HK1165870B - Balance spring with fixed centre of mass - Google Patents

Description

Balance spring with fixed centre of mass

Technical Field

The invention relates to a balance spring for forming a balance spring resonator, the curvature of which allows a substantially fixed centre of mass expansion.

Background

EP patents 2184652, 2196867 and 2105807 describe how to manufacture a curvilinear-lift balance spring made of micromachinable material, using three parts, two parts or a single part, respectively. These documents are incorporated herein by reference.

It is known to apply the phillips standard to determine the theoretical curvature of the end curve. However, the philips standard is actually an approximation standard, which is not necessarily satisfactory if a consistent lower variation (variation in rate) is required.

Disclosure of Invention

The aim of the present invention is to overcome all or part of the above drawbacks by proposing a balance spring that satisfies the predetermined conditions and is able to reduce the displacement of the centre of mass of the balance spring during retraction and extension.

The invention therefore relates to a balance spring comprising a first balance spring whose curve extends in a first plane, a second balance spring whose curve extends in a second plane parallel to the first plane, one end of the curve of the first balance spring being fixed to one end of the second balance spring to form a connecting element of a tandem double balance spring, characterized in that the curve of the first balance spring and the curve of the second balance spring both have a continuously variable pitch and are both symmetrical with respect to a line parallel to the first and second planes passing through a central projection plane of the connecting element, and in that each curve satisfies the relation:

and

the purpose is to reduce the displacement of its centroid during contraction and expansion.

According to other advantageous features of the invention:

each curve also satisfies the following relation:

；

-and, feasibly:

；

-and, feasibly:

；

-and, feasibly:

；

-and, feasibly:

。

each balance spring comprises at least one counterweight for compensating the unbalance caused by the mass of the connecting element;

-the balance spring is made of silicon;

the balance spring comprises at least one component coated with silicon dioxide to limit its sensitivity to temperature variations and mechanical shocks.

Moreover, the invention also relates to a resonator for a timepiece comprising an inertial mass, such as for example a balance, characterized in that the inertial mass cooperates with a balance spring as described in any one of the variants described above.

Drawings

Further characteristics and advantages will become clearer from the following description, given as a non-limiting example, with reference to the attached drawings, in which:

FIGS. 1 and 2 are schematic diagrams illustrating the relevant reasoning;

figures 3 to 5 are examples of calculations of 2.3-turn curves satisfying the second, third and fourth order bending moment equations, respectively;

FIGS. 6 to 8 are examples of calculations of 5.3-turn curves satisfying the second, third and fourth bending moment equations, respectively;

figures 9 and 10 are schematic views of a balance spring according to the invention;

FIG. 11 is a sectional view along the axis B-B;

fig. 12 is a simulation curve of the inequality of the balance spring according to fig. 9 and 10;

figure 13 is a simulation curve of the inequality of the balance spring in which the mass of the connecting element is not negligible;

figures 14 and 15 are schematic views of a balance spring compensating for the mass of the connecting element according to the invention;

fig. 16 is a simulation curve of the inequality of the balance spring of fig. 14 and 15.

Detailed Description

The deterioration of the mechanical watch with respect to its theoretical frequency is mainly due to the escapement and the balance spring resonator. Both types of variation can be based on themWhether it is caused by the amplitude of the balance or by the position of the clock movement. This is why the clock movement is tested in six positions in the non-isochronism test: 2 horizontal positions (dial up and down) and 4 vertical positions (grip turned 90 degrees from face up position). From the six different curves thus obtained, the maximum difference between said curves, also called "antinode", is determined, in seconds per day (s.j)^-1) The unit represents the maximum variation of the movement.

The escapement is difficult to regulate in response to the amplitude-induced deterioration of the balance. The balance spring is therefore generally regulated so that its variation from the same amplitude is substantially opposite to that of the escapement. Moreover, the balance spring is adjusted so that its deterioration is minimal between the four vertical positions.

Attempts have been made to state the necessary balance spring regulation in mathematical language in order to determine by calculation the ideal curve. The geometrical conditions for designing a satisfactory balance spring, i.e. in which the centre of mass of the balance spring is to be maintained on the balance axle, are clearly listed by Messrs Phillips and Grossmann. However, the existing conditions are rough approximations. Thus, the variations obtained by the following existing geometrical conditions are often disappointing, since very small displacements of the centroid can cause large variations.

