Rotating mobile system of a clock movement

Abstract

The invention relates to a rotating moving part (10) of a watch movement, the part (10) comprising a rotating part, for example a balance wheel (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 part, the part having a center of mass (G) at a position on its axis (16), the first bearing (18, 20) comprising a counter-pivot including a main body having a conical cavity (19) configured to receive the first pivot (17) of the axis (16) of the rotating part, the first pivot (17) being able to cooperate with the cavity (19) of the counter-pivot (22) in order to rotate within 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 invention

[0001] 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 equipped with such a mobile system. Background of the invention

[0002] In watch movements, the shafts of rotating mobiles usually have pivots at their ends, which rotate in bearings mounted in the plate or bridges of a watch movement. For some mobiles, particularly the balance wheel, it is customary to equip the bearings with a shock-absorbing mechanism. Indeed, since the pivots of a balance wheel's shaft are usually thin and the mass of the balance wheel is relatively high, the pivots can break under the effect of an impact in the absence of a shock-absorbing mechanism.

[0003] The configuration of a conventional shock absorber bearing 1 is represented by the figure 1. A domed olive-colored stone 2 is driven into a bearing support 3 commonly called a setting, on which a counter-pivot stone 4 is mounted. The setting 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 setting 3 further comprises a conical external wall arranged in correspondence with a conical internal wall disposed at the periphery of the bottom of the bearing block 5. There are also variants according to which the setting comprises an external wall having a convex, i.e. domed, surface.

[0004] However, the friction torque on the axis due to the weight of the mobile varies depending on the orientation of the mobile relative to the direction of gravity. These variations in the friction torque can notably lead to a variation in the oscillation amplitude for the balance wheel. Indeed, when the axis of the mobile is perpendicular to the direction of gravity, the weight of the mobile rests on the perforated jewels, 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 friction force generated by the weight is applied to the axis of rotation, and therefore has a zero lever arm relative to the axis.These lever arm differences generate friction torque differences, which can also generate walking differences if the isochronism is not There are also documents US3942848 and EP1986059 which propose alternative solutions to the problem of friction torque variation.

[0005] To control this problem, another configuration of shock absorber bearing was devised, partly shown in the figure 2The bearing comprises a counter pivot 7 of the toad type, comprising a cone-shaped cavity 8 for receiving a pivot 12 of the axis 9 of the rotating mobile, the bottom of the cavity being formed by the apex 11 of the cone. The pivot 12 is also conical 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 friction 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 permanently presses on the pivot. However, this spring adds to the weight of the mobile, and increases the 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.

[0006] An object of the invention is, therefore, to propose a mobile system of a clock movement which avoids the aforementioned problem.

[0007] 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 at 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 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.

[0008] The system is remarkable in that the minimum contact angle is less than or equal to 30°, preferably less than or equal to arctan 1 2 , which is approximately equal to 26.6°.

[0009] Thanks to the invention, the variation of 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 arctan 1 2 , the friction torque due to the weight in contact between the pivots and the bearing cavities is substantially the same regardless of the direction of gravity. Indeed, such an angle makes it possible to compensate for variations in contact force due to the change in orientation relative to gravity by different lever arms of the friction force on the two bearings.

[0010] Thus, this configuration of the counter-pivot allows to keep a low variation of the friction torque of the pivots inside the counter-pivots, whatever the position of the axis relative to the direction of gravity, which is for example important for a balance staff 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 relative to the direction of gravity.

[0011] According to an advantageous embodiment, the second bearing cooperates with the second pivot to allow the rotating mobile to rotate around its axis, the second bearing comprising a second cavity, the second pivot being able to cooperate with the second cavity of the counter-pivot 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.

[0012] According to an advantageous embodiment, the second minimum angle α b contact is greater than or equal to arctan 1 2 .

[0013] According to another advantageous embodiment, the minimum contact angles ( α b ,α h ) are defined by the following equations: tan α b = BH ¯ 4 GH ¯ tan α h = BH ¯ 4 GB ¯ R h R b = μ b μ h GH ¯ GB ¯ Or 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 wheel.

