EP2405313B1 - Spiral with immobile mass centre - Google Patents

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. The document EP 2 104 006 presents a variant of a double monoblock spiral.

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

où:

• P ⁽ⁿ⁾ est le moment du spiral d'ordre n ;
• L est la longueur du spiral ;
• s" 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

et en ce chaque courbe respecte les relations : $$P_x^{\left(0\right)}=0{\mathrm{et}\mathrm{<figure-callout\; id="1"\; label="P\; y"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">P</figure-callout>}}_y^{}=2{\mathrm{<figure-callout\; id="0"\; label="P\; y"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">P</figure-callout>}}_y^{}$$

afin de réduire les déplacements de son centre de masse lors de ses contraction et expansion.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.
For this purpose, the invention relates to a double spiral comprising a first spiral spring whose curve extends in a first plane, a second spiral spring whose curve extends in a second plane parallel to the first plane, a fastener solidarisant an end of the curve of the first spiral spring at one end of the curve of the second spiral spring in order to form a double spiral in series the curve of the first spiral spring and the curve of the second spiral spring each having a continuously variable pitch and ledits first and second spiral spring being symmetrical with respect to a straight line parallel to the first and second planes passing through the median projection plane of the fastener, each curve tending to make the following relationship substantially nil: $${\overrightarrow{P}}^{\left(\mathrm{not}\right)}=\frac{\mathrm{not}+1}{{\mathrm{The}}^{\mathrm{not}+1}}{\displaystyle {\int }_0^{\mathrm{The}}}\mathit{ds}\cdot s^{\mathrm{not}}\cdot \overrightarrow{x}\left(s\right)$$

or:

• P ^{( n )} is the moment of the spiral of order n;
• L is the length of the spiral;
• s " 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

and in that each curve respects the relations: $$P_x^{\left(0\right)}=0{\mathrm{and}P}_{\mathrm{there}}^{\left(1\right)}=2P_{\mathrm{there}}^{\left(0\right)}$$

in order to reduce the movements of its center of mass during its contraction and expansion.

• chaque courbe respecte en plus la relation suivante : $$P_x^{\left(2\right)}=3P_x^{\left(1\right)}:$$
  
• et, éventuellement : $${\mathrm{<figure-callout\; id="3"\; label="P\; y"\; filenames="imgf0001.png,imgf0005.png"\; state="\{\{state\}\}">P</figure-callout>}}_y^{}=4{\mathrm{<figure-callout\; id="2"\; label="P\; y"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">P</figure-callout>}}_y^{}-8P_y^{\left(0\right)}:$$
  
• et, éventuellement : $$P_x^{\left(4\right)}=5P_x^{\left(3\right)}-20P_x^{\left(1\right)};$$
  
• et, éventuellement : $$P_y^{\left(5\right)}=6P_y^{\left(4\right)}-40P_y^{\left(2\right)}+96P_y^{\left(0\right)}:$$
  
• et, éventuellement : $$P_x^{\left(6\right)}=7P_x^{\left(5\right)}-70P_x^{\left(3\right)}+336P_x^{\left(1\right)}\mathrm{.}$$
  
• chaque ressort-spiral comporte au moins un contrepoids afin de compenser le balourd formé par la masse de l'attache ;
• 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:

• each curve also respects the following relation: $$P_x^{\left(2\right)}=3P_x^{\left(1\right)}:$$
  
• and eventually : $$P_{\mathrm{there}}^{\left(3\right)}=4P_{\mathrm{there}}^{\left(2\right)}-8P_{\mathrm{there}}^{\left(0\right)}:$$
  
• and eventually : $$P_x^{\left(4\right)}=5P_x^{\left(3\right)}-20P_x^{\left(1\right)};$$
  
• and eventually : $$P_{\mathrm{there}}^{\left(5\right)}=6P_{\mathrm{there}}^{\left(4\right)}-40P_{\mathrm{there}}^{\left(2\right)}+96P_{\mathrm{there}}^{\left(0\right)}:$$
  
• and eventually : $$P_x^{\left(6\right)}=7P_x^{\left(5\right)}-70P_x^{\left(3\right)}+336P_x^{\left(1\right)}\mathrm{.}$$
  
• each spiral spring comprises at least one counterweight to compensate for the unbalance formed by the mass of the fastener;
• 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.

