HK1190469B

HK1190469B - A method of increasing concentricity in use of a spiral hairspring mechanical timepiece and a hairspring

Info

Publication number: HK1190469B
Application number: HK14102922.3A
Authority: HK
Inventors: Ho Ching
Original assignee: 动力专家有限公司
Priority date: 2012-07-17
Filing date: 2014-03-25
Publication date: 2018-04-20

Description

Method for improving concentricity when using spiral spring mechanical watch and spiral spring

Technical Field

The present invention relates to a new design for a mechanical watch hairspring. More precisely, the invention relates to a method for designing such a balance spring for improving concentricity during operation of a mechanical watch, and also to a spiral balance spring for a mechanical watch.

Background

The balance spring is a core component in a mechanical watch. The balance spring is one of the two main components of the oscillator of the watch, while the other is the balance wheel. The oscillator provides a means of time adjustment through its simple harmonic motion.

The balance acts as an inertial element and engages with the inner end (inner terminal) of the spiral balance spring. The spiral geometry of the balance spring is typically provided in the form of an archimedean spiral, which typically has a constant pitch. The outer end (outer terminal) of the balance spring is usually fixedly attached to a fixing stud (stud).

Ideally, the balance spring provides a restoring moment to the balance that is proportional to the displacement of the wheel from the equilibrium position, and the linear second-order system of the balance can be described using equations of motion. The equilibrium position of the oscillator is defined as the angular position of the balance, such that when the balance is at rest, the net moment applied to the balance by the balance spring is zero. The resulting oscillator is isochronous, which means that the natural frequency of the oscillator is independent of its amplitude.

Isochronism is an important characteristic of the oscillators used in watches, as they require a periodic torque input from the escapement (escapement) to counteract the effects of wear from friction. Due to a number of factors, the torque provided by the escapement may not be constant, which directly affects the oscillator amplitude. In this way, an isochronous oscillator may provide more reliable and stable time adjustment.

Typically, the spiral turn (turning) in the balance spring of the watch is kept as concentric as possible when the balance rotates around its equilibrium position, for reasons including:

1. the centroid of the non-concentric balance spring will not be near the axis of rotation. When the balance rotates, the centre of mass may shift in some way to generate a radial force that is counteracted by the bearings, which may cause excessive friction;

2. during operation, the non-concentric balance springs also have a geometry deviating from the archimedes' spiral, which produces a non-isochronous non-linear second-order system; and

3. in some cases, a non-concentric balance spring may significantly deform its spiral geometry, causing adjacent turns to collide and break down with each other, as well as creating a non-isochronous system.

In the prior art, the hairspring concentricity can be improved by: the geometry of the inner and outer end curves is modified based on the Phillips and rossier mathematical models for balance spring design.

Breguet corporation (Breguet) has implemented such theory in its Breguet over coil (Breguet over-coil) for the outer end. The coil uses a modified outermost turn that protrudes and bends inwardly. However, this method can only maintain partial concentricity and making the shape required in the outermost turn increases manufacturing difficulty and cost.

Another prior art method for increasing the concentricity of the balance spring is to selectively reinforce certain parts of the balance spring strip, which was first proposed in the article entitled "unbent concentric flat balance springs (spiral plates concentric springs' ly) published by chronometric switzerland (Societe Suisse Chorometer)" by emille (Emile) and Gaston Michel (Gaston Michel) in 1958.

The authors found by trial and error: the hairspring concentricity can be improved by reinforcing the hairspring portion using the angular strip. The difficulties in using such a balance spring include the difficulty of mass production and such a balance spring remains an academic exploratory object.

Also in the prior art, jadeite (Patek philippie) uses a variable width strip in its Spiromax hairspring to reinforce the hairspring portion, thereby achieving a reinforcing effect. Baidar also studied and patented the design methodology by calculating the location of the centroid when the hairspring relaxes (patent number EP 03009603.6). By widening the outer side on the outermost turn of the balance spring, reinforcement can be achieved.

To keep the balance spring equal, the balance spring design needs to be insensitive to temperature variations. The stiffness of the young's modulus of a material typically varies slightly with temperature.

In a balance spring, the young's modulus determines the spring constant and ultimately the natural frequency of the oscillator. Any change in the young's modulus of the balance spring with temperature will have a negative effect on the ability of the oscillator to reliably adjust time.

The problem of temperature sensitivity of young's modulus in modern hairsprings can be widely solved by using a nivaloy alloy (Nivarox) in the manufacturing process of the hairspring. A nivaloy is a metal alloy whose young's modulus is very low but not zero in temperature change sensitivity.

The advent of micro-machining and the use of silicon in the watch industry over the past decade has introduced new methods to design and manufacture hairsprings with improved isochronism. This technique enables the manufacture of a balance spring based on the variation of the strip width to selectively improve the bending stiffness of the spring along its entire arc length.

Furthermore, this technique has the prospect of obtaining a balance spring whose young's modulus is completely insensitive to temperature variations. The process of making the young's modulus of the balance spring insensitive to temperature variations is defined as temperature compensation.

It is in fact only possible to manufacture balance springs with variable strip width using micro-machining techniques, which are capable of manufacturing any flat part with high precision.

Micro-machining techniques may be used to improve balance spring concentricity based on theory, numerical simulations, or experiments. Spiromax of jadeite is an example of a silicon hairspring having a portion of increased strip width in the outermost turn near the outer end, and arranged and sized to improve hairspring concentricity.

Micro-machining techniques may also allow a thin silica coating to be applied over the silicon hairspring for temperature compensation purposes. The young's modulus of silicon decreases with increasing temperature, while the young's modulus of silicon dioxide tends to increase.

Thus, by accurately applying a silica coating of the correct thickness to the silicon body, a composite balance spring can be produced in which the thermal sensitivity of the young's modulus of the two materials substantially cancel each other. This may result in a balance spring whose overall young's modulus is theoretically insensitive to temperature variations.

Disclosure of Invention

It is therefore an object of the present invention to provide a balance spring which overcomes or at least substantially ameliorates at least some of the disadvantages exhibited by the prior art.

In a first aspect, the present invention provides a method of improving concentricity when used in a spiral spring mechanical watch; said balance spring having an inner end portion for engagement with the collet and an outer end portion for engagement with the stud, a first indexing disc (lamb) portion extending from the inner end portion towards the outer end portion, and a reinforcing portion at the outer ring of the balance spring, said reinforcing portion having a second moment of cross-section different from that of said first indexing disc portion; such that the bending stiffness of the reinforcing portion is greater than the bending stiffness of the individual index plate portions; wherein the method comprises the steps of:

the second moment of cross-section of the first indexing disc portion and the reinforcing portion is modified by minimising a cost function of the overall rotational amplitude of the balance spring in use, wherein the cost function is related to the net concentricity of the balance spring.

The cost function may be the integral of the magnitude of the stud reaction force over the entire range of rotational amplitudes of the balance spring in use; or may be the maximum in magnitude of the stud reaction force over the full range of rotational amplitudes of the balance spring in use.

