Classifications

• • G—PHYSICS
  • G04—HOROLOGY
  • G04B—MECHANICALLY-DRIVEN CLOCKS OR WATCHES; MECHANICAL PARTS OF CLOCKS OR WATCHES IN GENERAL; TIME PIECES USING THE POSITION OF THE SUN, MOON OR STARS
  • G04B17/00—Mechanisms for stabilising frequency
  • G04B17/32—Component parts or constructional details, e.g. collet, stud, virole or piton
  • G04B17/34—Component parts or constructional details, e.g. collet, stud, virole or piton for fastening the hairspring onto the balance
  • G04B17/345—Details of the spiral roll
• • G—PHYSICS
  • G04—HOROLOGY
  • G04B—MECHANICALLY-DRIVEN CLOCKS OR WATCHES; MECHANICAL PARTS OF CLOCKS OR WATCHES IN GENERAL; TIME PIECES USING THE POSITION OF THE SUN, MOON OR STARS
  • G04B1/00—Driving mechanisms
  • G04B1/10—Driving mechanisms with mainspring
  • G04B1/14—Mainsprings; Bridles therefor
• • G—PHYSICS
  • G04—HOROLOGY
  • G04B—MECHANICALLY-DRIVEN CLOCKS OR WATCHES; MECHANICAL PARTS OF CLOCKS OR WATCHES IN GENERAL; TIME PIECES USING THE POSITION OF THE SUN, MOON OR STARS
  • G04B1/00—Driving mechanisms
  • G04B1/10—Driving mechanisms with mainspring
  • G04B1/14—Mainsprings; Bridles therefor
  • G04B1/145—Composition and manufacture of the springs
• • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
  • Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
  • Y10T—TECHNICAL SUBJECTS COVERED BY FORMER US CLASSIFICATION
  • Y10T29/00—Metal working
  • Y10T29/49—Method of mechanical manufacture
  • Y10T29/49579—Watch or clock making

Definitions

• the invention relates to a ferrule.
• the invention also relates to a monolithic spring assembly spiral single or double - not split ferrule, intended to be driven on a balance shaft, including a monolithic assembly including a ferrule according to the invention.
• the invention also relates to a monolithic spiral-ferrule spring assembly comprising at least two stages as well as to a method of manufacturing such an assembly.
• One of the critical points for the use of a spiral spring in a high precision timepiece movement is the reliability of the fasteners (recesses) of the balance spring to the axis of the balance and to the balance bridge.
• the attachment of the hairspring to the axis of the balance is usually made by a ferrule, which was originally a small split cylinder intended to be driven on the balance shaft and drilled laterally to receive the end inside the spiral spring itself.
• micro-manufacturing techniques such as DRIE processes for silicon, quartz and diamond or UV-Liga for Ni and NiP, opens up possibilities for the shapes and geometries used.
• Silicon is a very interesting material for making clockwork spirals, and microfabrication techniques make it possible to produce the ferrule in a monolithic manner and come from manufacture with the spiral.
• a potential problem is that silicon does not have a plastic deformation domain.
• the ferrule can quickly break if the constraints exceed the constraint permissible maximum and / or the elastic limit of the material. It is thus necessary to make sure to dimension the shell both to maintain the spiral spring on the axis of the balance during operation of the oscillator (minimum torque) and also to assemble the ferrule with axes whose diameters have fluctuations and this, without breaking or undergo plastic deformation if the diameter of the axis of the balance remains within a given tolerance range.
• EP 1 826 634 proposes in its figure 4 in connection with the line 34 of column 3, a ferrule comprising elastic zones consisting of curved arms. This document does not indicate where the hairspring should be fixed.
• EP 1 513 029 and EP 2 003 523 propose ferrules having a triangular opening.
• the attachment of the spiral takes place at a point of attachment (reference 3 in the figures of these documents) located at one of the corners of the triangles.
• the ferrule is formed of an external stiffening structure to which are attached flexible arms which deform to accomodate the balance shaft.
• FIG. 10D a hairspring resonator spiral having a ferrule whose opening is circular.
• the beam is fixed in this case using rounded arms.
• the patent application WO2011026275 discloses a spiral-ferrule spring assembly with a ferrule having a bore provided with four bearing parts. circular to receive the balance shaft. The bearing portions are delimited by longitudinal grooves formed in the bore of the ferrule.
