CN103543630B - Method for improving concentricity when using spiral spring mechanical watch and spiral spring - Google Patents
Method for improving concentricity when using spiral spring mechanical watch and spiral spring Download PDFInfo
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- CN103543630B CN103543630B CN201310300281.8A CN201310300281A CN103543630B CN 103543630 B CN103543630 B CN 103543630B CN 201310300281 A CN201310300281 A CN 201310300281A CN 103543630 B CN103543630 B CN 103543630B
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Abstract
A method and spiral spring for improving concentricity when using a spiral spring mechanical watch; 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; 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 invention is easy to manufacture, the reinforcement can be used to improve the concentricity of the hairspring, and the hairspring can also realize the temperature compensation effect.
Description
Technical field
The present invention relates to a kind of new design for stem-winder hairspring.It more particularly relates to which a kind of is in machine
Tool table improves the hairspring design method of concentricity during running, further relate to the hairspring for stem-winder.
Background technology
Hairspring is a core component in stem-winder.Hairspring be table oscillator in one of two critical pieces, it is and another
One is escapement（balance wheel）.Oscillator provides the component of time adjustment by its simple harmonic motion.
Escapement be used as inertance element, and with the inner of helical hair spring（inner terminal）Engagement.The spiral shell of hairspring
Revolve geometry generally in the form of spiral of Archimedes to provide, the spiral of Archimedes generally has constant spiral shell
Away from.The outer end of hairspring（outer terminal）Generally fixedly it is attached to fixed stud（stud）On.
Ideally, hairspring provides the restoring moment being directly proportional to displacement of the wheel away from equilbrium position to escapement, and
The linear second-order system of escapement can be described using the equation of motion.The equilbrium position of oscillator is defined as the angle position of escapement
Put so that when escapement is static, when to be exactly the net torque that is applied on escapement of hairspring be zero.When the oscillator of gained is grade, this
Represent that the natural frequency of oscillator is unrelated with its amplitude.
Deng when be oscillator used in table a key property because table needs to come from escapement（escapement）
Regular torque input so that offset friction produce loss influence.Due to many factors, the torque that escapement is provided may
It is not constant, this directly can produce influence to oscillator amplitude.So, oscillator when waiting can provide more reliable and more steady
Fixed time adjustment.
Generally, due to following reason, when escapement rotates around its equilbrium position, the spiral in the hairspring of table is turn-taked
（turning）Keep as far as possible with one heart, the reason includes：
1st, the barycenter of nonconcentric(al) hairspring will not be near rotary shaft.When escapement rotates, barycenter can be in some way
Skew, to produce the radial load offset by bearing, this can cause excessive friction；
2nd, during running, nonconcentric(al) hairspring also has the geometry for deviateing spiral of Archimedes, and this can be produced
Nonlinear second-order system when non-etc.；And
3rd, in some cases, nonconcentric(al) hairspring can be such that its helical geometry significantly deforms so that adjacent turn
Circle mutually collision and breaking-up, and system when producing non-etc..
In the prior art, hairspring concentricity can be improved in the following manner：Based on the phenanthrene designed for hairspring
Li Pusi（Phillips）With Ross that（Lossier）Mathematical modeling, the geometry to inner curve and overcoil is carried out
Improve.
Breguet company（Breguet）Coil is crossed in its Breguet for being used for outer end（Breguet over-coil）It is middle to implement
Such theory.The coil of crossing is turn-taked using a kind of improved outermost, and this is turn-taked inwardly projecting and bent.However, such a side
Method only can with holding part with one heart, and be made outermost turn-take needed for shape can increase manufacture difficulty and cost.
Another method for improving hairspring concentricity is some parts optionally to hairspring bar in the prior art
Reinforced, this method is first in 1958 by Amire（Emile）With Garstang, John meter Xie Er（Gaston Michel）Written by
By Chronometrie Switzerland Co., Ltd（Societe Suisse Chronometrie）That delivers is entitled " unbending concentric
Flat hairspring（Spiraux plats concentriques sans courbes'ly(Concentric flat
hairsprings without curves)）" article in propose.
Author is had found by repetition test：Can be by being reinforced same to improve hairspring to the hairspring part using angle bead
Heart degree.Include the difficulty of batch production using such a hairspring where the shoe pinches, and such a hairspring is still a kind of academic exploration pair
As.
Equally in the prior art, Patek（Patek Philippe）Can using width in its Spiromax hairspring
The bar of change is reinforced to hairspring part, so as to realize consolidation effect.Patek calculates matter also by when hairspring relaxes
The positioning of the heart carrys out research and design methodology and obtains its patent right（Patent No. EP03009603.6）.Turned by the outermost to hairspring
Outside on circle is widened, it is possible to achieve reinforce.
For when hairspring is remained etc., hairspring design needs insensitive to temperature change.The Young's modulus of material it is firm
Degree is generally slightly varied from temperature.
In hairspring, Young's modulus determines spring constant and finally determines the natural frequency of oscillator.The Young of hairspring
Modulus has a negative impact the ability to oscillator reliably regulating time with any change of temperature.
By using nivarox during manufacture hairspring（Nivarox）, can solve extensively in modern times trip
The problem of Young's modulus is temperature sensitive in silk.Nivarox is its a kind of Young's modulus in temperature change sensitiveness side
Face is extremely low but the metal alloy that is not zero.
In past 10 years, micro-machined appearance and the use of silicon introduce new method to design and make in wrist-watch industry
Make the hairspring of isochronism raising.Such a technology manufactures the hairspring of the change based on bar width can be along its whole arc length
Selectively improve the bending stiffness of spring.
In addition, such a technology has the prospect for obtaining certain hairspring, the Young's modulus of the hairspring is complete to temperature change
It is insensitive.The process for making the Young's modulus of hairspring insensitive to temperature change is defined as temperature-compensating.
Actually only it is only possible to produce the hairspring with variable bar width using micro-processing technology, because micro Process skill
Art can manufacture any high-precision flat member.
Hairspring concentricity can be improved using micro-processing technology based on theoretical, numerical simulation or experiment.Patek
Spiromax is an example of silicon hairspring, and it has the increased part of bar width in being turn-taked close to the outermost of outer end, and
It is disposed to and size is adjusted to improve hairspring concentricity.
For the purpose of temperature-compensating, micro-processing technology can also allow to coat thin silica painting on silicon hairspring
Layer.The Young's modulus of silicon reduces as temperature is raised, and the Young's modulus of silica then tends to increase.
Therefore, by the way that the silica dioxide coating of correct thickness is accurately coated on silicon body, compound hairspring can be produced,
The heat sensitivity of the Young's modulus of two of which material is substantially cancelled out each other.Its a kind of total Young's modulus may so be produced
The hairspring insensitive to temperature change in theory.
The content of the invention
Therefore, it is an object of the present invention to provide a kind of hairspring, the hairspring overcomes or at least substantially improved prior art
Shown at least some shortcomings.
In a first aspect, the present invention provides a kind of method that concentricity is improved when hairspring stem-winder is used；It is described
Hairspring has the inner end part for being used for closing with interior staking, and the outer end end part for being engaged with stud, from inner end
Divide the first index dial extended towards outer end end part（limb）Part, and the footing at the outer ring of hairspring, institute
Stating footing has the cross-sectional profiles second moment for being different from the described first indexing disc portion；So that the bending of footing is firm
Degree is more than the bending stiffness of single indexing disc portion；Wherein it the described method comprises the following steps：
By the way that the cost function of the whole rotation amplitude of the hairspring in use is minimized, to the first indexing disc portion and institute
The cross-sectional profiles second moment for stating footing is improved, wherein the net concentricity of the cost function and the hairspring
It is relevant.
Cost function can be in the gamut of the rotation amplitude of hairspring in use, stud reaction force value
Integration；Or can be hairspring in use the gamut of rotation amplitude in, the maximum in stud reaction force value
Value.
Cost function can also be, in the gamut of the rotation amplitude of hairspring in use, when escapement angle is relative
When the center coordination of hairspring is zero, the integration of hairspring center coordination value；Or the rotation amplitude of hairspring in use
In gamut, when rotation amplitude is zero relative to the center coordination of hairspring, the maximum in hairspring center coordination value.
