EP2613206A1 - Hairspring with two spiral springs with improved isochronism - Google Patents

Abstract

The spring (1) has hairsprings (3, 5) comprising curves extending in planes, where each curve has continuously variable pitch. The curves are symmetrical relative to a straight line (A) parallel to the planes, and pass through a median projection plane (P) of an attachment element (4). Each curve is arranged such that specific relation is zero to reduce displacements of center of mass during contraction and expansion. Each hairspring has H-shaped counterweights (8, 8', 9, 9') to compensate for unbalance formed by a mass of the element and personalize anisochronism slope of the balance spring. The specific relation includes a moment of the balance spring of order n, length of the balance spring and curvilinear abscissa along the balance spring to the power of n and parameterization of the balance spring by the abscissa. The balance spring is formed from silicon and includes a part coated with silicon dioxide.

Description

Field of the invention

The invention relates to a hairspring used to form a pendulum - balance resonator whose curvature allows a substantially immobile center of mass development.

Background of the invention

The documents EP 2 184 652 , EP 2 196 867 and EP 2,105,807 explain how to manufacture curved spirals in micro-machinable materials respectively with three parts, two parts or integrally. These documents are incorporated by reference into the present description.

It is known to apply the Phillips criteria to determine the theoretical curvature of a terminal curve. However, the Phillips criteria are in fact an approximation that does not necessarily give satisfaction if an even smaller gap is desired.

Summary of the invention

The object of the present invention is to overcome all or part of the disadvantages mentioned above by proposing a hairspring respecting predetermined conditions capable of reducing the displacement of the center of mass of the hairspring in contraction and expansion.

où :

• P ⁽ⁿ⁾ est le moment du spiral d'ordre n ;
• L est la longueur du spiral ;
• sⁿ représente l'abscisse curviligne le long du spiral à la puissance d'ordre n ;
• x (s) est la paramétrisation du spiral par son abscisse curviligne.

afin de réduire les déplacements de son centre de masse lors de ses contraction et expansion et en ce que chaque ressort-spiral comporte en outre au moins deux contrepoids afin de compenser le balourd formé par la masse de l'attache et personnaliser la pente d'anisochronisme du spiral.To this end, the invention relates to a spiral comprising a first spiral spring whose curve extends in a first plane and whose inner turn comprises a ferrule, a second spiral spring whose curve extends in a second plane parallel to the foreground, a fastening solidarisant the outer turn of the first spiral spring to the outer turn of the second spiral spring for forming a double spiral in series characterized in that the curve of the first spiral spring and the curve of the second spiral spring each comprise a continuously variable pitch and are symmetrical with respect to a straight line parallel to the first and second planes and passing through the median projection plane of the clip, each curve tending to make the following relationship substantially nil: $${\overrightarrow{P}}^{\left(\mathrm{not}\right)}=\frac{\mathrm{not}+1}{{\mathrm{The}}^{\mathrm{not}+1}}\underset{0}{\overset{\mathrm{The}}{\int }}\mathit{ds}\cdot s^{\mathrm{not}}\cdot \overrightarrow{x}\left(s\right)$$

or :

• P ^{( n )} is the moment of the spiral of order n;
• L is the length of the spiral;
• s ⁿ represents the curvilinear abscissa along the spiral at the power of order n ;
• x ( s ) is the parameterization of the spiral by its curvilinear abscissa.

in order to reduce the movements of its center of mass during its contraction and expansion and in that each spiral spring further comprises at least two counterweights in order to compensate for the unbalance formed by the mass of the fastener and to customize the slope of the anisochronism of the spiral.