The cost function may also be the integral of the balance spring centroid location magnitude over the full range of rotational amplitudes of the balance spring in use, when the balance wheel angle is located at zero relative to the balance spring centroid; or the full range of the amplitude of rotation of the balance spring in use, the maximum of the values of balance spring centroid location when the amplitude of rotation is located at zero relative to the centroid of the balance spring.

Preferably, the second moment of cross-section of the first modified portion and of the reinforcing portion in the balance spring is based on: the position along the hairspring strip, the arc length of the hairspring modifications and a function determining the second moment variation of the cross-section along the hairspring modifications.

Preferably, the cross-sectional second moment variation is substantially constant.

The cross-sectional second moment variation may be based on a polynomial function, a trigonometric function, or a discontinuous function of two or more piecewise continuous functions.

The optimization algorithm used may be based on a gradient descent method that requires the calculation of the gradient of the cost function with respect to the design parameters.

In a second aspect, the present invention provides a spiral spring for a mechanical watch, the spiral spring having an inner end portion for engagement with a collet and an outer end portion for engagement with a stud, a first indexing disc portion extending from the inner end portion towards the outer end portion, and a reinforcing portion at an outer ring of the spring, the reinforcing portion having a cross-sectional second moment different from that of the first indexing disc portion; wherein the second moment of cross-sectional area of the first portion and the reinforcing portion is determined by the method of the first aspect.

Preferably, two or more spaced-apart indexing disk portions of a single indexing disk portion and reinforcing portion are rectangular in cross-section and all have the same width and the same height as each other.

Preferably, the single index pad portion and the reinforcing portion are formed of a first material, and further include an outer coating formed of a second material.

Preferably, the first material has a first young's modulus and the second material has a second young's modulus, the first and second young's moduli having opposite temperature dependence, and the single indexing disk portion and the reinforcing portion and the overcoat thickness are sized so that the elastic properties of the balance spring are insensitive to temperature variations.

Preferably, the first material is silicon and/or the second material is silicon dioxide.

The pitch of the individual indexing disk portions may be substantially constant and one of the indexing disk portions of the reinforcing portion has said pitch. The radially innermost indexing disk portion has the described pitch.

The pitch of a single indexing disk portion is preferably substantially constant and two adjacent indexing disk portions in the reinforcing portion are substantially equidistant from the path of said pitch.

Preferably, the spacing between two adjacent index disc portions in the reinforcing portion is substantially constant.

The reinforcing portion may be provided between two individual index plate portions. The single indexing disc portion and the innermost indexing disc portion of the reinforcing portion may have the same pitch.

The outermost index disk portion of the reinforcing portion may have the same pitch as an adjacent single index disk portion and the innermost index disk portion of the reinforcing portion may have the same pitch as an adjacent index disk portion of the reinforcing portion.

The reinforcing portion may be provided at an outer end portion of the balance spring, and each of the scale portions of the reinforcing portion has a terminal end.

The pitch of the adjacent individual index disc portions is preferably substantially constant and one of the index disc portions of the reinforcing portion has said pitch. Preferably, the innermost dial portion of the reinforcement portion has said pitch.

The outer dial portion of the reinforcement portion may be substantially shorter than the adjacent inner dial portion of the reinforcement portion. Alternatively, one of the indexing disc portions of the reinforcing portion may be substantially longer in length than the adjacent inner indexing disc portion of the reinforcing portion.

The reinforcing portion may comprise less than half of a helical turn.

Adjacent indexing disk portions of the reinforcing portion may be interconnected intermediate the ends of the reinforcing portion.

The two or more spaced-apart indexing disc portions of the single indexing disc portion and the reinforcing portion are preferably substantially coplanar.

This patent proposes a hairspring design based on one or more reinforced parts, so that the entire operating range of the oscillator is taken into account, typically in the range of-330 degrees to +330 degrees in terms of the balance angle.

The measure of concentricity may be a change in the position of the center of mass or a change in the reaction force at the stud over the entire operating range. This metric is used as a cost function for an automatic optimization algorithm that systematically varies the strip section parameters to achieve the maximum possible concentricity for a given hairspring geometry.

In a first further aspect, the present invention provides a spiral balance spring for a mechanical watch, said balance spring comprising:

an inner end portion and an outer end portion, a single indexing disc portion extending from the inner end portion toward the outer end portion; and

a reinforcing portion located at the outer ring of the balance spring and formed of two or more spaced-apart indexing disc portions such that the bending stiffness of the reinforcing portion is greater than the bending stiffness of a single indexing disc portion; and

wherein said reinforced portion of said balance spring has a stiffness to improve concentricity of turns about said axis of rotation during compression and expansion of said balance spring during oscillatory motion about said axis of rotation.

In a preferred embodiment, the first material is silicon and the second material is silicon dioxide.

The pitch of the individual indexing disk portions may be substantially constant and one of the indexing disk portions of the reinforcing portion may have said pitch. The radially innermost indexing disk portion may have said pitch.

The pitch of a single indexing disk portion may be substantially constant and two adjacent indexing disk portions in the reinforcing portion are preferably substantially equidistant from the path of said pitch.

The reinforcing portion may be provided between two individual index plate portions. Preferably, the single index plate portion and the innermost index plate portion of the reinforcing portion have the same pitch. The outermost index disk portion of the reinforcing portion may have the same pitch as an adjacent single index disk portion and the innermost index disk portion of the reinforcing portion may have the same pitch as an adjacent index disk portion of the reinforcing portion.

Preferably, the reinforcing portion is provided at an outer end portion of the balance spring, and each of the indexing disc portions of the reinforcing portion has a terminal end. Preferably, the pitch of the adjacent individual index disc portions is substantially constant and one of the index disc portions of the reinforcing portion has said pitch. Preferably, the innermost dial portion of the reinforcement portion has said pitch.

Preferably, the reinforcing portion comprises less than half of a helical turn.

In the present invention, a reinforcing portion may be used to improve hairspring concentricity if the size is suitably adjusted and positioned.

The invention allows substantially complete temperature compensation of a silicon hairspring having a silica coating, since each parallel leg of the plurality of spiral portions can maintain the same width as the other legs of the other spiral portions.

The present invention is easy to manufacture, thereby achieving a temperature compensation effect, since the thickness of silicon dioxide required for total temperature compensation varies according to the width of the silicon strip, and current manufacturing techniques only allow for a silicon dioxide coating of uniform thickness.