Preferably, the cross-sectional profiles second moment of improved Part I and footing is based on following item in hairspring：Edge
Position positioning, the arc length of hairspring improvement part and the determination for hairspring bar are secondary along the cross-sectional profiles of hairspring improvement part
The function of square change.
Preferably, the change of cross-sectional profiles second moment is substantially constant.
The change of cross-sectional profiles second moment can be connected based on polynomial function, trigonometric function or two or more segmentations
The discontinuous function of continuous function.
Optimized algorithm used can be based on gradient descent method, and the gradient descent method needs to calculate cost function relative
In the gradient of design parameter.
In second aspect, the present invention provides a kind of hairspring for stem-winder, the hairspring have for
The inner end part that interior staking is closed, and the outer end end part for being engaged with stud, outer end end is partially toward from inner end
Divide the first indexing disc portion of extension, and the footing at the outer ring of hairspring, the footing, which has, to be different from
The cross-sectional profiles second moment of the first indexing disc portion；Break the cross section of wherein described Part I and the footing
Face second moment is determined by the method in first aspect.
Preferably, two or more indexing disc portions spaced apart in single indexing disc portion and footing are
Rectangular cross section, and all there is same widths and identical height each other.
Preferably, single indexing disc portion and footing are formed by the first material, and are further comprised by the second material
Expect the external coating formed.
Preferably, the first material has the first Young's modulus, and the second material has the second Young's modulus, described first
Young's modulus and the second Young's modulus have an opposite temperature dependency, and single indexing disc portion and footing and outer
The size of coating layer thickness is adjusted so that the elastic characteristic of hairspring is insensitive to temperature change.
Preferably, first material is silicon, and/or second material is silica.
The pitch of single indexing disc portion can be with substantially constant, and one of the indexing disc portion of footing has
The pitch.Most radially inward indexing disc portion has the pitch.
Two adjacent indexing disc portion bases in the pitch preferably substantially constant, and footing of single indexing disc portion
Originally the path with the pitch is equidistant.
Preferably, the spacing substantially constant in footing between two adjacent indexing disc portions.
Footing can be arranged between two single indexing disc portions.Single indexing disc portion and footing are most
Interior indexing disc portion can have identical pitch.
Footing outermost indexing disc portion can the single indexing disc portion adjacent with one there is identical pitch, and
And the most interior indexing disc portion of footing and the adjacent indexing disc portion of footing have identical pitch.
Footing can be arranged on each of the outer end office of hairspring, and indexing disc portion of footing
All there is terminal（terminal end）.
In the pitch preferably substantially constant of adjacent single indexing disc portion, and the indexing disc portion of footing
One has the pitch.Preferably, the most interior indexing disc portion of footing has the pitch.
The outer indexing disc portion of footing can be substantially shorter than the adjacent interior indexing disc portion of footing.Or,
Indexing disc portion is substantially longer than the adjacent interior indexing disc portion of footing outside one in the indexing disc portion of footing.
Footing can include fewer than half spiral coil.
The adjacent indexing disc portion of footing can footing end intermediate interconnection.
Two or more indexing disc portion preferably bases spaced apart in single indexing disc portion and footing
This is coplanar.
This patent be based on one or more footings propose hairspring design so that the whole service scope of oscillator all by
It is considered that generally escapement angular range is in -330 degree to+330 degree.
The module of concentricity can be the reaction force at the change of centroid position or stud in whole service scope
Change.Such a module is used as the cost function of algorithms of automatic optimization, and the algorithms of automatic optimization systematically changes bar portion
Divide parameter, to realize the concentricity of maximum possible for given hairspring geometry.
In first is further, the present invention provides a kind of hairspring for stem-winder, and the hairspring includes：
Inner end part and outer end end part, single point of the extension of outer end end part is partially toward from the inner end
Scale part；And
The footing formed at the outer ring of hairspring and by two or more indexing disc portions spaced apart, makes
The bending stiffness for obtaining footing is more than the bending stiffness of single indexing disc portion；And
The footing of wherein described hairspring has rigidity, so that described during the oscillating movement around rotary shaft
In the compression and expansion process of hairspring, the concentricity turn-taked around the rotary shaft is improved.
Preferably, two or more indexing disc portions spaced apart in single indexing disc portion and footing are
Rectangular cross section, and all there is same widths and identical height each other.
Preferably, single indexing disc portion and footing are formed by the first material, and are further comprised by the second material
Expect the external coating formed.
Preferably, the first material has the first Young's modulus, and the second material has the second Young's modulus, described first
Young's modulus and the second Young's modulus have an opposite temperature dependency, and single indexing disc portion and footing and outer
The size of coating layer thickness is adjusted so that the elastic characteristic of hairspring is insensitive to temperature change.
In a preferred embodiment, first material is silicon, and second material is silica.
The pitch of single indexing disc portion can be with substantially constant, and one of the indexing disc portion of footing may
With the pitch.Most radially inward indexing disc portion may have the pitch.
The pitch of single indexing disc portion can be preferred with two in substantially constant, and footing adjacent indexing disc portions
Path of the ground substantially with the pitch is equidistant.
Preferably, the spacing substantially constant in footing between two adjacent indexing disc portions.
Footing can be arranged between two single indexing disc portions.Preferably, single indexing disc portion and reinforcing
Partial most interior indexing disc portion has identical pitch.Footing outermost indexing disc portion can be adjacent with one it is single
Indexing disc portion has an identical pitch, and footing most interior indexing disc portion can with footing adjacent index dial
Part has identical pitch.
Preferably, footing is arranged on every in the outer end office of hairspring, and the indexing disc portion of footing
One all has terminal.Preferably, the pitch substantially constant of adjacent single indexing disc portion, and the index dial of footing
One of part has the pitch.Preferably, the most interior indexing disc portion of footing has the pitch.
The outer indexing disc portion of footing can be substantially shorter than the adjacent interior indexing disc portion of footing.Or,
Indexing disc portion is substantially longer than the adjacent interior indexing disc portion of footing outside one in the indexing disc portion of footing.
Preferably, footing includes fewer than half spiral coil.
The adjacent indexing disc portion of footing can footing end intermediate interconnection.
Two or more indexing disc portion preferably bases spaced apart in single indexing disc portion and footing
This is coplanar.
In the present invention, if size is by properly adjusting and passing through suitable location, footing can be used for improving trip
Silk concentricity.
The present invention makes the silicon hairspring with silica dioxide coating carry out substantially complete temperature-compensating, because a plurality of spiral
Each parallel branch in part can keep same widths with other branch roads of other spiral parts.
The present invention is easily fabricated, so that effect temperature compensation is realized, because the silicon dioxide thickness needed for total moisture content compensation
According to the change width of silicon strip, and current manufacturing technology only allows silica dioxide coating in uniform thickness.
Brief description of the drawings
Hereafter by way of example and reference explanation accompanying drawing come illustrate in further detail the present invention preferred reality
Example is applied, in the accompanying drawings：
Fig. 1 shows the schematic diagram of traditional hairspring in relaxed state；Archimedian screw except constituting constant pitch
The outermost of line is turn-taked, and the hairspring has all parts；
Fig. 2 shows the schematic diagram of traditional hairspring shown in Fig. 1 with the escapement angle in -330 degree；
Fig. 3 shows the schematic diagram of traditional hairspring shown in Fig. 1 with the escapement angle in+330 degree；
Fig. 4 show according to the present invention hairspring schematic diagram, the hairspring have cross-sectional profiles second moment variable and
With outer end into about 90 degree and 270 degree of two possible improvement parts；
Fig. 5 show in order to by hairspring concentricity it is maximized according to the present invention algorithms of automatic optimization flow chart；
Fig. 6 is shown for the hairspring concentricity in the case of one and two improvement parts, according to the cost function of the present invention
History and Optimized Iterative；
Fig. 7 shows reaction force history and escapement angle in the case of one and two improvement parts；
Fig. 8 shows barycenter change and escapement angle in the case of one and two improvement parts；
Fig. 9 shows the deformation in the case of the escapement angle in -330 degree with the hairspring of an improvement part；
Figure 10 shows the deformation in the case of the escapement angle in+330 degree with the hairspring of an improvement part；
Figure 11 shows the deformation in the case of the escapement angle in -330 degree with the hairspring of two improvement parts；
Figure 12 shows the deformation in the case of the escapement angle in+330 degree with the hairspring of two improvement parts；
Figure 13 shows the embodiment that may have the both arms hairspring for improving concentricity using improvement part；
Figure 14 shows the graph of an exemplary embodiment of the hairspring according to the present invention；
Figure 15 shows the comparison of the skew barycenter relative to embodiment illustrated in fig. 14；
Figure 16 shows the comparison of the stud reaction force relative to embodiment illustrated in fig. 14；
Figure 17 shows an example of the deformation of the optimization Spiromax hairsprings in zero degree；
Figure 18 shows an example of the deformation of the optimization Spiromax hairsprings in -330 degree；And
Figure 19 shows an example of the deformation of the optimization Spiromax hairsprings in+300 degree.