• lesdits au moins deux contrepoids sont symétriques selon ladite même droite que les courbures ;
• deux contrepoids sont situés à côté de l'attache et deux autres contrepoids sont situés du côté opposé à l'attache afin de minimiser le balourd ;
• chaque contrepoids est sensiblement en forme de H, les bras parallèles du H étant sensiblement parallèles à la courbure locale du ressort-spiral auquel il est associé ;
• les raideurs et/ou les masses apportées localement par lesdits contrepoids et ladite attache sont utilisées pour modifier la pente d'anisochronisme du spiral ;
• les faces principales de l'attache sont sensiblement parallèles à ladite droite de symétrie ;
• la spire interne du deuxième ressort-spiral comporte un dispositif de décalage agencé pour s'attacher à un piton dans le plan du deuxième ressort-spiral ;
• le dispositif de décalage comporte une pièce en prolongement de la spire interne du deuxième ressort-spiral, ladite pièce étant plus rigide que ledit deuxième ressort-spiral afin de ne pas fournir de couple élastique ;
• la pièce en prolongement est reliée à la spire interne à l'aide d'un coude sensiblement en forme de U ;
• la pièce en prolongement est venue de matière avec le deuxième ressort-spiral ;
• la pièce en prolongement est rendue plus rigide par une épaisseur au moins trois fois supérieure par rapport à celle dudit deuxième ressort-spiral ;
• la pièce peut être partiellement ajourée pour diminuer sa masse ;
• la spire interne du premier ressort-spiral comporte un dispositif d'agrandissement de la virole dans le plan du premier ressort-spiral ;
• le dispositif d'agrandissement comporte un bourrelet prolongeant la spire interne du premier ressort-spiral, ledit bourrelet étant plus rigide que ledit premier ressort-spiral afin de ne pas fournir de couple élastique ;
• le bourrelet est sensiblement en forme de U ;
• le bourrelet est venu de matière avec le premier ressort-spiral ;
• le spiral est formé à partir de silicium ;
• le spiral comporte au moins une partie recouverte de dioxyde de silicium afin de limiter sa sensibilité aux variations de température et aux chocs mécaniques.

According to other advantageous features of the invention:

• said at least two counterweights are symmetrical along the same straight line as the curvatures;
• two counterweights are located next to the clip and two other counterweights are located on the opposite side of the clip to minimize unbalance;
• each counterweight is substantially H-shaped, the parallel arms of the H being substantially parallel to the local curvature of the spiral spring with which it is associated;
• the stiffness and / or masses brought locally by said counterweights and said fastener are used to modify the anisochronism slope of the spiral;
• the main faces of the fastener are substantially parallel to said line of symmetry;
• the inner coil of the second spiral spring comprises a shifter arranged to attach to a stud in the plane of the second spiral spring;
• the shifter comprises a piece extending from the inner turn of the second hairspring, said piece being more rigid than said second hairspring so as not to provide an elastic torque;
• the extension piece is connected to the inner coil with a substantially U-shaped bend;
• the piece in extension came from matter with the second spiral spring;
• the extension piece is made more rigid by a thickness at least three times greater than that of said second spiral spring;
• the piece can be partially perforated to reduce its mass;
• the inner coil of the first spiral spring comprises a device for enlarging the ferrule in the plane of the first spiral spring;
• the enlarging device comprises a bead extending the inner coil of the first spiral spring, said bead being more rigid than said first spiral spring so as not to provide elastic torque;
• the bead is substantially U-shaped;
• the bead came from material with the first spiral spring;
• the spiral is formed from silicon;
• the spiral comprises at least one portion coated with silicon dioxide in order to limit its sensitivity to temperature variations and mechanical shocks.

Therefore, advantageously according to the invention, a hairspring can be manufactured respecting predetermined conditions in order to reduce the displacement of the center of mass of the hairspring in contraction and expansion. This slight or negligible displacement advantageously makes it possible to reduce the belly of the anisochronism curves to a value that is substantially equal to or less than 0.5 sj ^-1 . In addition, advantageously according to the invention, the spiral anisochronism slope can be customized to compensate for that given by the exhaust delay.

In addition, the invention relates to a resonator for a timepiece comprising a balance characterized in that the rocker cooperates with a hairspring according to one of the previous variants.

Brief description of the drawings

• les figures 1 et 2 sont des schémas destinés à expliquer les raisonnements suivis ;
• les figures 3 à 5 sont des exemples de calcul de courbures à 2,3 spires respectant respectivement les équations des moments jusqu'à l'ordre 2, 3 et 4 ;
• les figures 6 à 8 sont des exemples de calcul de courbures à 5,3 spires respectant respectivement les équations des moments jusqu'à l'ordre 2, 3 et 4 ;
• les figures 9 et 10 sont des représentations en perspective d'un spiral selon l'invention ;
• la figure 11 est une représentation vue de dessus du spiral des figures 9 et 10.

