Method for controlling and manufacturing a hairspring for a timepiece

Abstract

1. A method for controlling a hairspring or a hairspring blank configured to form a hairspring, comprising: a. applying a time-varying vibrational excitation to the hairspring or hairspring blank to cover a predetermined frequency range; b. identifying at least one characteristic of the resonant frequency of the hairspring or hairspring blank, such as a resonant peak, upon or in response to vibrational excitation over a predetermined frequency range; c. applying the resonant frequency characteristics identified in step b. to a thermal coefficient predictor to determine the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the timepiece system including the hairspring.

Description

[Technical Field]

[0001] The present invention relates to the field of control and manufacturing of components for watchmaking, and more particularly to a method for controlling and manufacturing balance springs (also known as oscillators) for timepieces. Latest Technology

[0002] The movement of a mechanical watch is regulated by a mechanical governor or oscillator comprising an oscillator, i.e. an elastically deformable component whose oscillations determine the rate of the watch. For example, many watches include an oscillator with a hairspring as an oscillator mounted on the axis of the balance wheel and set to oscillate by the escapement. The natural frequency of the balance wheel-hairspring pair is used to regulate the rate of the watch and depends on several parameters, in particular the stiffness of the hairspring and the operating temperature.

[0003] In fact, the frequency f of the regulating element formed by a hairspring having stiffness R coupled to a balance wheel having inertia I is given by the following equation:

number

[0004] The stiffness of the hairspring also defines its natural vibration characteristics, such as its natural frequency and resonant frequency. In this application, the natural frequency of an elastic system (oscillator alone or oscillator-balance wheel pair) is the frequency at which this system oscillates when it is free to evolve, i.e., in the absence of an exciting force. Furthermore, the resonant frequency of an elastic system (e.g., oscillator only) subjected to an exciting force is the frequency at which a local maximum in the displacement amplitude can be measured for a given point of the elastic system. In other words, when an elastic system is excited with an excitation source of variable frequency over time, the displacement amplitude follows an upward slope before this resonant frequency and a downward slope after it, at any point that does not correspond to a vibration node. Typically, during such tests, a record of the displacement amplitude as a function of the exciting frequency has a displacement amplitude peak or resonant peak that is associated with or characterizes the resonant frequency.

[0005] The stiffness of a hairspring oscillator typically depends on the properties of the material from which it is made, as well as its dimensions, particularly the thickness (i.e., width) of the turns along its bar. More specifically, stiffness is given by the following formula:

number

number

[0006] As will be explained in more detail below, operating temperature is a parameter that affects the operation of the governor member, and Equation 1 can be derived in terms of temperature T to obtain the following equation:

number

number

[0007] The natural frequency of a regulating element formed by a hairspring of stiffness R coupled to a balance wheel of inertia I is, in particular, proportional to the square root of the stiffness of the hairspring. The main specification of the hairspring is its stiffness, which must be within a well-defined interval so that it can be paired with the balance wheel, which forms the inertia element of the oscillator. This pairing operation is essential for the precise regulation of the frequency of a mechanical oscillator.

[0008] In recent years, the importance of magnetic fields in the modern environment has led watchmakers to use silicon balance springs, which are less susceptible to magnetic disturbances than metal balance springs.

[0009] Highly advantageously, microfabrication techniques allow hundreds of silicon balance springs to be manufactured on a single wafer. In particular, it is known to manufacture multiple silicon oscillators with extremely high precision using photolithography and machining / etching methods in silicon wafers. While methods for manufacturing these mechanical oscillators typically use monocrystalline silicon wafers, wafers made from other materials can also be used, such as polycrystalline or amorphous silicon, other semiconductor materials, glass, ceramics, carbon, carbon nanotubes, or composites containing these materials. Monocrystalline silicon, in turn, belongs to the cubic crystal class m3m, in which the thermal expansion coefficient (alpha) is isotropic.

[0010] It is very important that the oscillator characteristics are as stable as possible in order to have a stable watch rate, with as small as possible the rate differences, especially depending on the operating temperature (summer-winter, whether the watch is worn or not).

[0011] Silicon has a highly negative first thermoelastic coefficient, resulting in a significant change in the stiffness of a silicon oscillator, and therefore its natural frequency, depending on temperature. To at least partially compensate for this drawback, documents EP 1422436, EP 2215531, and WO 2016128694 describe hairspring mechanical oscillators constructed from a core (or, in the case of WO 2016128694, two cores) made of monocrystalline silicon, whereby the temperature variation of Young's modulus is compensated by a layer of amorphous silicon oxide (SiO2) surrounding the core (or cores), the latter being one of the few materials with a positive thermoelastic coefficient. As shown in Equation 5 above, temperature variations can result in rate variations due to the thermal coefficient CT, which depends, inter alia, on the thermal coefficient of Young's modulus, the thermal expansion coefficient of the hairspring, and the thermal expansion coefficient of the outer edge of the balance wheel. The silicon balance spring and its thermal compensation therefore make it possible to adjust the term in Equation 5 relating to the balance spring to obtain the thermal coefficient CT of the oscillator. It is then possible to characterize the CT of a larger horological system integrating the balance spring, all the way up to the CT of the complete horological system, by determining the thermal drift of the caliber, which integrates the thermal drift of the escapement and gear train, including the effects of lubrication. From this perspective, the balance spring is considered the only adjustment variable to obtain the CT of the horological system integrating it as low as possible.

[0012] When hairsprings of silicon or another material are produced by mass production on wafers, the final functional yield is given by the number of hairsprings whose stiffness corresponds to the pairing interval divided by the total number of hairsprings on the wafer.

[0013] However, the microfabrication processes used in producing hairsprings on wafers, more specifically the etching processes, typically result in significant geometric variance between the dimensions of hairsprings on the same wafer, and therefore their stiffness, even though the etching pattern is the same for each hairspring. The variance in measured stiffness typically follows a Gaussian distribution. Therefore, to optimize manufacturing yield, the focus is on centering the mean of the Gaussian distribution around the nominal stiffness value and reducing the standard deviation of that Gaussian distribution.

[0014] Furthermore, the dispersion of stiffness is even greater between hair springs of two wafers etched at different times according to the same method specifications. This phenomenon is shown in Figure 1, which illustrates the stiffness dispersion curves Rd1, Rd2, and Rd3 of hair springs on three different wafers. Generally, for each wafer, the stiffness R distribution (with respect to the number N of hair springs with this stiffness) follows a normal or Gaussian law, with each dispersion curve centered around its respective mean value Rm1, Rm2, and Rm3.

[0015] Documents WO 2015113973 and EP 3181938 propose to overcome this problem by forming a hairspring according to dimensions larger than those necessary to obtain a hairspring with a predetermined stiffness, measuring the stiffness of this hairspring formed by coupling it to a balance wheel having a predetermined inertia, calculating the thickness of material to be removed to obtain the dimensions necessary to obtain a hairspring with the predetermined stiffness, and removing this thickness from the hairspring.Similarly, document EP 3181939 proposes to overcome the same problem by forming a hairspring according to dimensions smaller than those necessary to obtain a hairspring with a predetermined stiffness, determining the stiffness of this hairspring formed by coupling it to a balance wheel having a predetermined inertia, calculating the thickness of material to be added to obtain the dimensions necessary to obtain a hairspring with the predetermined stiffness, and adding this thickness to the hairspring.

[0016] In this way, as shown in FIG. 2, regardless of the average stiffness Rm1, Rm2, etc. on a given wafer, the stiffness distribution curves Rd1, Rd2, etc. can be re-centered about a nominal stiffness value, Rnom.

[0017] This technique requires high precision in measuring the frequency of the hairspring to determine its stiffness. In particular, measurement errors can be caused by the balance wheel with a given inertia or by the assembly that takes place. A step of calculating the thickness to be removed must then be carried out in order to remove the calculated thickness again with high precision. In addition, it should be noted that the coupling of the hairspring with the balance wheel with a given inertia requires delicate operations that require long preparation times. Finally, it should be noted that any assembly operations on parts or blanks still present on a wafer significantly increase the risk of contamination (e.g., the presence of silicon particles (debris) generated during handling operations).

[0018] The present invention aims to propose a method that does not have the above-mentioned drawbacks and that allows a faster production flow and / or a reduced risk of contamination and / or a larger sampling and / or a more accurate measurement of the thermal coefficient of Young's modulus (CTE) of a hairspring and / or the thermal coefficient (CT) of a timepiece system equipped with a hairspring, and therefore a more individualized correction of the hairsprings of the wafers in order to obtain a timepiece system whose operation is little or not disturbed by temperature variations. Summary of the Invention

[0019] More specifically, a first aspect of the invention is a method for controlling a hairspring or a hairspring blank configured to form a hairspring, the method comprising: a. applying a time-varying vibrational excitation to the hairspring or hairspring blank to cover a predetermined frequency range; b. identifying at least one characteristic of the resonant frequency of the hairspring or hairspring blank, such as a resonant peak, upon or in response to vibrational excitation over a predetermined frequency range; c. subjecting the resonant frequency characteristic identified in step b. (preferably at least one characteristic of the resonant frequency of the hairspring or hairspring blank, such as the resonant peak identified in step b.) to a thermal coefficient predictor to determine the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of a timepiece system including the hairspring.

[0020] The method according to the above embodiment includes the steps of vibratingly exciting the hairspring or hairspring blank, measuring its resonant frequency characteristics, and then, by prediction, estimating the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the timepiece system including the hairspring. There is no assembly of a balance wheel or another component, saving time. In addition, measurements are performed only on the hairspring or blank, which limits the possibility of errors and contamination induced by other components or component assemblies. Measurement accuracy is improved because there are fewer sources of variation due to other components or contamination. In other words, the hairspring or hairspring blank is tested alone. The vibrating excitation is applied to the part or single blank without being coupled to any balance wheel, weight, or oscillatory system. The method allows for the control of a single free part (i.e., having at least one free end that is not attached to any mechanism or balance wheel), which brings at least the advantages of increased productivity (no assembly with the oscillating system), increased quality (no contamination or damage to parts, more parts can be tested with the same budget), and increased accuracy (no errors associated with other components of the oscillating system).

