High quality coefficient bending vibration resonators for producing time standards, force sensors or gyrometers

Abstract

The resonator is suitable for reducing or suppressing the forces transmitted by the vibrating part of the resonator to a support (Pf). For this purpose, said vibrating part comprises two extensions (P1, P2) which are serpentine in shape such that the two segments of each extension have respective velocity components oriented in opposite directions. Such a resonator, in a balanced state, can be advantageously used in a gyrometer or force sensor.

Description

Detailed Description of the Invention

[0001] [Technical Field] The present invention relates to a resonator having a vibrating part formed on a wafer having parallel faces, and to a force sensor and a gyrometer including such a resonator. [Prior Art] Flexural vibration resonators are widely used to make time references, gyrometers, and force sensors. The best-known examples are quartz tuning forks for providing time references, as described in U.S. Pat. No. 3,683,213; double-headed tuning forks for forming force sensors, as described in U.S. Pat. No. 4,215,570; double-headed tuning forks for measuring rotational speed, as described in U.S. Pat. No. 61,529,400; and single-headed tuning forks with a separate structure for measuring rotational speed, as described in U.S. Pat. No. 6,414,416.

[0002] In the case of piezoelectric flexural resonators made of quartz, the orientation of the resonator beam is generally chosen along the crystal axis Yc, and the planar structure of the resonator is parallel to the crystal plane Xc-Yc. On the one hand, this allows optimally benefiting from the piezoelectric coupling to excite and detect flexural vibrations in the planes Xc-Yc and Yc-Zc. On the other hand, it allows benefiting from a faster etching rate along the axis Zc to etch the structure using an acid-type wet etching process, usually using a mixture of ammonium fluoride (NH4F) and hydrofluoric acid (HF).

[0003] In fact, the piezoelectric tensor of the trigonal class of crystals provides an optimal coupling between the deformation Syy and the electric field Exx along the axis of the beam. For this purpose, the bending vibration of the beam is excited by the direct piezoelectric effect using electrodes located along the beam to generate the electric field Exx and to detect the deformation Syy via charges generated by the indirect piezoelectric effect on these same electrodes.

[0004] Several alternative electrode configurations are possible. For example, as shown in Figure 1a, electrodes are placed on both sides of the wafer on which the resonator is formed for vibrational motion parallel to the Xc direction. Alternatively, as shown in Figure 1b, electrodes are placed on both sides of the wafer on which the resonator is formed for out-of-plane vibrational motion parallel to the Zc direction. Figures 1a and 1b further show the electric field component Exx required to induce bending in the beam for each electrode configuration shown.

[0005] Such a configuration, with electrodes on the wafer surface, is easy to implement. However, other electrode configurations are possible, such as electrodes located on the sides of the beam perpendicular to the wafer surface. Such other configurations, as described in U.S. Pat. No. 4,524,619, may be more effective at producing beam bending, but are more difficult to implement.

[0006] When these resonators are fabricated by wet chemical etching of wafers with parallel faces, the etched facets due to the crystal orientation of the etched planes create asymmetries in the resonator's morphology and subsequently alter its behavior. Indeed, for the trigonal symmetry of a Class 32 crystal such as quartz, it is known that a beam of orientation Yc chemically etched using a mixture of NHF-HF has perfectly orthogonal sides in the direction Xc- and a dihedral angle at the orthogonal sides in the direction Xc+-.

[0007] Due to the trigonal symmetry of quartz, this pattern repeats every 120° (degrees), as shown in Figure 2a. Figure 2b shows a typical result obtained in this way for a quartz tuning fork in which the wafer face is parallel to the plane Xc-Yc and the beam is oriented longitudinally along the axis Yc. Facets fd on the sides of the tuning fork beam break symmetry with respect to the plane P perpendicular to the plane of the wafer, and facets fo at the buried end of the beam break symmetry with respect to the central plane M of the resonator.

[0008] These symmetry disruptions cause poor dynamic balance of the resonator, which leads to losses of vibration energy in the resonator's mounting, and consequently to a reduction in the resonator's quality factor and the stability of its vibration frequency, which are detrimental to the use of the resonator for manufacturing precision force sensors or time standards.

[0009] When such a resonator is used to fabricate a vibrating gyrometer, the break in the resonator's symmetry typically creates a parasitic mechanical coupling between the two useful vibration modes of the gyrometer. This results in a measurement bias: when there is no rotation, the output signal from the gyrometer is no longer zero. The presence of such a non-zero measurement bias significantly reduces the accuracy of the gyrometer's measurements.

[0010] Compensation measures are then typically applied by adding mass to the ends of the beam and adjusting the symmetry by laser ablation to reduce imbalance and / or adjust the vibration frequency as described in U.S. Pat. No. 3,683,213, or to reduce quadrature coupling in the case of the vibratory gyrometer described in U.S. Pat. No. 61,529,400.

[0011] Quadrature coupling in a gyrometer arises from a mechanical coupling that connects two useful modes of gyrometer vibration: a mode commonly referred to as the "pilot mode," corresponding to the tuning fork vibration mode, and an out-of-plane mode of vibration, referred to as the "sensing mode," excited by Coriolis accelerations from the pilot mode when the resonator is rotated about the longitudinal axis of the beam. Any break in the symmetry of the resonator, primarily with respect to the midplane M (see Figure 2b), introduces a coupling stiffness between the pilot and sensing modes, resulting in parasitic motion of the resonator in the sensing mode in the absence of rotation.

[0012] Such defects severely limit gyrometer performance by introducing measurement bias. However, performing localized, individually tailored laser ablation on each fabricated resonator to correct such symmetry defects in the gyrometer is particularly costly and often imperfect, so the ultimate performance of the gyrometer remains limited.

[0013] Other inventive measures to substantially reduce quadrature coupling in vibrating quartz crystal gyrometers have been implemented, such as in French Patent No. 2,944,102 filed by the same applicant. In French Patent No. 2,944,102, the orientation of the vibrating beam is altered to exploit the torsional mode of vibration of the beam, resulting in coupling to the bending mode of vibration via Coriolis acceleration. These changes allow for perfect symmetry of the vibrating structure while still fabricating the resonator using a low-cost process of chemically etching the quartz crystal. As reported by Guerard et al. in their paper "Quartz Structures for Coriolis Vibrating Gyroscopes" (DOI: 10.1109 / ISISS.2014.6782534), quadrature coupling was reduced by three to four orders of magnitude, but the inherent thermal sensitivity of the gyrometer was impaired. Due to the inherent properties of quartz crystal, the significant thermal dependence of the torsional mode significantly reduced the inherent thermal sensitivity of the gyrometer.

