Patent Publication Number: US-10324417-B2

Title: Method for fabrication of a balance spring of a predetermined stiffness by removal of material

Description:
This application claims priority from European Patent Application No 15201330.6 of Dec. 18, 2015, the entire disclosure of which is hereby incorporated herein by reference. 
     FIELD OF THE INVENTION 
     The invention relates to a method for fabrication of a balance spring of a predetermined stiffness and, more specifically, such a balance spring used as a compensating balance spring cooperating with a balance having a predetermined inertia to form a resonator having a predetermined frequency. 
     BACKGROUND OF THE INVENTION 
     It is explained in EP Patent 1422436, incorporated in the present Application by reference, how to form a compensating balance spring comprising a silicon core coated with silicon dioxide and cooperating with a balance having a predetermined inertia for thermal compensation of said entire resonator. 
     The fabrication of such a compensating balance spring offers numerous advantages but also has drawbacks. Indeed, the step of etching several balance springs in a silicon wafer offers a significant geometric dispersion between the balance springs of the same wafer and a greater dispersion between the balance springs of two wafers etched at different times. Incidentally, the stiffness of each balance spring etched with the same etch pattern is variable, creating significant fabrication dispersions. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to overcome all of part of the aforecited drawbacks by proposing a method for fabrication of a balance spring whose dimensions are sufficiently precise not to require further correction operations. 
     The invention therefore relates to a method for fabrication of a balance spring of a predetermined stiffness including the following steps:
         a) forming a balance spring in dimensions greater than the dimensions necessary to obtain said balance spring of a predetermined stiffness;   b) determining the stiffness of the balance spring formed in step a) by measuring the frequency of said balance spring coupled with a balance having a predetermined inertia;   c) calculating the thickness of the material to be removed, based on the determination of the balance spring stiffness determined in step b), to obtain the dimensions necessary to obtain said balance spring of a predetermined stiffness;   d) removing from the balance spring formed in step a) said thickness of material to obtain the balance spring having the dimensions necessary for said predetermined stiffness.       

     It is thus understood that the method can guarantee very high dimensional precision of the balance spring, and incidentally, a more precise stiffness of said balance spring. Any fabrication parameter able to cause geometric variations in step a) can thus be completely rectified for each fabricated balance spring, or rectified on average for all the balance springs formed at the same time, thereby drastically reducing the scrap rate. 
     In accordance with other advantageous variants of the invention:
         in step a), the dimensions of the balance spring formed in step a) are between 1% and 20% greater than those necessary to obtain said balance spring of said predetermined stiffness;   step a) is achieved by means of deep reactive ion etching or chemical etching;   in step a), several balance springs are formed in the same wafer in dimensions greater than the dimensions necessary to obtain several balance spring of a predetermined stiffness or several balance springs of several predetermined stiffnesses;   the balance spring formed in step a) is made from silicon, glass, ceramic, metal or metal alloy;   step b) comprises phase b1): measuring the frequency of an assembly comprising the balance spring formed in step a) coupled with a balance having a predetermined inertia, and phase b2): deducing, from the measured frequency, the stiffness of the balance spring formed in step a);   according to a first variant, step d) comprises phase d1): oxidising the balance spring formed in step a) in order to transform said thickness of silicon-based material to be removed into silicon dioxide and thereby form an oxidised balance spring, and phase d2): removing the oxide from the oxidised balance spring to obtain the balance spring in the dimensions necessary for said predetermined stiffness;   according to a second variant, step d) comprises phase d3): chemical etching of the balance spring formed in step a) to obtain the balance spring in the dimensions necessary for said predetermined stiffness;   after step d), the method performs, at least once more, steps b), c) and d) to further improve the dimensional quality;   after step d), the method also includes step e): forming, on at least one part of said balance spring of a predetermined stiffness, a portion for correcting the stiffness of the balance spring and for forming a balance spring less sensitive to thermal variations;   according to a first variant, step e) comprises phase e1): depositing a layer on one part of the external surface of said balance spring of a predetermined stiffness;   in a second variant, step e) comprises phase e2): modifying the structure, to a predetermined depth, of one part of the external surface of said balance spring of a predetermined stiffness;   according to a third variant, step e) comprises phase e3): modifying the composition, to a predetermined depth, of one part of the external surface of said balance spring of a predetermined stiffness.       

