Patent Publication Number: US-2021173350-A1

Title: Horological resonator mechanism with inertial mass with adjustment of inertia and/or unbalance

Description:
FIELD OF THE INVENTION 
     The invention relates to an inertial mass with adjustment of inertia and/or unbalance for a horological resonator. 
     The invention also relates to an inertia and/or unbalance adjustment assembly for a horological resonator, including at least one such inertial mass with adjustment of inertia and/or unbalance. 
     The invention also relates to a horological resonator including at least one such inertial mass with adjustment of inertia and/or unbalance or at least one such inertia and/or unbalance adjustment assembly. 
     The invention also relates to a horological movement including at least one such horological resonator. 
     The invention also relates to a timepiece, in particular a watch, including at least one such horological movement. 
     The invention also relates to a method for adjusting inertia and/or unbalance of an inertial mass for a horological resonator. 
     The invention relates to the field of the adjustment of the running of horological mechanisms. 
     BACKGROUND OF THE INVENTION 
     The document EP 3252545 B1 in the name of Swatch Group Research &amp; Development Ltd describes a system for adjusting the inertia and the frequency of a balance of a mechanical horological movement without opening the watch case. This document also describes several geometries of adjustable balances. 
     The document FR 675597A in the name of Izurieta Chiriboga describes escapement devices and horological regulators, with various characteristics separately or in combination:
         special escapement member driven in a silent continuous rotation movement by the teeth of an escapement wheel;   teeth of this escapement wheel with a profile conjugate with that of the escapement member;   regulator member consisting of a disc driven in a continuous rotation movement by the escapement member either directly or indirectly; this disc is provided with a lever constrained to rotate with the disc, this lever moving in front of a graduation and carrying toothed sectors intended to act on wheels provided with inertia blocks attached to the disc and the various positions of which make it possible to vary the speed of rotation of the disc without impairing the indifferent equilibrium position of the assembly;   these wheels provided with inertia blocks are independent of each other, suitable graduations making it possible to know the respective adjustment thereof in order to preserve the indifferent equilibrium position;   the escapement wheel communicates a rotation movement to the escapement member, to the arbor of which the disc provided with the regulator device is directly fixed;   the rotation movement of the escapement member is communicated to an arbor carrying the disc and its regulator by means of a toothed wheel and a pinion, the latter, having a smaller number of teeth than the wheel, communicates to the regulator assembly a reverse rotation speed greater than that of the escapement member;   in the drive device, toothed wheel, pinion, the arbor of the pinion and of the escapement member is provided with a disc forming an additional mass.       

     The document CH 703462 in the name of Nivarox describes an equipped horology balance, with inertia setting for adjusting the inertia thereof and/or the balance thereof and/or the oscillation frequency thereof, including, at the periphery of the felloe thereof, at least one housing for receiving at least one insert, said insert including complementary guidance means with a profile complementary to guidance means that this housing includes. The balance and/or the insert includes elastic holding means that are arranged to allow, in a first insertion position where these elastic holding means are under constraint, the insertion of an insert in a housing, and to prevent, in a second holding position where these elastic holding means are released, the extraction of this insert out of this housing. The insert is able to move in translation and/or in rotation in its housing, in particular between discrete positions. 
     SUMMARY OF THE INVENTION 
     The present invention sets out to define a horological resonator mechanism including an inertial mass, in particular a balance with adjustable inertia, that can supplement the designs described in the documents EP 3252545 B1 and EP 3252546 B1 in the name of Swatch Group Research &amp; Development Ltd, making it possible to increase the range of adjustment of the inertia. 
     The invention also sets out to enable the operator or the user carrying out an adjustment of running to refer to a table directly correlating the deviation in running with discrete positions imposed on mobiles included in the inertial mass mechanism according to the invention. 
     For this purpose, the invention relates to an inertial mass with adjustment of inertia and/or of unbalance for a horological resonator, according to claim  1 . 
     The invention also relates to an inertia and/or unbalance adjustment assembly for a horological resonator, including at least one such inertial mass with adjustment of inertia and/or of unbalance. 
     The invention also relates to a horological resonator including at least one such inertial mass with adjustment of inertia and/or of unbalance or at least one such inertia and/or unbalance adjustment assembly. 
     The invention also relates to a horological movement including at least one such horological resonator. 
     The invention also relates to a timepiece, in particular a watch, including at least one such horological movement. 
     The invention also relates to a method for adjusting inertia and/or unbalance of an inertial mass for a horological resonator. 