• the aim of the invention is to propose new ferrule geometries giving full satisfaction, that is to say making it possible to obtain the highest possible tightening torque on the balance shaft and a stress in the most effective material. low possible.
• these ferrules must be as balanced as possible so as not to cause unbalance, which would degrade the chronometric properties of the spiral.
• the central opening of the ferrule for receiving a balance shaft is non-circular, - the contour of the central opening of the ferrule comprises at least two bearing surfaces for a balance shaft;
• the shell is formed of at least two balance beam receiving parts located opposite, in particular 180 °, one of the other and one of which comprises at least the first of the bearing surfaces for the balance shaft and a point of attachment or embedment of the spiral spring, and the other at least the second of the bearing surfaces for the balance shaft,
• these two balance shaft receiving parts being connected to one another by two connecting parts which have a lower rigidity than those of the receiving parts, so as to be able to deform elastically during the driving of a balance shaft.
• the invention relates to a monolithic spiral spring unit single or double - ferrule, the latter may be split or not.
• This set has the particularity of having at least two levels (or stages or parts), the spiral spring being located on a different level from that where the bearing surfaces of the ferrule for the balance shaft.
• This characteristic is particularly advantageous because it makes it possible to optimally optimize the holding torque of the ferrule on the balance shaft without having to increase its bulk in the plane of the spiral.
• this characteristic makes it possible to bring the point of attachment of the spiral spring closer to the axis of the balance, without being limited by the periphery of the ferrule.
• the invention also relates to a method of manufacturing a spiral spring monolithic assembly slotted ferrule or not, wherein the spiral is made on a different level from that where the support surfaces of the ferrule for the balance shaft.
• a ferrule according to the invention is defined by claim 1.
• a monolithic assembly according to the invention is defined by claim 4.
• a method of manufacturing an assembly is defined by claim 26.
• a method of manufacturing an assembly is defined by claim 27.
• a method of manufacturing a ferrule is defined by claim 28.
• a method of manufacturing a shell is defined by claim 29.
• a monolithic assembly according to the invention is defined by claim 30.
• An oscillator according to the invention is defined by claim 46.
• a watch movement or a timepiece according to the invention is defined by claim 47.
• FIG. 1 a ferrule according to the prior art, EP 1 513 029 and EP 2 003 523;
• FIG. 2 a ferrule of FIG. 10D of the prior art EP 1 655 642;
• FIG. 3 a ferrule according to the prior art WO2011026725;
• FIG. 4 a monolithic assembly with a double-spiral spring - closed-contour ferrule according to the invention
• FIGS. 5 to 7 other monolithic assemblies spiral spring double-shell closed contour according to the invention.
• Figure 8 the main steps of the process for obtaining a monolithic coil spring double-ferrule assembly according to a second aspect of the invention
• Figures 9 to 11 a monolithic spring coil double-ferrule assembly according to a second aspect of the invention.
• Figures 12 and 13 other monolithic assemblies spiral spring double - ferrule according to the second aspect of the invention.
• FIG. 14 a graph showing the evolution of the holding torque M of the shells of the sets of FIGS. 12, 13 and 3 as a function of the diameter of the balance shaft;
• FIG. 15 is a graph showing the evolution of the stress of the ferrules of the assemblies of FIGS. 12, 13 and 3 as a function of the diameter of the balance shaft;
• FIGS. 16 to 17 a representation of the stresses within the ferrules of the sets Figures 12 and 13 once a balance shaft driven into the opening (black: very weak elastic deformation, stresses less than half of the maximum stress, in gray: significant elastic deformation, stresses greater than half of the maximum stress );
• FIG. 18 a representation of the rigid (black) and flexible (gray) zones for the ferrule of FIG. 12;
• Figure 19 a monolithic coil spring double-ferrule assembly according to an advantageous variant of the second aspect of the invention, wherein the attachment points of the blades of the double spiral are close to the central opening;
• Figure 20 a sectional view of a ferrule according to an advantageous variant of the second aspect of the invention.
• Figure 21 a monolithic coil spring double-ferrule assembly according to the first aspect of the invention with indication of the position of the embedding points;
• Figure 22 a monolithic coil spring double-ferrule assembly according to the second aspect of the invention with indication of the position of the embedding points.
• FIG. 1 shows the ferrule proposed in the above-mentioned European patent applications EP 1 513 029 and In Figure 2 is shown the ferrule described in Figure 10D of the aforementioned European patent application EP 1 655 642.
