Method for controlling inertial clock elements

Abstract

A method for controlling an inertial element (100) or an inertial element blank (100) arranged to form an inertial element (100), the controlling method comprising the following steps: a. applying to the inertial element (100) or the inertial element blank (100) a time-varying vibrational excitation to cover a predetermined frequency range, b. identifying at least one characteristic of a resonant frequency of the inertial element (100) or the inertial element blank (100), such as a resonance peak, upon or in response to the vibrational excitation over the predetermined frequency range, c. subjecting said at least one resonant frequency characteristic identified in step b to a thermal coefficient prediction machine. to determine a coefficient of thermal expansion of the inertial element (100) and / or a thermal coefficient (CT) of a clock system comprising the inertial element (100)

Description

Technical field of the invention

[0001] The present invention relates to the field of control and manufacturing of parts for watchmaking. The invention relates more particularly to a method of controlling and manufacturing inertial elements (for example balance wheels) to be assembled in mechanical oscillators of mechanical watchmaking parts. State of the art

[0002] Mechanical watch movements are regulated by means of a mechanical regulator or oscillator comprising an elastic return member, i.e. an elastically deformable component, and an inertial element, the oscillations of which determine the rate of the watch. Many watches, for example, have an oscillator comprising a hairspring as an elastic return member, mounted on a balance staff also supporting a balance wheel and set into oscillation by an escapement. The natural frequency of the balance wheel-hairspring pair is used to regulate the rate of the watch and depends on several parameters, including the stiffness of the hairspring, the inertia of the balance wheel and the operating temperature.

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

[0004] The geometry of the balance also defines its intrinsic vibrational characteristics, such as the natural frequency and the resonance frequencies. In the present application, the natural frequency of an elastic system (an inertial element alone or a resonator-inertial element pair) is the frequency at which this system oscillates when it is in free evolution, i.e. without an exciting force. Furthermore, a resonance frequency of an elastic system (for example the inertial element alone) subjected to an exciting force is a frequency at which a local maximum of displacement amplitude can be measured for a given point of the elastic system. In other words, if the elastic system is excited with an excitation source of variable frequency over time, the displacement amplitude follows an upward slope before this resonance frequency, and follows a downward slope after, at any point which does not correspond to a vibration node.Typically, in such a test, the recording of the displacement amplitude as a function of the excitation frequency exhibits a displacement amplitude peak or resonance peak which is associated with or characterizes the resonance frequency.

[0005] The inertia of an inertial element typically depends on the characteristics of its material (its density), as well as its dimensions. The moment of inertia I gz of a solid with respect to a z axis passing through its center of gravity is given more specifically by: I gz = ∑ Δ m .r 2 with : r, the distance of an elementary volume from the z axis Δm, the mass of the elementary volume.

[0006] The natural frequency of the regulating organ formed by the hairspring of stiffness R coupled to a balance of inertia I is notably proportional to the square root of the stiffness of the hairspring and to the inverse of the square root of the inertia I gz . The main specification of a balance is its inertia I gz , which must be within a well-defined interval to be able to be paired with a spiral spring, having a given stiffness. This pairing operation is essential to precisely adjust the frequency of a mechanical oscillator.

[0007] To measure the inertia of a balance wheel, it can be coupled with a balance spring of known stiffness and reference, to measure the oscillation frequency. Alternatively, according to the Jaquerod and Defossez method, a balance wheel to be measured can be coupled with a complete reference oscillator of known inertia, which has a modified balance shaft with an elongated upper pivot that can receive the balance wheel to be measured. An oscillation frequency measurement with and without the balance wheel to be measured makes it possible to deduce the inertia of the balance wheel to be measured.

[0008] Thus, it is not possible to easily and quickly measure the inertia of a balance wheel without having to couple it to a reference element, balance spring or oscillator. In industrial production of balance wheels, these are manufactured by bar turning and their inertia is measured by sampling, in order to control the drifts, in particular linked to the wear of the cutting tools. The time required by the measuring operations can lead to production losses, if an inspection reveals a balance wheel outside the specifications, while production continues during the inspection. It is also not easy to determine the moment from which the parts produced are no longer within the planned specifications. In the context of production of parts by etching (for example silicon parts), the same long and complex operations are necessary to measure the inertia of a balance wheel.

[0009] Furthermore, the operating temperature is a parameter influencing the operation of the regulating organ, and we can derive equation 1 with respect to the 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, Ta, a reference temperature, as, the coefficient of thermal expansion of the balance spring α B , the coefficient of thermal expansion of the balance wheel.

[0010] We can rewrite this equation 3 as below: 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 thermoelastic coefficient.

[0011] The importance of magnetic fields in the modern environment has led watchmakers to use silicon parts in recent years, which are less sensitive to magnetic disturbances than metal parts. Very advantageously, several hundred silicon parts can be manufactured on a single wafer using micro-fabrication technologies.

[0012] It is very important that the characteristics of the oscillator are as stable as possible, in order to have a watch rate that is also stable, with in particular the least possible differences in rate depending on the operating temperature (summer-winter, wristwatch worn or not worn).

[0013] As shown in equation 4 above, temperature variations can lead to variations in rate with the thermal coefficient CT which depends in particular on the Young's modulus thermal coefficient, the thermal coefficient of expansion of the hairspring and the thermal coefficient of expansion of the balance rim. The oscillator parts and their thermo-compensation therefore make it possible to adjust the terms of equation 4 relating to the hairspring and / or the balance to obtain a thermal coefficient CT of the oscillator. By extension, we can also characterize the CT of a more extensive watchmaking system, which integrates the hairspring, going up to the CT of a complete caliber, by determining the thermal drift of the caliber integrating that of the escapement, the gear train, including the influence of lubrication.In this perspective, the hairspring and / or the balance wheel are considered as being the adjustment variables to obtain a CT of the watch system which integrates it, as low as possible. Statement of the invention

[0014] The present invention aims to propose an approach free from the above drawbacks, which allows a faster production flow and / or with less risk of pollution(s), and / or a larger sampling, and / or a more precise measurement of the coefficient of thermal expansion of an inertial element (typically a balance) and / or of the thermal coefficient (CT) of a watch system comprising the inertial element, and therefore a more individualized correction of the inertial elements of a wafer to obtain watch systems whose operation is little or not disturbed by temperature variations.

[0015] For this purpose, a first aspect of the invention relates to a method for controlling an inertial element or a rough inertial element arranged to form an inertial element, the control method comprising the following steps: a. applying to the inertial element or the inertial element blank a time-varying vibrational excitation to cover a predetermined frequency range, b. identifying at least one characteristic of a resonant frequency of the inertial element or the inertial element blank, such as a resonance peak, upon or in response to the vibrational excitation over the predetermined frequency range, c. submitting to a thermal coefficient prediction machine said at least one resonant frequency characteristic identified in step b. to determine a thermal expansion coefficient of the inertial element and / or a thermal coefficient (CT) of a watch system comprising the inertial element.

[0016] The method according to the above implementation comprises a step of vibratory excitation of the inertial element and the measurement of a characteristic of a resonance frequency, to then deduce by prediction a coefficient of thermal expansion of the inertial element and / or a thermal coefficient (CT) of a watch system comprising the inertial element. There is no assembly with an elastic return member (a balance spring) or another component, which saves time. In addition, the measurement can be carried out on inertial elements alone, which limits errors induced by other components or their assembly, as well as possible pollution. The measurement accuracy is improved because there are fewer sources of variability due to other components or pollution. In other words, the inertial element (or its blank) is tested alone.Vibration excitation is applied to the unitary part or blank, not coupled to any balance shaft, spiral spring, or oscillating system. The process allows to control unitary and free parts (i.e. with at least one free part, not attached to any mechanism or balance shaft), which brings at least advantages of productivity gains (no assembly with an oscillating system), quality gains (no pollution of parts, nor breakage, and more parts can be tested in the same budget), precision gain (no error related to other components of an oscillating system).

[0017] It will be noted that the determination of the coefficient of thermal expansion of the inertial element by the method according to the invention is well suited for metal parts, with several metals, composites, hybrids (with several types of materials or components) or even 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, it is easy to obtain the coefficient of thermal expansion of the composite, hybrid or even oxidized inertial element or of the composite, hybrid or even oxidized inertial element blank (the oxidized parts also being in some way composite parts (core or soul in silicon, with a shell in silicon oxide).

[0018] The method may further be defined by the following characteristics, taken individually or in combination.

[0019] According to one embodiment, the method comprises: a step of submitting to an inertia prediction machine said at least one resonant frequency characteristic identified in step b., or a characteristic of another resonant frequency, for example identified in step b., to determine an inertia of the inertial element, optionally, a step of performing a classification or pairing of the inertial element according to its inertia and at least one of the coefficient of thermal expansion of the inertial element and the thermal coefficient (CT) of a watch system comprising the inertial element.

[0020] According to one embodiment, the inertial element is a balance wheel. According to one embodiment, the inertial element comprises at least one felloe, and / or a central hub to be mounted on a balance shaft, and / or at least one arm connecting the central hub to the felloe. According to one embodiment, the inertial element may be a single-piece, one-piece, made from a single part, or the inertial element may be obtained by assembling several parts. According to one embodiment, the inertial element may be made from a single material (a metal, a non-metallic material (ceramic, etc.)).According to one embodiment, the inertial element can be alternatively formed with several different materials (several different metallic layers (or parts or pieces), joined or coated on each other, several different non-metallic layers (or parts or pieces) (silicon, glass, quartz, ceramic, carbon), joined or coated on each other, or a combination of metallic and non-metallic parts or pieces (silicon, glass, quartz, ceramic, carbon)). According to a particular embodiment, the inertial element can be made partly of silicon (monocrystalline or not), oxidized or not.

