distinct temperatures T1, T2, T3. A difference in the value of the resonance peak frequency can be observed between the three temperatures.

[0161] Furthermore, the plaintiff observed that the resonance frequency was significantly affected by different oxidation values.

[0162] (involving variations in the thermal coefficient of the Young's modulus (CTE) of the balance spring and therefore variations in the thermal coefficient (CT) of a watchmaking system including the balance spring) for certain resonance modes only.

[0163] In detail, a sensitivity analysis of the resonance frequency to the oxidation value was performed for approximately 240 resonance modes identified with the equation below: S = Var E Y Xi Var Y

[0164] There figure 12shows that the sensitivity of the resonance frequency to the oxide layer thickness for predicting the thermal coefficient of Young's modulus (CTE) of the balance spring and / or the thermal coefficient (CT) of a watchmaking system including the balance spring (CT curve) increases for certain resonance modes from approximately the 100th identified resonance mode onward. It can be concluded that it is advantageous to consider resonance modes with high resonance frequencies for predicting the thermal coefficient of Young's modulus (CTE) of the balance spring and / or the thermal coefficient (CT) of a watchmaking system including the balance spring. However, the same figure 12This shows that the sensitivity of the resonance frequency to the oxide layer thickness and / or the ratio of silicon core thickness to silicon oxide thickness, for predicting stiffness (R-curve), decreases for certain resonance modes starting from approximately the 100th identified resonance mode. It can be concluded that it is advantageous to consider resonance modes with low resonance frequencies when predicting spiral stiffness.

[0165] Furthermore, the applicant observed that for resonance modes with high frequencies, the sensitivity of the resonance frequency is particularly high for so-called "out-of-plane" resonance modes, whereas so-called "plane" resonance modes do not exhibit any particular sensitivity. It can be concluded that it is advantageous to consider "out-of-plane" resonance modes with high resonance frequencies to predict the Young's modulus thermal coefficient (TMC) of the balance spring and / or the thermal coefficient (TC) of a watchmaking system including the balance spring. Conversely, it is advantageous to consider "plane" resonance modes to predict the stiffness of the components.

[0166] Step 3 can be carried out by detaching the parts measured in step 1 and mounting them in a reference movement, and the operation of these movements can be measured according to the three temperatures 8°C, 23°C, 38°C.

[0167] To establish a thermal coefficient prediction model that can receive as input the vibrational characteristics and give as output the thermal coefficient of the Young's modulus (CTE) of the balance spring and / or the thermal coefficient (CT) of a watchmaking system including the balance spring, we can therefore use the resonance frequency data identified at the three temperatures for the parts taken into account, and the rate data at the three temperatures for these same parts.

[0168] Once the thermal coefficient prediction model is established, a thermal coefficient prediction machine can use it to predict, from, for example, resonance frequency data for an out-of-plane resonance mode with a high resonance frequency, the thermal coefficient of the Young's modulus (TCM) of the balance spring and / or the thermal coefficient (TC) of a watchmaking system including the balance spring. Of course, when predicting the thermal coefficient (TC) of a watchmaking system including the balance spring, the thermal coefficient prediction machine can take as input the reference of the watchmaking device in question, or its value or contribution to the thermal coefficient. Indeed, for a given caliber reference, the various parameters that influence the TC of the movement (temperature sensitivity of the balance wheel, gear train, bearings, lubricants, etc.) can be considered.) are constant and do not constitute adjustment variables.

[0169] There is no longer a need to assemble movements to measure the thermal coefficient (TC) of a watchmaking system including the balance spring; this time-consuming step and source of variability can be eliminated.

[0170] It would be possible to do an iterative treatment on parts of the same plate: after predicting the thermal coefficient of the Young's modulus (CTE) of the balance spring and / or the thermal coefficient (CT) of a watchmaking system including the balance spring, we could detach only the parts having the desired performance, and apply a new thermo-compensation step (oxidation and / or deoxidation) to the parts that are identified as incompatible or not conforming to the desired performance.