[0014] Japanese Patent Application No. 2005-068690 proposes a unique structure for vibrating quartz crystal gyrometers. This structure utilizes three beams oriented along the crystal axis Yc, with the sensitive axis perpendicular to the plane of the structure, taking advantage of the trigonal symmetry of quartz crystal. The resulting gyrometer thus benefits from a very good piezoelectric coupling between the pilot and sensing modes. However, when such a vibrating structure is etched by chemical etching, it is not symmetrical with respect to a plane perpendicular to the wafer surface. The relevant vibration modes do not allow for good dynamic balance of the resonator, and the quality factor of the useful vibration modes is reduced.

[0015] In the case of force sensors, the double-ended tuning fork structure described in U.S. Pat. No. 4,215,570 constitutes an interesting compromise, due in particular to the very thin groove separating the two beams intended to vibrate synchronously in opposite directions. This configuration ensures good coupling between the resonators while reducing deformation of the embedded ends of the beams. In this way, the parasitic longitudinal motions that occur when the beams vibrate and cause energy losses are reduced.

[0016] This longitudinal motion is utilized, for example, in musical tuning forks, which transmit beam vibrations through the tines to a resonating support to produce an audible tone that is very useful for tuning musical instruments. This example, utilizing longitudinal motion transmitted through the tines of a tuning fork, clearly demonstrates the energy leakage that occurs through the tines to the outside of the resonator. On the other hand, when fabricated by chemical etching, the double-ended tuning fork of U.S. Pat. No. 4,215,570 is not symmetrical about a plane perpendicular to the face of the resonator due to the presence of a dihedral angle on the orthogonal side in the Xc+ direction.

[0017] This geometric asymmetry also creates an asymmetry in the longitudinal force transmission in the two beams, leading to unequal frequency variations in the two beams of the tuning fork. This impairs the tuning fork's effectiveness and can significantly reduce the value of the quality factor, which is effective when the resonator is subjected to the axial tension to be measured. Alternatives to the double-ended tuning fork have been proposed for producing force sensors, such as those described in French Patent No. 8,418,587 filed by the same applicant. In fact, French Patent No. 8,418,587 proposes associating a simple single-beam resonator, intended to oscillate in bending, with a system for decoupling the oscillations of this beam from its support via an inertial mass at the end of the beam.

[0018] This resonator has two advantages: on the one hand, a single beam (tine) instead of two beams as for a tuning fork makes it possible to double the scale factor of the resonator, which means the variation of the frequency as a function of the axial tension being measured; on the other hand, the principle of decoupling, which provides a high tolerance to possible alignment errors.

[0019] However, such resonators remain bulky, which can limit their use in small devices such as resonators used as sensor elements and accelerometers that rely on frequency variations related to forces generated by a mass under test through the acceleration being measured.

[0020] Another inventive alternative has been proposed in French Patent No. 2,739,190 filed by the applicant, which incorporates a simple bending vibration resonator within the monolithic accelerometer structure, providing a system for isolating vibrations from the outside world within the monolithic accelerometer structure.

[0021] The optimization of simple bending vibration resonators has also been proposed in the applicant's refiled French patent no. 2,805,344 by improving the value of the figure of merit F×Q / Sf, where F is the frequency of the resonator, Q is the resonance quality factor and Sf is m / s 2 is a scale factor expressed in Hertz per second.

[0022] This improvement is achieved by using a non-constant cross section beam, which provides a 1.2x gain in the figure of merit F x Q / Sf, which describes the stability of the accelerometer bias, i.e., the stability of the resonant frequency in the absence of acceleration.

[0023] However, these simple resonators are not satisfactory for the application of variable frequency force sensors, which require that the resonator be inherently decoupled and insensitive to its mounting conditions in order to allow easy and reliable force measurements. Based on this, one aspect of the present invention is to propose a new force sensor that meets these inherent decoupling requirements. The new force sensor is no longer based on modifying the stiffness of a flexurally vibrating beam generated by an axial force that acts as a restoring torque and therefore modifies the resonance frequency, but rather modifies the flexural inertia generated by the displacement generated by the force applied to the resonator.

[0024] This force sensor principle, based on modifying bending inertia, has already been proposed, for example, in the paper "New resonant accelerometer based on rigidity change" (Y. Omura, Y. Nonomura, O. Tabata, TRANSDUCERS 97, 1997, International Conf. Solid-State Sensors and Actuators, Chicago). It is based on a non-decoupled resonator, but cannot meet the demanding applications where high-quality factor resonators are required for measurement accuracy and resolution.

[0025] It is important to recall at this stage that wet chemical etching for the production of crystal oscillators is an inexpensive process particularly suited to the collective fabrication of microdevices, while preserving the intrinsic quality factor of the crystal. In fact, chemical etching is based on local chemical reactions, which allow the dissolution of crystal atoms by atoms, without altering or degrading the crystal lattice of the material.

[0026] This is not the case for etching based on local abrasion, such as ultrasonic machining, which uses fine abrasive particles excited by ultrasonic waves generated between a probe (sonotrode) and the surface to be etched. Nor is this the case for etching based on ion bombardment, which uses the kinetic energy of ions. These last two techniques alter the crystal lattice at the edge of the etch over characteristic distances of tens of nanometers to several micrometers, due to the higher energy etching, which reduces the intrinsic quality factor of the resonator. This is especially true when miniaturization of the equipment is desired. [Technical issues] Based on this situation, one object of the present invention is to provide a new resonator that is improved with respect to at least some of the disadvantages of conventional resonators, as mentioned above.

[0027] In particular, one object of the present invention is to provide a resonator in which the loss of vibration energy to the outside is reduced in order to provide an increased value of the quality factor.

[0028] A secondary object of the present invention is to reduce symmetry defects that can affect the shape of the resonator due to differences in etching rates that exist between different crystal orientations of the material used to construct the resonator. Summary of the Invention In order to achieve at least one of these or other objects, a first aspect of the invention proposes a resonator comprising a part of a wafer having two flat, parallel, opposing faces, which is intended to vibrate in flexural motion during use of the resonator, called the vibrating part, and a support part located outside the vibrating part and connected to it by intermediate segments of the wafer, called the feet, which are integral with the vibrating part and form a rigid connection between the support part and the vibrating part.