[0021] It should be noted that the determination of the thermal coefficient of Young's modulus (CTE) of a hair spring or of a hair spring blank by the method according to the invention is well suited to oxidized parts, where the thickness of the oxide layer is not precisely known at this stage of the manufacturing process. According to the invention, it is easy to obtain the thermal coefficient of Young's modulus (CTE) of an oxidized hair spring or of an oxidized hair spring blank, which are in a sense composite parts (core made from silicon and shell made from silicon oxide).

[0022] According to one embodiment, vibration excitation can be performed using an impact device that applies the excitation to the component being tested for a relatively short time. In other words, it is possible to apply a displacement or acceleration to the component being tested for a very short time (over a period of less than 1 second, less than 500 ms, less than 100 ms, or less than 10 ms). In particular, the impact device can impact the balance spring or its support, causing the component to vibrate. An impact hammer or any device with a moving mass can be used. In the case of wafer-mounted components, it is possible to impact the wafer or the mount supporting the wafer. Depending on the component being tested and its position on the wafer, it is possible to apply the impact at a specific position on the wafer and / or in a specific direction. The component is vibrated, the vibration response is recorded over time, and resonant peaks and their frequencies can be extracted from this measurement, for example, using a Fourier transform.

[0023] According to one embodiment, a timepiece system including a hairspring comprises: - hairspring and balance wheel, - its escapement devices, such as the hairspring, balance wheel, and anchor escapement, - its gear train, including its hairspring, balance wheel, escapement device, and finishing gear train; - the entire watch movement, including its balance spring. In all of the above cases, it is possible to know in advance the values of the thermal coefficients of the components other than the hairspring, or at least their contribution to the thermal coefficient of the timepiece system. In practice, these values are standard and known in advance depending on the standards or components selected, and in the case of a silicon hairspring, it is possible to adjust the contribution of the hairspring in equation 5 above in order to obtain a thermal coefficient of the timepiece system that is within a range of values and / or within the desired tolerances.

[0024] According to one embodiment, a vibrational excitation is applied to a hairspring or hairspring blank having a free end (typically a central collet) and the other end fixed to a wafer or clamp. From a mechanical point of view, the vibrational excitation can be roughly considered as being applied to a mass (located at the center of gravity of the hairspring) connected by a spring (the elastic part of the hairspring) to a reference frame (a gripping clip for the hairspring only, or the rest of a substrate or plate for an unseparated blank made, for example, from silicon). The vibrational excitation moves the suspended mass. In other words, the vibrational excitation is applied to only the hairspring or only the hairspring blank.

[0025] It should also be noted that if it is determined that dimensional corrections and / or additional processing operations must be performed on the tested component (or on all single components mounted on the same wafer, or on single components mounted on areas of the wafer that may or may not include the tested component), this can be done on the single component without re-disassembly of anything (e.g., oxidation can be applied directly to the silicon component at the end of testing). It is therefore possible to add or remove material from the single component in order to perform doping to change the intrinsic values (stiffness, thermal coefficient (CTE) of the hairspring, Young's modulus). In other words, dimensional corrections and / or additional processing operations are performed on the single component.

[0026] The method according to the above embodiment therefore makes it possible to test the hairspring blank during production while limiting the risk of contamination or assembly errors. Dimensional corrections (in cross section, height and / or thickness) and / or additional processing operations are possible. The method according to the above embodiment also makes it possible to test the finished hairspring and, for example, sort it by stiffness increments or plan its pairing with a particular balance wheel.

[0027] According to one embodiment, Step b. b1. a first identifying step, which may include identifying a first characteristic of a first resonant frequency, such as a first resonant peak; b2. a second identifying step, which may include identifying a second characteristic of a second resonant frequency, such as a second resonant peak, where the second resonant frequency is different from the first resonant frequency; Step c. c1. a first prediction step, which may consist of subjecting the first characteristic of the first resonant frequency to another predictor to determine parameters different from the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient of the timepiece system including the hairspring, such as stiffness or defects of the hairspring or hairspring blank; c2. A second prediction step may comprise subjecting the second characteristic of the second resonant frequency to a thermal coefficient predictor to determine the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the timepiece system including the hairspring.

[0028] According to the above embodiment, the first resonant frequency is used to determine a parameter different from the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the timepiece system including the hairspring, such as the stiffness or defects of the hairspring or the hairspring blank. The second resonant frequency is used to determine the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the timepiece system including the hairspring. In other words, two different frequencies are retained or identified in order to predict or calculate two separate parameters: the stiffness or the presence of defects on the one hand, and the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the timepiece system on the other hand.

[0029] According to one embodiment, the other predictor may be provided to identify defects that require reworking or scrapping of the corresponding part. According to this embodiment, a hair spring with an identified defect cannot be used at all or cannot be used without physical reworking of its geometry and / or its composition and / or its material. In other words, when a defect is identified or determined, a step of separating and / or removing the part for physical reworking (correction or scrapping) of the corresponding part may be provided. The part then follows a manufacturing circuit dedicated to non-conforming parts, including a reworking or scrapping step.

[0030] According to one embodiment, steps b1 and b2 may be separated by a thermal compensation step, such as an oxidation step. Step a. a1. a first step of vibrational excitation, which can be carried out before step b1. and consists of applying to the hairspring or hairspring blank a first vibrational excitation which is variable over time so as to cover a first predetermined frequency range; a2. may comprise a second vibration excitation step, which may be carried out before step b2. and which consists of applying to the oxidized hair spring or the oxidized hair spring blank a second vibration excitation which is variable over time to cover either the first predetermined frequency range or the second predetermined frequency range.

[0031] According to the above embodiment, a first vibration excitation step is used to determine the stiffness or the presence of defects, and a second vibration excitation step is used to determine the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the timepiece system. Different vibration excitations can be imposed between steps a1 and a2.

[0032] According to one embodiment, Step a. may be carried out after the oxidation step; Steps b1. and b2. may take into account or be based on the same vibration response of the hairspring or hairspring blank, in other words a first part of the vibration response is used to identify a first resonant frequency and a second part of the same vibration response is used to identify a second resonant frequency.

[0033] According to one embodiment, the first resonant frequency may be selected to be the resonant frequency of a planar resonant mode, preferably a high resonant frequency, for example above 40 kHz or above 60 kHz; and / or The second resonant frequency can be selected to be the resonant frequency of an out-of-plane resonant mode.

[0034] According to the above-described embodiments, a planar resonance mode can be considered a resonance mode in which different portions of the hairspring or hairspring blank are displaced primarily within the plane of the component at rest. If this plane is defined by directions X and Y, and direction Z is perpendicular to the plane, the displacement in X or Y is equal to or greater than the displacement in Z. In an out-of-plane resonance mode, the displacement in Z is equal to or greater than the displacement in X or Y, preferably two to three times greater than the displacement in X or Y. The applicant has realized that an oxidized component can have significantly different out-of-plane resonance mode frequencies compared to its non-oxidized counterpart. As a result, it may be preferable to consider the out-of-plane resonance mode in order to accurately predict the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient of the timepiece system including the hairspring.

[0035] According to one embodiment, the first resonant frequency may be lower than the second resonant frequency, and / or the first resonant frequency may be selected in the range of values between 0 Hz and 100 kHz, preferably between 0 Hz and 50 kHz, more preferably between 0 Hz and 40 kHz, and very preferably between 10 kHz and 35 kHz; and / or The second resonant frequency may be selected in the range of values between 0 Hz and 300 kHz, preferably between 50 kHz and 250 kHz, more preferably between 60 kHz and 200 kHz, and very preferably between 100 kHz and 200 kHz. The Applicant has noticed that oxidized components may have significantly different resonant mode frequencies compared to their non-oxidized counterparts, for resonant frequencies above 40 kHz, preferably above 50 kHz, and very preferably above 60 kHz. It may therefore be preferable to take into account resonant modes with high resonant frequencies in order to accurately predict the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient of Young's modulus (CT) of the timepiece system including the hairspring.

[0036] According to one embodiment, step b. may consist in characterizing the resonant frequency sensitive to the thermal coefficient of the hairspring or hairspring blank.

[0037] Naturally, the frequency range of the spectrum obtained depends not only on the vibration excitation source but also on the sensor of the measuring instrument used. This frequency range therefore relates both to the excitation frequency range and to the frequency range to which the oscillation amplitude measuring instrument (such as a vibrometer) is sensitive. However, the excitation frequency range is selected to include at least one resonant frequency of the hairspring or blank being tested.

[0038] The predetermined resonant frequency that the finished balance spring should have can be a target natural frequency or resonant frequency, or a target natural frequency range, or a target resonant frequency range, defined by a tolerance around a target value.

[0039] In the above methods, the resonant frequency characteristic is a characteristic of the oscillatory response measured over a predetermined frequency range that includes at least one resonant frequency. Such a characteristic is typically identified after processing the raw measurement signal (e.g., measurement of the amplitude of displacement or velocity or acceleration of a particular point on the hairspring or hairspring blank), which processing may include, for example, a Fourier transform to identify the resonant peak and therefore the resonant frequency.

[0040] It should be noted that the method may determine the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the timepiece system including the hairspring in order to classify the part and / or provide pairing with other specific components and / or to calculate / estimate dimensional corrections and / or additional processing operations to be applied to obtain the target thermal coefficient of Young's modulus (CTE) of the hairspring and / or the target thermal coefficient (CT) of the timepiece system including the hairspring. However, only the identified resonant frequencies may be taken into account to directly calculate / estimate dimensional corrections and / or additional processing operations to be applied to obtain the target thermal coefficient of Young's modulus (CTE) of the hairspring and / or the target thermal coefficient (CT) of the timepiece system including the hairspring.

