EP3181938B1 - Method for manufacturing a hairspring with a predetermined stiffness by removing 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. EP 1 213 628 A shows a method of adjusting the oscillation frequency of a regulator assembly in which a spiral is manufactured with an elastic torque greater than a reference elastic torque corresponding to a reference frequency for the oscillation of said regulator assembly; a balance is assembled to said spiral to form said regulator assembly, and machining said spiral by means of a laser beam to reduce its elastic torque until said oscillation frequency is substantially equal to said frequency of reference.

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% supérieures 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 supérieures 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 les phases d1) : oxyder le spiral formé lors de l'étape a) afin de transformer ladite épaisseur de matériau à base de silicium à retirer en dioxyde de silicium et ainsi former un spiral oxydé, et d2) : retirer l'oxyde du spiral oxydé permettant d'obtenir le spiral aux dimensions nécessaires à ladite raideur prédéterminée ;
• selon une deuxième variante, l'étape d) comporte la phase d3) : graver chimiquement le spiral formé 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 ;
• après l'étape d), le procédé comporte, en outre, l'étape e) : former, sur au moins une partie dudit spiral d'une raideur prédéterminée, une portion permettant de corriger la raideur du spiral et de former un spiral moins sensible aux variations thermiques ;
• 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% greater 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), several spirals are formed in the same plate in dimensions larger 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 phases d1): oxidizing the spiral formed during step a) in order to transform said thickness of silicon-based material to be removed into silicon dioxide and thus form an oxidized spiral , and d2): removing the oxidized spiral oxide to obtain the spiral to the dimensions necessary for said predetermined stiffness;
• according to a second variant, step d) comprises phase d3): etching the spiral formed during step a) in order to obtain the hairspring with the dimensions required for said predetermined stiffness.
• after step d), the method performs at least one more step b), c) and d) to refine the dimensional quality;
• after step d), the method further comprises the step e): forming, on at least a portion of said hairspring of a predetermined stiffness, a portion for correcting the stiffness of the hairspring and forming a hairspring minus sensitive to thermal variations;
• 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 6 sont des sections de spiral à différentes étapes du procédé selon l'invention ;
• la figure 7 est une représentation en perspective d'une étape du procédé selon l'invention ;
• la figure 8 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 6 are spiral sections at different stages of the process according to the invention;
• the figure 7 is a perspective representation of a step of the method according to the invention;
• the figure 8 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: $$C=\frac{\mathit{Well}{\mathrm{<figure-callout\; id="3"\; label="e"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">e</figure-callout>}}^3}{12\mathrm{The}}$$

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 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 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 spiral expansion coefficient, 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 formulas (1) - (6) that it is possible to match the hairspring 5 with the balance 3 so that the frequency f of the resonator 1 is almost insensitive to temperature variations.

The invention relates more particularly to a resonator 1 in which the hairspring 5 is used to 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 hairspring compensator. 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 hairspring 5, 15 offers the advantage of being precise by the existing methods of engraving and to have good mechanical and chemical properties being in particular very little sensitive to the magnetic fields. It must however be coated or superficially modified to form a compensating hairspring.

Preferably, the silicon-based material used as a compensating spiral may be monocrystalline silicon whatever its crystalline orientation, doped monocrystalline silicon whatever its crystalline orientation, amorphous silicon, porous silicon, polycrystalline silicon, nitride of silicon, silicon carbide, quartz regardless of 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 as "DRIE"), is the most accurate, phenomena that occur during etching 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 8 a first step 33 intended to form at least one spiral 5a, for example based on silicon, with dimensions Da greater than 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% higher 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 7 . 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.

Consequently, during step 33, several spirals 5a may be formed in the same plate 23 in dimensions Da, H ₁ , E ₁ greater than the dimensions Db, H ₃ , E ₃ necessary to obtain several spirals 5c of a predetermined stiffness C or several spirals 5c of several predetermined stiffnesses C.

Step 33 is not limited to the formation of a hairspring 5a in dimensions Da, H ₁ , E ₁ greater than the dimensions Db, H ₃ , E ₃ required to obtain a hairspring 5c of predetermined stiffness C , formed using a single material. Thus, step 33 could equally well form a hairspring 5a with dimensions Da, H ₁ , E ₁ greater than the dimensions Db, H ₃ , E ₃ needed to obtain a hairspring 5c of stiffness C predetermined in 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 sample spirals 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 material to be removed on the assembly of the hairspring to obtain the overall dimensions Db necessary to obtain said hairspring 5c of a predetermined stiffness C , that is to say the volume of material to be withdrawn homogeneously or not on the surface of the hairspring 5a.