[0171] In summary, the invention simplifies the manufacturing and control processes of silicon resonators for producing movements with low or no sensitivity to temperature variations: By applying a specific vibrational excitation to oxidized parts, and providing the vibrational response, resonance frequencies, resonance peaks, or data extracted from the vibrational response to a thermal coefficient prediction machine, one can easily verify whether the parts have thermal compensation suitable for the movement in which they will be mounted. It can be noted that, optionally, at a previous manufacturing stage (before thermal compensation or oxidation, for example), a specific vibrational excitation can be performed, and the resulting vibrational response, resonance frequencies, resonance peaks, or data extracted from the vibrational response can be submitted to a machine for predicting stiffness or the presence of structural defects, such as: One or more turns glued or bridged to an adjacent turn, to the rest of the wafer, such as the insulating support, a porosity, local or otherwise, of the material or the oxide, an interface between a silicon core and an oxide layer with a void, a detachment, irregularities..., an irregular or interrupted oxide thickness..., a local defect or lack of material, such as a leakage defect, an excess of material, linked for example to a masking defect, a heterogeneity of the material (silicon, silicon oxide), a flatness defect (smoothing) of the lateral edges of the bar forming the spiral, a verticality defect of the lateral edges of the bar forming the spiral (a draft or undercut of the faces), turns that are deformed, wavy or off-center with respect to the theoretical position...

[0172] However, it can be noted that the data taken from the vibration response and used for these predictions of stiffness or presence of defects are not necessarily the same as those for the prediction of the thermal coefficient and it can even be considered that preferably, the data taken from the vibration response and used are different and distinct from those for the prediction of the thermal coefficient.

Claims

1. A method of inspection of a hairspring or a hairspring blank arranged to form a hairspring, the inspection method including the following steps: a. applying to the hairspring or to the hairspring blank a vibrational excitation variable over time to cover a predetermined frequency range; b. identifying at least one characteristic of a resonance frequency of the hairspring or of the hairspring blank, such as a resonance peak, during or in response to the vibrational excitation over the predetermined frequency range, characterized in that it also includes the following step: c. submitting to a thermal coefficient prediction machine said at least one resonance frequency characteristic identified in step b in order to determine a thermal coefficient of the Young's modulus (TCE) of the hairspring and / or a thermal coefficient (TC) of a clockmaking system comprising the hairspring.

2. The inspection method according to claim 1, wherein step b comprises: b1. a first identification step comprising the identification of a first characteristic of a first resonance frequency such as a first resonance peak, b2. a second identification step comprising the identification of a second characteristic of a second resonance frequency such as a second resonance peak, the second resonance frequency being different from the first resonance frequency, and wherein step c comprises: c1. a first prediction step consisting in submitting to another prediction machine the first characteristic of the first resonance frequency in order to determine a parameter different from the thermal coefficient of the Young's modulus (TCE) of the hairspring and / or from the thermal coefficient (TC) of a clockmaking system comprising the hairspring, such as a stiffness or a defect in the hairspring or in the hairspring blank, c2. a second prediction step consisting in submitting to the thermal coefficient prediction machine the second characteristic of the second resonance frequency in order to determine the thermal coefficient of the Young's modulus (TCE) of the hairspring and / or the thermal coefficient (TC) of a clockmaking system comprising the hairspring.

3. The inspection method according to claim 2, wherein steps b1 and b2 are separated by an oxidation step, and wherein step a comprises: a1. a first vibrational excitation step, carried out before step b1 and consisting in applying to the hairspring or to the hairspring blank a first vibrational excitation variable over time to cover a first predetermined frequency range, a2. a second vibrational excitation step, carried out before step b2 and consisting in applying to the oxidized hairspring or to the oxidized hairspring blank a second vibrational excitation variable over time to cover the first predetermined frequency range or a second predetermined frequency range.

4. The inspection method according to claim 2, wherein step a is implemented after an oxidation step, and wherein steps b1 and b2 take into account the same vibrational response of the hairspring or of the hairspring blank.

5. The inspection method according to any of claims 2 to 4, wherein: - the first resonance frequency is chosen to be a resonance frequency of an in-plane resonance mode, and / or - the second resonance frequency is chosen to be a resonance frequency of an out-of-plane resonance mode.

