EP3542224B1 - Watch escapement with optimized torque transmission - Google Patents

Description

Technical area

The present invention relates to the field of watchmaking. It relates, more particularly, to an exhaust with optimized torque transmission.

State of the art

A conventional escapement, such as a Swiss lever escapement, English lever escapement, Daniels escapement, or the like, comprises a lever which intermittently locks an escape wheel, and transmits energy from the going train to the regulating organ when the wheel is released. Oscillations of the regulating organ, such as a balance-spring, actuate the anchor in order to perform this periodic release of the escape wheel, and again supply an impulse to the regulating organ to maintain its oscillations.

To this end, the anchor comprises at least two pallets, one - entry - located upstream with respect to the direction of rotation of the escape wheel, the other - exit - located downstream. At each alternation of the regulating organ, the pallet which is engaged with the escapement wheel is raised, releasing the escapement wheel and transmitting an impulse to the regulating organ via an impulse face that includes each palette. At the same time, the other pallet is moved into the path of the teeth of the escape wheel, and blocks it. Then, the cycle starts again for the other pallet.

Typically, impulse faces consist of planes. Although these simple shapes are easy to manufacture, the torque transmission varies along the pulse phase, which is detrimental to the performance of the escapement.

Furthermore, such planar impulse faces often give rise to detachment of the pallet, in particular when it makes the transition from the impulse phase on the pallet to the impulse phase on the tooth, which also impairs the exhaust performance.

The document CH702689 describes an escapement in which the output vane and/or the input vane has an impulse face which is curved such that, during a whole part of the impulse phase, the angle defined by the impulse faces of the tooth and the pallet at the point of contact between these faces is at most equal to 7°. This certainly represents an improvement over flat impulse faces, but the shape chosen does not eliminate variations in torque transmission. A modeling study has shown that the derivative of the torque ratio between that of the lever and that of the escape wheel with respect to the angle of the escape wheel changes sign several times, and said torque ratio varies on the order of 25% to 35% along the concave part of the vane. In addition, the convex part at the start of the pulse face has an entirely conventional radius of curvature, which results from current manufacturing methods, and has in no way been optimized.

The object of the present invention is therefore to at least partially overcome the drawbacks mentioned above.

Disclosure of Invention

To this end, the invention relates to an escapement for a timepiece. This escapement comprises an escapement wheel mounted to pivot around an axis of rotation and intended to be driven by a driving source, said escapement wheel comprising a plurality of teeth.

The escapement further comprises an anchor mounted pivoting around an axis of rotation, and comprises an input pallet as well as an output pallet. Each pallet comprises a rest face arranged to block said escapement wheel during rest phases, as well as an impulse face arranged to interact with said escapement wheel in order to transmit impulses received from the latter to a member regulator arranged to perform oscillations, said lever being arranged to release said escape wheel periodically under the control of said regulating member.

avec $$R_2=\sqrt{R^2\ast {\mathit{sin}}^2\left(\alpha \right)+{\left(-R\ast \cos \left(\alpha \right)+L\right)}^2}$$

et avec $$\theta ={\tan }^{-1}\left(R\ast \frac{\sin \left(\alpha \right)}{L-R\ast \cos \left(\alpha \right)}\right).$$

According to the invention, at least one, preferably each, of said impulse faces is shaped such that, on at least part of said impulse face, and considered at each point of contact between the wheel of escapement and said impulse face, the tangent of said impulse face intersects the center distance between the escapement wheel and the lever at an angle which observes the relationship $${\alpha }_{\mathit{orientation}}=\alpha -\mathit{COF}+{\tan }^{-1}\left(\frac{\mathrm{VS}\ast R+\cos \left(\alpha -\theta \right)\ast R_2}{R_2\ast \sin \left(\alpha -\theta \right)}\right)+/-10\%$$

with $$R_2=\sqrt{R^2\ast {\mathit{sin}}^2\left(\alpha \right)+{\left(-R\ast \cos \left(\alpha \right)+L\right)}^2}$$

and with $$\theta ={\tan }^{-1}\left(R\ast \frac{\sin \left(\alpha \right)}{L-R\ast \cos \left(\alpha \right)}\right).$$

• α_orientation est l'angle entre ladite tangente et ledit entraxe ;
• α est l'angle entre une ligne joignant ledit point de contact et l'axe de rotation de ladite roue d'échappement et ledit entraxe ;
• COF est la tangente trigonométrique du coefficient de frottement entre la roue d'échappement et ladite face d'impulsion (c'est-à-dire tan(µ) selon la notation habituelle) ;
• R est la distance entre l'axe de rotation de ladite roue d'échappement et ledit point de contact, +/- 10% ;
• C est le rapport de couple entre celui de l'ancre et celui de la roue d'échappement (c'est-à-dire C_ancre/C_roue) audit point de contact ; et
• L est la longueur dudit entraxe.

