Piezoelectric element for a frequency self-regulation circuit, oscillating mechanical system and this encompassing device

Description

TECHNICAL FIELD OF THE INVENTION

[0001] The invention relates to a piezoelectric element for a frequency self-regulation circuit.

[0002] The invention also relates to an oscillating mechanical system comprising the piezoelectric element and a pendulum.

[0003] The invention further relates to a device comprising the oscillating mechanical system and a self-regulation circuit for the oscillation frequency of the oscillating mechanical system. STATE OF THE ART

[0004] Piezoelectric elements are commonly used in the field of electromechanical systems, for example for the making of oscillators used as a time base, or for applications in mass, force, gyroscope sensors and many others.

[0005] In the field of watchmaking, and particularly in mechanical or electromechanical watches, it is common practice to equip an oscillating mechanical system with a piezoelectric element. The oscillating mechanical system typically comprises a balance wheel on which a balance spring is mounted. One end of the balance spring is fixed to the balance wheel's pivot point, and the other end is fixed to a stationary element on the mainplate. The mechanical system is kept in oscillation by means of a generally mechanical energy source. This energy source could be, for example, a mainspring barrel driving a gear train with an escape wheel that engages with a pallet fork. This rotating pallet fork, for instance, actuates a pin located near the balance wheel's pivot point. The balance wheel and balance spring can thus form a regulating organ of a watch movement.This oscillating regulating organ determines the drive speed of the gear train with the escape wheel leading to the timekeeping hands. The piezoelectric element may include the balance spring, on which it is known to deposit layers of a piezoelectric material (of the PZT type), for example, on the inner and outer faces of the spring. Patent applications JP 2002-228774 and EP 2 590 035 A1 are examples of this. However, depositing such layers of piezoelectric material along the entire length of the balance spring introduces a costly additional step in the spring's manufacture, which is a disadvantage.

[0006] In these two patent applications, the oscillation frequency of the balance wheel combined with the piezoelectric balance spring is adjusted by means of a frequency self-regulating electronic circuit. This electronic circuit can be powered directly by the alternating voltage generated by the piezoelectric element, which has been rectified and stored in a capacitor. To adjust the oscillation frequency, a comparison is made between a reference frequency signal provided by an oscillator stage and the alternating signal from the generator. Based on this comparison, a frequency-matching signal is generated, which, when applied to the piezoelectric element, induces a compressive or extensor force on that element to slow down or accelerate the oscillation of the oscillating mechanical system.

[0007] Another example of a device comprising an oscillating mechanical system equipped with a piezoelectric element, and a circuit for self-regulating the oscillation frequency of the oscillating mechanical system, is provided by patent application WO 2011 / 131784 A1. According to a particular embodiment of this device, the piezoelectric element comprises a spiral spring formed from a band of piezoelectric material, a first electrode disposed on an inner face of the spring, and a second electrode disposed on an outer face of the spring. The electrodes are connected to the frequency self-regulating circuit. However, a drawback of the proposed piezoelectric element is that it does not allow the piezoelectric effect of the element to be used precisely and optimally without considerably complicating the system design. SUMMARY OF THE INVENTION

[0008] The invention therefore aims to provide a piezoelectric element for a frequency self-regulation circuit, simple to make and allowing the piezoelectric effect to be used precisely and optimally, in order to precisely regulate the oscillation frequency of an oscillating mechanical system and to overcome the aforementioned disadvantages of the prior art.

[0009] To this end, the invention relates to a piezoelectric element for a frequency self-regulation circuit, which includes the features mentioned in independent claims 1 and 2.

[0010] Particular shapes of the piezoelectric element are defined in dependent claims 3 to 13.