Other particularities and advantages will emerge clearly from the description which is given hereinafter, by way of indication and in no way limiting, with reference to the appended drawings, in which:

• the Figures 1 and 2 are diagrams intended to explain the reasoning followed;
• the Figures 3 to 5 are examples of calculation of curves with 2.3 turns corresponding respectively to the equations of moments up to order 2, 3 and 4;
• the Figures 6 to 8 are examples of computation of curves with 5.3 turns corresponding respectively to the equations of the moments up to the order 2, 3 and 4;
• the Figures 9 and 10 are perspective representations of a hairspring according to the invention;
• the figure 11 is a top view of the spiral of Figures 9 and 10 .

Detailed Description of the Preferred Embodiments

The variations of a mechanical watch relative to its theoretical frequency are mainly due to the exhaust and the balance resonator - spiral. There are two types of step variations depending on whether they are caused by the oscillation amplitude of the balance or by the position of the watch movement. This is why, for anisochronism tests, a watch movement is tested in six positions, 2 horizontal (dial up and down) and 4 vertical (stem rotated 90 ° from a position towards the top). From the six distinct curves obtained, we determine the maximum distance between them, also called "belly", expressing the maximum movement variation of the movement in seconds per day (sj ^-1 ).

The escapement induces a variation in operation as a function of the amplitude of the pendulum which is difficult to adjust. Therefore, the hairspring is generally adapted so that its variation as a function of the same amplitude is substantially opposite that of the exhaust. In addition, the spiral is adapted so that its variation is minimal between the four vertical positions.

The necessary adaptations of the spirals have been tried mathematically to determine by calculation the ideal curvatures. Geometric conditions have been stated in particular by MM. Phillips and Grossmann in order to build a satisfactory hairspring, that is to say whose center of mass of the hairspring stays on the axis of the balance. However, the current conditions are rough approximations. In fact, as very small displacements of the center of mass can generate great variations of step, the variations of step obtained according to the current geometric conditions are often disappointing.

This is why, advantageously according to the invention, new conditions are presented below in order to obtain better results of variation of step than by current geometrical conditions, in particular those enacted by MM. Phillips and Grossmann.

où :

• L est la longueur du spiral ;
• sⁿ représente l'abscisse curviligne le long du spiral à la puissance d'ordre n ;
• x (s) est la paramétrisation du spiral par son abscisse curviligne.

We define a "moment of the spiral of order n", P ^{( n )} , by the following formula: $${\overrightarrow{P}}^{\left(\mathrm{not}\right)}=\frac{\mathrm{not}+1}{{\mathrm{The}}^{\mathrm{not}+1}}\underset{0}{\overset{\mathrm{The}}{\int }}\mathit{ds}\cdot s^{\mathrm{not}}\cdot \overrightarrow{x}\left(s\right)$$

or :

• L is the length of the spiral;
• s ⁿ represents the curvilinear abscissa along the spiral at the power of order n ;
• x ( s ) is the parameterization of the spiral by its curvilinear abscissa.

Thus, in order to obtain an immobile center of mass, it is necessary, for each order n , that the moment of the spiral P ^{( n )} zero. All orders can not be calculated since there is an infinite number. Thus, the greater the number of orders whose zero relation (1) is respected, the more the amount of displacement of the center of mass will be reduced.

In the example shown in figure 1 , eight orders of moment of the spiral are represented by points which allow, by a parametrization using a polynomial comprising at least as many coefficients as orders (in our case at least eight), to define a theoretical curvature "Ideal".

In order to apply these conditions of the moment of the null spiral, we start from a spiral of the type of Figures 9 to 11 , that is to say, a hairspring 1 comprising a first hairspring 3 whose curve extends in a first plane, a second hairspring 5 whose curve extends in a second plane parallel to the foreground . Each end of spiral spring 3, 5 is preferably secured by a fastener 4 to form a double spiral series.

As explained above, the manufacture of such a hairspring is possible by the methods explained in the documents EP 2 184 652 , EP 2 196 867 and EP 2,105,807 from micro-machinable materials such as silicon respectively using three parts, two parts or in one piece. Of course, such a hairspring can be made from other processes and / or other materials.