• the invention applies to both sets with a single hairspring and those with a double hairspring. However, it is the latter that is best suited.
• double spiral is meant here a spiral comprising two blades wound in the same direction, but with a 180 degree offset, as described in EP 2 151 722 Al.
• the respective inner ends of these blades are integral with the ferrule and their respective attachment points are arranged symmetrically on opposite sides of the periphery of the ferrule.
• the "point of attachment” or “embedding point” of the hairspring is generally well defined in the case of a hairspring assembled on a ferrule made of a material other than the hairspring.
• the point of Recessing can be defined as the point where the local stiffness along the neutral fiber reaches a value that is 10x higher than the stiffness of the spiral blade. In the case of a spiral with variable blade thickness, the minimum value of the local stiffness along the blade will be considered.
• the local stiffness is equivalent to the bending rigidity, determined during the bending of the blade or the operation of the hairspring, over a portion of a given length, for example lpm.
• the embedding points 10,11 Corresponding examples are given as an example on the ferrule-spiral assemblies of FIGS. 21 and 22. In the case of FIG. 21 (which corresponds to the ferrule geometry of FIG. 12), it can be seen that the embedding point is located on the extension of the outer contour or periphery 32 of the ferrule. In the case of FIG. 22 (which corresponds to the ferrule geometry of FIG. 19), it can be seen that the embedding point is located in the immediate vicinity of the balance shaft, closer to the central opening of the beam. ferrule than is the contour 33 of the level of the ferrule which does not include the spiral.
• the ferrules according to the invention are dimensioned both to maintain the balance spring on the balance axis during operation of the oscillator, and also to be assembled with axes whose diameter shows a certain dispersion (no breakage or plastic deformation when driving for a shaft diameter within a given tolerance range).
• These shells normally have at least 2, and preferably 4, bearing surfaces for the balance shaft.
• the precise shape of the connecting parts is not crucial, as long as they manage to deform elastically, especially in bending, when driving a balance shaft.
• the receiving parts are therefore rigid or indeformable parts and the connecting parts, deformable parts, in particular deformable in bending or flexible.
• the flexibility of the latter comes from the fact that they are thinned compared to the receiving parts.
• the deformable parts have sections of smaller areas than the non-deformable parts. This thinning is performed, according to the invention, by providing the deformable parts narrower than the receiving portions.
• width is meant here the thickness measured in the plane of the ferrule, in other words, the distance between the outline of the ferrule and the contour of its central opening (for example, the minimum width e or e 'or the width at mid-distance of the rigid receiving portions b or b' in Figures 12 and 13).
• junctions between the receiving portions and the connecting portions are generally substantially at the base of a bearing surface (see below, and by way of example, Fig. 18, or Fig. 5 where they can be located each time on one side of the curved portion 14).
• a bearing surface see below, and by way of example, Fig. 18, or Fig. 5 where they can be located each time on one side of the curved portion 14.
• FIG. 4 represents the central part of an example of a monolithic assembly with a spiral spring which is not split according to the invention.
• the shell 1, in particular the receiving portions 17, 18, has two pairs of bearing points 2, 3 and 4, located on substantially planar arms 6, 7 and 8. , 9 which are not elastic and are placed in pairs near the attachment points 10,11 of the blades 12,13 of the double spiral.
• the non-elastic arms of the same pair protrude into the central opening of the ferrule and form between them an angle ⁇ which is preferably less than 170 degrees, more preferably greater than 90 degrees and less than 170 degrees, and is here about 120 degrees.
• Each arm 6,7,8 or 9 has a free end.
• the V-shape of the pairs of rigid arms has the effect of better wedge the axis of pendulum than would a single fulcrum.
• the ferrule-axis embedding is as rigid as possible, so that the points of contact between the ferrule and the axis of the balance do not move under the effect of the torque developed by the spiral during operation in motion, that is to say during the oscillations of the sprung balance once the spiral spring assembly - ferrule chased or assembled on the axis of a pendulum.
• the geometry with two receiving parts facing each other (in particular at 180 ° from each other) and each comprising a pair of bearing surfaces makes it possible to act as a vise held by the parts flexible connection. Under the effect of their elastic deformation, the connecting parts exert elastic return actions reminding the receiving portions towards each other and each in contact against the balance shaft.
• a single fulcrum such as a plane, convex or concave contact surface with a radius of curvature greater than the radius that is provided for the axis. of the pendulum.
