EP3929667A1 - Rotating mobile system of a clock movement - Google Patents

Abstract

The invention relates to a mobile rotating system (10) of a watch movement, the system (10) comprising a rotating mobile, for example a balance wheel (13), a first and a second bearing (18, 20), in particular shock absorbers shock, for a first and a second pivot (15, 17) of the axis (16) of the rotating mobile, the mobile having a center of mass (G) in a position of its axis (16), the first bearing (18 , 20) comprising a counter-pivot comprising a main body provided with a conical cavity (19) configured to receive the first pivot (17) of the axis (16) of the rotary wheel set, the first pivot (17) being able to cooperate with the cavity (19) of the counter-pivot (22) to be able to rotate in the cavity (19), at least one contact zone (29) between the first pivot (17) and the cavity (19) being generated, the normals of the contact zone (29) forming a minimum contact angle relative to the plane perpendicular to the axis (16) of the pivot (17), the minimum contact angle being less than or equal to 30°, preferably less than or equal to arctan12.

Description

Field of the invention

The present invention relates to a rotating mobile system of a watch movement, in particular a resonator mechanism. The invention also relates to a watch movement provided with such a mobile system.

Background of the invention

In watch movements, the axes of the rotating wheels generally have pivots at their ends, which rotate in bearings mounted in the plate or in bridges of a watch movement. For certain mobiles, in particular the balance, it is customary to equip the bearings with a shock-absorbing mechanism. Indeed, as the pivots of the axis of a balance are generally thin and the mass of the balance is relatively high, the pivots can break under the effect of a shock in the absence of a damping mechanism.

The configuration of a conventional shock absorbing bearing 1 is represented by the figure 1 . A domed olive stone 2 is driven into a bearing support 3 commonly called chaton, on which is mounted a counter-pivot stone 4. The chaton 3 is held in abutment against the bottom of a bearing block 5 by a damping spring 6 arranged to exert an axial stress on the upper part of the counter-pivot stone 4. The chaton 3 further comprises a conical outer wall arranged in correspondence with a conical inner wall disposed at the periphery of the bottom of the bearing block 5. There is also variants according to which the kitten comprises an outer wall having a convex surface, that is to say convex.

However, the friction torque on the axis due to the weight of the mobile varies as a function of the orientation of the mobile with respect to the direction of gravity. These variations in the friction torque can in particular cause a variation in the amplitude of oscillation for the balance. Indeed, when the axis of the mobile is perpendicular to the direction of gravity, the weight of the mobile rests on the stones with holes, and the friction force generated by the weight has a lever arm relative to the axis, which is equal to the radius of the pivot. When the axis of the mobile is parallel to the direction of gravity, it is the end of the pivot on which the weight of the mobile rests. In this case, if the end of the pivot is rounded, the frictional force generated by the weight is applied to the axis of rotation, and therefore has a zero lever arm with respect to the axis. These lever arm differences generate the friction torque differences, which can also generate rate differences if the isochronism is not perfect.

To control this problem, we have devised another configuration of the damper bearing, partly shown in the figure. figure 2 . The bearing comprises a counter-pivot 7 of the crapaudine type, comprising a cavity 8 in the form of a cone to receive a pivot 12 of the axis 9 of the rotating mobile, the bottom of the cavity being formed by the top 11 of the cone. The pivot 12 is also tapered to fit into the cavity 8, but the solid angle of the pivot 12 is smaller than that of the cone of the cavity 8. This configuration makes it possible to make the lever arm of the frictional force almost zero. in all orientations with respect to gravity, assuming that the pivot 12 always remains well centered in the cavity 8. For this, it is generally necessary to pre-stress the system, for example with a spring-mounted bearing, which presses continuously on the pivot. However, this spring adds to the weight of the mobile, and increases friction. In addition, it is difficult to guarantee a good surface condition of the bottom of the cavity, because it is difficult to access by polishing means.

Summary of the invention

An aim of the invention is therefore to provide a mobile system of a watch movement which avoids the aforementioned problem.

To this end, the invention relates to a mobile system comprising a rotating mobile, for example a balance, a first and a second bearing, in particular shock absorbers, for a first and a second pivot of the axis of the rotating mobile, the system comprising a center of mass in a position of its axis, the first bearing comprising a counter-pivot comprising a main body provided with a conical cavity configured to receive the first pivot of the axis of the rotating mobile, the first pivot being able to cooperate with the cavity of the counter-pivot in order to be able to rotate in the cavity, at least one contact zone between the first pivot and the cavity being generated, the normals of the contact zone forming a minimum contact angle relative to the plane perpendicular to the axis of the pivot.

qui est sensiblement égal à 26,6°.The system is remarkable in that the minimum contact angle is less than or equal to 30 °, preferably less than or equal to $\mathrm{<figure-callout\; id="1"\; label="arctan"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">arctan</figure-callout>}\left(\frac{1}{2}\right),$

which is substantially equal to 26.6 °.

le couple de frottement dû au poids au contact entre les pivots et les cavités des palier est sensiblement le même quel que soit le sens de la gravité. En effet, un tel angle permet de compenser les variations de force de contact dues au changement d'orientation par rapport à la gravité par des bras de levier de la force de frottement différents sur les deux paliers.Thanks to the invention, the variation in friction between the horizontal and vertical positions with respect to gravity is reduced. By choosing a minimum contact angle less than or equal to 30 °, or even less than or equal to $\mathrm{<figure-callout\; id="1"\; label="arctan"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">arctan</figure-callout>}\left(\frac{1}{2}\right),$

the friction torque due to the weight in contact between the pivots and the cavities of the bearings is substantially the same regardless of the direction of gravity. In fact, such an angle makes it possible to compensate for the variations in contact force due to the change in orientation with respect to gravity by lever arms of the different friction force on the two bearings.