This is why the following new conditions are advantageously stated according to the invention to obtain better worsening results than the existing geometries, in particular those published by Messrs Phillips and Grossmann.

Bending moment of balance wheel spring of order nDefined by the following equation:

(1)

wherein:

l is the length of the balance spring;

- sⁿrepresents the power n along the abscissa of the curve of the balance-spring;

- is a parameterized representation of the balance spring by its curve abscissa.

Thus, to obtain a fixed centre of mass, for each of the n steps, the bending moment of the balance springMust be zero. Since there are infinite orders and it is impossible to calculate all the orders, the larger the order satisfying the zero bending moment relation (1), the smaller the displacement amount of the centroid becomes.

In the example shown in fig. 1, the eighth-order bending moment of the balance spring is represented by points that determine an "ideal" theoretical curve, parameterized by a polynomial that includes at least as many coefficients as the order (in this case at least eight).

To apply these zero bending moment conditions of the balance spring, we start with a balance spring of the type shown in fig. 9 and 10, namely balance spring 1, balance spring 1 comprising a first balance spring 3 whose curve extends in a first plane, and a second balance spring 5 whose curve extends in a second plane parallel to the first plane. Each end of the balance springs 3,5 is fixed by a connecting element 4 to form a double-pendulum balance spring in series.

As described above, this type of balance spring can be manufactured from micro-machinable material (for example silicon) using the methods described in EP patents 2184652, 2196867 and 2105807, using three parts, two parts or a single part, respectively. Of course, a balance spring of this type may also be manufactured by other methods and/or other materials.

To simplify the calculations, the curve of first balance spring 3 and the curve of second balance spring 5 both preferably comprise a continuously variable pitch and are both symmetrical with respect to a line a parallel to the first and second planes passing through the centre of connecting element 4 and the central projection plane P of the balance staff.

Thus, as an example, for each balance spring 3,5, the first seven orders must satisfy the following relation:

(2)

(3)

(4)

(5)

(6)

(7)

(8)

as described above, the higher the order of the relations (2) to (8) is satisfied, the more limited the displacement of the centroid of balance spring 1 becomes. In contrast, the philips condition is close to relation (2), i.e., a first order approximation. Fig. 2 is a partially enlarged view of fig. 1, in which applications of the relations (2) - (5) are shown.

As mentioned above, with parameterisation, a number of hairspring curves can be determined according to the inertia chosen for the balance, the materials, the section and length of the balance spring and the coefficients in the parameterised polynomial. Specific solutions such as limiting the number of steps and/or turns may also be selected.

Possible curve simulations are shown in fig. 3 to 8. Thus, to form fig. 3, the parameterization is limited to relations (2) to (4), the balance spring having 2.3 turns and a parameterized polynomial of order 2. Fig. 4 shows the parameterization of the 3 rd order polynomial from relations (2) to (5), again limiting the winding to 2.3 turns. Finally, fig. 5 shows a parameterization with a 4 th order polynomial from relations (2) to (6), limiting the winding to 2.3 turns. Fig. 6 to 8 show the same criteria as fig. 3 to 5, respectively, but with the winding increased from 2.3 turns to 5.3 turns. There are an infinite number of curve solutions that satisfy the relationships (2) - (8) listed above.

A simulation of the inequality was performed according to the curvature shown in fig. 5 to construct balance spring 1 in fig. 9 and 10. Swimming deviceWire 3 comprises a one-piece collet 6 and the end of balance spring 5 opposite to connecting element 4 is fixed to a collet 7. Selecting up to 8mg.cm²And a silicon balance spring having a cross section of 0.0267mm x 0.1 mm and a length L of 46 mm. The simulation results shown in FIG. 12 indicate that the highly preferred result at 300 degrees is 0.3s.j^-1. The advantages of these new conditions compared to Phillips and Grossmann conditions, which still have to be adjusted to reduce the "anti-nodes", are therefore immediately apparent.