Figure 20 is illustratively shown the cantilever design with two beams connected with parallel configuration；
Figure 21 a show the cantilever design with single beam, and the beam has uniform crosssection；
Figure 21 b show the cross-sectional view for the cantilever design described in Figure 21 a；
Figure 22 a are shown with the cantilever design of arranged in series connection and two different beams of cross section；
Figure 22 b show the cross-sectional view for the cantilever design described through in two beams in Fig. 2 a of the first beam；
Figure 22 c show the cross-sectional view for the cantilever design described through in two beams in Figure 21 a of the second beam；
Figure 23 a show the cantilever design with two beam portions point being connected in series, and thus, a part is connected by parallel configuration
Two beams connect are constituted, and another part is made up of single beam；
Figure 23 b show the cross-sectional view for the cantilever design described through in Figure 23 a of any one beam；
Figure 24 shows the first embodiment of the hairspring according to the present invention；
Figure 25 shows a plurality of spiral part arrangement of the further embodiment of the hairspring according to the present invention；
Figure 26 shows a plurality of spiral part arrangement of another embodiment of the hairspring according to the present invention；
Figure 27 shows a plurality of spiral part arrangement of the still further embodiment of the hairspring according to the present invention；
Figure 28 shows a plurality of spiral part arrangement of the still another embodiment of the hairspring according to the present invention；And
Figure 29 shows an alternate embodiment of the hairspring according to the present invention.
Embodiment
With reference to Fig. 1, for illustrative and explanatory purpose, show that having 13.5 altogether turn-takes, in relaxed state
Traditional hairspring 10 rough schematic view.
Hairspring is turn-taked by two parts, i.e. main part 11a and outer portion 11b compositions.Main part 11a formation has
The spiral of Archimedes of constant pitch, wherein its inner are connected in interior stake 12.Interior stake 12 and then it is rigidly connected to escapement（Not
Show）On.Outer portion 11b has the pitch dramatically increased, so as to be the placement vacating space of stud 13.All part 11a and
11b has constant cross section.
Line 14 represents the tie point between interior stake 12 and hairspring main part 11a, and it is interior that this enables reader preferably to follow the trail of
The anglec of rotation of stake 12.
As those skilled in the art will understand, traditional hairspring 10 is only a reality of a variety of possible hairspring shapes
Example, but this example will be used as reference in the remainder of this document.
With reference to Fig. 2, traditional hairspring 10 shown in Fig. 1 is illustrated as in one direction and is expressed as hairspring 20, and it is in
The situation of compression, wherein interior stake 21 has turned clockwise 330 degree, this is typical amplitude of oscillation.Such as the skill of art
Art personnel will observe and understand, the size of population of hairspring track has reduced, but importantly, deformation not with the side of stud 22
With one heart, pitch is far longer than the pitch on opposite side to pitch on the side.
With reference to Fig. 3, traditional hairspring 10 shown in Fig. 1 be shown on the direction opposite with shown in Fig. 2 deformed and
Represented with hairspring 30.Hairspring 30 is in the situation of dilatancy, wherein 330 degree of rotate counterclockwise of interior stake 31.As will be observed that,
The size of overall hairspring track has increased, but importantly, the deformation is not also concentric with pitch on the side of stud 32, on the side
Pitch be far smaller than pitch on opposite side.
The shortage concentricity shown in Fig. 2 and Fig. 3 can be in balance rod bearing（balance staff bearing）（Fig. 2 and
Not shown in Fig. 3）During the centrifugal force for needing compensation to be produced by center of mass motion, extra friction is produced.
Such a loss of concentricity can also generate the hairspring of geometry change, and geometry change can cause spring constant
Change so that cause oscillator become it is non-wait when.In addition, in some cases, the pitch in hairspring some regions is becoming
The stud 22 in hairspring 20 is may be located remotely from the case of shape and becomes negative towards the stud 32 in hairspring 30, this implies adjacent turn
Contact between circle can then cause damage.With reference to Fig. 4, the signal of an embodiment according to hairspring 40 of the invention is shown
Figure, for example, the hairspring 40 has improved part 41a and 41b.
It can be improved by the bending stiffness to part selected in hairspring bar and improve hairspring isochronism.Realize this
One mode of purpose is to change the cross section of bar, and micro-processing technology makes manufacture become more by improving the width of hairspring bar
Simply.Hairspring can have one or more different improvement parts.
According to the present invention, in order to create the algorithms of automatic optimization for maximizing hairspring concentricity, the first step is clearly
Define design parameter, thus it is possible to vary the design parameter realizes optimum.
In the embodiment shown in fig. 4, each improvement part 41a or 41b need at least three design parameters to change to limit
Enter the geometry of part：Improved second moment of area Ia, the arc length L of improvement parta, and improvement part positioning θa。
Parameter IaThe ratio compared with the second moment of area of hairspring bar remainder can be defined as.Parameter LaIt can define
For the angular spread in the length or polar coordinates of improvement part.Parameter θaCan be in polar coordinates relative to stud 42 or interior stake connection
The arc distance or angular distance of 43 positioning measurements.
If improved second moment of area IaIt is the arc length of improvement part or the complex function of angular spread, then parameter
Quantity can be more than three.
Function in consideration can be the continuous function of multinomial or trigonometric function etc, or sectional-continuous function is not
Continuous combination.The theoretic upper limit is not present in quantity for different improvement parts.With the section two of hairspring bar remainder
Secondary square is compared, and the second moment of area of improvement part can be increase or reduction.
With reference to Fig. 5, the optimization process flow chart according to the present invention is shown.
Algorithms of automatic optimization can be through design, with the upper of the geometry by changing the one or more improvement parts of restriction
Design parameter is stated to maximize hairspring concentricity.
Its core is typical optimized algorithm, and design or systematic parameter are adjusted, so that by predefined cost function
Minimize or maximize, this may be limited by some constraintss.
Cost function can be counted via the computer model for the mechanism being used as design parameter in the consideration of input
Calculate.Then, whether algorithm evaluation cost function is satisfactory.If dissatisfied, then algorithm will be based on predefined law collection
Design parameter is adjusted for conjunction；New design parameter is used as the input of computer model, to calculate new cost function.
Then, such a circulation is repeated, until algorithm determines that corresponding optimal design parameter used can obtain satisfactory
Cost function untill.This process can be used for optimizing the hairspring improvement part for maximum concentricity.
In addition to the design parameter of above-mentioned hairspring improvement part, optimized algorithm needs to reflect determining for hairspring concentricity level
Adopted clearly cost function.
One possible measurement is the sidesway of hairspring barycenter in whole oscillator range of operation（drift）Degree.Hairspring
The sidesway of barycenter is defined as relative to the hairspring center coordination that α is equal at zero, the hairspring barycenter in given interior stake anglec of rotation α
Positioning.
Variable s is the arc position along hairspring bar.A (s) is the cross-sectional area at the s of arc position.Variable x (s, α) and y
(s, α) is limited to the x and y location of bar under arc position s and interior stake angle [alpha].