In these equations, all angles are expressed in radians, and

• α _orientation is the angle between said tangent and said spacing;
• α is the angle between a line joining said point of contact and the axis of rotation of said escape wheel and said center distance;
• COF is the trigonometric tangent of the coefficient of friction between the escapement wheel and said impulse face (that is to say tan(μ) according to the usual notation);
• R is the distance between the axis of rotation of said escape wheel and said point of contact, +/- 10%;
• C is the torque ratio between that of the anchor and that of the escape wheel (that is to say C _anchor /C _wheel ) at said point of contact; and
• L is the length of said center distance.

By doing so, the torque transmission between the escape wheel and the lever is improved, since it remains constant along the impulse phase. This constant transmission maximizes the torque transmitted, improves the efficiency of the escapement and minimizes disturbance to the regulating organ. It should be noted that a study has shown that the shape of the document palette CH702689 does not correspond to the shape defined above, and that the torque transmission is not substantially constant, as mentioned in the preamble. This is mainly (but not exclusively) due to the fact that the angle defined by the impulse faces of the tooth and the pallet at the point of contact between these faces is constant and is at most equal to 7° (preferably at plus equal to 5°), which can never be consistent with the above equations.

If we apply these equations to an escapement of conventional geometry, the impetus face of the inlet pallet is thus convex, and that of the output palette is concave, on the part of each face for which the relations are valid.

Advantageously, the shape of at least a part of each of said impulse faces observes said relationship, which has the effect that the transmission of torque is constant for each pallet.

Advantageously, the escape wheel comprises teeth having convex impulse faces. The transition between the various phases is thus smoothed, which prevents the pallet from lifting off the wheel during the cycle.

For the same purpose, the invention also relates to an escapement which comprises an escapement wheel mounted to pivot around an axis of rotation and intended to be driven by a power source, said escapement wheel comprising a plurality of teeth. The escapement further comprises an anchor mounted pivoting around an axis of rotation, and comprises an input pallet as well as an output pallet. Each pallet comprises a rest face arranged to block said escapement wheel as well as an impulse face arranged to interact with said escapement wheel in order to transmit impulses received from the latter to a regulating member arranged to perform oscillations , said anchor being arranged to release said escape wheel periodically under the control of said regulating member.

According to the invention, on at least part of an impulse face that each of said teeth comprises, and considered at each point of contact between said impulse face and one of said pallets (in particular the downstream beak of one of the latter), the tangent of said impulse face intersects the center distance between the escapement wheel and the lever at an angle which observes the relationship $${\alpha }_{\mathit{orientation}}={\tan }^{-1}\left(\frac{R\ast \mathit{Threshold}\ast \alpha \ast \cos \left(\alpha \right)+\mathrm{VS}\ast R\ast \cos \left(\alpha \right)+R\ast \cos \left(\alpha \right)-L}{R\ast \sin \left(\alpha \right)\ast \left(\mathit{Threshold}\ast \alpha +\mathrm{VS}-1\right)}\right)+/-10\%$$

• α_orientation est l'angle entre ladite tangente et ledit entraxe ;
• α est l'angle entre une ligne joignant ledit point de contact et l'axe de rotation de ladite roue d'échappement et ledit entraxe ;
• Seuil est est une valeur d'un seuil de décollement entre la roue d'échappement et l'ancre choisi par exemple par expérimentation ou par modélisation qui est égale ou inférieure à 0.01 ;
• R est la distance entre l'axe de rotation de ladite roue d'échappement et ledit point de contact, +/- 10% ;
• C est le rapport de couple entre celui de l'ancre et celui de la roue d'échappement audit point de contact ;
• L est la longueur dudit entraxe.

In this equation,

• α _orientation is the angle between said tangent and said spacing;
• α is the angle between a line joining said point of contact and the axis of rotation of said escape wheel and said center distance;
• Threshold is a value of a separation threshold between the escape wheel and the anchor chosen for example by experimentation or by modeling which is equal to or less than 0.01;
• R is the distance between the axis of rotation of said escape wheel and said point of contact, +/- 10%;
• C is the torque ratio between that of the anchor and that of the escape wheel at said point of contact;
• L is the length of said center distance.