[0029] In this resonator of the invention, the vibrating part has a first plane of symmetry, called the mid-plane, parallel to both faces of the wafer and equidistant from these two wafer faces, and a second plane of symmetry, called the plane of symmetry orthogonal to the wafer, perpendicular to the mid-plane and passing longitudinally through the connection formed by the legs between the support and the vibrating part. The intersection of the mid-plane and the plane of symmetry orthogonal to the wafer forms the central axis of the vibrating part.

[0030] The vibrating part comprises two extensions each intended to vibrate in flexural motion, the two extensions extending symmetrically from the foot on either side of a plane of symmetry perpendicular to the wafer.

[0031] According to several features of the invention, each extension has a longitudinal groove passing through the vibration part perpendicular to the central plane from the plane of symmetry perpendicular to the wafer towards but not reaching the distal end of the extension, so that each extension is serpentine in shape.

[0032] The grooves of each of the two extensions are symmetrical with respect to the second plane of symmetry perpendicular to the wafer and intersect at the second plane of symmetry perpendicular to the wafer, so that the vibration part comprises two primary segments each connecting the foot to the distal end of one of the extensions, and two secondary segments interconnected by their proximal ends in the plane of symmetry perpendicular to the wafer and each extending to the distal end of one of the extensions to connect to one of the primary segments at its distal end.

[0033] Due to this configuration of the vibrating section, when the vibration mode of the vibrating section includes only motion parallel to the central plane and is symmetrical with respect to the plane of symmetry perpendicular to the wafer, the two primary segments have, at each moment during vibration, instantaneous velocity components parallel to the central axis, and the directions of the instantaneous velocity components of the two primary segments are opposite to the instantaneous velocity components of the two secondary segments parallel to the central axis.

[0034] These opposite velocity directions allow their associated momentum components to at least partially compensate each other, thereby reducing the motion transmitted to the foot by the vibrating part, resulting in a resonator with low vibration energy losses and a high quality factor.

[0035] Advantageously, the vibrating part may have a mass distribution such that vibration modes that involve only motion parallel to the central plane and are symmetrical with respect to the plane of symmetry perpendicular to the wafer do not cause motion of the feet parallel to the central axis.

[0036] In other words, the compensation for the momentum component of the vibrating part parallel to the central axis of the resonator can be exact or nearly exact, in which case the vibration energy loss through the legs of the resonator is zero or nearly zero, and the quality factor can be very high.

[0037] In a preferred embodiment of the present invention, the material of the wafer may be single crystal, trigonal crystal class, and piezoelectric. In this case, the central axis of the vibrating part is parallel to the axis Xc of the material, and the two primary segments and two secondary segments of the vibrating part are parallel to the axis Yc of the material. In other words, one of the two extensions of the vibrating part may be parallel to the crystal axis Yc+, and the other of the two extensions of the vibrating part may be parallel to the crystal axis Yc-. In such an embodiment, the two extensions of the vibrating part may form an angle equal to 60° between them.

[0038] In particular, the wafer may be made of α-quartz (α-SiO2) or any other crystal of the trigonal system of symmetry class 32, such as gallium orthophosphate (GaPO4), germanium oxide (GeO2), or gallium arsenate (GaAsO4), or crystals of the LGX family, where crystals of the LGX family include langasite (LGS or La3Ga5SiO2). 14 ), langatate (LGT or La3Ga5,5TaO,5O 14), or langanite (LGN or La3Ga5,5NbO,5O 14 )

[0039] Alternatively, the two extensions of the vibrating section may form an angle equal to 180° between them. When the material of the wafer is monocrystalline, trigonal, and piezoelectric, the resonator of the present invention further comprises excitation means and detection means. The excitation means are adapted to generate a bending deformation of the vibrating section, and comprise first and second electrodes electrically insulated from each other. The first electrode comprises a strip of conductive material on each side of the wafer and for each primary or secondary segment, the strip of conductive material being arranged longitudinally at the center of the width of the segment. The second electrode comprises two strips on each side of the wafer and for each primary or secondary segment, the two strips being arranged on either side of the strip of the first electrode. The detection means are adapted to measure the amplitude of the bending deformation of the vibrating section generated by the excitation means during use of the resonator, and comprise circuits for detecting currents appearing in the first and second electrodes.

[0040] In general, according to the invention, each extension of the vibrating part may comprise, at its distal end, an extension parallel to the mid-plane relative to the outer longitudinal edges of the primary and secondary segments of this extension. Such an extension provides an additional degree of freedom to provide compensation for the momentum component of the vibrating part parallel to the central axis. This therefore facilitates the design of resonators according to the invention with a high quality factor.

[0041] Also generally, in the present invention, the resonator may be in the form of a segment and may further comprise an additional portion of the wafer, called a stem, extending from the interconnected proximal ends of the secondary segments in a direction parallel to the central axis and away from the feet, and this stem may also contribute to obtaining compensation for the momentum component of the vibrating part parallel to the central axis.

[0042] The resonator can include two vibrating parts formed in the same wafer, each with its own stem, and the two vibrating parts can be interconnected by their stems and oriented opposite each other so that the central axes of the two vibrating parts overlap.

[0043] According to another possibility, the resonator may comprise two vibrating parts formed in the same wafer, interconnected by their respective legs and oriented opposite to each other so that their respective central axes overlap.

[0044] A second aspect of the invention proposes a force sensor comprising a resonator according to the invention, with two vibrating parts interconnected by their respective stems, such a sensor being applied between the respective legs of the two vibrating parts and adapted to measure tension parallel to the central axis of said two vibrating parts.

[0045] Finally, a third aspect of the invention relates to a gyrometer comprising at least one resonator according to the first aspect of the invention, the operation of which uses the coupling created by Coriolis acceleration between a vibration mode having a motion parallel to said mid-plane and a vibration mode having a motion perpendicular to this mid-plane.

[0046] Preferably, the gyrometer may include a resonator having two vibrating parts oriented in opposite directions and interconnected by their respective legs. This configuration of the gyrometer allows for two separate uses, each with a single rotational response axis, depending on the pilot mode selected. According to a first possible selection of the pilot mode, the two vibrating parts vibrate synchronously in opposite directions. Coriolis accelerations generated by rotation of the two vibrating parts about an axis parallel to their common central axis excite dynamically balanced out-of-plane vibration modes.