Drawings

Preferred embodiments of the present invention are described in further detail below by way of example and with reference to the accompanying illustrative drawings, in which:

figure 1 shows a schematic view of a conventional balance spring in a relaxed state; said balance spring having all parts except the outermost turns constituting an archimedes spiral of constant pitch;

figure 2 shows a schematic view of the conventional balance spring shown in figure 1 with the balance angle at-330 degrees;

figure 3 shows a schematic view of the conventional balance spring of figure 1 with the balance angle at +330 degrees;

figure 4 shows a schematic view of a balance spring according to the invention with two possible modifications of variable second moment of cross-section and of about 90 and 270 degrees from the outer end;

figure 5 shows a flow chart of an automatic optimization algorithm according to the invention in order to maximize hairspring concentricity;

figure 6 shows cost function history and optimization iterations according to the invention for hairspring concentricity for the case of one and two improvement sections;

FIG. 7 shows the reaction force history versus balance angle for the case of one and two modifications;

figure 8 shows the centre of mass change and balance angle in the case of one and two modifications;

figure 9 shows a variant of the balance spring with a modified portion in the case of a balance angle of-330 degrees;

figure 10 shows a variant of the balance spring with a modified portion in the case of a balance angle of +330 degrees;

figure 11 shows a variant of a balance spring with two modified portions, in the case of a balance angle of-330 degrees;

figure 12 shows a variant of a balance spring with two modified portions, in the case of a balance angle of +330 degrees;

figure 13 shows an embodiment of a double arm balance spring with improved parts possible with increased concentricity;

figure 14 shows a photographic image of an exemplary embodiment of a balance spring according to the present invention;

FIG. 15 shows a comparison of offset centroids relative to the embodiment shown in FIG. 14;

FIG. 16 shows a comparison of stud reaction forces with respect to the embodiment shown in FIG. 14;

figure 17 shows an example of a variant of an optimised Spiromax hairspring at zero degrees;

figure 18 shows an example of a variant of an optimised Spiromax hairspring at-330 degrees; and

figure 19 shows an example of a variant of an optimised Spiromax hairspring at +300 degrees.

FIG. 20 illustratively shows a cantilever structure having two beams connected in a parallel configuration;

FIG. 21a shows a cantilever structure with a single beam having a uniform cross-section;

FIG. 21b shows a cross-sectional view of the cantilever structure depicted in FIG. 21 a;

FIG. 22a shows a cantilever structure with two beams connected in a series arrangement and differing in cross-section;

FIG. 22b shows a cross-sectional view of the cantilever structure depicted in FIG. 2a through the first of the two beams;

FIG. 22c shows a cross-sectional view of the cantilever structure depicted in FIG. 21a through the second of the two beams;

figure 23a shows a cantilever structure with two beam sections connected in series, whereby one section consists of two beams connected in a parallel arrangement and the other section consists of a single beam;

FIG. 23b shows a cross-sectional view of the cantilever structure depicted in FIG. 23a through either beam;

figure 24 shows a first embodiment of a balance spring according to the invention;

figure 25 shows a multiple spiral portion arrangement of a further embodiment of a balance spring according to the invention;

figure 26 shows a multiple spiral portion arrangement of another embodiment of a balance spring according to the invention;

figure 27 shows a multiple spiral portion arrangement of a still further embodiment of a balance spring according to the invention;

figure 28 shows a multiple spiral portion arrangement of yet another embodiment of a balance spring according to the invention; and

figure 29 shows an alternative embodiment of a balance spring according to the invention.

Detailed Description

Referring to fig. 1, for illustrative and explanatory purposes, a simplified schematic diagram of a conventional balance spring 10 in a relaxed state, having a total of 13.5 turns, is shown.

The balance spring coil is made up of two parts, namely a body part 11a and an outer part 11 b. The body portion 11a forms an archimedes spiral with a constant pitch, with its inner end connected to the collet 12. The collet 12 is in turn rigidly connected to a balance wheel (not shown). The outer portion 11b has a significantly increased pitch to make room for the placement of the stud 13. All the portions 11a and 11b have a constant cross section.

Line 14 indicates the connection point between collet 12 and balance spring body portion 11a which enables the reader to better track the angle of rotation of collet 12.

As will be appreciated by those skilled in the art, conventional balance spring 10 is only one example of the many possible balance spring shapes, but this example will be used as a reference in the remainder of this document.

Referring to fig. 2, the conventional balance spring 10 shown in fig. 1 is shown in one orientation and is represented as balance spring 20, which is in a compressed deformed condition in which collet 21 has been rotated clockwise 330 degrees, which is a typical oscillation amplitude. As will be observed and understood by those skilled in the art, the overall size of the balance spring track has been reduced, but more importantly, the deformation is not concentric with the pitch on the side of the stud 22 which is much larger than the pitch on the opposite side.

Referring to fig. 3, conventional balance spring 10 shown in fig. 1 is shown deformed in the opposite direction to that shown in fig. 2 and is represented by balance spring 30. Balance spring 30 is in an expanded deformed condition in which collet 31 has rotated 330 degrees counter clockwise. As will be observed, the size of the overall balance spring trajectory has increased, but more importantly, the deformation is also not concentric with the pitch on the side of stud 32, which is much smaller than the pitch on the opposite side.

The lack of concentricity shown in fig. 2 and 3 may create additional friction when balance staff bearings (not shown in fig. 2 and 3) need to compensate for the centrifugal force created by the motion of the center of mass.

This loss of concentricity also creates a hairspring with a change in geometry that causes a change in the spring constant, causing the oscillator to become non-isochronous. Furthermore, in some cases the pitch of the thread on certain areas of the balance spring may become negative in the case of deformation, away from the stud 22 in the balance spring 20 and towards the stud 32 in the balance spring 30, which implies that the contact between adjacent turns will then cause damage. With reference to fig. 4, a schematic view of an embodiment of a balance spring 40 according to the invention is shown, for example said balance spring 40 having modified portions 41a and 41 b.

The isochronism of the balance spring can be improved by improving the bending stiffness of selected parts of the balance spring strip. One way to achieve this is to vary the cross-section of the strands and micro-machining techniques make manufacturing easier by improving the width of the strands. The balance spring may have one or more different modifications.

According to the invention, in order to create an automatic optimization algorithm for maximizing the hairspring concentricity, the first step is to clearly define the design parameters that can be varied to achieve the best results.

In the embodiment shown in fig. 4, each modified portion 41a or 41b requires at least three design parameters to define the modified portion geometry: improved second moment of area I_aThe arc length L of the modified portion_aAnd improving the positioning of the part theta_a。

Parameter I_aCan be defined as the ratio of the second moment of area compared to the rest of the balance spring. Parameter L_aMay be defined as the length of the modified portion or as an angular span in polar coordinates. Parameter theta_aThe measured arc distance or angular distance may be positioned in polar coordinates relative to the stud 42 or collet connection 43.

If the second moment of area I is improved_aIs a complex function of the arc length or angular span of the improvement section, then the number of parameters may be greater than three.

The function under consideration may be a continuous function such as a polynomial or trigonometric function, or a discontinuous combination of piecewise continuous functions. There is no theoretical upper limit to the number of different modified fractions. The second moment of area of the modified portion may be increased or decreased compared to the second moment of area of the remainder of the balance spring strip.

Referring to FIG. 5, a flow diagram of an optimization process according to the present invention is shown.