    
    
     
       SUMMARY DESCRIPTION OF THE DRAWINGS 
       Other features and advantages of the invention will emerge from a reading of the following detailed description, with reference to the accompanying drawings, where: 
         FIG. 1  shows, schematically, and in plan view, an inertial mass according to the invention, in the form of a complete balance, resulting from assembling a lower flange, an upper flange, an elastic crown and mobiles for adjusting inertia and/or unbalance, which are here satellites with unbalance, here non-limitatively arranged two-by-two in symmetry with respect to the oscillation axis of this balance; 
         FIG. 2  shows, schematically, and in side view, the assembly of the lower flange and of the upper flange of the complete balance of  FIG. 1 ; 
         FIG. 3  shows, in a similar way to  FIG. 1 , solely the lower flange; 
         FIG. 4  shows, in a similar way to  FIG. 2 , the lower flange of  FIG. 3 ; 
         FIG. 5  shows, in a similar way to  FIG. 1 , the crown meshing with four satellites, two of a first type with 15 teeth arranged at noon and six o&#39;clock, and two of a second type with 17 teeth arranged at three o&#39;clock and nine o&#39;clock; 
         FIG. 6  shows, in a similar way to  FIG. 1 , the single upper flange; 
         FIG. 7  shows, in a similar way to  FIG. 2 , the upper flange of  FIG. 6 ; 
         FIG. 8  shows, in a similar way to  FIG. 2 , a variant where the upper flange and the lower flange are assembled by means of struts, for example laser welded; 
         FIG. 9A  is a detail of  FIG. 5  showing the meshing between the crown and a satellite of the first type, which include teeth with different profiles, and the points of contact between them forming a triangle of forces, which confers stable positioning on the satellite; 
         FIG. 9B  illustrates another variant wherein each mobile  3  is carried by a shaft or a journal provided with two slight protuberances, and thus the point of contact form together a trapezium of forces, which confers a positioning of the satellite that is even better than with the triangle of forces formed by the points of contact in  FIG. 9A ; 
         FIGS. 10 and 11  show, in a similar way to  FIG. 9 , the detail of the meshing of a crown with internal teeth with substantially straight flanks, with mobiles for inertia and/or unbalance adjustment that are respectively a satellite of the first type with a set of teeth with 15 teeth substantially in the form of an involute of a circle, and a satellite of the second type with a set of teeth with 17 teeth substantially with a square profile; 
         FIG. 12  is a distribution diagram showing on the x axis the two 255 possible positions with this particular combination of mobiles for adjusting inertia and/or unbalance, in particular first satellites with 15 teeth and second satellites with 17 teeth, and on the y axis the deviation in running, in seconds per day, which allows each of these combinations; a substantially sinusoidal distribution with a moiré effect, and the large number of combinations, allowing both high resolution and a large adjustment range; the following description gives, partially, an example of a table indicating, for each position of the satellites and of the crown, the corresponding variation in inertia, which results directly in the associated deviation in running; 
         FIG. 13  shows all the inertias relating to the total range of variation in inertia corresponding to the 255 positions, ordered in increasing inertia values, and illustrates the very small difference that can be controlled between two consecutive discrete inertia values; 
         FIG. 14  shows, in a similar way to  FIG. 5 , the same set of crown and satellites, where the crown includes external teeth, which cooperate directly or indirectly with a driving wheel that is not a fixed member, and which may be external to the horological movement, or which meshes with a wheel internal to the horological movement; 
         FIG. 15  shows, in a similar way to  FIG. 5 , the same crown and satellite set, where the internal teeth of the crown mesh with a small wheel, which may be internal to the horological movement, or, as shown in this figure, which is the end of a tool external to the movement, guided by a bore that the lower flange includes; the inertial mass and this external tool then constituting an inertia adjustment assembly; 
         FIG. 16  shows, in side view, the cooperation shown in  FIG. 15 , and  FIG. 17  is a detail of the end of this tool; 
         FIG. 18  shows, in a similar way to  FIG. 1 , another inertial mass constructed on the same principle, shown with a tool adapted for introducing the satellites: a ring includes external eccentric means constituting cams for the radial movement of sliding carriages arranged to immobilise or release the toothed elastic crown, when this ring is rotated through 90°, the sliding carriages compress and deform the annular spring, which makes it possible to place the satellites easily without colliding with the elastic crown; 
         FIGS. 19 and 20  are details of flanges of certain variants; 
         FIGS. 21 to 26  show, in a similar way to  FIGS. 1 to 7 , a balance allowing adjustment of the inertia and of the unbalance, and including satellites cooperating with elastic blades: the satellites pivoting on journals (or shafts) formed on the flanges, the elastic blades allowing a small radial movement of the satellites, and indexing the angular movement of the satellites in discrete positions; 
         FIGS. 28 to 30  show, in plan view, another inertial mass constructed on the same principle, the unbalances of the satellites of which are synchronised, and are not diametrically opposed, and details of the construction thereof. 
