EP3181939B1 - Method for manufacturing a hairspring with predetermined stiffness by adding material - Google Patents

Description

Field of the invention

The invention relates to a method of manufacturing a hairspring of predetermined stiffness and, more precisely, such a hairspring used as a compensating hairspring cooperating with a predetermined inertia beam to form a resonator having a predetermined frequency.

Background of the invention

It is explained in the document EP 1 422 436 how to form a compensating hairspring comprising a silicon core coated with silicon dioxide and cooperating with a predetermined inertia beam to thermally compensate the assembly of said resonator.

Making such a compensating hairspring provides many benefits but also has disadvantages. In fact, the step of etching several spirals in a silicon wafer offers a non-negligible geometrical dispersion between the spirals of the same wafer and a greater dispersion between spirals of two wafers etched at different times. Incidentally, the stiffness of each spiral engraved with the same engraving pattern is variable by creating significant manufacturing dispersions. WO2012007460 shows a method of adjusting oscillation frequency of a sprung-balance assembly by removing or / and adding or / and moving material on at least one component of said assembly.

Summary of the invention

The object of the present invention is to overcome all or part of the disadvantages mentioned above by proposing a manufacturing process a spiral whose dimensions are precise enough not to require retouching.

For this purpose, the invention relates to a method of manufacturing a hairspring of a predetermined stiffness according to claim 1.

It is therefore clear that the method makes it possible to guarantee a very high dimensional accuracy of the hairspring and, incidentally, to guarantee a more precise stiffness of said hairspring. Each manufacturing parameter, which can induce geometric variations during step a), can be completely rectified for each spiral manufactured or rectified on average for all the spirals formed at the same time to drastically reduce the scrap rate.

• lors de l'étape a), les dimensions du spiral formé lors de l'étape a) sont entre 1% et 20% inférieures à celles nécessaires pour obtenir ledit spiral à ladite raideur prédéterminée ;
• l'étape a) est réalisée à l'aide d'un gravage ionique réactif profond ou d'un gravage chimique ;
• lors de l'étape a), plusieurs spiraux sont formés dans une même plaquette selon des dimensions inférieures aux dimensions nécessaires pour obtenir plusieurs spiraux d'une raideur prédéterminée ou plusieurs spiraux de plusieurs raideurs prédéterminées ;
• le spiral formé lors de l'étape a) est à base de silicium, de verre, de céramique, de métal ou d'alliage métallique ;
• l'étape b) comporte les phases b1): mesurer la fréquence d'un ensemble comportant le spiral formé lors de l'étape a) couplé avec un balancier doté d'une inertie prédéterminée et b2) : déduire de la fréquence mesurée, la raideur du spiral formé lors de l'étape a) ;
• selon une première variante, l'étape d) comporte la phase d1) : déposer une couche sur une partie de la surface externe du spiral formé lors de l'étape a) afin d'obtenir le spiral aux dimensions nécessaires à ladite raideur prédéterminée ;
• selon une deuxième variante, l'étape d) comporte la phase d2) : modifier la structure selon une profondeur prédéterminée d'une partie de la surface externe du spiral formé lors de l'étape a) afin d'obtenir le spiral aux dimensions nécessaires à ladite raideur prédéterminée ;
• selon une troisième variante, l'étape d) comporte la phase d3) : modifier la composition selon une profondeur prédéterminée d'une partie de la surface externe du spiral obtenu lors de l'étape a) afin d'obtenir le spiral aux dimensions nécessaires à ladite raideur prédéterminée ;
• après l'étape d), le procédé effectue au moins une nouvelle fois les étapes b), c) et d) pour affiner la qualité dimensionnelle ;
• selon une première variante, l'étape e) comporte la phase e1) : déposer une couche sur une partie de la surface externe dudit spiral d'une raideur prédéterminée ;
• selon une deuxième variante, l'étape e) comporte la phase e2) : modifier la structure selon une profondeur prédéterminée d'une partie de la surface externe dudit spiral d'une raideur prédéterminée ;
• selon une troisième variante, l'étape e) comporte la phase e3) : modifier la composition selon une profondeur prédéterminée d'une partie de la surface externe dudit spiral d'une raideur prédéterminée.