[0021] According to one embodiment, the vibration excitation can be carried out with a shock device that applies an excitation to the part to be tested in a relatively short time. In other words, it is possible to impose a displacement or an acceleration on the parts to be tested in a very short time (over a duration of less than one second, less than 500 ms, less than 100 ms, less than 10 ms). In particular, the shock device can apply a shock to the inertial element or to its support to vibrate the parts. An impact hammer or any device with a moving mass can be used. In the case of parts attached to a wafer, it is possible to apply the shock to the wafer, or to a support supporting the wafer. Depending on the part to be tested and its position on the wafer, it is possible to apply the shock to a particular location on the wafer and / or in a particular direction.The parts begin to vibrate and the vibrational response can be recorded over time, in order to extract resonance peaks and their frequencies from this measurement, for example using a Fourier transform.

[0022] According to one embodiment, the clock system comprising the inertial element may comprise: a hairspring, a support shaft, and the inertial element (a balance wheel), a hairspring, a support shaft, the inertial element (a balance wheel), and an escapement device, such as a lever escapement, a hairspring, a support shaft, and the inertial element (a balance wheel), an escapement device, and a train, such as a finishing train, the entire movement of the watch, including the inertial element.

[0023] In all the above cases, it is possible to know in advance the value of the thermal coefficient of the parts other than the inertial element, or at least their contribution to the thermal coefficient of the watch system. In practice, these values are standard and known in advance depending on the references or components chosen, and in the case of a silicon inertial element, it is possible to adjust the contribution of the inertial element in equation 4 above to obtain a thermal coefficient of the watch system which will be within a range of values and / or within a desired tolerance(s).

[0024] According to one embodiment, the vibration excitation is applied to the inertial element or its blank having a free end or part (typically the central hub, or a portion of the rim) and another end fixed to the wafer or to a clamp. From a mechanical point of view, it can be considered schematically that the vibration excitation is applied to a mass (located at the center of gravity of the inertial element) connected to a reference frame (a gripping clamp for an inertial element alone, or the rest of a substrate or a plate for a blank for example made of silicon and not detached) by a spring (the elastic part of the inertial element). The vibration excitation sets the suspended mass in motion. In other words, the vibration excitation is applied to the inertial element alone or to the inertial element blank alone.

[0025] It can also be noted that if it is determined that a dimensional correction and / or additional treatment(s) must be made to the tested part (or to all the unit parts attached to the same wafer, or to the unit parts attached to an area of a wafer, including or not the tested part), this can be done on the unit part(s) without re-disassembling anything (for example, it is possible to apply an additional treatment directly after the test, or for example, oxidation on a silicon part). It is therefore possible to add or remove material from the unit part(s), to apply a coating, an oxidation, or a doping to vary intrinsic values (inertia, or coefficient of thermal expansion of the inertial element in particular). In other words, the dimensional correction and / or additional treatment(s) are carried out on the unit part(s).Such corrective treatment of the thermal expansion coefficient of the inertial element provides an additional adjustment lever for the watchmaker to adjust the thermal coefficient of the timepiece (in addition to the known and typically practiced adjustments on the hairspring for example).

[0026] The method according to the above implementation therefore makes it possible to test inertial element blanks during manufacture while limiting the risks of pollution or assembly errors. A dimensional correction (of section, height and / or thickness) and / or additional treatment(s) are then possible. The method according to the above implementation also makes it possible to test finished inertial elements, for example to carry out a classification by inertia increments, and / or to plan a pairing with a particular hairspring.

[0027] According to one embodiment, step b. comprises: b1. a first identification step comprising identifying a first characteristic of a first resonant frequency such as a first resonant peak, b2. a second identification step comprising identifying a second characteristic of a second resonant frequency such as a second resonant peak, the second resonant frequency being different from the first resonant frequency, and step c. comprises: c1. a first prediction step of submitting to another prediction machine the first characteristic of the first resonant frequency to determine a parameter different from the thermal expansion coefficient of the inertial element and / or the thermal coefficient (CT) of a watch system comprising the inertial element, such as an inertia of the inertial element or of the inertial element blank, c2.a second prediction step consisting of submitting to the thermal coefficient prediction machine the second characteristic of the second resonant frequency to determine the thermal expansion coefficient of the inertial element and / or the thermal coefficient (CT) of a clock system comprising the inertial element.

[0028] According to the above embodiment, the first resonant frequency is used to determine a parameter different from the coefficient of thermal expansion of the inertial element and / or the thermal coefficient (CT) of a watch system comprising the inertial element, such as for example an inertia of the inertial element or of the inertial element blank. The second resonant frequency is used to determine the coefficient of thermal expansion of the inertial element and / or the thermal coefficient (CT) of a watch system comprising the inertial element. In other words, two different frequencies are retained or identified to predict or calculate two distinct parameters (inertia on the one hand, the coefficient of thermal expansion of the inertial element and / or the thermal coefficient (CT) of a watch system on the other hand).

[0029] According to one embodiment, steps b1 and b2 are separated by a complementary treatment step (such as a coating step, a step of adding or removing a second material, an oxidation step), and step a. comprises: a1. a first vibrational excitation step, carried out before step b1. and consisting of applying to the inertial element or to the inertial element blank a first vibrational excitation varying over time to cover a first predetermined frequency range, a2. a second vibrational excitation step, carried out before step b2. and consisting of applying to the treated (for example oxidized) inertial element or to the treated (for example oxidized) inertial element blank a second vibrational excitation varying over time to cover the first predetermined frequency range or a second predetermined frequency range.

[0030] According to the above implementation, the first vibration excitation step makes it possible to determine an inertia, and the second vibration excitation step makes it possible to determine the thermal expansion coefficient of the inertial element and / or the thermal coefficient (TC) of a clock system. Different vibration excitations can be imposed between steps a1 and a2.

[0031] According to one embodiment, steps a., b. and c. are performed to determine at least one of the following parameters: the coefficient of thermal expansion of the inertial element, and / or the thermal coefficient (TC) of a clock system comprising the inertial element, and / or the inertia of the inertial element, and once said at least one parameter has been determined, the method may preferably comprise: a step consisting of comparing said at least one determined parameter with at least one predetermined threshold and preferably with a predetermined tolerance range, and if said at least one determined parameter exhibits a non-conformity with said at least one predetermined threshold or with the predetermined tolerance range, then the method may preferably comprise: a step of processing or correcting or modifying the inertial element to adjust and make said at least one determined parameter conform with said at least one predetermined threshold or with the predetermined tolerance range, optionally, steps a., b., and c.to determine again said at least one parameter among: the coefficient of thermal expansion of the inertial element, and / or the thermal coefficient (CT) of a clock system comprising the inertial element, and / or the inertia of the inertial element.

[0032] According to a preferred embodiment: the method comprises initially determining the inertia of the inertial element and at least one of the coefficient of thermal expansion of the inertial element, and the thermal coefficient (CT) of a watch system comprising the inertial element, the step of processing or correcting or modifying the inertial element is provided to adjust the inertia of the inertial element and at least one of the coefficient of thermal expansion of the inertial element, and the thermal coefficient (CT) of a watch system comprising the inertial element.

[0033] According to one embodiment, one of the following parameters is determined from a first resonant frequency, and at least one other of the following parameters is determined from a second resonant frequency: the coefficient of thermal expansion of the inertial element, the thermal coefficient (TC) of a clock system comprising the inertial element, the inertia of the inertial element.

[0034] According to one embodiment, the method comprises a final step of performing a classification or pairing of the inertial element taking into account the inertia of the inertial element and at least one of the coefficient of thermal expansion of the inertial element, and the thermal coefficient (CT) of a clock system comprising the inertial element.

[0035] According to one embodiment, step a. is implemented after a complementary processing step (such as a coating step, a step of adding or removing a second material, an oxidation step), and in which steps b1. and b2. take into account the same vibrational response of the inertial element or of the inertial element blank. In other words, a first part of the vibrational response is used to identify the first resonance frequency and a second part of the same vibrational response is used to identify the second resonance frequency.

[0036] According to one embodiment: the first resonant frequency is chosen to be a resonant frequency of a plane resonant mode, preferably for high resonant frequencies, for example above 40 kHz, or above 60 kHz, and / or the second resonant frequency is chosen to be a resonant frequency of an out-of-plane resonant mode.

[0037] According to the above implementation, a plane resonance mode can be considered to be a resonance mode in which the different parts of the inertial element or inertial element blank move mainly in the plane of the part at rest. If this plane is defined by X and Y directions, with a Z direction normal to the plane, then the X or Y displacements are greater than or equal to the Z displacements. In an out-of-plane resonance mode, the Z displacements are greater than or equal to the X or Y displacements, and preferably the Z displacements are two to three times greater than the X or Y displacements.

[0038] According to one embodiment, the first resonant frequency is lower than the second resonant frequency and / or: the first resonant frequency is chosen in 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, more preferably from 2 kHz to 40 kHz, and very preferably from 10 kHz to 35 kHz, and / or the second resonant frequency is chosen in 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 very preferably from 100 kHz to 200 kHz. The applicant has noticed that a treated or corrected part (for example coated or oxidized) can have different frequencies and / or resonance modes compared to the same untreated or uncorrected parts (for example uncoated or unoxidized) for resonance frequencies above 40 kHz, preferably above 50 kHz and very preferably above 60 kHz.Accordingly, to accurately predict a thermal expansion coefficient of the inertial element and / or a thermal coefficient (TC) of a clock system including the inertial element, it may be preferable to consider resonance modes with high resonance frequencies.

[0039] According to one embodiment, step b. may consist of identifying a characteristic of a resonance frequency sensitive to the coefficient of thermal expansion of the inertial element or of the inertial element blank.