In addition, the invention relates to a resonator for a timepiece comprising an inertia such as, for example, a balance characterized in that the inertia 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 d'un spiral selon l'invention ;
• la figure 11 est une représentation en coupe brisée selon l'axe B-B ;
• la figure 12 est une courbe de simulation de l'anisochronisme du spiral selon les figures 9 et 10 ;
• la figure 13 est une courbe de simulation de l'anisochronisme d'un spiral dont la masse de l'attache n'est pas négligeable ;
• les figures 14 et 15 sont des représentations d'un spiral selon l'invention compensant la masse de l'attache ;
• la figure 16 est une courbe de simulation de l'anisochronisme du spiral selon les figures 14 et 15.

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 representations of a spiral according to the invention;
• the figure 11 is a broken sectional representation along the axis BB;
• the figure 12 is a simulation curve of the spiral anisochronism according to Figures 9 and 10 ;
• the figure 13 is a simulation curve of the anisochronism of a spiral whose mass of the fastener is not negligible;
• the Figures 14 and 15 are representations of a hairspring according to the invention compensating for the mass of the fastener;
• the figure 16 is a simulation curve of the spiral anisochronism according to Figures 14 and 15 .

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: $${\overrightarrow{P}}^{\left(\mathrm{not}\right)}=\frac{\mathrm{not}+1}{{\mathrm{The}}^{\mathrm{not}+1}}{\displaystyle {\int }_0^{\mathrm{The}}}\mathit{ds}\cdot s^{\mathrm{not}}\cdot \overrightarrow{x}\left(s\right)$$

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 because in infinite number, plus a large number of orders whose relationship (1) zero is respected, 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 and 10 , 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 being secured by a fastener 4 to form a double spiral in 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 with three parts, two parts or monobloc manner. 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 a continuously variable pitch and are symmetrical with respect to a straight line A parallel to the first and second passing planes. by the centers of the median plane P of projection of the fastener 4 and the axis of the balance.

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

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

$$P_y^{\left(3\right)}=4P_y^{\left(2\right)}-8P_y^{\left(0\right)}$$

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

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

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

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

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

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

$$P_{\mathrm{there}}^{\left(3\right)}=4P_{\mathrm{there}}^{\left(2\right)}-8P_{\mathrm{there}}^{\left(0\right)}$$

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

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

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

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 , the parametrization was limited to relations (2) to (4) with a spiral with 2.3 turns and a polynomial of parameterization 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.

A simulation of anisochronism was performed from the curvature presented at figure 5 forming the spiral 1 of the Figures 9 and 10 . The spiral spring 3 comprises a ferrule 6 in one piece and the end of the spiral spring 5, which is opposite the fastener 4, is secured to a stud 7. It has been chosen a pendulum inertia s' raising to 8 mg.cm ² and a spiral 1 of silicon of a section of 0.0267 mm x 0.1 mm and a length L of 46 mm. The result of the simulation illustrated in figure 12 has a very favorable result of 0.3 sj ^-1 at 300 °. We immediately understand the advantage of these new conditions compared to those including MM. Phillips and Grossmann with whom adjustments are still necessary to reduce the "belly".

In the particular case where the hairspring is formed from three parts as explained in the document EP 2 184 652 , the attachment can become a non-negligible mass and considerably amplify the anisochronism as visible in the figure 13 in which the gait variation reaches 11.8 sj ^-1 at 200 °.

In addition to respecting the most relationships (2) - (8), it then becomes necessary to compensate for the unbalance generated by the fastener, that is to say, to compensate the weight of the fastener relative to its distance from the axis of the pendulum. Thus, in a preferred manner, the invention proposes to cancel the unbalance of the fastener by symmetrically relating an unbalance to the two spiral springs 3, 5. Preferably, the reported unbalance is formed by two counterweights 8 ', 9' substantially identical on each spiral spring 3 ', 5' as illustrated in FIGS. Figures 14 and 15 . Preferably, the masses of the counterweights 8 ', 9' are substantially equal and their sum is greater or lesser than that of the fastener 4 'according to the difference in distance between, on the one hand, the fastener 4' and the balance shaft, and, on the other hand, the counterweights 8 ', 9' and said balance shaft. It is understood that in case of substantially equivalent distance, the masses added counterweight 8 ', 9' will form a mass substantially equivalent to that of the fastener 4 '. This advantageously makes it possible to obtain, with the same criteria above, a favorable variation in the path from 1.4 sj ^-1 to 200 ° as illustrated in FIG. figure 16 .