The automatic optimization algorithm may be designed to maximize balance spring concentricity by varying the above-mentioned design parameters defining the geometry of the one or more improvement sections.

At the heart of this is that typical optimization algorithms adjust design or system parameters to minimize or maximize a predefined cost function, which may be limited by certain constraints.

The cost function may be calculated via a computer model of the mechanism under consideration using the design parameters as inputs. The algorithm then evaluates whether the cost function is satisfactory. If not, the algorithm will adjust the design parameters based on a predefined set of laws; the new design parameters are used as input to the computer model to calculate a new cost function.

This loop is then repeated until the algorithm determines that the corresponding optimized design parameters used result in a satisfactory cost function. This process can be used to optimise the balance spring improvement for maximum concentricity.

In addition to the design parameters of the hairspring improvement section described above, the optimization algorithm requires a well-defined cost function reflecting the level of hairspring concentricity.

One possible measure is the degree of side shift (drift) of the balance spring's centre of mass over the oscillator's operating range. The side shift of the balance spring centre of mass is defined as the location of the balance spring centre of mass relative to where alpha equals zero, given the collet rotation angle alpha.

The variable s is the position of the arc along the sliver line. A(s) is the cross-sectional area at arc position s. The variables x (s, α) and y (s, α) define the x and y positions of the strip at the arc position s and the collet angle α.

The term L is the total arc length of the balance spring. X (α) and Y (α) are the centroids side-shifted in the X and Y directions, respectively, with respect to the centroid of the loose spring. Equations 1 and 2 only determine the centroid sideshift at a particular collet angle α.

A single metric J reflecting the side shift of the center of mass over the entire oscillator operating range can be determined by taking the equation from α_cwTo α_ccwIs defined by the integral of the value of the side shift, wherein α_cwAnd α_ccwTypically equal to-330 degrees and 330 degrees, respectively.

The cost function J can be described as the mean lateral shift of the balance spring centroid, the minimum of which is related to the maximum of the balance spring concentricity.

Since computer simulations of balance spring deformation for a single collet angle a may take several hours, it is generally not practical to calculate equation 3 as an integral.

However, the integral can be approximated by applying trapezoidal law of integration or another numerical integration method to a limited number of α.

In equation 4, the collet angle α is discretized in N evenly spaced values, which means that only N simulations are needed for the calculated J_approxAn approximation. A larger value of N indicates a more accurate approximation to the cost function.

As an alternative to integration of the centroid sidesway shift within the collet angle a, minimizing the maximum value of the centroid sidesway shift value may also be used to maximize balance spring concentricity.

Equation 5 essentially translates the optimization problem into a min-max type of problem, which may be easier to implement herein.

Another well-defined cost function that reflects the level of hairspring concentricity is the magnitude of the reaction force at the stud_cwAnd α_ccwThe magnitude of the reaction force of the stud therebetween is integer.

Variable R_x(α) and R_y(α) the stud reaction forces in the x and y directions, respectively, this merit function may also be described as the average stud reaction force, the minimum of which corresponds to the maximum of the hairspring concentricity.

The cost function from equation (6) can also be approximated by discretizing alpha into N evenly spaced values and then approximating the integral using trapezoidal rule.

The min-max alternative to integration may also be used as a measure of hairspring concentricity.

In essence, both centroid side shift and stud reaction force can be used to determine the level of hairspring concentricity in an automated optimization algorithm.

In order to minimize the cost function described above and thus maximize hairspring concentricity, the search algorithm needs to efficiently match the design parameter I_a、L_a、θ_a、I_b、L_b、θ_bEtc. to achieve optimization.

The subscripts a and b represent the first and second modified portions with additional possible modified portions.

Among the algorithms available for this purpose, the gradient descent method is known as one of the most efficient and popular methods.

When applied to a hairspring automatic optimization algorithm, the gradient descent method calculates the gradient of one of the cost functions J described above.

Subsequently, the design parameters are refined by taking steps in each iteration in the opposite direction to the gradient defined in equation 9. Assume that the vectors of design parameters are defined as follows:

the update rules for the design parameters are then defined by the following equations:

the subscript in the design parameter vector is the number of iterations, and the variable J is the step size.

Given enough iterations, such an update rule will bring the cost function closer to the local minimum. In the middle of the optimization process, the step length J can be adjusted according to the proximity to the local minimum.

It is generally not possible to obtain a gradient of the cost functionBecause the cost function J itself is the result of numerical simulation of the balance spring.

However, numerical differentiation techniques may be used to approximate the gradient of the cost function. However, the optimization time will increase significantly because the simulation needs to be run several times each time a numerical differential is performed iteratively.

The gradient descent method requires initial guessing of design parameters at the beginning of the optimization process. Close proximity to the initial guess of the solution can greatly reduce the optimization time.

One possible way to obtain a valid estimate of the initial guess is to perform a coarse brute-force search (coarse break-force search) within a reasonable range of design parameters. Brute force search is itself an independent optimization algorithm that computes a cost function over a range of design parameters, resulting in a minimum cost function.

To obtain reasonably accurate results, brute force searches alone require an impractically large number of hairspring simulation experiments. However, a rough preliminary review of the design parameter ranges using brute force searching may result in an effective initial guess, which may be further refined using gradient descent. The result is a reduction in the net amount of optimization time during the use of any single optimization algorithm alone.

Other automatic optimization algorithms may be used to optimize the hairspring concentricity design, including but not limited to genetic algorithms, memory based algorithms, and simulated annealing algorithms. In general, all optimization algorithms will work with the cost function and design parameters described above. While each of the other algorithms has advantages and disadvantages, respectively, most algorithms are more difficult to implement than the gradient descent method.

Referring to fig. 6, the results of the optimization history for the gradient descent method of hairspring concentricity are shown. The x-axis and y-axis are the iteration number and cost function history, respectively.

In this case, the cost function is defined as the integral of the stud reaction force over a range of internal stud angles α from-330 degrees to +330 degrees (which is the standard operating range for a typical oscillator).

One curve shows the optimization history of a balance spring with a single reinforced portion at the outermost turn, and the other curve shows the optimization history of a balance spring also with two reinforced portions at the outermost turn.

Both curves shown are eventually stable at local minima in the cost function, and the design with two reinforced portions is significantly better than the design with one reinforced portion.

Referring to fig. 7, the variation in magnitude of the stud reaction force over the range of collet angles a is shown for the following balance spring:

(i) there is no reinforcing portion and there is no reinforcing portion,

(ii) having an optimized reinforcement part, an

(iii) With two optimized reinforcement sections.

It will be seen from fig. 8 that the reaction force at the stud of the balance springs (ii) and (iii) of the optimized portion is significantly lower than that of the balance spring (i) with constant second moment of area.

Furthermore, the results show that between-330 degrees and +330 degrees (typical amplitudes in mechanical tables), the stud reaction force using the "two" optimized reinforcement part is very low.

Referring to fig. 8, the magnitude of the change in centroid side shift for the same three balance spring designs over a is shown.