In the particular case of a balance spring made up of three components as described in EP patent No. 2184652, the connecting element may become unable to ignore the mass and amplify the inequality considerably as shown in fig. 13, where the variation reaches 11.8s.j at 200 degrees^-1。

In addition to the satisfaction of the relations (2) to (8) of the highest order, it is also necessary to compensate for the imbalance caused by the connecting element, i.e. to compensate for the mass of the connecting element with respect to its distance from the balance staff. Preferably, therefore, the invention proposes to counteract the unbalance of the connecting element by adding an unbalance symmetrically to the two balance springs 3, 5. Preferably, as shown in fig. 14 and 15, the increased unbalance comprises two counterweights 8',9' substantially identical on each hairspring 3', 5'. Preferably, the masses of weights 8 'and 9' are substantially the same and their sum is greater or less than the mass of connecting element 4 'according to the difference in distance, on the one hand the distance between connecting element 4' and the balance staff and on the other hand the distance between weights 8',9' and said balance staff. It is obvious that the masses added together of the weights 8',9' may constitute a mass substantially equal to the mass of the connecting element 4' if the distances are substantially equal. As shown in fig. 16, this advantageously means that 1.4s.j can be achieved at 200 degrees using the same criteria described above^-1The preference of (c) becomes worse.

The invention is of course not limited to the examples described but is capable of numerous modifications and variants, which are obvious to a person skilled in the art. In particular, other determination criteria may be provided such as, for example, limiting the ratio between the inner and outer diameters so that the balance spring tip is not too close to the origin at which the balance staff must be positioned.

Moreover, when the balance spring is made of silicon, it may be at least partially coated with silicon dioxide, in order to make it less sensitive to temperature variations and mechanical shocks.

Finally, each counterweight 8',9' may be different. In particular, each counterweight may be composed of two different masses, that is to say there may be four counterweights.

Claims (10)

1. Balance spring (1,1') comprising a first balance spring (3,3') the curve of which extends in a first plane, a second balance spring (5,5') the curve of which extends in a second plane parallel to the first plane, one end of the curve of the first balance spring (3,3') being fixed to one end of the curve of the second balance spring (5,5') so as to form a connecting element (4,4') of a double balance spring (1,1') in series, characterized in that the curve of the first balance spring (3,3') and the curve of the second balance spring (5,5') both comprise a continuously variable pitch and are both symmetrical with respect to a line (a) parallel to the first and second planes and passing through a central projection plane of the connecting element (4,4'), and in that each curve satisfies the relation:

and

the aim is to reduce the displacement of the centre of mass of the balance spring during retraction and extension,

wherein the content of the first and second substances,andbalance spring bending moments of order n in x and y directions, respectivelyBending moment of balance wheel spring of order nDefined by the following equation:

wherein:

l is the length of the balance spring;

- sⁿrepresents the power n along the abscissa of the curve of the balance-spring;

-is a parameterized representation of the balance spring by its curve abscissa.

2. A balance spring (1,1') according to claim 1, wherein each curve further satisfies the following relation:

to further reduce the displacement of the centre of mass of the balance spring during retraction and extension.

3. A balance spring (1,1') according to claim 2, wherein each curve further satisfies the following relation:

to further reduce the displacement of the centre of mass of the balance spring during retraction and extension.

4. A balance spring (1,1') according to claim 3, wherein each curve further satisfies the following relation:

to further reduce the displacement of the centre of mass of the balance spring during retraction and extension.

5. A balance spring (1,1') according to claim 4, wherein each curve further satisfies the following relation:

to further reduce the displacement of the centre of mass of the balance spring during retraction and extension.

6. A balance spring (1,1') according to claim 5, wherein each curve further satisfies the following relation:

to further reduce the displacement of the centre of mass of the balance spring during retraction and extension.

7. Balance spring (1,1') according to claim 1, characterized in that each balance spring (3',5') comprises at least one counterweight (8',9') to compensate the imbalance created by the mass of the connecting element (4').

8. A balance spring (1,1') according to claim 1, characterized in that it is made of silicon.

9. Balance spring (1,1') according to claim 8, characterized in that it comprises at least one component coated with silicon dioxide to limit its sensitivity to temperature variations and mechanical shocks.

10. Resonator for a timepiece, comprising an inertial body, characterized in that it cooperates with a balance spring according to any one of the preceding claims.