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, 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.

Finally, each counterweight 8 ', 9' can be different. They can in particular be formed each of two distinct masses that is to say that there could be four counterweights.

Claims (10)

1. Dual balance spring (1, 1') including a first hairspring (3, 3') the curve of which extends in a first plane, a second hairspring (5, 5') the curve of which extends in a second plane parallel to the first plane, an attachment member (4, 4') securing one end of the curve of the first hairspring (3, 3') to one end of the curve of the second hairspring (5, 5') so as to form a dual balance spring (1, 1') in series, the curve of the first hairspring (3, 3') and the curve of the second hairspring (5, 5') each including a continuously variable pitch, said first and second hairsprings being symmetrical relative to a straight line (A) parallel to the first and second planes and passing through the median plane of projection of the attachment member (4, 4'), characterised in that each curve tends so that the following relation is substantially equal to zero: $${\overrightarrow{P}}^{\left(n\right)}=\frac{n+1}{L^{n+1}}{\displaystyle {\int }_0^L}\mathit{ds}\cdot s^n\cdot \overrightarrow{x}\left(s\right)$$

   

   where:

   - P ⁽ⁿ⁾ is the moment of the hairspring of the order n

   - L is the length of the balance spring;

   - sⁿ represents the curvilinear abscissa along the balance spring to the power of n;

   - x (s) is the parameterization of the balance spring by the curvilinear abscissa thereof

   and in that: $$P_x^{\left(0\right)}=0{\mathrm{and}\mathit{P}}_y^{\left(1\right)}=2P_y^{\left(0\right)}$$

   

   in order to reduce displacements of the centre of mass thereof during contraction and expansion.
2. Balance spring (1, 1') according to the preceding claim, characterized in that each curve also respects the following relation: $$P_x^{\left(2\right)}=3P_x^{\left(1\right)}$$

   

   so as to further reduce the displacements of the centre of mass thereof during contraction and expansion.
3. Balance spring (1, 1') according to the preceding claim, characterized in that each curve also respects the following relation: $$P_y^{\left(3\right)}=4P_y^{\left(2\right)}-8P_y^{\left(0\right)}$$

   

   so as to further reduce the displacements of the centre of mass thereof during contraction and expansion.
4. Balance spring (1, 1') according to the preceding claim, characterized in that each curve also respects the following relation: $$P_x^{\left(4\right)}=5P_x^{\left(3\right)}-20P_x^{\left(1\right)}$$

   

   so as to further reduce the displacements of the centre of mass thereof during contraction and expansion.
5. Balance spring (1, 1') according to the preceding claim, characterized in that each curve also respects the following relation: $$P_y^{\left(5\right)}=6P_y^{\left(4\right)}-40P_y^{\left(2\right)}+96P_y^{\left(0\right)}$$

   

   so as to further reduce the displacements of the centre of mass thereof during contraction and expansion.
6. Balance spring (1, 1') according to the preceding claim, characterized in that each curve also respects the following relation: $$P_x^{\left(6\right)}=7P_x^{\left(5\right)}-70P_x^{\left(3\right)}+336P_x^{\left(1\right)}$$

   

   so as to further reduce the displacements of the centre of mass thereof during contraction and expansion.
7. Balance spring (1') according to any of the preceding claims, characterized in that each hairspring (3', 5') includes at least one counterweight (8', 9') so as to compensate for the unbalance formed by the mass of the attachment member (4').
8. Balance spring (1, 1') according to any of the preceding claims, characterized in that it is formed from silicon.
9. Balance spring (1, 1') according to the preceding claim, characterized in that it includes at least one part coated with silicon dioxide so as to limit the sensitivity thereof to temperature variations and mechanical shocks.
10. Resonator for a timepiece including an inertia, characterized in that the inertia cooperates with a balance spring according to any of the preceding claims.

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