In order to simplify the calculations, the curve of the first spiral spring 3 and the curve of the second spiral spring 5 preferably comprise, each step, a continuously variable pitch and are symmetrical with respect to a line A parallel to the first and second passing planes. by the center of the median plane P of projection of the fastener 4 and the center of the axis of the balance.

$$P_y^{\left(1\right)}=2P_y^{\left(0\right)}$$

$$P_x^{\left(2\right)}=3P_x^{\left(1\right)}$$

$$P_y^{\left(y\right)}=4P_y^{\left(2\right)}-8P_y^{\left(0\right)}$$

$$P_x^{\left(4\right)}=5P_x^{\left(3\right)}-20P_x^{\left(1\right)}$$

$$P_y^{\left(5\right)}=6P_y^{\left(4\right)}-40P_y^{\left(2\right)}+96P_y^{\left(0\right)}$$

$$P_x^{\left(6\right)}=7P_x^{\left(5\right)}-70P_x^{\left(3\right)}+336P_x^{\left(1\right)}$$

Therefore, by way of example, for each spiral spring 3, 5, the first seven orders must respect the following relationships: $$P_x^{\left(0\right)}=0$$

$$P_{\mathrm{there}}^{\left(1\right)}=2P_{\mathrm{there}}^{\left(0\right)}$$

$$P_x^{\left(2\right)}=3P_x^{\left(1\right)}$$

$$P_{\mathrm{there}}^{\left(\mathrm{there}\right)}=4P_{\mathrm{there}}^{\left(2\right)}-8P_{\mathrm{there}}^{\left(0\right)}$$

$$P_x^{\left(4\right)}=5P_x^{\left(3\right)}-20P_x^{\left(1\right)}$$

$$P_{\mathrm{there}}^{\left(5\right)}=6P_{\mathrm{there}}^{\left(4\right)}-40P_{\mathrm{there}}^{\left(2\right)}+96P_{\mathrm{there}}^{\left(0\right)}$$

$$P_x^{\left(6\right)}=7P_x^{\left(5\right)}-70P_x^{\left(3\right)}+336{\mathrm{<figure-callout\; id="1"\; label="P\; x"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">P\; </figure-callout>}}_x^{}$$

As explained above, the more the number of relations (2) - (8) are respected, the more the displacement of the center of mass of the spiral 1 will be limited. By way of comparison, the Phillips conditions approach the relation (2), that is to say a first-order approximation. An application of relations (2) - (5) is represented in figure 2 which is a partial and enlarged view of the figure 1 .

Using a parameterization as explained above, it is possible to define a wide variety of spring-spiral curves depending on the inertia chosen of the balance, the material, the section and the length of the balance spring, but also the coefficients parametrization polynomials. It is also possible to choose particular solutions by limiting for example the number of orders and / or the number of turns.

Simulations of possible curves are represented at Figures 3 to 8 . So, to form the figure 3 , parametrization was limited to relations (2) to (4) with a spiral with 2.3 turns and a parametrization polynomial of degree 2. The figure 4 corresponds to the parametrization with a polynomial of degree 3 from relations (2) to (5) always limiting the winding to 2.3 turns. Finally, figure 5 corresponds to the parameterization with a polynomial of degree 4 from relations (2) to (6) by limiting the winding to 2.3 turns. The Figures 6 to 8 correspond to the same criteria respectively as the Figures 3 to 5 but by increasing the winding of 2.3 turns to 5.3 turns. We realize that there is an infinity of curve solutions while respecting the relations (2) - (8) stated.

As illustrated in Figures 9 to 11 , the end 6 of the spiral spring 3 is connected to a ferrule 10 in one piece and the end 7 of the spiral spring 5, which is opposite the fastener 4, is arranged to cooperate with a stud (not shown ). Moreover, as visible to Figures 9 to 11 , the main faces 11, 12 of the fastener 4 are substantially parallel to the line of symmetry A.

In the particular case of Figures 9 to 11 wherein the hairspring 1 is formed from three parts as explained in the document EP 2 184 652 , in addition to respecting the most relations (2) - (8), it then becomes necessary to compensate for the unbalance generated by the fastener 4, that is to say to compensate for the mass of the fastener 4 with respect to its distance from the axis of the balance.

Thus, as illustrated in Figures 9 to 11 each spiral spring 3, 5 preferably comprises at least two counterweights 8-9, 8'-9 'which are symmetrical along the same line A as the bends in order to compensate for the unbalance formed by the mass of the fastener 4 and customize the anisochronism slope of the hairspring 1. Preferably, the masses of the counterweights 8, 8 'and 9, 9' are substantially equal and their sum is greater or lesser than that of the fastener 4 according to the difference distance between, on the one hand, the fastener 4 and the balance shaft, and, on the other hand, the counterweights 8, 8 ', 9, 9' and said balance shaft.