Thus, this configuration of the counter-pivot makes it possible to keep a small variation in the friction torque of the pivots inside the counter-pivots, whatever the position of the axis with respect to the direction of gravity, which is by important example for a balance axis of a movement of a timepiece. The cone shape of the cavity, as well as that of the pivot, minimize the difference in friction torque between the different positions of the axis with respect to the direction of gravity.

According to an advantageous embodiment, the second bearing cooperates with the second pivot to allow the rotating mobile device to rotate about its axis, the second bearing comprising a second cavity, the second pivot being able to cooperate with the second cavity of the counter-pivot in order to be able to rotate in the second cavity, at least a second contact zone between the second pivot and the second cavity being generated, the normals of the second contact zone forming a second minimum contact angle with respect to the plane perpendicular to the axis of the second pivot, the minimum contact angles of the two pivots and of the two bearings being defined by the following equation: cot α _h + cot α _b ≥ 2.5, preferably cotα _h + cotα _b ≥ 3, or even cotα _h + cotα _b ≥ 4.

According to an advantageous embodiment, the second minimum contact angle α _b is greater than or equal to $\mathrm{<figure-callout\; id="1"\; label="arctan"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">arctan</figure-callout>}\left(\frac{1}{2}\right)\mathrm{.}$

$${\tan \alpha }_h=\frac{\overline{\mathit{BH}}}{4\overline{\mathit{GB}}}$$

$$\frac{R_h}{R_b}=\frac{{\mathit{\mu }}_b}{{\mathit{\mu }}_h}\frac{\overline{\mathit{GH}}}{\overline{\mathit{GB}}}$$

où BH est la distance entre les extrémités des deux pivots, GH est la distance entre l'extrémité du premier pivot en contact avec le premier palier et le centre de masse du balancier, et GB est la distance entre l'extrémité du deuxième pivot en contact avec le deuxième palier et le centre de masse du balancier.According to another advantageous embodiment, the minimum contact angles ( α _b , α _h ) are defined by the following equations: $${\tan \alpha }_b=\frac{\overline{\mathit{BH}}}{4\overline{\mathit{GH}}}$$

$${\tan \alpha }_h=\frac{\overline{\mathit{BH}}}{4\overline{\mathit{GB}}}$$

$$\frac{R_h}{R_b}=\frac{{\mathit{\mu }}_b}{{\mathit{\mu }}_h}\frac{\overline{\mathit{GH}}}{\overline{\mathit{GB}}}$$

where BH is the distance between the ends of the two pivots, GH is the distance between the end of the first pivot in contact with the first bearing and the center balance mass, and GB is the distance between the end of the second pivot in contact with the second bearing and the center of mass of the balance.

• si GB < GH: $${\tan \alpha }_b=\frac{1}{\frac{2\overline{\mathit{GH}}}{\overline{\mathit{BH}}}\sqrt{\left(1+\frac{2\overline{\mathit{GH}}}{\overline{\mathit{BH}}}\right)\left(1+\frac{2\overline{\mathit{GB}}}{\overline{\mathit{BH}}}\right)}}$$
  
  $${\tan \alpha }_h=\frac{1}{\sqrt{\left(1+\frac{2\overline{\mathit{GH}}}{\overline{\mathit{BH}}}\right)\left(1+\frac{2\overline{\mathit{GB}}}{\overline{\mathit{BH}}}\right)}}$$
  
• si GB > GH: $${\tan \alpha }_b=\frac{1}{\sqrt{\left(1+\frac{2\overline{\mathit{GH}}}{\overline{\mathit{BH}}}\right)\left(1+\frac{2\overline{\mathit{GB}}}{\overline{\mathit{BH}}}\right)}}$$
  
  $${\tan \alpha }_h=\frac{1}{\frac{2\overline{\mathit{GB}}}{\overline{\mathit{BH}}}\sqrt{\left(1+\frac{2\overline{\mathit{GH}}}{\overline{\mathit{BH}}}\right)\left(1+\frac{2\overline{\mathit{GB}}}{\overline{\mathit{BH}}}\right)}}$$
  
  où BH est la distance entre les extrémités des deux pivots, GH est la distance entre l'extrémité du premier pivot en contact avec le premier palier et le centre de masse du balancier, et GB est la distance entre l'extrémité du deuxième pivot en contact avec le deuxième palier et le centre de masse du balancier.

According to another advantageous embodiment, the minimum contact angles ( α _b , α _h ) are defined by the following equations:

• if GB <GH: $${\tan \alpha }_b=\frac{1}{\frac{2\overline{\mathit{GH}}}{\overline{\mathit{BH}}}\sqrt{\left(1+\frac{2\overline{\mathit{GH}}}{\overline{\mathit{BH}}}\right)\left(1+\frac{2\overline{\mathit{GB}}}{\overline{\mathit{BH}}}\right)}}$$
  
  $${\tan \alpha }_h=\frac{1}{\sqrt{\left(1+\frac{2\overline{\mathit{GH}}}{\overline{\mathit{BH}}}\right)\left(1+\frac{2\overline{\mathit{GB}}}{\overline{\mathit{BH}}}\right)}}$$
  
• if GB> GH: $${\tan \alpha }_b=\frac{1}{\sqrt{\left(1+\frac{2\overline{\mathit{GH}}}{\overline{\mathit{BH}}}\right)\left(1+\frac{2\overline{\mathit{GB}}}{\overline{\mathit{BH}}}\right)}}$$
  
  $${\tan \alpha }_h=\frac{1}{\frac{2\overline{\mathit{GB}}}{\overline{\mathit{BH}}}\sqrt{\left(1+\frac{2\overline{\mathit{GH}}}{\overline{\mathit{BH}}}\right)\left(1+\frac{2\overline{\mathit{GB}}}{\overline{\mathit{BH}}}\right)}}$$
  
  where BH is the distance between the ends of the two pivots, GH is the distance between the end of the first pivot in contact with the first bearing and the center of mass of the balance, and GB is the distance between the end of the second pivot in contact with the second bearing and the center of mass of the balance.

According to another advantageous embodiment, the contact zone or zones go around the pivot and the cavity around the axis of the balance.