[0041] According to one embodiment, in step a) the frequency range is applied to multiple hairsprings or hairspring blanks simultaneously. The vibration excitation can typically be imposed on a wafer supporting, for example, hundreds of hairspring blanks still attached to the wafer, thus improving speed.

[0042] According to one embodiment, the frequency range is: -centered on a predetermined resonant frequency, and The predetermined frequency is determined to include at least one frequency range having 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 1 kHz, the frequency range is 850 Hz to 1150 Hz.

[0043] According to one embodiment, the hairspring has at least two expected predetermined resonant frequencies, and the frequency range is predetermined to cover the at least two expected predetermined resonant frequencies. By covering or sweeping a wide range of frequencies, several resonant peaks (or resonant frequencies) can be measured, which can provide better accuracy.

[0044] 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 the edge of the wafer supporting the hairspring blank, or preferably above or below the hairspring or hairspring blank to be excited in particular.

[0045] According to one embodiment, the acoustic source can be coupled to an excitation cone selected to excite at least one hairspring or one hairspring blank. Preferably, if the wafer supports several hairspring blanks, the acoustic source can be coupled to an excitation cone selected to excite at least a portion, preferably all, of the hairspring blanks.

[0046] According to one embodiment, the acoustic source may be selected and / or tuned to generate a vibrational excitation that is variable over time to cover a predetermined frequency range, the frequency range being: - have an amplitude sufficient to generate vibrations of the hairspring or hairspring blank of sufficient amplitude to be detected by means for measuring the displacement amplitude, or the velocity or acceleration, of at least one point of the hairspring or hairspring blank; and / or - for a duration sufficient to estimate the vibration spectrum of the hairspring or hairspring blank.

[0047] According to one embodiment, step b comprises the use of optical measuring means, such as a laser Doppler vibrometer, which relies on the Doppler effect.

[0048] According to one embodiment, step b may be based on measuring over time the amplitude or velocity or acceleration of the displacement of at least one point of the hairspring or hairspring blank, preferably carried out at least in part during step a.

[0049] According to one embodiment, step b comprises: - determining the resonance frequency of the hairspring or hairspring blank according to the operational or modal deformation of at least one point of the hairspring or hairspring blank, the operational or modal deformation being typically defined by the amplitude or speed of the displacement or acceleration and the direction of oscillation (outside or within a specific plane) according to the excitation frequency.

[0050] According to one embodiment, the hairspring or hairspring blank is contained in a base plane, and step b comprises: - step b'' measuring the amplitude or velocity or acceleration of the displacement of at least one point of the hairspring or hairspring blank in a direction perpendicular to the base plane, and / or - measuring the amplitude or velocity or acceleration of the displacement of at least one point of the hairspring or hairspring blank in a direction contained in the base plane.

[0051] Measuring displacement or velocity in several directions allows for better identification of resonant peaks and frequencies.

[0052] According to one embodiment, step b. - identifying a resonance peak of the hairspring or hairspring blank according to the amplitude or speed of the displacement of at least one point of the hairspring or hairspring blank.

[0053] According to one embodiment, the characteristics of the resonant frequency can be determined based on the width of the resonant peak at the mid-height of its maximum, this processing method making it possible to limit calculation errors that may be made by relying solely on determining the frequency location of the peak defined by its maximum.

[0054] According to one embodiment, step b comprises processing the measurement signals, for example by means of a Fourier transform, in order to identify resonant peaks of displacement or velocity or acceleration and / or phase amplitude according to the excitation frequency.

[0055] According to one embodiment, the thermal coefficient predictor may be a calculating machine for predicting or calculating, from the frequency characteristics, the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the timepiece system including the hairspring. In other words, the predictor is not a regulating or self-regulating or feedback loop system for adjusting the resonant frequency in response to a comparison of the measured value with a target value.

[0056] In other words, this predictor is a computing machine which may be a calculation unit intended to implement one or more mathematical formulas to predict the thermal coefficient of Young's modulus (CTE) value of the hairspring and / or the thermal coefficient (CT) value of a timepiece system including the hairspring when it receives as input values of physical properties measured on the hairspring or on a hairspring blank.

[0057] According to one embodiment, a predictor, e.g., this computational unit, may be provided to implement one or more mathematical formulas (e.g., with a multinomial distribution) constructed by linear regression from experimental or simulation data.

[0058] According to one embodiment, the predictor, eg, the computing unit, may be a predictor that uses artificial intelligence software.

[0059] According to one embodiment, the predictor, for example the calculation unit, may be a predictor using at least one neural network designed to receive as input values or graphs taken from the spectrum of vibration measurements and to give as output the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the timepiece system including the hairspring.

[0060] According to one embodiment, the thermal coefficient predictor may perform a classification, performed for example by a neural network, to predict the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the timepiece system including the hairspring.

[0061] According to one embodiment, the thermal coefficient predictor may perform a regression method, for example a linear regression, to predict the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the timepiece system including the hairspring.

[0062] According to one embodiment, the thermal coefficient predictor may perform a classification based on k-means or k-medians splitting to predict the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the timepiece system including the hairspring.

[0063] According to one embodiment, the control method can include a preliminary step consisting of taking into account the material of the hairspring or hairspring blank and adjusting the maximum amplitude of the vibration excitation and / or the frequency range of the predetermined frequency range according to the material of the hairspring or hairspring blank.

[0064] According to one embodiment, if step c. determines that the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the timepiece system including the hairspring is outside the range of expected values, the method may comprise at least one step of identifying or separating or reworking or discarding the hairspring or hairspring blank.

[0065] According to one embodiment, if step c. determines that the Thermal Coefficient of Young's Modulus (CTE) of the hairspring and / or the Thermal Coefficient (CT) of the timepiece system including the hairspring is outside the range of expected values, the method may comprise at least one step consisting of defining a step of treating the hairspring or the hairspring blank, such as a thermal compensation, oxidation or deoxidation step, in order to set the Thermal Coefficient of Young's Modulus (CTE) of the hairspring and / or the Thermal Coefficient (CT) of the timepiece system including the hairspring within the range of expected values.

[0066] According to one embodiment, if step a. is performed on a plurality of hairsprings or hairspring blanks mounted on a wafer, and step c. determines that the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient of the timepiece system including the hairspring (CT) is outside the range of expected values for the first hairspring or first hairspring blank but is within the range of expected values for the second hairspring or second hairspring blank, provision may be made to remove only the second hairspring or second hairspring blank and to provide a step of treating the first hairspring or first hairspring blank, such as a thermal compensation, oxidation or deoxidation step, in order to obtain the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient of the timepiece system including the hairspring (CT) within the range of expected values. Provision may be made to repeat steps a. and b., either by repeating steps a. and b. or by not repeating steps a. and b.

[0067] According to one embodiment, steps a and b are repeated at least several times for the same measurement point of the hairspring or hairspring blank.

[0068] According to one embodiment, steps a and b are synchronized. Such synchronization offers the possibility to detect phase shifts, or damping, or couplings, which can be taken into account to improve the prediction accuracy or to adjust or retune the vibration excitation source.

[0069] A second aspect of the present invention is a method for manufacturing a hairspring having at least one expected predetermined resonant frequency, comprising the steps of: A / forming at least one hairspring or hairspring blank having dimensions that fall within the predetermined tolerances necessary to obtain the expected predetermined resonant frequency; B / Controlling the hairspring or hairspring blank according to the control method of the first aspect.

[0070] According to one embodiment, the method of manufacture comprises: C / If step c. determines that the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the timepiece system including the hairspring is outside the range of expected values, it may include a step consisting of identifying, separating, reworking or discarding the hairspring or hairspring blank formed in step A / .

[0071] According to one embodiment, the hairspring blank may be formed on a wafer along with a plurality of other hairspring blanks.

[0072] A third aspect of the present invention is a predictor learning method for performing step c. of the control method according to the first aspect, comprising: i—forming a hairspring or a hairspring blank and subjecting it to a thermal compensation process; ii - applying to each of the hairsprings or each of the hairspring blanks a vibrational excitation that varies over time (i.e. a variable vibrational excitation that includes the one used during the control method, or preferably the same variable vibrational excitation) to cover a predetermined frequency range (i.e. a predetermined frequency range that includes the one used during the control method, or preferably the same predetermined frequency range); iii - during steps ii- and / or iii-, determining at least one characteristic of the resonance frequency of each hairspring or each hairspring blank (i.e. the characteristic of a resonance frequency identified during the control method or preferably the characteristic of the same resonance frequency) when applying the predetermined frequency range and recording the temperature of the part; iv' - mounting a number of hairsprings or hairspring blanks on an oscillating mechanism having a predetermined inertia and measuring, at at least one predetermined temperature, and preferably at least two predetermined temperatures, for each hairspring or hairspring blank the sustained oscillation frequency and / or the rate of the timepiece system formed by or comprising the oscillating mechanism; and / or iv'' - modelling a number of hairsprings or hairspring blanks in an oscillating mechanism with a given inertia in a simulation tool and calculating for each hairspring or hairspring blank the sustained oscillation frequency and / or the thermal coefficient of the timepiece system comprising the hairspring and / or the rate of the timepiece system comprising the hairspring at at least one given temperature, preferably at least two given temperatures; v - optionally estimating at least one expected resonant frequency from the resonant frequencies determined in step iii- and / or from the sustained oscillation frequency measured in step iv'- and / or calculated in step iv''- and / or from the rate of the timepiece system, vi) From the measurements of step iv') and / or the calculations of step iv'', deduce the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient of the timepiece system including the hairspring (CT), vii - For each hairspring or hairspring blank, the predictor: -the characteristics of the resonant frequency identified in step iii-; optionally, the same characteristics of the expected resonant frequency, - the temperature recorded during steps ii- and / or iii-, The present invention may also relate to a predictor learning method including a step of providing the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the timepiece system including the hairspring, estimated in step vi. [Brief explanation of the drawings]

