EP3958066A1 - Method of manufacturing of a thermocompensated ceramic hairspring - Google Patents

Abstract

The invention relates to a process for the production of a spiral spring (1) intended to equip a balance-spring resonator of a watch movement or other precision instrument, the spiral spring (1) comprising a core (2) manufactured in a ceramic material based on silicon, the core (2) having a first stiffness (k_A) and a first thermoelastic coefficient (β_A); and a coating (4) of silicon dioxide of thickness (t_R) and at least partially covering the core (2), the coating (4) having a second stiffness (k_R) and a second thermoelastic coefficient (β_R) of opposite sign to the first thermoelastic coefficient (β_A). The method includes a step of adjusting the section of the core (2) and the thickness (t_R) of the coating (4) so as to obtain a desired value for the thermoelastic coefficient of the spiral spring (β_S) and a spiral spring stiffness (k_S). The invention also relates to a balance-spring resonator comprising the spiral spring and a balance. The spiral spring has an invariance of the expansion and elasticity properties.

Description

Technical area

The present invention relates to a heat-compensated spiral spring intended to equip a balance-spring resonator of a clock movement or other precision instrument. The invention also relates to a balance-hairspring resonator comprising the hairspring and a balance wheel and a method for adjusting the hairspring.

State of the art

The regulating organ of mechanical watches is conventionally composed of an inertia flywheel, called a balance wheel, and a spiral-shaped spring, called a hairspring or spiral spring, fixed by one end to the axis of the balance wheel and by the other end on a bridge, called cock, in which pivots the axis of the pendulum. More precisely, the spiral spring equipping, to date, the movements of mechanical watches is an elastic metallic blade of rectangular section wound on itself in the shape of an Archimedean spiral and comprising 12 to 15 turns.

The balance-spring oscillates around its equilibrium position (or dead point). When the balance wheel leaves this position, it winds the hairspring. This creates a restoring torque which, when the pendulum is released, causes it to return to its equilibrium position. As it has acquired a certain speed, therefore a kinetic energy, it exceeds its dead point until the opposing torque of the hairspring stops it and forces it to turn in the other direction. Thus, the hairspring regulates the period of oscillation of the balance wheel.

dans laquelle 86400 représente le nombre d'oscillations effectuées en 24 heures à une fréquence de 1 Hz.The precision of mechanical watches therefore depends on the stability of the fundamental natural frequency f _o of the resonator formed by the balance-spring. When the temperature varies, the thermal expansions of the hairspring and the balance wheel, as well as the variation of the Young's modulus of the hairspring, modify the natural fundamental frequency of this oscillating assembly, disturbing the accuracy of the watch. The fundamental natural frequency f _o is linked to the frequency variations Δf via the march M of the oscillating assembly according to equation 1: $$\mathrm{M}=\mathrm{86400}\left(\mathrm{\Delta f}/{\mathrm{f}}_{\mathrm{oh}}\right)$$

where 86400 represents the number of oscillations performed in 24 hours at a frequency of 1 Hz.

où k_s est la raideur du ressort spiral et J_B est le moment d'inertie du balancier par rapport à son axe de rotation. En particulier, le moment d'inertie du balancier peut s'exprimer comme: $${\mathrm{J}}_{\mathrm{B}}=\mathrm{m}{{\mathrm{r}}_{\mathrm{B}}}^{\mathrm{2}}$$

où m est la masse du balancier et r_B est le rayon du balancier. La raideur nominale ks du ressort spiral plat peut être estimée à partir de l'équation 4: $${\mathrm{k}}_{\mathrm{s}}=\left(\mathrm{E\; h}{\mathrm{w}}^{\mathrm{3}}\right)/\mathrm{12}\mathrm{L}$$

où E est le module d'Young du ressort spiral, w l'épaisseur du spiral, h la largeur du spiral et L la longueur du spiral.More specifically, the fundamental natural frequency f _o of a mechanical balance-spring resonator can be expressed according to equation 2: $${\mathrm{f}}_{\mathrm{oh}}=\mathrm{1}/\mathrm{2}{\left({\mathrm{k}}_{\mathrm{S}}/{\mathrm{<figure-callout\; id="1"\; label="J\; B"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">J</figure-callout>}}_{\mathrm{B}}\right)}^{\mathrm{1}/\mathrm{2}}$$

where k _s is the stiffness of the spiral spring and J _B is the moment of inertia of the balance relative to its axis of rotation. In particular, the moment of inertia of the pendulum can be expressed as: $${\mathrm{J}}_{\mathrm{B}}=\mathrm{<figure-callout\; id="2"\; label="m\; r\; B"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">m</figure-callout>}{{\mathrm{r}}_{\mathrm{B}}}^{}{{\mathrm{}}_{}}^{\mathrm{2}}$$

where m is the mass of the pendulum and r _B is the radius of the pendulum. The nominal stiffness ks of the flat spiral spring can be estimated from equation 4: $${\mathrm{k}}_{\mathrm{s}}=\left(\mathrm{<figure-callout\; id="3"\; label="Eh\; w"\; filenames="imgf0001.png"\; state="\{\{state\}\}">Eh</figure-callout>}{\mathrm{w}}^{}{\mathrm{}}^{\mathrm{3}}\right)/\mathrm{12}\mathrm{I}$$

where E is the Young's modulus of the hairspring, w the thickness of the hairspring, h the width of the hairspring and L the length of the hairspring.