         FIG. 31  shows, in a similar way to  FIG. 1 , another inertial mass constructed on the same principle, which includes a rigid toothed crown, and the satellites of which are able to rotate about pivots each suspended by an elastic blade on at least one of the flanges of the inertial mass, or on these two flanges at the same time; as in  FIGS. 20 and 21 , this inertial mass forms part of the family of inertial masses synchronised by a crown; 
         FIG. 32  is a three-dimensional diagram showing schematically, in an extremely simplified way, a network of points in space, which can be formed by a very large number of points provided that a consistent number of satellites are used, such as for example the six mobiles for independent adjustment of  FIG. 25 , with which it is possible to define tens of thousands of points each corresponding to an unbalance value and an inertia value, these points are shown schematically here by crosses in an envelope sphere, wherein the density of points is variable according to the position in space, this cloud of points of shown purely schematically, and in no way represents the local differences in density of points according to the zones in the sphere, which are dependent on each case; 
         FIG. 33  is a block diagram showing a timepiece, in particular a watch, including a movement with a resonator equipped with at least one inertial mass according to the invention. 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     The invention relates to an inertial mass  100  with adjustment of inertia and/or of unbalance for a horological resonator  400 . 
     The invention is particularly illustrated for the case of a horological resonator  400  of the hairspring type, where the inertial mass is a balance. Naturally the invention is applicable to other types of mechanical resonator, and in particular to flexible-guidance resonators on elastic blades. The invention is also applicable to electromechanical resonators and, in general, to any resonator where it is wished to be able to correct the running in a simple fashion by acting on the inertia of at least one inertial mass of such a resonator. 
     According to the invention, this inertial mass  100  includes a plurality of mobiles  3  for adjusting inertia and/or unbalance, toothed or fluted, or including discrete angular indexing means. Each of these mobiles  3  for adjusting inertia and/or unbalance is mounted pivotably about a mobile axis DM with respect to at least one flange that the inertial mass  100  includes: lower flange  10  or upper flange  40  in the case of the figures. The centre of mass of each mobile  3  for adjusting inertia and/or unbalance is off-centre with respect to this mobile axis DM. This mobile axis DM is itself off-centre with respect to the centre of inertia of the inertial mass  100 . This unbalance is in particular but not limitatively achieved by means of a recess  312 ,  322 , which each of these mobiles  3  includes. Advantageously, these recesses  312 ,  322  are arranged for the introduction of a special tool, or tweezers, or the like, for angular adjustment of the mobile  3  concerned. 
     The invention is described here in the particular and non-limitative case of drives by teeth. Naturally the invention is also applicable to other driving and indexing means, such as flutes, spikes or other. 
     Each mobile  3  for adjusting inertia and/or unbalance cooperates by meshing or indexing cooperation with a single crown for adjusting inertia and/or unbalance  20 , toothed or fluted, or provided with complementary indexing means, depending on the type of indexing means that each mobile  3  for adjusting inertia and/or unbalance includes, under permanent constraint, which is exerted by an elastic return force that is exerted by the crown  20  and/or by an elastic return force exerted by the mobile  3  for adjusting inertia and/or unbalance or by the flange  10 ,  40  that carries this mobile  3 . 
     Thus the crown  20  is either flexible or rigid. 
     In a particular embodiment, at least two different types of mobile  3  for adjusting inertia and/or unbalance have different numbers of teeth or flutes. 
     According to the invention, at least two mobiles  3  for adjusting inertia and/or unbalance can be indexed independently of each other for combined adjustment of unbalance and inertia of the inertial mass  100 . 
     In a particular embodiment, all the mobiles  3  for adjusting inertia and/or unbalance  3  of the same inertial mass  100  can be indexed in a combined fashion, that is to say are kinematically linked so as to turn through the same angle during an adjustment operation. 
     In another particular embodiment, at least one mobile for adjusting inertia and/or unbalance  3  can be indexed independently of a set of at least two other mobiles  3  that can be indexed together in a combined fashion. 
     In yet another particular embodiment, at least three mobiles  3  for adjusting inertia and/or unbalance can be indexed independently of each other for combined adjustment of unbalance and inertia of the inertial mass  100 . 
     In yet another particular embodiment, all the mobiles  3  for adjusting inertia and/or unbalance of the same inertial mass  100  can be indexed independently of each other for a combined adjustment of unbalance and inertia of the inertial mass  100 . 
       FIGS. 1 to 18  relate to the case of an elastic crown,  FIG. 19  the case of elastic supports at one of the flanges, and  FIG. 20  the case of elastic satellites. 