By doing so, a detachment of the pallet from the tooth can be eliminated when the pallet makes the transition from the so-called "impulse on the pallet" phase to the "impulse on the tooth" phase, since the strong acceleration which occurs with typical tooth shapes is significantly reduced. Since the pallet remains constantly in contact with the tooth and does not lift off, the transmission of torque from the escape wheel to the lever, and thus the efficiency of the escapement, is improved. Even if the document CH702689 generically mentions that the escape wheel teeth may be slightly curved, this does not correspond to the specific shape defined above. Moreover, and as mentioned in the preamble, the combination of the shape of the teeth as well as that of the blades is particularly susceptible to detachment during the transition of the tooth between the rest face and the impulse face, and can therefore never be conforms to the above equation.

If this equation is applied to an escapement having a conventional geometry, the impulse faces of the teeth of the escape wheel will be convex.

Advantageously, said Threshold value is a function of the first derivative of the speed ratio of the anchor on the escape wheel during the impulse on the beak of said pallet. Alternatively, this value can be set arbitrarily.

Advantageously, the escapement according to the invention comprises each of the aforementioned optimizations, that is to say that relating to the impulse faces of the pallets, as well as that relating to the impulse face of the teeth of the wheel. exhaust.

The invention also relates to a timepiece movement comprising an escapement as defined above, as well as to a timepiece comprising such a movement.

Brief description of the drawings

• la figure 1 représente une vue schématique en plan d'un échappement selon l'invention ;
• la figure 2 représente une vue agrandie d'une dent de la roue d'échappement et de la palette d'entrée ;
• la figure 3 représente une vue agrandie de la palette de sortie ;
• la figure 4 représente une modélisation schématique du point de contact entre l'ancre et la roue d'échappement ;
• la figure 5 représente une vue schématique exagérée du développement de la tangente du profil de la face d'impulsion de la palette d'entrée le long de la phase d'impulsion ;
• la figure 6 représente une vue schématique exagérée du développement de la tangente du profil de la face d'impulsion de la palette de sortie le long de la phase d'impulsion ;
• la figure 7 représente un graphique du développement de la tangente du profil de la face d'impulsion de la palette d'entrée le long de la phase d'impulsion, en termes d'angle et en termes du temps ;
• la figure 8 représente un graphique du développement de la tangente du profil de la face d'impulsion de la palette de sortie le long de la phase d'impulsion, en termes d'angle et en termes du temps ;
• la figure 9 représente une vue schématique exagérée du développement de la tangente du profil de la face d'impulsion d'une dent de la roue d'échappement le long de la phase d'impulsion ;
• la figure 10 représente un graphique du développement de la tangente du profil de la face d'impulsion d'une dent de la roue d'échappement le long de la phase d'impulsion ; et
• la figure 11 représente un graphique du développement du rapport de vitesse de l'ancre sur la roue d'échappement au cours de la phase d'impulsion.

The invention will be better understood on reading the following description of an embodiment, given by way of example and made with reference to the drawings in which:

• the figure 1 shows a schematic plan view of an escapement according to the invention;
• the picture 2 shows an enlarged view of an escape wheel tooth and the entrance pallet;
• the picture 3 represents a magnified view of the output palette;
• the figure 4 represents a schematic model of the point of contact between the lever and the escapement wheel;
• the figure 5 shows an exaggerated schematic view of the development of the tangent of the input vane impulse face profile along the impulse phase;
• the figure 6 shows an exaggerated schematic view of the development of the tangent of the output vane impulse face profile along the impulse phase;
• the figure 7 plots the development of the tangent of the input vane impulse face profile along the impulse phase, in terms of angle and in terms of time;
• the figure 8 shows a graph of the development of the tangent of the output vane impulse face profile along the impulse phase, in terms of angle and in terms of time;
• the figure 9 shows an exaggerated schematic view of the development of the tangent of the impulse face profile of an escape wheel tooth along the impulse phase;
• the figure 10 shows a graph of the development of the tangent of the profile of the impulse face of an escape wheel tooth along the impulse phase; and
• the figure 11 represents a graph of the development of the velocity ratio of the anchor on the escape wheel during the impulse phase.

Embodiment(s) of the Invention

The figure 1 illustrates an escapement 1 according to the invention. This escapement 1 takes the general form of a Swiss lever escapement, in which each pallet takes part in providing an impulse to the regulating organ.

As generally known, the escapement includes an escape wheel 3, arranged to be driven by a power source not shown. This driving source can be for example a mainspring or an electric motor, which is in kinematic connection with the escapement wheel 3 via a going train (also not shown).

The escapement wheel 3 is pivotally mounted on a shaft (not shown), the theoretical axis of which is indicated by the reference sign 5. In the variant illustrated, the teeth of the escapement wheel 7 each have an upstream face 7a, which interacts with the pallets when the escape wheel 3 is blocked, and an impulse face. However, the invention applies to other shapes of escape wheel, for example with pointed teeth (English lever escapement), or to less conventional shapes.