The figure shows consistently: for almost all values of alpha, the stud reaction force and the centroid sideshift values are reduced by an automatic optimization algorithm. The best results are obtained with a balance spring with two optimised stiffening portions, due to the greater degree of freedom in design.

With reference to figures 9 and 10, it is shown that the concentricity of both balance springs 90, 100 is improved by the automatic optimization algorithm according to the invention, which shows the deformed geometry of a balance spring with an optimized reinforcement portion.

The collet of balance springs 90 and 100 are rotated 330 degrees clockwise and counter clockwise respectively. The concentricity enhancement here is more visually noticeable and clearly illustrated when compared to the concentricity of fig. 2 and 3.

Fig. 11 and 12 show the deformed geometry of balance springs 110, 120 with two optimized reinforcing portions. The collet of balance springs 110 and 120 are rotated 330 degrees clockwise and counter clockwise respectively. In the hairspring shown with an optimized reinforcement, the concentricity is further improved compared to the concentricity of fig. 9 and 10.

The higher concentricity achieved by the above described automatic optimization algorithm allows the implementation of a new type of balance spring with multiple arms.

Referring now to fig. 13, there is shown an example of a multiple arm balance spring 130 having two arms 131a and 131 b.

Two arms 131a and 131b extend from the central post 132. Arms 131a and 131b terminate at outer ends 132a and 132b, respectively. Double-arm balance spring 130 is axisymmetrical with arm 131a, and arm 131a is identical with arm 131 b.

Referring to figure 14 there is shown a photographic image of an embodiment of a balance spring 200 according to the present invention suitable for optimisation according to the present invention. Balance spring 200 includes an inner end portion 210 for engagement with collet 220, and an outer end portion 230 for engagement with start point 240, a first indexing disc portion 250 extending from inner end portion 210 towards outer end portion 230, and a reinforcing portion 260 located at the outer turn of balance spring 200.

In this embodiment, the reinforcement portion is a bifurcated portion including an inner dial 262 and an outer dial 264, and a strut 266 extending therebetween.

The reinforcement portion 260 is reinforced by increasing the second moment of area which is increased by spacing the bifurcated dividing discs 262, 264 which together increase the second moment of area in this portion of the balance spring.

As will be understood and appreciated by those skilled in the art, by spacing the two indexing disks 262 and 264, the second moment of area of the bifurcated portion will correspondingly increase the bending stiffness.

It should be noted that the cross-sectional dimensions of both the first indexing disk portion and the reinforcing portion are the same, and therefore, each of the two indexing disks 262 and 264 in both the first indexing disk portion and the reinforcing portion have the same cross-sectional area.

Thus, since the first indexing disc portion and the reinforcing portion are formed of the same material and have the same cross-sectional area, and since the young's modulus is constant because the balance spring is made from a single piece of material, the effect of temperature on the various portions of the balance spring is the same with respect to the change in young's modulus that occurs in response to a change in temperature.

Balance spring 200 in the present embodiment is formed by a micro-machining technique that is high in dimensional accuracy when producing such an article or product.

The micro-machining technique in this embodiment allows temperature insensitivity by using a first material with a first young's modulus of the balance spring deformation and a second material as the coating material with a second young's modulus, said first young's modulus and said second young's modulus having opposite temperature dependencies, so that the size of the outer coating can be suitably adjusted and the outer coating can have a thickness such that the elastic properties of the balance spring are insensitive to temperature variations.

A suitable material for forming a balance spring according to the present embodiment is silicon with a silicon dioxide layer.

In order to improve the concentricity and reduce the variation of the mass effect during the expansion and contraction of the balance spring, a reinforcing portion is included in the balance spring.

Furthermore, the size of the reinforcing portion may be optimised according to the method of the invention to provide suitable stiffness, minimising deflection of the balance spring during rotation and reducing mass deflection. This can be achieved by using the above described minimization of the cost function in relation to the present invention.

It can be shown that, given certain conditions, the second moment of area of the divergent portion can be designed to be equal to the second moment of area of the stiffening portion of increased width.

For example a balance spring of standard width and height b0 and h respectively. The two balance spring portions are compared. One section has a single strip with a larger width and n times b 0. The other portion has two diverging strips each having a width equal to the standard value b0 and separated by a distance d measured from the centerline of each strip.

Assuming that d remains constant for all bifurcations, d can be set using the parallel axis theorem so that the second moment of area relative to the z-axis is equal for the widened and bifurcated portions. The result d is calculated as follows:

it should be noted that if n is equal to 2, the bifurcated strips touch each other and become one widened strip.

The optimization algorithm can be easily adapted to the widened portion and the bifurcated portion. In the former case, the partial width is used as one of the design parameters to be varied in the optimization algorithm. In the latter case, the distance of the forking bars is used as one of the design parameters to be varied. It should be noted that by using equation (12), the two methods can be used interchangeably.

It should be noted that further details and description of the balance spring of the invention will be further described below with reference to fig. 20 to 29, in which balance spring 200 is an embodiment of the same.

With reference to fig. 15, the centroid shift generated as a function of rotation between-300 and 300 degrees (typical range of a balance spring) is shown, with a comparison between one, two and a Spiromax balance spring according to the prior art.

It will be seen that the two-part optimised reinforcement according to the invention has a reduced centre of mass offset compared to one optimised reinforcement and a Spiromax hairspring.

With reference to fig. 16, a comparison is shown between the reaction forces at the starting point of the balance spring in the overall range of motion between-330 degrees and 330 degrees, in which the second moments of area of the one, two and Spiromax balance springs are constant.

It should be noted that the single optimized reinforcement part balance spring, whose stiffness is optimized according to the invention, has a stud reaction force that is less than that of a Spiromax balance spring.

Importantly, however, it appears that the balance spring according to the invention, with two optimised reinforcing portions, has a significantly lower stud reaction force, which is almost zero compared with the other balance spring.

Stud reaction indicates reaction at the collet bearing and those skilled in the art will appreciate that this reduces friction and wear at the collet and therefore improves life.

Those skilled in the art will appreciate that a balance spring according to the invention with two optimised reinforcing portions will result in a balance spring with a small mass offset and a very low reaction force at the stud.

The concentricity of such a balance spring according to the invention is thus improved throughout the angular movement, and accordingly an isochronism improved balance spring for watches is provided.

Referring to figures 17, 18 and 19, there is shown a modification of a Spiraomax type balance spring at 0 degrees, -330 degrees and +330 degrees respectively. It should be noted that there is a distortion between the windings exhibiting a mass shift which, in use, reduces concentricity and increases the reaction forces at the collet and stud, thus making the isochronism of the balance spring worse than that of the balance spring according to the invention (especially compared with a balance spring having two optimised reinforcing portions).

Although hairspring designs with three or more upper arms are more complex to implement, in theory these hairspring designs may have sufficient hairspring concentricity.