     In the non-limitative example that follows, the inertial mass  100  is a balance, in particular and non-limitatively with a diameter of approximately 10 mm, which includes:
         a lower flange  10 , here including a felloe  11 , shoulders  13  and  14 , arms  12 , a central bore  17  at the oscillation axis DO of the inertial mass  100 , and brackets  15  carrying guidance piercings  16 ;   an upper flange  40  including here a felloe  41 , shoulders  43  and  44 , and countersinks  45  at the periphery of a large central hollow around the oscillation axis DO of the inertial mass  100 , the shoulders  43  and  44  advantageously include first orifices  431  in a first step of 15 divisions with associated marking, and second orifices  441  at a second step of 17 divisions with an associated marking;   mobiles for adjusting inertia and/or unbalance  3 , which here consist of
           two first satellites  31  of a first type, with a first central bore  311 , with an unbalance created non-limitatively by first hollows  312 , and a first set of teeth  310  including 15 identical teeth, each first satellite  31  including a first marking  39  of the transfer or mark type on a tooth or similar, to mark the angular position thereof; this marking  39  is shown with a darker zone in  FIG. 10 , in  FIG. 5 , and in  FIG. 1  through first orifices  431  that the upper flange  40  includes;   two second satellites  32  of a second type, with a second central bore  321 , with an unbalance created non-limitatively by second hollows  322 , and a second set of teeth  320  including 17 identical teeth, each second satellite  32  including a second marking  390  of the transfer or mark type on a tooth, or similar, to mark the angular position thereof; this second marking  390  is shown with a darker zone on  FIG. 11 , on  FIG. 5 , and on  FIG. 1  through second orifices  441  that the upper flange  40  includes;   
           an elastic crown  20 , which includes a felloe  2  carrying at least one set of teeth, according to the case internal teeth  21  and/or external teeth  22 ; in the case of  FIG. 5  the internal set of teeth  21  includes 72 teeth.       

     The choice of the term “satellite” employed here does not necessarily imply the presence of a sun as in other known mechanisms including sun, crown and satellites. 
     Such satellites  31 ,  32 , are of very small size. Thus, in order to have good precision of manufacture, micromachining technologies are particularly advantageous. It is possible to use all micromachinable materials. For reasons of strength, the preferential technology is the “LIGA” method (from the German “Lithographie, Galvanoformung, Abformung”, or “lithography/galvanisation by electrodeposition/forming”), in particular, but non-limitatively of the nickel phosphorus (non-magnetic) type with one or two levels. Naturally it is possible to use variants of this method, in particular using UV rays instead of X-rays, of the original method, or of other similar technologies well known to a person skilled in the art, in particular specialising in MEMS (from the English “microelectromechanical systems”) and of the manufacture of components made from micromachinable material made from silicon, oxidised silicon, DLC or similar. 
       FIGS. 1, 5, 9, 10, 11, 14, 15  illustrate a particular and advantageous case where the mobiles for adjusting inertia and/or unbalance  3 , in particular satellites  31 ,  32 , are mounted in diametrically opposed pairs with respect to the oscillation axis DO of the inertial mass  100 . The mounting of this balance forming the inertial mass  100  of these figures is as follows:
         the four satellites  31  and  32  are placed, in pairs diametrically opposed with respect to the oscillation axis DO of the inertial mass  100 , on the lower flange  10 , in particular by cooperation of bores  311 , respectively  321 , that they include, with journals  131 ,  141 , of the lower flange  10  (or vice versa), with the orientation visible in  FIGS. 1 and 5 , which corresponds to the position of each satellite that corresponds to the middle of the inertia adjustment range,   the crown  20 , which is an elastic crown, is force-fitted around the four satellites  31  and  32 . The crown  20  is slightly too small and is therefore under tension and has a spring role and provides the taking up of clearances; this crown  20  includes a felloe  2  carrying at least one set of teeth, according to the case internal teeth  21  and/or external teeth  22 ,   driving of the upper flange  40 , either directly on the lower flange  10  as can be seen in  FIG. 2  at protrusions  46  on the upper flange  40  cooperating with housings  16  in the lower flange, or vice versa, or by means of struts  1040  as can be seen in  FIG. 8 . In a variant, laser welding spots are made or an irreversible junction is produced by a similar method, in order to guarantee holding of the two lower  10  and upper  40  flanges on each other,   the balance  100  is next conventionally matched with its balance spring. The balance/balance spring assembly can then, as for a standard balance, be balanced and set at the frequency roughly by removal or addition of material, and then finely by means of the object of the invention.       

     More particularly, each mobile  3  for adjusting inertia and/or unbalance is enclosed between the lower flange  10  and the upper flange  40 . 
     More particularly, the crown  20  is enclosed between the lower flange  10  and the upper flange  40 . 
     Preferably the lower flange  10  or the upper flange  40  includes, facing at least one mobile  3 , and preferably facing each mobile  3 , at least one marking and/or one orifice  431 ,  441 , for marking a single visual indicator that this mobile  3  for adjusting inertia and/or unbalance includes. 