According to other advantageous variants of the invention:

• during step a), the dimensions of the hairspring formed during step a) are between 1% and 20% lower than those necessary to obtain said hairspring at said predetermined stiffness;
• step a) is carried out using deep reactive ion etching or chemical etching;
• during step a), a plurality of spirals are formed in the same plate in dimensions smaller than the dimensions necessary to obtain several spirals of a predetermined stiffness or several spirals of several predetermined stiffnesses;
• the spiral formed during step a) is based on silicon, glass, ceramic, metal or metal alloy;
• step b) comprises the phases b1): measuring the frequency of an assembly comprising the hairspring formed during step a) coupled with a balance having a predetermined inertia and b2): deducing from the measured frequency, the stiffness of the spiral formed during step a);
• according to a first variant, step d) comprises the phase d1): depositing a layer on a portion of the outer surface of the spiral formed during step a) in order to obtain the spiral to the dimensions necessary for said predetermined stiffness;
• according to a second variant, step d) comprises phase d2): modifying the structure to a predetermined depth of a portion of the outer surface of the hairspring formed during step a) in order to obtain the hairspring of necessary dimensions at said predetermined stiffness;
• according to a third variant, step d) comprises phase d3): modifying the composition to a predetermined depth of a portion of the outer surface of the hairspring obtained during step a) in order to obtain the hairspring with the necessary dimensions at said predetermined stiffness;
• after step d), the method performs at least one more step b), c) and d) to refine the dimensional quality;
• according to a first variant, step e) comprises the phase e1): depositing a layer on a portion of the outer surface of said hairspring of a predetermined stiffness;
• according to a second variant, the step e) comprises the phase e2): modifying the structure according to a predetermined depth of a part of the external surface of said hairspring with a predetermined stiffness;
• according to a third variant, step e) comprises phase e3): modifying the composition to a predetermined depth of a portion of the outer surface of said hairspring of a predetermined stiffness.

Brief description of the drawings

• la figure 1 est une vue en perspective d'un résonateur assemblé selon l'invention ;
• la figure 2 est un exemple de géométrie de spiral selon l'invention ;
• les figures 3 à 5 sont des sections de spiral à différentes étapes du procédé selon l'invention ;
• la figure 6 est une représentation en perspective d'une étape du procédé selon l'invention ;
• la figure 7 est un diagramme du procédé selon l'invention.

Other particularities and advantages will emerge clearly from the description which is given hereinafter, by way of indication and in no way limiting, with reference to the appended drawings, in which:

• the figure 1 is a perspective view of an assembled resonator according to the invention;
• the figure 2 is an example of spiral geometry according to the invention;
• the Figures 3 to 5 are spiral sections at different stages of the process according to the invention;
• the figure 6 is a perspective representation of a step of the method according to the invention;
• the figure 7 is a diagram of the process according to the invention.

Detailed Description of the Preferred Embodiments

dans laquelle m représente sa masse et r son rayon de giration qui dépend également de la température par l'intermédiaire du coefficient de dilatation α_b du balancier.As illustrated in figure 1 , the invention relates to a resonator 1 of the balance 3-spiral type 5. The balance 3 and the spiral 5 are preferably mounted on the same axis 7. In such a resonator 1, the moment of inertia I of the balance 3 responds to the formula: $$I={\mathit{<figure-callout\; id="2"\; label="mr"\; filenames="imgf0002.png"\; state="\{\{state\}\}">mr</figure-callout>}}^2$$

in which m represents its mass and r its radius of gyration, which also depends on the temperature via the coefficient of expansion α _b of the balance.

dans laquelle E est le module d'Young du matériau utilisé, h sa hauteur, e son épaisseur et L sa longueur développée.In addition, the stiffness C of the spiral 5 with a constant section corresponds to the formula: $$C=\frac{\mathit{Well}{\mathrm{<figure-callout\; id="3"\; label="e"\; filenames="imgf0001.png"\; state="\{\{state\}\}">e</figure-callout>}}^3}{12\mathrm{The}}$$

in which E is the Young's modulus of the material used, h its height, e its thickness and L its developed length.

dans laquelle E est le module d'Young du matériau utilisé, h sa hauteur, e son épaisseur, L sa longueur développée et / l'abscisse curviligne le long de la spire.In addition, the stiffness C of a spiral 5 with a variable section corresponds to the formula: $$C=\frac{\mathrm{<figure-callout\; id="12"\; label="E"\; filenames="imgf0001.png"\; state="\{\{state\}\}">E</figure-callout>}}{12}\frac{1}{{\displaystyle \underset{0}{\overset{\mathrm{The}}{\int }}\frac{1}{h\left(l\right)e^3\left(l\right)}\mathit{dl}}}$$

wherein E is the Young's modulus of the material used, h its height, its thickness e, L its developed length and / the curvilinear abscissa along the coil.