[0040] Of course, the frequency range of the spectrum obtained does not only depend on the source of vibration excitation but also on the sensor of the measuring instrument used. Thus, the frequency range is linked both to the excitation frequency range and to the frequency range over which the 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 inertial element or blank tested.

[0041] The predetermined resonant frequency that the inertial element must have when finished can be a target natural frequency or a target resonant frequency, or a target natural frequency range, or a target resonant frequency range defined by a tolerance around a target value.

[0042] In the above method, the characteristic of a resonant frequency is a characteristic of the oscillatory response measured over a predetermined frequency range, comprising at least one resonant frequency. Such a characteristic is typically identified after processing a raw measurement signal (for example, measuring the amplitudes or speeds or accelerations of displacement of certain points of the inertial element or of the inertial element blank), the processing possibly including, for example, a Fourier transform to identify resonance peaks and therefore resonance frequencies.

[0043] It may be noted that the method may determine a coefficient of thermal expansion of the inertial element and / or a thermal coefficient (TC) of a watch system comprising the inertial element and / or an inertia of the inertial element to perform a classification of the part (according to its inertia and / or its coefficient of thermal expansion), and / or to provide for pairing with other particular components (in particular according to the inertia and / or the coefficient of thermal expansion of the inertial element and according to the stiffness and / or the thermal coefficient of Young's modulus and / or the coefficient of thermal expansion of the balance spring) and / or to then calculate / deduce a dimensional correction and / or an additional treatment(s) to be applied to obtain a target coefficient of thermal expansion of the inertial element and / or a target thermal coefficient (TC) of a watch system comprising the inertial element and / or a predetermined oscillation frequency of an oscillatorincluding the inertial element. However, only the identified resonance frequency can be taken into account to directly calculate / deduce a dimensional correction and / or additional processing to be applied to obtain a target thermal expansion coefficient of the inertial element and / or preferably a target thermal coefficient (TC) of a watch system including the inertial element. Thus, it can be proposed to adjust the TC of the watch movement by working on the inertial element, which provides additional flexibility.

[0044] In particular, according to a preferred embodiment, it is possible performing steps a., b., and c. to predict the inertia of the inertial element and at least one of the coefficient of thermal expansion of the inertial element and the thermal coefficient (CT) of a watch system comprising the inertial element, performing a pairing of the inertial element with a hairspring according to the parameters predicted above. It is possible to previously (separately) predict a stiffness and / or a thermal coefficient of Young's modulus of the hairspring and / or a coefficient of thermal expansion of the hairspring with a similar vibrational method.

[0045] According to one embodiment, before the pairing step, a correction or processing of the inertial element may be performed to adjust at least one of the inertia of the inertial element, the coefficient of thermal expansion of the inertial element, and the thermal coefficient (CT) of a clock system comprising the inertial element.

[0046] According to one embodiment, in step a, the frequency range is applied simultaneously to a single or a plurality of inertial elements or to a single or a plurality of inertial element blanks. Speed is improved because the vibrational excitation can typically be imposed on a wafer supporting several hundred inertial element blanks, which would for example still be attached to the wafer.

[0047] According to one embodiment, the frequency range is predetermined to encompass at least one frequency range: centered on the predetermined resonant frequency, and with a range of at least 30% of the predetermined resonant frequency, i.e. ±15% of the predetermined resonant frequency. For example, if the predetermined resonant frequency is 10 kHz, then the frequency range will be from 8500 Hz to 11500 Hz.

[0048] According to one embodiment, the inertial element has at least two expected predetermined resonant frequencies, and the frequency range is predetermined to cover at least the two expected predetermined resonant frequencies. By covering or sweeping a wide frequency range, multiple resonant peaks (or resonant frequencies) can be measured, which can provide improved accuracy.

[0049] According to one embodiment, step a. comprises the use of a source, such as a piezoelectric source, making it possible to induce or impose an acoustic excitation on a slice of a wafer supporting the inertial element blank, or preferably on, or even under the inertial element or the inertial element blank to be specifically excited.

[0050] According to one embodiment, the acoustic source can be coupled to an excitation cone chosen to excite at least one inertial element or an inertial element blank. Preferably, if a plate supports several inertial element blanks, then the acoustic source can be coupled to an excitation cone chosen to excite at least a portion and preferably all of the inertial element blanks.

[0051] According to one embodiment, the acoustic source can be chosen and / or adjusted to generate the variable vibrational excitation over time to cover the predetermined frequency range: with an amplitude sufficient to generate vibrations of the inertial element or of the inertial element blank of sufficient amplitude to be detected by the means for measuring amplitude or speed or acceleration of displacement of at least one point of the inertial element or of the inertial element blank and / or for a duration sufficient to deduce therefrom vibration spectra of the inertial element or of the inertial element blank.

[0052] According to one embodiment, step b. comprises the use of an optical measuring means, such as a laser Doppler vibrometer.

[0053] According to one embodiment, 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 inertial element or of the inertial element blank, preferably carried out at least partially during step a.

[0054] According to one embodiment, step b. comprises: a step of identifying a resonance frequency of the inertial element or the inertial element blank as a function of an operational or modal deformation of at least one point of the inertial element or the inertial element blank. An operational or modal deformation is typically defined by an amplitude or speed of displacement or even an acceleration and a direction of oscillation (outside or in a particular plane) as a function of the excitation frequency.

[0055] According to one embodiment, the inertial element or the inertial element blank is contained in a base plane, and step b. comprises: a step b" of measuring an amplitude or a speed or an acceleration of displacement of at least one point of the inertial element or of the inertial element blank in a direction normal to the base plane, and / or a step b'" of measuring an amplitude or a speed or an acceleration of displacement of at least one point of the inertial element or of the inertial element blank in a direction contained in the base plane.

[0056] Measurements of displacements or speeds in several directions allow for better identification of resonance peaks and frequencies.

[0057] According to one embodiment, step b. comprises: a step of identifying a resonance peak of the inertial element or the inertial element blank as a function of an amplitude or a speed of movement of at least one point of the inertial element or the inertial element blank.

[0058] According to one embodiment, the characteristic of the resonant frequency is identified on the basis of the width of the resonant peak, at half height of the maximum value of the resonant peak. This processing method makes it possible to limit calculation errors which could be made based solely on the identification of the frequency position of the peak defined by its maximum value.

[0059] According to one embodiment, step b. comprises a step of processing the measurement signal with, for example, a Fourier transform, to identify resonance peaks of displacement amplitude or speed or acceleration, and / or phase, as a function of the excitation frequency.

[0060] According to one embodiment, the thermal coefficient prediction machine may be a calculation machine for predicting or calculating from the frequency characteristics the thermal expansion coefficient of the inertial element and / or the thermal coefficient (TC) of a clock system comprising the inertial element. In other words, the prediction machine is not a regulated or self-regulated or feedback loop system for adjusting a resonant frequency in response to a measurement and a comparison with a target value.

[0061] In other words, the prediction machine is a calculation machine, which may be a calculation unit intended to implement one or more mathematical formulas to predict a thermal expansion coefficient value of the inertial element and / or a thermal coefficient (TC) value of a clock system comprising the inertial element, when it receives as input a value of a physical characteristic measured on the inertial element or the inertial element blank.

[0062] According to an implementation, the prediction machine, for example a 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.

[0063] According to one implementation, the prediction machine, for example a computing unit, may be a prediction machine using artificial intelligence software.

[0064] According to one implementation, the prediction machine, for example the calculation unit, may be a prediction machine using at least one neural network designed to receive as input values or graphs taken from the vibration measurement spectra and designed to give as output a thermal expansion coefficient of the inertial element and / or a thermal coefficient (CT) of a clock system comprising the inertial element.

[0065] 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 expansion coefficient of the inertial element and / or the thermal coefficient (CT) of a clock system comprising the inertial element.

[0066] According to one embodiment, the thermal coefficient prediction machine implements a regression method, for example a linear regression, to predict the thermal expansion coefficient of the inertial element and / or the thermal coefficient (CT) of a clock system comprising the inertial element.

[0067] According to one embodiment, the thermal coefficient prediction machine can implement a classification based on a partitioning into k-means or k-medians to predict the coefficient of thermal expansion of the inertial element and / or the thermal coefficient (TC) of a clock system comprising the inertial element.

[0068] According to one embodiment, the control method comprises a preliminary step of taking into account the material of the inertial element or the inertial element blank, and adjusting a maximum amplitude of the vibration excitation and / or a frequency range of the predetermined frequency range as a function of the material of the inertial element or the inertial element blank.

[0069] According to one embodiment, if step c. determines that the coefficient of thermal expansion of the inertial element and / or the thermal coefficient (TC) of a watch system comprising the inertial element is outside a range of expected values, then the method comprises at least one step of identifying or isolating or reworking (e.g. performing further processing) or scrapping the inertial element or the inertial element blank.

[0070] According to one embodiment, if step c. determines that the coefficient of thermal expansion of the inertial element and / or the thermal coefficient (CT) of a watch system comprising the inertial element is outside a range of expected values, then the method comprises at least one step of defining a step of processing the inertial element or the inertial element blank, such as a step of adding or removing material, or a step of adding or removing a second material, or coating or a step of thermo-compensation, oxidation or deoxidation, to obtain the coefficient of thermal expansion of the inertial element and / or the thermal coefficient (CT) of a watch system comprising the inertial element within the range of expected values

[0071] According to one embodiment, step a. is performed for a plurality of inertial elements or inertial element blanks attached to a wafer, and if step c. determines that the coefficient of thermal expansion of the inertial element and / or the thermal coefficient (CT) of a watch system comprising the inertial element is outside a range of values expected for first inertial elements or first inertial element blanks and within the range of values expected for second inertial elements or second inertial element blanks, then provision may be made to detach only the second inertial elements or second inertial element blanks and to provide a step of processing the first inertial elements or first inertial element blanks, such as a step of adding or removing material, or a step of adding or removing a second material, or a thermo-compensation step,oxidation or deoxidation, to obtain the coefficient of thermal expansion of the inertial element and / or the thermal coefficient (TC) of a clock system comprising the inertial element in the expected range of values. It is possible to repeat these steps, by repeating or not steps a. and b.,

[0072] According to one embodiment, step a. and step b. are repeated at least several times for the same measurement point of the inertial element or the inertial element blank.