    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Other features and advantages will appear clearly from the following description, given by way of non-limiting illustration, with reference to the annexed drawings, in which: 
         FIG. 1  is a perspective view of an assembled resonator according to the invention. 
         FIG. 2  is an example geometry of a balance spring according to the invention. 
         FIGS. 3 to 6  are cross-sections of the balance spring in different steps of the method according to the invention. 
         FIG. 7  is a perspective view of a step of the method according to the invention. 
         FIG. 8  is a diagram of the method according to the invention. 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     As illustrated in  FIG. 1 , the invention relates to a resonator  1  of the type with a balance  3 -balance spring  5 . Balance  3  and balance spring  5  are preferably mounted on the same arbor  7 . In this resonator  1 , the moment of inertia I of balance  3  responds to the formula:
 
 I=mr   2   (1)
 
where m represents its mass and r the turn radius which also depends on temperature through the expansion coefficient α b  of the balance.
 
     Further, the stiffness C of balance spring  5  of constant cross-section responds to the formula: 
                   C   =       E   ⁢           ⁢   h   ⁢           ⁢     e   3         12   ⁢           ⁢   L               (   2   )               
where E is the Young&#39;s modulus of the material used, h the height, e the thickness and L the developed length thereof.
 
     Further, the stiffness C of a balance spring  5  of constant cross-section responds to the formula: 
                   C   =       E   12     ⁢     1       ∫   0   L     ⁢       1       h   ⁡     (   l   )       ⁢       e   3     ⁡     (   l   )           ⁢   dl                   (   3   )               
where E is the Young&#39;s modulus of the material used, h the height, e the thickness and L the developed length and l the curvilinear abscissa along the balance spring.
 
     Further, the stiffness C of a balance spring  5  of variable thickness but constant cross-section responds to the formula: 
                   C   =         E   ⁢           ⁢   h     12     ⁢     1       ∫   0   L     ⁢       1       e   3     ⁡     (   l   )         ⁢   dl                   (   4   )               
where E is the Young&#39;s modulus of the material used, h the height, e the thickness and L the developed length and l the curvilinear abscissa along the balance spring.
 
     Finally, the elastic constant C of sprung balance resonator  1  answers to the formula: 
     
       
         
           
             
               
                 
                   f 
                   = 
                   
                     
                       1 
                       
                         2 
                         ⁢ 
                         π 
                       
                     
                     ⁢ 
                     
                       
                         C 
                         I 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     According to the invention, it is desired that a resonator has substantially zero frequency variation with temperature. The frequency variation f with temperature T in the case of a sprung-balance resonator substantially follows the following formula: 
                       Δ   ⁢           ⁢   f     f     =       1   2     ⁢       {           ∂   E       ∂   T       ⁢     1   E       +     3   ·     α   s       -     2   ·     α   b         }     ·   Δ     ⁢           ⁢   T             (   6   )               
where:
 
             -       Δ   ⁢           ⁢   f     f           
is a relative frequency variation;
         ΔT is the temperature variation;       

     
       
         
           
             
               - 
               
                 
                   ∂ 
                   E 
                 
                 
                   ∂ 
                   T 
                 
               
             
             ⁢ 
             
               1 
               E 
             
           
         
       
         
         
           
              is the relative Young&#39;s modulus variation with temperature, i.e. the thermoelastic coefficient (TEC) of the balance spring; 
             α s  is the expansion coefficient of the balance spring, expressed in ppm. °C. −1 ; 
             α b  is the expansion coefficient of the balance, expressed in ppm. °C. −1    
           
         
       