• the arms 6, 7, 8 and 9 and the corresponding bearing surfaces 2, 3, 4 and 5 are planar, that is to say that their radius of curvature on the side of the central opening 26 is infinite.
• the bearing surfaces may also be convex, that is to say that their radius of curvature may be negative on the side of the central opening 26, or concave, that is to say that their radius of curvature may be positive on the side of the central opening 26.
• the positive radius of curvature is strictly greater than 0.51 times the diameter d max of the largest circle that can be drawn inside the contour of the central opening (when the shell is not deformed, especially when it is not mounted on the balance shaft) circle which is also called “registered circle” in the rest of the description.
• the positive radius of curvature is greater than 0.62 times the diameter of maXf which allows to define a single point of contact between the bearing portion and the balance shaft.
• a radius of curvature greater than 0.75 times, or even 1 times, the diameter d max of the inscribed circle is also adapted.
• the diameter of the axis is slightly greater than d max , for example within a tolerance range between 1.01 and 1.02 d max .
• the shell 1 has a symmetry of rotation of order 2, and has two axes of symmetry in reflection, one being formed by the bisector of the angle a, the other being perpendicular to the latter and located equidistant from the intersection of the arms. It can be considered that it comprises two rigid balance shaft receiving parts connected by two flexible connecting parts, as can be seen in Figure 18 which will be detailed below.
• the rigid parts 17 and 18 are those from which both the arms 6.7 and 8.9 and the blades 12 and 13 of the double spiral start.
• the flexible portions 15 and 16 are linking portions connecting symmetrically the rigid parts, so as to form the shell 1 with its central opening.
• the symmetry of the geometry of the ferrule of FIG. 4 is aimed at obtaining a balance so as not to create an imbalance.
• the central non-circular opening of the ferrule may be defined as comprising a central recess 26 for receiving the balance shaft, substantially delimited by the bearing surfaces 2,3,4 and 5, and two peripheral recesses 27,28 formed substantially and symmetrically between the arms 6,8, on the one hand and 7,9 on the other hand, and the elastic portions 15 and 16.
• the recesses 27 and 28 are symmetrical to each other with respect to the angle bisector a.
• the geometry makes it possible to precisely define the bearing points, of which there are four in the case of FIG. 4.
• the arms 6 to 9 make it possible to precisely define the points of support of the shell on the balance shaft. while maximizing the length of the flexible elastic portions. By cons, these arms 6 to 9 do not bend or negligibly and can not be considered as elastic arms.
• FIGS. 16 and 17 This is confirmed by numerical simulations reported in FIGS. 16 and 17, which indicate the levels of stresses present following the driving of a balance shaft with a nominal diameter of 0.503 mm in two ferrules of different geometry represented in FIGS. 12 and 13 (reference can also be made to FIGS. 14 and 15 which show the holding torques and the maximum stresses for these ferrules for different axle diameters).
• the parts which are not or slightly elastically deformed, and which can be considered to be rigid, are indicated in black in FIGS. 16 and 17 (stress level less than half of the maximum stress attained as a result of driving the axis about 500 MPa in the case of Figures 16 and 17).
• the ferrule is thus formed of two rigid balance shaft receiving parts 17, 18 symbolized in black in FIG. 18, connected to one another by two flexible or elastic connection parts 15, 16, symbolized in gray. in Figure 18.
• the advantage of this arrangement is to maximize the length of the flexible connection parts, while ensuring a sufficient holding torque on the balance shaft, with a stress level significantly lower than the maximum allowable stress for the material.
• the simulations show that the ferrule according to the invention makes it possible to obtain a holding torque (M) on the higher axis than with flexible arms located inside a closed contour (for the same size).
• M holding torque
• the flexible portions occupy about 70% of the total length of the contour.
• the flexible portions occupy 50% or more of the total length of the contour, in particular between 50% and 90%, more preferably between 60 and 80%.
• the angle sectors measured from the center of the shell (which corresponds to the center of the circle inscribed in the central opening) and occupied respectively by a rigid receiving portion and a flexible connecting portion are 54 ° and 126 ° ° approx.
• the angle sector measured from the center of the shell and occupied by a flexible connection portion is greater than or equal to 50 °, in particular between 90 ° and 160 °, more preferably between 110 ° and 145 °.