The teeth 7 of the escape wheel 3 interact in a known way with an anchor 9, which pivots around a theoretical axis of rotation 11. In the variant illustrated, this theoretical axis 11 coincides with a shaft (not illustrated), but an anchor of the “suspended” type as described in the document CH708113 , or any other suitable type is also possible. The line joining the axis of rotation 5 of the escape wheel 3 and that of the lever defines a center distance 12.

The general shape of the illustrated anchor 9 is conventional. To this end, it comprises a rod 9a extending from the axis of rotation 11 and ending in a fork 9c, which interacts with a regulating member (not shown) in a known manner in order to cause it to oscillate with a predetermined periodicity, which need not be described here in detail. Furthermore, a pair of arms 9b extend on either side of the axis of rotation 11 in directions substantially perpendicular to the rod 9a, and end in pallets 13, 15. It goes without saying that d other forms of anchor less usual can also be used within the scope of the invention.

Each of these pallets 13, 15 is arranged to block and to periodically release the escape wheel, the latter being blocked by one of the pallets 13, 15, then re-blocked by the other, in sequence.

Pallet 13 shown on the right in the figure 1 is the input pallet, located upstream with respect to the direction of rotation of the escape wheel 3 indicated by the arrow, and the pallet 15, located downstream, is the output pallet.

In the variant illustrated, the pallets 13, 15 come in one piece with the anchor 9, but the invention also applies to pallets attached to the arms 9b. Each pallet 13, 15 comprises, as generally known, a rest face 13a respectively 15a, and a pulse face 13b respectively 15b. The rest faces 13a, 15a serve to block the escape wheel 3 during phases of rest, and the impulse faces 13b, 15b cooperate with the teeth 7 to transmit an impulse to the lever and thus to the regulating organ during the impulse phase. Each of these teeth 7 comprises a resting beak 7c, which interacts with the resting faces 13a, 15a of the pallets 13, 15, as well as an oblique impulse face 7b. The resting beak 7c which is located between the upstream face 7a and the impulse face 7b, as well as this impulse face 7b, contribute to transmitting an impulse to the anchor 9.

In a typical escapement of the type which has just been defined, the rest faces 13a, 15a are typically planes, the angle of which is chosen so that, during the phases of rest, the force F resulting from the contact between the rest face 13a, 15a and tooth 7 comprises a component which tends to keep pallet 13 or 15, as the case may be, engaged with escape wheel 3. This force F consequently generates a torque around the axis of rotation 11 of the anchor 9 which tends to cause the anchor to rotate counterclockwise (depending on the orientation of the figure 1 ) when the input paddle 13 is engaged, and clockwise when the output paddle 15 is engaged.

In a typical escapement, the impulse faces of the pallets 13b, 15b are typically planes, which leads, during the impulses, to a reduction in the torque transmitted from the escapement wheel 3 to the lever 9 along of each pulse phase. This torque variation is inefficient, and limits the performance of exhaust 1.

The invention therefore relates mainly to the shape of the impulse faces 13b, 15b of the pallets 13, 15, as well as that of the impulse face 7b of the teeth 7 of the escape wheel 3. Since the active faces 13a, 13b, 15a, 15b of the paddles are not, or at least should not be, planar, the terminology of "face" is used instead of the usual formulation "plane of...".

The figure 4 illustrates schematic modeling that can be used to calculate the shape of vane impulse faces. In the diagram that constitutes this figure, the geometric relationship between the point of contact C' between the impulse face 13b of the input pallet and a tooth 7 of the escapement wheel 3, the escapement wheel 3, and center distance 12 is shown.

avec $$R_2=\sqrt{R^2\ast {\mathit{sin}}^2\left(\alpha \right)+{\left(-R\ast \cos \left(\alpha \right)+L\right)}^2}$$

et avec $$\theta ={\tan }^{-1}\left(R\ast \frac{\sin \left(\alpha \right)}{L-R\ast \cos \left(\alpha \right)}\right)$$

So that the force F exerted by the escapement wheel 3 on the input pallet 13 generates a torque which is constant along the impulse phase, the angle α _orientation between the tangent of the impulse face 13b of the input vane and center distance 12 must observe the following relationship, obtained by solving the forces, at each point along the momentum phase: $${\alpha }_{\mathit{orientation}}=\alpha -\mathit{COF}+{\tan }^{-1}\left(\frac{\mathrm{VS}\ast R+\cos \left(\alpha -\theta \right)\ast R_2}{R_2\ast \sin \left(\alpha -\theta \right)}\right)$$

with $$R_2=\sqrt{R^2\ast {\mathit{sin}}^2\left(\alpha \right)+{\left(-R\ast \cos \left(\alpha \right)+L\right)}^2}$$

and with $$\theta ={\tan }^{-1}\left(R\ast \frac{\sin \left(\alpha \right)}{L-R\ast \cos \left(\alpha \right)}\right)$$

To the relation which defines α _orientation , one can add a tolerance of +/- 10%, preferably +/- 7%, more preferably +/- 5% or even +/- 3% or +/- 2% in order to to present realistic manufacturing tolerances.