[0073] According to one embodiment, step a. and step b. are synchronized. Such synchronization provides the possibility of detecting a phase shift, or an attenuation, or a coupling, the taking into account of which can improve the accuracy of the prediction, or make it possible to adjust or recalibrate the source of vibrational excitation.

[0074] A second aspect of the invention may relate to a method of manufacturing an inertial element having at least one expected predetermined resonant frequency comprising the steps of: A / forming at least one inertial element (a balance) or an inertial element blank having dimensions within predetermined tolerances necessary to obtain the expected predetermined resonance frequency, B / controlling the inertial element or the inertial element blank according to the control method of the first aspect.

[0075] According to one embodiment, the manufacturing method may comprise a step consisting of: C / identifying or isolating or reworking or reprocessing or scrapping the inertial element or the inertial element blank formed during step A / , if step c. determines that the coefficient of thermal expansion of the inertial element and / or the thermal coefficient (CT) of a watch system comprising the inertial element is outside a range of expected values.

[0076] According to one embodiment, the inertial element or inertial element blank may be formed on a wafer, along with a plurality of other inertial elements or inertial element blanks.

[0077] A third aspect relates to a method of training a prediction machine to implement step c. of the control method according to the first aspect, comprising the steps of: i- forming inertial elements or inertial element blanks and applying a thermo-compensation step thereto, ii- applying to each of the inertial elements or each of the inertial element blanks a vibrational excitation that varies over time to cover a predetermined frequency range, iii- identifying at least one characteristic of a resonance frequency of each inertial element or each inertial element blank when applying the predetermined frequency range and recording the temperature of the parts during step ii- and / or iii-, iv'- mounting a plurality of inertial elements or inertial element blanks in an oscillating mechanism comprising an elastic return member having a predetermined stiffness so as to measure for each inertial element or inertial element blank a sustained oscillation frequency or a rate of the clockwork system formed by, or comprising,the mechanism oscillating at at least one predetermined temperature and preferably at least two predetermined temperatures, and / or iv"- modeling in a simulation tool a plurality of inertial elements or inertial element blanks in an oscillating mechanism comprising an elastic return member having a predetermined stiffness so as to calculate for each inertial element or inertial element blank a sustained oscillation frequency and / or a thermal coefficient of a watch system comprising the inertial element and / or the rate of the watch system comprising the inertial element at at least one predetermined temperature and preferably at least two predetermined temperatures, and / or iv'"- modeling in a simulation tool at least one inertial element so as to find said at least one characteristic of a resonance frequency identified in step iii-, v- optionally,deduce at least one expected resonance frequency from said at least one resonance frequency identified in step iii-, and / or from the sustained oscillation frequency and / or from the rate of the watch system measured in step iv'- and / or calculated in step iv"- vi- deduce a coefficient of thermal expansion of the inertial element and / or the thermal coefficient (CT) of a watch system comprising the inertial element from the measurements of step iv'-, and / or from the calculations of step iv"-, and / or from the modeling of step iv‴, vii- provide to the prediction machine, and for each inertial element or inertial element 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 coefficient of thermal expansion of the inertial element and / or the thermal coefficient (CT) of a clock system comprising the inertial element deduced in step vi-., Description of the figures

[0078] Other characteristics and advantages of the present invention will appear more clearly on reading the following detailed description of embodiment(s) of the invention given as non-limiting example(s) and illustrated by the appended drawings, in which: There figure 1 represents a perspective view of an inertial element, The figures 2A-2F are a simplified representation of a manufacturing process of an inertial element, here a balance wheel, on a plate, The figure 3 schematically represents the implementation of the evaluation of the inertia of inertial element blanks by vibration analysis, The figure 4 represents an example of frequencies applied to a silicon wafer supporting inertial element blanks, to impose a vibrational excitation, The figure 5 represents an example of measurement of the displacement amplitudes of a point of an inertial element blank, in response to the imposed frequency range of the figure 4 , There figure 6 represents in detail a resonance peak identified at a particular frequency on the figure 5 , There figure 7 represents resonance peaks measured on several parts and superimposed for the particular frequency of the figure 6 , There figure 8 represents an example prediction model built from data extracted from the figure 7 , There figure 9 shows the influence of temperature on the resonance frequency of a particular resonance mode, The figure 10 shows the influence of the components of an oscillator on the running of a timepiece, depending on the temperature. Detailed description of embodiment(s)

[0079] There figure 1 represents a perspective view of an inertial element 100 (here a balance) coupled to a balance staff 120. The balance staff 120 supports a double roller 130 in a conventional manner. To form a resonator or an oscillator, the inertial element 100 mounted on its balance staff 120 must still be coupled to an elastic return member, typically a spiral spring, which is not shown figure 1 .

[0080] In this example, the inertial element 100 comprises a rim 101, arms 102 and a central hub 103. The inertial element 100 may be made of a metallic material, or with several metallic materials, but the inertial element 100 may also be made at least partially of a non-metallic material, such as for example silicon, carbon, glass, quartz, ceramic. A composite inertial element 100 may be provided, i.e. formed of several materials: the arms 102 and / or the rim 101 may comprise a first material and a second material to provide, for example, optimized thermal sensitivity, the rim 101 may comprise or be coated with a dense material to provide a particular inertia, for example, the arms 102 may be made from a first material, the rim 101 from a second (and possibly a third) material, the arms 102 and / or the rim 101 may be coated or have a protective layer...

[0081] An inertial element 100 may be provided formed by an assembly of several parts. In particular, it may be provided, for example, to fix weights on the rim 101.

[0082] According to a particular embodiment, the inertial element 100 can be formed from silicon, and the figures 2A-2F are a simplified representation of a method of manufacturing an inertial element 100 on a wafer 10.

[0083] Plate 10 is illustrated in figure 2A as a SOI wafer (“silicon on insulator”) and comprises a substrate or “handler” 20 carrying a sacrificial silicon oxide (SiO 2 ) layer 30 and a monocrystalline silicon layer 40. For 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 to 500 µm. The monocrystalline silicon layer 40 may have any crystalline orientation.

[0084] A lithography step is shown in figures 2B And 2C . By "lithography" is meant all the operations allowing an image or pattern to be transferred onto or above the wafer 10 towards the latter. Referring to the figure 2B , in this exemplary embodiment, the layer 40 is covered with a protective layer 50, for example made of a polymerizable resin. This layer 50 is structured, typically by a photolithography step using an ultraviolet light source as well as, for example, a photomask (or another type of exposure mask) or a stepper and reticle system. This lithographic structuring forms the patterns for the plurality of inertial elements in the layer 50, as illustrated in figure 2C .

[0085] Subsequently, in the stage of the figure 2D , the patterns are machined, in particular etched, to form the plurality of inertial elements 100 in the layer 40. The etching can be carried out by a deep reactive ion etching technique (also known by the acronym DRIE for “Deep Reactive Ion Etching”). After the etching, the remaining portion of the protective layer 50 is subsequently removed.

[0086] To the figure 2E , the inertial elements 100 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. At this stage, blanks of the inertial element 100 are obtained. Smoothing (not shown) of the etched surfaces may 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 based on hydrofluoric acid (HF). It may also be provided to form a layer of silicon oxide on the parts.

[0087] At the last stage of the manufacturing process at the figure 2F , the different parts of the inertial elements 100 made of silicon are covered with a layer 104 of silicon oxide (SiO2), typically by a thermal oxidation step. The formation of this layer 104, which generally has a thickness of 2-5 µm, also affects the final inertia of the inertial element and therefore must be taken into account during the previous steps to obtain inertia characteristics of the inertial element leading to obtaining a particular natural frequency of the balance spring couple in a given watch mechanism. figure 2F therefore shows an inertial element 100 with, in the section considered, the rim 101 and the hub 103. It can be noted that the arms 102 which obviously connect the rim 101 and the hub 103 are in a plane other than the section plane of the figure 2F . It can also be noted that the inertial element 100 remains attached to the plate 10 by bridges not visible on the figure 2F .

[0088] The present invention proposes to determine at least one characteristic of a resonance frequency of at least one inertial element 100 to deduce a coefficient of thermal expansion of the inertial element and / or a thermal coefficient (CT) of a clock system comprising the inertial element.

[0089] In general, the present invention proposes to determine at least one characteristic of a resonance frequency of at least one inertial element 100, whether it is manufactured individually or in a batch of several inertial elements. According to a particular embodiment, the present invention proposes to determine at least one characteristic of a resonance frequency of at least one inertial element 100 on the wafer in step 2F, to deduce a coefficient of thermal expansion of the inertial element and / or a thermal coefficient (CT) of a watch system comprising the inertial element and possibly in step 2E or even 2F, to deduce an inertia.

[0090] In particular, the present invention may propose to identify the above parameters from the inertial element alone or without disassembly of the wafer or measurement in a test subassembly, according to a method more efficient than the methods of the prior art.

[0091] Thus, the invention proposes to determine at least one characteristic of a resonance frequency of at least one inertial element 100 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 coefficient of thermal expansion of the inertial element and / or the thermal coefficient (CT) of a watch system comprising the inertial element.