According to an advantageous embodiment, the first pivot has a conical shape.

According to an advantageous embodiment, the first pivot has a convex portion and the cavity has a concave portion, part of each portion forming the contact zone.

According to an advantageous embodiment, the first pivot has a concave portion and the cavity has a convex portion, a part of each portion forming the contact zone.

According to an advantageous embodiment, the first pivot has a convex portion and the cavity has a convex portion, a part of each portion forming the contact zone.

According to an advantageous embodiment, the two minimum contact angles are equal.

According to an advantageous embodiment, the end of the pivot is defined by the intersection between the normal in contact and the axis of the pivot.

According to an advantageous embodiment, the pivots have a rounded end.

According to an advantageous embodiment, the rounded ends of the two pivots have identical radii.

The invention also relates to a watch movement comprising a plate and at least one bridge, said plate and / or the bridge comprising such a mobile system.

Brief description of the drawings

• la figure 1 représente une section transversale d'un palier de maintien amortisseur de choc pour un axe d'un mobile tournant selon un premier mode de réalisation de l'état de la technique ;
• la figure 2 représente schématiquement un contre-pivot d'un palier et un pivot d'un axe d'un mobile tournant selon un deuxième mode de réalisation de l'état de la technique ;
• la figure 3 représente une vue en perspective d'un système mobile tournant, ici un mécanisme résonateur comprenant un mobile tournant, tel un balancier, selon un premier mode de réalisation de l'invention ;
• la figure 4 représente une vue en coupe du système mobile tournant de la figure 3 ;
• la figure 5 représente un pivot et un palier selon le premier mode de réalisation de l'invention ;
• la figure 6 représente schématiquement un modèle des paliers et des pivots d'un système mobile tournant selon le premier mode de réalisation de l'invention ;
• la figure 7 est un graphique montrant les angles de contact optimaux pour les deux paliers et pivots pour chaque position du centre de masse sur l'axe du balancier dans une première configuration,
• la figure 8 est un graphique montrant la différence des rayons optimaux des extrémités des deux pivots en fonction de la position du centre de masse
• la figure 9 est un graphique montrant la variation de couple de frottement en fonction de l'orientation □ □
• la figure 10 est un graphique montrant comment varie les angles optimaux en fonction de la position relative du centre de masse, dans une deuxième configuration où les extrémités des pivots sont identiques,
• la figure 11 est un graphique montrant la variation de ε en fonction de la position relative du centre de masse pour la deuxième configuration,
• la figure 12 est un graphique montrant la variation de couple de frottement en fonction de l'orientation □ pour la deuxième configuration,
• la figure 13 est un graphique montrant la variation des angles optimaux en fonction de la position relative du centre de masse pour une troisième configuration, et
• la figure 14 est un graphique montrant la variation de couple de frottement en fonction de l'orientation □ pour la troisième configuration,
• la figure 15 représente schématiquement une vue agrandie d'un palier et d'un pivot d'un système mobile tournant selon un deuxième mode de réalisation de l'invention ;
• la figure 16 représente schématiquement une vue agrandie d'un palier et d'un pivot d'un système mobile tournant selon un troisième mode de réalisation de l'invention ; et
• la figure 17 représente schématiquement une vue agrandie d'un palier et d'un pivot d'un système mobile tournant selon un quatrième mode de réalisation de l'invention

Other characteristics and advantages of the present invention will become apparent on reading several embodiments given solely by way of nonlimiting examples, with reference to the appended drawings in which:

• the figure 1 shows a cross section of a shock-absorbing retaining bearing for an axis of a rotating mobile device according to a first embodiment of the state of the art;
• the figure 2 schematically shows a counter-pivot of a bearing and a pivot of an axis of a rotating mobile device according to a second embodiment of the state of the art;
• the figure 3 represents a perspective view of a rotating mobile system, here a resonator mechanism comprising a rotating mobile, such as a balance, according to a first embodiment of the invention;
• the figure 4 shows a sectional view of the rotating mobile system of the figure 3 ;
• the figure 5 represents a pivot and a bearing according to the first embodiment of the invention;
• the figure 6 schematically represents a model of the bearings and pivots of a rotating mobile system according to the first embodiment of the invention;
• the figure 7 is a graph showing the optimum contact angles for the two bearings and pivots for each position of the center of mass on the balance axis in a first configuration,
• the figure 8 is a graph showing the difference of the optimal radii of the ends of the two pivots as a function of the position of the center of mass
• the figure 9 is a graph showing the variation of friction torque as a function of the orientation □ □
• the figure 10 is a graph showing how the optimal angles vary as a function of the relative position of the center of mass, in a second configuration where the ends of the pivots are identical,
• the figure 11 is a graph showing the variation of ε as a function of the relative position of the center of mass for the second configuration,
• the figure 12 is a graph showing the variation of friction torque as a function of the orientation □ for the second configuration,
• the figure 13 is a graph showing the variation of the optimal angles as a function of the relative position of the center of mass for a third configuration, and
• the figure 14 is a graph showing the variation of friction torque as a function of the orientation □ for the third configuration,
• the figure 15 schematically shows an enlarged view of a bearing and a pivot of a rotating mobile system according to a second embodiment of the invention;
• the figure 16 schematically shows an enlarged view of a bearing and a pivot of a rotating mobile system according to a third embodiment of the invention; and
• the figure 17 schematically shows an enlarged view of a bearing and a pivot of a rotating mobile system according to a fourth embodiment of the invention

Detailed description of preferred embodiments

In the description, the same numbers are used to designate identical objects. In a watch movement, the bearing serves to maintain an axis of a rotating mobile, for example a balance axis, by allowing it to perform rotations around its axis. The watch movement generally comprises a plate and at least one bridge, not shown in the figures, said plate and / or the bridge comprising an orifice, the movement further comprising a rotating mobile and a bearing inserted in the orifice.