[0011] Using a piezoelectric crystal for the spiral spring allows for a simple and economical fabrication of the piezoelectric element, while maintaining good piezoelectric performance. Furthermore, the specific arrangement of the first and second electrodes, with a predetermined angular distribution on the spring, enables the electrodes to collect all or part of the electrical charges induced by mechanical stress, overcoming the problem of charge polarity change due to the change in the crystalline orientation of the piezoelectric crystal. This charge polarity change occurs according to a periodic angular distribution within the spiral spring. Indeed, the crystalline structure of the piezoelectric material induces a dependence of the piezoelectric coefficient on the orientation of the mechanical stress in a horizontal XY plane.In other words, depending on the direction of the stress in the XY plane, the electric charges created can be positive or negative, and their value can range from zero to a maximum value, as illustrated for example on the . figure 2 in the case of quartz. Thanks to the piezoelectric element according to the invention, the problem of canceling positive and negative electrical charges in each of the electrodes is overcome. Without limiting the scope of the present invention, the piezoelectric crystal is, for example, a single quartz crystal.

[0012] According to a first embodiment of the invention, the first and second electrodes are arranged on a portion of an outer coil of the spiral spring, said portion comprising one end of the spiral spring and defining a predetermined angular sector. An advantage of this first embodiment is the simplicity of manufacturing the piezoelectric element, and in particular its electrodes.

[0013] According to a second embodiment of the invention, the first electrode comprises first portions arranged on the first face of the piezoelectric material strip and second portions arranged on at least one face of the piezoelectric material strip distinct from the first face; and the second electrode comprises first portions arranged on the second face of the piezoelectric material strip and second portions arranged on at least one face of the piezoelectric material strip distinct from the second face. The first and second portions of the first electrode, and of the second electrode respectively, are alternately connected to each other in junction zones. The junction zones are distributed along the spiral spring according to a predetermined angular periodicity.One advantage of this second embodiment is to maximize the collection of electrical charges created, and therefore to maximize the amount of electrical energy collected.

[0014] Advantageously, the piezoelectric element comprises a first groove cut into the first face of the piezoelectric strip, and a second groove cut into the second face of the piezoelectric strip. The first electrode is disposed, at least partially, in the first groove, and the second electrode is disposed, at least partially, in the second groove. This increases the capacitive coupling between the electrodes, and thus enhances the piezoelectric performance of the element.

[0015] To this end, the invention also relates to an oscillating mechanical system comprising the piezoelectric element for a frequency self-regulation circuit, which includes the characteristics mentioned in claim 14.

[0016] To this end, the invention also relates to a device comprising the oscillating mechanical system and the self-regulation circuit of the oscillation frequency of the oscillating mechanical system, which includes the characteristics mentioned in claim 15.

[0017] Specific forms of the device are defined in claims 16 and 17. BRIEF DESCRIPTION OF THE FIGURES

[0018] The purposes, advantages, and characteristics of the piezoelectric element for a frequency self-regulating circuit, and of the oscillating mechanical system and the device comprising it, will become clearer from the following description based on at least one non-limiting embodiment illustrated by the drawings in which: there figure 1 represents, in simplified terms, a device comprising an oscillating mechanical system equipped with a piezoelectric element according to the invention, and a circuit for self-regulating the oscillation frequency of the oscillating mechanical system; figure 2 is an amplitude diagram of the piezoelectric effect of the piezoelectric element according to an exemplary embodiment of the invention, along the orientation of a stress in an XY plane; the figure 3 represents the piezoelectric element according to a first embodiment of the invention; the figure 4represents a portion of an outer coil of a spiral spring of the piezoelectric element of the figure 3 ; there figure 5 represents a portion of a spiral spring of the piezoelectric element according to a second embodiment of the invention, in a first variant of the electrodes arranged on the spiral spring; the figure 6 represents a portion of a spiral spring of the piezoelectric element according to the second embodiment of the invention, in a second variant of the electrodes arranged on the spiral spring; the figure 7 is a cross-sectional view of the piezoelectric element of the figure 6 , taken according to a section plane VII-VII; the figure 8 is a cross-sectional view of the piezoelectric element of the figure 6 , taken according to a section plane VIII-VIII; and the figure 9 represents a simplified block diagram of the electronic components of the self-regulating circuit of the figure 1according to one example of implementation, the circuit being connected to the piezoelectric element of the oscillating mechanical system. DETAILED DESCRIPTION OF THE INVENTION

[0019] The following description refers to a piezoelectric element for a frequency self-regulating circuit, specifically a circuit for regulating the oscillation frequency of an oscillating mechanical system. All the electronic components of the frequency self-regulating circuit, which are well known to anyone skilled in this technical field, are described only in simplified form. As described below, the self-regulating circuit is primarily used to regulate the oscillation frequency of a pendulum on which the spiral spring of the piezoelectric element is mounted. However, other oscillating mechanical systems can also be considered, but in the remainder of this description, reference will be made only to an oscillating mechanical system in the form of a pendulum on which the spiral spring of the piezoelectric element is mounted.