The axisymmetric layout of the multi-arm balance spring may further improve isochronism, since any radial force transmitted to the collet through one arm will be cancelled out by the net radial force transmitted through the other arm. If the effect of gravity is neglected, the balance bar bearing is theoretically not subjected to any radial forces, so that the oscillator is substantially not subjected to bearing friction.

However, multi-arm hairsprings are only feasible with a highly concentric design, since the traditional hairspring arms tend to enter each other during deformation, increasing the possibility of collision between adjacent arms, even for extremely small balance angles.

The present invention provides a balance spring for watches which can be manufactured with high dimensional and mechanical accuracy by using micro-machining techniques.

The concentricity of the balance spring according to the invention is improved by providing a reinforcing location which reduces the mass excursion of the spring about the axis of rotation during use, this reduction in excursion reducing the radial inertial effects of the spring on acceleration and movement and hence the radial forces at the central bearing.

Furthermore, the isochronism of the balance spring according to the invention is improved, since it becomes less sensitive to temperature.

This has the effect of increasing the isochronism of the balance spring and oscillator mechanism, thereby providing a more appropriately positioned balance spring for timing purposes.

Further, the reduction of the radial force also reduces the friction on the bearings located at the center of the oscillator assembly, and because the friction affects the motion of the oscillator, the reduction also increases the isochronism and, in addition, reduces wear and damage to the bearings.

This results in a hairspring oscillator mechanism that has an increased lifetime and requires less maintenance and repair due to component wear. The increase in concentricity during movement increases isochronism due to the reduction in the non-linear second order system, and reduces the tendency of the turns of the balance spring to engage one another during compression and expansion, where the engagement and collision of the middle coil with the adjacent coil changes the mechanical characteristics of the balance spring, which can have a significant adverse effect on isochronism.

Furthermore, the collision and impact of adjacent intermediate turns may cause damage to the balance spring and may fail, reducing its reliability and increasing the costs due to maintenance and repair.

This aspect of the invention will be further described below with reference to fig. 20 to 29, with reference to balance spring 200 described above with reference to fig. 14, of which balance spring 200 is an embodiment.

To describe the manner in which the features of the invention can be characterized, an explanation is provided with reference to fig. 20 to 23c, using the theory of solid mechanics, in particular using the statics of the cantilever, which uses the euler-bernoulli beam formula.

Although this formula and the accompanying theory are strictly based on a straight cantilever model, the formula also provides reasonably accurate results for spiral hairsprings with elongated strips, since the majority of the restoring moment of a typical hairspring comes from the bending of the hairspring strip.

Therefore, the euler-bernoulli beam formula is widely used in the watch industry to estimate the bending stiffness of a balance spring.

Referring to fig. 20, a cantilever structure 310 is shown comprised of two beams 311A, 311B connected in parallel. It is emphasized that the term "parallel" is used throughout the specification, the understanding of which should be extended to the connection of structural elements in a parallel arrangement, which elements are not necessarily parallel in a strict geometric definition.

Analysis of this cantilever structure 310 shows its effect on the bending stiffness of the structure, defined as the ratio between the applied moment and the resultant deflection of the beam.

The right end of the cantilever structure 310 has a clamped boundary condition 315 that resists displacement and rotation. The left end of the cantilever structure 310 is free, but has a plate 314 adhered to the beams 311A, 311B to ensure that they bend together and do not translate or rotate relative to each other. The two beams 311A, 311B are each L in length, B in width, and h in height. The two beams 311A, 311B are also separated by a constant distance d as measured from their centerlines 312A, 312B. The cantilever structure 310 also has a neutral axis 313, which in this case is equidistant between beam centerlines 312A and 312B.

The cantilever structure 310 has greater bending stiffness when compared to a single cantilever beam of the same length and cross-section as each of the beams 311A, 311B for two reasons:

(i) the cantilever structure 310 has a cross-sectional area larger than a single beam; and

(ii) the two beams 312A, 312B of the cantilever structure 310 are positioned very far from the neutral axis 313, thereby increasing the second moment of area and thus providing greater bending stiffness.

Bending stiffness k of the individual beams 311A, 311B₁The calculation can be performed using the following Euler-Bernoulli Beam equation, in which Young's modulus is represented by E

The distance d is redefined as nb, where n is the ratio of d to b, in order to simplify the equation. In contrast, the bending stiffness k of the cantilever structure 310₂The calculation can be further performed using the parallel axis theorem as follows:

assuming that the cantilever structure 310 is flat, the value of n must be greater than 1 or the two beams 311A, 311B will overlap.

As will be understood by those skilled in the art, k is for a flat cantilever structure 310₂Is always greater than k₁. In fact, defined as k_2,minK of (a)₂Is k₁Eight times the value.

In accordance with the present invention, one skilled in the art will appreciate that k can be set by adjusting the length L of the strip₁<k₂<k_2,mmWherein the length of the adjustment strip can be implemented using existing micro-machining techniques.

Equations (13) and (14) show the effect of increasing the bending stiffness of the cantilever structure 310 by arranging the two beams 311A, 311B in parallel.

The parallel axis structure may also be applied to the cantilever structure 310 and the same conclusion is drawn that the cantilever structure 310 has more than two beams 311A, 311B in a parallel arrangement.

The same conclusions can be drawn from a cantilever structure 310 with parallel beams 311A, 311B even when the beam distance d is not constant, but deriving the bending stiffness of the structure 310 would be more complex and require calculus or like techniques in the calculation.

To illustrate the advantages of the parallel bar design in temperature compensation, the effect on the young's modulus of the silicon dioxide coating on the silicon beam is described and illustrated with reference to fig. 21a and 21 b. This illustrative analysis considers only the sensitivity of young's modulus to temperature changes and does not include the effects of thermal expansion.

Since the effect of temperature on young's modulus is several orders of magnitude greater than the effect of thermal expansion, only the use of the effect on young's modulus is considered to produce reasonably robust and substantially identical results.

Referring to fig. 21a and 21b, a cantilever structure 320 having a single beam 321 of uniform cross-section is shown using all reference coordinates based on the right-hand rule of solid mechanics. The beam 321 has a width b, a height h, and a length L. The left end 322 is free and the right end 323 is clamped. Cross section 324 of beam 321 shows a silicon core 325 with a silicon dioxide coating 326 of thickness ζ.

The young's modulus of silicon and silicon dioxide can be approximated by a linear function with respect to temperature change, as follows:

E_Si(ΔT)=E_Si,0(1+e_SiΔT) (15)

in equations (15) and (16), E_si,0、E_SiO2,0、e_siAnd e_SiO2Are constant and at is a temperature change. Constant E_si,0、E_SiO2,0、e_siAnd e_SiO2Values of about 148GPa, 72.4GPa, -60ppm/K and 215ppm/K at room temperature, respectively.

Constant e_SiAnd e_SiO2Opposite sign, and this indicates that as temperature increases, the young's modulus of silicon decreases, while the young's modulus of silicon dioxide increases.