The figures 3 and 4 show a rotating mobile system provided with a balance 13 and a spiral spring 24, the balance 13 comprising an axis 16. The axis 16 comprises a pivot 15, 17 at each end. Each level 18, 20 comprises a cylindrical bearing block 83 provided with a housing 14, a counter-pivot 22 arranged in the housing 14, and an opening 19 made in one face of the bearing 18, 20, the opening 19 leaving a passage for inserting the pivot 15, 17 in the bearing up to the counter-pivot 22. The counter-pivot 22 is mounted on a bearing support 23 and comprises a main body provided with a cavity configured to receive the pivot 15, 17 of the axis 16 of the rotating mobile. The pivots 15, 17 of the axis 16 are inserted into the housing 14, the axis 16 being maintained while being able to rotate to allow the movement of the rotating mobile.

The two bearings 18, 20 are shock absorbers, and further include an elastic support 21 of the counter-pivot 22 to absorb shocks and prevent the pin 16 from breaking. An elastic support 21 is for example a flat spring with axial deformation on which the counter-pivot 22 is assembled. The elastic support 21 is fitted into the housing 14 of the bearing block 13 and it maintains the counter-pivot 22 in the housing 14. Thus, when the timepiece is subjected to a violent impact, the elastic support 21 absorbs the shock and preserves the impact. axis 16 of the rotating mobile.

In a first embodiment of the figures 5 and 6 , the pivot 15, 17 has the shape of a first substantially circular cone 26 having a first opening angle 31. The opening angle 31 is the half-angle formed inside the cone by its outer wall.

The cavity 28 of the counter-pivot 22 has the shape of a second cone having a second opening angle 32 at the top. So that the pivot 15, 17 can rotate in the cavity, the second opening angle 32 is greater than the first opening angle 31 of the first cone 26.

The pivot 15, 17 and the cavities 28 cooperate to form a contact zone 29. The contact zone 29 is defined by the parts of the second cone and of the pivot 15, 17 which are in contact. The contact zone 29 goes around the pivot 15, 17 and the cavity 28.

The normals to the contact zone 29 are straight lines perpendicular to the contact zone 29. The normals form a minimum angle, called the minimum contact angle, with respect to the plane perpendicular to the axis of the pivot.

According to the invention, the minimum contact angle is less than or equal to 30 °, preferably less than or equal to $\mathrm{<figure-callout\; id="1"\; label="arctan"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">arctan</figure-callout>}\left(\frac{1}{2}\right)\mathrm{.}$

par rapport au plan perpendiculaire au pivot, le second angle du second cône doit être inférieur ou égal à 60°, voire inférieur ou égal à $2\ast \arctan \left(\frac{1}{2}\right)=53.13°\mathrm{.}$

In this first embodiment where the cavity 28 and the pivots 15, 17 are conical, the normal corresponds to the line perpendicular to the wall of the second cone, that is to say the cone of the cavity 28. Thus, l The minimum contact angle is equivalent to the half-opening angle of the second cone of cavity 28. So that the minimum contact angle is less than or equal to 30 °, or even less than or equal to $\mathrm{<figure-callout\; id="1"\; label="arctan"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">arctan</figure-callout>}\left(\frac{1}{2}\right),$

with respect to the plane perpendicular to the pivot, the second angle of the second cone must be less than or equal to 60 °, or even less than or equal to $2\ast \mathrm{<figure-callout\; id="1"\; label="arctan"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">arctan</figure-callout>}\left(\frac{1}{2}\right)=53.13°\mathrm{.}$

• □ _b et □ _h sont les angles entre les génératrices des cônes et l'axe de symétrie des cônes, pour le palier du bas et celui du haut ;
• R_b et R_h sont les rayons des calottes sphériques des bouts des pivots en bas et en haut de l'axe du balancier ;
• B et H sont les centres des calottes sphériques des bouts des pivots en bas et en haut de l'axe du balancier ;
• G est la position du centre de masse, supposé sur la droite BH (balancier équilibré) ;
• □ _b et □ _h sont les coefficients de frottement en bas et en haut.

These angle values are calculated from equations modeling the friction of the pivots and the bearings. To be able to describe the formulas which give the optimal angles, one defines the following geometrical quantities, sketched on the figure 6 :

• □ _b and □ _h are the angles between the generatrices of the cones and the axis of symmetry of the cones, for the lower and upper bearing;
• R _b and R _h are the radii of the spherical caps of the ends of the pivots at the bottom and at the top of the axis of the balance;
• B and H are the centers of the spherical caps of the ends of the pivots at the bottom and at the top of the axis of the balance;
• G is the position of the center of mass, assumed to be on the line BH (balanced pendulum);
• □ _b and □ _h are the coefficients of friction at the bottom and at the top.

• les deux ensembles d'orientation sont les suivants :
  • O₁: l'angle □ entre l'axe du balancier et la gravité parcourt tout l'intervalle [0°, 180°],
  • O₂: l'angle □ entre l'axe du balancier et la gravité parcourt les 3 valeurs ponctuelles 0°, 90° et 180°,
• les deux types de contraintes sur la géométrie sont les suivantes :
  • C₁: aucune contrainte sur les rayons R_b et R_h et les angles □ _b et □ _h ,
  • C₂: pour des questions de facilité de fabrication, on impose R_b = R_h , et on suppose □ _b = □ _h ,

To evaluate the difference in friction as a function of gravity, we distinguish two sets of orientation and two types of stresses applied to the geometry of the mobile system:

• the two sets of orientation are:
  • O ₁ : the angle □ between the axis of the balance and gravity runs through the entire interval [0 °, 180 °],
  • O ₂ : the angle □ between the axis of the balance and gravity runs through the 3 point values 0 °, 90 ° and 180 °,
• the two types of constraints on the geometry are the following ones:
  • C ₁ : no constraint on the radii R _b and R _h and the angles □ _b and □ _h ,
  • C ₂ : for reasons of ease of manufacture, we impose R _b = R _h , and we assume □ _b = □ _h ,