In these equations, all angles are expressed in radians. α is the angle between a line joining said point of contact and the axis of rotation of said escape wheel 3, and said center distance 12, defined mathematically. This angle therefore decreases along the pulse phase on the input paddle 13 since the point of contact C′ approaches the center distance 12 when the wheel exhaust 3 spins. COF is the trigonometric tangent (in radians) of the coefficient of friction between the escapement wheel and said impulse face, that is to say tan(μ) according to conventional notation; R is the distance between the axis of rotation of said escape wheel and said point of contact, with a tolerance of +/- 10%, preferably +/- 7%, more preferably +/- 5% or even +/- 3% or +/- 2% in order to present realistic manufacturing tolerances; C is the torque ratio between that of the anchor relative to that of the escape wheel, ie C _anchor / C _wheel ; and L is the length of said center distance 12.

It should be noted that, in view of the tolerance on the value of R as well as that on α _orientation , the invention encompasses a family of possible curves. This is inevitable given the manufacturing tolerances, since it is very difficult to manufacture, in a reproducible manner, a curve which is mathematically perfect.

For the output pallet 15, the same relation is also valid, because the geometry is similar, the point of contact C′ being of course located on the other side of the center distance 12.

The figure 5 illustrates, in an exaggerated way, the development of α _orientation of the impulse face 13b of the input pallet 13 along its impulse phase. It is clear that, when the escape wheel 3 rotates and the contact point C′ evolves along an arc of a circle, that the _orientation angle α increases when α decreases for the reasons explained above. The figure 7 illustrates this growth as a function of the angle a(t) of the contact point C' over time, and the values of the _orientation angle α thus calculated at a plurality of points can be used to define tangents which can be combined in a smoothed manner to define the shape of the impulse face 13b of the input vane 13, over at least part of its length. This part can extend over for example at least 20%, at least 40%, at least 50%, at least 60% or even at least 80% or 90% of the length of said pulse face 13b. From these figures, it is clear that said impulse face 13 will be convex.

In the same way, the figure 6 illustrates, also exaggeratedly, the development of α _orientation of the impulse face 15b of the output vane 15 along its pulse phase. It is clear that, when the escape wheel 3 rotates and the contact point C′ evolves according to an arc of a circle, the _orientation angle α decreases. The figure 8 illustrates this decrease as a function of the angle α of the contact point C′; indeed during the movement a moves away from the center distance or α is strictly negative in the counterclockwise sense, so α(t) decreases during the movement. Again, the angles α _orientation thus calculated can be used to define tangents which can be combined in order to define the shape of the impulse face 15b of the output vane 15, over at least part of its length. This part can extend over for example at least 20%, at least 40%, at least 50%, at least 60% or even at least 80% or 90% of the length of said pulse face 15b. In the case of the output pallet 15, the angle α increases during the corresponding pulse phase, since the point of contact C' moves away from the center distance 12. From these figures, it is clear that said impulse face 15 will be concave.

By means of the above, the shapes of the impulse planes 13b, 15b, of the pallets can be determined for an escapement having a given geometry, and this by taking into account the shape of the impulse faces 7b of the teeth 7 of the escapement wheel 3, which determines the development of the position of the point of contact with the pallets 13, 15 along the impulse phases.

Even if the shapes of the pallets 13, 15 as determined above can be used in conjunction with an escapement wheel of known shape, it is advantageous to adapt the shape of the impulse faces 7b so that a separation of the escape wheel pallet is avoided.

Indeed, in the case of a conventional escapement, when tooth 7 of escape wheel 3 makes the transition from the rest face 13a, 15a of a pallet to its impulse face 13b, 15b (known as the name "impulse on the pallet" since the tooth 7 interacts with the impulse face 13b, 15b of the pallet), there is an acceleration of the escape wheel 3 and of the anchor 9. Moreover, during the last part of the impulse phase, when the tooth interacts with the downstream beak 13c, 15c of the pallet 13, 15 (known as the "impulse on the tooth", since it is the downstream nose 13c, 15c of the pallet which interacts with the tooth 7), a second, even stronger acceleration is created. If these accelerations are too high, the pallet 13, 15 can take off from the escape wheel 3, which has the effect that the contact between these two elements is broken.