soit $$\mathrm{\Delta f}/{\mathrm{f}}_{\mathrm{o}}=\mathrm{1}/\mathrm{2}\left({\mathrm{\beta }}_{\mathrm{S}}+\mathrm{3}{\mathrm{\alpha }}_{\mathrm{S}}-\mathrm{2}{\mathrm{\alpha }}_{\mathrm{B}}\right)$$

où Δk_S / ks est la variation de la raideur du ressort spiral par rapport à sa raideur nominale et ΔJ_B / J_B est la variation de l'inertie du balancier par rapport à son inertie nominale, ce qui permet d'introduire pour les perturbations thermiques, βs le coefficient thermoélastique linéaire du ressort spiral, α_S le coefficient de dilatation linéaire du ressort spiral, et α_B le coefficient de dilatation linéaire du balancier.For a temperature variation of 1°C, the relative variation of the balance-spring resonator frequency Δf with respect to its fundamental natural frequency f _o corresponds to: $$\mathrm{\Delta f}/{\mathrm{f}}_{\mathrm{oh}}=\mathrm{1}/\mathrm{2}\left({\mathrm{\Delta k}}_{\mathrm{s}}/{\mathrm{k}}_{\mathrm{s}}-{\mathrm{\Delta J}}_{\mathrm{B}}/{\mathrm{J}}_{\mathrm{B}}\right)$$

that is $$\mathrm{\Delta f}/{\mathrm{f}}_{\mathrm{oh}}=\mathrm{1}/\mathrm{2}\left({\mathrm{\beta }}_{\mathrm{S}}+\mathrm{3}{\mathrm{\alpha }}_{\mathrm{S}}-\mathrm{2}{\mathrm{\alpha }}_{\mathrm{B}}\right)$$

where Δk _S / ks is the variation of the stiffness of the spiral spring with respect to its nominal stiffness and ΔJ _B / J _B is the variation of the inertia of the balance with respect to its nominal inertia, which makes it possible to introduce for the thermal disturbances, βs the linear thermoelastic coefficient of the spiral spring, α _S the linear expansion coefficient of the spiral spring, and α _B the linear expansion coefficient of the balance wheel.

It will easily be understood that the stiffness ks of a spiral spring must be as constant as possible, whatever, in particular, the temperature and the magnetic field. For example, since the discovery of Elinvar alloys based mainly on Fe-Ni-Cr with a positive thermoelastic coefficient β _S (β _S equal to 30 to 40 × 10 ^-6 ), the thermal compensation of the mechanical oscillator is obtained by adjusting the thermoelastic coefficient βs of the hairspring as a function of the coefficients of thermal expansion of the hairspring α _S and of the balance wheel α _B , according to equation 5.

By adjusting the term (β _S +3α _S ) to a multiple of the value of the thermal expansion coefficient of the balance wheel, i.e. 2α _B , it is possible to cancel equation 5. Thus, the thermal variation of the natural frequency of the resonator can be eliminated.

The document EP1422436 describes a spiral spring cut from a {001} monocrystalline silicon wafer. The hairspring comprises a layer of SiO ₂ , having a thermoelastic coefficient opposite to that of silicon and formed around the external surface of the hairspring, in order to minimize the thermal drift of the balance-hairspring assembly. The layer of silicon dioxide also allows an improvement in the mechanical properties of the silicon substrate.

The thermoelastic coefficient of silicon is strongly influenced by temperature and compensation for this effect is necessary for its use in watchmaking applications. Indeed, the thermoelastic coefficient of silicon is of the order of -60 × 10 ^-6 /°C and the thermal drift of a silicon spiral spring is thus about 2 minutes/day, for a temperature variation of 23°C +/-15°C. It makes it incompatible with watchmaking requirements which are of the order of 0.6 seconds/day/°C in the temperature range between 8°C and 38°C.

The document EP2590325 describes a spiral spring whose ceramic body of the borosilicate glass or silicon carbide type is coated with a layer of SiO ₂ , so that the resonator thus formed has an almost zero frequency variation as a function of temperature. By the value of its thermocompensation coefficient, the SiO ₂ coating ensures quasi independence of the temperature on the Young's modulus of the material of the body of the resonator.

Brief summary of the invention

The invention relates to the selection of ceramic materials comprising the element silicon in their formulation for horological applications. In particular, the invention relates to a spiral spring intended to equip a balance-spring resonator of a watch movement or other precision instrument, the spiral spring comprising a core made of a ceramic material containing the element silicon in its formulation and comprising a section, the web having a first stiffness and a first thermoelastic coefficient; and a coating of silicon dioxide of thickness and at least partially covering the core, the coating having a second stiffness and a second thermoelastic coefficient of opposite sign to the first thermoelastic coefficient; the section of the core and the thickness of the coating being independently adjustable so as to obtain (i) a thermoelastic coefficient of the spiral spring as a function of the first thermoelastic coefficient and of the second thermoelastic coefficient, and (ii) a stiffness of the spiral spring in function of the first stiffness and the second stiffness.

The invention also relates to a balance-spring oscillator comprising the balance spring having a linear expansion coefficient of the balance spring, and a balance having a linear expansion coefficient of the balance; the section of the core and the thickness of the coating being adjusted so that the combination of the second thermoelastic coefficient and from the first thermoelastic coefficient results in a thermoelastic coefficient of the spiral spring compensating for a value corresponding to the difference between three times the linear expansion coefficient of the spiral spring and twice the linear expansion coefficient of the balance wheel; the cross-section of the core and the thickness of the coating also being adjusted so that the combination of the first stiffness and the second stiffness gives a stiffness of the spiral spring making it possible to obtain the fundamental natural setpoint frequency of the balance resonator- spiral.

• la formation du revêtement de dioxyde de silicium ayant une épaisseur prédéterminée sur au moins une portion de l'âme de manière à obtenir une valeur prédéterminée du second coefficient thermoélastique; et
• l'ajustement de la section de l'âme de manière à obtenir une valeur prédéterminée de la première raideur; l'ajustement de la section de l'âme étant réalisé avant l'étape de formation d'un revêtement de dioxyde de silicium.

A method of adjusting the spiral spring is also presented, the method comprising:

• forming the silicon dioxide coating having a predetermined thickness on at least a portion of the core so as to obtain a predetermined value of the second thermoelastic coefficient; and
• adjusting the section of the web so as to obtain a predetermined value of the first stiffness; the adjustment of the section of the core being carried out before the step of forming a coating of silicon dioxide.