Indeed, it has been shown empirically that two single counterweights on the opposite side of the fastener did not allow to lower the belly of the variation of walking below 1.4 sj ^-1 . This is because even if the counterweights perfectly balance the unbalance for a rotation angle of the ferrule of 0 °, this is no longer the case when the ferrule rotates at a certain angle because the radial distance of the fastener 4 does not vary in the same way as the radial distance of the counterweights 9, 9 '.

That is why to better balance the unbalance over a range of usual rotation angle of 0 ° to substantially 300 °, is added at least two additional counterweight 8, 8 'by placing them in other places on the spiral springs 3, 5. Thus, it has been found that four counterweights 8, 8 ', 9, 9' all aligned on the axis A as visible in FIG. figure 11 , two 8, 8 'next to the fastener 4 and two 9, 9' on the opposite side to the fastener 4 optimize the imbalance by making it virtually zero whatever the angle of the ferrule 10.

Preferably according to the invention, each counterweight 8, 8 ', 9, 9' is substantially H-shaped, the parallel arms of the H being substantially parallel to the local curvature of the spiral spring 3, 5 with which it is associated. As visible to Figures 9 to 11 , we note that these shapes in H provide a local extra thickness of each spiral spring 3, 5 which locally increases their stiffness.

Thus, advantageously according to the invention, the stiffnesses and / or the masses brought locally by the counterweights 8, 8 ', 9, 9' and the fastener 4 are used to modify the anisochronism slope of the hairspring 1.

A simulation of the belly and the slope of anisochronism of the spiral 1 according to the invention was carried out by varying the length of the fastener 4 or the counterweights 8, 8 ', 9, 9' along the spiral 1: Tie 4 Counterweight 9,9 ' Counterweight 8, 8 ' Slope Belly [Mm] [Mm] [Mm] [S / d / 100 °] [S / d] 0.22 0.1 0.1 -8.54 0.26 0.1 0.1 0.1 -7.51 0.35 0.22 0.04 0.22 -12.97 1.14 0.22 0.22 0.04 -7.88 0.54 0.22 0.44 0.22 -5.49 0.22 0.22 0.33 0.22 -5.05 0.29 0.22 0.33 0.25 -4.3 0.49

The length represents the length of the portion of the hairspring 1 which is stiffened by the fastener 4 or the counterweight 8, 8 ', 9, 9'. For the simulation, it was chosen a pendulum inertia amounting to 2.5 mg.cm ² and a spiral 1 silicon of a section of 0.033 mm x 0.1 mm and a length L of 45 mm.

It can be seen that by decreasing the length of the fastener 4, the slope of anisochronism tends to recover while the belly advantageously remains less than 0.4 sj ^-1 . In addition, by decreasing the length of the counterweights 9, 9 ', the slope of anisochronism tends to recover while the belly is advantageously less than 0.3 sj ^-1 . Finally, by increasing the length of the counterweights 8, 8 ', the slope of anisochronism tends to recover while the belly remains advantageously less than 0.5 sj ^-1 .

Of course, the mass of the fastener 4 and therefore the counterweights 8, 8 ', 9, 9' can also be modified to adapt the slope of anisochronism: Tie 4 Counterweight 9, 9 ' Counterweight 8, 8 ' Tie 4 Slope Belly [Mm] [Mm] [Mm] [mm ³ ] [S / d / 100 °] [S / d] 0.22 0.1 0.1 0.016 -8.54 0.26 0.22 0.1 0.1 0,008 -5.58 0.56 0.22 0.1 0.1 0,002 -4.58 0.53

It can be seen that by decreasing the mass of the fastener 4, the slope of anisochronism tends to recover while the belly advantageously remains less than 0.6 sj ^-1 . Therefore, advantageously according to the invention, the anisochronism slope of the hairspring 1 can be customized to compensate for that given by the exhaust delay.

Of course, the present invention is not limited to the illustrated example but is susceptible of various variations and modifications that will occur to those skilled in the art. In particular, other framing criteria may be provided such as a limitation of the ratio between the inner radius and the outer radius so that the ends of the spiral springs are not too close to the point of origin where must be present the balance shaft.

In addition, advantageously according to the invention, the inner coil 7 of the second spiral spring 5 comprises, preferably, a shifter 13 arranged to attach to a peg (not shown) in the plane of the second spiral spring. 5. The shifting device 13 is particularly useful for preventing particular shapes of the hairspring 1 make it impossible to mount because of the proximity of its free end 7 relative to the balance shaft.