We denote by M _{fr, max} , respectively M _{fr, min} , the maximum friction torque, respectively minimum, on all the angles □ considered (either the whole range [0 °, 180 °] in the case of O ₁ , or the 3 values 0 °, 90 ° and 180 ° in the case of O ₂ ). We try to minimize the maximum relative variation of torque, defined by $$\epsilon =\frac{M_{\mathrm{Fr},\max }-M_{\mathrm{Fr},\min }}{M_{\mathrm{Fr},\min }}$$

$${\tan \alpha }_h=\frac{\overline{\mathit{BH}}}{4\overline{\mathit{GB}}}$$

$$\frac{R_h}{R_b}=\frac{{\mathit{\mu }}_b}{{\mathit{\mu }}_h}\frac{\overline{\mathit{GH}}}{\overline{\mathit{GB}}}$$

où BH est la distance entre les extrémités des deux pivots 15, 17, et GH est la distance entre l'extrémité du pivot 15, 17 et le centre de masse G du balancier 2.In the case O1, for a rotating mobile axis provided with two pivots, as shown schematically on the figure 6 , the optimal minimum contact angle ( α ) between the pivot-bearing couples is defined by the following equations: $${\tan \alpha }_b=\frac{\overline{\mathit{BH}}}{4\overline{\mathit{GH}}}$$

$${\tan \alpha }_h=\frac{\overline{\mathit{BH}}}{4\overline{\mathit{GB}}}$$

$$\frac{R_h}{R_b}=\frac{{\mathit{\mu }}_b}{{\mathit{\mu }}_h}\frac{\overline{\mathit{GH}}}{\overline{\mathit{GB}}}$$

where BH is the distance between the ends of the two pivots 15, 17, and GH is the distance between the end of the pivot 15, 17 and the center of mass G of the balance 2.

These equations come from a three-dimensional model of the contact between the pivot and the counter-pivot, in which the end of the pivot is modeled by a sphere. In the general case, B and H are defined by the intersection between the normal in contact and the axis of the pivot. Preferably, the tips of the pivots are rounded, B and H are defined by the center of the sphere. Thus, the radius of the rounded end corresponds to the segment between the contact and the intersection of the normal to the contact and the axis of the pivot 15, 17.

This relationship applies to pivots with different shapes. The radii R _b and R _h of the rounded ends may be different from each other.

Thus, depending on the position of the center of mass G, the first cones of the two pivots 15, 17 can have different opening angles. But if they meet this relationship, the variation in friction between the vertical and horizontal positions is reduced compared to other geometries of pivots and cavities. In this case, the relative variation in torque □ is 41%.

These relations are also suitable for the set O ₂ of the three positions of the angle □ between the axis of the balance and gravity (0 °, 90 ° and 180 °) with zero variation, where □ □ = 0 %.

Ainsi, l'angle d'ouverture souhaitable pour des cônes est d'environ 53.2°. Dans les autres cas, les angles de contact des deux couples paliers-pivots sont différents. On remarque ainsi, qu'il y a toujours l'un des deux angles de contact avec une valeur inférieure ou égale à $\arctan \left(\frac{1}{2}\right)$

et l'autre angle avec une valeur supérieure ou égale à $\arctan \left(\frac{1}{2}\right)\mathrm{.}$

Un autre cas où le centre de masse se trouve à un quart de longueur de l'axe d'un premier pivot, l'angle de contact optimal de ce premier pivot est de 45°, tandis que le second pivot a un angle de contact optimal égal à $\arctan \left(\frac{1}{3}\right)=$

18.435°. Ainsi pour les cavités coniques, on a un cône d'angle d'ouverture égal à 90°, et l'autre cône d'angle d'ouverture égal à $2\ast \arctan \left(\frac{1}{3}\right)=28,07°\mathrm{.}$

The graph of the figure 7 shows the optimum contact angles for the two bearings and pivots for each position of the center of mass on the balance axis. The particular case where the center of mass G is in the middle of B and H, and if the friction coefficients are equal between the bottom and the top, then we have symmetrical bearings ( R _b = R _h ), with □ _b and □ _h = $\mathrm{<figure-callout\; id="1"\; label="arctan"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">arctan</figure-callout>}\left(\frac{1}{2}\right)=\mathrm{approx}\mathrm{.26.6}°\mathrm{.}$

Thus, the desirable opening angle for cones is about 53.2 °. In the other cases, the contact angles of the two bearing-pivot pairs are different. We notice thus, that there is always one of the two contact angles with a value less than or equal to $\mathrm{<figure-callout\; id="1"\; label="arctan"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">arctan</figure-callout>}\left(\frac{1}{2}\right)$

and the other angle with a value greater than or equal to $\mathrm{<figure-callout\; id="1"\; label="arctan"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">arctan</figure-callout>}\left(\frac{1}{2}\right)\mathrm{.}$

Another case where the center of mass is a quarter of the length of the axis of a first pivot, the optimum contact angle of this first pivot is 45 °, while the second pivot has an optimal contact angle equal to $\mathrm{<figure-callout\; id="1"\; label="arctan"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">arctan</figure-callout>}\left(\frac{1}{3}\right)=$

18.435 °. Thus for conical cavities, there is one cone with an opening angle equal to 90 °, and the other cone with an opening angle equal to $2\ast \mathrm{<figure-callout\; id="1"\; label="arctan"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">arctan</figure-callout>}\left(\frac{1}{3}\right)=28,07°\mathrm{.}$

Each optimum contact angle is within a range of 14 ° to 90 °. The smallest contact angle is that of the pivot closest to the center of mass.

The graph of the figure 8 shows the difference in the optimal radii of the ends of the two pivots as a function of the position of the center of mass. Thus, it is noted that for a center of mass in the middle of the balance axis, the radii are preferably equal for both ends.

An example of the variation of the friction torque as a function of the orientation □ is shown in graph 9. The curve is symmetrical with respect to the 90 ° position. The torque gradually increases from 0 to 45 °, then decreases from 45 ° to 90 °, increases again from 90 ° to 135 °, and decreases from 135 ° to 180 °. This variation curve is the same whatever the optimal case, except for a scale factor.