[0047] According to another possible option, this time in pilot mode, the two vibrating parts vibrate in phase, and the Coriolis acceleration generated by rotation about an axis perpendicular to their common central axis and parallel to the central plane excites another out-of-plane vibration mode that is dynamically balanced. In a preferred embodiment of a gyrometer having such two vibrating parts, the two vibrating parts are connected by their respective legs while being oriented opposite to each other. The wafer may be made of quartz crystal, each of the two vibrating parts being oriented at 60° to each other and having an extension parallel to the crystal axis Yc. This configuration allows for optimal piezoelectric coupling to the vibration mode to be excited or detected, and also allows for symmetrical manufacture of the resonator when it is manufactured by chemical etching.

[0048] The features and advantages of the present invention will become more apparent from the following detailed description of several non-limiting embodiments, taken in conjunction with the accompanying drawings.

[0049] BRIEF DESCRIPTION OF THE DRAWINGS [Figure 1a] has already been discussed, but it recalls the first possible electrode configuration suitable for piezoelectric coupling, which can be used to excite and detect bending vibrations of the beam in the plane, in the case of a beam material that is piezoelectric and belongs to the trigonal symmetry class 32, such as α-quartz.

[0050] [Figure 1b] corresponds to [Figure 1a] of a second possible electrode configuration, already discussed, that can be used to excite and detect out-of-plane vibrations.

[0051] [Figure 2a], as already discussed, is reminiscent of trigonal symmetry.

[0052] [Figure 2b] shows a resonator in the form of a tuning fork, already discussed, known from the prior art and obtained by chemically etching quartz crystal with a mixture of ammonium fluoride and hydrofluoric acid. The tuning fork in [Figure 2b] suffers from a symmetry breakdown that occurs when the two beams (tines) of the tuning fork are parallel to the Y axis.

[0053] [Figure 3a] shows the momentum associated with a tuning fork with parallel beams, as known from the prior art.

[0054] [Figure 3b] corresponds to [Figure 3a] for a tuning fork with non-parallel beams.

[0055] [Figure 3c] corresponds to Figure 3b for a double-ended tuning fork with non-parallel tines, which allows for overall compensation of the unbalanced momentum within each tuning fork.

[0056] FIG. 4a is a plan view of a first resonator made of a trigonal piezoelectric material according to the present invention.

[0057] [Figure 4b] corresponds to [Figure 4a] and shows the beneficial modes of vibration of the first resonator and the associated momentum deformations.

[0058] [Figure 4c] corresponds to [Figure 4a] and shows electrodes that make it possible to excite and detect useful modes of vibration in the case of a resonator made of a trigonal piezoelectric crystal of symmetry class 32, such as quartz.

[0059] [Fig. 4d] is a cross-sectional view of the first resonator corresponding to [Fig. 4c].

[0060] [Figure 5a] corresponds to [Figure 4a] when two possible refinements of the invention are used.

[0061] [Figure 5b] corresponds to [Figure 5a] and shows the deformation of useful vibration modes.

[0062] FIG. 6a is a plan view of a second resonator according to the present invention made of a piezoelectric material.

[0063] [Figure 6b] corresponds to [Figure 6a] and shows the deformation of the useful vibration modes of the second resonator.

[0064] [Figure 6c] corresponds to [Figure 6a] when a possible refinement of the invention is used.

[0065] [Figure 6d] corresponds to [Figure 6b] for the resonator of [Figure 6c].

[0066] FIG. 7a is a perspective view of a first gyrometer according to the present invention, showing the deformations associated with the pilot mode of this first gyrometer.

[0067] [Figure 7b] corresponds to [Figure 7a], but shows the deformation arising from the pilot mode of [Figure 7a] by rotation about the first axis.

[0068] [Figure 7c] corresponds to [Figure 7b] for the second axis of rotation.

[0069] [Figure 7d] corresponds to [Figure 7b] for the third axis of rotation.

[0070] [Figure 8a] shows the deformation of the second gyrometer according to the invention, produced in the first pilot mode.

[0071] [Figure 8b] corresponds to [Figure 8a] and shows the deformation of the first sensing mode of the second gyrometer produced by rotation about the first axis, starting from the first pilot mode.

[0072] [FIG. 8c] shows another deformation of the second gyrometer generated in the second pilot mode.

[0073] [Figure 8d] corresponds to [Figure 8b] and shows the deformation of the second sensing mode of the second gyrometer produced by rotation about the second axis, starting from the second pilot mode.

[0074] [FIG. 9a] is a perspective view of the second gyrometer, showing the electrodes of the second gyrometer.

[0075] [Fig. 9b] is a first cross-sectional view of a second gyrometer corresponding to [Fig. 9a].

[0076] [Fig. 9c] is a second cross-sectional view of a second gyrometer corresponding to [Fig. 9a].

[0077] FIG. 10a is a plan view of a first force sensor according to the present invention.

[0078] FIG. 10b corresponds to FIG. 10a and shows the deformations associated with useful modes of vibration of the first force sensor.

[0079] FIG. 10c corresponds to FIG. 10a and shows the static deformation of the first force sensor when subjected to axial tension.

[0080] FIG. 11a is a plan view of a second force sensor according to the present invention.

[0081] FIG. 11b corresponds to FIG. 11a and shows the deformations associated with useful modes of vibration of the second force sensor.

[0082] [Figure 11c] corresponds to [Figure 11a] and shows the static deformation of the second force sensor when subjected to axial tension. Detailed Description of the Invention For the sake of clarity, the dimensions of the elements shown in these figures do not correspond to actual dimensions or to actual dimensional ratios. In particular, all represented resonator deformations are enlarged to an exaggerated extent for better visibility. Furthermore, identical reference signs shown in different figures denote elements or dimensions that are identical or have the same function.

[0083] A first resonator according to the present invention will now be described with reference to Figures 4a to 4d. This first resonator comprises a support or fixed part, designated by reference character Pf, a vibrating part, and legs Pd connecting the vibrating part to the fixed part Pf. Preferably, the fixed part Pf, the vibrating part, and the legs Pd are formed simultaneously by chemical etching on a wafer having parallel surfaces so that the materials of the three resonator parts are continuous.

[0084] The wafers used may have a thickness of a few micrometers to a few millimeters when the thickness is measured perpendicular to the plane of the wafer. The vibrating portion of the resonator in [Figures 4a] to [Figure 4d] includes two extensions P1 and P2 extending from the leg Pd and forming a non-zero angle α between them. The two extensions P1 and P2 extend symmetrically on either side of a central axis that coincides with the longitudinal direction of the leg Pd.