[0073] Other details of the invention will emerge more clearly from reading the following description, given with reference to the accompanying drawings, in which: [Figure 1] 1 shows the uncorrected stiffness dispersion curves for the hairspring on three different wafers. [Figure 2] 1 shows the centering of the average stiffness on the wafer around the nominal value. [Figure 3A] 1 is a simplified diagram of a method for manufacturing a mechanical oscillator, here a hairspring, on a wafer. [Figure 3B] 1 is a simplified diagram of a method for manufacturing a mechanical oscillator, here a hairspring, on a wafer. [Figure 3C] 1 is a simplified diagram of a method for manufacturing a mechanical oscillator, here a hairspring, on a wafer. [Figure 3D] 1 is a simplified diagram of a method for manufacturing a mechanical oscillator, here a hairspring, on a wafer. [Figure 3E] 1 is a simplified diagram of a method for manufacturing a mechanical oscillator, here a hairspring, on a wafer. [Figure 3F] 1 is a simplified diagram of a method for manufacturing a mechanical oscillator, here a hairspring, on a wafer. [Figure 4] 1 shows a device for assessing the torque of a hairspring. [Figure 5] 10A and 10B illustrate schematic diagrams of an embodiment of the evaluation of the stiffness of a hairspring by vibration analysis. [Figure 6] 1 shows an example of a frequency applied to a silicon wafer supporting a hairspring blank to impose a vibrational excitation. [Figure 7] Figure 6 shows an example of measuring the displacement amplitude of a point on a hairspring blank according to an imposed frequency range. [Figure 8] FIG. 7 shows in detail the resonance peaks identified at particular frequencies. [Figure 9] For the tested part, the measured and superimposed resonance peaks for specific frequencies are shown in Figure 8. [Figure 10] An example of a predictive model constructed from data extracted from FIG. 9 is shown. [Figure 11] 1 illustrates the effect of temperature on the resonant frequency of a particular resonant mode. [Figure 12]1 shows the sensitivity of the resonant frequency to the oxide thickness of a silicon hairspring. DETAILED DESCRIPTION OF THE INVENTION

[0074] 3A to 3F are simplified diagrams of a method for manufacturing a mechanical oscillator 100 on a wafer 10. The oscillator is in particular intended to equip a regulating element of a timepiece, and according to this example, is in the form of a silicon hairspring 100 intended to equip the balance wheel of a mechanical watch movement.

[0075] Wafer 10 is shown in FIG. 3A as an SOI (silicon on insulator) wafer and includes a substrate or "handler" 20 having a sacrificial silicon oxide (SiO) layer 30 and a single-crystal silicon layer 40. For example, substrate 20 may have a thickness of 500 μm, sacrificial layer 30 may have a thickness of 2 μm, and silicon layer 40 may have a thickness of 120 μm. Single-crystal silicon layer 40 may have any crystal orientation.

[0076] The lithography process is illustrated in Figures 3B and 3C. "Lithography" refers to a series of operations that allow an image or pattern on or above wafer 10 to be transferred back. Referring to Figure 3B, in this exemplary embodiment, layer 40 is covered with a protective layer 50 made, for example, of a polymerizable resin. This layer 50 is typically structured by a photolithography process using an ultraviolet light source and, for example, a photomask (or another type of exposure mask) or a stepper-reticle system. This lithographic structuring forms a pattern for multiple oscillators in layer 50, as illustrated in Figure 3C.

[0077] 3D, the pattern is then machined, and in particular etched, to form a plurality of transducers 100 in layer 40. Etching can be performed by deep reactive ion etching (also known as DRIE). After etching, the remaining portions of protective layer 50 are subsequently removed.

[0078] 3E, the oscillator is released from the substrate 20 by locally removing the sacrificial layer 30 or by etching all or part of the silicon of the substrate or the handler 20. Smoothing of the etched surface (not shown) may also be performed before the release step, for example by a thermal oxidation step followed by a deoxidation step consisting of, for example, a wet etch based on hydrofluoric acid (HF).

[0079] In the final step of the manufacturing method of Figure 3F, the turns 110 of the silicon oscillator 100 are covered with a layer 120 of silicon oxide (SiO2), typically by a thermal oxidation step, in order to produce a thermally compensated oscillator. The formation of this layer 120, which generally has a thickness of 2 to 5 μm, also influences the final stiffness of the oscillator and must therefore be taken into account during the preceding steps in order to obtain the vibration characteristics of the hairspring that lead to obtaining a specific natural frequency of the hairspring / balance wheel pair in a given watch mechanism.

[0080] As mentioned above, in the steps preceding the fabrication of the thermal compensation layer, different resonators formed in a wafer generally have significant geometric variances between each other, and therefore significant variances between their stiffnesses, despite the fact that the steps of forming patterns and machining / etching through these patterns are the same for all resonators.

[0081] Furthermore, this dispersion in stiffness is even greater between the balance springs of two etched wafers at different times, even when the same method specifications are used.

[0082] Finally, it should be noted that more specific manufacturing defects can appear during manufacturing. For example, during the machining process shown in FIG. 3D, material can remain between two adjacent turns. In contrast to the one shown in FIG. 3E, parts can also be found where material residues still exist between the turns or the substrate. Material bridges can also form between two adjacent turns during oxidation, as shown in FIG. 3F. Finally, contamination can also occur due to debris or particles adhering between two turns or between a turn and the substrate. All these defects strongly affect vibration behavior and cannot be corrected by adding or removing material from the entire part, as known in the prior art.

[0083] While the above description refers to a silicon resonator 100, it is conceivable to fabricate resonators from glass, ceramic, carbon nanotubes, or other metals. In particular, conventional steel or wafer-stripped hairsprings can be tested. In this case, the metal or wafer-stripped hairspring is clamped or sampled with reference to a tool that positions the metal hairspring opposite a radiation source and a displacement measuring device.

[0084] As is known, the measurement of the stiffness of a hairspring can be carried out in a so-called static manner, i.e. by determining its torque without oscillating the hairspring. Reference can be made, for example, to document EP 3654111.

[0085] An alternative to the method described in this document involves performing torque measurements using a rheometer, such as that commercially available from Anton Paar. A device provided for this purpose is illustrated in FIG. 4. Advantageously, it allows the hairspring 200 to be evaluated to be placed on a mount 202 and positioned in such a way that the hairspring can be secured at its last turn by a retaining member 204. Once the last turn is secured, the mount 202 moves away from the hairspring 200, thus completely freeing the hairspring from any elastic constraint. Next, the head of a rheometer 206 is positioned opposite the collet of the hairspring. It has a counter-shape to the non-circular collet, but its reduced size allows the rheometer head to engage within the collet with controllable precision without contacting the hairspring. The rheometer head is then rotated in the direction of the hairspring contraction. When the head contacts the collet, it drives the collet and the rheometer measures the torque exerted by the elastic return of the hairspring over a given angle. However, such measurements remain unitary measurements and involve many risks of breakage, contamination, etc., and require a significant amount of processing time.

[0086] The invention proposes to determine in step 3F at least one characteristic of the resonant frequency of a sample of oscillators 100 on the wafer, to estimate the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the clock system including the hairspring, and optionally to estimate stiffness and / or structural defects in step 3E. In particular, the invention proposes to determine the above parameters without disassembling or measuring the wafer in a test subassembly, according to a method more efficient than those of the prior art.

[0087] The invention therefore proposes to determine at least one characteristic of the resonant frequency of a sample of oscillators by vibration measurements and to apply a predictive method (for example a numerical model or a classification or categorization method) to relate the results of said vibration measurements to the identification of the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the timepiece system including the hairspring.

[0088] For this purpose, the stylistic properties of the hairspring attached to the wafer are utilized. During the learning phase, it is possible to arrange the predictor by establishing, by analytical and numerical methods, a predictive model relating the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the timepiece system including the hairspring to certain specifically chosen frequencies (either resonant peaks or natural frequencies or natural frequencies associated with half-widths).

[0089] Once the learning phase is complete (the modes and excitation frequencies to be utilized have been determined), it is possible to proceed to a prediction phase in which the predictor is used to predict the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the timepiece system including the hairspring by utilizing the prediction model to control the oscillators of the produced wafers. The results of the prediction can be used to verify the manufactured parts and / or to determine additional treatments to correct the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the timepiece system including the hairspring, and / or to discard parts that are non-compliant with respect to the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the timepiece system including the hairspring.

[0090] It is therefore possible to integrate control methods into the manufacturing process in order to obtain parts whose oscillators, when coupled to the balance wheel of each given watch mechanism, are clean enough to produce a specific, predetermined natural vibration frequency that is reached, maintained and independent of temperature variations.