The spiral spring as well as the balance-spring resonator of the invention exhibit an invariance of the expansion and elasticity properties in a defined range of temperatures comprised, according to the COSC (Swiss Official Chronometer Testing Institute), between 8°C and 38°C. Such a resonator is also insensitive to external magnetic fields.

The adjustment method makes it possible to adjust the section of the core and the thickness of the coating independently so as to obtain a desired value of the thermoelastic coefficient of the spiral spring and a desired value of the stiffness of the spiral spring.

The ceramic material containing the silicon element in its formulation is advantageous in horological applications due to its mechanical properties of use and, in particular, to its toughness which is much greater than that of silicon. All of the expected properties being supported by prior performance of aging tests under controlled temperature and atmosphere.

Brief description of figures

• la figure 1 montre une vue du dessus d'un ressort spiral selon l'invention;
• la figure 2 montre une vue en coupe transversale droite (figure 2a) et longitudinale (figure 2b) du ressort spiral comprenant une âme et un revêtement, selon un mode de réalisation;
• la figure 3 montre un exemple de ressort spiral thermocompensé comprenant une virole et un piton, selon l'invention;
• la figure 4 montre des micrographies d'une coupe du ressort spiral comprenant un revêtement en dioxyde de silicium, selon un premier (figure 4a) et second (figure 4b) mode de réalisation;
• les figures 5 et 6 montrent des micrographies d'une coupe du ressort spiral comprenant un revêtement en dioxyde de silicium selon une vue à un agrandissement de × 5000 (figure 5), à un agrandissement de × 18000 (figure 6); et
• la figure 7 est une micrographie d'une coupe du ressort spiral dans montrant une bonne adhérence entre l'âme et le revêtement en dioxyde de silicium.

Examples of implementation of the invention are indicated in the description illustrated by the appended figures in which:

• the figure 1 shows a top view of a spiral spring according to the invention;
• the figure 2 shows a right cross-sectional view ( figure 2a ) and longitudinal ( figure 2b ) the spiral spring comprising a core and a coating, according to one embodiment;
• the picture 3 shows an example of a heat-compensated spiral spring comprising a ferrule and a stud, according to the invention;
• the figure 4 shows micrographs of a section of the spiral spring comprising a silicon dioxide coating, according to a first ( figure 4a ) and second ( figure 4b ) embodiment;
• the figure 5 and 6 show micrographs of a cross-section of the coil spring including a silicon dioxide coating as viewed at a magnification of ×5000 ( figure 5 ), at ×18000 magnification ( figure 6 ); and
• the figure 7 is a micrograph of a cross section of the coil spring showing good adhesion between the core and the silicon dioxide coating.

Example(s) of embodiment of the invention

The figure 1 shows a top view of a spiral spring 1 and the figures 2a and 2b show a view in longitudinal and transverse section of the spiral spring 1 according to the invention. According to one embodiment, the spiral spring 1 comprises a core 2 formed in a ceramic material containing the element silicon in its composition (hereafter ceramic material) and a coating 4 of silicon dioxide covering at least partially the outer surface 3 of core 2. In the present description the term "core" is used to describe a central part, or even the body, of the spiral spring. The coating 4 corresponds to a layer deposited superficially on the core, or body. In the example of figures 1 and 2 , the core has a helical shape and comprises at least one turn of rectangular section of thickness w and height h. It will however be understood that the geometry of the core can be other than that illustrated in this example, for example, the core can have a circular cross section, or polygonal, or other. The spiral spring 1 can be seen as being formed of a composite structure of the "sandwich" type consisting of a central part, the core 2, and the coating 4 (see figure 2b ).

Core 2 made of ceramic material has a first thermoelastic coefficient β _A and a first stiffness k _A . The SiO ₂ coating has a second thermoelastic coefficient β _R of opposite sign to the first thermoelastic coefficient β _A , and a second stiffness k _R .

The most common ceramic materials with dielectric properties include aluminas (Al ₂ O ₃ ), aluminum nitrides (AIN), beryllium oxide (BeO), quartz, silicon nitride (Si ₃ N ₄ ), silicon aluminum oxynitride (SiAlON). In an alternative embodiment, the ceramic material comprises silicon nitride, silicon carbide, or silicon oxynitride. More particularly, the ceramic material may comprise one or a combination of the compounds: silicon nitride (Si ₃ N ₄ ), SiC or silicon and aluminum oxynitride (SiAlON), which comprise the element silicon in their composition. Preferably, the ceramic material comprises at least one of the following composite structures: Si ₃ N ₄ -SiC, Si ₃ N ₄ -TiCN, Si ₃ N ₄ -SiAlON, Si ₃ N ₄ -AlN, Si ₃ N ₄ -Al ₂ O ₃ , Si ₃ N ₄ -ZrO ₂ , SiC-SiAlON, Si-SiC, SiC-Si ₃ N ₄ -Si ₂ N ₂ O or SiAlON-TiN, or a composite comprising at least one of these compounds. The ceramic material can also comprise a composite of fiber type such as SiC fibers dispersed in a ceramic matrix (SiC for example) of SiC (composite SiC - SiC), or even a composite of acicular structure (example β Si ₃ N ₄ ) in a matrix of equiaxed structure (for example α Si ₃ N ₄ ) (composite Si ₃ N ₄ - Si ₃ N ₄ ). In one embodiment preferred, the ceramic material comprises at least one of the following composite structures: Si ₃ N ₄ -SiAlON or α-Si ₃ N ₄ -β-Si ₃ N ₄ .