• si GB < GH: $${\tan \alpha }_b=\frac{1}{\frac{2\overline{\mathit{GH}}}{\overline{\mathit{BH}}}\sqrt{\left(1+\frac{2\overline{\mathit{GH}}}{\overline{\mathit{BH}}}\right)\left(1+\frac{2\overline{\mathit{GB}}}{\overline{\mathit{BH}}}\right)}}$$
  
  $${\tan \alpha }_h=\frac{1}{\sqrt{\left(1+\frac{2\overline{\mathit{GH}}}{\overline{\mathit{BH}}}\right)\left(1+\frac{2\overline{\mathit{GB}}}{\overline{\mathit{BH}}}\right)}}$$
  
• si GB > GH: $${\tan \alpha }_b=\frac{1}{\sqrt{\left(1+\frac{2\overline{\mathit{GH}}}{\overline{\mathit{BH}}}\right)\left(1+\frac{2\overline{\mathit{GB}}}{\overline{\mathit{BH}}}\right)}}$$
  
  $${\tan \alpha }_h=\frac{1}{\frac{2\overline{\mathit{GB}}}{\overline{\mathit{BH}}}\sqrt{\left(1+\frac{2\overline{\mathit{GH}}}{\overline{\mathit{BH}}}\right)\left(1+\frac{2\overline{\mathit{GB}}}{\overline{\mathit{BH}}}\right)}}$$
  
  où BH est la distance entre les extrémités des deux pivots, GB et GH sont la distance entre une extrémité du pivot et le centre de masse du balancier. Le modèle à trois dimensions du contact entre le pivot et le contre-pivot comporte en outre le principe que les deux pivots ont la même forme, en particulier pour le bout arrondi du pivot de rayon semblable R_b =R_h.

In a second embodiment of the modeling of the mobile system, where the two pivots have shapes identical to those of the first model, the minimum contact angle is defined in two distinct cases by the following equations:

• if GB <GH: $${\tan \alpha }_b=\frac{1}{\frac{2\overline{\mathit{GH}}}{\overline{\mathit{BH}}}\sqrt{\left(1+\frac{2\overline{\mathit{GH}}}{\overline{\mathit{BH}}}\right)\left(1+\frac{2\overline{\mathit{GB}}}{\overline{\mathit{BH}}}\right)}}$$
  
  $${\tan \alpha }_h=\frac{1}{\sqrt{\left(1+\frac{2\overline{\mathit{GH}}}{\overline{\mathit{BH}}}\right)\left(1+\frac{2\overline{\mathit{GB}}}{\overline{\mathit{BH}}}\right)}}$$
  
• if GB> GH: $${\tan \alpha }_b=\frac{1}{\sqrt{\left(1+\frac{2\overline{\mathit{GH}}}{\overline{\mathit{BH}}}\right)\left(1+\frac{2\overline{\mathit{GB}}}{\overline{\mathit{BH}}}\right)}}$$
  
  $${\tan \alpha }_h=\frac{1}{\frac{2\overline{\mathit{GB}}}{\overline{\mathit{BH}}}\sqrt{\left(1+\frac{2\overline{\mathit{GH}}}{\overline{\mathit{BH}}}\right)\left(1+\frac{2\overline{\mathit{GB}}}{\overline{\mathit{BH}}}\right)}}$$
  
  where BH is the distance between the ends of the two pivots, GB and GH are the distance between one end of the pivot and the center of mass of the balance. The three-dimensional model of the contact between the pivot and the counter-pivot furthermore includes the principle that the two pivots have the same shape, in particular for the rounded end of the pivot of similar radius R _b = R _h .

et l'autre angle avec une valeur supérieure ou égale à $\arctan \left(\frac{1}{2}\right)\mathrm{.}$

Le cas particulier où le centre de masse G est au milieu de B et H, et si les coefficients de frottement sont égaux entre le bas et le haut, alors on a des paliers avec □ _b et ${\square }_h=\arctan \left(\frac{1}{2}\right)=26.6°$

environ.The graphics of figures 10 and 11 show how the optimal angles and the variation vary as a function of the relative position of the center of mass. Also in this case, there is always one of the two angles with a value less than or equal to $\mathrm{<figure-callout\; id="1"\; label="arctan"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">arctan</figure-callout>}\left(\frac{1}{2}\right)$

and the other angle with a value greater than or equal to $\mathrm{<figure-callout\; id="1"\; label="arctan"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">arctan</figure-callout>}\left(\frac{1}{2}\right)\mathrm{.}$

The particular case where the center of mass G is in the middle of B and H, and if the friction coefficients are equal between the bottom and the top, then we have bearings with □ _b and ${\square }_h=\mathrm{<figure-callout\; id="1"\; label="arctan"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">arctan</figure-callout>}\left(\frac{1}{2}\right)=26.6°$

about.

An example of torque variation as a function of the orientation □ is shown on the figure 12 . In this case, the curve is symmetrical for a value greater than 90 °. Thus, for pivots of the same shape and of the same radius, the point of symmetry of the curve is offset from that at 90 ° of the first embodiment.

• si GB < GH: $${\tan \alpha }_b={\tan \alpha }_h=\frac{\overline{\mathit{BH}}}{4\overline{\mathit{GH}}}$$
  
• si GB > GH: $${\tan \alpha }_b={\tan \alpha }_h=\frac{\overline{\mathit{BH}}}{4\overline{\mathit{GB}}}$$
  
  où BH est la distance entre les extrémités des deux pivots, GB et GH sont la distance entre une extrémité du pivot et le centre de masse du balancier.