dans laquelle E est le module d'Young du matériau utilisé, h sa hauteur, e son épaisseur, L sa longueur développée et / l'abscisse curviligne le long de la spire.In addition, the stiffness C of a spiral 5 of varying thickness but at constant height corresponds to the formula: $$C=\frac{\mathit{Well}}{12}\frac{1}{{\displaystyle \underset{0}{\overset{\mathrm{The}}{\int }}\frac{1}{e^3\left(l\right)}\mathit{dl}}}$$

wherein E is the Young's modulus of the material used, h its height, its thickness e, L its developed length and / the curvilinear abscissa along the coil.

Finally, the frequency f of the spring-balance resonator 1 corresponds to the formula: $$f=\frac{1}{2\pi }\sqrt{\frac{C}{I}}$$

où :

• $\frac{\mathrm{\Delta }f}{f}$
  
  est la variation relative de fréquence ;
• ΔT est la variation de la température ;
• $-\frac{\partial E}{\partial T}\frac{1}{E}$
  
  est la variation relative du module d'Young en fonction de la température, c'est-à-dire le coefficient thermoélastique (CTE) du spiral ;
• α_s est le coefficient de dilatation du spiral, exprimé en ppm.°C^-1;
• α_b est le coefficient de dilatation du balancier, exprimé en ppm.°C^-1;

According to the invention, it is desired that the variation of the frequency as a function of the temperature of a resonator is substantially zero. The variation of the frequency f as a function of the temperature T in the case of a balance-spring resonator substantially follows the following formula: $$\frac{\mathrm{\Delta }f}{f}=\frac{1}{2}\left\{\frac{\partial E}{\partial T}\frac{1}{E}+3\cdot {\alpha }_s-2\cdot {\alpha }_b\right\}\cdot \mathrm{\Delta }T$$

or :

• $\frac{\mathrm{\Delta }f}{f}$
  
  is the relative frequency variation;
• Δ T is the variation of the temperature;
• $-\frac{\partial E}{\partial T}\frac{1}{E}$
  
  is the relative variation of the Young's modulus as a function of the temperature, that is to say the thermoelastic coefficient (CTE) of the spiral;
• α _s is the coefficient of expansion of the spiral, expressed in ppm ° C ^-1 ;
• α _b is the coefficient of expansion of the balance, expressed in ppm ° C ^-1 ;

Oscillations of any resonator for a time base or frequency to be maintained, the thermal dependence also includes a possible contribution of the maintenance system such as, for example, a Swiss lever escapement (not shown) cooperating with the ankle 9 of the plate 11 also mounted on the axis 7.

It is therefore understood from the formulas (1) - (6) that it is possible by the choice of materials used to couple the hairspring 5 with the balance 3 so that the frequency f of the resonator 1 is almost insensitive to the variations of temperature.

The invention more particularly relates to a resonator 1 in which the hairspring 5 is used to thermally compensate the whole of the resonator 1, that is to say all the parts and in particular the balance 3. Such a hairspring 5 is generally called a compensating spiral. Therefore, the invention relates to a manufacturing method for ensuring a very high dimensional accuracy of the spiral and, incidentally, to ensure a more precise stiffness of said spiral.

According to the invention, the compensating spiral 5, 15 is formed based on a material, optionally coated with a thermal compensation layer, and intended to cooperate with a predetermined balance beam 3 of inertia. However, nothing prevents to provide a pendulum with movable weights to offer a setting parameter before or after the sale of the timepiece.

The use of a material, for example based on silicon, glass or ceramic, for the manufacture of a spiral 5, 15 offers the advantage of being precise by the existing methods of engraving and of having good mechanical and chemical properties, in particular being very insensitive to magnetic fields. It must however be coated or superficially modified to form a compensating hairspring.

Preferably, the silicon-based material used for producing the compensating balance spring may be monocrystalline silicon regardless of its crystalline orientation, doped monocrystalline silicon regardless of its crystalline orientation, amorphous silicon, porous silicon or polycrystalline silicon, silicon nitride, silicon carbide, quartz whatever its crystalline orientation or silicon oxide. Of course other materials can be envisioned as a glass, a ceramic, a cermet, a metal or a metal alloy. For simplicity, the explanation below will be focused on a silicon-based material.