[0091] It is noted that a predictor is a device that makes it possible to predict, and thus to pre-determine or calculate, from one or more measured resonance frequencies, the value of the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the timepiece system including the hairspring, without coupling the hairspring to the balance wheel and without carrying out tests at several temperatures. The predictor can be expected to: - based on a mathematical model (e.g. a polynomial relating one or more resonance frequencies to the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the timepiece system including the hairspring), - using a neural network to receive as input values or graphs taken from the spectrum of vibration measurements to give as output the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the timepiece system including the hairspring, -Use artificial intelligence to enforce the system. Vibrational Excitation

[0092] Measuring the oscillatory response makes it possible to deduce at least one characteristic of the resonant frequency, for example the value of the resonant frequency. In detail, a vibrational excitation must first be imposed on the wafer. Several options are available: a. Frequency domain measurements: 1 - Excitation at a specific frequency f0 (continuous single frequency excitation), using a piezoelectric source (or any other source making it possible to induce or impose an acoustic excitation) on the edge of the wafer, above or below the (preferred) excited hairspring blank 200. In this variant, the excitation is maintained. 2- Alternatively, a piezoelectric source (or any other source that allows inducing or imposing acoustic excitation) can be used at the edge of the wafer, specifically (preferably) above or below the hairspring blank 200, to excite it with a frequency that is variable over time to cover a predetermined frequency range, for example, in the range of 0 to 300 kHz, preferably 0 to 275 kHz, preferably 0 to 250 kHz, preferably 5 kHz to 250 kHz, preferably 10 to 235 kHz. The entire frequency range can be swept or covered in a time interval that can range from a fraction of a second to several seconds. For example, it may be provided to sweep or cover a range of frequencies in the frequency range in less than 0.5 seconds, less than 1 second, or less than 1.5 seconds. In this variant, the excitation frequency is continuously varied. b. Measurement in the time domain: An excitation hammer (or any other source for inducing an acoustic impulse excitation) is used on the edge of the wafer, specifically above or below the hairspring to be excited (preferably), to give an acoustic pulse that is as short as possible (multi-frequency pulse excitation). In this variant, the excitation is point-like and not sustained.

[0093] Furthermore, the measurements can be carried out by following a specific sampling, for example according to a sampling range of 4, 2 or 1 Hz. Indeed, the resolution for processing the acquired data, for example according to a Fourier transformation, directly depends on the duration of this acquisition.

[0094] Furthermore, if the frequency range extends to, for example, 300 kHz, one can choose a signal sampling frequency of at least 600 kHz. In general, one can follow Shannon's theorem, which advises choosing a sampling frequency greater than twice the maximum frequency present in the measured signal.

[0095] Generally, it also becomes possible to eventually change the direction of excitation, i.e., the direction of motion imposed by the source (vibrations can be imposed in one or more axial directions, and this or these directions can be changed over time). When a wafer containing multiple oscillators is excited, it is possible to adjust the direction of vibration to point towards any one of the oscillators, depending on the displacement amplitude described below.

[0096] Finally, an acoustic source can be coupled to the divergence cone aimed at the transducer to be excited and tuned to emit an excitation signal having sufficient amplitude to impose vibrational excitation on the transducer and to be accurately detected and measured by the selected measurement equipment. Measurement of displacement amplitude, velocity or acceleration

[0097] During excitation, the amplitude and phase (relative to the excitation source) of the oscillations in the three directions X, Y (in-plane) and Z (out-of-plane) of the specifically excited hairspring are recorded using suitable measuring means, including but not limited to the following possible measuring means: -Interferometric optical method: a.3D Doppler effect (laser vibrometer using the Doppler effect), b. Holographic, - strobe optical method, - chromatic confocal profilometry with high temporal resolution, -Optical reflectance measurements, a. Vibration analysis by beam deflection with a multi-dial detector or camera; b. Analysis by TCSPC type time analysis, -Acoustic method using ultrasound by the Doppler effect.

[0098] 5 shows a schematic diagram of a silicon wafer 25 on which a number of hair spring blanks 200 are formed. A vibration excitation source 400 is coupled to the wafer 25 so as to impose a vibration excitation. As a result, each hair spring blank 200 vibrates, and a laser vibrometer 300, focused on a point on the right-hand hair spring blank 200, can measure the vibration amplitude of the measurement point over time. Displacement can be measured in a direction perpendicular to the plane of the wafer 25, but it is equally possible to measure displacement in one or more directions contained in the plane of the wafer 25.

[0099] Once a particular point has been investigated, the laser vibrometer 300 can be moved onto another measurement point on the hair spring blank 200 or to another hair spring blank 200 on the wafer 25. Of course, the hair spring blank 200 can alternatively be displaced relative to the laser vibrometer.

[0100] 6 shows an example of vibration excitation over time. In the given example, the excitation frequency is varied over time between 0 Hz and 50 kHz (but up to 300 kHz is possible), imposing a series of rising edges, each rising edge separated by a rest period without excitation. For each measurement point on the hairspring blank 200, multiple rising edges (between two rising fronts and 60 rising edges) can be imposed, each lasting, for example, 0.5 seconds to 2 seconds. Selecting the reference point to measure

[0101] With regard to the displacement amplitude measurements, during the learning phase, a step can be provided consisting of identifying points on the oscillator where the oscillatory response is significant. Indeed, in the case of a hairspring subjected to oscillations, particularly if the frequency varies over time, the oscillatory response causes nodes to appear on the hairspring, i.e. at specific points on the hairspring where the displacement amplitude is low or zero. If the displacement measurements are made at points on the hairspring that are known to be nodes at one or more specific frequencies, the identification of the resonant frequency characteristics will be adversely affected.

[0102] It is therefore advantageous to provide a preliminary step of measuring the displacement at a number of predetermined points on the hairspring, for example at least 10 predetermined points, preferably at least 20 predetermined points, and very preferably at least 30 predetermined points. It is possible to provide for selecting predetermined points located on an orthonormal reference frame XY in the plane of the hairspring.

[0103] At the end of this preliminary step of measuring the amplitude at predetermined points, it is possible to provide a step of identifying a resonant frequency for each measurement point and then selecting reference points whose measurement of the displacement amplitude during excitation indicates that these resonant frequencies are not nodes. In other words, the identified nodes have a displacement amplitude at at least one resonant frequency that is lower than zero or a first threshold peak value, and these points that form nodes are separated from the reference points considered for subsequent measurements. It should also be noted that the reference points will vary depending on the position of the hairspring blank 200 on the wafer 25.

[0104] Typically, it can be considered that at least two reference points are selected, preferably at least four. If the transducer has a radius Ra and is fixed or embedded on the wafer by the outer ends of the studs, it is preferable to select four reference points selected at and located at: Within a first area (e.g., on the central bead) that is less than -0.20 × Ra, or Within a second area between -0.05 × Ra and 0.30 × Ra (for example, on the second coil starting from the bead), or Within a third area between -0.35 × Ra and 0.65 × Ra (for example, on the centrally located coil of the hairspring), or Within the fourth area of -0.65 × Ra to 0.85 × Ra (for example, on a coil placed three-quarters of the way along the hairspring). Therefore, the reference point is distant from the fixed part on the wafer and necessarily has a significant oscillation displacement capacity, which ensures better accuracy of the displacement measurement.

[0105] Furthermore, it is also possible to measure the displacement of points on the body of the wafer and / or on the excitation source to identify or measure, for example, phase shifts or vibration damping, or vibration coupling or resonances arising from the wafer. These additional measurements make it possible to ensure that identified peaks are in fact peaks of the hairspring alone. It is also possible to synchronize the measurement of the displacement amplitude with the vibration excitation.

[0106] Alternatively, it is possible to plan to measure the displacement / movement / vibration at specific points, preferably located on areas of the part that do not deform. In particular, it is possible to plan to target the measurement at points on the collet of the hairspring or hairspring blank. In fact, the collet can be considered as non-deformable during vibration excitation, and all points on the collet have the same displacement / movement / vibration. As a result, small errors in the location of the measurement points on the collet have little effect on the final result. Furthermore, selecting specific measurement points on the part makes it possible to identify and select a specific frequency range for performing stiffness predictions.

[0107] According to one embodiment, where several components are tested in succession while still attached to the substrate or tool, - capturing an image of the part to be tested; - analyzing the images to recognize, for example, the type of each part and / or the position of each part; - selecting one or more points to be measured for each part and / or selecting an excitation vibration spectrum to be imposed for each part and / or each selected point, For each part to be tested, it is possible to provide a step of positioning the substrate or tool supporting the part to be tested in the vibration excitation and measurement device. According to this embodiment, in the case of wafers still carrying the hairspring blank, the excitation and measurement can be automated: - one or more images of the wafer are taken; - an automatic image analysis is carried out in order to know at least the XY position of each part (it is also possible to recognize the type or model of the part), Depending on the location and / or type of the recognized part, specific pre-established measurement points are identified or selected (e.g. on the bead), and specific excitation cycles can also be selected depending on the type of part or specific points, For example, using a tool with a wafer carrying and XY movable table, each hairspring blank is automatically and successively positioned opposite an excitation source and measuring device to be tested by aiming at the correct measuring point and applying the correct excitation specifications.

[0108] According to one embodiment, a step may be provided that consists of providing specific orientations for the excitation direction and / or the measurement direction depending on the measurement point selected on the part to be tested, depending on the excitation frequency, and / or depending on the model of the part to be tested. For this purpose, the excitation direction (or the axial direction of the excitation source) may be selected to be perpendicular to the part to be tested in order to maximize the displacement perpendicular to the plane formed by the stationary part. It is possible to select an excitation direction (or the axial direction of the excitation source) that is oblique to the part to be tested in order to maximize the displacement contained in the plane formed by the stationary part. With respect to the measurement, the measurement direction (or the axial direction of the laser beam of the measuring device) may be selected to be perpendicular to the part to be tested in order to maximize the measurement accuracy of the displacement perpendicular to the plane formed by the stationary part. It is possible to select a measurement direction (or the axial direction of the laser beam of the measuring device) that is oblique to the part to be tested in order to maximize the measurement accuracy of the displacement contained in the plane formed by the stationary part.

[0109] According to an embodiment in which several components are mounted on a substrate such as a wafer, sampling can be realized by removing one or several components and testing them individually, from which it is possible to deduce the specific excitation frequencies to be applied and / or the specific measurement points to be used and / or the specific regions of the vibration spectrum to be considered in order to derive the desired resonant frequency characteristics from them. In other words, this pre-sampling makes it possible to test a single component under good conditions (limited measurement errors and interferences) in order to select the best test conditions for the remaining components fixed on the substrate.

