CH705234A1 - Method for determining the geometry of a hairspring. - Google Patents

Abstract

The present invention relates to a method for determining the geometry of a hairspring of a watchmaking regulating organ, aiming to make the geometric center of a hairspring coincide with its center of gravity. The method according to the invention is characterized in that it consists in defining at least one continuous polynomial function characterizing the entire spiral. The invention also relates to a hairspring of a clock-adjusting member obtained by such a method and a timepiece comprising such a hairspring.

Description

Technical area

[0001] The present invention relates to the field of mechanical watchmaking. It relates more particularly to a method for determining the geometry of a balance spring of a watch regulating organ.

State of the art

[0002] In theory, the center of gravity of a hairspring coincides with its geometric center. In practice, the balance springs used in watchmaking only have a portion of the Archimedean spiral, this one adjoining, in the center, a central curve ending in a ferrule and, on the outside, an outer curve presenting different profiles. Thus, it is known that the turns of a flat balance spring deform eccentrically when the balance spring is working, due to the fact that the center of gravity of the balance spring does not initially correspond to the center of rotation of the balance spring and / or due to the displacement. of the center of gravity during the expansions / contractions of the hairspring. This eccentricity disrupts the adjustment of the sprung balance and makes the latter anisochronous.

[0003] Several different solutions have been proposed to keep the centers of gravity and of rotation coincident during the work of a flat balance spring and thus make the deformations of the turns concentric. Among these solutions, we have in particular: - the Breguet hairspring with a so-called Philips curve, in which an outer curve is brought into a second plane above the flat hairspring; - the angle balance spring exhibited in 1958 by MM. Emile and Gaston Michel in the article "Concentric flat spirals without curves" published by the Swiss Chronometry Society (BE 526 689A and CH 327 796A).

[0004] The first solution amounts to modifying an initial plane hairspring into a hairspring extending in several planes. This solution does not fall within the scope of the present invention, which is only concerned with planar balance springs.

[0005] The second solution consists in stiffening a determined portion of the coil by giving it the shape of an angle. This angle iron is located either on the outer turn or on a central turn. The idea of having a stiffening portion on the outer coil was taken up in document EP1473604, which proposes a stiffened portion ending before the outer end of the hairspring. In particular, this document proposes a hairspring in which there is a sufficient gap between the last turn and the penultimate coil, so that the penultimate coil remains free radially during the expansions of the hairspring. This document also explains how the shape of this stiffening portion is modeled and determined.

[0006] Thus, this document confirms, like most of the other publications known from the state of the art, that those skilled in the art have always considered that a hairspring is an assembly of three parts: a central part, a spiral part and outer part.

[0007] However, in the opinion of the authors of this solution, while a central reinforcement provides a clear improvement in terms of isochronism of the sprung balance, the reinforcement on the outer coil is not satisfactory.

[0008] The present invention aims to improve the isochronism of a sprung balance by stiffening a portion of the outer turn of the hairspring, and provides for this purpose a regulating member as defined in the appended claim 1, modes particular embodiments being defined in dependent claims 2 to 10, as well as a timepiece, such as a watch, incorporating the aforementioned regulating member.

[0009] The present invention provides a completely different and innovative approach for determining a geometry of a balance spring allowing the geometric center of a balance spring to coincide with its center of gravity, particularly during its expansions.

Disclosure of the invention

[0010] More specifically, the invention relates to a method for determining the geometry of a balance spring of a watch regulating organ as defined in the claims.

Brief description of the drawings

[0011] Other details of the invention will emerge more clearly on reading the following description, made with reference to the appended drawing in which: FIG. 1 <sep> shows curves representing the radius of a hairspring according to the invention and according to the state of the art, as a function of the angle 0 of the hairspring, from the shell, - fig. 2 <sep> shows two of the three approaches described below for calculating the thickness of the hairspring as a function of the angle 0 of the hairspring, and - fig. 3 and 4 <sep> represent the behavior of balance springs obtained according to the invention, and - Figs. 5, 6 and 7 <sep> illustrate comparative results, obtained by simulations, between a state-of-the-art hairspring and the hairspring of FIG. 3, obtained according to the invention.

Mode (s) of carrying out the invention

[0012] In FIG. 1, curve 1 made in dotted lines shows the evolution of the radius of a conventional balance-spring as a function of the angle 0 of the balance-spring, from the ferrule. We can see the three distinct areas of the hairspring, mentioned in the introduction above. At the start of the curve, the hairspring does not start with a zero radius, due to its attachment to the ferrule. This characteristic point is represented by the letter A. Then, we have the spiral part, which ends at point B, which is defined by the space required for the peak, which is the fixing member of the outer coil of the balance spring. . Finally, the radii of the third part of the curve, which ends in C, are also defined by the geometry of the pin and that of the balance. Thus, points A, B and C are fixed by the geometry of the members and attachment elements of the balance spring, in general, the ferrule and the eyebolt. The curve has two breaks, separating the three parts which are therefore discontinuous, in the mathematical sense of the term.