     More particularly, the lower flange  10  and the upper flange  40  are fixed to each other irreversibly. 
     In this embodiment according to  FIGS. 1, 5, 9, 10, 11, 14, 15 , the main role of the elastic crown  20  is to synchronise the angular positions of the two pairs of satellites  31 ,  32 , so as to vary only the inertia without introducing any unbalance. In addition, the tension of the elastic crown  20  applied to the journals  131 ,  141  of the lower  10  and upper  40  flanges eliminates the clearances between the various components, and creates stable positions at each advance by one step, in particular of a tooth, of each of the four mobiles  3  at a time, which makes it possible to dispense with a jumper, which is in general necessary in horology in order to impose stable positions but which is a great consumer of space. 
     In this particular example, the combination of the positions of the four satellites  31  and  32  makes it possible to obtain 255 stable positions, and at a maximum the same number of different inertias, by turning the crown  20 , by the combination of the 15 teeth and the 17 teeth that these satellites  31  and  32  respectively include. 
       FIG. 9A  shows the position of the points of contact:
           38  between the crown  20  and the satellite  31  or  32 ,   and  37  between the satellite and the guide shaft of the satellite, in particular a journal  131 .
 
This position forming a triangle of forces with the points  38  and  37  is stable and corresponds to a minimum elastic potential energy.
       

       FIG. 9B  illustrates another variant in which each mobile  3  is carried by a shaft or a journal provided with two slight protuberances  3110 , and thus the points of contact form together a trapezium of forces, which confers a positioning of the satellite that is even better than with a triangle, because of less deformability. This is because the triangle can change from isosceles (nominal position) to regular (off-centre position) because of the friction between a circular shaft and bore, whereas the trapezium of forces scarcely deforms at all. 
     During rotation, the crown  20  is subjected to bending that forces the whole of the system to reposition itself in a stable and centrosymmetrical position. 
     The crown  20  comprises internal synchronisation teeth  21  and, in a variant, external teeth  22 .  FIGS. 15 and 18  illustrate other variants of a complete resonator, the external teeth  22  of the crown  20  are concealed by the upper flange. 
       FIGS. 10 and 11  illustrate a particular variant where, advantageously, the form of the teeth of the crown and of the satellites differs according to the component concerned. The forms of the teeth  39 , and respectively  390 , of the first satellites  31  with 15 teeth, and respectively of the second satellites  32  with 17 teeth, are optimised in order to minimise the clearance in a stable position and not to jam duration rotation. The forms of the teeth are different, since the teeth pitches are not the same, since in this particular variant the primitive diameters (and therefore the unbalances) are identical. 
     It is also possible, in another variant that is not illustrated, to have teeth with the same form for the two pairs of satellites, changing the diameter of one of the pairs in order to have equivalent teeth pitches. 
     In order to adjust the inertia of the balance, it can therefore be seen, in this same example of  FIGS. 1, 5, 9, 10, 11, 14, 15 , that the combination of the positions of the four satellites  31  and  32  makes it possible to obtain at a maximum 255 different inertia values (15 teeth×17 teeth, as shown by the graph of the running on  FIG. 12 , according to rotation clicks of the crown  20  (data for inertia and masses of the specific planetary wheels and balance). The zero position corresponds to the situation in  FIG. 5 , and the crown  20  is then turned in the anticlockwise direction. 
     The sinusoidal trend of the running graph according to the adjustments of unbalance is a moiré effect, or a beat of the combination of the two pairs of unbalances slightly offset at the number of teeth. 
     It can be seen that, around the maxima of the sines, the resolution per notch is fine, and that there are a plurality of maxima at different heights, which confers on the system both high resolution and a large adjustment range. As there does not exist any linear relationship between the number of clicks and the inertia, the following table is an extract of a global table setting out all the adjustments for the 255 positions, and indicates only a few angular positions of the satellites (out of the 255 possible) and of the crown, and the corresponding variations in inertia with respect to the median value at position  128 . The graph shows the variation in inertia for the 255 positions relative to the total range of inertia variation (Imax−Imin). The satellites in this balance are in the median position of the adjustment of the inertia. 