• This angle sector is for example defined as the smallest sector of continuous angle between two receiving parts where there is an area where the stress in the material is greater than 50% of the maximum stress reached following the driving of the axis.
• the ferrule comprises only one pair of non-elastic arms 2,3.
• a curved portion 14 intended to serve as a third bearing surface for the balance shaft.
• the geometry contains only a symmetry of reflection around the bisector of the angle a (if you do not take into account the attachment point of the spiral blades).
• the shape and dimensions of the convex portion 14 are chosen so as to balance the ferrule as much as possible.
• the third bearing surface may also be flat or concave, with a radius of curvature strictly greater than 0.51 times, preferably greater than 0, 62, 0, 75 or 1 times the inscribed diameter d max .
• the ferrule according to the invention is particularly suitable for fixing a double spiral to a balance shaft. Indeed, most of the ferrules known from the state of the art do not deform symmetrically with respect to the attachment points. With a ferrule such as that shown in Figure 1, one of the blades would be fixed at the same point as the blade of the simple spiral shown, or at the top of the triangle formed by the rigidifying structure. The second blade must have a point of attachment located 180 ° from the first, the opposite, in the middle of one side of the triangle. The displacement of the attachment points following the chase relative to the center of the hairspring and / or the external fasteners would therefore not be equivalent for the two attachment points, which would degrade chronometric performance. In addition, the embedding point of the second blade could be deformed during the expansion and contraction of the hairspring, which would also adversely affect the chronometric performance.
• the invention in another aspect, relates to a ferrule having at least two levels or stages or parts.
• the point of attachment or anchoring of the hairspring (or the points of attachment in the case of a double hairspring) is then located on a different level than the one where the major is located. part or all of the bearing surfaces. This is in particular applied to a monolithic spiral-ferrule spring assembly.
• the inventors have in fact discovered that it is possible to maximize the torque resistance of the ferrule, while minimizing its bulk, by lengthening the ferrule in the plane perpendicular to the spiral. This makes it possible to dissociate the attachment function of the hairspring to the axis via the ferrule (first level, in the plane of the hairspring) of that of resistance to the axis, in particular of holding the ferrule on the axis (first and second level, and preferably exclusively on the second level, out of the plane of the hairspring), while distributing the elastic stress as evenly as possible along the flexible portions.
• a monolithic spiral-ferrule spring assembly corresponding to that of FIG. 4 made on 2 levels is represented in front and rear perspectives in FIGS. 9 and 10.
• flanks are not perfectly superimposed, they have a shift of a few microns between the first and the second layer.
• FIG. 11 shows the totality of the spring-spiral assembly according to FIGS. 9 and 10, with the outer ends of the double-spiral blades which are integral with a fastening element intended to be connected to the movement of a piece of watchmaking.
• the ferrule or the spiral-ferrule assembly can be manufactured according to known methods, such as that which is the subject of the patent application No. EP 1 655 642.
• the ferrule or the spiral-ferrule spring assembly according to the second aspect of the invention can be manufactured according to known methods, such as those which are the subject of the patent applications No. EP 1 835 339 or EP 2 104 007.
• the starting substrate used is a wafer ("wafer” in English) of the "SOI"("Silicon-on-Insulator") type, composed of two parts of monocrystalline Si separated by a thin layer of silicon oxide, SiC> 2 (FIG. 8a, with monocrystalline Si in white and SiC> 2 in oblique hatch).
• the wafer is oxidized to form a surface SiC> 2 layer on either side of the substrate (FIG. 8b) which will serve as a mask for deep-reactive ion etching ("Deep Reactive Ion Etching"). "DRIE” in English).
• a photolithography is then performed on a first face to define a first photoresist pattern (FIG.
• the shell has at least two levels, and the point of attachment or embedment of the hairspring (or the points of attachment in the case a double spiral) is located on a different level from that where the bearing surfaces are and at a distance from the center of the ferrule less than the distance between the center of the ferrule and its contour or periphery.
• the ferrule 100 comprises a bore 101 intended to receive the balance shaft, as well as at least a first portion 102 and a second portion 103. The first and second portions are separated by a plane 104 perpendicular to the axis 107 of the bore, this axis also representing the center of the ferrule.
• the element (s) 105 for attaching the shell to a spiral spring are exclusively located on the first part.
• the element 106 connecting the ferrule to the balance shaft, for example formed bearing surfaces, is essentially, preferably exclusively, located on the second part.