Item L is total arc length of hairspring.X (α) and Y (α) are, relative to the barycenter of loose hairspring, to distinguish in the x and y direction
Barycenter sidesway.Equation 1 and 2 only determines the barycenter sidesway under specific interior stake angle [alpha].
Reflect that the single metric standard J of sidesway can be by taking from α in whole oscillator range of operation for barycentercwTo αccw
The integration of sidesway value be defined, wherein αcwAnd αccwGenerally respectively equal to -330 spend and 330 degree.
Cost function J can be described as the average sidesway of hairspring barycenter, and the minimum value and hairspring of the average sidesway are concentric
The maximum of degree is related.
Because the computer simulation of the hairspring deformation for single interior stake angle [alpha] may take several hours, therefore with product
Point come accounting equation 3 it is typically unpractiaca.
However, it is possible to by approaching product with the trapezoidal rule or another numerical integrating of integration to limited quantity α
Point.
In equation 4, interior stake angle [alpha] is discretized in the value of N number of equispaced, and this expression only needs N number of simulation to use
In the J of calculatingapproxApproximation.N values are larger, represent more accurately approaching for cost function.
It is as the alternative solution of the integration of barycenter sidesway in stake angle [alpha] inside, the maximum of barycenter sidesway value is minimum
Change can be used for maximizing hairspring concentricity.
The problem of optimization problem is substantially changed into min-max type by equation 5, this may be easier to reality herein
Apply.
Reflect value of another clearly defined cost function of hairspring concentricity level for the reaction force at stud.
Reaction force at stud can be calculated via the computer simulation of the hairspring of a certain interior stake angle [alpha].Single metric
Standard J can also be used to αcwAnd αccwBetween stud reaction force value integer.
Variable Rx(α) and Ry(α) is respectively the stud reaction force on x and y directions.This cost function can also be described as
Average stud reaction force, maximum of the minimum value equivalent to hairspring concentricity of the average stud reaction force.
From equation（6）Cost function can also be approached, mode is by the way that α is separated into N number of equispaced
Value and integration is then approached using trapezoidal rule.
The min-max alternative solution of integration is also used as the module of hairspring concentricity.
Substantially, barycenter sidesway and stud reaction force may be used to determine hairspring concentricity in algorithms of automatic optimization
Level.
In order to minimize above-mentioned cost function and therefore maximize hairspring concentricity, searching algorithm needs effectively pair to set
Count parameter Ia、La、θa、Ib、Lb、θbEtc. being adjusted, to realize optimization.
Subscript a and b represent the first and second improvement parts with extra possible improvement part.
In the polyalgorithm available for this purpose, gradient descent method be known as most effective and most popular method it
One.
When applying to hairspring algorithms of automatic optimization, gradient descent method calculates one of above-mentioned cost function J gradient.
Then, design parameter is improved, and method is by each iteration, in the gradient phase with being limited in equation 9
Taken measures on anti-direction.Assuming that the vector definition of design parameter is as follows：
Then, the renewal rule for design parameter is defined by below equation：
Iterations is designated as under in design parameter vector, and variable J is step-length.
After given enough iteration, such a renewal rule will make cost function move closer to local minimum.
The centre of optimization process, step-length J can be adjusted according to the degree of approach with local minimum.
It is generally impossible to obtain cost function gradientClear and definite solution because cost function J inherently hairspring numerical value
The result of simulation.
However, it is possible to use numerical differentiation technology approaches cost function gradient.However, the optimization time will dramatically increase,
Because simulation is required for operation several times when each iteration performs numerical differentiation.
When optimization process starts, gradient descent method needs initially to speculate design parameter.It is sufficiently close to solution most
The optimization time can be greatly reduced by just speculating.
A possible way for obtaining the effective estimation initially speculated is performed roughly in the zone of reasonableness of design parameter
Power is searched for（coarse brute-force search）.Inherently a kind of independent optimized algorithm of force search, it can set
Cost function is calculated in the range of meter parameter, so as to obtain minimum value function.
In order to obtain fairly precise result, force search needs unpractical a large amount of hairspring simulated experiments by oneself.
However, the search that uses force, which carries out rough preliminary browse to design parameter scope, can obtain effective initial conjecture, it is described
Initially conjecture can use gradient descent method further to be simplified.Result is that any one single optimized algorithm is being used alone
During, the optimization time, net total amount was reduced.
The concentricity design that other algorithms of automatic optimization can be used for hairspring is optimized, and including but not limited to gene is drilled
Algorithm, memory type algorithm and simulated annealing.Generally, all optimized algorithms will all join with above-mentioned cost function and design
Number cooperation.Although each algorithm in other algorithms all each has the advantage that and shortcoming, most of algorithm declines than gradient
Method is more difficult to implement.
With reference to Fig. 6, the result of the optimization history for the gradient descent method of hairspring concentricity is shown.X-axis and y-axis are respectively
Iterations and cost function history.
In this case, cost function is defined as in the range of from -330 degree to the interior stake angle [alpha] of+330 degree（The model
Enclose be typical oscillator standard operation range）, the integration of stud reaction force.
One curve shows to turn-take in outermost the optimization history of the hairspring with single footing, and another curve
Show also to turn-take in outermost the optimization history of the hairspring with two footings.
It is stable at the final local minimum in cost function of two shown curves, and with two reinforcing portions
The design divided is significantly better than the design with a footing.
With reference to Fig. 7, the magnitude variations of the stud reaction force of following hairspring are directed to including showing in the range of stake angle [alpha]：
(i) without footing,
(ii) there is the footing of an optimization, and
(iii) there is the footing of two optimization.
It will be seen that from Fig. 8, optimize the hairspring of part（ii）With（iii）Reaction force at stud, which is substantially less than, to be had
The hairspring of constant section second moment（i）.
In addition, result is shown, between -330 degree and+330 degree（Typical amplitudes in stem-winder）, use " two " optimizations
Footing stud reaction force it is extremely low.
With reference to Fig. 8, show in the range of α for three kinds of hairspring designs of identical, the value of barycenter sidesway change.
The figure is as one man shown：For almost all of α values, stud reaction force and barycenter sidesway value pass through automatic
Optimized algorithm and reduce.It is a greater degree of free due to having in the design, therefore with the hairsprings of two optimization footings
Best result can be obtained.
With reference to Fig. 9 and Figure 10, show respectively by the algorithms of automatic optimization according to the present invention, hairspring 90,100 it is concentric
Degree increases, and there is shown with the deformation geometry shape of the hairspring with an optimization footing.
The interior stake of hairspring 90 and 100 is rotated both clockwise and counterclockwise 330 degree respectively.Compared with Fig. 2 and Fig. 3 concentricity
When, concentricity enhancing here is visually more notable and is more clearly shown that.
Figure 11 and Figure 12 show the deformation geometry shape of the hairspring 110,120 with two optimization footings.Hairspring 110
Interior stake with 120 is rotated both clockwise and counterclockwise 330 degree respectively.Compared with Fig. 9 and Figure 10 concentricity, have one in shown
In the hairspring of individual optimization footing, concentricity is further enhanced.
The higher concentricity realized by above-mentioned algorithms of automatic optimization allows to implement the new hairspring with multiple arms.
Referring now to Figure 13, showing an example of the multi-arm hairspring 130 with two arms 131a and 131b.
Therefrom intracardiac stake 132 extends by two arms 131a and 131b.Arm 131a and 131b are respectively at outer end 132a and 132b
Terminate.Both arms hairspring 130 and arm 131a axial symmetry, arm 131a are identical with arm 131b.
With reference to Figure 14, show to be applied to an embodiment of the hairspring 200 according to the present invention of the optimization according to the present invention
Graph.Hairspring 200 includes the inner end portion 210 for being used to engage with interior stake 220, and outer for what is engaged with starting point 240
Part 230 is held, the first indexing disc portion 250 extended from inner end part 210 towards outer end portion 230, and positioned at hairspring
Footing 260 at 200 outer rings.
In this embodiment, footing is forked section, including interior index dial 262 and outer index dial 264, Yi Ji
The depression bar 266 extended between both.