As visible to Figures 9 to 11 , the shifter 13 comprises a part 14 in extension of the inner coil 7 of the second spiral spring 5. Preferably, the piece 14 is more rigid than the second spiral spring 5 so as not to provide an elastic torque to the balance spring - spiral resonator. In addition, the part 14 is preferably made more rigid by a greater thickness, such as for example at least three times greater, with respect to the thickness of the second spiral spring 5, that is to say the width of its blade . It is therefore understood that the shape of the part 14 is partly adapted according to the curvature of the turns of the second spiral spring 5 so that no contact takes place.

In addition, according to a particular alternative, it is preferred that the piece 14 is integral with the second spiral spring 5 and, preferably, that the latter comprises a height substantially equal to that of the piece 14, it is to say that the latter is contained in the same plane.

The extension piece 14 is furthermore preferably connected to the inner coil 7 of the second spiral spring 5 by means of a substantially U-shaped bend 15 in order to further limit the supply of a any elastic couple. It is understood that the extension piece 14 and the elbow 15 can virtually bring the fixed point formed by the peak (not shown) at the end 7 of the hairspring 1.

In addition, the part 14 has a recess 16, blind or through, of substantially asymmetrical section and intended to cooperate with the peak (not shown). Finally, as visible Figures 9 to 11 , the piece 14 may be partially perforated by holes 19 to reduce its mass and thus make it less penalizing its weight when mounting the hairspring 1.

Similarly, the inner coil 6 of the first spiral spring 3 comprises an enlarging device 17 of the ferrule 10 in the plane of the first spiral spring 3. The enlargement device 17 is particularly useful for preventing particular shapes spiral 1 make it impossible to mount because of the proximity of its free end 6 relative to the balance shaft. It is therefore understood that without the enlarging device 17, the shell 10 would necessarily be of smaller diameter because of the proximity of the inner coil 6.

Preferably, the enlarging device 17 comprises a bead 18 extending the inner coil 6 of the first spiral spring 3, the bead 18 being more rigid than the first spiral spring 3 so as not to provide an elastic torque. In addition, the bead 18 is preferably made more rigid by a greater thickness relative to the thickness of the first spiral spring 3, that is to say the width of its blade.

In addition, according to a particular alternative, it is preferred that the bead 18 is substantially U-shaped. Finally, the bead 18 is preferably integral with the first spiral spring 3.

Therefore, advantageously according to the invention, a hairspring can be manufactured respecting predetermined conditions in order to reduce the displacement of the center of mass of the hairspring in contraction and expansion. This slight or negligible displacement advantageously makes it possible to reduce the belly of the anisochronism curves to a value that is substantially equal to or less than 0.5 sj ^-1 . In addition, advantageously according to the invention, the spiral anisochronism slope can be customized to compensate for that given by the exhaust delay.

Finally, the configuration of Figures 9 to 11 defines a very robust axis A of symmetry which makes it possible to minimize the chronometric defects induced by disturbances in the direction orthogonal to the axis A. It is therefore understood that it is possible to maximize the manufacturing accuracy in the fastener-counterweight direction, that is to say the axis A, as the only critical direction instead of two usually.

Of course, the present invention is not limited to the illustrated example but is susceptible of various variations and modifications that will occur to those skilled in the art. In particular, the counterweights 8, 8 ', 9, 9' may be of different shape and / or geometry without departing from the scope of the invention. It is also possible to increase their number and / or distribute them in a different way, that is to say in particular that the counterweights 8, 8 ', 9, 9' are not necessarily symmetrical along the line A as the curvatures .

Thus, for example, it is perfectly possible, for each spiral spring 3, 5, to add two additional counterweights, that is to say to have four counterweights, in order to distribute them substantially at 90 ° one another.

In addition, when the spiral is silicon, it can be at least partially covered with silicon dioxide to make it less sensitive to temperature variations and mechanical shocks. It is then understood that the sectional variation of the counterweights 8, 8 ', 9, 9' also modifies the local thermal compensation of the spiral.

Finally, it may be envisaged also to compensate the unbalance induced by the bead 18 by adding an additional counterweight on the opposite side of ferrule 10.

