CH717571A2 - Mobile rotating system of a watch 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 between the first pivot (17) and the cavity (19) being generated, the normals of the contact zone 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 nce less than or equal to arctan.

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

[0002] In watch movements, the axes of rotating mobiles 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 wheel, 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 absorber bearing 1 is shown in Figure 1. A domed olive-shaped stone 2 is driven into a bearing support 3 commonly called a kitten, on which is mounted a counter-pivot stone 4. The bezel 3 is held 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 bezel 3 further comprises a conical outer wall arranged in correspondence with a conical internal wall arranged at the periphery of the bottom of the bearing block 5. There are also variants according to which the bezel comprises an external wall having a surface of convex shape, that is to say curved.

[0004] However, the friction torque on the axis due to the weight of the mobile varies according to the orientation of the mobile relative to the direction of gravity. These variations in the friction torque can in particular lead to a variation in the amplitude of oscillation 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 stones with holes, and the frictional force generated by the weight has a lever arm with respect 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 differences in lever arms generate differences in friction torque, which can also generate differences in rate if the isochronism is not perfect.

To control this problem, another damping bearing configuration has been devised, partly shown in FIG. of the axis 9 of the rotary wheel set, the bottom of the cavity being formed by the top 11 of the cone. Pivot 12 is also tapered to fit into cavity 8, but the solid angle of pivot 12 is smaller than that of the cone of cavity 8. This configuration allows the lever arm of the frictional force to be reduced to 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 bearing mounted on a spring, which constantly presses 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 object of the invention is, therefore, to provide a mobile system of a watch movement which avoids the aforementioned problem.

[0007] To this end, the invention relates to a mobile system comprising a rotating mobile, for example a pendulum, 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 capable of cooperating 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 pivot axis.

The system is remarkable in that the minimum contact angle is less than or equal to 30°, preferably less than or equal to arctan, which is substantially equal to 26.6°.

[0009] 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 arctan , 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 . Indeed, such an angle makes it possible to compensate for the variations in contact force due to the change of orientation with respect to gravity by different lever arms of the friction force on the two bearings.

[0010] 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, this which is for example important for a balance shaft 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.

[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 capable of cooperating 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: cotαh+cotαb≥ 2.5, preferably cotαh+ cotαb≥ 3, or even cotαh+ cotαb≥ 4.

According to an advantageous embodiment, the second minimum contact angle αb is greater than or equal to arctan.

According to another advantageous embodiment, the minimum contact angles (αb, αh) are defined by the following equations: 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 minimum contact angles (αb, αh) are defined by the following equations: - if GB < GH:

- if GB > GH: 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.

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

[0016] 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, 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 to the contact and the axis of the pivot.

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

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

Other characteristics and advantages of the present invention will appear on reading several embodiments given solely by way of non-limiting examples, with reference to the appended drawings in which: FIG. 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; FIG. 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; FIG. 3 represents a perspective view of a rotating mobile system, here a resonator mechanism comprising a rotating mobile, such as a pendulum, according to a first embodiment of the invention; FIG. 4 represents a cross-sectional view of the rotating mobile system of FIG. 3; Figure 5 shows a pivot and a bearing according to the first embodiment of the invention; FIG. 6 schematically represents a model of the bearings and pivots of a rotating mobile system according to the first embodiment of the invention; FIG. 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 axis of the balance wheel in a first configuration, Figure 8 is a graph showing the difference in the optimum 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

FIG. 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, FIG. 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, FIG. 12 is a graph showing the variation in friction torque as a function of orientation for the second configuration, FIG. 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 FIG. 14 is a graph showing the variation in friction torque as a function of orientation for the third configuration, FIG. 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; FIG. 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 FIG. 17 schematically 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

In the description, the same numbers are used to designate identical objects. In a watch movement, the bearing is used to maintain an axis of a rotating mobile, for example a pendulum 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 wheel set and a bearing inserted in the orifice.

Figures 3 and 4 show a rotating mobile system provided with a balance 13 and a spiral spring 24, the balance 13 having an axis 16. The axis 16 includes 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 one face of the bearing 18, 20, the opening 19 leaving a passage for inserting the pivot 15, 17 into the bearing as far as 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 shaft 16 are inserted into the housing 14, the shaft 16 being held while being able to rotate to allow the movement of the rotating mobile.

The two bearings 18, 20 are shock absorbers, and further comprise an elastic support 21 against the 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 mobile.

In a first embodiment of 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.

[0030] The cavity 28 of the pivot against 22 has the shape of a second cone having a second opening angle 32 at the top. 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.

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 arctan.