Each type of material may be surface-modified or layer-coated to thermally compensate for the base material as explained above.

If the step of etching spirals in a silicon-based wafer, by means of a deep reactive ion etching (also known by the abbreviation "DRIE"), is the most accurate, phenomena that occur during the engraving or between two successive engravings can nevertheless induce geometric variations.

Of course, other types of manufacturing can be implemented, such as laser etching, localized ion etching (known by the abbreviation "FIB"), galvanic growth, growth by chemical vapor deposition or chemical engraving, which are less accurate and for which the process would make even more sense.

Thus, the invention relates to a method 31 for manufacturing a spiral 5c. According to the invention, the method 31 comprises, as illustrated in FIG. figure 7 a first step 33 intended to form at least one hairspring 5a, for example based on silicon, according to dimensions Da less than the dimensions Db necessary to obtain said hairspring 5c of a predetermined stiffness C. As visible at figure 3 , the spiral section 5a has a height H ₁ and a thickness E ₁ .

Preferably, the dimensions Da of the hairspring 5a are substantially between 1% and 20% lower than those Db of the hairspring 5c necessary to obtain said hairspring 5c of a predetermined stiffness C.

Preferentially according to the invention, step 33 is carried out using a deep reactive ion etching in a wafer 23 of a silicon-based material as illustrated in FIG. figure 6 . It can be seen that the opposite faces F ₁ , F ₂ are corrugated because a deep reactive ion etching of the Bosch type causes a slot etching structured by the successive stages of attack and passivation.

Of course, the method can not be limited to a particular step 33. By way of example, step 33 could equally well be obtained by chemical etching in a wafer 23 of a material for example based on silicon. In addition, step 33 means that one or more spirals are formed, i.e., step 33 makes it possible to form bulk spirals or alternately formed in a wafer of a material.

Therefore, in step 33, several spirals 5a may be formed in the same plate 23 in dimensions Da, H ₁ , E ₁ smaller than the dimensions Db, H ₂ , E ₂ needed to obtain several spirals 5c of a predetermined stiffness C or several spirals 5c of several predetermined stiffnesses C.

Step 33 is also not limited to the formation of a hairspring 5a in dimensions Da, H ₁ , E ₁ smaller than the dimensions Db, H ₂ , E ₂ necessary to obtain a hairspring 5c of a predetermined stiffness C, formed using a single material. Thus, the step 33 could equally well form a hairspring 5a according to dimensions Da, H ₁ , E ₁ smaller than the dimensions Db, H ₂ , E ₂ needed to obtain a hairspring 5c of a predetermined stiffness C of a composite material. that is to say comprising several different materials.

The method 31 includes a second step 35 for determining the stiffness of the hairspring 5a. Such a step 35 may be carried out directly on the hairspring 5a still attached to the wafer 23 or on the hairspring 5a previously detached from the wafer 23, on the whole, or on a sample of the spirals still attached to a wafer 23 or on a spiral sample previously detached from a wafer 23.

According to the invention, the hairspring 5a being detached or not from the wafer 23, the step 35 includes a first phase intended to measure the frequency f of an assembly comprising the hairspring 5a coupled with a balance having a predetermined inertia I. then, using the relation (5), deduce, in a second phase, the stiffness C spiral 5a.

Such a measurement phase can in particular be dynamic and carried out according to the teachings of the document EP 2 423 764 . However, alternatively, a static method, carried out according to the teachings of the document EP 2 423 764 can also be used to determine the stiffness C of the spiral 5a.

Of course, as explained above, the method is not limited to the etching of a single spiral per wafer, step 35 may also consist of a determination of the average stiffness of a representative sample or of all spirals formed on the same plate.

According to the invention, from the determination of the stiffness C of the spiral 5a, the method 31 comprises a step 37 intended to calculate, using the relation (2), the thickness of the missing material for obtain the hairspring 5c of a predetermined stiffness C, that is to say the volume of material to be added and / or to modify homogeneously or not on the surface of the hairspring 5a.

The method is continued with a step 39 intended to modify the hairspring 5a formed during step a), to compensate for said thickness of missing material making it possible to obtain the hairspring 5c with the dimensions Db, H ₂ , E ₂ required for said stiffness C predetermined. It is therefore understood that it does not matter that the geometric variations have occurred on the thickness and / or the height and / or the length of the hairspring 5a insofar as, according to equation (2), it is the product h · E ³ which determines the rigidity of the turn.