[0110] Determining vibration characteristics Depending on the region preselected for excitation, there are several scenarios. a. Frequency domain measurement 1-Excitation-preserving variant: i. Integrating the oscillation amplitude and phase in time long enough to have good spectral resolution at the excitation frequency f0; ii. Shift the oscillation frequency by delta f to excite at frequency f + Δf and repeat integration step i; iii. Reconstruct the oscillation amplitude and phase spectrum as a function of excitation frequency (possibly with multiple peaks at multiple frequencies). 2- Variant with excitation whose frequency varies over time: i. Recording the oscillation amplitude and phase over time during a frequency sweep through a frequency range; ii. repeating step i- at least once, preferably at least three times; iii. Reconstruct the oscillation amplitude and phase spectrum as a function of excitation frequency (possibly with multiple peaks at multiple frequencies). b. Time domain measurements: i. Record the temporal displacement of the coil along X, Y, and Z for a sufficiently long duration to obtain a sufficiently representative signal, such as a few seconds. ii. One can choose to record the signal so that the reference signal can be compared with other signals measured elsewhere, and one can choose to perform Fourier transform type signal processing to identify resonant frequencies in the recorded signal.

[0111] As a result, at least one resonant peak can be identified for each excited transducer. It is proposed to determine the resonant frequency not based on the upper end, i.e., the maximum amplitude, of the resonant peak, but rather on the area of the curve located between 25% and 75% of the maximum amplitude value of the resonant peak, e.g., its width at mid-height. Indeed, this processing method, focusing on the portion of the curve between 25% and 75% of the maximum amplitude value of the resonant peak, allows for limiting errors due to approximation calculations for reconstructing the singular point of the maximum amplitude and the tip of the resonant peak. The area of the curve located between 25% and 75% of the maximum amplitude value of the resonant peak has better accuracy than the portion above 75% (typically the peak), providing better accuracy in determining the exact resonant frequency. For example, it is possible to take the midpoint of the segment connecting two points at the mid-height of the resonant peak to determine the resonant frequency associated with that peak.

[0112] FIG. 7 shows an example of a vibration spectrum of a point on the hairspring blank 200 of FIG. 5, reconstructed from measurements of the displacement amplitude of the considered measurement point in response to the vibration excitation of FIG. 6, which is free of defects and ranges from 10 kHz to 15 kHz. The presence of three amplitude peaks can be seen at approximately 11 kHz, 12.3 kHz, and 13.7 kHz. Although not shown, when the vibration excitation sweeps a frequency range comprised between 0 Hz and 300 kHz, amplitude peaks typically between 10 and 250 kHz can be identified. Each amplitude peak has a resonant frequency, and the maximum amplitude varies greatly.

[0113] FIG. 8 details a process that can be performed on an amplitude peak of a defect-free part, e.g., an 11 kHz amplitude peak. The objective is to find the resonant frequency and assign it as accurate a value as possible. Instead of basing this process on the maximum value of the peak, applicants realized that better accuracy can be achieved by determining the length of the segment connecting the ascending and descending portions of the curve at the mid-height of the peak. The resonant frequency is typically the central value of this segment. However, to improve accuracy, especially if the actual location of the resonant peak is shifted due to, for example, the selected sampling frequency, interpolation can be performed on points near the resonant peak to shift the selected point on a non-central segment.

[0114] FIG. 9 shows amplitude peaks constructed for approximately ten tested hairspring blanks 200 for an example amplitude peak at approximately 10 kHz. It can be noted that for each hairspring blank, the frequency location of the amplitude peak varies (approximately 9.8 kHz to 10.02 kHz) and the maximum displacement amplitude varies by a ratio of approximately 1 to 5. Because the amplitude peaks are not actually symmetrical, it may be prudent to determine the resonant frequency based on the width of the peak at mid-height. The width of the peak at mid-height can also be used to determine damping and compare this damping to a reference value.

[0115] From these tests in FIG. 9, the following resonant frequencies could be derived: [Table 1]

[0116] 3A-3F, a first optional measurement may be performed on the component depicted in FIG. 3E to estimate the stiffness of the unoxidized component in order to determine whether dimensional corrections are necessary. It is also conceivable to perform the first optional measurement after an oxidation step that adds a predetermined thickness of oxide, from which any dimensional corrections can be performed. Once the component has been oxidized (i.e., by a thermal compensation process), the invention proposes to perform a second measurement to determine the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient of the timepiece system including the hairspring (CT).

[0117] Therefore, the steps taken to determine the stiffness of a part will be described first. Determination of the stiffness and / or actual dimensions of the bars of the tested transducer

[0118] During the learning phase, it is necessary to provide data on the stiffness and / or dimensions of the actual bars of the tested oscillator in order to establish a predictive model that can receive as input the vibration characteristics (typically the resonant frequency) and give as output the stiffness and / or dimensional corrections. For this purpose, it is possible to plan specific measurements of the natural frequencies of the hairspring-balance wheel system in an environment similar to that of the particular watch mechanism.

[0119] Two alternatives can be implemented: According to the first alternative, a given balance wheel can be directly coupled to the oscillator still attached to the wafer, the natural oscillation frequency of the oscillator-balance wheel pair can be measured, this natural frequency can be compared with the expected natural frequency, and the actual stiffness or actual dimensions can be calculated, in particular based on equations 1 to 3 above. According to the second alternative, the manufacture of the tested oscillator can be completed in order to individually attach or couple the oscillator to the balance wheel in order to again measure the natural oscillation frequency of the oscillator-balance wheel pair.

[0120] In the two alternatives described above, an intermediate step is taken to determine the stiffness of each oscillator, after which the actual dimensions of the bar of the tested oscillator can be determined. In other words, by analyzing the free oscillations of a hairspring coupled to a reference balance wheel, it is possible to determine the natural or resonant frequency and then the stiffness or dimensions of the oscillator bar. In this approach, a laser aimed at the balance arm or hairspring holder records the transit time of the balance arm or polarizer. An estimate of the period, then an estimate of the frequency, and finally an estimate of the stiffness is derived. The collected data is essentially a point cloud of transit times.

[0121] Indeed, several solutions have been proposed for assessing the stiffness of a hairspring on a wafer, in particular those described by M. Vermot et al. in "Traite de construction horlogere" (2011), pages 178-179. For example, a dynamic assessment can be performed by coupling the hairspring to a reference balance wheel with known inertia. By measuring the frequency of the assembly, the stiffness of the hairspring can be accurately derived. This assessment can be performed on the wafer or by removing the hairspring from the wafer. The above-mentioned references and prior art provide details about this method.

[0122] Similarly, the stiffness can also be estimated from the measurement of the reaction torque on the hairspring using a rheometer. The signal obtained represents the torque generation as a function of amplitude. Analysis of the slope of this curve for low amplitudes (linear part) makes it possible to derive the stiffness and therefore the dimensions of the vibrator bar. The dimensions of the hairspring bar can then be determined.

[0123] On the other hand, it allows the natural and / or resonant frequencies and / or stiffness of each resonator tested on the wafer to be estimated by simulation, for which purpose it is possible to reconstruct the resonator by numerical modeling, simulate its vibration response to an imposed spectrum by numerical calculation, and also to carry out dimensional measurements of each resonator tested in order to find the stiffness of the resonator.

[0124] High-resolution 3D X-ray tomography techniques allow the extraction of a point cloud that gives the 3D material density of the balance spring, and an adapted reconstruction of the images allows the mapping of the balance spring sections. These different types of data make it possible to estimate the dimensions of the bars and, by geometric methods, to infer the stiffness of the balance spring.

[0125] Another approach is to analyze the forced oscillations of the hairspring on a reference balance wheel using an escapement. As mentioned above, laser measurements (point clouds) of the balance arm's transit time make it possible to measure the frequency and derive the stiffness. An alternative can be considered from acoustic acquisition (Witschi-type microphones) that record the impulses of the different operating phases of the escapement / lever system. The measured data are either point clouds of the balance arm's transit time, or the time evolution of the sound pressure level. These types of experimental data make it possible to derive the period, then the frequency, then the stiffness, and finally the dimensions of the oscillator bar.

[0126] Returning to the tests described above in FIG. 9, stiffness measurements were made by coupling each hairspring blank 200 to a reference balance wheel, allowing the following stiffnesses to be derived: [Table 2] Establishing a predictive model

[0127] To be able to predict stiffness, it is first necessary to establish or build reference data, such as a reference spectrum. During a training phase, oscillation amplitude measurements are performed on the physical oscillator to identify the resonant frequency. A correlation phase must then be planned in which a predictive model is built to be able to relate the resonant frequency measured on the oscillator to the stiffness and / or dimensional (thickness) corrections provided.

[0128] The above-described operations (vibration measurement, identification of the resonance peak, determination of the bandwidth at mid-height and its mean or correction value, and the stiffness and / or dimensions of the bar) make it possible to provide a database that can correlate the position of the hairspring on the wafer, the spectrum or oscillation period or mid-height bandwidth, and its mean or correction value with the effective stiffness and / or dimensions of the hairspring bar. As seen above, this database can be constructed from numerical simulations of a hairspring finite element model. These simulations make it possible to generate reference spectra or oscillation periods related to stiffness. This database can also be supplemented by experimental measurements by measuring the vibration spectrum, oscillation period, and position of the hairspring on the wafer and their associated stiffness. One advantage of this approach lies in the fact that the training database is strengthened as the test progresses. This makes it possible to have an adaptive model depending on the wafer and hairspring, which can contribute to reducing the standard deviation in stiffness on the wafer.

[0129] This database can be used to build predictive models, offering several solutions.

[0130] A numerical model, for example a polynomial, can be constructed to calculate the actual thickness, dimensional correction, or actual stiffness as a function of the resonant frequency value.

[0131] Classification is performed by performing a k-means partition of the input data (results of vibration measurements, typically frequencies of resonant peaks) and output data (stiffness and / or dimensions of the vibrator bar), which can then be correlated to establish a match.