[0020] There figure 1represents a device 1, which includes an oscillating mechanical system 2, 3 and a self-regulating circuit 10 for the oscillation frequency fosc of the oscillating mechanical system. In a mechanical watch, the oscillating mechanical system may include a balance wheel 2, which is formed of a metal ring connected, for example, by three arms 5 to a pivot 6, and a piezoelectric element 3, which includes a balance spring 7. As shown in the figures 3 to 8 The piezoelectric element 3 further comprises at least two electrodes 8a-8d electrically connected to the frequency self-regulating circuit 10. Returning to the figure 1 One end 7a of the balance spring 7 is held fixed by a stud 4 on a balance bridge (not shown). This balance bridge is attached to the mainplate (not shown) of the watch movement. A second end 7b of the balance spring 7 is fixed directly to the axis of rotation 6 of the balance wheel 2.

[0021] The balance wheel 2, with its balance spring 7, is kept in oscillation by means of a power source (not shown), which can be electrical, but is preferably mechanical. This mechanical power source can be a mainspring barrel, which traditionally drives a gear train with an escape wheel cooperating with a pallet fork. This rotating pallet fork, for example, actuates a pin fixed near the balance wheel's axis of rotation. The balance wheel with the balance spring can thus form a regulating organ of a clockwork movement.

[0022] The spiral spring 7 is made using a band of piezoelectric material generally less than 0.25 mm thick, for example, on the order of 0.1 to 0.2 mm. The piezoelectric material can be a piezoelectric crystal or a piezoelectric PZT ceramic. Preferably, the piezoelectric crystal is a single crystal, typically single-crystal quartz in the embodiment examples of figures 2 to 8 The spiral spring 7 is, for example, machined from Z-cut single-crystal quartz, that is, quartz cut perpendicular to the Z-axis or optical axis of a single-crystal quartz bar. A spiral with spaced turns from a piezoelectric crystal strip is obtained by micromachining in a hydrofluoric acid bath as described in US patent application 2015 / 0061467 A1, which is incorporated herein by reference. At least two metallic electrodes are deposited on at least two faces of the piezoelectric crystal strip in an arrangement that will be described in more detail later. More specifically, the electrodes are arranged along part or all of the length of the spiral spring 7 in a predetermined angular distribution. Each electrode is, for example, an Au / Cr (Gold / Chromium) type electrode.

[0023] There figure 2This represents the amplitude of the piezoelectric effect of element 3 when it includes a quartz spiral spring 7, according to the orientation of a stress in a horizontal XY plane. As this figure shows, the crystal structure of quartz induces a dependence of the piezoelectric coefficient on the orientation of the mechanical stress in the XY plane. In other words, depending on the direction of the stress in the XY plane, the electrical charges created by the spiral spring 7 can be positive or negative, and their value can range from zero to a maximum. Since the crystal structure of quartz is trigonal, the maximum electrical charge is repeated every 60°, with a change in charge polarity also occurring every 60°.

[0024] A first embodiment of the invention will now be described with reference to figures 3 and 4According to this first embodiment, the piezoelectric element 3 comprises two electrodes 8a, 8b. The two electrodes 8a, 8b are arranged on a portion 12 of an outer coil 14 of the spiral spring 7. The portion 12 comprises the first end 7a of the spiral spring 7 and defines a predetermined angular sector. In the preferred embodiment in which the spiral spring 7 is formed from a quartz strip, the predetermined angular sector is substantially equal to 60°. Thus, and with reference to the figure 2 This first embodiment of the invention prevents the mutual cancellation of electrical charges due to the change in polarity induced by the change in crystalline orientation of the quartz spiral spring 7. Electrodes 8a and 8b collect a portion of the electrical charges induced by mechanical stress, thus preventing the mutual cancellation of charges.