Thus, a homogeneous thickness over the entire external surface may be added and / or modified, a non-homogeneous thickness over the entire external surface may be added and / or modified, a uniform thickness only over a portion of the outer surface may be added and / or modified, or a non-homogeneous thickness only on a portion of the outer surface may be added and / or modified. By way of example, step 39 could consist of adding material only according to the thickness E ₁ or according to the height H ₁ of the spiral 5a.

In a first variant, step 39 comprises a phase d1 intended to deposit a layer on a portion of the outer surface of the hairspring 5a formed during step 33 in order to obtain the hairspring 5c with dimensions Db, H ₂ , E ₂ required for said predetermined stiffness C. Such a phase d1 can, for example, be obtained by thermal oxidation, by galvanic growth, by physical vapor deposition (known by the abbreviation "PVD"), by chemical vapor deposition (known by the abbreviation "CVD"), by atomic layer deposition (known by the abbreviation "ALD") or by any other additive method.

Such a phase d1 may, for example, be carried out by a chemical vapor deposition for forming polysilicon on the hairspring 5a in monocrystalline silicon in order to obtain the hairspring 5c with dimensions Db, H ₂ , E ₂ necessary for the predetermined stiffness C.

As visible at figure 4 , the spiral section 5c has a height H ₂ and a thickness E ₂ . It can be seen that the hairspring 5c is formed of a central portion 22 based on monocrystalline silicon and a peripheral portion 24 made of polycrystalline silicon according to the overall dimensions Db required for the predetermined stiffness C.

In a second variant, step 39 may consist of a d2 phase to modify the structure in a predetermined depth of a portion of the outer surface 5a of the spiral to obtain the spiral 5c the dimensions Db, H _2, E ₂ necessary for the predetermined stiffness C. As an example shown in figure 4 if amorphous silicon is used to form the hairspring 5a, it may be provided to crystallize it to a predetermined depth forming a central portion 22 of amorphous silicon and a peripheral portion 24 of polycrystalline silicon to obtain the hairspring 5c with dimensions Db , H ₂ , E ₂ required for the predetermined stiffness C.

In a third variant, step 39 may consist of a phase d3 intended to modify the composition to a predetermined depth of a portion of the outer surface of the hairspring 5a of a predetermined stiffness C. As an example shown in figure 4 if monocrystalline or polycrystalline silicon is used to form the hairspring 5a, it may be provided to dope or diffuse interstitial or substitutional atoms therein at a predetermined depth forming a central portion 22 of monocrystalline or polycrystalline silicon and a portion peripheral 24 doped or diffused with the aid of atoms different from the silicon in order to obtain the spiral 5c with the dimensions Db, H ₂ , E ₂ necessary for the predetermined stiffness C. It will be understood that this third variant does not necessarily imply an increase in volume but at least superficially increases the Young's modulus making it possible to obtain the predetermined stiffness C.

For these three variants, it is visible that the crenellated form is always reproduced on a portion of the peripheral portion 24 and the central portion 22. Thus, a smoothing step before step 39 can be provided to attenuate or even to remove, the possible crenellated form of the spiral 5a.

Step 39 may finish process 31. However, after step 39, method 31 may also perform, at least one more time, steps 35, 37 and 39 in order to further refine the dimensional quality of the hairspring . These iterations of steps 35, 37 and 39 may, for example, be of particular interest when the execution of the first iteration of steps 35, 37 and 39 is performed on the set, or on a sample, of the spirals still attached to a wafer 23, then in a second iteration, on the assembly, or a sample, spirals previously detached from the wafer 23 having undergone the first iteration.

The method 31 may also continue with all or part of the process 40 illustrated in FIG. figure 7 comprising optional steps 41, 43 and 45. Advantageously according to the invention, the method 31 can thus continue with step 41 intended to form, on at least a part of the hairspring 5c, a portion 26 for correcting the stiffness of the spiral 5c and form a spiral 5, 15 less sensitive to thermal variations.

In a first variant, step 41 may consist of a phase e1 intended to deposit a layer on a portion of the outer surface of said hairspring 5c of a predetermined stiffness C.