[0132] It is also possible to plan to process the images of the resonance peaks by a neural network, such as a perceptron, to perform a classification according to the stiffness or dimensions of the bars, the classes being defined by value increments.

[0133] In summary, the learning phase includes a testing phase (excitation of the transducer with measurement of vibration characteristics to reconstruct the vibration spectrum and identify resonant frequencies). A measurement phase of the transducer bar stiffness and / or dimensions is also performed. Once input data (resonant frequencies) and output data (bar stiffness and / or dimensions) for significant samples are available, a predictive model building phase can be performed.

[0134] Returning to the example discussed and described in relation to FIG. 9, the data collected is as follows: [Table 3] Linear regression modeling was performed on the above data for the first six rows and the following relationship could be established: R=0.0015F-10.894 where: R is 10 -7 Stiffness in N.mm. F is the resonant frequency in Hz.

[0135] Therefore, stiffness can be predicted and compared to the actual stiffness measured as shown in the table below, where the first 6 rows are the data used to build or train the linear regression and the last 4 rows are the predictions only. [Table 4] A maximum error of 4.40% can be measured and Figure 10 shows the linear regression line for the values of the first six lines.

[0136] It should be noted that it is advantageous to verify that the established prediction model has good sensitivity, i.e., for two different input values, the model gives two distinct output values. The applicant has noticed that the sensitivity of the prediction model is not the same for all resonance peaks. In particular, with reference to the established prediction equation shown in Figure 10, the leading coefficient is 0.0015 x 10 -7 N.mm / Hz. On the other hand, the applicant has noticed that the leading coefficient may be larger for high resonance frequencies, providing a better prediction sensitivity for predicting clear stiffness or dimensional correction values even from close resonance frequency values. During the learning phase, it is advantageous to provide a step of comparing the prediction sensitivities to consider and select specific resonance peaks at high frequencies (e.g., above 5 kHz), and then verifying / confirming that it is preferable to predict stiffness and / or dimensional correction as accurately as possible according to the measured vibration response.

[0137] On the other hand, the applicant has also realized that even if the resonant frequencies are close, the resonant modes (in particular the deformation and / or displacement modes of the oscillator) may differ significantly, which may also affect the sensitivity of the prediction of the stiffness and / or dimensional corrections. During the learning phase, it is advantageous to provide a step of comparing the sensitivity of the predictions in order to select to subsequently consider this or that resonant frequency rather than another one in order to predict the stiffness and / or dimensional corrections as accurately as possible as a function of the vibration response.

[0138] The above observations regarding considering the sensitivity of the predictions may provide for classifying the different identified resonance peaks during the learning phase according to the sensitivity of the prediction to stiffness and / or dimensional corrections. The excitation frequency range (applied during the pure prediction phase) can then be defined to include at least one or more resonance peaks or frequencies that provide the best sensitivity. Thus, imposing variable vibration excitation over such a predetermined frequency range ensures that accurate predictions can be made for the identified resonance peaks, or for each of the identified resonance peaks that overlap or reinforce each other.

[0139] Generally, the learning phase makes it possible to select either resonant peaks at high frequencies and / or resonant peaks corresponding to particular resonant modes that allow accurate and reliable values to be predicted, and the frequency range is predetermined to include at least one resonant peak, preferably multiple resonant peaks, so that either a single prediction as precise as possible or multiple predictions (one per resonant peak deemed relevant) can be made, and then cross-checking, averaging or adjusting the predicted values.

[0140] For example, it is possible to predict several values of stiffness or dimensional correction from several peaks or resonant frequencies, and then calculate the final value from the predicted values by performing a weighted average by assigning a weight to each predicted value, each weight being determined according to the sensitivity identified for each corresponding peak or resonant frequency.

[0141] Alternatively and preferably, it is possible to have just one model that takes all peak or resonant frequencies as input and returns stiffness or dimensional corrections, and a learning phase of the model is used to precisely calculate weightings for the peak or input resonant frequencies. Predicted Phase

[0142] Once the learning phase is complete, it is possible to proceed to a prediction phase, for example during an oscillator control method, which may typically be performed on a hairspring blank produced on a wafer and still attached to this wafer to infer the stiffness and / or dimensions of the sample hairspring bars in order to determine whether dimensional corrections should be applied.

[0143] Once the model is trained, the control procedure that is implemented can be as follows: 1) Identifying the location of the hairspring on the wafer and vibrating the spectrum or oscillation period (as described above); 2) predicting the stiffness and / or dimensions of the hairspring bar by applying a predictive model; 3) Determine if dimensional corrections are necessary to reach the target natural frequency or stiffness.

[0144] During the control method it is also possible to quantify the exact corrections to be made, so that the manufacturing method can include, in addition to the above controls: 1) Knowing the effective stiffness of the hairspring, estimated according to the model and the target stiffness and / or target bar dimensions, and applying the necessary correction amount. Steps 1) and 2) of the control method are repeated to control the stiffness / dimensions of the hairspring and confirm that the target values have been reached within the tolerance thresholds, or these steps and dimensional corrections are repeated until the stiffness / dimensions of the hairspring predicted by the model reach the target values. sampling

[0145] It is known that hundreds of hairsprings are manufactured on a wafer and that the dimensions of the bars of the manufactured hairsprings can vary according to the area of the wafer. If the stiffness evaluation can be carried out on a single hairspring, it is in fact carried out on a sample of hairsprings distributed on the wafer.

[0146] If the evaluations carried out show that the results obtained differ from one hairspring to another, a correction can be made uniformly across the entire wafer or differentiated between regions, thereby reducing the standard deviation of the stiffness distribution. Furthermore, if the stiffness of all hairsprings is known by applying a model, it is possible to determine the optimal correction that makes it possible to reduce the overall distribution.

[0147] It is even possible to consider going as far as to evaluate all the hairsprings on the wafer, in particular with vibration evaluation, since it can be carried out very quickly and allows for automation of the method.

[0148] Although the above examples are given mainly on the basis of producing hairsprings with initial bar dimensions larger than the target bar dimensions, it is also possible to provide hairsprings with initial bar dimensions smaller than the target bar dimensions. The correction step consists, for example, in adding material as described in the aforementioned document EP 3 181 939.

[0149] The method consisting in determining the resonant frequency by subjecting only the hairspring blank to vibration excitation makes it possible to obtain measurement data quickly, for example without having to carry out balance wheel assembly operations, while limiting measurement errors since only the hairspring blank is tested (there are no errors that may be associated with the balance wheel, such as its mass, its assembly position, etc.). Prediction of the thermal coefficient of Young's modulus (CTE) of a hairspring and / or the thermal coefficient (CT) of a watch system including a hairspring

[0150] For the part relating to the prediction of the thermal coefficient of Young's modulus (CTE) of a hairspring and / or the thermal coefficient (CT) of a timepiece system including a hairspring, the following procedure may be used. Step 1: Measurement or calculation of the natural or resonant frequencies on the wafer at several temperatures T (e.g., 8°C, 23°C, and 38°C). Step 2: Remove the hairspring, assemble it with the balance wheel, and install the hairspring into the movement. Step 3: Measure the thermal coefficient of transport (CT) according to, for example, the Swiss Official Chronometer Testing Institute (COSC) procedure (24 hours at 8°C, 24 hours at 23°C and 24 hours at 38°C). Step 4: Build a predictive model between the natural or resonant frequencies measured in step 1 and the thermal coefficients of movement (CT) measured in step 4.

[0151] It may be difficult to perform vibration measurements for several temperatures in step 1. It is possible to consider performing vibration measurements for a single temperature (e.g., 23°C, clean room temperature) and then build a numerical model that can estimate the evolution of the natural frequency with temperature, following the procedure below. -Build a finite element model of a hairspring with a silicon oxide layer. -Assign relevant material parameters and their evolution to temperature. -Perform mode analysis in the temperature range [8℃ 38℃]. - Plot the evolution of the natural or resonant frequency as a function of temperature and for different thicknesses of the oxide layer.

[0152] These evolution laws make it possible to predict the desired natural frequency from a single experimental vibration measurement performed at 23° C. However, different heating systems, such as in an oven or by conduction, can be imagined to experimentally identify these laws.

[0153] The results of such predictions can be observed in Figure 11, where the resonant frequencies of the same resonant mode (e.g., number x of 240 identified resonant modes) are plotted for three separate temperatures T1, T2, and T3. Differences in the values of the resonant peak frequencies can be observed between the three temperatures.

[0154] Furthermore, the applicant has realised that the resonant frequency is significantly affected by different oxidation values (including variations in the thermal coefficient of Young's modulus (CTE) of the hairspring and therefore variations in the thermal coefficient (CT) of the timepiece system including the hairspring) for only certain resonant modes.

[0155] Specifically, sensitivity analysis of the resonant frequency to the oxidation value was performed for approximately 240 resonant modes specified by the following equation:

number

[0156] FIG. 12 shows that the sensitivity of the resonant frequency to the oxide layer thickness for predicting the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of a timepiece system including the hairspring (curve CT) increases for several resonant modes starting from approximately the 100th identified resonant mode. It can be concluded that it is advantageous to consider resonant modes with high resonant frequencies for predicting the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of a timepiece system including the hairspring. On the other hand, FIG. 12 shows that the sensitivity of the resonant frequency to the oxide layer thickness and / or the ratio of the silicon core thickness to the silicon oxide thickness for predicting the stiffness (curve R) decreases for several resonant modes starting from approximately the 100th identified resonant mode. It can be concluded that it is advantageous to consider resonant modes with low resonant frequencies for predicting the stiffness of the hairspring.

[0157] Furthermore, the applicant has noticed that for resonance modes with high frequencies, the sensitivity of the resonance frequency is particularly high for those called "out-of-plane" resonance modes, while those called "in-plane" resonance modes do not have any particular sensitivity. It can be concluded that it is advantageous to consider "out-of-plane" resonance modes with high resonance frequencies in order to predict the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of a timepiece system including the hairspring. Conversely, it is advantageous to consider "in-plane" resonance modes in order to predict the stiffness of the component.