Assuming that the cantilever structure 20 in fig. 21a and 21b is subjected to a moment on the y-axis, the equivalent young's modulus of the composite beam 321 can be calculated as follows:

with respect to Δ T derivation and substitution into equations (15) and (16), equation (5) becomes as follows:

equation (18) describes E_eqSensitivity with respect to Δ T, and in order to achieve total temperature compensation, it needs to be set to zero by changing ζ.

For a wide range of aspect ratios, defined as b: h, the optimum zeta: b ratio is completely stable at about 6% for a cross-section with a silicon core and a silica coating. The results show that with a silica coating, an overall temperature compensation is theoretically possible for a silicon balance spring of uniform cross section.

The same conclusion cannot be drawn for a balance spring with a variable cross-section. This can be demonstrated by a simple cantilever example with two different cross sections.

Referring to fig. 22a, 22B and 22c, a cantilever structure 330 is shown with two beams 311A, 331B in series, the two beams 311A, 331B having different cross-sections 334A, 334B. All reference coordinates are based on the right hand rule according to established solid mechanics.

The beam 331A has a free end 332 at its left end and engages the beam 331B at its right end 333. Beam 331B is attached to beam 331A at its left end 333 and has a clamped boundary condition 334 at its right end. Beam 331A has a width b_AHeight of h_AAnd a length L_AAnd the width of the beam 331B is B_BHeight of h_BAnd a length L_B。

Cross section 335A of beam 331A shows a silicon core 336A with a silicon dioxide coating 337A having a thickness ζ, and cross section 335B of beam 331B shows a silicon core 336B with a silicon dioxide coating 337B having a thickness ζ. Since current micro-machining techniques cannot achieve variable coating thicknesses on the same part, both cross-sections 335A, 335B have the same silica coating thickness.

Assuming that the cantilever structure 330 is subjected to a moment on the y-axis, the equivalent young's modulus of each of the beams 331A, 331B can be calculated as follows:

E_eq,A(ΔT)=E_A,0(ζ)[1+e_A(ζ)ΔT](19)

E_eq，B(ΔT)=E_B,0(ζ)[1+e_B(ζ)ΔT](20)

it should be noted that E_eq,A(Delta T) and E_eq,B(Δ T) corresponds to the equivalent young's modulus of beams 331A and 331B, respectively. Item E_A,0(ζ)、E_A,0(ζ)、e_A(ζ) and e_B(ζ) can be expanded according to equations (15), (16), and (17) as follows:

the bending stiffness of each of the beams 331A, 331B can be calculated using the euler-bernoulli beam equation as follows:

K_A(ΔT)=K_A,0(ζ)[1+e_A(ζ)ΔT](25)

K_B(ΔT)=K_B,0(ζ)[1+e_B(ζ)ΔT](26)

it should be noted that K_A(Delta T) and K_B(Δ T) is the bending stiffness of beams 331A and 331B, respectively. Item K_A,0(ζ)、K_B,0(ζ)、k_A(ζ) and k_B(ζ) may be developed as follows:

since the two beams 331A, 331B are connected in series, their equivalent stiffness can be calculated as follows:

with respect to Δ T derivation and substitution into equations (25) and (26), equation (17) becomes as follows:

equation (30) describes K_eqSensitivity with respect to Δ T, and coefficient N₂、N₁、N₀、D₂、D₁And D₀The definition is as follows:

N₁(ζ)=2K_A,0K_B,0e_A(ζ)e_B(ζ)(K_A,0+K_B,0) (32)

D₂(ζ)=[K_A,0e_A(ζ)+K_B,0e_B(ζ)]²(34)

D₀(ζ)=(K_A,0+K_B,0)²(36)

to achieve total temperature compensation, the silica coating thickness must be set such that equation (30) is zero for all Δ T values. Assuming that the denominator of equation (30) is non-zero, then the numerator of equation (30) need only be set to zero for all Δ T values.

However, the numerator of equation (30) is a quadratic function of Δ T, which means that there are only two values of Δ T, and the numerator may be equal to zero. Equation (30) demonstrates that: for a cantilever structure 330 with two beams 311A, 331B in series and of different cross-sections, total temperature compensation is not possible.

Performing a similar analysis on a cantilever structure with a discrete or continuously variable cross-section would lead to the same conclusion, which proves that the total temperature compensation is theoretically impossible to achieve for a silicon balance spring with a variable cross-section.

Instead, in theory, total temperature compensation is feasible for a balance spring with parallel strips.

Referring to fig. 23a and 23b, a cantilever structure 340 having two beam portions 341, 342 in series is shown. The beam portion 342 has two beams 342A, 342B connected in a parallel arrangement. All reference coordinates are based on the right-hand rule.

The beam 341 has a free end 343 at its left end and is attached to the beam portion 342 at its right end 344. The beam portion 342 has two beams 342A, 342B connected in a parallel arrangement, and the entire beam portion 342 is attached to the beam 341 at its left end and has a clamped boundary condition 345 at its right end. All beams 341, 342A, 342B have the same cross-section 346 with a cross-sectional width B, a height h and a silica coating thickness ζ. The beam 341 has a length L_AAnd the beams 342A, 342B have a length L_B。

Due to the parallel arrangement, the bending stiffness of the beam portion 342 is greater than the bending stiffness of the beam 341. By adjusting the length L of the beam portions 341, 342_AAnd L_BAnd the distance d between beams 342A and 342B, the cantilever structure 340 may be designed such that it has the same bending stiffness as the cantilever structure 330 in fig. 22A and 22B.

However, since each beam 341, 342A, 342B has the same cross-sectional geometry, the ratio of the silica coating thickness to the beam width, ζ: B, is the same for all beams 341, 342A, 342B. The total temperature compensation of either beam portion 341, 342 is the same for the other beam portion. This proves that the total temperature compensation of a silicon balance spring with parallel strips according to the invention is theoretically possible.

With reference to fig. 24, a first embodiment of a balance spring 350 according to the invention is shown, said balance spring 350 having a plurality of spiral portions 355 with parallel branches 355A, 355B of rectangular section, wherein a single outer end 357 is connected to a stud 358.

Balance spring 350 is made up of a collet 351 at the center. The inner main bar 353 spirals outwardly from an inner end 352 attached to the collet 351 until reaching a hairspring portion 355 which is split into two parallel branches 355A, 355B at a point 354A.

The two branches 355A, 355B are rejoined together at point 354B into a single outer main bar 356 until they reach a fixed and clamped outer end 357. The bending stiffness of the balance spring portion 355 with the parallel branches 355A, 355B is greater than the bending stiffness of the inner and outer main bars 353, 356. An automatic design optimization algorithm such as the gradient method can maximize the concentricity of balance spring 350 by using the length and displacement of portion 355 and the distance between branches 355A and 355B.

To further provide for variation in design parameters, the distance between branches 355A and 355B may vary along the length of portion 355. For example, branches 355A, 355B may diverge and converge, it being understood that the available space may be limited to allow the coil spring to contract and expand without adjacent turns contacting each other and without the spring contacting other elements of the escapement.