In the case where the parts 22/24 are a silicon-based material, the phase e1 may consist in oxidizing the spiral 5c to coat it with silicon dioxide in order to correct the stiffness of the spiral 5c and form a spiral 5, 15 which is thermally compensated. Such a phase e1 can, for example, be obtained by thermal oxidation. Such thermal oxidation can, for example, be carried out between 800 and 1200 ° C under an oxidizing atmosphere using water vapor or oxygen gas to form silicon oxide on the spiral 5c.

This produces the balance spring 5, 15 as shown in FIG. figure 5 which, advantageously according to the invention, comprises a composite core 22/24 based on silicon and a coating 26 based on silicon oxide. Advantageously according to the invention, the balance spring 5, 15 compensator thus has a very high dimensional accuracy especially as to the height H ₃ and the thickness E ₃ , and, incidentally, a thermal compensation of the entire resonator 1 very thin .

In the case of a silicon spiral, the overall dimensions Db can be found using the teachings of the document EP 1 422 436 to apply it to the resonator 1 which is intended to be manufactured, that is to say to compensate for all the constituent parts of the resonator 1 as explained above.

In a second variant, step 41 may consist of a phase e2 intended to modify the structure to a predetermined depth of a portion of the outer surface of said hairspring 5c of a predetermined stiffness C. For example, if an amorphous silicon is used for the peripheral portion 24 and, optionally, the central portion 22, it can be provided to crystallize it to a predetermined depth in the peripheral portion 24 and, optionally, in the central portion 22.

In a third variant, step 41 may consist of a phase e3 intended to modify the composition to a predetermined depth of a portion of the outer surface of said hairspring 5c of a predetermined stiffness C. By way of example, if a monocrystalline or polycrystalline silicon is used for the peripheral part 24 and, possibly, the central part 22, it can be provided to dope it or to diffuse interstitial or substitutional atoms to a predetermined depth. in the peripheral portion 24 and, optionally, in the central portion 22.

• une ou plusieurs spires de section(s) plus précise(s) que celle obtenue par un unique gravage ;
• des variations d'épaisseur et/ou de pas le long de la spire ;
• une virole 17 monobloc ;
• une spire interne 19 du type à courbe Grossmann ;
• une attache 14 de pitonnage monobloc ;
• un élément d'encastrement externe monobloc ;
• une portion 13 de la spire externe 12 surépaissie et/ou de la spire interne 19 par rapport au reste des spires.

Advantageously according to the invention, it is thus possible to manufacture, as illustrated in FIG. figure 2 , without more complexity a spiral 5c, 5, 15 comprising in particular:

• one or more turns of more precise section (s) than that obtained by a single engraving;
• variations in thickness and / or pitch along the turn;
• a shell 17 monobloc;
• an internal turn 19 of the Grossmann curve type;
• a one-piece pegging fastener 14;
• a one-piece external recess element;
• a portion 13 of the outer turn 12 thickened and / or the inner coil 19 relative to the rest of the turns.

Finally, the method 31 can also comprise step 45 intended to assemble a compensating hairspring 5, 15 obtained during step 41, or a hairspring 5c obtained during step 39, with a predetermined inertia beam obtained during of step 43 to form a resonator 1 of the balance-balance type which is thermally compensated or not, that is to say whose frequency f is sensitive or not to temperature variations.

Of course, the present invention is not limited to the illustrated example but is susceptible of various variations and modifications that will occur to those skilled in the art. In particular, as explained above, the balance, even if it comprises a predefined construction inertia, may comprise movable weights to provide a setting parameter before or after the sale of the timepiece.

In addition, an additional step, between step 39 and step 41, or between step 39 and step 45, could be provided in order to deposit a functional or aesthetic layer, such as, for example, a layer of curing or a luminescent layer.

It is also conceivable in the case where the method 31 performs, after step 39, one or more iterations (s) of steps 35, 37 and 39 that step 35 is not systematically implemented.