[0092] The present invention may also propose to determine whether a geometric correction of the inertial elements 100 is necessary. If so, the present invention may propose to precisely calculate a physical correction to be made: addition / removal of material, correction of thickness of material or oxide to be modified (to be removed or added) to obtain the dimensions leading to obtaining the coefficient of thermal expansion of the inertial element and / or the thermal coefficient (CT) of a watch system comprising the inertial element and / or the inertia (adjusting the natural frequency and / or the resonance frequencies) corresponding to target values, according to a more efficient method than the methods of the prior art.

[0093] Concretely, the present invention can propose to precisely calculate a physical correction to be made to obtain a target thermal expansion coefficient for the inertial element alone and / or to obtain the lowest possible thermal coefficient (CT) for a clock system comprising the inertial element.

[0094] In particular, it is possible to provide, in the case where a part of the inertial element comprises two layers of different materials forming a bimetallic strip, to specifically add or remove a part of one of the two layers to correct the thermal compensation and / or the behavior of the bimetallic strip.

[0095] Thus, the invention proposes to determine at least one characteristic of a resonance frequency of a sample of inertial elements 100 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 coefficient of thermal expansion of the inertial element and / or to the thermal coefficient (CT) of a clock system comprising the inertial element and / or to the inertia of the inertial elements 100 and / or to the necessary geometric correction.

[0096] The modal properties of the inertial element 100 are thus exploited, still attached to a clamping clamp in the case of an individually manufactured inertial element, or still attached to the wafer 10 in the case of an inertial element manufactured in batch. During a learning phase, and by an analytical and numerical approach, it is possible to set up a prediction machine by establishing a predictive model linking the coefficient of thermal expansion of the inertial element and / or the thermal coefficient (CT) of a watch system comprising the inertial element and / or the inertia to certain frequencies (natural frequency or resonance frequencies associated with a resonance peak or a width at half-maximum) specifically chosen.

[0097] Once the learning phase is complete (once the modes to be used and the excitation frequencies have been determined), it is possible to move on to a prediction phase and use the prediction machine by using the predictive model to control the inertial elements 100 of a produced wafer, in order to predict their coefficient of thermal expansion and / or the thermal coefficient (TC) of a watch system comprising the inertial element and / or their inertia, and / or perform a classification and / or determine whether a correction of the dimensions is necessary, and if so, calculate or predict the exact correction to be made to the dimensions of the inertial elements 100 (by removal if the blank is produced with dimensions greater than the required final dimensions, or by addition of material if the blank is produced with dimensions smaller than the required final dimensions, for example).

[0098] Thus, it is possible to integrate the control method into a manufacturing method to correct, if necessary, the inertia characteristics of the inertial elements 100 to obtain a particular and predetermined natural oscillation frequency, once the inertial elements 100 are each coupled to an elastic return member of a given watch mechanism. Vibrational excitation

[0099] Measuring the vibration response of the inertial elements 100 makes it possible to deduce at least one characteristic of a resonance frequency, such as for example a value of a resonance frequency (a resonance peak). In detail, one must first impose a vibration excitation on the inertial element, or on a clamp holding the inertial element, or on the plate supporting the inertial element. Several options are offered: a. Measurements in the frequency domain: 1- Use a piezoelectric source (or any other source of vibrational excitation - for example an electromagnet - allowing to induce or impose a vibrational excitation such as an acoustic excitation) on a clamping clamp holding the part to be tested, or on the edge of the wafer 10, or on, or even under the blank of inertial element 100 to be excited specifically (preferably) which excites at a particular frequency f 0 (continuous single-frequency excitation). In this variant, the excitation is maintained.2- Alternatively, the piezoelectric source (or any other source of vibrational excitation - for example an electromagnet - making it possible to induce or impose a vibrational excitation such as an acoustic excitation) can also be used on a clamping clamp holding the part to be tested, or on the edge of the wafer 10, or on, or even under the blank of the inertial element 100 to be excited specifically (preferably) which excites at a frequency that varies over time to cover a predetermined frequency range, ranging for example from 0 to 500 kHz, preferably from 0 to 100 kHz, preferably from 5 kHz to 100 kHz, preferably from 5 kHz to 80 kHz, and preferably from 10 kHz to 80 kHz. The entire frequency range can be scanned or covered in a time interval that can range from a fraction of a second to a few seconds. For example, one may expect to sweep or cover the frequency range of the frequency range in less than 0.5 s, less than 1 s, or less than 1.5 s.In this variant, the excitation frequency changes continuously or according to a variable profile. b. Measurements in the time domain: use an excitation hammer (or any other source of vibration excitation allowing the induction of a pulsed vibration excitation, or even a pulsed acoustic excitation) on a clamping clamp holding the part to be tested, or on the edge of the wafer 10, on, or under the inertial element 100 to be excited specifically (preferred) which gives the shortest possible acoustic pulse (multi-frequency pulsed excitation). In this variant, the excitation is punctual and not sustained.

[0100] Furthermore, measurements can be performed following a particular sampling, for example according to a sampling range of 4, 2 or 1 Hz. Indeed, the resolution for processing the acquisition data according to, for example, a Fourier transform depends directly on the duration and frequency of this acquisition.

[0101] Furthermore, a signal sampling frequency of at least 200 kHz can be chosen if the frequency range extends up to 100 kHz, for example.

[0102] Generally speaking, we can finally plan to change the direction of excitation, that is to say the direction of the movements imposed by the source of vibratory excitation (we can impose vibrations in one or more axial direction(s), and make this or these direction(s) evolve over time).

[0103] The excitation can be carried out on a clamping clamp holding the part to be tested, or in the case of batch manufacturing, on a wafer 10 comprising a plurality of inertial element blanks 100. Provision can be made to adjust the direction of the vibrations so as to point at one or other of the inertial elements 100, as a function of the displacement amplitude measurements described below.

[0104] Finally, it is possible to couple the acoustic source to a divergent cone directed towards the inertial element blanks 100 to be excited, and to adjust the acoustic source to emit an excitation signal with an amplitude sufficient to impose a vibrational excitation of the inertial element blank(s) 100 and having an amplitude sufficient to be detected and measured precisely by the chosen measuring instruments. Measurement of amplitude or speed, or acceleration of displacement

[0105] During excitation, the amplitude and phase (relative to the source of vibration excitation) of oscillation in the 3 directions X, Y (in the plane) and Z (out of plane) of the specifically excited inertial element are recorded using a suitable measuring means. The following possible measuring means may be mentioned, without limitation: 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 temporal analysis type TCSPC, Acoustic methods by ultrasound by Doppler effect.

[0106] There figure 3 schematically represents a silicon wafer 10 on which a plurality of inertial element blanks 100 are formed. A vibration excitation source 300 is coupled to the wafer 10, so as to be able to impose a vibration excitation. Consequently, each inertial element blank 100 will start to vibrate, and a laser vibrometer 200, here focused on a point of the inertial element blank 100 on the right, will be able to measure the vibration amplitudes of the measurement point over time.

[0107] It is possible to provide for measuring the displacements in a direction normal to the plane of the plate 10, but it is just as possible to measure the displacements in one or more directions contained in the plane of the plate 10. It is of course possible to provide a vibratory excitation source 300 detached or separated from the plate 10 to generate an acoustic excitation of all or part of the inertial element blanks 100.

[0108] Of course, the figure 3 could represent an inertial element 100 (made of any material, for example metallic) held by a clamping clamp and part of which is placed opposite the vibratory excitation source 300 on one side and a laser vibrometer 200 on the other side.

[0109] Once a particular point has been studied, the laser vibrometer 200 can be moved to another measurement point on the inertial element blank 100, or moved to another inertial element blank 100 on the wafer 10. Of course, the inertial element blank 100 can alternatively be moved relative to the laser vibrometer.

[0110] There figure 4 represents an example of vibrational excitation over time. In the example given, the excitation frequency varies over time, between 0 Hz and 50 kHz for example, and a succession of rising edges can be imposed, each spaced by a rest period without excitation. For each measurement point on the inertial element blank 100, a plurality of rising edges can be imposed (between 2 rising edges and 60 rising edges), each lasting between 0.5 s and 2 s for example. Selection of reference points to measure

[0111] With regard to the displacement amplitude measurement, during the learning phase, a step can be provided consisting of identifying points of the inertial element 100 for which the vibration response is significant. Indeed, in the case of an inertial element 100 to which a vibration is imposed, especially if the frequency varies over time, the vibration response will cause nodes to appear on the inertial element 100, i.e. particular points of the inertial element 100 whose displacement amplitude is low or zero. If a displacement measurement is carried out on a point of the inertial element which turns out to be a node at one or more particular frequency(ies), the identification of resonance frequency characteristics will be negatively affected.

[0112] Thus, it is advantageous to provide a preliminary step of measuring displacement on a plurality of predetermined points of the inertial element 100, for example at least ten predetermined points, preferably at least twenty predetermined points, and very preferably at least thirty predetermined points. It is possible to provide for selecting the predetermined points arranged on an orthonormal XY reference frame in the plane of the inertial element.

[0113] At the end of this preliminary step of amplitude measurement on the predetermined points, it is possible to provide for identifying for each measurement point resonance frequencies, and then a step of selecting reference points for which the measurement of displacement amplitude during the excitation shows that they are not nodes at these resonance frequencies. In other words, the identified nodes have, at at least one resonance frequency, a displacement amplitude that is zero or less than a first threshold peak value, and these points forming nodes are separated from the reference points to be considered for the subsequent measurements. It may also be noted that the reference points may be different depending on the position of the inertial element blank 100 on the wafer 10.