[0158] Step 3 can be performed by removing the parts measured in step 1 and attaching them to a reference movement, and the speed of these movements can be measured according to three temperatures: 8°C, 23°C, and 38°C.

[0159] Therefore, the resonant frequency data identified at three temperatures of the considered components and the operating data of these same components at three temperatures can be used to establish a thermal coefficient prediction model that can take the vibration characteristics as input and output the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the watch system including the hairspring.

[0160] Once the thermal coefficient prediction model has been established, the thermal coefficient predictor can use it to predict the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the timepiece system including the hairspring, for example, from the resonant frequency data of the out-of-plane resonant mode having a high resonant frequency. Naturally, with regard to predicting the thermal coefficient (CT) of the timepiece system including the hairspring, the thermal coefficient predictor can receive as input the reference of the relevant watch device, or its value or contribution to the thermal coefficient. Indeed, for a given caliber reference, the different parameters that affect the CT of the movement (sensitivity to temperature of the balance wheel, gear train, bearings, lubricants, etc.) can be considered constant and do not constitute adjustment variables.

[0161] It is no longer necessary to assemble the movement to measure the thermal coefficient (CT) of the watch system, including the hairspring, eliminating this time-consuming variable step.

[0162] Iterative processing may be performed on the components of the same wafer, and after predicting the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of the watch system including the hairspring, it is possible to remove only those components that have the desired performance and apply a new thermal compensation process (oxidation and / or deoxidation) to those components that are identified as incompatible or not meeting the desired performance.

[0163] In summary, the present invention makes it possible to simplify the manufacturing and control methods of silicon oscillators for producing movements with low or no sensitivity to temperature changes by: - Applying specific vibrational excitation to the oxidized parts. - providing the vibration response or the resonant frequencies or the resonant peaks or the data extracted from the vibration response to a thermal coefficient predictor, in this way it is possible to easily check whether a part has the correct thermal compensation for the movement in which it is to be installed. It should be noted that optionally, in a previous manufacturing step (e.g., before thermal compensation or oxidation), a specific vibration excitation can be performed and the vibration response or resonant frequencies or resonant peaks or data extracted from the vibration response can be sent to a stiffness predictor or a machine for predicting the presence of structural defects, for example, as follows: one or more turns bonded or bridged to adjacent turns, the remainder of the wafer, e.g., insulating supports, etc. localized or non-localized porosity of the material or oxide, The interface between the silicon core and the oxide layer having voids, detachments, irregularities, etc. Irregular or discontinuous oxide thickness, Material defects or localized shortages, such as penetration defects, Excess material due to e.g. masking defects, Inhomogeneity of materials (silicon, silicon oxide), Defects in the flatness (smoothing) of the side edges of the bars that form the hairspring; Defects in the perpendicularity of the side edges of the bars forming the hairspring (surface draft or undercuts), coils that are deformed, wavy or off-centre relative to their theoretical position

[0164] However, it should be noted that the data derived from the vibration response and used for these stiffness or defect presence predictions is not necessarily the same as the data for the thermal coefficient predictions; preferably, the data derived from the vibration response and used is different from and can even be considered separate from the data for the thermal coefficient predictions.

Claims

1. 1. A method for controlling a hairspring or a hairspring blank configured to form a hairspring, comprising: applying a time-varying vibrational excitation to the hair spring or hair spring blank to cover a predetermined frequency range; b) identifying at least one characteristic of a resonant frequency of the hair spring or hair spring blank, such as a resonant peak, during or in response to the vibrational excitation over the predetermined frequency range; c. passing the resonant frequency characteristics identified in step b. through a thermal coefficient predictor to determine the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of a timepiece system including the hairspring.

2. The step b. b1. A first identifying step including identifying a first characteristic of a first resonant frequency, such as a first resonant peak; b2. a second identifying step including 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; Said step c. but, a first prediction step consisting of subjecting the first characteristic of the first resonant frequency to another predictor to determine parameters different from the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient of Young's modulus (CT) of a timepiece system including the hairspring, such as stiffness or defects of the hairspring or the hairspring blank; c2. A control method according to claim 1, comprising a second prediction step consisting of applying the second characteristic of the second resonant frequency to the thermal coefficient predictor to determine the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of a timepiece system including the hairspring.

3. Steps b1 and b2 are separated by an oxidation step, Step a. a1. a first step of vibrational excitation, which is carried out before step b1. and consists of applying to the hair spring or the hair spring blank a first vibrational excitation which is variable over time so as to cover a first predetermined frequency range; a2. a second vibration excitation step, performed before step b2., of applying to the oxidized hair spring or the oxidized hair spring blank a second vibration excitation that is time-variable to cover the first predetermined frequency range or a second predetermined frequency range.

4. Step a. is carried out after the oxidation step; 3. The control method according to claim 2, wherein steps b1. and b2. take into account the same vibration response of the hairspring or the hairspring blank.

5. - said first resonant frequency is selected to be the resonant frequency of a planar resonant mode, and / or A control method according to any one of claims 2 to 4, wherein the second resonant frequency is selected to be the resonant frequency of an out-of-plane resonant mode.

6. the first resonant frequency is lower than the second resonant frequency, and / or said first resonant frequency is selected in the range of values between 0 Hz and 100 kHz, preferably between 0 Hz and 50 kHz, more preferably between 0 Hz and 40 kHz, and very preferably between 10 kHz and 35 kHz; and / or Control method according to any one of claims 2 to 5, wherein the second resonant frequency is selected in the range of values between 0 Hz and 300 kHz, preferably between 50 kHz and 250 kHz, more preferably between 60 kHz and 200 kHz, and very preferably between 100 kHz and 200 kHz.

7. 7. The control method according to claim 1, wherein the hairspring has at least two predetermined expected resonance frequencies, and the frequency range is predetermined to cover at least the two predetermined expected resonance frequencies.

8. 8. A control method according to claim 1, wherein step b) is based on measuring over time the amplitude or velocity or acceleration of the displacement of at least one point of the hairspring or the hairspring blank, preferably at least partly carried out during step a).

9. The hairspring or the hairspring blank is contained within a base plane, and step b comprises: - step b'' measuring the amplitude or velocity or acceleration of the displacement of at least one point of the balance spring or of the balance spring blank in a direction perpendicular to the base plane, and / or A control method according to any one of claims 1 to 8, comprising a step b''', measuring the amplitude or speed or acceleration of the displacement of at least one point of the hair spring or of the hair spring blank in a direction contained in the base plane.

10. Step b. A control method according to claim 8 or 9, comprising a step of identifying a resonance peak of the hairspring or the hairspring blank according to the amplitude or speed of displacement of at least one point of the hairspring or the hairspring blank.

11. The method of claim 10 , wherein the characteristic of the resonant frequency is determined based on a width of the resonant peak at a mid-height of a maximum value of the resonant peak.

12. 12. A control method according to any one of claims 1 to 11, wherein the thermal coefficient predictor implements a regression method, for example a linear regression, to predict the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of a timepiece system including the hairspring.

13. 12. A control method according to claim 1, comprising a preliminary step consisting of taking into account the material of the hairspring or the hairspring blank and adjusting the maximum amplitude of the vibrational excitation and / or the frequency range of the predetermined frequency range depending on the material of the hairspring or the hairspring blank.

14. 14. The control method according to claim 1, wherein if step c. determines that the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient of Young's modulus (CT) of a timepiece system including the hairspring is outside a range of expected values, the method comprises at least one step of identifying, separating, reworking or discarding the hairspring or the hairspring blank.

15. 14. A control method according to any one of claims 1 to 13, wherein if step c. determines that the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of a timepiece system including the hairspring is outside a range of expected values, the method comprises at least one step consisting of prescribing a step of treating the hairspring or the hairspring blank, such as a thermal compensation, oxidation or deoxidation step, in order to set the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of a timepiece system including the hairspring within the range of expected values.

16. A predictor learning method for implementing step c. of the control method according to any one of claims 1 to 15, comprising: i - forming a hairspring or a hairspring blank and subjecting it to a thermal compensation process; ii - applying to each of said hairspring or said hairspring blank an oscillatory excitation which is variable over time so as to cover a predetermined frequency range; iii - during steps ii- and / or iii-, determining at least one characteristic of the resonant frequency of each hairspring or each hairspring blank when applying said predetermined frequency range and recording the temperature of the part; iv' - mounting a number of hairsprings or hairspring blanks on an oscillating mechanism of predetermined inertia and measuring, for each hairspring or hairspring blank, at at least one predetermined temperature, preferably at least two predetermined temperatures, the sustained oscillation frequency or the rate of the timepiece system formed by or comprising said oscillating mechanism; and / or iv'' - modelling a number of hairsprings or hairspring blanks in an oscillating mechanism with a given inertia in a simulation tool and calculating for each hairspring or hairspring blank the sustained oscillation frequency and / or the thermal coefficient of a timepiece system comprising said hairspring and / or said rate of a timepiece system comprising said hairspring at at least one given temperature, preferably at least two given temperatures; v - optionally estimating at least one expected resonant frequency from the resonant frequencies determined in step iii- and / or from the sustained oscillation frequency measured in step iv'- and / or calculated in step iv''- and / or from the rate of the timepiece system, vii—estimating from the measurements of step iv′- and / or the calculations of step iv″- the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of a timepiece system including the hairspring, vii--in said predictor, for each hairspring or hairspring blank, the characteristic of the resonant frequency identified in step iii), - optionally the same characteristics of said expected resonant frequency, the temperatures recorded during steps ii and / or iii, - providing the thermal coefficient of Young's modulus (CTE) of the hairspring and / or the thermal coefficient (CT) of a timepiece system including the hairspring, estimated in -step vi-.

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