• a connecting element of the ferrule to the axis of balance is essentially located on the second part, it is meant that more than half of the connection forces of the ferrule to the axis of balance are applied at the level of second part.
• the bore 101 forms a central opening for receiving the balance shaft.
• an SOI wafer is used to make such a ferrule or a monolithic ferrule-spiral assembly including such a ferrule, the first and the second portion being in silicon and separated by a silicon oxide layer.
• SOI wafers where the inner layer of S1O 2 separating the two layers of Si is thick or very thick (for example 2-3 microns as usual, but preferably greater than 5 or even 10 microns) makes it possible to produce a flexible ferrule superimposing the turns as shown in FIG. 19, which shows such a monolithic spiral double - ferrule assembly made on 2 levels.
• the flexible ferrule is in all respects similar to that of Figure 4.
• the attachment points of the spiral are not located on the contour as in Figure 21, but the most possible near the central opening of the shell and therefore of the balance shaft, as in the example of Figure 22.
• the blades of the spiral are thus partially superimposed on the shell, on a little less than 180 ° in the example of Figure 19 (corresponding to a little less than half a winding turn of the spiral blade).
• the two-level manufacturing process makes it possible to produce this kind of structure, since the dissolution attack of Si0 2 (FIG. 8) will also attack the oxide which solidifies the blades with the ferrule if the attack time is sufficient. , thus freeing these.
• the fastening element of the spiral to the ferrule or the embedding point 10, 11 is at a distance D1 from the axis of the bore 107 less than half the diameter D2 of a cylinder in which the second part, especially at a distance Dl less than or equal to the average of half the diameter D2 and half the diameter of the inscribed circle dmax.
• D1 is 0.330 mm
• D2 is 1.180 mm
• the embedding point is closer of the central opening that is the contour 33 of the ferrule.
• a ferrule as described above may in particular be included in a monolithic spiral-ferrule spring assembly.
• this type of approach is not limited to a double spiral, but is also perfectly suited to a simple hairspring, and is not limited to a closed-sided ferrule, but is also suitable for a split ferrule. Any combination of ferrule and spiral can be obtained in this way, with the effect of a spiral - ferrule spring assembly with significantly improved chronometric properties. simulations
• the spiral layer height (first part) is 150 microns and the layer height of the level bearing the bearing surfaces (second part) is 500 microns.
• the balance shafts have a tolerated diameter of between 0.5 and 0.506 mm, with a nominal value of 0.503 mm.
• the graph of FIG. 14 shows the evolution of the simulated holding torque M of the ferrule as a function of the diameter of the balance shaft for each of the spiral / ferrule assemblies of FIGS. 12, 13 and 3, respectively.
• the minimum holding torque is indicated in FIG. 14 by the broken line.
• the holding torque is greater than the minimum torque required, even for small diameters below the minimum tolerance.
• the graph of FIG. 15 shows the evolution of the stress s of the ferrule as a function of the diameter of the balance shaft for each of the spiral / ferrule assemblies of FIGS. 12, 13 and 3, respectively.
• the maximum allowable stress for the material is indicated by the broken line.
• the advantage of the ferrule of FIG. 13 is that it is more flexible, that its stress level is lower and that the slope of the torque as a function of the diameter of the axis is smaller than for the ferrule of FIG. 12. As a corollary, the holding torque is lower.
• the stress very quickly exceeds the maximum value allowed.
• this type of ferrule is not suitable for assembly by driving. Indeed, such a geometry of the contour does not ensure both good performance and deformation without breakage of the ferrule following the driving of the balance shaft.
• the inscribed diameter is only 0.2 micron smaller than the lower limit of the tolerance so that the stresses are less than the maximum allowable stress for the lower limit of the tolerance, which requires extremely precise manufacturing tolerances.
• This example illustrates the advantage of a closed contour ferrule, with rigid receiving portions connected by flexible connecting portions.
• This difference in rigidity can be estimated in first approximation by the theory of beams with small deformations: for a beam, the rigidity k of an element of width e, thickness h and length L is proportional to e 3 xh / L 3 .
• a ratio k r / k f greater than 10 is chosen, more preferably greater than 50, even more preferably greater than 100.
• the width difference between the rigid receiving portions and the flexible connecting portions is preferable to obtain lower rigidity on the connecting portions than on the receiving portions.
• the average width of the connecting portions may be preferably less than the average width of the receiving portions, more preferably less than a factor of two to the average width of the receiving portions.