[0014] According to another advantageous embodiment, the minimum contact angles (α b ,α h ) are defined by the following equations: if GB < GH: tan α b = 1 2 GH ¯ BH ¯ 1 + 2 GH ¯ BH ¯ 1 + 2 GB ¯ BH ¯ tan α h = 1 1 + 2 GH ¯ BH ¯ 1 + 2 GB ¯ BH ¯ if GB > GH: tan α b = 1 1 + 2 GH ¯ BH ¯ 1 + 2 GB ¯ BH ¯ tan α h = 1 2 GB ¯ BH ¯ 1 + 2 GH ¯ BH ¯ 1 + 2 GB ¯ BH ¯ Or 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 wheel.

[0015] According to another advantageous embodiment, the contact zone(s) go around the pivot and the cavity around the balance shaft.

[0016] According to an advantageous embodiment, the first pivot has a conical shape.

[0017] According to an advantageous embodiment, the first pivot has a convex portion and the cavity has a concave portion, a part of each portion forming the contact zone.

[0018] 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.

[0019] 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.

[0020] According to an advantageous embodiment, the two minimum contact angles are equal.

[0021] According to an advantageous embodiment, the end of the pivot is defined by the intersection between the normal to the contact and the axis of the pivot.

[0022] According to an advantageous embodiment, the pivots have a rounded end.

[0023] According to an advantageous embodiment, the rounded ends of the two pivots have identical radii.

[0024] 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. Summary description of the drawings

[0025] Other characteristics and advantages of the present invention will appear on reading several embodiments given solely as non-limiting examples, with reference to the appended drawings in which: there figure 1 represents a cross-section of a shock-absorbing holding bearing for an axis of a rotating mobile according to a first embodiment of the state of the art; la figure 2 schematically represents a counter-pivot of a bearing and a pivot of an axis of a rotating mobile 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 wheel, according to a first embodiment of the invention; the figure 4 represents a sectional view of the rotating mobile system of the figure 3 ; there Figure 5represents 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; figure 7 is a graph showing the optimal 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 in the optimal radii of the ends of the two pivots as a function of the position of the center of mass figure 9 is a graph showing the variation of friction torque as a function of orientation □□ the figure 10 is a graph showing how the optimal angles vary depending on 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 εdepending on 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 orientation □ for the second configuration, la figure 13 is a graph showing the variation of 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 orientation □ for the third configuration, the figure 15 schematically represents 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 represents 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 17schematically represents 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

[0026] In the description, the same numbers are used to designate identical objects. In a watch movement, the bearing serves to hold an axis of a rotating mobile, for example a balance staff, allowing it to rotate 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.

[0027] THE figures 3 And 4show a rotating mobile system provided with a balance 13 and a spiral spring 24, the balance 13 having an axis 16. The axis 16 comprises a pivot 15, 17 at each end. Each bearing 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 a face of the bearing 18, 20, the opening 19 leaving a passage for inserting the pivot 15, 17 into 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 held while being able to rotate to allow the movement of the rotating mobile.

[0028] The two bearings 18, 20 are shock absorbers, and also comprise an elastic support 21 for the counter-pivot 22 to absorb shocks and prevent the axis 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 holds the counter-pivot 22 in the housing 14. Thus, when the timepiece undergoes a violent shock, the elastic support 21 absorbs the shock and preserves the axis 16 of the rotating wheel.

[0029] 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 external wall.

[0030] The cavity 28 of the counter-pivot 22 has the shape of a second cone having a second opening angle 32 at the apex. In order for the pivot 15, 17 to be able to rotate in the cavity, the second opening angle 32 is greater than the first opening angle 31 of the first cone 26.

[0031] The pivot 15, 17 and the cavities 28 cooperate to form a contact area 29. The contact area 29 is defined by the portions of the second cone and the pivot 15, 17 which are in contact. The contact area 29 goes around the pivot 15, 17 and the cavity 28.

[0032] 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.

[0033] According to the invention, the minimum contact angle is less than or equal to 30°, preferably less than or equal to arctan 1 2 .