[0025] Preferably, as illustrated on the figure 4The piezoelectric element 3 may include at least one groove 16a cut into an upper face of the piezoelectric crystal strip, designated the upper face. When the piezoelectric crystal strip is wound with electrodes 8a and 8b, the upper face bearing electrode 8a is perpendicular to the axis of rotation of the balance wheel and parallel to the plane of the balance spring, while the inner face for electrode 8b faces the axis of rotation of the balance wheel. The first electrode 8a of the two electrodes is disposed in the groove 16a of the upper face, and the second electrode 8b is disposed on the inner face.

[0026] THE figures 5 to 8 illustrate a second embodiment of the invention in which the elements analogous to the first embodiment, described above, are identified by identical references, and are therefore not described again.

[0027] According to a first variant embodiment shown in the figure 5 A first electrode 8a, one of the two electrodes, comprises first portions 18a arranged on the outer face of the piezoelectric crystal strip, and second portions 18b arranged on a face of the strip designated the upper face. A second electrode 8b comprises first portions 20a arranged on the inner face of the piezoelectric crystal strip, and second portions 20b arranged on the upper face. Preferably, the two electrodes 8a, 8b extend along the entire length of the spiral spring 7, although only a portion of the latter, and therefore only a first portion 18a, 20a and a second portion 18b, 20b of each electrode 8a, 8b, are shown in the diagram. figure 5 .

[0028] The first portions 18a and the second portions 18b of the first electrode 8a are alternately connected to each other in first junction zones 22. The first portions 20a and the second portions 20b of the second electrode 8b are alternately connected to each other in second junction zones 24, adjacent to the first junction zones 22. The first and second junction zones 22, 24 are distributed on the spiral spring 7 according to a predetermined angular periodicity. The second portions 18b, 20b of the first and second electrodes 8a, 8b extend successively and alternately from one another on the upper face of the piezoelectric crystal strip, according to this same predetermined angular periodicity. In an alternative not shown, the second parts 18b, 20b of the first and second electrodes 8a, 8b could extend in the same way on one face of the piezoelectric crystal strip designated lower face.In the preferred embodiment example in which the spiral spring 7 is formed from a quartz strip, the predetermined angular periodicity is substantially equal to 60°.

[0029] According to a second embodiment shown in f Figures 6 to 8 In addition to the first and second electrodes 8a, 8b, the piezoelectric element 3 also includes a third and fourth electrode 8c, 8d. As illustrated in the figure 6The third electrode 8c, which has the same polarity as the first electrode 8a, is connected to it at a first connection terminal 26. The fourth electrode 8d, which has the same polarity as the second electrode 8b, is connected to it at a second connection terminal 28. The first and second connection terminals 26, 28 are each connected to the frequency self-regulation circuit 10. In a particular embodiment, not shown in the figures, the first and second connection terminals 26, 28 are arranged on the pin 4 which now fixes the first end 7a of the spiral spring 7.

[0030] The first electrode 8a comprises first portions 30a arranged on the outer face of the piezoelectric crystal strip, and second portions 30b arranged on each face of the strip, distinct from the outer face. The second electrode 8b comprises first portions 32a arranged on the upper face of the piezoelectric crystal strip, and second portions 32b arranged on each face of the strip, distinct from the upper face. The third electrode 8c comprises first portions 34a arranged on the inner face of the piezoelectric crystal strip, and second portions arranged on each face of the strip, distinct from the inner face. The fourth electrode 8d comprises first portions 36a arranged on the lower face of the piezoelectric crystal strip, and second portions arranged on each face of the strip, distinct from the lower face.Preferably, the four electrodes 8a, 8b, 8c, 8d extend over the entire length of the spiral spring 7, although only a portion of the latter is shown on the . figure 6 The second parts of the third and fourth electrodes 8c, 8d are therefore not visible on the figures 6 to 8 .