Claims (19)

1. Method (31) for fabrication of a balance spring (5c) of predetermined thickness (C) comprising the following steps:

   a) forming (33) a balance spring (5a) in dimensions (Da, H₁ , E₁ ) smaller than the dimensions (Db, H₂ , E₂ ) necessary to obtain said balance spring (5c) of a predetermined stiffness (C);

   b) determining (35) the stiffness (C) of the balance spring (5a) formed in step a) by measuring the frequency (f) of said balance spring (5a) coupled with a balance having a predetermined inertia;

   c) calculating (37) the missing thickness of material, based on the determination of the stiffness (C) of the balance spring (5a) determined in step b), required to obtain said balance spring (5c) of a predetermined stiffness (C);

   d) modifying (39) the balance spring (5a) formed in step a), to compensate for said missing thickness of material required to obtain the balance spring (5c) having the dimensions (Db, H₂ , E₂ ) necessary for said predetermined stiffness (C).
2. Fabrication method (31) according to the preceding claim, characterized in that, in step a), the dimensions (Da, H₁ , E₁ ) of the balance spring (5a) formed in step a) are between 1% and 20% smaller than those (Db, H₂ , E₂ ) necessary to obtain said balance spring (5c) of said predetermined thickness (C).
3. Fabrication method (31) according to claim 1 or 2, characterized in that step a) is achieved by means of a deep reactive ion etch.
4. Fabrication method (31) according to claim 1 or 2, characterized in that step a) is achieved by means of a chemical etch.
5. Fabrication method (31) according to any of the preceding claims, characterized in that, in step a), several balance springs (5a) are formed in the same wafer (23) in dimensions (Da, H₁ , E₁ ) smaller than the dimensions (Db, H₂ , E₂ ) necessary to obtain several balance springs (5c) of a predetermined stiffness (C) or several balance springs (5c) of several predetermined stiffnesses (C).
6. Fabrication method (31) according to any of the preceding claims, characterized in that the balance spring (5a) formed in step a) is made from silicon.
7. Fabrication method (31) according to any claims 1 to 5, characterized in that the balance spring (5a) formed in step a) is made from glass.
8. Fabrication method (31) according to any claims 1 to 5, characterized in that the balance spring (5a) formed in step a) is made from ceramic.
9. Fabrication method (31) according to any claims 1 to 5, characterized in that the balance spring (5a) formed in step a) is made from metal.
10. Fabrication method (31) according to any claims 1 to 5, characterized in that the balance spring (5a) formed in step a) is made from metal alloy.
11. Fabrication method (31) according to any of the preceding claims, characterized in that step b) includes the following phases:

    b1) measuring the frequency (f) of an assembly comprising the balance spring (5a) formed in step a) coupled to a balance having a predetermined inertia;

    b2) deducing from the measured frequency (f), the stiffness (C) of the balance spring (5a) formed in step a).
12. Fabrication method (31) according to any of the preceding claims, characterized in that step d) includes the following phase:

    d1) depositing a layer on one part of the external surface of the balance spring (5a) formed in step a) to obtain the balance spring (5c) having the dimensions (Db, H₂ , E₂ ) necessary for said predetermined stiffness (C).
13. Fabrication method (31) according to any of claims 1 to 11, characterized in that step d) includes the following phase:

    d2) modifying the structure, to a predetermined depth, of one part of the external surface of the balance spring (5a) formed in step a) to obtain the balance spring (5c) having the dimensions (Db, H₂ , E₂ ) necessary for said predetermined stiffness (C).
14. Fabrication method (31) according to any of claims 1 to 11, characterized in that step d) includes the following phase:

    d2) modifying the composition, to a predetermined depth, of one part of the external surface of the balance spring (5a) obtained in step a) to obtain the balance spring (5c) having the dimensions (Db, H₂ , E₂ ) necessary for said predetermined stiffness (C).
15. Fabrication method (31) according to any of the preceding claims, characterized in that, after step d), the method performs, at least once more, steps b), c) and d) to further improve the dimensional quality.
16. Fabrication method (31) according to any of the preceding claims, characterized in that, after step d), the method also includes the following step:

    e) forming, on at least one part of said balance spring (5c) of a predetermined stiffness (C), a portion for correcting the stiffness of the balance spring (5c) and for forming a balance spring (5, 15) that is less sensitive to thermal variations.
17. Fabrication method (31) according to claim 16, characterized in that step e) includes the following phase:

    e1) depositing a layer on one part of the external surface of said balance spring (5c) of a predetermined stiffness (C).
18. Fabrication method (31) according to claim 16, characterized in that step e) includes the following phase:

    e2) modifying the structure, to a predetermined depth, of one part of the external surface of said balance spring (5c) of a predetermined stiffness (C).
19. Fabrication method (31) according to claim 16, characterized in that step e) includes the following phase:

    e3) modifying the composition, to a predetermined depth, of one part of the external surface of said balance spring (5c) of a predetermined stiffness (C).

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