[0013] In FIG. 1, we see, by way of example, a curve representative of the invention. Indeed, the particularly original idea on which the invention is based consists in defining at least one continuous polynomial function characterizing the entire balance spring. According to this example, it is a question of expressing the radius of the hairspring according to a polynomial function of the type:

To determine the coefficients of the polynomial, it is fixed that the curve representative of the function must pass through points A, B, C determined by the geometry of the regulating organ and by the practical contingencies of the hairspring attachment. Two other points D and E are determined on the curve, corresponding respectively, by way of example, to the break point between the first and the second part and in the middle of the hairspring. The radius and the initial position of these two points are liable to vary.

[0015] Thus, by arbitrarily positioning the points D and E, that is to say by varying their radius to constant 8, sets of polynomial coefficients are determined. These coefficients are determined by mathematical calculations, numerically or analytically.

For each of the sets of parameters, the elastic behavior of the hairspring obtained is then simulated and the displacement of the center of gravity of the hairspring with respect to its geometric center, during expansions and contractions, is examined.

[0017] By successive iterations, the sets of parameters are ultimately determined which make it possible to obtain a balance spring with ad-hoc properties.

[0018] A degree 4 polynomial already makes it possible to obtain a satisfactory curve, that is to say with a center of gravity of the balance spring very close to the center of rotation of the balance spring, including during expansions. Polynomials of higher degrees can also be considered.

[0019] From this concept, the determination of the coefficients of the polynomial can be optimized. In particular, due to physical and mechanical constraints on the hairspring, the coefficients are determined by respecting the ratio hs / es> F, with F being between 1 and 10. h is the height of the hairspring, that is - say the dimension orthogonal to the plane of the hairspring and e and the thickness, that is to say the smallest dimension in the plane of the hairspring.

[0020] The coefficients are also determined while respecting the following pitch / thickness ratio:

where R (θ) is the radius, e the thickness of the hairspring with α [-] the minimum radius-thickness ratio, between 1 and 5 (limits included).

This approach makes it possible to characterize the entire profile of a hairspring, while guaranteeing a continuous profile, that is to say without breaking between different functions. This approach makes it possible to make any type of profile defined by a polynomial function.

[0022] The thickness is also a parameter which can be used to act on the behavior of the hairspring. The thickness can also be defined polynomially as a function of the angle θ by a function of the type

The number of boundary conditions for defining the parameters "b" of this equation is defined by j + 1.

The initial position of the center of gravity of a hairspring depending only on the variation of the radius as a function of θ, another aspect of the invention proposes to compensate for the off-center of the center of gravity by using the variation of the thickness . Advantageously, it is proposed to vary the thickness inversely proportional to the radius as a function of θ. We then obtain a variation of the thickness which is expressed as follows (es in fig. 2):

It is thus possible to make the center of gravity of the hairspring coincide with its center of rotation, at least when the hairspring is at rest. The coefficients are then optimized in order to have an ideal compromise between the initial centering of the center of gravity and its displacement during the contraction and expansion of the hairspring.

[0026] A variant of the method according to the invention proposes, to determine the thickness of the hairspring, to multiply the function inverse to the function of the radius by an exponential function.

[0027] The thickness is then defined by the following three equations (eslog in Fig. 2):

while ensuring that

where eslogmoy is the average thickness obtained for eslog (θ) with θ ranging between θ min and θ max, and esmoy is the average thickness obtained for es (θ) (seen in equation (4)) with θ ranging between 8 min and 8 max.

Whatever the model chosen, when the set of coefficients is determined, the displacement of the center of gravity is then calculated numerically, typically by finite elements. The reduction in this displacement makes it possible to reduce the reaction force to the pivot. An experiment design or an optimization is used to best reduce the displacements of the center of gravity and / or the variations in the reaction force to the pivot.

[0029] By way of non-limiting example, the following results which were obtained can be provided. A first example of a hairspring obtained according to the invention is illustrated in FIG. 3. The proposed hairspring is defined by a polynomial of degree 4 as given above in equation (1): Rs (θ) = a4θ <4> + a3θ <3> + a2θ <2> + a1θ + a0 with a4 = 2.89 × 10 <-10> <> a3 = -3.24 × 10 <-8> <> a2 = 1.01 × 10 <-6> <> a1 = 2.00 × 10 <-5> <> a0 = 5.50 × 10 <-4>

[0030] On the basis of these coefficients, FIG. 3a shows the hairspring obtained in top view, FIG. 3b shows the thickness curves for the es and eslog curves as given above, fig. 3 represents the pitch / thickness ratio, while fig. 3d represents the inner and outer radii as a function of 8, still optimizing on the basis of the equations given above.