It will therefore be appreciated that the balance spring 355 in this embodiment may be of any size and shape and may be placed anywhere with sufficient clearance, depending on the original balance spring geometry.

However, parallel branches 355A, 355B with a substantially constant separation distance are generally preferred, thereby facilitating ease of calculation and optimization of the spring characteristics.

With reference to figures 25, 26 and 27, three further embodiments of a balance spring according to the invention are shown, having a plurality of spiral portions with two parallel branches. As will be appreciated by those skilled in the art, these embodiments can be readily extended to include multiple helical portions having more than two parallel branches.

With reference to fig. 25, a multiple helix portion arrangement 360 of a further embodiment of a balance spring according to the invention is shown, in which two parallel branches 363a363B suddenly branch off from a single branch of two adjacent single helix portions 361a361B of the balance spring and then suddenly converge to another single branch.

Referring to fig. 26, there is shown a plurality of spiral segments 370 of another embodiment of a balance spring according to the invention. The left main stripe 371A is smoothly connected to one of the parallel branches 373A, which in turn is smoothly connected to the right main stripe 371B.

The parallel branch 373A abruptly branches from the left main stripe 371A at the intersection 372A and then abruptly converges to the right main stripe 371B at the intersection 372B.

With reference to fig. 27, a plurality of spiral segments 380 of a still further embodiment of a balance spring according to the present invention is shown. The left main bar 381A is smoothly connected to one of the parallel branches 383B.

The parallel branch 383A abruptly branches off from the left main strip 381A at an intersection point 382A and then smoothly connects to the right main strip 381B. Parallel branch 383B abruptly converges to right main bar 381B at intersection point 382B.

Referring to fig. 28, a layout of a plurality of spiral segments 390 is shown, including a support bar (strut) 394, according to yet another embodiment of the present invention.

The parallel branches 393A, 393B are connected to the main bars 391A, 391B on the left and right side by intersections 392A, 392B, respectively.

Because the entire plurality of helical portions 390 are curved, the parallel branches 393A and 393B may be curved with slightly different radii of curvature. Depending on the geometry of the balance spring and the magnitude of the bending, parallel branches 393A and 393B may be urged toward each other and may contact each other. The support bar 394 prevents this from occurring and if the width of the bar 394 is much less than the length of the helical portion 390, the bar 394 has minimal effect on the statics of the plurality of helical portions 390.

It will be appreciated that more than one strut 394 may be used depending on the geometry, shape, size and application of the balance spring.

With reference to fig. 29, an alternative embodiment of a balance spring 400 according to the invention is shown.

The balance spring design has a collet 401 at its center. The main bar 403 has an inner end 402 connected to the collet 401 and spirals outward until it reaches a plurality of helical portions 405 at intersections 404. The main strip 403 then splits into two parallel branches 405A and 405B, which separately terminate in fixed and clamped outer ends 406A, 406B, respectively, as opposed to the parallel branches 455A, 455B rejoining at the outer ends in the embodiment depicted in fig. 24.

Those skilled in the art will appreciate that this embodiment will also achieve enhanced reinforcement near the outer ends in accordance with the present invention, although the two parallel branches 405A and 405B will not repolymerize.

With respect to silicon hairsprings manufactured by micro-machining techniques, the disadvantage of the prior art is that a more freedom of design to improve concentricity and the desire for total temperature compensation cannot be achieved simultaneously.

Micromachining techniques are generally limited to the fabrication of planar components. Although micro-machining techniques can theoretically produce a balance spring with breguet type coils with multiplied overlapping layers, such manufacturing capability is currently unreliable and at least adds significant additional complexity to the manufacturing process.

The balance spring according to the invention provides improved concentricity by providing a reinforcing location which reduces the mass deflection of the spring about the axis of rotation during use, which reduces the effect of radial inertia of the spring due to acceleration and movement, thereby reducing radial forces at the central bearing.

While the invention has been described with reference to examples or preferred embodiments described above, it will be understood that those are examples to assist understanding of the invention and are not limiting. Variations or modifications, and improvements made thereon, which are obvious or trivial to persons skilled in the art, should be considered as equivalents of this invention.

Claims

1. A method of improving concentricity when using a spiral spring mechanical watch, characterized by: the balance spring having an inner end portion for engagement with the collet and an outer end portion for engagement with the stud, a first indexing disc portion extending from the inner end portion towards the outer end portion, and a reinforcing portion at the outer ring of the balance spring, the reinforcing portion having a cross-sectional second moment different from that of the first indexing disc portion; such that the bending stiffness of the reinforcing portion is greater than the bending stiffness of a single index plate portion; the method comprises the following steps:

improving the second moment of cross-section of the first indexing disc portion and the reinforcing portion by minimising a cost function of the overall rotational amplitude of the balance spring in use, the cost function being related to the net concentricity of the balance spring;

the second moment of cross-section of the first indexing disc portion and reinforcing portion modified in the balance spring is based on: the position along the hairspring strip, the arc length of said modified portion of said hairspring, and a function determining the second moment variation of said cross-section along said modified portion of said hairspring.

2. The method of claim 1, wherein: the cost function is the integral of the magnitude of the stud reaction force over the full range of the rotational amplitude of the balance spring in use.

3. The method of claim 1, wherein: the cost function is the maximum value of the magnitude of the stud reaction force over the entire range of the rotational amplitude of the balance spring in use.

4. The method of claim 1, wherein: the cost function is the integral of the magnitude of the rotational amplitude of the balance spring in use, when the balance wheel angle is positioned zero with respect to the centre of mass of the balance spring.

5. The method of claim 1, wherein: said cost function is the maximum of the magnitude of said rotation amplitude of the balance spring in use, when said rotation amplitude is positioned zero with respect to the center of mass of the balance spring.

6. The method of claim 1, wherein: the variation of the second moment of the cross-sectional area is constant.

7. The method of claim 1, wherein: the variation of the second moment of the cross-sectional area is based on a polynomial function.

8. The method of claim 1, wherein: the variation of the second moment of the cross-sectional profile is based on a trigonometric function.

9. The method of claim 1, wherein: the change in the second moment of cross-sectional area is a discontinuous function based on a combination of two or more piecewise continuous functions.

10. The method of claim 1, wherein: the optimization algorithm used is based on a gradient descent method which requires the calculation of the gradient of the cost function with respect to the design parameters.

11. A spiral balance spring for a mechanical watch, characterized in that: the spiral spring having an inner end portion for engagement with the collet and an outer end portion for engagement with the stud, a first indexing disc portion extending from the inner end portion towards the outer end portion, and a reinforcing portion at the outer ring of the spring, the reinforcing portion having a cross-sectional second moment different from that of the first indexing disc portion; the second moment of cross-section area of the first index plate portion and the reinforcement portion is determined by the method of any one of claims 1 to 10.

12. The spiral spring according to claim 11, wherein: the single indexing disk portion and two or more spaced apart indexing disk portions of the reinforcing portion are rectangular in cross-section and all have the same width and the same height as each other.