[0114] Typically, it can be considered that at least two reference points will be selected, and preferably at least four reference points will be selected. In the case where the inertial element 100 has a radius Ra and is anchored or embedded on the plate 10 by a bridge, it is preferably possible to select four chosen and located reference points: in a first zone less than 0.20 x Ra (for example on the hub 103), or in a second zone between 0.05 x Ra and 0.30 x Ra (for example on the arms 102), or in a third zone between 0.35 x Ra and 0.65 x Ra (for example on the arms 102, especially if the latter do not have a constant cross-section), or in a fourth zone between 0.65 x Ra and 0.85 x Ra (for example on the rim 101). Also, the reference points can be chosen to be far from the part anchored or bridged on the plate 10 and can naturally have a significant oscillatory displacement capacity, which ensures better precision of the displacement measurement.

[0115] Furthermore, it is also possible to measure the displacements of a point of the body of the wafer 10, and / or of a point of the source of vibration excitation, to identify or measure for example a phase shift or a vibration attenuation, or even a resonance resulting from a vibration coupling or from the wafer 10. These additional measurements make it possible to ensure that the identified peaks are indeed those of the inertial element 100 alone. It is also possible to synchronize the measurement of the displacement amplitude and the vibration excitation. Determination of vibration characteristics

[0116] We then have several scenarios depending on the area previously chosen for the excitation: a. Frequency domain measurements 1- variant with sustained excitation: i. Temporally integrate the oscillation amplitude and phase long enough to have good spectral resolution at the excitation frequency fa, ii. Shift the oscillation frequency by delta f to excite at frequency f 0 + Δ f and repeat integration step i, iii. Reconstruct the oscillation amplitude and phase spectra as a function of the excitation frequency (possibly with several peaks at several frequencies). 2- variant with excitation whose frequency varies over time: i. Temporally record the oscillation amplitude and phase during the frequency sweep of the frequency range, ii. Repeat step i- at least once, preferably at least three times, iii. Reconstruct the oscillation amplitude and phase spectra as a function of the excitation frequency (possibly with several peaks at several frequencies). b.Time domain measurements: i. Record the temporal displacement of the measurement point along X, Y and Z over a sufficiently long period of time to obtain a sufficiently representative signal, such as a few seconds. ii. One can choose to record the signal to make it a reference signal to compare with other signals measured on other parts. One can also choose to perform Fourier transform type signal processing to identify resonance frequencies in the recorded signal.

[0117] As a result, at least one resonance peak can be identified for each inertial element blank or each excited inertial element, and it is proposed to determine the resonance frequency not on the basis of the top of the resonance peak, i.e. on the maximum amplitude, but rather on an area of the curve located between 25% and 75% of the maximum amplitude value of the resonance peak, for example from its width at half-height. Indeed, this processing method which focuses on a part of the curve between 25% and 75% of the maximum amplitude value of the resonance peak makes it possible to limit the errors due to the singularity of the maximum amplitude point and to the approximation calculations to reconstruct the top part of the resonance peak.The area of the curve between 25% and 75% of the maximum amplitude value of the resonance peak has better accuracy than the part above 75% (typically the peak), which provides better accuracy on the exact resonance frequency determined. For example, the middle of the segment connecting the two points at mid-height of the resonance peak can be used to determine the resonance frequency associated with the peak in question.

[0118] There figure 5 represents an example of a vibration spectrum for a point of a rough draft of an inertial element 100 of the figure 1 Or 3 , reconstructed from the displacement amplitude measurements of the measurement point considered in response to the vibratory excitation of the figure 4 , between 15 kHz and 65 kHz. Three amplitude peaks can be noted, at approximately 25 kHz, 37 kHz, and 53 kHz. Although not shown, typically between 10 and 30 amplitude peaks can be identified if the vibrational excitation sweeps a frequency range between 0 Hz and 50 kHz. Each amplitude peak has a resonance frequency, and the maximum amplitudes vary greatly.

[0119] There figure 6 represents in detail the processing that can be done on an amplitude peak, the one at 37.5 kHz for example. The aim is to find the resonance frequency and give it as precise a value as possible. Instead of basing this processing on the maximum value of the peak, the applicant realized that better accuracy could be achieved by determining the length of the segment connecting the rising and falling parts of the curve, at mid-height of the peak. The resonance frequency is typically the value in the middle of this segment. However, interpolation can be performed on points in the vicinity of the resonance peak to improve accuracy, and the chosen point on the segment can be shifted, which will not be the middle, especially if the actual position of the resonance peak is shifted, for example, due to the chosen sampling frequency.

[0120] There figure 7 represents, for the example of an amplitude peak at approximately 37 kHz, the amplitude peaks constructed for around ten inertial element blanks 100 tested. It can be noted that from one inertial element blank to another, the frequency position of the amplitude peak varies (from approximately 37 kHz to 38 kHz), and that the maximum displacement amplitude varies in a ratio of approximately 1 to 5. Since the peaks of the amplitude peaks are not truly symmetrical, it seems sensible to determine the resonance frequency on the basis of the width of the peak at half-height. Determination of the inertia and / or actual dimensions of the inertial elements tested

[0121] To establish a prediction model that can receive as input the vibration characteristics (typically a resonance frequency) and output an inertia and / or a dimensional correction, it is necessary, during the learning phase, to provide the data relating to the real inertia and / or the real dimensions of the inertial elements tested to link them to the resonance frequencies of the figure 7 for example. Also, for this purpose, one can plan to concretely measure a natural frequency of oscillation of a spiral - balance system in an environment similar to that of a particular watch mechanism.

[0122] Alternatively, the tested inertial elements can be finished manufacturing in order to mount or couple them with a reference elastic return member (of known stiffness) individually to again measure a natural oscillation frequency of the reference elastic return member - inertial element pair.

[0123] An intermediate step can be taken to determine the inertia of each inertial element, and then the inertia and / or actual dimensions of the inertial elements tested can be determined. In other words, it is possible to determine the natural frequency or a resonance frequency and then the inertia or dimensions of the inertial element by analyzing the free oscillations of an inertial element coupled to a reference elastic return member. In this approach, a laser pointed at the balance arms records the passage times of the balance arms or a polarizer. An estimate of the period, then the frequency and finally the inertia and / or actual dimensions can then be deduced. The data collected are essentially point clouds of the passage times.

[0124] On the other hand, it is possible to estimate by simulation a natural frequency and / or a resonance frequency and / or the inertia for each inertial element or inertial element blank tested on the wafer. For this purpose, dimensional measurements can be made of each inertial element or inertial element blank tested to reconstruct by numerical modeling the part in question in order to simulate by numerical calculation its vibration response to the imposed spectrum, and to also find the inertia of the inertial element or inertial element blank.

[0125] A high-resolution 3D X-ray tomography approach would allow the extraction of point clouds giving the 3D material density of the inertial elements, and, through appropriate image reconstruction, a mapping of the section of the inertial elements. These different types of data make it possible to deduce the dimensions of the inertial elements and to estimate the inertia of the inertial elements by a geometric approach combined with weighing and / or by knowing the material density of the inertial elements.

[0126] Another approach consists of analyzing the forced oscillations of an inertial element coupled to an elastic reference return member and an escapement. A laser measurement of the passage times of the balance arms (point clouds), as presented above, makes it possible to measure the frequency and deduce the inertia. An alternative can be considered from an acoustic acquisition (Witschi type microphone) which records the shocks of the different operating phases of the escapement / lever system. The measured data are either point clouds of the passage times of the balance arms, or the temporal evolution of the acoustic pressure level. These types of experimental data make it possible to deduce the period, then the frequency, then the inertia and finally the dimensions of the bar of the inertial element. Establishment of the prediction model

[0127] During the learning phase, oscillation amplitude measurements are carried out on physical inertial elements, and resonance frequencies are identified (see figure 7 for example). In order to be able to subsequently link the resonance frequencies measured on inertial elements to inertias and / or dimensional corrections to be made, a correlation phase must be planned during which a predictive model is constructed.

[0128] The operations described above (vibration measurements, identification of resonance peaks, mid-height bandwidth and its mid or corrected value, determination of the inertia and / or dimensions of the inertial elements) make it possible to feed a database that can relate the position of the inertial element on the wafer, spectra or periods of oscillation or mid-height bandwidth and its mid or corrected value with the inertias and / or effective dimensions of the inertial element. As seen above, this database can be built from numerical simulations on a finite element model of the inertial element. These simulations make it possible to generate reference spectra or periods of oscillation associated with the inertias.This database can also be supplemented with experimental measurements by measuring vibration spectra, oscillation periods and the positions of inertial elements on the wafer as well as their associated inertias. One of the advantages of this approach is that the training database is enriched as the tests progress. This can allow for an adaptive model depending on the wafers and inertial elements and contributes to the reduction of the standard deviation in inertia on the wafers.

[0129] This database can be used to build a prediction model, and several solutions are offered.

[0130] A numerical model, for example polynomial, can be constructed to calculate, as a function of a resonance frequency value, a real dimension, a dimensional correction or a real inertia.

[0131] Categorization can also be performed by performing a k-means partitioning of the input data (the results of vibration measurements, typically the frequency of resonance peaks) and the output data (the inertia, and / or the dimensions of the inertial elements) and linking them together to establish a correspondence.

[0132] 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 inertias or dimensions of the inertial elements, the classes being able to be defined by value increments.

[0133] In summary, the training phase includes a test phase (excitation of the inertial elements or inertial element blanks with measurement of the vibration characteristics to reconstruct a vibration spectrum and identify resonance frequencies). A measurement phase of the inertias and / or dimensions of the inertial elements is also performed. Once the input data (the resonance frequencies) and the output data (the inertias and / or dimensions of the inertial elements) for a significant sample are available, the prediction model construction phase can be performed.

[0134] It may be noted that it may be advantageous to verify that the established prediction model has good sensitivity, i.e. that for two different input values, the model gives two distinct output values. The applicant noticed that the sensitivity of the prediction model was not the same for all resonance peaks. In particular, reference may be made to the figure 8 which represents a graphical construction of the prediction formula established with the data from the figure 7 , where we can note a director coefficient of 0.0034 mg.cm 2< / Hz and an ordinate at the origin of -114.46 mg.cm 2< for the resonance peaks located around 37kHz.