[0031] The first parts 30a and the second parts 30b of the first electrode 8a are alternately connected to each other in first junction zones 38. The first parts 32a and the second parts 32b of the second electrode 8b are alternately connected to each other in second junction zones 40. The first parts 34a and the second parts of the third electrode 8c are alternately connected to each other in third junction zones 42. The first parts 36a and the second parts of the fourth electrode 8d are alternately connected to each other in fourth junction zones 44. The various junction zones 38-44 are distributed on the spiral spring 7 according to a predetermined angular periodicity.

[0032] As illustrated on the figure 7Each junction zone 38-44 extends across two adjacent faces of the piezoelectric crystal strip. Thus, the first, second, third, and fourth electrodes 8a, 8b, 8c, 8d extend successively and alternately from one another across each face of the piezoelectric crystal strip, according to a predetermined angular sub-periodicity. In the preferred embodiment in which the spiral spring 7 is formed from a quartz strip, the predetermined angular sub-periodicity is approximately 60°.

[0033] With reference to the figure 2This second embodiment of the invention prevents the mutual cancellation of electrical charges due to the change in polarity induced by the change in crystalline orientation of the quartz spiral spring 7. Through a periodic change in the electrode faces, the electrodes collect all the electrical charges induced by mechanical stress, thus preventing the mutual cancellation of charges. Within the device 1, which includes the oscillating mechanical system 2, 3, all the electrical charges created by the oscillating system 2, 3 are collected, thereby maximizing the amount of electrical energy collected and supplied to the circuit 10.

[0034] Although not represented on the figures 5 to 8, the piezoelectric element 3 according to this second embodiment can advantageously include electrode support grooves, cut into opposite faces of the piezoelectric crystal strip, which are the upper and lower faces.

[0035] During the oscillation of the balance wheel 2 with the balance spring 7, a compressive or extensor force is alternately applied to the piezoelectric crystal strip, which together generate an alternating voltage. The oscillation frequency of the balance wheel 2 with the balance spring 7 is typically between 3 and 10 Hz. The self-regulating circuit 10 receives this alternating voltage via the electrodes to which it is connected. The self-regulating circuit can be connected directly to the electrodes or via two metal wires.

[0036] There figure 9This represents the various electronic components of an example embodiment of the self-regulating circuit 10, which regulates the oscillation frequency of the oscillating mechanical system. Other examples of frequency self-regulating circuits may be considered interchangeably without departing from the scope of the invention.

[0037] The self-regulating circuit 10 is connected to two electrodes or groups of electrodes of the piezoelectric element 3. The self-regulating circuit 10 is able to rectify the alternating voltage VP received from the piezoelectric element 3 via a conventional rectifier 51. The rectified voltage of the alternating voltage VP is stored in a capacitor Cc. This rectified voltage between the terminals VDD and VSS of the capacitor Cc can be sufficient to power all the electronic components of the self-regulating circuit without the need for an additional voltage source such as a battery or an energy conversion element, such as a solar cell, a thermoelectric generator, or the like.

[0038] The self-regulating circuit 10 includes an oscillator stage 55, connected, for example, to a MEMS-type resonator 56. The oscillating circuit of the oscillator stage with the MEMS resonator provides an oscillating signal, which may have a frequency lower than 500 kHz, for example, on the order of 200 kHz. Thus, the oscillator stage 55 can preferably provide a reference signal VR, the frequency of which may be equal to the frequency of the oscillating signal of the oscillator circuit.

[0039] To regulate the oscillation frequency of the oscillating mechanical system, a comparison must be performed in the self-regulating circuit 10 between the alternating voltage VP and the reference signal VR. For this purpose, the self-regulating circuit 10 includes comparison means 52, 53, 54, and 57 to compare the frequency of the alternating voltage VP with the frequency of the reference signal VR. If the frequency of the reference signal corresponds to the frequency of the oscillating circuit of the oscillator stage 55, i.e., a frequency of approximately 200 kHz, the comparison means must be designed to account for the significant frequency difference between the alternating voltage VP and the reference signal VR.

[0040] The comparison means consist first of all of a first alternation counter 52, which receives as input the alternating voltage VP of the piezoelectric element, and which provides a first counting signal NP to a processor processing unit 57. The comparison means also include a second alternation counter 54, which receives as input the reference signal VR, and which provides a second counting signal NR to the processor processing unit 57.