Footing 260 is reinforced by improving second moment of area, and the second moment of area is by by the indexing of bifurcated
Disk 262,264 is spaced apart and is improved, and the index dial 262,264 of the bifurcated is common in this part of hairspring to improve section
Second moment.
It is as those skilled in the art will understand and clear, by the way that two index dials 262 and 264 are spaced apart, bifurcated
Partial second moment of area can correspondingly improve bending stiffness.
It should be noted that the cross section size of the first indexing disc portion and footing is all identical, and therefore, first index dial
Each of two index dials 262 and 264 in part and the footing all have identical cross-sectional area.
Therefore, because the first indexing disc portion and footing are formed from the same material and with identical cross section face
Product, and because Young's modulus is because hairspring is made up of single piece of material and is constant, therefore on being produced according to temperature change
Young's modulus change, influence of the temperature to hairspring various pieces be identical.
Hairspring 200 in the present embodiment is formed by micro-processing technology, the micro-processing technology produce such article or
Dimensional accuracy is higher during product.
Micro-processing technology in the present embodiment allows to temperature-insensitive, and mode is to use the first poplar deformed with hairspring
First material of family name's modulus, and the second material is used as the coating material with the second Young's modulus, the first Young mould
Amount and second Young's modulus have an opposite temperature dependency, thus external coating size can carry out suitably adjustment and
The external coating can have a certain thickness so that the elastic characteristic of hairspring is insensitive to temperature change.
It is the silicon with silicon dioxide layer for being formed according to the suitable material of the hairspring of the present embodiment.
In order to improve concentricity during the expansion and contraction of hairspring and reduce the change of mass effect, footing quilt
Included in hairspring.
In addition, the size of footing can be optimized in the method in accordance with the invention, so as to provide suitable rigidity, make
The minimizing deformation of hairspring during rotation is obtained, and reduces mass shift.This can be by using on the above-mentioned of the present invention
The minimum of cost function is realized.
Can show, it is given it is some under the conditions of, the second moment of area of forked section can be designed to and width increase
Footing second moment of area it is equal.
For example, normal width and height are respectively b0 and h hairspring.Two hairspring parts are compared.One part
With width it is larger and for b0 n times of single bar.Another part has the bar of two bifurcateds, and each bar width is equal to standard
Value b0 and it is separated at distance d out, this is obtained apart from d from the central line measurement of each.
Assuming that d keeps constant for whole forked sections, it can use parallel-axis theorem that d is set so that for adding
Wide portion and forked section, the second moment of area relative to z-axis are equal.As a result d is calculated as follows：
If it should be noted that n is equal to 2, then bifurcated bar contacts with each other, and becomes one and widen bar.
Optimized algorithm can be readily adapted for use in widened section and forked section.In the former case, partial width
As by one of design parameter changed in optimized algorithm.In the latter case, the distance of bifurcated bar is used as becoming
One of design parameter of change.It should be noted that by using equation（12）, two methods can be with used interchangeably.
It should be noted that further being retouched to the other details of the hairspring of the present invention and explanation hereinafter with reference to Figure 20 to Figure 29
State, wherein, hairspring 200 is an embodiment of the hairspring.
With reference to Figure 15, show according between -300 degree and 300 degree（The typical range of hairspring）Rotate the barycenter produced inclined
Move, make wherein optimizing at one between footing, two optimization footings and Spiromax hairsprings according to prior art
Compare.
It will be seen that, compared with one optimizes footing and Spiromax hairsprings, added according to the optimization of two parts of the present invention
Gu the centroid motion of part reduces.
With reference to Figure 16, show in the range of the overall movement between -330 degree and 330 degree, in the reaction of hairspring starting point
Comparison between power, the section of one of optimization footing, two optimization footings and Spiromax hairsprings is secondary
Square is constant.
It should be noted that its rigidity is according to the single optimization footing hairspring that optimizes of the present invention, with less than
The stud reaction force of Spiromax hairsprings.
Have significantly it is important, however, that it is shown according to the hairspring with two optimization footings of the present invention
Relatively low stud reaction force, compared with another hairspring, such a reaction force is almost nil.
Reaction force including stud reaction force is indicated at stake bearing, and those skilled in the art will appreciate that,
This can reduce the friction and loss at interior stake, and therefore improve the life-span.
Those skilled in the art will appreciate that, it can be obtained according to the hairspring with two optimization footings of the present invention
Mass shift is smaller and the extremely low hairspring of reaction force at stud.
Therefore, in whole angular movement, the concentricity of such a hairspring according to the present invention is improved, so as to correspondingly carry
The hairspring improved for a kind of isochronism for table.
With reference to Figure 17, Figure 18 and Figure 19, show to be respectively at 0 degree, the Spiraomax types trip of -330 degree and+330 degree
The deformation of silk.It should be noted that there is distortion between the winding that display quality is offset, the mass shift can be reduced together in use
Reaction force at heart degree and the interior stake of increase and stud, so that characteristic when waiting of hairspring is worse than the hairspring according to the present invention
（Especially compared with the hairspring with two optimization footings）, wherein footing is optimization footing.
Although implementing more complicated with three or three with the hairspring design of upper arm, in theory these hairsprings
Design can have enough hairspring concentricitys.
The axial symmetry layout of multi-arm hairspring can further improve isochronism, because being delivered to by an arm in interior stake
The net radial load that any radial load can be transmitted by other arms is offset.If ignoring Action of Gravity Field, then balancing pole in theory
Bearing does not suffer from any radial load, so that oscillator is not exposed to bearing friction substantially.
However, multi-arm hairspring is only feasible when with height concentric design, because traditional hairspring arm is intended to becoming
Enter during shape each other, so as to even for minimum escapement angle, can also improve the possibility collided between alternate arm
Property.
The present invention provides a kind of hairspring for table, and by using micro-processing technology, the hairspring, which can be made into, to be had
Higher dimensioning accuracy and mechanical accuracy.
Be improved according to the concentricity of hairspring of the present invention, mode be by providing a reinforcing position, so can be
Hairspring can be reduced because accelerating and moving by reducing the reduction in mass shift of the hairspring on rotary shaft, such a skew during use
Radial inertial effect, so as to reduce the radial load at centre bearing.
Further, since it is gradually insensitive to temperature, it is improved according to the isochronism of the hairspring of the present invention.
The effect that this isochronism that can produce hairspring and vibrator mechanism is improved, so as to provide being in for timing purposes
The hairspring of more correct position.
In addition, the reduction of radial load can also reduce the friction on the bearing of oscillator assembly center, and because rub
The motion of oscillator can be influenceed by wiping power, therefore this reduction can also increase isochronism, in addition, it may also reduce loss to bearing and broken
It is bad.
This can produce a kind of hairspring vibrator mechanism, the hairspring vibrator mechanism life-span increase, and need less
Due to the maintenance and repair needed for component deterioration.Due to the reduction of nonlinear second-order system, therefore during movement, concentricity is carried
Height can improve isochronism, while the trend being engaged with each other of turn-taking of hairspring during compression and expansion can be reduced, wherein in the middle of hairspring
The engagement and collision of circle and adjacent turn can change the mechanical property of hairspring, and this can produce significant adverse effect to isochronism.
In addition, collision and shock that adjacent centre is turn-taked may be such that hairspring is damaged and may failed, meeting simultaneously
Reduce the reliability of hairspring and increase due to the cost needed for maintenance and repair.
Hairspring 200 with reference to described by above with reference to Figure 14, hereinafter with reference to this side of Figure 20 to Figure 29 to the present invention
Face is described further, and hairspring 200 is an embodiment therein.
In order to describe the mode that feature of present invention is showed, a kind of explanation is provided referring to figures 20 through 23c, the explanation makes
Theoretical with Solid Mechanics, especially using the statics of cantilever beam, the cantilever statics uses Euler-Bernoulli Jacob's beam formula.
Although strictly speaking such a formula and Adjoint theory are to be based on straight Flexural cantilever model, the formula is also with elongated
The helical hair spring of bar provides fairly accurate result, because the restoring moment of the typical hairspring of the overwhelming majority is from hairspring bar
Bending.