Table I reports values of density, open porosity, Young's modulus, maximum bending stress, Weibull's modulus, toughness and thermal conductivity for Si3N4, SiC and SiAlON. Table I - Characteristics If ₃ N ₄ SiC SiAlON Density 3.2 3.10 3.25 Open porosity (%) 0 < 3 0 to 5 Young's modulus (GPa) 300 410 300 Maximum bending stress (MPa) 750 (3 point tests) 410 (4 point tests) 450 Weibull modulus 15 10 ≥ 10 Tenacity (MPa√m ) 6.5 3.2 ≥ 4 Thermal conductivity (W/mK) at 20°C 22 110 20

Examples of the ceramic material in the bulk state include Si ₃ N ₄ , supplied by the company HC STARCK CERAMICS under the reference SSN Star Ceram ^™ N700, or by the company UMICORE under the reference FRIALIT HP79; the SiC supplied by the company ESK CERAMICS for the SiC, under the reference EKASIC ^™ F SiC 100; and SiAlON by the company KENNAMETAL for SiAlON under the reference TK4. Table I compares the properties of these materials in the bulk state.

The ceramic material has good properties both at room temperature and at high temperature. Such ceramic materials are conventionally used as constituent materials of motors, bearings, gas turbine elements, in particular because of their good thermal resistance, their low thermal expansion, their good mechanical properties and their good resistance to heat. the corrosion. Mention may also be made of their use in the semiconductor industry, for example for silicon nitride masks. The ceramic material is advantageous for horological applications since it has a low density and a linear expansion coefficient of the same order of magnitude as that of silicon. It also has a Young's modulus which is double or even triple that of silicon, a resistance to bending, a toughness much greater than that of silicon, as well as insensitivity to magnetic fields. The monolithic ceramic material is also advantageous due to its refractory properties and its good resistance to dry and wet corrosion.

The production of the ceramic material can be carried out using a sintering process or any other suitable process. Unlike the manufacture of a spiral spring in silicon which requires its production from a machined plate of the "wafer" type, the core 2 in the ceramic material can be machined from any block in the ceramic material. so as to obtain a thickness (for example 150 μm) corresponding substantially to the desired height of the spiral spring 1. Preliminary machining of plates from industrial blocks can be carried out by cutting, grinding, lapping and then mechanical or chemical polishing. The machining itself can be done using a wet or dry etching process. For example, the machining can be carried out using a reactive ion etching process such as the DRIE (Deep Reaction Ion Etching) process. The DRIE process promotes deep engraving and good precision on the engraved shapes. It also promotes the formation of vertical walls on the core 2 thus etched.

It is also possible to machine the core 2 with the spiral shape using a laser cutting process. For example, a pulsed laser beam with a diameter between 10 microns and 30 microns can be used. The wavelength selected can be λ=532 nm, with a duration of the pulses comprised between 5 and 15 picoseconds, and this, for a rate comprised in the interval 200 KHz to 1000 KHz. It is also possible to perform the cut with single laser pulses or pulse trains with energies between 5 and 80 micro joules, , separated by intervals of 1 to 5 microseconds. Pulse trains can be composed of 2 to 10 laser pulses separated by 10 to 50 ns.

The thickness t _R of the coating 4 can be adjusted so as to obtain a desired value of the thermoelastic coefficient of the spiral spring βs. Indeed, the thermoelastic coefficient of the spiral spring βs depends on the combination of the first thermoelastic coefficient β _A and the second thermoelastic coefficient β _R and can therefore be modified by modifying the thickness t _R of the coating 4.

In addition, the section of the core 2 can be adjusted so as to obtain a desired value for the stiffness of the spiral spring ks. The stiffness of the spiral spring ks is determined by a combination of the stiffness of the web k _A and the stiffness of the coating k _R .

In fact, according to the invention, the section of the core 2 as well as the thickness t _R of the coating 4 can be adjusted independently in order to modify independently the value of the stiffness of the spiral spring ks and the value of the thermoelastic coefficient of the spiral spring βs.

In practice, the thickness of coating 4 will be between 0.1 μm and 10 μm, and preferably between 1 μm and 6 μm, or even more preferably between 2 μm and 5 μm.

The invention also relates to the adjustment of the spiral spring 1 so as to adjust the stiffness ks of the spiral spring 1 and the minimization of the variations of the properties of expansion and elasticity of the spiral spring 1 so as to minimize the thermal variations of the spiral spring 1 .

• l'ajustement de la section de l'âme 2 de manière à obtenir une valeur prédéterminée de la première raideur k_A; et
• la formation du revêtement de dioxyde de silicium 4 ayant une épaisseur prédéterminée t_R sur au moins une portion de l'âme 2 de manière à obtenir une valeur prédéterminée du second coefficient thermoélastique β_R.

According to one embodiment, a method for adjusting the spiral spring 1 comprises:

• the adjustment of the section of the core 2 so as to obtain a predetermined value of the first stiffness k _A ; and
• the formation of the silicon dioxide coating 4 having a predetermined thickness t _R on at least a portion of the core 2 in such a way in obtaining a predetermined value of the second thermoelastic coefficient β _R .

The adjustment of the section of the core 2 is carried out before the step of forming a coating of silicon dioxide. The section of the core 2 can be adjusted by removing material from the periphery of the core. Preferably, the removal of the material on the core 2 formed of the ceramic material is carried out by means of an isotropic chemical attack of the core 2. For example, the removal of the material can be carried out by an attack in a hot solution of phosphoric acid with or without nitric acid and water, to adjust the thickness of the silicon nitride core.

The predetermined value of the first stiffness k _A corresponds to the value that the first stiffness k _A of the core 2 (without the coating) must have allowing the spiral spring 1 (the core with the coating) to have a desired value for the stiffness ks of the spiral spring 1. The stiffness ks of the spiral spring 1 corresponds to a combination of the first stiffness k _A and the second stiffness k _R .