[0034] In this first embodiment where the cavity 28 and the pivots 15, 17 are conical, the normal corresponds to the straight line perpendicular to the wall of the second cone, that is to say the cone of the cavity 28. Thus, the minimum contact angle is equivalent to the half-opening angle of the second cone of the cavity 28. For the minimum contact angle to be less than or equal to 30°, or even less than or equal to arctan 1 2 , relative 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 ∗ arctan 1 2 = 53.13 ° .

[0035] These angle values ​​are calculated from equations modeling the friction of pivots and bearings. To be able to describe the formulas that give the optimal angles, we define the following geometric 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 bearings; R b And R h are the radii of the spherical caps of the ends of the pivots at the bottom and top of the balance shaft; B and H are the centers of the spherical caps of the ends of the pivots at the bottom and top of the balance shaft; G is the position of the center of mass, assumed to be on the line BH (balanced balance); □ b and □ h are the coefficients of friction at the bottom and top.

[0036] To evaluate the difference in friction as a function of gravity, we distinguish two sets of orientation and two types of constraints applied to the geometry of the mobile system: the two orientation sets are as follows: O 1: the angle □ between the balance axis and gravity spans the entire interval [0°, 180°], O 2: the angle □ between the balance axis and gravity spans the 3 point values ​​0°, 90° and 180°, the two types of constraints on the geometry are as follows: C 1: no constraints on the radii R b And R h and angles □ b and □ h , C 2: for ease of manufacturing, we impose R b = R h , and we assume □ b = □ h ,

[0037] We denote by M fr,max , respectively M fr,min , the maximum friction torque, respectively minimum, on all the angles □ considered (i.e. 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 seek to minimize the maximum relative variation of torque, defined by ε = M fr , max − M fr , min M fr , min

[0038] In case O1, for a rotating mobile axis equipped with two pivots, as shown in the diagram figure 6 , the optimal minimum contact angle (α) between the pivot-bearing pairs is defined by the following equations: tan α b = BH ¯ 4 GH ¯ tan α h = BH ¯ 4 GB ¯ R h R b = μ b μ h GH ¯ GB ¯ Or 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 pendulum 2.

[0039] These equations are derived 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 to the contact and the axis of the pivot. Preferably, the ends 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.

[0040] This relationship applies to pivots with different shapes. The radii R b And R h rounded tips may differ from each other.

[0041] 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 respond to this relationship, the variation of friction between the vertical and horizontal positions is reduced compared to other geometries of pivots and cavities. In this case, the relative variation of torque □ is 41%.

[0042] These relations are also suitable for the set O 2 of the three positions of the angle □ between the balance axis and gravity (0°, 90° and 180°) with zero variation, where □□= 0% .

[0043] The graph of the figure 7shows the optimal contact angles for the two bearings and pivots for each position of the center of mass on the balance shaft. The special 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 = arctan 1 2 = env . 26.6 ° . Thus, the desirable opening angle for cones is approximately 53.2°. In other cases, the contact angles of the two bearing-pivot pairs are different. We thus note that there is always one of the two contact angles with a value less than or equal to arctan 1 2 and the other angle with a value greater than or equal to arctan 1 2 . Another case where the center of mass is a quarter of the length of the axis of a first pivot, the optimal contact angle of this first pivot is 45°, while the second pivot has an optimal contact angle equal to arctan 1 3 = 18.435 ° . So for conical cavities, we have a cone with an opening angle equal to 90°, and the other cone with an opening angle equal to 2 ∗ arctan 1 3 = 28 , 07 ° .

[0044] Each optimal contact angle falls within a range from 14° to 90°. The smallest contact angle is that of the pivot closest to the center of mass.

[0045] 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, we note that for a center of mass in the middle of the balance shaft, the radii are preferably equal for the two ends.

[0046] An example of friction torque variation as a function of orientation □ is shown in Figure 9. The curve is symmetrical about the 90° position. The torque increases gradually 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 regardless of the optimal case, up to a scaling factor.