Claims (19)

Spiral (1) comprising a first spiral spring (3) whose curve extends in a first plane and whose inner coil (6) comprises a ferrule (10), a second spiral spring (5) whose curve s extends in a second plane parallel to the foreground, a fastener (4) solidarisant the outer turn of the first spiral spring (3) to the outer turn of the second spiral spring (5) to form a spiral (1) double series characterized in that the curve of the first spiral spring (3) and the curve of the second spiral spring (5) each comprise a continuously variable pitch and are symmetrical with respect to a line (A) parallel to the first and second planes and passing through the median projection plane (P) of the fastener (4), each curve being such that the following relationship is substantially zero: $${\overrightarrow{P}}^{\left(\mathrm{not}\right)}=\frac{\mathrm{not}+1}{{\mathrm{The}}^{\mathrm{not}+1}}\underset{0}{\overset{\mathrm{The}}{\int }}\mathit{ds}\cdot s^{\mathrm{not}}\cdot \overrightarrow{x}\left(s\right)$$

or : - P ^{( n )} is the moment of the spiral of order n; - L is the length of the hairspring; - s ⁿ represents the curvilinear abscissa along the spiral at the power of order n ; - x ( s ) is the parameterization of the spiral by its curvilinear abscissa. in order to reduce the displacements of its center of mass during its contraction and expansion and in that each spiral spring (3, 5) further comprises at least two counterweights (8, 8 ', 9, 9') in order to compensate for the unbalance formed by the mass of the fastener (4) and customize the anisochronism slope of the spiral (1). Spiral (1) according to the preceding claim, characterized in that said at least two counterweights (8, 8 ', 9, 9') are symmetrical along the same line (A) as the curvatures. Spiral (1) according to claim 1 or 2, characterized in that two counterweights (8, 8 ') are located next to the fastener (4) and two other counterweights (9, 9') are located on the opposite side to the clip (4) to minimize unbalance. Spiral (1) according to one of the preceding claims, characterized in that each counterweight (8, 8 ', 9, 9') is substantially H-shaped, the parallel arms of the H being substantially parallel to the local curvature of the spring -spiral (3, 5) with which it is associated. Spiral (1) according to one of the preceding claims, characterized in that the stiffnesses and / or the masses provided locally by said counterweights (8, 8 ', 9, 9') and said fastener (4) are used to modify the slope of anisochronism of the spiral (1). Spiral (1) according to one of the preceding claims, characterized in that the main faces (11, 12) of the fastener (4) are substantially parallel to said line of symmetry (A). Spiral (1) according to one of the preceding claims, characterized in that the inner coil (7) of the second spiral spring (5) comprises an offset device (13) arranged to be attached to a pin in the plane of the second spiral spring (5). Spiral (1) according to the preceding claim, characterized in that the shifter (13) comprises an extension piece (14) of the inner coil (7) of the second spiral spring (5), said piece being more rigid than said second spiral spring so as not to provide an elastic torque. Spiral (1) according to the preceding claim, characterized in that the extension piece (14) is connected to the inner coil with a bend (15) substantially U-shaped. Spiral (1) according to claim 8 or 9, characterized in that the extension piece (14) is integral with the second spiral spring (5). Spiral (1) according to one of claims 8 to 10, characterized in that the extension piece (14) is made more rigid by a thickness at least three times greater than that of said second spiral spring. Spiral (1) according to one of claims 8 to 11, characterized in that the piece (14) may be partially perforated to reduce its mass. Spiral (1) according to one of the preceding claims, characterized in that the inner coil (6) of the first spiral spring (3) comprises an enlarging device (17) of the shell (10) in the plane of the first spiral spring (3). Spiral (1) according to the preceding claim, characterized in that the enlarging device (17) comprises a bead (18) extending the inner coil (6) of the first spiral spring (3), said bead being more rigid than said first spring spiral so as not to provide elastic torque. Spiral (1) according to the preceding claim, characterized in that the bead (18) is substantially U-shaped. Spiral (1) according to claim 14 or 15, characterized in that the bead (18) is integral with the first spiral spring (3). Spiral (1) according to one of the preceding claims, characterized in that it is formed from silicon. Spiral (1) according to the preceding claim, characterized in that it comprises at least one portion coated with silicon dioxide in order to limit its sensitivity to temperature variations and mechanical shocks. Resonator for a timepiece comprising a balance characterized in that the rocker cooperates with a hairspring (1) according to one of the preceding claims.

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