[0085] This central axis corresponds to the intersection of a first plane of symmetry, parallel to the plane of the wafer and located at its mid-thickness, and a second plane of symmetry, perpendicular to the plane of the wafer and to which the two extensions P1 and P2 correspond via reflection symmetry. In the remainder of this specification, and by analogy with tuning fork resonators such as those described in U.S. Pat. No. 3,683,213, the two extensions P1 and P2 are also referred to as beams P1 and P2. According to the invention, each beam P1, P2 is provided with a longitudinal groove, designated FL1 and FL2, respectively. These two longitudinal grooves FL1 and FL2 intersect (converge) at the central axis of the resonator.

[0086] In this way, each beam P with subscript i equal to 1 or 2 i Has two blades L iext and L iint In the general part of this specification, the blade L 1ext is called the primary segment of the extension P1, and the blade L 1int is called the secondary segment of the extension P1. 2ext is called the primary segment of the extension P2, and the blade L 2int is called the secondary segment of the extension P2. Therefore, the two blades L 1ext and L 2ext is connected to the foot Pd and extends to the distal end of each of the extensions P1 and P2. 1ext is L 1int connected to L 2ext is L 2intEach extension P1, P2 is therefore serpentine (meander) between the central axis and its distal end.

[0087] Furthermore, Blade L 1int and L 2int These two blades L 1int and L 2int The longitudinal grooves FL1 of the beam P1 and the longitudinal grooves FL2 of the beam P2 are also connected to each other by the proximal ends of the two blades L 1int and L 2int The joints at the proximal ends of the blades L 1ext and L 2ext As shown in Figure 4b, when the resonator vibrates, the distal ends of beams P1 and P2 move symmetrically away from the central axis, causing blade L 1ext and L 2ext have momenta MV1 and MV2, respectively, directed obliquely but symmetrically towards the same side as the leg Pd of the resonator, and the blade L 1int and L 2int The joint (joint, connection) of is parallel to the central axis, and momentum MV 12 It has.

[0088] Therefore, the blade L 1int and L 2int Each of the blades L has a momentum directed obliquely but symmetrically towards the opposite side of the resonator leg Pd. 1ext , L 2ext , L 1int , and L 2int The distribution of mass in the vibrating part between can be made so that the movement of the foot Pd due to these momentum is zero or nearly zero.

[0089] Due to this lack of motion of the legs Pd, the quality factor of the resonator can be high, since the transfer of vibration energy from the vibrating part to the supporting part Pf is zero or very low. The optimized distribution of mass among the four blades of the vibrating part is still symmetrical with respect to the central axis, and the two blades L 1ext and L 2ext Common thickness e ext where the common thickness e ext is, e int Two blades denoted by L 1int and L 2int When such an optimization is applied, the resonator is said to be in equilibrium. The blade thickness e ext and e int is measured parallel to the plane of the wafer.

[0090] According to two improvements of the present invention, which are shown together in Fig. 5a but can be used independently of each other, the vibrating part of the resonator can be supplemented with two inertial masses MI1 and MI2 as a first improvement and a stem Pc as a second improvement. Preferably, the two inertial masses MI1 and MI2 are located at the distal ends of the two beams P1 and P2 and are identical. The two inertial masses MI1 and MI2 can be formed by extending the corresponding beams P1 and P2 at their distal ends, respectively.

[0091] Stem Pc Blade L 1int and L 2int The stem Pc may be formed by an additional blade extending parallel to the central axis from the coupling at the proximal end of the resonator in a direction away from the foot Pd and superimposed on the coupling. Advantageously, the stem Pc is also symmetrical with respect to the central axis. By adding two inertial masses MI1 and MI2 and / or the stem Pc to the vibrating part of the resonator, a balanced state of the resonator with an additional degree of freedom can be obtained.

[0092] [Figure 5b] shows the motion of the inertial masses MI1 and MI2 and the motion of the stem Pc at the same moment during the vibration of the resonator. At this time, the two inertial masses MI1 and MI2 have momentum components along the central axis that are opposite to the momentum component of the stem Pc. These momentum components of the inertial masses MI1 and MI2 and the stem Pc are transferred to the four blades L. 1ext , L 2ext , L 1int and L 2int In combination with the momentum component of the foot Pd, application of the present invention results in a motion of the foot Pd that is zero or substantially zero.

[0093] It should be noted that the equilibrium state of such a resonator is known from the prior art and is naturally obtained for a tuning fork with parallel beams, as shown in Figure 3a, since the two beams P1 and P2 are identical. The momenta of the two beams P1 and P2 are again denoted MV1 and MV2, respectively. Such a resonator according to Figure 3a does not induce any movement of the leg Pd parallel to the central axis X of the resonator during vibration, since the momenta MV1 and MV2 are perpendicular to this central axis.

[0094] Furthermore, in the vibration mode in which the two beams P1 and P2 move synchronously in opposite directions, the momenta MV1 and MV2 of the two beams are compensated for if the two beams P1 and P2 are identical. At this time, the tuning fork resonator is in equilibrium. Therefore, since no vibration energy is transferred from the beams P1 and P2 to the foot Pd, the deformation of this foot at the embedded end of the two beams P1 and P2 is ignored. This deformation of this foot results in bending moments Mf1 and Mf2 and shear forces T1 and T2, especially when the gap separating the two beams P1 and P2 is narrow.

[0095] However, as mentioned above, such a resonator with parallel, symmetric beams cannot be fabricated simply by chemically etching a wafer of trigonal Class 32 crystalline material, because etching facets would appear and would destroy the symmetry of the shape between the two beams P1 and P2. To obtain two beams with symmetric shapes, a resonator can be fabricated with two beams P1 and P2 parallel to the axes Yc+ and Yc- of the trigonal Class 32 crystalline material and with the central axis of the resonator parallel to the crystal axis Xc.

[0096] However, the two beams P1 and P2 of the tuning fork are then no longer parallel, and the balanced state of the resonator can no longer be achieved. By using the longitudinal grooves FL1 and FL2 according to the invention in the resonators of Figures 4a to 4d, the balanced state of the resonator can again be achieved, even though the beams P1 and P2 are no longer parallel to each other.