                                                     variation   15 tooth   17 tooth               in inertia   satellite   satellite   crown           dl/(Imax-Imin)   position i   position j   position k                                                        1   −0.500   9   11   −4       2   −0.492   9   10   −124       3   −0.489   10   11   −123       4   −0.481   10   10   12       5   −0.475   9   12   116       6   −0.468   8   11   115       7   −0.464   10   12   −3       . . .   . . .   . . .   . . .   . . .       125   −0.0061   6   6   8       126   −0.0027   1   10   63       127   −0.0003   2   11   64       128   0   13   15   0       129   −0.0003   9   2   −64       130   −0.0027   10   3   −63       131   −0.0061   5   7   −8       . . .   . . .   . . .   . . .   . . .       251   0.475   2   1   −116       252   0.481   1   3   −12       253   0.489   1   2   123       254   0.492   2   3   124       255   0.500   2   2   4                    
If an example is taken according to the position corresponding to line  4  in the above table:
         the first satellite  31  with 15 teeth is at the position i=10, and the second satellite  32  with 17 teeth is at the position j=10;   measurement of the running indicates that it is necessary to increase the inertia by a value of 0.969:   0.969 is added to −0.481 (first column in the table) and 0.488 is obtained for the resulting new inertia;   the closest inertia value on the table is sought and the values are taken from line  253  in the table: the first satellite  31  with 15 teeth must go to the position i=1, and the second satellite  32  with 17 teeth must go to the position j=2;   to make the change it is necessary to turn the crown from position  12  to position  123  (last column in the table). To assist the operator, an algorithm advantageously makes it possible to calculate the number of turns of the satellites to be made.       

     It will be understood that the diametrically opposite satellites are adjusted identically, in order to guarantee that the centre of mass of the whole of the inertial mass  100  remains on its oscillation axis DO. Differentiated adjustments would certainly make it possible to obtain even more possibilities of adjustment of inertia and/or of unbalance, but at the cost of a resulting unbalance that is off-centre with respect to the oscillation axis DO, which is not generally desired. 
     In this particular example, the satellites have 15 to 17 teeth, but there exists a large number of combinations of numbers of teeth that make it possible to have satellites of different sizes with a number of combinations of positions that follows the size of the satellite or the number of teeth. The graph in  FIG. 13  shows all these relative inertias ordered by increasing values. The least good resolution corresponds to the maximum jump between two consecutive values. It can be seen clearly that these maximum jumps are very small compared with the entire range. 
     In a particular variant, the number of teeth or flutes of at least one type of satellite is a prime number. 
     In another particular variant, the numbers of teeth or flutes of at least two different types of satellite have numbers that are prime with each other. 
     In yet another variant, the numbers of teeth or flutes of all the various types of satellite are numbers that are prime with each other. 
     In addition, by modifying the angular phase difference between the teeth of the satellite and their unbalance, it is possible not only to achieve  255  unique discrete levels, but also reduced maximum jumps. The resolution can thus be optimised. 
     For controlling the adjustment of inertia and/or of unbalance when the resonator is in position in a watch, it is possible to adjust the inertia with a wheel internal to the movement, which is visible in  FIG. 14 . 
     The documents EP 3252545 B1 and EP 3252546 B1 in the name of Swatch Group Research &amp; Development Ltd, incorporated here by reference, relate to a mechanism that makes it possible to turn the crown with a driving wheel  5 , which a drive mechanism  50  includes. Preferably, the form of the external teeth  22  of the crown  20 , and the form of the teeth  51  of the driving wheel  5 , is very pointed, in order to minimise the forces and the risk of damaging the teeth during engagement. 
     Manipulation is easy, since the unitary tangential movement of a notch is 0.44 mm at the crown  20 , a sufficiently long path for this example diameter of 10 mm. 
     Another variant, as can be seen in  FIGS. 15 to 17 , consists of adjusting the inertia with an external wheel  6  mounted at the end of a tool  7  manipulated by the watchmaker: the inertia can thus be modified directly on the balance with a tool composed of a screwdriver with a toothed wheel at the end, or similar. In order to facilitate the positioning of the tool, the lower flange  10  advantageously includes piercings  16 , for example on brackets  15 , in particular facing countersinks  45  on the felloe  41  of the upper flange  40 , in order to centre and guide the distal end of this tool  7 , in particular a journal  71  or the like, in order to guide the end of the tool  7  that projects beyond its external wheel  6 . The upper flange  40  includes a countersink  45  in line with each piercing  16  (in particular produced in a bracket  15 ), and thus the teeth  61  on the external wheel  6  of the tool  7  can mesh directly with the internal teeth  21  on the crown  20 . 
     By having the possibility of adjusting the inertia with such an external tool  7 , it is also possible, in another similar embodiment, to envisage a conventional balance  100  without internal integral adjustment. In this case it is possible to eliminate the external teeth on the crown  20 . 
     In a variant, keeping the external teeth  22  on the crown  20 , it is possible to envisage putting the satellites  31 ,  32  outside the crown  20 . 
       FIG. 18  illustrates a tool adapted for introducing the satellites during assembly: a ring  9  includes internal eccentric cams  91  for the radial movement of sliding carriages  8  arranged so as to immobilise or release the elastic crown  20 , when this ring is rotated through 90°, the sliding carriages compress and deform the elastic ring  20 , which makes it possible to place the satellites  3  easily without colliding with the elastic crown  20 . 