The predetermined value of the first stiffness k _A can be calculated as a function of the second stiffness k _R , which depends on the thickness t _R of the coating 4 and on the desired value of the stiffness ks of the spiral spring 1. The calculation of the predetermined value of the first stiffness k _A can be achieved using numerical simulations using finite elements depending on the desired stiffness of the spiral spring ks.

In one embodiment, the method comprises a step of measuring a first measured stiffness k _Am , and a step of comparing the first measured stiffness k _Am with a predetermined (desired) value of the first stiffness k _A . The quantity of material to be removed for the adjustment of the section of the core 2 so as to obtain the predetermined value of the first stiffness k _A can then be determined from the difference between the first measured stiffness k _Am and the predetermined value of the first stiffness k _A . The relationship between the first stiffness k _A and the quantity of material to be removed is given by equation 4 in which the stiffness of the spiral spring ks is replaced by the first stiffness k _A of the core 2 and where E is the Young's modulus of the core, w, h and L respectively the thickness, the height and the length of the soul 2.

The measurement of the first stiffness k _A can be carried out alternately with the step of adjusting the section of the web 2. Alternatively, the measurement of the first stiffness k _Am can be carried out simultaneously with the step of adjusting of web section 2.

Preferably, the adjustment of the section of the core 2 includes a removal of material corresponding to a thickness of approximately 0.1 μm to 3 μm at the periphery of the core 2.

The formation of the silicon dioxide coating 4 is carried out at least on a portion of the core 2. For example, the coating 4 can cover all the faces 3 of the core 2, or only certain faces 3 of the core 2 According to an embodiment where the core is produced on a substrate by etching, the coating 4 may cover only the three free faces of the core 2 but not the face integral with the substrate. The thickness t _R of the coating 4 is determined so as to obtain a predetermined value of the second thermoelastic coefficient β _R of the coating 4.

The growth of the coating 4 in silicon dioxide, corresponding to a so-called passive oxidation, can be carried out by thermo-oxidation in the presence of oxidizing agents or by rapid thermo-oxidation at temperatures between 800° C. and 1600° C., and preferably at temperatures between 1000°C and 1200°C. Oxidizing agents can include oxygen and/or water vapor (wet thermo-oxidation). Oxidizing agents may also include, for example and without being exhaustive, ozone, oxygen-nitrogen mixtures, or oxygen-helium.

The growth of the silicon oxide layer can also be carried out by plasma oxidation at low temperature (between 300° C. and 600° C. and preferably between 400° C. and 500° C.) using an oxygen plasma. In this case, the core 2 can be placed in the anodic position so as to avoid sputtering effects in the oxide layer. To this end, the core 2 can be brought into contact with an oxygen plasma generated by a radiofrequency source, or by a microwave source, both positioned a few centimeters from the core 2. The surface of the soul 2 is mainly subjected to ionized species of the plasma (ions, electrons). A cathode is located several tens of centimeters from the core to be oxidized. It is also possible to produce the silicon oxide layer by plasma-enhanced chemical vapor deposition (PECVD) with a thickness varying between 0.2 and 10 micrometers and, preferably, between 2 and 5 micrometers. .

Advantageously, the partially covalent chemical bonds of the silicon-based ceramics comprising a silicon nitride, carbide or oxynitride promote the continuity of the structures at the interface between the ceramic material and the SiO ₂ layer.

The composition and the structure of the coating 4 of silicon dioxide depend on the production method of the monolithic ceramic material. In the case where the ceramic material comprises silicon nitride produced by solid phase sintering under hot isostatic pressure (HIP SN) or by chemical vapor deposition (CVD) technology, the two processes being carried out without adding material , the coating 4 essentially contains amorphous SiO ₂ without disturbing the texture of the ceramic material.

$${\mathrm{Si}}_{\mathrm{3}}{\mathrm{N}}_{\mathrm{4}}+{\mathrm{SiO}}_{\mathrm{2}}\to \mathrm{2}{\mathrm{Si}}_{\mathrm{2}}{\mathrm{N}}_{\mathrm{2}}\mathrm{O}+{\mathrm{N}}_{\mathrm{2}}$$

Les produits gazeux de ces réactions (N₂) provoquent la formation de porosités (bulles) dans le revêtement 4.When the ceramic material is produced by a liquid phase sintering process in the presence of additions of the magnesium oxide (MgO), yttrium oxide (Y ₂ O ₃ ), rare earth oxide (Re ₂ O ₃ ) type, the coating 4 comprises compounds dispersed in the silica coating and the compound Si ₂ N ₂ O at the interface between the ceramic and the silica coating (for example the compound Y ₂ Si ₂ O ₇ in the case of addition of Y ₂ O ₃ ). In particular, the oxidation reaction forming coating 4 can be expressed by equations 6 and 7: $${\mathrm{Yes}}_{\mathrm{3}}{\mathrm{NOT}}_{\mathrm{4}}+\mathrm{3}/\mathrm{4}{\mathrm{<figure-callout\; id="2"\; label="O"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">O</figure-callout>}}_{\mathrm{2}}\to \mathrm{3}/\mathrm{2}{\mathrm{<figure-callout\; id="2"\; label="Yes"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">Yes</figure-callout>}}_{\mathrm{2}}{\mathrm{NOT}}_{\mathrm{2}}\mathrm{O}+\mathrm{1}/\mathrm{2}{\mathrm{NOT}}_{\mathrm{2}}$$

$${\mathrm{<figure-callout\; id="3"\; label="Yes"\; filenames="imgf0001.png"\; state="\{\{state\}\}">Yes</figure-callout>}}_{\mathrm{3}}{\mathrm{NOT}}_{\mathrm{4}}+{\mathrm{<figure-callout\; id="2"\; label="SiO"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">SiO</figure-callout>}}_{\mathrm{2}}\to \mathrm{2}{\mathrm{<figure-callout\; id="2"\; label="Yes"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">Yes</figure-callout>}}_{\mathrm{2}}{\mathrm{NOT}}_{\mathrm{2}}\mathrm{O}+{\mathrm{NOT}}_{\mathrm{2}}$$

The gaseous products of these reactions (N ₂ ) cause the formation of porosities (bubbles) in the coating 4.