The process is continued with a step 39 for removing the surplus material of the hairspring 5a to the dimensions Db necessary to obtain said hairspring 5c of a predetermined stiffness C. 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 uniform thickness over the entire outer surface may be removed, a non-uniform thickness over the entire outer surface may be removed, a uniform thickness only on a portion of the outer surface may be removed or a non-uniform thickness only on a portion the outer surface can be removed. By way of example, step 37 could consist in removing material only according to the thickness E ₁ or the height H ₁ of the spiral 5 a.

In a first variant relating to a silicon-based material, step 39 comprises a first phase d1 intended to oxidize the hairspring 5a in order to transform said thickness of silicon-based material to be removed into silicon dioxide and thus form a spiral 5b oxidized. Such a phase d1 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 5a.

As visible at figure 4 the section of the spiral 5b has a height H ₂ and a thickness E ₂ . It can be seen that the hairspring 5b is formed of a central part 22 based on silicon according to the overall dimensions Db required for the hairspring 5c at said predetermined stiffness C and a peripheral portion 24 made of silicon dioxide. In addition, it is visible that the crenellated form is always reproduced on a portion of the peripheral portion 24 but is no longer or less present the central portion 22.

Step 39 ends, as shown in figure 5 , with a second phase d2 intended to remove the oxide of the spiral 5b allowing to obtain a hairspring 5c with the silicon-based single portion 22 with the overall dimensions Db necessary to obtain said predetermined stiffness C , the section comprising in particular a height H ₃ and a thickness E ₃ . Such a phase d2 may, for example, be obtained by chemical etching. Such a chemical bath may comprise, for example, a hydrofluoric acid for removing the silicon oxide spiral 5b.

In a second variant, step 39 comprises a single d3 phase for chemically etching the spiral 5a to obtain the spiral 5c silicon based the dimensions Db, H _3, E ₃ necessary for said predetermined stiffness C. Of course, depending on the material used, other variants such as laser etching or localized ion etching, for removing the excess material from the hairspring 5a to the dimensions Db necessary to obtain said hairspring 5c of a predetermined stiffness C , can to be considered.

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 8 comprising optional steps 41, 43 and 45. Advantageously according to the invention, the method 31 can thus continue with the step 41 intended to form, on at least a part of the hairspring 5c, a portion 28 for forming a hairspring 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 portion 22 is a silicon-based material, the e1 phase may consist of oxidizing the spiral 5c to coat it with silicon dioxide to form a spiral which is thermocompensated. 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 6 which, advantageously according to the invention, comprises a core 26 based on silicon and a coating 28 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 ₄ and the thickness E ₄ , 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, it can be expected to crystallize it to a predetermined depth.

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 spring 5c of a stiffness C predetermined. For example, if a monocrystalline or polycrystalline silicon is used, it may be provided to dope or to diffuse interstitial or substitutional atoms to a predetermined depth.

• 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 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 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 curing layer 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 (18)

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 ) greater than the dimensions (Db, H₃, E₃ ) 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 thickness of the material to be removed, based on the determination of the stiffness (C) of the balance spring (5a) determined in step b), to obtain the dimensions (Db, H₃, E₃ ) necessary to obtain said balance spring (5c) of a predetermined stiffness (C);

   d) removing (39) from the balance spring (5a) formed in step a), said thickness of material to obtain the balance spring (5c) having the dimensions (Db, H₃, E₃ ) 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% greater than those (Db, H₃, E₃ ) 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 ) greater than the dimensions (Db, H₃, E₃ ) 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 claim 6, characterized in that step d) includes the following phases:

    d1) oxidising the balance spring (5a) formed in step a) in order to transform said thickness of silicon material to be removed into silicon dioxide and thereby form an oxidised balance spring (5b);

    d2) removing the oxide from the oxidised balance spring (5b) to obtain the balance spring (5c) having the dimensions (Db, H₃, E₃ ) 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 phases:

    d3) chemically etching the balance spring (5a) formed in step a) to obtain the balance spring (5c) having the dimensions (Db, H₃, E₃ ) necessary for said predetermined stiffness (C).
14. 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.
15. 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.
16. Fabrication method (31) according to claim 15, 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).
17. Fabrication method (31) according to claim 15, 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).
18. Fabrication method (31) according to claim 15, 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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