Therefore, Euler-Bernoulli Jacob's beam formula is widely used in the bending stiffness of estimation hairspring in wrist-watch industry.
With reference to Figure 20, the cantilever design 310 being made up of two beams 311A, 311B being connected in parallel is shown.Require emphasis
It is that, throughout the specification using term " parallel ", structural detail should be extended to the understanding of the term and connected with parallel configuration,
These elements might not be parallel in strict geometric definition.
The analysis of this cantilever design 310 shows the influence of its bending stiffness to structure, and the definition of bending stiffness is outer
The ratio exerted a force between square and the resultant deflection of beam.
The right-hand member of cantilever design 310 has the boundary condition 315 clamped, and the boundary condition resists and is subjected to displacement and revolves
Turn.The left end of cantilever design 310 is free, but with the plate 314 that adheres on beam 311A, 311B, with ensure they one
Rise and bend and will not translate relative to each other or rotate.Two each length of beam 311A, 311B are L, and width is b, Yi Jigao
Spend for h.When center line 312A, 312B measurement from them, two beams 311A, 311B also separate constant distance d.Cantilever knot
Structure 310 also has neutral axis 313, in this case, and the neutral axis is equidistant between beam center line 312A and 312B.
Due to following two reasons, when single with each of beam 311A, 311B all identicals with length and cross section
When cantilever beam is compared, cantilever design 310 has larger bending stiffness, and the reason is：
(i) cantilever design 310 has the cross-sectional area more than single beam；And
(ii) two beams 312A, 312B of cantilever design 310 are positioned extremely away from neutral axis 313, so as to improve section two
Secondary square and therefore provide larger bending stiffness.
Single beam 311A, 311B bending stiffness k1Following Euler-Bernoulli Jacob's beam formula can be used to be calculated, wherein
Young's modulus is represented with E
Nb is redefined as apart from d, for reduced equation, wherein n is d: b ratio.On the contrary, cantilever design 310
Bending stiffness k2Further it can be calculated using following parallel-axis theorem：
Assuming that cantilever design 310 is flat, then n value have to be larger than 1, not so two beams 311A, 311B will be overlapping.
As those skilled in the art will understand, for flat cantilever design 310, k2Minimum feasible value it is always big
In k1.In fact, being defined as k2,minK2Minimum feasible value be k1Eight times of value.
According to the present invention, those skilled in the art will appreciate that, k can be set by the length L of adjustment bar1<k2<
k2,mm, the wherein length of adjustment bar can use existing micro-processing technology to implement.
Equation（13）With（14）Show to improve the curved of cantilever design 310 by the way that two beams 311A, 311B are arranged in parallel
The effect of stiffness.
Parallel axle construction can also apply to cantilever design 310 and obtain same conclusions, and the cantilever design 310 has
More than two beam 311A, 311B of parallel configuration.
When beam is non-constant apart from d, it can also be obtained from the cantilever design 310 with beam 311A, 311B in parallel
Go out same conclusions, but derive that the bending stiffness of structure 310 will be more complicated and needs the technologies such as calculus when calculating.
In order to illustrate in temperature-compensating and bracing design advantage, describe and illustrated with reference to Figure 21 a and Figure 21 b to silicon
The influence of the Young's modulus of silica dioxide coating on beam.Such a illustrative analysis only considers Young's modulus to the quick of temperature change
Perception, and do not include the influence of thermal expansion.
Because influence of the temperature to Young's modulus is more than the order of magnitude of thermal expansion influence several, therefore only consider using to poplar
The heat affecting of family name's modulus is quite consolidated and essentially identical result to produce.
With reference to Figure 21 a and Figure 21 b, using all reference coordinates based on the Solid Mechanics right-hand rule, show with transversal
The cantilever design 320 of the uniform single beam 321 in face.The width of beam 321 is b, is highly h, and length is L.Left end 322 is freely
, and right-hand member 323 is to clamp.The cross section 324 of beam 321 shows the silicon core for ζ silica dioxide coating 326 with thickness
The heart 325.
The Young's modulus of silicon and silica can be approached by the linear function relative to temperature change, following institute
Show：
ESi(ΔT)=ESi,0(1+eSiΔT) (15)
In equation（15）With（16）In, Esi,0、ESiO2,0、esiAnd eSiO2All it is constant, and Δ T is temperature change.Often
Number Esi,0、ESiO2,0、esiAnd eSiO2It is respectively about 148GPa, 72.4GPa, -60ppm/K and 215ppm/K number at room temperature
Value.
Constant eSiAnd eSiO2Contrary sign, and this indicates that as temperature is raised the Young's modulus of silicon declines, and silica
Young's modulus then improve.
Assuming that the equivalent Young's modulus of cantilever design 20 in Figure 21 a and 21b by the torque in y-axis, then composite beam 321
Calculating can be as follows：
On Δ T derivations and substitute into equation（15）With（16）, equation（5）Become as follows：
Equation（18）Describe EeqRelative to Δ T sensitiveness, and in order to realize total temperature-compensating, it is necessary to by changing
Become ζ and be set to zero.
For the ratio of width to height for the wide scope for being defined as b: h, for the cross section with silicon core and silica dioxide coating, most
Good ζ: b ratio complete stability is about 6%.The result is shown by silica dioxide coating, for the silicon hairspring of cross-sectional uniformity,
Total moisture content compensation is feasible in theory.
For the hairspring of variable cross-section, it is impossible to draw identical conclusion.This can be by with two varying cross-sections
Simple cantilever beam example prove.
With reference to Figure 22 a, Figure 22 b and Figure 22 c, the cantilever design 330 of two beams 311A, 331B with series connection, institute are shown
Stating two beams 311A, 331B has varying cross-section 334A, 334B.All reference coordinates are based on the Solid Mechanics according to foundation
The right-hand rule.
Beam 331A has free end 332 in its left end, and is engaged in its right-hand member 333 with beam 331B.Beam 331B is left at it
End 333 is attached on beam 331A, and has the boundary condition 334 clamped in its right-hand member.Beam 331A width is bA, it is highly hA,
And length is LA, and beam 331B width is bB, it is highly hB, and length is LB。
Beam 331A cross section 335A shows the silicon core 336A for ζ silica dioxide coating 337A with thickness, and
Beam 331B cross section 335B shows the silicon core 336B for ζ silica dioxide coating 337B with thickness.Due to current micro-
Process technology can not realize variable coating layer thickness in same parts, therefore two cross sections 335A, 335B have identical
Silicon oxide coating thickness.
Assuming that equivalent Young's modulus of the cantilever design 330 by the torque in y-axis, then each of beam 331A, 331B
Calculating can be as follows：
Eeq,A(ΔT)=EA,0(ζ)[1+eA(ζ)ΔT] (19)
EEq, B(ΔT)=EB,0(ζ)[1+eB(ζ)ΔT] (20)
It should be noted that Eeq,A(Δ T) and Eeq,B(Δ T) corresponds respectively to beam 331A and 331B equivalent Young's modulus.Item EA,0
(ζ)、EA,0(ζ)、eA(ζ) and eB(ζ) can be according to equation（15）、（16）With（17）It is unfolded as follows：
The bending stiffness of each can use Euler-Bernoulli Jacob's beam formula to be calculated as follows in beam 331A, 331B：
KA(ΔT)=KA,0(ζ)[1+eA(ζ)ΔT] (25)
KB(ΔT)=KB,0(ζ)[1+eB(ζ)ΔT] (26)
It should be noted that KA(Δ T) and KB(Δ T) is beam 331A and 331B bending stiffness respectively.Item KA,0(ζ)、KB,0(ζ)、kA
(ζ) and kB(ζ) can be unfolded as follows：
Because two beams 331A, 331B are connected in series, therefore their equivalent stiffness can be with calculated as below：
On Δ T derivations and substitute into equation（25）With（26）, equation（17）Become as follows：
Equation（30）Describe KeqRelative to Δ T sensitiveness, and coefficient N2、N1、N0、D2、D1And D0It is defined as follows：
N1(ζ)=2KA,0KB,0eA(ζ)eB(ζ)(KA,0+KB,0) (32)
D2(ζ)=[KA,0eA(ζ)+KB,0eB(ζ)]2 (34)
D0(ζ)=(KA,0+KB,0)2 (36)
In order to realize total temperature-compensating, silicon oxide coating thickness must be configured so that for all Δ T values,
Equation（30）All it is zero.Assuming that equation（30）Denominator for non-zero, then for all Δ T values, it is only necessary to by equation（30）
Molecule be set as zero.