[0041] To account for the frequency difference between the alternating voltage VP and the reference signal VR, a measurement window 53 is provided between the first half-cycle counter 52 and the second half-cycle counter 54. This measurement window 53 determines the counting time of the second half-cycle counter 54. The processor unit 57 provides configuration parameters to the measurement window 53 to determine the counting time for the second half-cycle counter. These configuration parameters are stored in memory not shown in the processor unit. These configuration parameters may differ depending on whether it is a ladies' or men's watch. The various operations processed in the processor unit 57 can be controlled by a clock signal provided, for example, by the oscillating circuit of the oscillator stage 55.

[0042] The counting time of the second half-cycle counter 54 is adjusted proportionally to the counting time of a predetermined number of half-cycles counted by the first half-cycle counter 52 in the first counting signal NP. The processor unit 57 can optionally also control the first half-cycle counter 52 to define the start and end of a counting period. However, it can also be envisaged that the first half-cycle counter 52 provides information on the start and end of a predetermined number of counted half-cycles to the processor unit 57. If, for example, 200 half-cycles are to be counted in the first half-cycle counter, the measurement window 53 is configured so that the second half-cycle counter 54 counts a number of half-cycles of the reference signal VR for a duration approximately 5000 times shorter.This duration can also depend on the counting time, for example, of the 200 alternations of the first alternation counter 52. This allows to reduce the electrical consumption of the self-regulation circuit.

[0043] The start of counting, controlled by the measuring window 53, can be determined by the first half-cycle counter 52, but can also preferably be controlled directly by the processor unit 57. The processor unit 57 can first receive the first counting signal NP, corresponding to a first predetermined number of counted half-cycles of the alternating voltage VP in a first time interval. This first counting signal is stored, for example, in a register of the processor unit. Subsequently, the processor unit 57 can receive the second counting signal NR, corresponding to a second number of counted half-cycles in the second half-cycle counter 54 in a second time interval controlled by the measuring window 53. This second counting signal NR can also be stored in another register of the processor unit.Finally, a comparison of the two counting signals is carried out in the processor unit 57 to determine if the frequency of the alternating voltage VP is too high or too low relative to the frequency of the reference signal.

[0044] Based on the comparison performed between the two counting signals NP and NR in the processor unit, said processor unit controls a frequency matching unit 58, the output of which is connected to the two electrodes or groups of electrodes of the piezoelectric element 3. This frequency matching unit 58 can be provided to supply a frequency matching signal, which is a DC voltage VA, the level of which is a function of the difference between the two counting signals communicated by the processor unit. A switchable network of capacitors or resistors can be provided for this purpose. A DC voltage value can be supplied via a voltage follower from the matching unit 58 to one or the other electrode or group of electrodes of the piezoelectric element 3.This makes it possible to induce a certain force on the piezoelectric element to slow down or speed up the oscillation of the oscillating mechanical system depending on the comparison of the two counting signals.

[0045] The self-regulating circuit 10 can also include well-known thermal compensation elements, as well as a reset unit for each activation of the self-regulating circuit 10. All the electronic components of the self-regulating circuit, as well as the MEMS resonator 56 and the capacitor Cc, for example, are part of a single compact electronic module. All these electronic components can be advantageously integrated into a single monolithic silicon substrate, thus requiring only a single self-powered electronic module for frequency regulation of the oscillating mechanical system.

[0046] The preceding description of the piezoelectric element according to the invention was made with reference to a spiral spring formed from a single-crystal quartz strip. However, the use of quartz as a piezoelectric crystal is by no means limiting within the scope of the present invention, and other piezoelectric crystals can also be considered for forming the spiral spring, such as, for example, without this list being exhaustive, topaz, berlinite, lithium niobate, lithium tantalate, gallium phosphate, gallium arsenate, aluminum silicate, germanium dioxide, a single crystal from the tourmaline group, a single crystal from the III-V semiconductor group with a zinc-blende structure, or a single crystal from the II-VI semiconductor group with a wurtzite structure.