The composition of the surface layer of the ceramic core 2 is also modified by different mechanisms of cationic diffusion of the elements of the additions.

The presence of the silicon element in the substrate of ceramic material constituting the core 2 of the spiral spring 1 allows good adhesion of the coating 4 to the ceramic substrate. This good adhesion is due to a continuity on the atomic scale between the substrate and the coating 4 in an accommodation zone (also known according to the English expression "terrace region") of a few atomic distances from the surface of the substrate.

The ceramic material containing the silicon element in its composition preferably has a resistivity which is typically very high (>10 ¹² Ω.m) and therefore can be considered as a dielectric material. When the silica coating 4 is produced on such a dielectric ceramic material, the silicic stratum grows from the extreme surface of the substrate, ensuring good adhesion of the coating to the substrate, and eliminating the diffusion of oxygen at the inside the core 2, as observed during silica oxidation operations.

The figure 4a and 4b relate to micrographs obtained by scanning electron microscopy, showing a sectional view of the spiral spring 1 comprising the core 2 in the ceramic material and the coating 4 in silicon dioxide formed by the thermal oxidation process in air at 1200°C during two hours ( figure 4a ), and by the low temperature plasma oxidation process using an oxygen plasma ( figure 4b ), under conditions favoring the passive oxidation of the ceramic material. A coating protecting the coating 4 during the metallographic cutting operation is also visible to the figure 4a and 4b .

The figure 5 and 6 show micrographs, obtained by scanning electron microscopy, of a section of the spiral spring comprising the coating 4 of silicon dioxide according to a view at an enlargement of × 5000 ( figure 5 ), at ×18000 magnification ( figure 6 ). Coating 4 is formed by a low temperature plasma oxidation process. The figure 7 shows another micrograph, also obtained by scanning electron microscopy, of a section of the spiral spring in which good adhesion between the core and the silicon dioxide coating can be seen, even in the areas with granular tearing (a such an area is represented on the figure 7 by number 8).

The thickness of the silicon oxide layer can be estimated using parameters such as oxidation time; the degree of humidity and the temperature. Indeed, the kinetic laws of growth of the layers of oxides are known (parabolic laws, arctangent laws, or linear functions).

In another embodiment, the method comprises a step of reducing the thickness of the coating 4. This step, in which a fraction of the thickness of the coating 4 is removed by chemical attack, makes it possible to adjust the stiffness ks more finely. of the spiral spring 1. This step, which is carried out after the step of forming the silicon dioxide coating 4 on the core 2, also makes it possible to make a fine adjustment of the predetermined value of the second thermoelastic coefficient β _R .

An important aspect of the method of the invention is that the obtaining of the predetermined value of the first stiffness k _A can be carried out in a single step.

In the case of a silicon core of the prior art, the adjustment of the section of the core by the removal of the material is typically carried out using a first step of growth of an oxide layer on the core and a second step of etching the oxide layer. Indeed, on silicon, the growth of the oxide layer takes place largely at the detriment of the silicon substrate, typically in a portion corresponding to approximately 44% of the total thickness of the layer. This two-step adjustment process is necessary to control the silicon removal with sufficient precision. On the contrary, the removal of the material from the core 2 of the invention in ceramic material can be carried out by chemical attack in an isotropic and controlled manner. Therefore, the adjustment of the section of the core 2 can be carried out before the step of forming a coating of silicon dioxide 4.

The invention also relates to a balance-spring resonator (not shown) for a clockwork movement or other precision instrument comprising the spiral spring 1 cooperating with a balance.

In such a resonator, the value of the stiffness ks of the spiral spring 1 is determined so as to obtain a reference value within its tolerance for the fundamental natural frequency f _o of the balance-spring resonator (see Equation 2). As described above, the value of the stiffness ks of the hairspring 1 is determined by the section of the core 2 and the thickness t _R of the coating 4. The fundamental natural frequency f _o of the balance wheel-hairspring resonator is typically comprised between 2 Hz and 20 Hz, or even between 2 Hz and 5 Hz.

The predetermined value of the thermoelastic coefficient of the spiral spring β _S can also be adjusted so as to compensate for the term (3α _S ― 2α _B ) of equation 5.

The core 2 of ceramic material containing the silicon element typically has a first negative thermoelastic coefficient β _A which must be partially compensated by the silica coating 4 having a second positive thermoelastic coefficient β _R of approximately 140×10 ^-6 / °C. In the case of a copper-beryllium balance wheel, the combination of the first thermoelastic coefficient β _A and the second thermoelastic coefficient β _R should result in a predetermined value of the thermoelastic coefficient β _S of the spiral spring 1 around +18×10 ^-6 /°C. The predetermined value of the coefficient thermoelastic β _S of the spiral spring 1 can be obtained by adjusting the section of the core 2 and the thickness t _R of the coating 4.

Compensation of the term (3α _S ― 2α _B ) of equation 5 by the thermoelastic coefficient of the spiral spring β _S makes it possible to minimize the thermal drift of the balance-spring resonator, and therefore the variations in the instantaneous diurnal rate of a watch comprising such a resonator. The balance-hairspring resonator may exhibit an invariance of the properties of expansion and elasticity of the hairspring 1 in a defined range of temperatures comprised, according to the COSC, between 8° C. and 38° C. Such a resonator is also insensitive to external magnetic fields.

The picture 3 shows an example of a heat-compensated ceramic spiral spring 1 produced according to the method of the invention with a ferrule 5 and a stud 6 (the ferrule and the stud are produced concomitantly with the spiral spring 1).

The present invention is also applicable to other types of resonators capable of regulating a mechanical watch movement, such as in particular a resonator in the form of a tuning fork.