    
     Since the oscillations of any resonator intended for a time or frequency base must be maintained, the maintenance system may also contribute to thermal dependence, such as, for example, a Swiss lever escapement (not shown) cooperating with the impulse pin  9  of the roller  11 , also mounted on arbor  7 . 
     It is thus clear from formulae (1)-(6) that it is possible to couple balance spring  5  with balance  3  such that the frequency f of resonator  1  is virtually insensitive to temperature variations. 
     The invention more particularly concerns a resonator  1  wherein the balance spring  5  is used for temperature compensation of the entire resonator  1 , i.e. all the parts and particularly the balance  3 . Such a balance spring  5  is generally called a compensating balance spring. This is why the invention relates to a method that can guarantee very high dimensional precision of the balance spring, and incidentally, guarantee a more precise stiffness of said balance spring. 
     According to the invention, compensating balance spring  5 ,  15  is formed from a material, possibly coated with a thermal compensation layer, and intended to cooperate with a balance  3  having a predetermined inertia. However, there is nothing to prevent the use of a balance with movable inertia-blocks able to offer an adjustment parameter prior to or after the sale of the timepiece. 
     The utilisation of a material, for example made from silicon, glass or ceramic, for the fabrication of a balance spring  5 ,  15  offers the advantage of being precise via existing etching methods and of having good mechanical and chemical properties while being virtually insensitive to magnetic fields. It must, however, be coated or surface modified to be able to form a compensating balance spring. 
     Preferably, the silicon-based material used for the compensating balance spring may be single crystal silicon, regardless of crystal orientation, doped single crystal silicon, regardless of crystal orientation, amorphous silicon, porous silicon, polycrystalline silicon, silicon nitride, silicon carbide, quartz, regardless of crystal orientation, or silicon oxide. Of course, other materials may be envisaged, such as glass, ceramics, cermets, metals or metal alloys. For the sake of simplification, the following explanation will concern a silicon-based material. 
     Each material type can be surface-modified or coated with a layer to thermally compensate the base material as explained above. 
     Although the step of etching balance springs in a silicon-based wafer, by means of deep reactive ion etching (DRIE) is the most precise, phenomena which occur during the etch or between two successive etches may nonetheless cause geometric variations. 
     Of course, other fabrication types may be implemented, such as laser etching, focused ion beam etching (FIB), galvanic growth, growth by chemical vapour deposition or chemical etching, which are less precise and for which the method would be even more meaningful. 
     Thus, the invention relates to a method  31  for fabrication of a balance spring  5   c . According to the invention, method  31  comprises, as illustrated in  FIG. 8 , a first step  33  intended to form at least one balance spring  5   a , for example from silicon, in dimensions Da greater than the dimensions Db necessary to obtain said balance spring  5   c  of a predetermined stiffness C. As seen in  FIG. 3 , the cross-section of balance spring  5   a  has a height H 1  and a thickness E 1 . 
     Preferably, the dimensions Da of balance spring  5   a  are substantially between 1% and 20% greater than those Db of balance spring  5   c  necessary to obtain said balance spring  5   c  of a predetermined stiffness C. 
     Preferably according to the invention, step  33  is achieved by means of a deep reactive ion etch in a wafer  23  of silicon-based material, as illustrated in  FIG. 7 . It is noted that the opposite faces F 1 , F 2  are undulating since a Bosch deep reactive ion etch results in an undulating etch, structured by the successive etch and passivation steps. 
     Of course, the methods cannot be limited to a particular step  33 . By way of example, step  33  could also be obtained by means of a chemical etch in a wafer  23 , for example of silicon-based material. Further, step  33  means that one or more balance springs are formed, i.e. step  33  can form individual loose balance springs or, alternatively, balance springs formed in a wafer of material. 
     Consequently, in step  33 , several balance springs  5   a  can be formed in the same wafer  23  in dimensions Da, H 1 , E 1  greater than the dimensions Db, H 3 , E 3  necessary to obtain several balance springs  5   c  of a predetermined stiffness C or several balance springs  5   c  of several predetermined stiffnesses C. 
     Step  33  is also not limited to forming a balance spring  5   a  in dimensions Da, H 1 , E 1  greater than the dimensions Db, H 3 , E 3  necessary to obtain a balance spring  5   c  of a predetermined stiffness C, produced using a single material. Thus, step  33  could also form a balance spring  5   a  in dimensions Da, H 1 , E 1  greater than the dimensions Db, H 3 , E 3  necessary to obtain a balance spring  5   c  of a predetermined stiffness C made from a composite material, i.e. comprising several distinct materials. 