6. The inspection method according to any of claims 2 to 5, wherein the first resonance frequency is lower than the second resonance frequency, and / or: - the first resonance frequency is chosen from a range of values ranging 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, and / or - the second resonance frequency is chosen from a range of values ranging from 0 Hz to 300 kHz, preferably from 50 kHz to 250 kHz, more preferably from 60 kHz to 200 kHz, and most preferably from 100 kHz to 200 kHz.

7. The inspection method according to any of claims 1 to 6, the hairspring having at least two predetermined expected resonance frequencies, wherein the frequency range is predetermined to cover at least the two predetermined expected resonance frequencies.

8. The inspection method according to any of claims 1 to 7, 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.

9. The inspection method according to any of claims 1 to 8, wherein the hairspring or the hairspring blank is 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.

10. The inspection method according to any of claims 8 or 9, 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.

11. The inspection method according to claim 10, wherein the characteristic of the resonance frequency is identified based on the width of the resonance peak at half the maximum value of the resonance peak.

12. The inspection method according to any of claims 1 to 11, wherein the thermal coefficient prediction machine implements a regression method, for example a linear regression, to predict the thermal coefficient of the Young's modulus (TCE) of the hairspring and / or the thermal coefficient (TC) of a clockmaking system comprising the hairspring.

13. The inspection 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 from the predetermined frequency range as a function of the material of the hairspring or of the hairspring blank.

14. The inspection method according to any of claims 1 to 13, wherein, if step c determines that the thermal coefficient of the Young's modulus (TCE) of the hairspring and / or the thermal coefficient (TC) of a clockmaking system comprising the hairspring is outside a range of expected values, then the method comprises at least one step consisting in identifying or isolating or reworking or discarding the hairspring or the hairspring blank.

15. The inspection method according to any of claims 1 to 13, wherein, if step c determines that the thermal coefficient of the Young's modulus (TCE) of the hairspring and / or the thermal coefficient (TC) of a clockmaking system comprising the hairspring is outside a range of expected values, then the method comprises at least one step consisting in defining a step of treating the hairspring or the hairspring blank, such as a thermo-compensation, oxidation or deoxidation step, to obtain the thermal coefficient of the Young's modulus (TCE) of the hairspring and / or the thermal coefficient (TC) of a clockmaking system comprising the hairspring within the range of expected values.

16. A method for learning a prediction machine to implement step c of the inspection method of any of claims 1 to 15, comprising the steps consisting in: i- forming hairsprings or hairspring blanks and applying a thermo-compensation step to them, ii- applying to each of the hairsprings or to each of the hairspring blanks a vibrational excitation variable 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 and recording the temperature of the pieces during steps ii- and / or iii-, iv'- mounting a plurality of hairsprings or hairspring blanks in an oscillating mechanism with a predetermined inertia so as to measure, for each hairspring or hairspring blank, a sustained oscillation frequency or a rate of the clockmaking system formed by, or comprising, the oscillating mechanism at least at one predetermined temperature and preferably at least at two predetermined temperatures, and / or iv''- modeling in a simulation tool a plurality of hairsprings or hairspring blanks in an oscillating mechanism with a predetermined inertia so as to calculate for each hairspring or hairspring blank a sustained oscillation frequency and / or a thermal coefficient of a clockmaking system comprising the hairspring and / or the rate of the clockmaking system comprising the hairspring at least at one predetermined temperature and preferably at least at two predetermined temperatures, v- optionally, deducing at least one expected resonance frequency from said at least one characteristic of a resonance frequency identified in step iii-, and / or of the sustained oscillation frequency and / or of the rate of the clockmaking system measured in step iv'- and / or calculated in step iv"- vi- deducing a thermal coefficient of the Young's modulus (TCE) of the hairspring and / or the thermal coefficient (TC) of a clockmaking system comprising the hairspring from the measurements of step iv'- and / or from the calculations of step iv"- vii- providing to the prediction machine, and for each hairspring or hairspring blank: - the characteristic of the resonance frequency identified in step iii-; - optionally, the same characteristic of the expected resonance frequency; - the temperature recorded during steps ii- and / or iii-; - the thermal coefficient of the Young's modulus (TCE) of the hairspring and / or the thermal coefficient (TC) of a clockmaking system comprising the hairspring deduced in step vi-

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