Starting from the same model illustrated in the figure 4 , it is possible to determine the profile of the impulse face 7b of the teeth 7 of the escapement wheel which avoids such separation during the transition from the impulse face 7b to the downstream beak 7d.

From the geometry of the contact between the escapement wheel 3 and the impulse face 13b, 15b of one of the pallets, it is possible to calculate a torque ratio C between the torque of the lever and the torque of the escapement wheel as a function of the angle α as follows: $$\mathrm{VS}\left(\alpha \right)=-\frac{{\mathrm{R}}_2}{R}\ast \frac{\cos \left({\mathrm{\alpha }}_{\mathit{orientation}}-\theta +\mathit{COF}\right)}{\cos \left({\alpha }_{\mathit{orientation}}-\alpha +\mathit{COF}\right)}$$

In this case, α _orientation represents the angle formed between the tangent of the impulse face 7b of the tooth 7 at the contact point C' and the center distance 12, the other variables being as described above in the context of the profile of the impulse faces 13b, 15b of the vanes 13, 15. To avoid separation, the value C must be lower than a predefined threshold value (see below).

où C est le rapport de couple à ce changement de bec et Seuil est une valeur d'un seuil de décollement calculé par expérimentation ou par modélisation, ou même défini arbitrairement. Plus concrètement, on peut par exemple définir un dérivé limite du rapport de vitesse de l'ancre 9 sur la roue 3, par modélisation. Le paramètre Seuil est tellement influencé par la géométrie de l'échappement, mais des modélisations ont indiqués qu'une valeur d'au maximum 0.01, de préférence au maximum 0.005 sont généralement applicables, ou peut servir en tout cas comme points de départ.During the impulse phase on the tooth, that is to say when the downstream beak 13c, 15c is in contact with the impulse face 7b of a tooth 7 of the escape wheel 3, $$\mathrm{VS}\left(\alpha \right)\le \mathit{Threshold}\ast \alpha +\mathrm{VS}$$

where C is the torque ratio at this change of beak and Seuil is a value of a separation threshold calculated by experimentation or by modeling, or even defined arbitrarily. More concretely, it is possible for example to define a limit derivative of the speed ratio of the anchor 9 on the wheel 3, by modeling. The Threshold parameter is so influenced by the geometry of the escapement, but modeling has indicated that a value of at most 0.01, preferably at most 0.005 are generally applicable, or can serve as starting points anyway.

et $${\alpha }_{\mathit{orientation}}={\tan }^{-1}\left(\frac{R\ast \mathit{Seuil}\ast \alpha \ast \cos \left(\alpha \right)+C\ast R\ast \cos \left(\alpha \right)+R\ast \cos \left(\alpha \right)-L}{R\ast \sin \left(\alpha \right)\ast \left(\mathit{Seuil}\ast \alpha +C-1\right)}\right)$$

As a result, $$\mathit{Threshold}\ast \alpha +\mathrm{VS}=\frac{{\mathrm{R}}_2}{R}\ast \frac{\cos \left({\mathrm{\alpha }}_{\mathit{orientation}}-\theta +\mathit{COF}\right)}{\cos \left({\alpha }_{\mathit{orientation}}-\alpha +\mathit{COF}\right)}$$

and $${\alpha }_{\mathit{orientation}}={\tan }^{-1}\left(\frac{R\ast \mathit{Threshold}\ast \alpha \ast \cos \left(\alpha \right)+\mathrm{VS}\ast R\ast \cos \left(\alpha \right)+R\ast \cos \left(\alpha \right)-L}{R\ast \sin \left(\alpha \right)\ast \left(\mathit{Threshold}\ast \alpha +\mathrm{VS}-1\right)}\right)$$

To this relation, we can add a tolerance of +/- 10%, preferably +/-7%, more preferably +/- 5% or even +/- 3% or +/- 2% to the value of α _orientation , in order to present realistic manufacturing tolerances. It should be noted that, in view of the tolerance on the value of R as well as that on α _orientation , the invention encompasses a family of possible curves. This is inevitable given the manufacturing tolerances, since it is very difficult to manufacture, in a reproducible manner, a curve which is mathematically perfect.

Consequently, when α increases along the momentum phase, α _orientation also increases, approximately linearly. Thus, the profile of the impulse face 7b of the teeth 7 is convex, as illustrated in exaggerated form on the figure 9 . The development of α _orientation as a function of the angle α is also illustrated in the figure 10 .