       FIGS. 19 and 20  are details of flanges of certain variants. 
       FIGS. 21 to 27  relate to an inertial mass that does not include an elastic toothed crown and the satellites  31 ,  32  of which are independent of one another, and are indexed by elastic blades  28  secured to one of the flanges of the inertial mass. 
       FIGS. 28 to 30  illustrate a balance with three mobiles for adjusting inertia and/or unbalance formed by three satellites  60 , which, in this figure, conceal three arms joining the felloe at the central part of axis DO. These three third identical satellites  60  here have sets of teeth  61  with 30 teeth, and the crown  20  includes 72 teeth. Adjustment of the inertia is simplified given a sinusoidal monotonic relationship between clicks and inertia, but there are only 16 adjustment positions. Maintenance of the centre of mass on the oscillation axis is provided by the synchronisation of identical adjustments on each of the third satellites  60 . All the unbalances are synchronised. 
       FIG. 31  relates to another inertial mass  100 , which includes a rigid toothed crown  20 , and the satellites  3  of which are mounted elastically on flexible blades  28  formed in at least one of the two flanges, or in both flanges, the principle being in all respects identical to that illustrated by  FIGS. 1 to 15 . 
     The invention also relates to an inertia and/or unbalance adjustment assembly  150  for a horological resonator  400  including at least one such inertial mass with inertia and/or unbalance adjustment  100 , this assembly  150  including this inertial mass with inertia and/or unbalance adjustment  100 . According to the invention, this inertia and/or unbalance adjustment assembly  150  includes firstly a two-dimensional ( FIG. 12 ) or three-dimensional ( FIG. 32 ) diagram, associated secondly with a table or file of values, defining together the inertia and/or unbalance value of the inertial mass with adjustment of inertia and/or unbalance  100  according to the position occupied by each of the mobiles  3  for adjustment of inertia and/or unbalance that this inertial mass  100  with adjustment of inertia and/or unbalance includes. 
     More particularly, this inertia and/or unbalance adjustment assembly  150  includes a tool including an external wheel  6  arranged to mesh with teeth  21 ,  22  that the crown  20  of this inertial mass  100  includes, or the like. 
     The invention also relates to a horological resonator  400  including at least one such inertial mass with adjustment of inertia and/or unbalance  100  or at least one such inertia and/or unbalance adjustment assembly  150 . 
     The invention also relates to a horological movement  500  including at least one such resonator  400 . This movement  500  advantageously includes a drive mechanism  50 , arranged to cooperate with teeth on the crown  20 .  FIG. 14  illustrates the case where this drive mechanism  50  includes a driving wheel  5 , which includes teeth  51  arranged to cooperate with the external teeth  22  on the crown  20 , in the non-limitative illustrated case where the crown includes such teeth. Naturally a similar arrangement is possible if the crown  20  includes an indexing means other than teeth, such as flutes or the like, the driving wheel  5  then includes the appropriate profile, complementary to that of the crown  20 . 
     In a particular embodiment, not illustrated in order not to overload the figures, this drive mechanism  50  is disengageable, in order not to restrict the inertial mass  100  during the oscillation of the resonator mechanism  400 , nor to interfere with this oscillation in any way whatsoever. FIGS. 1, 14, 16, 20, 21 of the documents EP 3252545 B1 and EP 3252546 B1 in the name of Swatch Group Research &amp; Development Ltd describe such an engagement mechanism with magnetocoupler integrated in the watch. 
     The invention also relates to a timepiece  1000 , in particular a watch, including at least one horological movement  500  including at least one such resonator  400 . 
     The invention lends itself to numerous variants. Thus another variant, illustrated by  FIGS. 21 to 26 , relates to a balance with satellites  31 ,  32 , cooperating with elastic blades  28 : the satellites  31 ,  32  then pivot on shafts  27  carried by the flange or flanges. The elastic blades  28  allow a radial movement of the satellites, and index the angular movement thereof. The spring function for taking up clearance of the crown is adopted by these elastic blades  28 .  FIG. 25  illustrates six mobiles  3  with independent adjustments; other configurations can be envisaged, in particular with four independent mobiles, or other. 
     The variant illustrated includes three pairs of satellites with, in the example, but not limited to, 15 and 17 teeth, which make it possible to adjust the unbalance and the inertia of the balance: in this way the advantage of the ease of adjustment with discrete positions independent of each other of the satellites is kept. The tool in  FIG. 16  can also be used for carrying out the adjustment. Naturally other variants can be imagined, for example a balance with an even number of satellites of each kind, for example eight satellites, including four for adjustment of the unbalance and four for adjusting the inertia, which then makes it possible to clearly decouple the two adjustments. Thus, some mobiles  3  are allocated solely to adjustment of inertia, and the other mobiles  3  are allocated solely to adjustment of the unbalance. It is also possible to imagine mobiles  3  having diameters different from each other, and/or mobiles  3  carried on different portage diameters, and/or mobiles  3  with unbalances that are different from each other, and/or mobiles  3  with hollows  312 ,  322  different from each other, and/or mobiles  3  made from materials with different densities, or other, so as to cover an extensive set of points, in a similar fashion to the cloud of points in  FIG. 32 . 