     Method  31  includes a second step  35  intended to determine the stiffness of balance spring  5   a . This step  35  may be performed directly on a balance spring  5   a  still attached to wafer  23  or on a balance spring  5   a  previously detached from wafer  23 , on all, or on a sample of the balance springs still attached to a wafer  23 , or on a sample of balance springs previously detached from a wafer  23 . 
     Preferably according to the invention, regardless of whether or not balance spring  5   a  is detached from wafer  23 , step  35  includes a first phase intended to measure the frequency f of an assembly comprising balance spring  5   a  coupled to a balance having a predetermined inertia I and then, using the relation (5), to deduce therefrom, in a second phase, the stiffness C of balance spring  5   a.    
     This measuring phase may, in particular, be dynamic and performed in accordance with the teaching of EP Patent 2423764, incorporated by reference in the present Application. However, alternatively, a static method, performed in accordance with the teaching of EP Patent 2423764, may also be implemented to determine the stiffness C of balance spring  5   a.    
     Of course, as explained above, since the method is not limited to the etching of only one balance spring per wafer, step  35  may also consist in the determination of the mean stiffness of a representative sample, or of all the balance springs formed on the same wafer. 
     Advantageously according to the invention, based on the determination of the stiffness C of balance spring  5   a , method  31  includes a step  37  intended to calculate, using relation (2), the thickness of material to be removed from the entire balance spring to obtain the overall dimensions Db necessary to obtain said balance spring  5   c  of a predetermined stiffness C, i.e. the volume of material to be removed, in a homogeneous or non-homogeneous manner, from the surface of balance spring  5   a.    
     The method continues with a step  39  intended to remove the surplus material from balance spring  5   a  to achieve the dimensions Db necessary to obtain said balance spring  5   c  of a predetermined stiffness C. It is therefore understood that it does not matter whether geometric variations have occurred in the thickness and/or the height and/or the length of balance spring  5   a  given that, according to equation (2), it is the product h·e 3  that determines the stiffness of the coil. 
     Thus, a homogeneous thickness can be removed from the entire external surface, a non-homogeneous thickness can be removed from the entire external surface, a homogeneous thickness can be removed from only one part of the external surface, or a non-homogeneous thickness can be removed from only one part of the external surface. By way of example, step  37  could consist in only removing material from the thickness E 1  or from the height H 1  of balance spring  5   a.    
     In a first variant relating to a silicon-based material, step  39  comprises a first phase d1 intended to oxidise balance spring  5   a  in order to transform said thickness of silicon-based material to be removed into silicon dioxide and thereby form an oxidised balance spring  5   b . This phase d1 may, for example, be obtained by thermal oxidation. This thermal oxidation may, for example, be achieved between 800 and 1200° C. in an oxidising atmosphere with the aid of water vapour or dioxygen gas to form silicon oxide on balance spring  5   a.    
     As seen in  FIG. 4 , the cross-section of balance spring  5   b  has a height H 2  and a thickness E 2 . It is noted that balance spring  5   b  is formed of a central silicon-based part  22 , in the overall dimensions Db necessary for balance spring  5   c  of said predetermined stiffness C, and a peripheral silicon dioxide part  24 . Further, it is seen that the undulating shape is always reproduced on a portion of peripheral part  24  but is no longer or barely present on central part  22 . 
     Step  39  finishes, as illustrated in  FIG. 5 , with a second phase d2 intended to remove the oxide from balance spring  5   b  to obtain a balance spring  5   c  with only silicon-based part  22  in the overall dimensions Db necessary to obtain said predetermined stiffness C, the cross-section having, in particular, a height H 3  and a thickness E 3 . This phase d2 may, for example, be obtained by chemical etching. A chemical bath may comprise, for example, a hydrofluoric acid for removing the silicon oxide from balance spring  5   b.    
     In a second variant, step  39  includes only one phase d3 intended to chemically etch balance spring  5   a  to obtain silicon-based balance spring  5   c  in 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 focused ion beam etching, allowing excess material to be removed from balance spring  5   a  to the dimensions Db necessary to obtain said balance spring  5   c  of a predetermined stiffness C, may be envisaged. 