Again, as is the case for the vanes 13, 15, the angle α _orientation can be calculated at several points, in order to determine the profile of said impulse face 7b in the manner mentioned above.

The figure 11 is a normalized graph illustrating a comparison of the speed ratio of the lever 9 on the escapement wheel 3 on a clearance and an impulse, for a conventional escapement (“Rv Standard Profiles”) and an escapement according to the invention (“ Rv Curved profiles”). This graph illustrates both the effect of the shape of the impulse faces 13b, 15b which ensures constant torque transmission during the impulse phase on the impulse face 7b of a tooth 7, as well as the effect of the curved profile of the teeth 7 of the escape wheel.

With regard to the transmission of constant torque, looking at the part of the graph indicated by "impulse on the pallet", for the conventional escapement, the speed ratio "Rv Standard profiles" decreases along this phase, for the reasons mentioned above. On the other hand, for the escapement according to the invention, the speed ratio “Rv Curved Profiles” remains constant, since the torque ratio remains constant. It is also clear from this graph that the integral of the function "Rv Curved Profiles" during the impulse phase on the face is greater than that of "Rv Standard Profiles", and therefore more energy is supplied to the anchor during this phase of the impulse. Indeed, the aforementioned Threshold value can be determined by considering the desired slope for the “Rv Curved Profiles” line during the impulse on the tooth, which represents the first derivative of the angular velocity ratio.

This graph also illustrates the effect of the curved profile of the impulse face 7b of the teeth 7 of the escapement wheel 3. Since this face 7b is curved, the slope of the gear ratio curve has a slope significantly less than that which occurs in the classic case “Rv standard profiles”. Detachment can thus be avoided.

In the case where the shape of the impulse planes 7b of the teeth 7 of the escapement wheel 3 is straight, the corresponding curve will follow that of "Rv Curved profiles" up to the intersection with the vertical line having the standardized value 800, and then will be confused with that of "Rv Standard Profiles" until the end of the pulse phase.

Although this profile of the impulse faces 7b of the teeth 7 of the escapement wheel 3 is illustrated here in combination with the optimized shapes of the pallets 13, 15, it can nevertheless be used with known pallets, for example pallets having standard plans.

Calculations have shown that the shape of the impulse faces 13b, 15b of the pallets 13, 15 increases the efficiency by about 2 to 3 points, and the shape of the impulse face 7b of the teeth 7 of the escape wheel increases it by about 2 to 3 additional points. The combination of the two optimizations therefore adds approximately 4 to 6 points of efficiency to the exhaust.

The anchor 9 and/or the escape wheel 3 described above can, for example, be manufactured by micro-machining processes, such as LIGA, 3D printing, masking and engraving from a slab of material, stereolithography, or the like. Suitable materials can, for example, be chosen from monocrystalline, polycrystalline or amorphous metals (such as steel, nickel-phosphorus, brass or similar), non-metals such as silicon, its oxide, its nitride or its carbide, alumina in all its forms, diamond (including adamantine carbon), these non-metallic materials being monocrystalline or polycrystalline. All these materials may optionally be coated with another hard and/or anti-friction material, such as adamantine carbon or silicon oxide.

The use of these curved profiles leads to an improvement in the efficiency of the escapement 1 of the order of 5% if the profiles are adopted on the pallets 13, 15 and on the escape wheel 3.

Although the invention has been described above in connection with specific embodiments, additional variants are also possible without departing from the scope of the invention as defined by the claims.

Claims (11)

1. Escapement (1) for a timepiece, comprising:

   - an escapement wheel (3) mounted in a pivotable manner about a corresponding axis of rotation (5) and intended to be driven by a power source, said escapement wheel (3) including a plurality of teeth (7);

   - an anchor (9) mounted in a pivotable manner about a corresponding axis of rotation (11), said anchor (9) comprising an entry pallet (13) and an exit pallet (15), each pallet (13, 15) comprising a rest face (13a, 15a) arranged to block said escapement wheel (3), as well as an impulsion face (13b, 15b) arranged to interact with said escapement wheel (3) in order to transmit impulsions received from the latter to a regulating member arranged to produce oscillations, said anchor (9) being arranged to release said escapement wheel (3) periodically under the control of said regulating member,

   characterized in that at least one of said impulsion faces (13b, 15b) is configured in such a way that, on at least one part of said impulsion face (13b, 15b), and considered at each point of contact (C') between the escapement wheel (3) and said impulsion face (13b, 15b), the tangent of said impulsion face (13b, 15b) intersects the center-to-center line (12) between the escapement wheel (3) and the anchor (9) at an angle (α_orientation) which observes the relationship: $${\alpha }_{\mathit{orientation}}=\alpha -\mathit{COF}+{\tan }^{-1}\left(\frac{C\ast R+\cos \left(\alpha -\theta \right)\ast R_2}{R_2\ast \sin \left(\alpha -\theta \right)}\right)+/-10\%$$