For the case O ₂ (0 °, 90 °, 180 °) with C ₂ ( R _b = R _h , □ _b = □ _h ), we obtain two distinct cases:

• if GB <GH: $${\tan \alpha }_b={\tan \alpha }_h=\frac{\overline{\mathit{BH}}}{4\overline{\mathit{GH}}}$$
  
• if GB> GH: $${\tan \alpha }_b={\tan \alpha }_h=\frac{\overline{\mathit{BH}}}{4\overline{\mathit{GB}}}$$
  
  where BH is the distance between the ends of the two pivots, GB and GH are the distance between one end of the pivot and the center of mass of the balance.

In this case, the relative variation of torque □ is 0%: the friction couples are perfectly equal at □ = 0 °, 90 ° and 180 °. On the other hand, the friction torque varies for angles different from these 3 values.

environ. Un exemple de variation de couple en fonction de l'orientation □ est représenté sur le graphique de la figure 14.The graph of the figure 13 shows the variation of the optimal angles as a function of the relative position of the center of mass for this configuration. The two angles are equal and have a value less than or equal to $\mathrm{<figure-callout\; id="1"\; label="arctan"\; filenames="imgf0001.png,imgf0004.png"\; state="\{\{state\}\}">arctan</figure-callout>}\left(\frac{1}{2}\right)=26.6°$

about. An example of torque variation as a function of the orientation □ is shown on the graph of the figure 14 .

Whatever the choice of the model associated with the system, the minimum contact angles of the two pivots and of the two bearings verify the following equation: cot α _b + cot α _h ≥√12.

The figures 15 to 17 show other examples of pivots and cavities answering the equations cited above, while having shapes which are not entirely conical, such as the preceding examples.

Thus, in a first variant embodiment of the figure 15 , the first pivot 33 has a convex portion 37 and the cavity 35 has a convex portion 38, a part of each portion forming the contact zone 41. The cavity 35 comprises a bottom 39, then a first flared portion 42 extending from the bottom 39, the convex portion 38 is connected to the first flared portion 42, and a second flared portion 65 extends from the convex potion 38 to a cylindrical wall 66 of the cavity 35. The second flared portion 65 is more wide than the first 42. The portion convex 38 has a rounded shape oriented towards the interior of the cavity 35.

The pivot 33 has a rounded point 40 at its end, then a convex portion 37 extending from the point 40, and a conical portion 71 extending from the convex portion 37 to a cylindrical portion 72 of the pivot 33.

The pivot 33 is inserted into the cavity 35, the dimensions of the pivot 33 and of the cavity 35 being such that the convex portion 37 of the pivot 33 is in contact with the convex portion 38 of the cavity 35. The two convex portions 37, 38 in contact define the contact zone 41. Only a part of each convex portion 37, 38 is in contact with one another. The contact zone 41 is made here above the first flared portion 42 to promote a smaller minimum contact angle. The normals of the contact zone 41 around the pivot 33 form a minimum contact angle with the plane perpendicular to the pivot, this minimum angle corresponds to a case corresponding to the preceding equations according to the invention, for example here of 25 °.

For the second variant of the figure 16 , the first pivot 43 has a convex portion 47 and the cavity 45 has a concave portion 48. The cavity 45 comprises a bottom 49, then a first flared portion 52 extending from the bottom 49, the concave portion 48 is connected to the bottom. first flared portion 52, and a second flared portion 67 extends from the convex potion 48 to a cylindrical wall 68 of the cavity. The second flared portion 67 is wider than the first 52. The concave portion 48 has a rounded shape oriented towards the outside of the cavity 45.

The pivot 43 comprises a rounded protuberance 50 at its end, a convex portion 47 connected to the protuberance 50 by a flared portion 75, the convex portion 47 being connected to a cylindrical portion 68 of the pivot 43.

The pivot 43 is inserted into the cavity 45, the dimensions of the pivot 43 and of the cavity 45 being such that the convex portion 47 of the pivot 43 is in contact with the concave portion 48 of the cavity 45. The two convex 47 and concave 48 portions in contact define the contact zone 51. Only a part of each convex 47 or concave 48 portion is in contact with one another. The contact zone 51 is made here below the second flared portion 67 to promote a smaller minimum contact angle. The normals of the contact zone 51 around the pivot 43 form a minimum contact angle with the plane perpendicular to the pivot 43, this minimum angle corresponds to a case corresponding to the preceding equations according to the invention, for example here of 25 °.

In the third variant, shown on figure 17 , the first pivot 53 has a concave portion 57 and the cavity 55 has a convex portion 58, a part of each portion forming the contact zone 61.

The pivot 53 has a concave portion 57 and the cavity 55 has a convex portion 58. The cavity 55 comprises a bottom 59, then a first cylindrical portion 62 extending from the bottom 59, the convex portion 58 being connected to the first portion cylindrical 62, and a flared portion 69 extends from the convex potion 58 to a cylindrical wall 70 of the cavity 55. The convex portion 58 has a rounded shape oriented towards the interior of the cavity 55.

The pivot 53 comprises a rounded end 60, a concave portion 57 connected to the rounded end 60 on the one hand, and to a cylindrical portion 70 of the pivot 53 on the other hand.

The pivot 53 is inserted into the cavity 55, the dimensions of the pivot 53 and of the cavity 55 being such that the concave portion 57 of the pivot 53 is in contact with the convex portion 58 of the cavity 55. The two convex 58 and concave portions 57 in contact define the contact zone 61. Only a part of each convex 58 or concave 57 portion is in contact with one another. The contact zone 61 is made here above the cylindrical portion 62 of the cavity 55 to promote a smaller minimum contact angle. The normals of the contact zone 61 around the pivot 53 form a minimum angle of contact with the plane perpendicular to the pivot 53, this minimum angle corresponds to a case corresponding to the preceding equations according to the invention, for example here of 25 °.

Naturally, the invention is not limited to the embodiments described with reference to the figures and variants could be envisaged without departing from the scope of the invention.