[0135] On the one hand, the applicant has noticed that the direction coefficient could be larger for high resonance frequencies, which provides better prediction sensitivity, to predict distinct inertia or dimensional correction values, even from close resonance frequency values. It is advantageous to provide, during the learning phase, a step of comparing the sensitivity of the prediction to verify / confirm that it is preferable to consider and choose certain resonance peaks at high frequencies (for example above 10 kHz, preferably above 20 kHz) to then predict as accurately as possible an inertia and / or a dimensional correction as a function of the measured vibration response.

[0136] On the other hand, the applicant also noticed that even for close resonance frequencies, the resonance modes (in particular the deformation and / or displacement modes of the inertial elements) could differ significantly, which can also affect the sensitivity of the inertia prediction and / or dimensional correction. It is advantageous to provide, during the learning phase, a step for comparing the sensitivity of the prediction in order to choose to subsequently consider this or that resonance frequency and not another in order to predict as accurately as possible an inertia and / or a dimensional correction as a function of the vibration response.

[0137] From the above remarks relating to the study of the sensitivity of the prediction, it is possible to plan, during the learning phase, to classify the different resonance peaks identified according to the prediction sensitivity of the inertia and / or the dimensional correction. It is then possible to plan to define the excitation frequency range (which will be applied during a pure prediction phase) to include at least one or more resonance peaks or frequencies which give(s) the best sensitivity. Thus, imposing a variable vibrational excitation on the frequency range thus predetermined will guarantee to be able to make an accurate prediction for the identified resonance peak or predictions for each of the identified resonance peaks, which overlap or reinforce each other.

[0138] Generally speaking, the learning phase makes it possible to choose either resonance peaks at high frequencies and / or resonance peaks which correspond to particular resonance modes making it possible to predict precise and reliable values, and the frequency range will be predetermined to include at least one resonance peak and preferably several, in order to be able to make either a single prediction as precise as possible, or several predictions (one per resonance peak deemed interesting) in order to then carry out cross-checks, averages or even adjustments of the predicted values.

[0139] For example, it is possible to predict several inertia values or dimensional corrections from several peaks or resonance frequencies, and then calculate a definitive value, by carrying out, from the predicted values, a weighted average by assigning weights to each predicted value, each weight being determined according to the sensitivity identified for each corresponding peak or resonance frequency.

[0140] Alternatively and preferably, it is possible to provide for having only one model which takes all the peaks or resonance frequencies as input and which returns the inertia or the dimensional correction, the learning phase of the model being used precisely to calculate the weightings on the input peaks or resonance frequencies. Prediction phase

[0141] Once the learning phase is complete, one can move on to a prediction phase, for example during an inertial element inspection process. The inspection process can typically be carried out on inertial element blanks made on a wafer and still attached to this wafer, so as to estimate the inertia and / or the dimensions of the inertial elements of the sample, in order to determine whether a dimensional correction is necessary.

[0142] Once the model is trained, the control procedure to be deployed is as follows: 1) Locating the position of the inertial element on the wafer, measuring the vibration spectra or oscillation period (as described above), 2) Predicting the inertia and / or dimensions of the inertial element by applying the predictive model, 3) Determining whether a dimensional correction is necessary to achieve the target natural frequency or inertia.

[0143] During the control process, it is also possible to quantify the exact correction to be made, so that the manufacturing process can include, in addition to the above control: 1) Knowing the effective inertia of the inertial element estimated according to the model and the target inertia and / or the target dimensions: apply the necessary correction dose.

[0144] Repeat step 1) and step 2) of the inspection process to check the inertia / dimensions of the inertial element and confirm that the target values are met, within a tolerance threshold, or repeat these steps and the dimensional correction until the inertia / dimension predicted by the model reaches the target values. Sampling

[0145] It is known that several hundred inertial elements are produced on a wafer and that the dimensions of the produced inertial elements can vary depending on the regions of the wafer. While the inertia evaluation can be carried out on a single inertial element, in practice, it will be carried out on a sample of inertial elements, distributed over the wafer.

[0146] From the evaluations carried out, corrections can be made for the entire wafer in a homogeneous manner, or differentiated by region, if the results obtained vary from one inertial element to another. This allows us to reduce the standard deviation of the dispersion of inertias on the same wafer. Furthermore, if we know the inertias of all the inertial elements by applying the model, we can determine the optimal correction to reduce the overall dispersion.

[0147] We can even consider going as far as an evaluation of all the inertial elements of the wafer, in particular with a vibration evaluation, because this is very quick to carry out.

[0148] It is possible to provide for the manufacture of inertial elements having initial dimensions larger than the target dimensions and the correction step can then consist of removing material (by time-controlled dissolution, by time-controlled oxidation, etc.). Alternatively, it is also possible to provide for the production of inertial elements having dimensions or a mass smaller than the target dimensions or mass and the correction step can then consist of adding material (by time-controlled coating, etc.).

[0149] The method, consisting of identifying resonance frequencies by imposing a vibration excitation on the inertial element blanks alone, makes it possible to quickly obtain measurement data, without having to, for example, carry out assembly operations with an elastic return member, while limiting measurement errors because only the inertial element blank is tested (there is no error that can be linked to the elastic return member, such as its stiffness, its assembly position, its free length, pollution, etc.). Prediction of the coefficient of thermal expansion of the inertial element and / or the thermal coefficient (TC) of a clock system comprising the inertial element

[0150] For the section relating to the prediction of the coefficient of thermal expansion of the inertial element and / or the thermal coefficient (TC) of a clock system comprising the inertial element, we can proceed as follows: Step 1: measurements or calculations of the natural or resonant frequencies on wafer at several temperatures T (for example 8°C, 23°C and 38°C); Step 2: detach inertial elements, assemble them with a hairspring and mount them in movements; Step 3: measure the thermal coefficients (TC) in motion according to the procedure of the Swiss Official Chronometer Testing Institute (COSC) for example (24h at 8°C, 24h at 23°C and 24h at 38°C); Step 4: build a prediction model between the natural or resonant frequencies measured in step 1 and the thermal coefficients (TC) of the movement measured in step 4.

[0151] In step 1, it may be difficult to perform vibration measurements for multiple temperatures. One could consider performing vibration measurements for a single temperature (e.g., 23°C, clean room temperature) and then constructing a numerical model capable of estimating the evolution of natural frequencies with temperature using the following procedure: Construct a finite element model of an inertial element with a silicon oxide layer; Assign the relevant material parameters and their evolution with temperature; Carry out a modal analysis over the temperature range [8°C - 38°C]; Plot the evolution of the natural or resonant frequencies as a function of temperature and for different oxide layer thicknesses.

[0152] We can of course proceed in the same way for a multi-material inertial element, and in particular with a balance comprising a bimetallic strip or a bi-material part which causes a deformation aimed at compensating or even cancelling an expansion or a radial displacement of the rim as a function of the temperature.

[0153] 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 in an oven or by conduction to identify these laws experimentally.

[0154] The result of such a prediction can be observed figure 9 , where the resonance frequencies of the same resonance mode (number 10 among, for example, 200 identified resonance modes) are represented for three distinct temperatures T1, T2, T3. We can see a difference in the value of the resonance peak frequency between the three temperatures.

[0155] Step 3 can be carried out by detaching the parts measured in step 1 and mounting them in a reference movement, and the running of these movements can be measured according to the three temperatures 8°C, 23°C, 38°C.

[0156] To establish a thermal coefficient prediction model that can receive as input the vibration characteristics and output the thermal expansion coefficient of the inertial element and / or the thermal coefficient (TC) of a watch system including the inertial element, we can therefore use the resonance frequency data identified at the three temperatures for the parts taken into account, and the running data at the three temperatures for these same parts.

[0157] 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 having a high resonance frequency, the thermal expansion coefficient of the inertial element and / or the thermal coefficient (TC) of a watch system comprising the inertial element. Of course, when it comes to predicting the thermal coefficient (TC) of a watch system comprising the inertial element, the thermal coefficient prediction machine can receive as input the reference of the watch device in question, or its value or its contribution to the thermal coefficient. It can indeed be considered that for a given caliber reference, the different parameters which intervene in the CT of the movement (temperature sensitivity of the balance, the gear train, the bearings, the lubricants, etc.)) are constant and do not constitute adjustment variables.

[0158] There is no longer any need to assemble movements to measure the thermal coefficient (TC) of a watch system including the inertial element; this time-consuming and variability-prone step can be eliminated.

[0159] There would be the possibility of carrying out an iterative treatment on parts of the same wafer: after predicting the coefficient of thermal expansion of the inertial element and / or the thermal coefficient (CT) of a watch system comprising the inertial element, it would be possible to detach only the parts having the desired performances, and apply a new thermo-compensation step (oxidation and / or deoxidation) to the parts which are identified as not compatible or not conforming to the desired performances.

[0160] We can therefore predict the thermal expansion coefficient of the inertial element easily and by considering equation 4, we can plan to adjust this thermal expansion coefficient of the inertial element to obtain a thermal coefficient (CT) as low as possible for a clock system (here the oscillator) including the inertial element. Indeed, the figure 10 schematically shows the rate of a timepiece as a function of temperature, and the contribution of the oscillator components. The two positive terms are related to the hairspring: CTE is the Young's modulus thermal coefficient and 3α s is the thermal expansion coefficient of the hairspring. The negative term is -2α b , which is the thermal expansion coefficient of the inertial element (the balance wheel).

[0161] With a bi-material balance (for example with a bimetallic serge comprising two different metals or a silicon balance covered with an oxide layer, or with a coated metal part), it is possible to adjust the term -2α b within an adjustment range shown in gray figure 10 and included between the two adjustment limit curves of -2α b .