[0047] 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 α b = 1 2 GH ¯ BH ¯ 1 + 2 GH ¯ BH ¯ 1 + 2 GB ¯ BH ¯ tan α h = 1 1 + 2 GH ¯ BH ¯ 1 + 2 GB ¯ BH ¯ if GB > GH: tan α b = 1 1 + 2 GH ¯ BH ¯ 1 + 2 GB ¯ BH ¯ tan α h = 1 2 GB ¯ BH ¯ 1 + 2 GH ¯ BH ¯ 1 + 2 GB ¯ BH ¯ Or 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 wheel. The three-dimensional model of the contact between the pivot and the counter-pivot further 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 .

[0048] The graphs of the Figures 10 and 11 show how the optimal angles and the variation □ vary depending on the relative position of the center of mass. In this case too, there is always one of the two angles with a value less than or equal to arctan 1 2 and the other angle with a value greater than or equal to arctan 1 2 . The special case where the center of mass G is in the middle of B and H, and if the coefficients of friction are equal between the bottom and the top, then we have bearings with □ b And □ h = arctan 1 2 = 26.6 ° approximately.

[0049] An example of torque variation as a function of orientation □ is shown in the figure 12 In this case, the curve is symmetrical for a value greater than 90°. Thus, for pivots of the same shape and radius, the point of symmetry of the curve is offset from that at 90° of the first embodiment.

[0050] 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 α b = tan α h = BH ¯ 4 GH ¯ if GB > GH: tan α b = tan α h = BH ¯ 4 GB ¯ Or 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.

[0051] In this case, the relative variation of torque □is 0%: the friction torques are perfectly equal at □ = 0°, 90° and 180°. On the other hand, the friction torque varies for angles different from these 3 values.

[0052] 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 arctan 1 2 = 26.6 ° approximately. An example of torque variation as a function of orientation □ is shown in the graph of the figure 14 .

[0053] Whatever the choice of model associated with the system, the minimum contact angles of the two pivots and the two bearings verify the following equation: cot α b +cot α h ≥√12.

[0054] THE figures 15 to 17 show other examples of pivots and cavities satisfying the equations cited above, while having shapes that are not entirely conical, such as the previous examples.

[0055] Thus, in a first variant of the 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 portion 38 to a cylindrical wall 66 of the cavity 35. The second flared portion 65 is wider than the first 42. The convex portion 38 has a rounded shape oriented towards the inside of the cavity 35.

[0056] The pivot 33 has a rounded tip 40 at its end, then a convex portion 37 extending from the tip 40, and a conical portion 71 extending from the convex portion 37 to a cylindrical portion 72 of the pivot 33.

[0057] The pivot 33 is inserted into the cavity 35, the dimensions of the pivot 33 and 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 each other. The contact zone 41 is 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 make a minimum contact angle with the plane perpendicular to the pivot, this minimum angle corresponds to a case meeting the preceding equations according to the invention, for example here of 25°.

[0058] 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 first flared portion 52, and a second flared portion 67 extends from the convex portion 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.

[0059] The pivot 43 comprises a rounded protrusion 50 at its end, a convex portion 47 connected to the protrusion 50 by a flared portion 75, the convex portion 47 being connected to a cylindrical portion 68 of the pivot 43.

[0060] The pivot 43 is inserted into the cavity 45, the dimensions of the pivot 43 and 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 each other. The contact zone 51 is 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 make a minimum contact angle with the plane perpendicular to the pivot 43, this minimum angle corresponds to a case meeting the preceding equations according to the invention, for example here of 25°.

[0061] In the third variant, shown on the 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.

[0062] 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 cylindrical portion 62, and a flared portion 69 extends from the convex portion 58 to a cylindrical wall 70 of the cavity 55. The convex portion 58 has a rounded shape oriented towards the inside of the cavity 55.

[0063] 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.

[0064] The pivot 53 is inserted into the cavity 55, the dimensions of the pivot 53 and 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 57 portions in contact define the contact zone 61. Only a part of each convex 58 or concave 57 portion is in contact with each other. The contact zone 61 is 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 make a minimum contact angle with the plane perpendicular to the pivot 53, this minimum angle corresponds to a case meeting the preceding equations according to the invention, for example here of 25°.