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, the minimum contact angle is equivalent to the half-angle of opening 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, with respect on 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 = 53.13°. [0035] These angle values are calculated from equations modeling the friction of the pivots and the bearings. In order to be able to describe the formulas which give the optimum angles, the following geometric quantities are defined, sketched in figure 6: and are the angles between the generatrices of the cones and the axis of symmetry of the cones, for the bottom landing and that of the high ; Rbet Rh are the radii of the spherical caps of the ends of the pivots at the bottom and at the top of the balance wheel axis; 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 balance shaft; G is the position of the center of mass, assumed on the line BH (balanced pendulum); and are the coefficients of friction at the bottom and at the top.; To evaluate the difference in friction as a function of gravity, two sets of orientation and two types of constraints applied to the geometry of the mobile system are distinguished: - the two sets of orientation are as follows: O1: the angle between the pendulum axis and gravity covers the entire interval [0°, 180°], O2: the angle between the axis of the pendulum and gravity runs through the 3 point values 0°, 90° and 180°, - the two types of constraints on the geometry are as follows: C1: no constraint on the radii Rbet Rhand the angles and , C2: for reasons of ease of manufacture, we impose Rb= Rh, and we assume; We denote by Mfr,max, respectively Mfr,min, the maximum friction torque, respectively minimum, over all the angles considered (i.e. the entire range [0°, 180°] in the case of O1, or the 3 values 0°, 90° and 180° in the case of O2). We seek to minimize the maximum relative variation of torque, defined by; [0038] In the case O1, for a rotating spindle provided with two pivots, as shown schematically in Figure 6, the minimum optimal contact angle (a) between the pivot-bearing pairs is defined by the following equations: 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.;[0039] 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 with 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. This relationship applies to pivots having different shapes. The radii R and Rh of the rounded ends may be different from each other. [0041] Thus, depending on the position of the center of mass G, the first cones of the two pivots 15, 17 may 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 torque variation is 41%. [0042] These relationships are also suitable for the set O2 of the three positions of the angle between the axis of the pendulum and gravity (0°, 90° and 180°) with zero variation, where; The graph of Figure 7 shows the optimum contact angles for the two bearings and pivots for each position of the center of mass on the axis of the balance wheel. 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 symmetrical bearings (Rb= Rh), with et = arctan = env . 26.6°. 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 thus notice that there is always one of the two contact angles with a value less than or equal to arctan and the other angle with a value greater than or equal to arctan . Another case where the center of mass is a quarter length from the axis of a first pivot, the optimal contact angle of this first pivot is 45°, while the second pivot has a contact angle optimal equal to arctan = 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*arctan=28.07°.

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

The graph in Figure 8 shows the difference in the optimum 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.

An example of friction torque variation as a function of orientation L 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.

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:

- if GB > GH: 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 wheel. The three-dimensional model of the contact between the pivot and the counter-pivot also includes the principle that the two pivots have the same shape, in particular for the rounded end of the pivot of similar radius Rb=Rh.

The graphs of Figures 10 and 11 show how the optimal angles vary and the variation 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 arctan and the other angle with a value greater than or equal to arctan . 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 et = arctan = approximately 26.6°.

An example of torque variation as a function of orientation is shown in Figure 12. In this case, the curve is symmetrical for a value greater than 90°. Thus, for pivots of the same shape and the same radius, the point of symmetry of the curve is shifted with respect to that at 90° of the first embodiment.

For the case O2(0°, 90°, 180°) with C2 (Rb= Rh, = ), two distinct cases are obtained: - if GB < GH:

- if GB > GH: 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 wheel.

In this case, the relative torque variation 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.

The graph of 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 = approximately 26.6°. An example of torque variation as a function of orientation is shown on the graph in 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 satisfy the following equation: cotαb+cotαh≥√12.

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

Thus, in a first embodiment of Figure 15, the first pivot 33 has a convex portion 37 and the cavity 35 has a convex portion 38, 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 cavity 35. The second flared portion 65 is wider than the first 42. The convex portion 38 has a rounded shape oriented towards the interior of the cavity 35.

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.

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 each other. 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 angle of contact 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 25°.

For the second variant of 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 part 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 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 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.

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 portions 47 and concave 48 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 form a minimum angle of contact 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 25°.

In the third variant, shown in Figure 17, 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.

The pivot 53 has a concave portion 57 and the cavity 55 has a convex portion 58. The cavity 55 includes 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 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 portions 58 and concave 57 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 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 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)

1. 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, 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 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 (αh) relative to the plane perpendicular to the axis (16) of the pivot (17), characterized in that the minimum contact angle (αh) is lower oh u equal to 30°, preferably less than or equal to arctan. 2. Mobile system according to claim 1, characterized in that the second bearing (20) cooperates with the second pivot (15) to allow the rotating mobile to rotate around 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 (αb) with respect to the plane perpendicular to the axis of the second pivot (15), characterized in that the minimum contact angles (αh, αb) of the two pivots (15, 17) and of the two bearings (18, 20) are defined by the following equation: cotαh+ cotαb≥ 2 .5, preferably cotαh+ cotαb≥ 3, or even cotαh+ cotαb≥ 4. 3. Mobile system according to claim 1 or 2, characterized in that the second minimum contact angle (αb) is greater than or equal to arctan. 4. Mobile system according to any one of the preceding claims, characterized in that the minimum contact angles (αh, αb) are defined by the following equations: 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 pendulum, 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 balance wheel 2. 5. Mobile system according to any one of claims 1 to 3, characterized in that the minimum contact angles (αb, αh) are defined by the following equations: – if GB < GH: – if GB > GH: 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. 6. 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 of the axis (16) of the balance. 7. Mobile system according to any one of the preceding claims, characterized in that the first pivot (17) has a conical shape. 8. 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), a part of each portion (47, 48) forming the contact zone (51). 9. 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), a part of each portion forming the contact zone (61). 10. 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), a part of each portion (37, 38) forming the contact zone (41). 11. Mobile system according to any one of the preceding claims, characterized in that the two minimum contact angles (αb, αh) are equal. 12. 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 to the contact and the axis of the pivot. 13. 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 (Rb, Rh ). 14. 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.