The invention is characterized by one or more of the following elements:

• une âme (2) fabriquée dans un matériau céramique contenant l'élément silicium dans sa composition et comprenant une section, l'âme (2) ayant une première raideur (k_A) et un premier coefficient thermoélastique (β_A); et
• un revêtement (4) de dioxyde de silicium d'épaisseur (t_R) et couvrant au moins partiellement l'âme (2), le revêtement (4) ayant une seconde raideur (k_R) et un second coefficient thermoélastique (β_R) de signe opposé au premier coefficient thermoélastique (β_A);
• caractérisé en ce que la section de l'âme (2) et l'épaisseur (t_R) du revêtement (4) sont ajustables indépendamment de manière à obtenir:
  • un coefficient thermoélastique du ressort spiral (β_S) en fonction du premier coefficient thermoélastique (β_A) et du second coefficient thermoélastique (β_R); et
  • une raideur du ressort spiral (ks) en fonction de la première raideur (k_A) et la seconde raideur (k_R).

Spiral spring (1) intended to equip a mechanical balance-spring resonator of a watch movement or other precision instrument, the spiral spring (1) comprising:

• a core (2) made of a ceramic material containing the element silicon in its composition and comprising a section, the core (2) having a first stiffness (k _A ) and a first thermoelastic coefficient (β _A ); and
• a coating (4) of silicon dioxide of thickness (t _R ) and at least partially covering the core (2), the coating (4) having a second stiffness (k _R ) and a second thermoelastic coefficient (β _R ) of opposite sign to the first thermoelastic coefficient (β _A );
• characterized in that the section of the core (2) and the thickness (t _R ) of the coating (4) are independently adjustable so as to obtain:
  • a thermoelastic coefficient of the coil spring (β _S ) as a function of the first thermoelastic coefficient (β _A ) and the second thermoelastic coefficient (β _R ); and
  • a stiffness of the spiral spring (ks) as a function of the first stiffness (k _A ) and the second stiffness (k _R ).

The thickness of the coating (4) is between 0.1 μm and 10 μm, and preferably between 1 μm and 3 μm.

The ceramic material comprises a silicon nitride, carbide or oxynitride.

The ceramic material comprises at least one of the following compounds: Si ₃ N ₄ or SiAlON.

The ceramic material comprises at least one of the following composite structures: Si ₃ N ₄ -SiAlON, or α-Si ₃ N ₄ -O-Si ₃ N ₄ .

• la section de l'âme (2) et l'épaisseur (t_R) du revêtement (4) étant ajustées de manière à ce que la combinaison du second coefficient thermoélastique (β_R) et du premier coefficient thermoélastique (β_A) résulte dans un coefficient thermoélastique du ressort spiral (β_S) compensant une valeur correspondant à la différence entre trois fois le coefficient de dilatation linéaire du ressort spiral (as) et deux fois le coefficient de dilatation linéaire du balancier (α_B);
• caractérisé en ce que
• la section de l'âme (2) et l'épaisseur (t_R) du revêtement (4) sont également ajustées de manière à ce que la combinaison de la première raideur (k_A) et la seconde raideur (k_R) donne une raideur du ressort spiral (ks) permettant d'obtenir la fréquence propre fondamentale de consigne (f_o) du résonateur balancier-spiral.

Balance-spring resonator for a clock movement or other precision instrument comprising the spiral spring (1), the spiral spring (1) having a linear coefficient of expansion of the spiral spring (α _S ), and a balance wheel having a coefficient of expansion linear of the pendulum (α _B );

• the section of the core (2) and the thickness (t _R ) of the coating (4) being adjusted so that the combination of the second thermoelastic coefficient (β _R ) and the first thermoelastic coefficient (β _A ) results in a thermoelastic coefficient of the spiral spring (β _S ) compensating for a value corresponding to the difference between three times the linear expansion coefficient of the spiral spring (as) and twice the linear expansion coefficient of the balance (α _B );
• characterized in that
• the section of the core (2) and the thickness (t _R ) of the coating (4) are also adjusted so that the combination of the first stiffness (k _A ) and the second stiffness (k _R ) gives a stiffness of the balance-spring (ks) making it possible to obtain the set fundamental natural frequency (f _o ) of the balance-spring resonator.

Balance-spring resonator in which the set fundamental natural frequency (f _o ) of the balance-spring resonator is between 2 Hz and 20 Hz and preferably between 2 Hz and 5 Hz.

• la formation du revêtement de dioxyde de silicium (4) ayant une épaisseur prédéterminée (t_R) sur au moins une portion de l'âme (2) de manière à obtenir une valeur prédéterminée du second coefficient thermoélastique (β_R);
  caractérisé en ce que
• la méthode comprend également l'ajustement de la section de l'âme (2) de manière à obtenir une valeur prédéterminée de la première raideur (k_A); et
• en ce que l'ajustement de la section de l'âme (2) est réalisé avant l'étape de formation d'un revêtement de dioxyde de silicium (4).

Method of adjusting a spiral spring (1) comprising:

• forming the silicon dioxide coating (4) having a predetermined thickness (t _R ) on at least a portion of the core (2) so as to obtain a predetermined value of the second thermoelastic coefficient (β _R );
  characterized in that
• the method also includes adjusting the section of the core (2) so as to obtain a predetermined value of the first stiffness (k _A ); and
• in that the adjustment of the section of the core (2) is carried out before the step of forming a coating of silicon dioxide (4).

The method where the predetermined value of the first stiffness (k _A ) is calculated based on a stiffness of the spiral spring (ks) determined by a combination of the first stiffness (k _A ) and the second stiffness (k _R ).

The method where the calculation of the predetermined value of the first stiffness (k _A ) is carried out using numerical simulations using finite elements according to the stiffness of the spiral spring (ks) desired.