A second example of a hairspring obtained according to the invention is illustrated in FIG. 4. The proposed hairspring is defined by a polynomial of degree 4 as given above in equation (1): Rs (θ) = a48 <4> + a3 × <3> + a2 × <2> + a1 × + a0 with a4 = 2.78 × 10 <-> <10> a3 = -3.31 × 10 <-8> a2 = 1.09 × 10 <-6> a1 = 1.88 × 10 <-5> a0 = 5.50 × 10 <-4>

[0032] Figs. 4a, 4b, 4cet 4dcorrespond respectively to FIGS. 3a, 3b, 3c and 3d, but for the second example given above.

[0033] In order to be able to compare with the balance springs of the state of the art, FIGS. 5, 6 and 7 give comparative curves between a state-of-the-art hairspring and the hairspring as defined in the first example given.

[0034] FIG. 5 represents isochronism (in s / d) as a function of the period of oscillation of a sprung balance, between 150 and 330 °. Curve 50 corresponds to the hairspring obtained according to the method of the invention and curve 52 corresponds to the state of the art hairspring. It should be noted that walking with the state-of-the-art hairspring considers a hairspring blocked by the pins (situation only present between 90 ° and 330 °).

There is a much greater stability of the rate for the hairspring according to the invention.

[0036] FIG. 6 represents the resulting force at the pivot (in N). Curves 60 and 61 correspond to the hairspring obtained according to the method of the invention, respectively in expansion and contraction, and curves 62 and 63 correspond to the state-of-the-art hairspring, respectively in expansion and contraction. The breaks visible with the prior art hairspring represent contact with the pins. It is noted that, due to the behavior of the hairspring, the resulting force at the pivot is less for the hairspring according to the invention.

[0037] FIG. 7 represents the displacement (in mm) of the center of gravity as a function of the amplitude of the sprung balance. The curves 70 and 71 correspond to the hairspring obtained according to the method of the invention, respectively expanding and contracting, and curves 72 and 73 correspond to the state-of-the-art hairspring, respectively expanding and contracting. The breaks visible with the prior art hairspring represent contact with the pins. It can be seen that, due to the behavior of the hairspring, the position of the center of gravity is very stable as a function of the amplitude, that is to say that the center of gravity moves very little.

[0038] Once the geometry of the hairspring is determined, it can preferably be produced by deep etching techniques, which allow any geometries to be produced. The hairspring can therefore be made from silicon or other elastic materials suitable for manufacture by deep etching, by LIGA or by other cutting means.

[0039] Of course, nothing prevents investigating the geometries of balance springs more distant from traditional geometries, by setting points A, B, C different and any, within the limit of the geometry of the regulating organ.

Claims (15)

1. Method for determining the geometry of a balance spring of a watch regulating organ, characterized in that it consists in defining at least one continuous polynomial function characterizing the entire balance spring. 2. Method according to claim 1, characterized in that it further consists in optimizing the coefficients of said function by calculations and simulations. 3. Method according to claim 2, characterized in that said calculations and simulations are done numerically. 4. Method according to one of the preceding claims, characterized in that said function is a function which characterizes the radius of the hairspring and which is expressed as follows: 5. Method according to claim 4, characterized in that the geometries of the stud and of the shell determine invariant points of the function Rs (θ). 6. Method according to one of claims 4 and 5, characterized in that the coefficients are determined while respecting the ratio hs / es> F, with F = from 1 to 10. 7. Method according to one of claims 4 to 6, characterized in that the coefficients are determined while respecting the pitch / thickness ratio: where R (θ) is the radius, e the thickness of the hairspring with α [-] the minimum radius-thickness ratio, between 1 and 5 (limits included). 8. Method according to one of claims 2 to 7, characterized in that it consists in defining a second polynomial function, defining the thickness of the balance spring according to: 9. Method according to claim 8, characterized in that the thickness varies inversely proportional to the radius, with: 10. Method according to claim 9, characterized in that the thickness varies according to the function: while ensuring that 11. Method according to one of the preceding claims, characterized in that the coefficients are calculated by iteration and modeling. 12. Method according to one of claims 2 to 11, characterized in that the optimization of the coefficients is carried out by calculating the displacement of the center of gravity of the hairspring obtained and reducing this displacement. 13. Method according to one of claims 2 to 12, characterized in that the optimization of the coefficients is done by calculating the reaction force to the pivot obtained and by reducing the variations of this reaction force. 14. Spiral of a watch regulating organ obtained by the method according to one of claims 1 to 13. 15. Timepiece comprising a hairspring according to claim 14.