[0065] 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

1. Rotary wheel set system (10) of a horological movement, the system (10) comprising a rotary wheel set, for example a balance (13), a first and a second bearing (18, 20), particularly shock-absorbers, for a first and a second pivot (15, 17) of the arbor (16) of the rotary wheel set, the wheel set including a mass centre (G) in a position of its arbor (16), the first bearing (18, 20) including a endstone (22) comprising a main body equipped with a conical cavity (19) configured to receive the first pivot (17) of the arbor (16) of the rotary wheel set, the first pivot (17) being capable of cooperating with the cavity (19) of the endstone (22) in order 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 (αh) relating to the plane perpendicular to the arbor (16) of the pivot (17), the minimum contact angle (αh) being less than to arctan 1 2 , the second bearing (20) cooperating with the second pivot (15) to make it possible for the rotary wheel set to rotate about its arbor (16), the second bearing (20) comprising a second cavity (89), the second pivot (15) being capable of cooperating with the second cavity (89) of the endstone (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 (αb) in relation to the plane perpendicular to the arbor of the second pivot (15), the minimum contact angles (αh, αb) of the two pivots (15, 17) and of the two bearings (18, 20) being defined by the following equation: cotαh + cotαb ≥ 2,5, preferably cotαh + cotαb ≥ 3, or even cotαh + cotαb ≥ 4, characterised in that the second minimum contact angle (αb) is greater than arctan 1 2 .

2. Wheel set system according to claim 1, characterised in that the minimum contact angles (αh, αb) are defined by the following equations: tan α b = BH ¯ 4 GH ¯ tan α h = BH ¯ 4 GB ¯ R h R b = μ b μ h GH ¯ 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 mass centre (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 mass centre (G) of the balance 2.

3. Wheel set system according to claim 1, characterised in that the minimum contact angles αb, αh) are defined by the following equations: - if GB < GH: tan α b = 1 2 GH ¯ BH ¯ 1 + 2 GH ¯ BH ¯ 1 + 2 GB ¯ BH ¯ tan α h = 1 1 + 2 GH ¯ BH ¯ 1 + 2 GB ¯ BH ¯ - if GB > GH: tan α b = 1 1 + 2 GH ¯ BH ¯ 1 + 2 GB ¯ BH ¯ tan α h = 1 2 GB ¯ BH ¯ 1 + 2 GH ¯ BH ¯ 1 + 2 GB ¯ BH ¯ 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 mass centre (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 mass centre (G) of the balance.

4. Wheel set system according to any one of the preceding claims, characterised in that the contact zone or zones (29, 90) go around the pivot (15, 17) and the cavity (31, 89) about the arbor (16) of the balance.

5. Wheel set system according to any one of the preceding claims, characterised in that the first pivot (17) has a conical shape.

6. Wheel set system according to any one of claims 1 to 4, characterised in that the first pivot (43) has a convex portion (47) and the cavity (45) has a concave portion (48), a section of each portion (47, 48) forming the contact zone (51).

7. Wheel set system according to any one of claims 1 to 4, characterised in that the first pivot (53) has a concave portion (57) and the cavity (55) has a convex portion (58), a section of each portion forming the contact zone (61).

8. Wheel set system according to any one of claims 1 to 6, characterised in that the first pivot (33) has a convex portion (37) and the cavity (35) has a convex portion (38), a section of each portion (37, 38) forming the contact zone (41).

9. Wheel set system according to any one of the preceding claims, characterised in that the two minimum contact angles (αb,αh) are equal.

10. Wheel set system according to any one of the preceding claims, characterised in that the end of the pivot (15, 17) is defined by the intersection between the normal at the contact and the arbor of the pivot.

11. Wheel set system according to any one of the preceding claims, characterised in that the pivots (15, 17) have a rounded tip, the rounded tips of the two pivots (15, 17) having identical radii (Rb,Rh).

12. Horological movement comprising a plate and at least one bridge, said plate and / or the bridge including an orifice, characterised in that it includes a rotary wheel set system (10) according to any one of the preceding claims.

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