[0097] However, we have found that it is possible to achieve the balanced state of the resonator of Figure 3b with non-parallel beams by creating a vibrating section symmetrical with respect to the YZ plane. Thus, the vibrating section includes four beams P1, P2, P3, and P4, which may have a symmetrical shape resulting from chemical etching of a trigonal Class 32 crystalline material. The leg Pd of the resonator is then located where the four beams intersect.

[0098] In this case, the resonator is balanced for a vibration mode in which the two tuning forks vibrate in sync (in phase). However, as shown in Figure 3c, the resulting double-ended tuning fork resonator configuration is bulkier and may not be well suited for applications requiring significant miniaturization. In such applications, the resonators of Figures 4a-4d or 5a-5b may be preferable.

[0099] In the case of the resonators of Figures 4a-4d or 5a-5b, the angle α between the two beams P1 and P2 is equal to 60°. Thus, by orienting the beams P1 and P2 longitudinally parallel to the crystal axes Yc+ and Yc-, the central axis parallel to the crystal axis Xc, and the plane of the wafer perpendicular to the axis Z, a symmetrical implementation can be obtained by chemically etching a wafer with parallel faces made of a crystalline material of the trigonal class 32.

[0100] For example, the wafer material can be a single crystal α-quartz, which is piezoelectric. In this case, the resonator can be provided with two electrodes, as shown in Figures 4c and 4d. In a known manner, these electrodes can be used both to excite a symmetric vibration mode and to detect the vibration amplitude in this same mode. The reference symbols in these two figures have the following meanings:

[0101] Regarding the first electrode that can be connected to ground: The segment of the first electrode supported by the support Pf of the PC1 resonator el 1-PC1 Segment of the first electrode supported by the leg Pd of the resonator Blade L on the first of the two sides of the el1 wafer 1ext along the outer edge of the blade L 1ext A segment of the first electrode supported by Blade L on the first side of the el3 wafer 1ext along the inner edge of the blade L 1ext A segment of the first electrode supported by Blade L on the first side of the el4 wafer 1int along the inner edge of the blade L 1int A segment of the first electrode supported by Blade L on the first side of the el6 wafer 1int along the outer edge of the blade L 1int A segment of the first electrode supported by el7 and el9 Blade L 2int, they correspond to el6 and el4, respectively.

[0102] el 10 and el 12 Blade L 2ext , they correspond to el3 and el1, respectively.

[0103] el 1-6 an electrical connection segment between segments el1 and el6 at the distal end of beam P1 on the first side of the wafer; el 3-4 an electrical connection segment between segments el3 and el4 at the distal end of beam P1 on the first side of the wafer; el 7-9 an electrical connection segment between segments el7 and el9 at the distal end of beam P2 on the first side of the wafer; el 10-12 At the distal end of beam P2 and on the first surface of the wafer, segment el 10 and el 12 Electrical connection segments between The first electrode segments el6 and el7 are interconnected at the central axis, as are segments el4 and el9, and segments el3 and el 10 The same is true.

[0104] For the second electrode, which can be connected to a source of alternating voltage V: PC2 and el 2-PC2 are PC1 and el, respectively. 1-PC1 Corresponding to, Also, in the case of the second electrode, Blade L on the first side of the el2 wafer 1ext A second electrode segment supported at its center by el5, el8, and el 11 are the blade L 1int , L 2int , and L 2ext It supports el2 for the following.

[0105] el 2-5an electrical connection segment between segments el2 and el5 at the distal end of beam P1 on the first side of the wafer; The second electrode segments el5 and el8 are interconnected at the central axis, and segments el2 and el 11 are interconnected at a central axis.

[0106] For the second side of the wafer, the electrode segments el, where the integer subscript n varies from 1 to 12 10n is the segment el n The electrode segments el 10n includes electrical connection segments similar to those described for the first side of the wafer. Finally, the same electrode segments of two electrodes located on each of the two sides of the wafer are They are electrically interconnected by electrical connections carried by the resonator or by external electrical connections.

[0107] Each electrode segment may consist of a strip of conductive material, such as gold (Au), deposited using thin film deposition techniques, and have a width equal to 200 μm (micrometers). According to the provided list, three parallel strips are arranged on each blade face, which means a total of 12 conductive strips per face of the wafer, namely el1 to el2 on the first face. 12 , and el on the second surface 101 ~el 112 This means that the

[0108] As already explained with reference to [Fig. 1a], the three conductive strips on each blade surface allow for effective excitation and detection of bending vibrations of the blade parallel to the plane Xc-Yc when this blade extends longitudinally along the crystal axis Yc+ or Yc-. To increase the efficiency of the piezoelectric coupling, the strips of the first electrode are relatively thin, with a strip width equal to the length of the blade L. 1ext , L 2ext , L 1int and L 2int Thickness e ext or e intIn the case of strips of the second electrode, the width of the strips of the second electrode may be 2 to 5 times the width of the strips of the first electrode.

[0109] The electrode arrangement for piezoelectric excitation and detection is suitable for the bending mode of vibration, where two beams P1 and P2 move in synchronous opposite directions, as shown in Figure 4b. However, other electrode configurations are alternatively possible, for example, by depositing strips of conductive material on the sides of the blade perpendicular to the plane of the wafer. In this case, strips el1 and el 101 But Blade L 1ext The other strips are replaced by a single strip on the side of the 1int , L 2int and L 2ext The same is true for pairs of strips of the first electrode, each supported separately by a piezoelectric element. As a result, each blade side supports two strips. One strip is adjacent to the edge of the blade's side, and the other strip is adjacent to the edge opposite the edge to which the first strip is adjacent. One of the two strips belongs to the first electrode, and the other belongs to the second electrode. This alternative electrode configuration is more efficient for piezoelectric coupling than those in Figures 4c and 4d, but at the cost of greater complexity in its manufacture.

[0110] The resonator can thus be associated with an electronic oscillator loop connected to the input of the segment PC1 of the first electrode on the resonator's support Pf. The resonator can also be associated with an electronic oscillator loop connected to the output of the segment PC2 of the second electrode on the resonator's support Pf. A vibration mode in which the two beams P1 and P2 operate in synchronous opposition is thus excited by an AC voltage V applied by the electronic oscillator loop between the two electrodes. The vibration amplitude of the resonator for this same mode is detected by the current generated in the two electrodes by the vibration of the resonator. For this purpose, a current detection circuit can be used in the electronic oscillator loop, which advantageously has a high input impedance.