   

   where $$R_2=\sqrt{R^2\ast {\mathit{sin}}^2\left(\alpha \right)+{\left(-R\ast \cos \left(\alpha \right)+L\right)}^2}$$

   

   and where $$\theta ={\tan }^{-1}\left(R\ast \frac{\sin \left(\alpha \right)}{L-R\ast \cos \left(\alpha \right)}\right)$$

   

   in which all the angles are expressed in radians, and

   - α_orientation is the angle between said tangent with said center-to-center line (12);

   - α is the angle between a line joining said point of contact (C') and the axis of rotation (5) of said escapement wheel and said center-to-center line (12);

   - COF is the trigonometric tangent of the coefficient of friction between the escapement wheel (3) and said impulsion face (13b, 15b);

   - R is the distance between the axis of rotation (5) of said escapement wheel (3) and said point of contact (C'), +/- 10%;

   - C is the torque ratio between that of the anchor (9) and that of the escapement wheel (3);

   - L is the length of said center-to-center line (12).
2. Escapement (1) according to Claim 1, in which the impulsion face (13b) of the entry pallet (13) is convex.
3. Escapement (1) according to one of Claims 1 and 2, in which the impulsion face (15b) of the exit pallet (15) is concave.
4. Escapement (1) according to one of the preceding claims, in which the form of at least one part of each of said impulsion faces (13b, 15b) observes said relationship.
5. Escapement (1) according to one of the preceding claims, in which the escapement wheel (3) includes teeth (7) having convex impulsion faces (7b).
6. Escapement (1) for a timepiece, comprising:

   - an escapement wheel (3) mounted in a pivotable manner about a corresponding axis of rotation (5) and intended to be driven by a power source, said escapement wheel (3) including a plurality of teeth (7);

   - an anchor (9) mounted in a pivotable manner about a corresponding axis of rotation (11), said anchor (9) comprising an entry pallet (13) and an exit pallet (15), each pallet (13, 15) comprising a rest face (13a, 15a) arranged to block said escapement wheel (3), as well as an impulsion face (13b, 15b) arranged to interact with said escapement wheel (3) in order to transmit impulsions received from the latter to a regulating member arranged to produce oscillations, said anchor (9) being arranged to release said escapement wheel (3) periodically under the control of said regulating member,
   characterized in that, on at least one part of an impulsion face (7b) that each of said teeth (7) includes, and considered at each point of contact (C') between said impulsion face (7b) and one of said pallets (13, 15), the tangent of said impulsion face (7b) intersects the center-to-center line (12) between the escapement wheel (3) and the anchor (9) at an angle (α_orientation) which observes the relationship $$\begin{array}{c}{\alpha }_{\mathit{orientation}}={\tan }^{-1}\left(\frac{R\ast \mathit{Seuil}\ast \alpha \ast \cos \left(\alpha \right)+C\ast R\ast \cos \left(\alpha \right)+R\ast \cos \left(\alpha \right)-L}{R\ast \sin \left(\alpha \right)\ast \left(\mathit{Seuil}\times \alpha +C-1\right)}\right)\\ +/-10\%\end{array}$$

   

   in which

   - α_orientation is the angle between said tangent and said center-to-center line (12);

   - α is the angle between a line joining said point of contact (C') and the axis of rotation (5) of said escapement wheel (3) and said center-to-center line (12);

   - Seuil is a value for a loss of contact threshold between the escapement wheel (3) and the anchor (9), and is less than or equal to 0.01;

   - R is the distance between the axis of rotation (5) of said escapement wheel (3) and said point of contact (C'), +/- 10%;

   - C is the torque ratio between that of the anchor (9) and that of the escapement wheel (3);

   - L is the length of said center-to-center line (12).
7. Escapement (1) according to the preceding claim, in which the escapement wheel (3) includes teeth (7) having convex impulsion faces (7b).
8. Escapement (1) according to one of Claims 6 and 7, in which said value Seuil is a function of the first derivative of the speed ratio of the anchor (9) on the escapement wheel (3) at the time of the impulsion on the lip of said pallet (13, 15).
9. Escapement (1) according to one of Claims 1 to 4 and according to one of Claims 6 to 8.
10. Timepiece movement comprising an escapement (1) according to one of the preceding claims.
11. Timepiece comprising a movement according to Claim 10.

Images