However, equation（30）Molecule be Δ T quadratic function, this represents only have two of Δ T values, and molecule can be equal to
Zero.Equation（30）Prove：For two beams 311A, 331B with series connection and that cross section is different cantilever design 330, stagnation temperature
It is impossible to spend compensation.
Identical conclusion will be drawn by performing similar analysis on discrete or continuous variable cross section cantilever design,
This proves the silicon hairspring for variable cross-section, and total moisture content compensation is impossible in theory.
On the contrary, in theory, total moisture content compensation is feasible for the hairspring with simultaneously bracing.
With reference to Figure 23 a and Figure 23 b, the cantilever design 340 of two beam portions point 341,342 with series connection is shown.Beam portion point
342 have two beams 342A, the 342B connected with parallel configuration.All reference coordinates are based on the right-hand rule.
Beam 341 has free end 343 in its left end, and is attached to beam portion point 342 in its right-hand member 344.The tool of beam portion point 342
Have two beams 342A, the 342B connected with parallel configuration, and whole beam portion point 342 its left end be attached on beam 341 and
Its right-hand member has the boundary condition 345 clamped.All beams 341,342A, 342B have identical cross section 346, wherein transversal
Face width is b, is highly h and silicon oxide coating thickness is ζ.The length of beam 341 is LA, and beam 342A, 342B length is
LB。
Due to being arranged in parallel, the bending stiffness of beam portion point 342 is more than the bending stiffness of beam 341.By adjusting beam portion point
341st, 342 length LAAnd LBAnd the distance between beam 342A and 342B d, the design of cantilever design 340 can be caused its with
Cantilever design 330 in Figure 22 a and Figure 22 b has identical bending stiffness.
However, because each beam 341,342A, 342B have identical cross-section geometry, therefore for all beams
341st, ratio ζ: b of 342A, 342B, silicon oxide coating thickness and beam width is all identical.Any one beam portion point 341,342
Total moisture content compensation is identical for another beam portion point.This is proved, according to the present invention with the total of the simultaneously silicon hairspring of bracing
Temperature-compensating is feasible in theory.
With reference to Figure 24, the first embodiment of the hairspring 350 according to the present invention is shown, the hairspring 350 has a plurality of spiral
Part 355, the spiral part has parallel branch 355A, 355B of square-section, wherein single outer end 357 is connected to stud
On 358.
Hairspring 350 is made up of the interior stake 351 of center.Interior main bar 353 is outside from the inner 352 being attached in interior stake 351
Spiral, untill reaching hairspring part 355, wherein the hairspring part is divided into two parallel branch at point 354A
355A、355B。
Liang Ge branches 355A, 355B regroups together at point 354B and entered in single outer main bar 356, Zhi Daoqi
Untill reaching the outer end 357 fixed and clamped.The bending stiffness of hairspring part 355 with parallel branch 355A, 355B is big
In the bending stiffness of interior main bar 353 and outer main bar 356.The Automated Design optimized algorithm of gradient method etc. can be by the same of hairspring 350
The distance between heart degree is maximized, and mode is the length and displacement by using part 355, and branch 355A and 355B.
In order to further provide for the change of design parameter, the distance between branch 355A and 355B can be along parts 355
Length and change.For example, branch 355A, 355B can disperse and polymerize, it should be appreciated that free space may be restricted
To allow coil spring contracts and expansion, without making adjacent turn-take be in contact with each other, and spring will not be made to contact escapement
Other elements.
It is to be understood, therefore, that the hairspring 355 in the present embodiment can be any size and shape, and according to initial
Hairspring geometry, can be placed on from anywhere in enough gaps.
However, parallel branch 355A, 355B with substantially constant separation distance are typically preferred, so as to be easy to calculate
And it is easy to optimize spring characteristics.
With reference to Figure 25, Figure 26 and Figure 27, three further embodiments of the hairspring according to the present invention, the hairspring are shown
With a plurality of spiral part with two parallel branch.As those skilled in the art will understand, these embodiments can be with
It is easily extended to include a plurality of spiral part with two or more parallel branch.
With reference to Figure 25, show that a plurality of spiral part of the further embodiment of the hairspring according to the present invention arranges 360, wherein
Two parallel branch 363A363B are suddenly from the single branch in two adjacent wall scroll spiral part 361A361B of hairspring point
Fork, and then another single branch is aggregated to suddenly.
With reference to Figure 26, a plurality of spiral fragment 370 of another embodiment according to hairspring of the invention is shown.Left main bar
371A is smoothly connected on one of parallel branch 373A, the branch and then is smoothly connected on right main bar 371B.
Parallel branch 373A is at intersection point 372A suddenly from left main bar 371A bifurcateds, the then polymerization suddenly at intersection point 372B
To right main bar 371B.
With reference to Figure 27, a plurality of spiral fragment 380 of the still further embodiment according to hairspring of the invention is shown.Left main bar
381A is smoothly connected on one of parallel branch 383B.
Parallel branch 383A, suddenly from left main bar 381A bifurcateds, is then smoothly connected to right main bar at intersection point 382A
381B.Parallel branch 383B is aggregated to right main bar 381B suddenly at intersection point 382B.
With reference to Figure 28, the layout of a plurality of spiral fragment 390 of another embodiment again according to the present invention, including branch are shown
Strut（support strut）394.
Parallel branch 393A, 393B are connected to main bar 391A, 391B by intersection point 392A, 392B respectively in left side and right side
On.
Because whole a plurality of spiral part 390 is bent, therefore parallel branch 393A and 393B can be with slightly different songs
Rate radius bend.According to the geometry of hairspring and bending value, parallel branch 393A and 393B can be pushed away towards each other
Move and can contact with each other.The occurrence of support bar 394 prevents such a, and if the width of pole 394 is far smaller than
The length of spiral part 390, then influence of the pole 394 on the statics of a plurality of spiral part 390 is minimum.
It will be appreciated that, more than one pole 394 can be used according to the geometry of hairspring, shape, size and application.
With reference to Figure 29, an alternate embodiment of the hairspring 400 according to the present invention is shown.
Hairspring design has interior stake 401 at its center.Main bar 403 have be connected to the inner 402 in interior stake 401 and
To inverted position turn, untill it reaches a plurality of spiral part 405 at intersection point 404.Then, main bar 403 is divided into two parallel connections point
Branch 405A and 405B, regroup difference with parallel branch 455A, 455B in the embodiment described by Figure 24 at outer end, described
The two parallel branch are individually terminated in outer end 406A, 406B fixed and clamp.
Those skilled in the art will appreciate that, according to the present invention, the present embodiment will also be realized to be added near outer ends enhancing
Gu, although two parallel branch 405A and 405B will not regroup.
The present invention provides a kind of hairspring for table, and by using micro-processing technology, the hairspring, which can be made into, to be had
Higher dimensioning accuracy and mechanical accuracy.
On the silicon hairspring manufactured by micro-processing technology, prior art is improved the disadvantage is that, more freely designing
Concentricity and expectation total moisture content compensation can not be realized simultaneously.
Micro-processing technology is usually limited to the manufacture of flat member.Although micro-processing technology can be produced in theory to be had
Breguet type crosses the hairspring of coil, and the overlapping layer that the Breguet type crosses coil is multiplied, but such a manufacturing capacity is current
And it is unreliable, and can at least significantly increase the additional complexity of manufacturing process.
The concentricity improved is provided according to the hairspring of the present invention, mode be by providing a reinforcing position, so can be
Mass shift of the hairspring on rotary shaft can be reduced during use, such a reduction on skew can reduce hairspring because accelerating and transporting
The radial inertial effect of movable property life, so as to reduce the radial load at centre bearing.