[0047] Therefore, although the description of the invention given above was made with reference to a change in polarity of charges respecting a periodic angular distribution of 60°, due to the crystalline structure of quartz; other periodic angular distributions can also be envisaged without departing from the scope of the invention defined by the claims, according to the different types of piezoelectric crystals used to form the spiral spring.

[0048] The two embodiments of the piezoelectric element according to the invention, described above in the context of regulating the oscillation frequency of the oscillating mechanical system, can also be advantageously used to measure this oscillation frequency, and / or to perform phase corrections of the system and / or to collect energy.

Claims

1. A piezoelectric element (3) for a self-regulating frequency control circuit (10), the piezoelectric element (3) comprising: - a balance spring (7) formed of a strip of piezoelectric material; - a first electrode (8a), to be connected to the self-regulating frequency control circuit (10), and fitted on at least a first side of the strip of piezoelectric material; - a second electrode (8b), to be connected to the self-regulating frequency control circuit (10), and fitted on at least a second side of the strip of piezoelectric material; characterised in that the piezoelectric material is a piezoelectric crystal or a piezoelectric ceramic; and in that the first and second electrodes (8a, 8b) are fitted on a portion of an outer coil of the balance spring (7), said portion comprising one end of the balance spring and defining a predetermined angular sector.

2. A piezoelectric element (3) for a self-regulating frequency control circuit (10), the piezoelectric element (3) comprising: - a balance spring (7) formed of a strip of piezoelectric material; - a first electrode (8a), to be connected to the self-regulating frequency control circuit (10), and fitted on at least a first side of the strip of piezoelectric material; - a second electrode (8b), to be connected to the self-regulating frequency control circuit (10), and fitted on at least a second side of the strip of piezoelectric material; characterised in that the piezoelectric material is a piezoelectric crystal or a piezoelectric ceramic, in that the first electrode (8a) comprises first parts fitted on the first side of the strip of piezoelectric material, and second parts fitted on at least one side of the strip of piezoelectric material different to the first side, in that the second electrode (8b) comprises first parts fitted on the second side of the strip of piezoelectric material, and second parts fitted on at least one side of the strip of piezoelectric material different to the second side, in that the first and second parts of the first electrode (8a) and of the second electrode (8b), respectively, are alternately connected to each other in junction zones, and in that the junction zones are distributed over the balance spring (7) at a predetermined angular frequency.

3. The piezoelectric element (3) according to claim 1, characterised in that the first and second electrodes (8a, 8b) are fitted on one portion (12) of an outer coil (14) of the balance spring (7), said portion (12) comprising one end (7a) of the balance spring (7) and defining a predetermined angular sector.

4. The piezoelectric element (3) according to claim 1, characterised in that the first electrode (8a) comprises first parts (18a; 30a) fitted on the first side of the strip of piezoelectric material and second parts (18b; 30b) fitted on at least one side of the strip of piezoelectric material different to the first side; in that the second electrode (8b) comprises first parts (20a; 32a) fitted on the second side of the strip of piezoelectric material and second parts (20b; 32b) fitted on at least one side of the strip of piezoelectric material different to the second side; the first and second parts of the first electrode (8a) respectively the second electrode (8b) being alternately connected to each other in junction zones (22, 24; 38, 40); and in that said junction zones (22, 24; 38, 40) are distributed over the balance spring (7) with a predetermined angular periodicity.

5. The piezoelectric element (3) according to claim 4, characterised in that the second parts (18b) of the first electrode (8a) and the second parts (20b) of the second electrode (8b) are fitted on a third side of the strip of piezoelectric material; and in that said second parts (18b, 20b) of the first and second electrodes (8a, 8b) extend in succession and alternately one after the other on the third side of the strip of piezoelectric material with said predetermined angular periodicity.