[0162] Thus, it is possible to retouch the inertial element after the prediction of the thermal coefficient of the inertial element to obtain a thermal expansion coefficient which will lead to adjusting the thermal coefficient (CT) of the oscillator and have a sum (CTE + 3α s -2α b ) as close as possible to zero so that the variations of the rate M of the timepiece as a function of the temperature remain within the limits MM and M m represented. Of course, the corrections made to adjust the thermal expansion coefficient can modify the inertia of the inertial element, and it is appropriate to take into account and / or control and / or measure this parameter after the modifications or corrections to make a pairing which leads to obtaining an oscillator having a predetermined oscillation frequency and adequate temperature behavior.

[0163] In summary, the invention makes it possible to simplify the manufacturing and control processes of inertial elements made of metallic or silicon material in order to manufacture movements with low or zero sensitivity to temperature variations: by applying a particular vibration excitation to metallic, composite, bi-material or oxidized parts, by providing the vibration response or resonance frequencies or resonance peaks or data extracted from the vibration response to a thermal coefficient prediction machine. With this method, it is possible to simply check whether the parts have a thermo-compensation adapted to the movement in which they will be mounted. It can be noted that it is also possible, optionally, for example at a particular manufacturing stage (before coating or oxidation for example) to carry out a particular vibration excitation and submit the vibration response or resonance frequencies or resonance peaks or data extracted from the vibration response to an inertia prediction machine.

[0164] However, it can be noted that the data drawn from the vibration response and used for these inertia predictions are not necessarily the same as those for the thermal coefficient prediction and it can even be considered that preferably, the data drawn from the vibration response and used for the inertia prediction are different and distinct from those for the thermal coefficient prediction because the sensitivities may not be the same.

Claims

1. A method for controlling an inertial element (100) or an inertial element blank (100) arranged to form an inertial element (100), the control method comprising the following steps: a. applying to the inertial element (100) or the inertial element blank (100) a time-varying vibrational excitation to cover a predetermined frequency range, b. identifying at least one characteristic of a resonance frequency of the inertial element (100) or the inertial element blank (100), such as a resonance peak, upon or in response to the vibrational excitation over the predetermined frequency range, c. subjecting said at least one resonance frequency characteristic identified in step b to a thermal coefficient prediction machine. to determine a coefficient of thermal expansion of the inertial element (100) and / or a thermal coefficient (CT) of a clock system comprising the inertial element (100).

2. Control method according to claim 1, comprising: - a step of submitting to an inertia prediction machine said at least one resonant frequency characteristic identified in step b., or a characteristic of another resonant frequency, for example identified in step b., to determine an inertia of the inertial element (100), - optionally, a step of performing a classification or a pairing of the inertial element according to its inertia and at least one of the coefficient of thermal expansion of the inertial element (100) and the thermal coefficient (CT) of a watch system comprising the inertial element (100).

3. A control method according to claim 1 or 2, wherein step b. comprises: b1. a first identification step comprising identifying a first characteristic of a first resonant frequency such as a first resonant peak, b2. a second identification step comprising identifying a second characteristic of a second resonant frequency such as a second resonant peak, the second resonant frequency being different from the first resonant frequency, and wherein step c. comprises: c1.a first prediction step consisting of submitting to another prediction machine the first characteristic of the first resonant frequency to determine a parameter different from the thermal expansion coefficient of the inertial element (100) and / or the thermal coefficient (CT) of a watch system comprising the inertial element (100), such as an inertia of the inertial element (100) or of the inertial element blank (100), c2. a second prediction step consisting of submitting to the thermal coefficient prediction machine the second characteristic of the second resonant frequency to determine the thermal expansion coefficient of the inertial element (100) and / or the thermal coefficient (CT) of a watch system comprising the inertial element (100).

4. Control method according to claim 3, 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 of applying to the inertial element (100) or to the inertial element blank (100) a first vibrational excitation varying over time to cover a first predetermined frequency range, a2. a second vibrational excitation step, carried out before step b2. and consisting of applying to the oxidized inertial element (100) or to the oxidized inertial element blank (100) a second vibrational excitation varying over time to cover the first predetermined frequency range or a second predetermined frequency range.

5. Control method according to claim 3, in which step a. is implemented after an oxidation step, and in which steps b1. and b2. take into account the same vibrational response of the inertial element (100) or of the inertial element blank (100).

6. Control method according to one of claims 3 to 5, in which: - the first resonance frequency is chosen to be a resonance frequency of a plane resonance mode, and / or - the second resonance frequency is chosen to be a resonance frequency of an out-of-plane resonance mode.

7. Control method according to one of claims 3 to 6, wherein the first resonant frequency is lower than the second resonant frequency and / or: - the first resonant frequency is chosen in 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 very preferably from 10 kHz to 35 kHz, and / or - the second resonant frequency is chosen in 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 very preferably from 100 kHz to 200 kHz.

8. Control method according to one of claims 1 to 7, the inertial element (100) having at least two expected predetermined resonant frequencies, in which the frequency range is predetermined to cover at least the two expected predetermined resonant frequencies.

9. Control method according to one of claims 1 to 8, in which 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 inertial element (100) or of the inertial element blank (100), preferably carried out at least partially during step a.

10. Control method according to one of claims 1 to 9, the inertial element (100) or the inertial element blank (100) being contained in a base plane, in which step b. comprises: - a step b" of measuring an amplitude or a speed or an acceleration of displacement of at least one point of the inertial element (100) or of the inertial element blank (100) in a direction normal to the base plane, and / or - a step b'" of measuring an amplitude or a speed or an acceleration of displacement of at least one point of the inertial element (100) or of the inertial element blank (100) in a direction contained in the base plane.

11. Control method according to one of claims 1 to 10, in which step b. comprises: - a step of identifying a resonance peak of the inertial element (100) or of the inertial element blank (100) as a function of an amplitude or a speed of movement of at least one point of the inertial element (100) or of the inertial element blank (100).

12. A control method according to claim 11, wherein the characteristic of the resonant frequency is identified on the basis of the width of the resonant peak, at half height of the maximum value of the resonant peak.

13. Control method according to one of claims 1 to 12, in which the thermal coefficient prediction machine implements a regression method, for example a linear regression, to predict the thermal expansion coefficient of the inertial element (100) and / or the thermal coefficient (CT) of a clock system comprising the inertial element (100).

14. Control method according to one of claims 1 to 13, comprising a preliminary step of taking into account the material of the inertial element (100) or of the inertial element blank (100), and of adjusting a maximum amplitude of the vibration excitation and / or a frequency range of the predetermined frequency range as a function of the material of the inertial element (100) or of the inertial element blank (100).

15. A control method according to one of claims 1 to 14, wherein, if step c. determines that the coefficient of thermal expansion of the inertial element (100) and / or the thermal coefficient (CT) of a watch system comprising the inertial element (100) is outside a range of expected values, then the method comprises at least one step of identifying or isolating or reworking or scrapping the inertial element (100) or the inertial element blank (100).

16. A control method according to one of claims 1 to 14, wherein, if step c. determines that the coefficient of thermal expansion of the inertial element (100) and / or the thermal coefficient (CT) of a watch system comprising the inertial element (100) is outside a range of expected values, then the method comprises at least one step of defining a step of processing the inertial element (100) or the inertial element blank (100), such as a step of adding or removing material, or adding or removing a second material, or coating, thermo-compensation, oxidation or deoxidation, to obtain the coefficient of thermal expansion of the inertial element (100) and / or the thermal coefficient (CT) of a watch system comprising the inertial element (100) within the range of expected values 17. A method of learning a prediction machine for implementing step c. of the control method of one of claims 1 to 16, comprising the steps of: i- forming inertial elements or inertial element blanks (100) and applying a thermo-compensation step thereto, ii- applying to each of the inertial elements or each of the inertial element blanks (100) a vibrational excitation that varies over time to cover a predetermined frequency range, iii- identifying at least one characteristic of a resonance frequency of each inertial element (100) or each inertial element blank (100) when applying the predetermined frequency range and recording the temperature of the parts during step ii- and / or iii-,iv'- mounting a plurality of inertial elements or inertial element blanks (100) in an oscillating mechanism comprising an elastic return member having a predetermined stiffness so as to measure for each inertial element (100) or inertial element blank (100) a sustained oscillation frequency or a rate of the clockwork system formed by, or comprising, the oscillating mechanism at at least one predetermined temperature and preferably at least two predetermined temperatures,and / or iv"- modeling in a simulation tool a plurality of inertial elements or inertial element blanks (100) in an oscillating mechanism comprising an elastic return member having a predetermined stiffness so as to calculate for each inertial element (100) or inertial element blank (100) a sustained oscillation frequency and / or a thermal coefficient of a watch system comprising the inertial element (100) and / or the rate of the watch system comprising the inertial element (100) at at least one predetermined temperature and preferably at least two predetermined temperatures, and / or iv'"- modeling in a simulation tool at least one inertial element so as to find said at least one characteristic of a resonance frequency identified in step iii-, v- optionally, deduce at least one expected resonance frequency from said at least one resonance frequency identified in step iii-,and / or the sustained oscillation frequency and / or the rate of the watch system measured in step iv'- and / or calculated in step iv"- vi- deduce a coefficient of thermal expansion of the inertial element (100) and / or the thermal coefficient (CT) of a watch system comprising the inertial element (100) from the measurements of step iv'-, and / or the calculations of step iv"-, and / or the modeling of step iv‴, vii- provide to the prediction machine, and for each inertial element (100) or inertial element blank (100): - 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 coefficient of thermal expansion of the inertial element (100) and / or the thermal coefficient (CT) of a clock system comprising the inertial element (100) deduced in step vi-.,

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