The method further comprising a step of measuring a first measured stiffness (k _Am ) and comparing the first measured stiffness (k _Am ) with the predetermined value of the first stiffness (k _A ).

The process in which the adjustment of the section of the core (2) comprises a removal of material corresponding to a thickness of about 0.1 µm to 3 µm at the periphery of the core (2).

The method in which material removal is determined from the difference between the first measured stiffness (k _Am ) and the predetermined value of the first stiffness (k _A ).

The process in which material removal is carried out using isotropic chemical attack of the core (2).

The method in which the measurement of the first stiffness (k _A ) is carried out alternately with the step of adjusting the section of the core (2).

The method in which the measurement of the first stiffness (k _A ) is carried out simultaneously with the step of adjusting the section of the web (2).

The method further comprising reducing the thickness of the coating (4) so as to adjust the stiffness (ks) of the spiral spring (1) and/or the predetermined value of the second thermoelastic coefficient (β _R ).

Notations used in the text and in the figures

1

spiral spring

2

soul

3

core surface

4

silicon oxide coating

5

ferrule

6

piton

7

coating

8

area with granular pullouts

αB

linear expansion coefficient of a pendulum

aS

linear expansion coefficient of a spiral spring

βA

first thermoelastic coefficient of the core constituting the hairspring

βR

second thermoelastic coefficient of a coating

βS

thermoelastic coefficient of the heat-compensated spiral spring

Δf

variation of the frequency of a balance-spring resonator

ΔJB

variation of the moment of inertia of the balance

ΔkS

variation of the spiral spring stiffness

r

coating thickness

fo

fundamental natural frequency of the balance wheel resonator

J.B.

balance moment of inertia

JBo

nominal moment of inertia of the balance

kA

first stiffness of the soul

km

first measured stiffness of the core constituting the hairspring

kR

second coating stiffness

kS

stiffness of the thermally compensated spiral spring

w

spiral spring thickness

m

pendulum mass

I

spiral spring length

rB

pendulum radius

h

spiral spring height

Claims (12)

Method for manufacturing a spiral spring (1) having a desired stiffness (Ks) and a desired thermal coefficient (βs), intended to equip a mechanical balance-spring resonator of a clock movement or other precision instrument, comprising the steps : to produce a core (2) made of a ceramic material containing the silicon element, to measure a first stiffness of the web (2) (k _AM ) and to compare the first measured stiffness (k _AM ), with respect to a predetermined value of the stiffness of the web (K _A ) adapted to the desired stiffness the spiral spring (Ks), the core having a first thermoelastic coefficient (β _A ); [0025], [0026]; to adjust the section of the core (2) so as to obtain the predetermined value of the first stiffness (Ka) [0032] adapted to the desired stiffness of the spiral spring (Ks) [0028], [0034]; to form a coating of silicon dioxide (4) on at least a portion of the core (2) said coating (4) having a thickness (t _R ), a second stiffness (k _R ) and a second coefficient thermoelastic (β _R ) of opposite sign to the first thermoelastic coefficient (β _A ) [0020], [0027]; the first stiffness of the web (k _A ) and the thickness (t _R ) of the coating being defined so that the spring has the desired stiffness (Ks), and the first thermoelastic coefficient (β _A ) of the core and the second thermoelastic coefficient (β _R ) of the coating being determined so that the spring has the desired thermal coefficient (βs). Method according to claim 1, in which the step of adjusting the section of the core is carried out by removing material, the quantity of material to be removed is determined according to the predetermined value of the first stiffness (K _A ) according to equation 4' [0036]: $${\mathrm{K}}_{\mathrm{AT}}=\left(\mathrm{Eh}{\mathrm{w}}^{\mathrm{3}}\right)/\mathrm{12}\mathrm{I}$$

in which : K _A designates the predetermined value of the first stiffness of the web (2); E denotes the Young's modulus of the core (2); w denotes the thickness of the core (2); h designates the height of the web (2); and L denotes the length of the web (2); Method according to one of Claims 1 and 2, in which the quantity of material to be removed corresponds to a thickness of approximately 0.1 µm to 3 µm at the periphery of the core (2). [0038] Method according to one of Claims 1 to 3, in which the steps of measuring a first measured stiffness (K _AM ) and of removing a quantity of material are carried out alternately or simultaneously. [0037] Method according to one of Claims 1 to 4, in which the predetermined value of the first stiffness (Ka) is calculated as a function of the second stiffness (k _R ), dependent on the thickness (t _R ) of the coating (4) and the desired value of the spring rate (Ks). [0035] Method according to one of Claims 1 to 5, in which the predetermined value of the first stiffness (k _A ) is determined with the aid of numerical simulations using finite elements as a function of the stiffness of the spiral spring (ks) desired ( R10). Method according to one of Claims 1 to 6, in which the step of removing a quantity of material is carried out by means of an isotropic chemical attack on the core (2). [0033], [0053]. Method according to one of Claims 1 to 7, in which the step of adjusting the section of the core (2) does not include the formation of a coating of silicon dioxide. [0053] Method according to one of Claims 1 to 7, in which the step of forming the coating of silicon dioxide (4) is carried out by thermo-oxidation in the presence of oxidizing agents or by rapid thermo-oxidation at temperatures between 800°C and 1600°C [0040] or by plasma oxidation at a temperature between 300°C and 600°C using an oxygen plasma, or by plasma-assisted chemical vapor deposition [0041] Process according to Claim 9, in which the thickness (t _R ) of the said coating (4) is estimated from parameters such as oxidation time, degree of hygrometry and temperature, according to the kinetic laws of growth of the layers of oxide [0050]. Method according to one of Claims 1 to 10, further comprising a step of reducing the thickness of the coating (4) so as to adjust the stiffness (Ks) of the spring and/or the predetermined value of the second thermoelastic coefficient (βR ). (R18) Spiral spring (1) obtained according to the method of one of claims 1 to 11.

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