Further, since it is gradually insensitive to temperature, it is improved according to the isochronism of the hairspring of the present invention.
The effect that this isochronism that can produce hairspring and vibrator mechanism is improved, so as to provide being in for timing purposes
The hairspring of more correct position.
In addition, the reduction of radial load can also reduce the friction on the bearing of oscillator assembly center, and because rub
The motion of oscillator can be influenceed by wiping power, therefore this reduction can also increase isochronism, in addition, it may also reduce loss to bearing and broken
It is bad.
This can produce a kind of hairspring vibrator mechanism, the hairspring vibrator mechanism life-span increase, and need less
Due to the maintenance and repair needed for component deterioration.Due to the reduction of nonlinear second-order system, therefore during movement, concentricity is carried
Height can improve isochronism, while the trend being engaged with each other of turn-taking of hairspring during compression and expansion can be reduced, wherein in the middle of hairspring
The engagement and collision of circle and adjacent turn can change the mechanical property of hairspring, and this can produce significant adverse effect to isochronism.
In addition, collision and shock that adjacent centre is turn-taked may be such that hairspring is damaged and may failed, meeting simultaneously
Reduce the reliability of hairspring and increase due to the cost needed for maintenance and repair.
Although invention has been described for reference example or above preferred embodiment, it is to be understood that those are to be used to help
The example of the understanding of the present invention is helped, rather than it is restricted.Change or modification and the improvement made thereon, to affiliated neck
It is apparent or inappreciable for the technical staff in domain, these should be regarded as the equivalent of the present invention.
Claims (12)
1. a kind of method for improving concentricity when using hairspring stem-winder, it is characterised in that：The hairspring, which has, to be used for
The inner end part closed with interior staking, and the outer end end part for being engaged with stud, institute is partially toward from the inner end
State the first indexing disc portion of outer end end part extension, and the footing at the outer ring of the hairspring, the reinforcing
Part has the cross-sectional profiles second moment for being different from the first indexing disc portion；So that the bending stiffness of the footing
More than the bending stiffness of single indexing disc portion；It the described method comprises the following steps：
By the way that the cost function of the whole rotation amplitude of the hairspring in use is minimized, to the described first indexing disc portion and institute
The cross-sectional profiles second moment for stating footing is improved, and the net concentricity of the cost function and the hairspring has
Close；
The cross-sectional profiles second moment of improved first indexing disc portion and footing is based on following item in the hairspring：
Position, the arc length of the improvement part of the hairspring, and determined along described in the hairspring along the position of hairspring bar
The function of the cross-sectional profiles second moment change of improvement part.
2. according to the method described in claim 1, it is characterised in that：The cost function is the rotation of hairspring in use
In the gamut of rotational oscillation width, the integration of the value of the stud reaction force.
3. according to the method described in claim 1, it is characterised in that：The cost function is the rotation of hairspring in use
In the gamut of rotational oscillation width, the maximum of the value of the stud reaction force.
4. according to the method described in claim 1, it is characterised in that：The cost function is the rotation of hairspring in use
In the gamut of rotational oscillation width, when escapement angle is zero relative to the center coordination of hairspring, the center coordination of the hairspring
The integration of value.
5. according to the method described in claim 1, it is characterised in that：The cost function is the rotation of hairspring in use
In the gamut of rotational oscillation width, when the rotation amplitude is zero relative to the center coordination of hairspring, the barycenter of the hairspring is determined
The maximum of the value of position.
6. according to the method described in claim 1, it is characterised in that：The change of the cross-sectional profiles second moment is constant.
7. according to the method described in claim 1, it is characterised in that：The change of the cross-sectional profiles second moment is based on multinomial
Formula function.
8. according to the method described in claim 1, it is characterised in that：The change of the cross-sectional profiles second moment is to be based on triangle
Function.
9. according to the method described in claim 1, it is characterised in that：The change of the cross-sectional profiles second moment is to be based on two
Or the discontinuous function of the combination of two or more sectional-continuous function.
10. according to the method described in claim 1, it is characterised in that：Optimized algorithm used is based on gradient descent method, the ladder
Degree descent method needs to calculate gradient of the cost function relative to design parameter.
11. a kind of hairspring for stem-winder, it is characterised in that：The hairspring has in for being closed with interior staking
End part, and the outer end end part for being engaged with stud are held, outer end end part is partially toward from the inner end and prolongs
The the first indexing disc portion stretched, and the footing at the outer ring of the hairspring, the footing, which has, to be different from
The cross-sectional profiles second moment of the first indexing disc portion；The cross section of first indexing disc portion and the footing
Second moment of area is determined by method any one of claim 1 to 10.
12. hairspring according to claim 11, it is characterised in that：In single indexing disc portion and the footing
Two or more indexing disc portions spaced apart be rectangular cross section, and each other all have same widths and identical height
Degree.
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| HK12106963.6 | 2012-07-17 | ||
| HK12106963.6A HK1178377A2 (en) | 2012-07-17 | 2012-07-17 | Hairspring design for concentricity |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN103543630A CN103543630A (en) | 2014-01-29 |
| CN103543630B true CN103543630B (en) | 2017-09-08 |
Family
ID=49115686
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201310300281.8A Active CN103543630B (en) | 2012-07-17 | 2013-07-17 | Method for improving concentricity when using spiral spring mechanical watch and spiral spring |
Country Status (2)
| Country | Link |
|---|---|
| CN (1) | CN103543630B (en) |
| HK (1) | HK1178377A2 (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP4372479A1 (en) * | 2022-11-18 | 2024-05-22 | Richemont International S.A. | Method for manufacturing timepiece hairsprings |
Families Citing this family (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP3159747A1 (en) * | 2015-10-22 | 2017-04-26 | ETA SA Manufacture Horlogère Suisse | Compact hairspring with constant cross-section |
| JP6789140B2 (en) * | 2017-01-31 | 2020-11-25 | セイコーインスツル株式会社 | Temperature-compensated balance, movement and watch |
| CN115146377B (en) * | 2022-06-23 | 2023-02-24 | 西北工业大学 | Coordinated design method for structural rigidity of aircraft with layout of connecting wings |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP2233989A1 (en) * | 2009-03-24 | 2010-09-29 | Manufacture et fabrique de montres et chronomètres Ulysse Nardin Le Locle SA | Hairspring and its index-assembly |
| CN101878454A (en) * | 2007-11-28 | 2010-11-03 | 尤利西斯·雅典钟表及天文时计制造厂(勒洛克勒)股份有限公司 | Mechnical oscillator with thermoelastic coefficient of optimization |
| CN102023558A (en) * | 2009-09-21 | 2011-04-20 | 劳力士有限公司 | Flat hairspring for a clock balance wheel and balance wheel -hairspring assembly |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP2410387B1 (en) * | 2010-07-19 | 2016-07-06 | Nivarox-FAR S.A. | balance wheel with inertia adjustment without insert |
-
2012
- 2012-07-17 HK HK12106963.6A patent/HK1178377A2/en not_active IP Right Cessation
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2013
- 2013-07-17 CN CN201310300281.8A patent/CN103543630B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101878454A (en) * | 2007-11-28 | 2010-11-03 | 尤利西斯·雅典钟表及天文时计制造厂(勒洛克勒)股份有限公司 | Mechnical oscillator with thermoelastic coefficient of optimization |
| EP2233989A1 (en) * | 2009-03-24 | 2010-09-29 | Manufacture et fabrique de montres et chronomètres Ulysse Nardin Le Locle SA | Hairspring and its index-assembly |
| CN102023558A (en) * | 2009-09-21 | 2011-04-20 | 劳力士有限公司 | Flat hairspring for a clock balance wheel and balance wheel -hairspring assembly |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP4372479A1 (en) * | 2022-11-18 | 2024-05-22 | Richemont International S.A. | Method for manufacturing timepiece hairsprings |
Also Published As
| Publication number | Publication date |
|---|---|
| HK1178377A2 (en) | 2013-09-06 |
| CN103543630A (en) | 2014-01-29 |
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