6. The piezoelectric element according to claim 4, characterised in that it comprises a third electrode (8c) and a fourth electrode (8d); the third electrode (8c) being connected to the first electrode (8a) at a first connection terminal (26) to be connected to the self-regulating frequency control circuit (10), the third electrode (8c) comprising first parts (34a) fitted on a third side of the strip of piezoelectric material and second parts fitted on at least one side of the strip of piezoelectric material different to the third side; the fourth electrode (8d) being connected to the second electrode (8b) at a second connection terminal (28) to be connected to the self-regulating frequency control circuit (10), the fourth electrode (8d) comprising first parts (36a) fitted on a fourth side of the strip of piezoelectric material and second parts fitted on at least one side of the strip of piezoelectric material different to the fourth side; the first and second parts of the third electrode (8c) respectively the fourth electrode (8d) being alternately connected to each other in junction zones (42, 44); and in that said junction zones (42, 44) are distributed over the balance spring (7) with said predetermined angular periodicity.

7. The piezoelectric element (3) according to claim 6, characterised in that each second part of the first, second, third, respectively fourth electrode extends over each side of the strip of piezoelectric material different to the first, second, third, respectively fourth side; and in that the first, second, third and fourth electrodes (8a-8d) extend in succession and alternately one after the other on each side of the strip of piezoelectric material, with a predetermined angular sub-periodicity.

8. The piezoelectric element (3) according to claims 5 to 7, characterised in that the electrodes are fitted over the entire length of the balance spring.

9. The piezoelectric element (3) according to claim 1, characterised in that the piezoelectric crystal is a single crystal chosen from the group consisting of topaz, berlinite, lithium niobate, lithium tantalate, gallium phosphate, gallium arsenate, aluminium silicate, germanium dioxide, a single crystal tourmaline, a single crystal from the group of zinc-blende-structure III-V semiconductors, or a single crystal from the group of wurtzite structure II-VI semiconductors.

10. The piezoelectric element (3) according to claim 1, characterised in that the piezoelectric crystal is single crystal quartz.

11. The piezoelectric element (3) according to claim 10, characterised in that the balance spring (7) is machined in Z -cut single crystal quartz.

12. The piezoelectric element (3) according to claim 9 or 10 when it depends from claim 2 or 3, characterised in that the predetermined angular sector, the predetermined angular periodicity or the predetermined angular sub-periodicity is substantially equal to 60°.

13. The piezoelectric element (3) according to any of the preceding claims, characterised in that it further comprises at least one groove (16a) cut into the first upper or lower side of the strip of piezoelectric material, said first electrode (8a) being at least partially fitted in said groove (16a), said second electrode (8b) being at least partially fitted on a second outer or inner side.

14. An oscillating mechanical system for a self-regulating frequency control circuit (10), comprising a balance (2) and a piezoelectric element (3) provided with a balance spring (7), the balance spring (7) being mounted on said balance (2), characterised in that the piezoelectric element (3) conforms to any of the preceding claims.

15. A device (1) comprising the oscillating mechanical system according to claim 14 and a self-regulating circuit (10) for controlling the oscillation frequency of the oscillating mechanical system, said self-regulating control circuit (10) comprising an oscillator stage (55) for providing a reference signal (VR), means (52, 53, 54, 57) for comparing the frequency between two signals, and a frequency adaptation unit (58) connected to the piezoelectric element (3) of the oscillating mechanical system and providing a frequency adaptation signal (VA), characterised in that the piezoelectric element (3) of the oscillating mechanical system can generate an alternating voltage (VP) at a frequency corresponding to the oscillating mechanical system, the first and second electrodes (8a, 8b) of the piezoelectric element being connected to the self-regulating control circuit (10) in order to receive the frequency adaptation signal (VA) from the frequency adaptation unit (58), on the basis of the result of a frequency comparison, in the frequency comparison means, between the alternating voltage (VP) and the reference voltage (VR)16. The device (1) according to claim 15, characterised in that the self-regulating circuit (10) for controlling the oscillation frequency of the oscillating mechanical system further comprises a rectifier (51) for rectifying the alternating voltage (VP) generated by the piezoelectric element (3) and for storing the rectified voltage on at least one capacitor (Cc), in order to supply the self-regulating control circuit with electricity.

17. The device (1) according to claim 15 or 16, characterised in that the oscillator stage (55) of the self-regulating control circuit (10) comprises an oscillating circuit connected to a MEMS resonator (56) to provide an oscillating signal, so that the oscillator stage (55) provides the reference signal (VR), all the electronic components of the self-regulating control circuit being grouped together to form a single electronic module.