[0111] Here, according to the present invention, we provide several criteria that allow balancing of the resonator according to [Fig. 4a] to [Fig. 4d], i.e., without inertial masses MI1, MI2 or stem Pc. The resonator frequency F for the bending vibration mode in which the two beams P1 and P2 operate synchronously and symmetrically in opposite directions can be approximated using the following equation (Equation 1):

[0112]

number

[0113] Multiple meanings have already been provided for the following: e int : Blade L, measured parallel to the wafer surface and expressed in meters 1int and L 2int Common thickness of e ext : Blade L, measured parallel to the wafer surface and expressed in meters 1ext and L 2ext Common thickness of L int : blade L, expressed in meters 1int and L 2int Common length of L ext : blade L, expressed in meters 1ext and L 2ext Common length of F l : the common width of the longitudinal grooves FL1 and FL2 of the extensions P1 and P2, measured parallel to the plane of the wafer and expressed in meters E: Newtons per square meter (N / m 2 ) is the Young's modulus of the wafer material. ρ: kilograms per cubic meter (kg / m 3 ) the density of the wafer material To allow compensation at the foot Pd for the momentum component parallel to the axis Xc, the dimension e int , e ext , L int and L extIt is also necessary to satisfy the following condition (Equation 2):

[0114]

number

[0115] However, this condition is not satisfied for blade L 1ext , L 2ext Each length and width L ext / e ext But Blade L 1int , L 2int Each length and width L int / e int Equation 2 can also be written in the following form (Equation 3):

[0116]

number

[0117] The certainty of 1-k is the quotient e ext / e int We can give a first bound for this quotient, which is greater than 0.4.

[0118] Furthermore, by construction, the following equation is given by the angle α separating the two beams P1 and P2 from the blade L ext and L int Concatenate the lengths of (Equation 4):

[0119]

number

[0120] These last three equations are written in five unknowns, e ext , e int , L ext , L int and F l which allows a person skilled in the art to select the dimensions of the resonator according to the intended application and technical constraints, in particular according to the space available for the resonator in each application.

[0121] To ensure the symmetry of the resonator obtained by chemical etching as already described using a crystal wafer of trigonal symmetry class 32, for example, piezoelectric α-quartz, each of the beams P1 and P2 is oriented parallel to the crystal axis Yc, with one of the beams P1 and P2 parallel to Yc+ and the other parallel to Yc-, for an angle α of 60° between them. 1int and L 2int The aspect ratio P is common to all int =L int / e int , and Blade L 1ext and L 2ext Different aspect ratios are common in P ext =L ext / e ext , and the quotient e between 1 and 5 int / e ext For example, we can calculate the dimensions of a balanced resonator with L int ~2.5mm (millimeters), e int ~0.24mm, L ext ~3.3mm, e ext ~0.15mm, F l 0.27 mm results in a frequency F of the resonator equal to 32 kH (kilohertz).

[0122] This same value at a frequency F of 32 kHz is L int ~4.95mm, e int ~1.5mm, L ext ~8.9mm, e ext ~1.7 mm, and F l .about.0.7 mm can also be obtained, which shows the range of dimensional possibilities for obtaining a balanced resonator when using the present invention.

[0123] For resonators subject to bending vibration, the intrinsic quality factor of the resonator is limited by the thermoelastic losses generated by the heat exchange between the fibers of each blade, which are compressed and stretched during vibration, as theorized by C. Zener in his paper "Internal friction in solids" (Physical Review 52, ​​August 1937, pp. 230-235). For quartz crystals and simple beams with bending vibrations at frequencies between a few kilohertz and a few hundred kilohertz, the thermoelastic quality factor is proportional to the frequency F of the resonator multiplied by the square of the vibration thickness, and Q thermoelastic (Crystal)∝Fe 2 For silicon, and for the same frequency interval as for quartz, this thermoelastic coefficient is proportional to the frequency F of the resonator divided by the square of the vibration thickness e, and Q thermoelastic (silicon) ∝ F / e 2 The thermoelastic quality factor leads to very different dimensional determinations for the resonators between these two crystals.

[0124] Therefore, for a quartz crystal, and for a resonator with desired frequency stability performance, the thickness e int and e ext sizing corresponding to significant values ​​of is preferred, whereas for silicon it is not preferred.

[0125] Compared to the resonator configuration according to [Fig. 4a], the addition of the stem Pc modifies the momentum generated by the vibration along the axis Xc, and the momentum component of the stem Pc is transferred to the blade L. 1int and L 2int This adds to the momentum component of the resonator. Therefore, it is possible to increase the possibility of determining the dimensions that will bring the resonator into equilibrium. In particular, the addition of the stem Pc increases the momentum of the blade L compared to the configuration without the stem [Fig. 4a]. 1ext and L 2ext Thickness e ext This allows for an increase in

[0126] Also, compared to the resonator configuration according to [Figure 4a], the distribution of momentum between all parts of the vibrating section can be modified by adding inertial masses MI1 and MI2 to the distal ends of the beams P1 and P2. In particular, the addition of inertial masses MI1 and MI2 improves the momentum distribution between the blades L 1int and L 2int Thickness e int and their length L int This allows for an increase for an equal value of

[0127] The resonator of [Fig. 6a] or [Fig. 6c] corresponds to the resonator of [Fig. 5a], but the angle α is equal to 180° instead of 60°, and for [Fig. 6a] it has no stem, and for [Fig. 6c] it has a stem Pc. Then, the blade L ext and L int The lengths of the resonators are equal, and the condition for the equilibrium state of the resonator of equation 3, which was already provided for a resonator without stem Pc and without inertial masses MI1 and MI2, can no longer be satisfied. To compensate for the momentum, the inertial masses MI1 and MI2 are required when the angle α is equal to 180°.

[0128] The modes of vibration shown in [Fig. 6b] when the resonator has no stem, or in [Fig. 6d] when the resonator includes a stem Pc, are mainly those of the two blades L 1int and L 2int The above two blades L 1int and L 2int The blade is a combination of two blades L 1int and L 2int and has a total length equal to the sum of the lengths of int It has.