• the two connecting portions have a minimum width and / or a width halfway between the receiving portions less than the maximum width of the receiving portions.
• the minimum width e of the connecting portions is then preferably less than 0.5 ⁇ , more preferably equal to or less than 0.3 ⁇ a, where a is the maximum width of the receiving portions.
• the width in the middle of the connecting portions, halfway between the receiving portions is preferably less than 0.7xa, even more preferably equal to or less than 0.5xa.
• the thickness of the receiving parts and the connecting parts in particular by thinning the connecting parts relative to the receiving parts, but it is more favorable to vary the width than the thickness to vary the rigidity.
• those skilled in the art will be able to adapt the dimensions of the casing of cases in case, according to the thickness of the hairspring, the space available, taking care to ensure a sufficient resistance to torque and to maintain the constraints well from here. the maximum allowable stress in order to remain in the elastic deformation range.
• the height is determined by the dimensions of the spiral, among other things by the necessary torque and the size (diameter).
• the height of the shell, and therefore arms carrying the bearing surfaces and flexible parts, will necessarily be fixed by the height of the spiral and can not be adjusted freely.
• the holding torque values are lower by a ratio of 500/150 compared to a multilayer assembly provided with a spiral of the same height (150 microns), since the maintenance of performs on 150 microns instead of 500 microns. As a result, these holding torque values would be less than the minimum value (line interrupted in Fig. 14) required for axis diameters close to the minimum tolerance (0.5 micron).
• the supporting parts also carried by the level comprising the hairspring, which would make it possible, in the example mentioned above, to increase the holding torque values to a ratio of 650: 150 with respect to a together at one level.
• the tolerances of the manufacturing process make the production of continuous surfaces on two levels very delicate. It is therefore preferable to separate the fastening functions of the hairspring and connecting the ferrule to the balance shaft on two distinct levels, and not to provide support portions on the level which has the element (s) for attaching the ferrule to the spiral spring.
• a way to increase the holding torque of a ferrule to a single layer or stage is to increase the torque developed by the flexible parts without increasing the stress, which implies a larger diameter of the ferrule. This has the consequence that the point of attachment of the blades of the spiral must be remote from the balance shaft, which degrades the chronometric properties.
• a monolithic spiral / ferrule assembly at least two levels, for example two silicon stages separated by a silicon oxide layer, offers the possibility of maximizing the holding torque by optimizing its bulk. , that is to say by avoiding increasing the diameter of the ferrule.
• a ferrule in which the second portion 103 extends, along the axis of the bore 107, over a length greater than once the thickness E of the spiral spring, or even greater than 3 times the thickness E of the spiral spring, is therefore particularly suitable, in particular to form a monolithic spiral-ferrule assembly.
• Figures 6 and 7 show variants of the monolithic spiral / ferrule assembly according to the invention.
• the monolithic spiral / ferrule assembly with two stages of FIG. 7 comprises flexible parts which are not symmetrical.
• the heat compensation of the spiral of the spiral spring assembly single or double - ferrule is carried out by known means.
• a layer of material may be used on the surface of the turns which compensates for the first thermal coefficient of the Young's modulus of the base material.
• a suitable material for the layer is Si0 2 .
• each connecting portion is mainly biased in bending, once the monolithic assembly mounted on the balance shaft.
• mainly flexural biased it is meant that, in each connecting portion, it is possible to identify a neutral fiber oriented substantially in a direction along which the connecting portion extends and separating an area stressed in tension from an area solicited in compression.
• each connecting portion has a portion remote from the balance axis of at least 0.5 times the radius of the balance axis, or even at least 0.9 times the radius of the balance shaft, once the assembly mounted on the balance shaft.
• the receiving portions and the connecting portions form an element capable of continuously surrounding the balance axis, that is to say capable of seamlessly surrounding the axis axis balance. They thus form a closed ferrule, as opposed to a split ferrule.
• Rigid part means a part not deforming or not substantially during operation or during mounting the monolithic assembly on the balance shaft or a part whose deformation is not sought and / or does not perform any function during operation or during assembly of the monolithic assembly.
• the term "deformable part” means a part deforming elastically during operation or during assembly of the monolithic assembly on the balance shaft or a part whose elastic deformation is sought or performs a function during the operation or when mounting the monolithic assembly.
• the monolithic spiral-ferrule spring assembly comprises:

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