Claims (14)

Rotating mobile system (10) of a watch movement, the system (10) comprising a rotating mobile, for example a balance (13), a first and a second bearing (18, 20), in particular shock absorbers, for a first and a second pivot (15, 17) of the axis (16) of the rotating mobile, the mobile comprising a center of mass (G) in a position of its axis (16), the first bearing (18, 20) comprising a counter-pivot (22) comprising a main body provided with a conical cavity (19) configured to receive the first pivot (17) of the axis (16) of the rotating mobile, the first pivot (17) being able to cooperate with the cavity (19) of the counter-pivot (22) to be able to rotate in the cavity (19), at least one contact zone (29) between the first pivot (17) and the cavity (19) being generated, the normals of the contact zone (29) forming a minimum contact angle ( α _h ) relative to the plane perpendicular to the axis (16) of the pivot (17), characterized in that the minimum contact angle ( α _h ) is less r or equal to 30 °, preferably less than or equal to $\arctan \left(\frac{1}{2}\right)\mathrm{.}$

Mobile system according to Claim 1, characterized in that the second bearing (20) cooperates with the second pivot (15) to allow the rotating mobile device to rotate about its axis (16), the second bearing (20) comprising a second cavity (89), the second pivot (15) being able to cooperate with the second cavity (89) of the counter-pivot (22) in order to be able to rotate in the second cavity (89), at least one second contact zone (90) between the second pivot (17, 30) and the second cavity (89) being generated, the normals of the second contact zone (90) forming a second minimum contact angle ( α _b ) with respect to the plane perpendicular to the axis of the second pivot (15), characterized in that the minimum contact angles ( α _h , α _b ) of the two pivots (15, 17) and of the two bearings (18, 20) are defined by the following equation: cotα _h + cotα _b ≥ 2.5, preferably cotα _h + cotα _b ≥ 3, or even cotα _h + cotα _b ≥ 4. Mobile system according to claim 1 or 2, characterized in that the second minimum contact angle ( α _b ) is greater than or equal to $\arctan \left(\frac{1}{2}\right)\mathrm{.}$

Mobile system according to any one of the preceding claims, characterized in that the minimum contact angles ( α _h , α _b ) are defined by the following equations: $${\tan \alpha }_b=\frac{\overline{\mathit{BH}}}{4\overline{\mathit{GH}}}$$

$${\tan \alpha }_h=\frac{\overline{\mathit{BH}}}{4\overline{\mathit{GB}}}$$

$$\frac{R_h}{R_b}=\frac{{\mathit{\mu }}_b}{{\mathit{\mu }}_h}\frac{\overline{\mathit{GB}}}{\overline{\mathit{GB}}}$$

where BH is the distance between the ends of the two pivots, GH is the distance between the end of the first pivot (17) in contact with the first bearing (18) and the center of mass (G) of the balance, and GB is the distance between the end of the second pivot (15) in contact with the second bearing (20) and the center of mass (G) of the balance 2. Mobile system according to any one of claims 1 to 3, characterized in that the minimum contact angles ( α _b , α _h ) are defined by the following equations: - if GB <GH: $${\tan \alpha }_b=\frac{1}{\frac{2\overline{\mathit{GH}}}{\overline{\mathit{BH}}}\sqrt{\left(1+\frac{2\overline{\mathit{GH}}}{\overline{\mathit{BH}}}\right)\left(1+\frac{2\overline{\mathit{GB}}}{\overline{\mathit{BH}}}\right)}}$$

$${\tan \alpha }_h=\frac{1}{\sqrt{\left(1+\frac{2\overline{\mathit{GH}}}{\overline{\mathit{BH}}}\right)\left(1+\frac{2\overline{\mathit{GB}}}{\overline{\mathit{BH}}}\right)}}$$

- if GB> GH: $${\tan \alpha }_b=\frac{1}{\sqrt{\left(1+\frac{2\overline{\mathit{GH}}}{\overline{\mathit{BH}}}\right)\left(1+\frac{2\overline{\mathit{GB}}}{\overline{\mathit{BH}}}\right)}}$$

$${\tan \alpha }_h=\frac{1}{\frac{2\overline{\mathit{GB}}}{\overline{\mathit{BH}}}\sqrt{\left(1+\frac{2\overline{\mathit{GH}}}{\overline{\mathit{BH}}}\right)\left(1+\frac{2\overline{\mathit{GB}}}{\overline{\mathit{BH}}}\right)}}$$

where BH is the distance between the ends of the two pivots (15, 17), GH is the distance between the end of the first pivot (15) in contact with the first bearing (18) and the center of mass (G) of the balance , and GB is the distance between the end of the second pivot (17) in contact with the second bearing (20) and the center of mass (G) of the balance. Mobile system according to any one of the preceding claims, characterized in that the contact zone or zones (29, 90) go around the pivot (15, 17) and the cavity (31, 89) around the 'axis (16) of the balance. Mobile system according to any one of the preceding claims, characterized in that the first pivot (17) has a conical shape. Mobile system according to any one of claims 1 to 6, characterized in that the first pivot (43) has a convex portion (47) and the cavity (45) has a concave portion (48), part of each portion (47, 48) forming the contact zone (51). Mobile system according to any one of claims 1 to 6, characterized in that the first pivot (53) has a concave portion (57) and the cavity (55) has a convex portion (58), part of each portion forming the contact zone (61). Mobile system according to any one of claims 1 to 6, characterized in that the first pivot (33) has a convex portion (37) and the cavity (35) has a convex portion (38), part of each portion (37, 38) forming the contact zone (41). Mobile system according to any one of the preceding claims, characterized in that the two minimum contact angles ( α _b , α _h ) are equal. Mobile system according to any one of the preceding claims, characterized in that the end of the pivot (15, 17) is defined by the intersection between the normal in contact and the axis of the pivot. Mobile system according to any one of the preceding claims, characterized in that the pivots (15, 17) have a rounded end, the rounded ends of the two pivots (15, 17) having identical radii ( R _b , R _h ). Watch movement comprising a plate and at least one bridge, said plate and / or the bridge comprising an orifice, characterized in that it comprises a rotating mobile system (10) according to any one of the preceding claims.

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