       FIG. 32  thus illustrates a particular configuration in which at least three mobiles can be indexed independently of one another for a combined adjustment of unbalance and inertia of the inertial mass  100 . By analogy with  FIG. 12 , which is a flat distribution diagram of 255 different inertia values,  FIG. 32  is a three-dimensional diagram showing schematically, in an extremely simplified way, a network of points in space, which can be formed by a very large number of points provided that a corresponding number of satellites are used, such as for example the six mobiles  3  with independent adjustment in  FIG. 25 , with which it is possible to define tens of thousands of points each corresponding to an unbalance value and an inertia value, these points are shown schematically here by crosses in an envelope sphere, in which the density of points is variable according to the position in space (as is also the case in  FIG. 12 ). The unbalance value B is given by the projection of a point M in question on the plane XY, according to the coordinates Xb and Yb, while the value of the inertia I is given by its projection on the axis Z and its coordinate Zi: a point M in the sphere corresponds to a unique position of each of the mobiles  3 . 
     The spring function can also be provided by the satellites  3  themselves, microstructuring techniques making it possible to form elastic radii. 
     The invention also relates to a method for adjusting inertia and/or unbalance of an inertial mass for a horological resonator, according to which:
         an inertia and/or unbalance adjustment assembly  150  for a horological resonator  400  is obtained, according to the invention, said assembly  150  including such an inertial mass for adjusting inertia and/or unbalance  100 , and the associated elements, that is to say firstly a said two-dimensional or three-dimensional diagram, and secondly a said table or file of values;   a measurement of the running of the resonator is made;   the algebraic value of the correction of inertia to be made is determined;   the value closest to this correction of inertia is sought in said table or file;   the new position to be given to each mobile  3  is determined;   each satellite mobile is positioned by rotating the crown and/or said satellite mobile according to the configuration of said inertial mass.       

     More particularly, the new position to be given to each mobile  3  is determined so as to minimise the unbalance resulting from the mobiles  3 . 
     Naturally this method is applicable both to the two-dimensional diagram in  FIG. 12  and to the three-dimensional diagram in  FIG. 32 . 
     All in all, the invention is distinguished in that:
         a crown forming a spring cooperates with satellites, takes up clearances and creates stable and precise positions without creating a dynamic unbalance;   a wide choice of combinations of satellites, with different numbers of teeth, different diameters and different unbalances creates, by a moiré effect, a large number of discrete inertia values of the balance while having a high range/resolution ratio.       

     The invention thus offers numerous advantages:
         possibility of use of strong and precise micromachined components. The absence of thin blades increases the strength thereof;   fine and reproducible adjustment of the inertia of an oscillator inertial mass, and therefore of the running;   high resolution;   possibility of adjustment from inside and/or outside the watch;   large inertia and/or unbalance adjustment range, and absence of dynamic unbalance;   taking up clearances by the slight constraint between the crown and the satellites, and maintenance of the mobiles in several tens or hundreds of stable positions;   exact adjustment on the basis of a table of positions;   precise and easily legible indication of the adjustment of the inertia;   easy manipulation since the unitary travel (one click) is relatively large on a horological scale;   maintenance of the centre of mass on the oscillation axis of the inertial mass if a centrosymmetrical geometry is chosen, with an identical adjustment of the diametrically opposed satellites;   absence of stop in rotation and therefore absence of risk of breaking during adjustment;   in the case where the inertial mass is a balance:   at each position, all the geometry is equivalent, except for the unbalance of the satellites and the fine flexible felloe. This minimises the dynamic unbalances of the balance;   wide countersink at the centre of the balance for housing the balance spring;   conventional mounting of the balance felloe on the balance shaft.       

     All in all, the invention makes it possible to effect a precise adjustment of inertia by virtue of inertia and/or unbalance adjustment mobiles that are synchronised by a single crown. 
     The moiré effect is due to the combination of phase difference of N pairs of adjustment mobiles, and the use of a table for decoding the inertia/running obtained affords security of use making it possible to proceed directly with the adjustment with precision, the algorithm essential to decoding constituting in this regard a precious contribution of the invention. 
     The invention allows adjustment of unbalance of the balance by mobiles with unbalances non-synchronised by a crown, and especially which are independent of the satellite mobiles. And these mobiles with unbalances non-synchronised by a crown can be added to the first system.