     Method  31  may end with step  39 . However, after step  39 , method  31  may also perform, at least once more, steps  35 ,  37  and  39  in order to further improve the dimensional quality of the balance spring. These iterations of steps  35 ,  37  and  39  may, for example, be of particular advantage when the first iteration of steps  35 ,  37  and  39  is performed on all, or on a sample, of the balance springs still attached to a wafer  23 , and then, in a second iteration, on all, or a sample, of the balance springs previously detached from wafer  23  and having undergone the first iteration. 
     Method  31  may also continue with all or part of process  40  illustrated in  FIG. 8 , comprising optional steps  41 ,  43  and  45 . Advantageously according to the invention, method  31  may thus continue with step  41  intended to form, on at least one part of balance spring  5   c , a portion  28  for forming a balance spring  5 ,  15  that is less sensitive to thermal variations. P In a first variant, step  41  may consist of a phase e1 intended to deposit a layer on one part of the external surface of said balance spring  5   c  of a predetermined stiffness C. 
     In the case where part  22  is a silicon-based material, phase e1 may consist in oxidising balance spring  5   c  to coat it with silicon dioxide in order to form a balance spring that is temperature compensated. This phase e1 may, for example, be obtained by thermal oxidation. This thermal oxidation may, for example, be achieved between 800 and 1200° C. in an oxidising atmosphere with the aid of water vapour or dioxygen gas to form silicon oxide on balance spring  5   c.    
     There is thus obtained compensating balance spring  5 ,  15 , as illustrated in  FIG. 6  which, advantageously according to the invention, comprises a silicon core  26  and a silicon oxide coating  28 . Advantageously according to the invention, compensating balance spring  5 ,  15  therefore has a very high dimensional precision, particularly as regards height H 4  and thickness E 4 , and, incidentally, very fine temperature compensation of the entire resonator  1 . 
     In the case of a silicon-based balance spring, the overall dimensions D b  may be found by using the teaching of EP Patent 1422436 to apply to the resonator  1  which is intended to be fabricated, i.e to compensate all of the constituent parts of resonator  1 , as explained above. 
     In a second variant, step  41  may consist in a phase e2 intended to modify the structure, to a predetermined depth, of one part of the external surface of said balance spring  5   c  of a predetermined stiffness C. By way of example, if an amorphous silicon is used, the silicon could be crystallised to a predetermined depth. 
     In a third variant, step  41  may consist in a phase e3 intended to modify the composition, to a predetermined depth, of one part of the external surface of said balance spring  5   c  of a predetermined stiffness C. By way of example, if a single crystal or polycrystalline silicon is used, the silicon could be doped or diffused with interstitial or substitutional atoms, to a predetermined depth. 
     Advantageously according to the invention, it is thus possible, with no further complexity, to fabricate, as illustrated in  FIG. 2 , a balance spring  5   c ,  5 ,  15  comprising in particular:
         one or more coils of more precise cross-section(s) than that obtained by means of a single etch;   variations in thickness and/or in pitch along the coil;   a one-piece collet  17 ;   an inner coil  19  of the Grossman curve type   a one-piece balance spring stud attachment  14 ;   a one-piece external attachment element;   a portion  13  of the outer coil  12  that is thicker than the rest of the coils.       

     Finally, method  31  may also comprise step  45  intended to assemble a compensating balance spring  5 ,  15  obtained in step  41 , or a balance spring  5   c  obtained in step  39 , to a balance having a predetermined inertia obtained in step  43 , to form a resonator  1  of the sprung balance type, which may or may not be temperature compensated, i.e. whose frequency f is or is not sensitive to temperature variations. 
     Of course, the present invention is not limited to the illustrated example but is capable of various variants and modifications that will appear to those skilled in the art. In particular, as explained above, the balance, even if it has an inertia predefined by design, may comprise movable inertia-blocks offering an adjustment parameter prior to or after the sale of the timepiece. 
     Further, an additional step, between step  39  in step  41 , or between step  39  in step  45 , could be provided for depositing a functional or aesthetic layer, such as, for example, a hardening layer or a luminescent layer. 
     It is also possible to envisage, when method  31  performs, after step  39 , one or more iterations of steps  35 ,  37  and  39 , that step  35  is not systematically implemented.