[0129] The frequency F of the resonator for this mode of vibration can be approximated by the following equation (Equation 5):

[0130]

number

[0131] where: L int : the total blade length measured between the two inertial masses MI1 and MI2 and expressed in metres e int : width of the blade opposite the foot Pd, measured parallel to the wafer surface and expressed in meters L c : length of stem Pc measured parallel to the plane of the wafer and expressed in meters e c : width of stem Pc measured parallel to the plane of the wafer and expressed in meters E: Newtons per square meter (N / m 2 ) is the Young's modulus of the wafer material. ρ: kilograms per cubic meter (kg / m 3 ) the density of the wafer material To be able to compensate for the momentum along the axis Xc, the dimension e int , e ext , L int , e Mi , L Mi , L c and e c However, it is also necessary to satisfy the following double inequality (equation 6):

[0132]

number

[0133] It has the following additional meanings:

[0134] e ext : width of the blade connected to the foot Pd measured parallel to the plane of the wafer and expressed in meters e Mi : common width of inertial masses MI1 and MI2 measured parallel to the blade and expressed in metres L Mi : the common length of the inertial masses MI1 and MI2 measured parallel to the axis Xc and expressed in metres J: Inertial momentum per unit surface area of ​​inertial masses MI1 and MI2 (Equation 7)

[0135]

number

[0136] The double inequality of Equation 6 allows the dimensions of the resonators of Figures 6a-6d to be determined, so that they are balanced based on specific values ​​that are initially selected according to the desired characteristics of these resonators.

[0137] Using the criteria provided above, the sizing for each of the resonators shown above can be continued using numerical simulations, such as finite element calculations, to achieve more accurate balancing of these resonators.

[0138] Using the resonators described above, gyrometers with one or more sensitive axes can be formed. The sensitive axis of a gyrometer is the axis of rotation around which the gyrometer measures the rotation rate. To obtain a gyrometer with three sensitive axes, which allows measuring rotation rate components along axes X, Y, and Z, respectively, the angle α of the resonator must be neither 0° nor 180°.

[0139] Such a resonator is preferred in which the angle α is equal to 60°. During rotation of the resonator, the Coriolis acceleration results in an additional displacement of each blade of the resonator that is perpendicular to the displacement of this blade in the pilot mode.

[0140] [Fig. 7a] shows the beams P1 and P2 for a resonator according to the invention with α equal to 60°. 2、 The mode of vibration excited by the electrodes, i.e., the pilot mode, is a mode in which two beams P1 and P2 move synchronously in opposite directions parallel to the wafer surface, like a tuning fork.

[0141] MV1, MV 2, and MV c shows the momentum of beams P1 and P2 and stem Pc. [Figure 7b] shows the rotational velocity Ω y Γ generated by rotation around the X axis with C The corresponding Coriolis acceleration, denoted by [Figure 7c], is the rotational velocity Ω y Figure 7d shows the Coriolis acceleration caused by rotation around the y-axis with a rotational velocity Ω z 1 shows the Coriolis acceleration caused by rotation around the z-axis with

[0142] These Coriolis accelerations are normal to the wafer due to rotation about axes X and Y, and the symbol of a dot surrounded by a circle represents the Coriolis acceleration directed towards the reader, while the symbol of a cross surrounded by a circle represents the Coriolis acceleration directed in the direction of the reader's line of sight.

[0143] However, since the inertial forces resulting from these Coriolis accelerations are not compensated for in the legs Pd, it is preferable to provide additional means to limit the loss of vibrational energy that occurs through the legs Pd of the resonator.

[0144] For example, a decoupling structure such as that described in U.S. Pat. No. 6,414,416 filed by the applicant can be used in a gyrometer with a single sensitive axis, which is axis X (see FIG. 7b), because this decoupling structure is effective in reducing or avoiding the transmission of torsional moments to the mounting part of the resonator via its legs Pd.

[0145] For a gyrometer with only one sensitive axis, the axis Y (see Figure 7c), the rotation rate Ω YThe mode of vibration coupled by to the pilot mode of [Fig. 7a] is one in which the two beams P1 and P2 undergo out-of-plane bending in phase with each other and the stem Pc undergoes out-of-plane bending out-of-phase with respect to the beams P1 and P2. However, the resulting forces are not compensated in the leg Pd of the resonator, and residual momentum is transferred to the mounting part of the resonator via that leg Pd. The forces generated during rotation about axis Z (see [Fig. 7d]) from the pilot mode of [Fig. 7a], parallel to the wafer, are not compensated.

[0146] To achieve compensation for the force and momentum transmitted to the resonator's mounting part Pf, a new gyrometer is proposed according to the present invention, which comprises two vibrating parts, each similar to the vibrating part in FIG. 7a, with a common foot Pd and facing away from each other. The two vibrating parts are fabricated from the same wafer, so their material is continuous across the foot Pd. Such a gyrometer, shown in FIGS. 8a-8d, is useful for measuring rotation about axis X or axis Y.

[0147] Similar to the pilot mode, two vibration excitation modes are possible. Each of the two vibration excitation modes maintains the balance provided by the dual-resonator structure. Anti-synchronous mode (opposite phase mode): As shown in [Figure 8a], the two beams P1 and P2 of one vibrating section move in opposite directions and in synchronous with the beams P3 and P4 of the other vibrating section, moving away from and towards each other. Synchronous mode (in-phase mode): As shown in [Figure 8c], the two beams P1 and P2 of one vibrating section move in synchronous (in phase) with the beams P3 and P4 of the other vibrating section, moving away from and towards each other. In these two figures, each MV symbol indicates the momentum of the beam or superimposed stem.

[0148] [Figure 8b] shows the Coriolis acceleration Γ for the excitation mode of vibration in [Figure 8a] used as the pilot mode. C[Figure 8d] shows the compensation of the inertial force resulting from the Coriolis acceleration Γ for the excitation mode of vibration of [Figure 8c] used as the pilot mode. C One of these two excitation modes is selected as the pilot mode via the configuration of electrodes on the two vibrating parts.

[0149] For example, for a piezoelectric quartz crystal or any other piezoelectric crystal of the same symmetry class, a gyrometer can be constructed from two vibrating sections positioned head-to-tail. Each vibrating section has two beams, with these beams parallel to the crystal axes Yc+ and Yc-, forming a 60° angle between the two sections. Figures 9a-9c show a set of strips of conductive material placed on the faces of all segments of the two vibrating sections.

[0150] The two vibrating parts are respectively designated by letters A and B. The cross-sectional view of vibrating part A corresponds to that of [Fig. 9b], and the cross-sectional view of vibrating part B corresponds to that of [Fig. 9c].

[0151] For a gyrometer whose sensitive axis is axis X parallel to the crystal axis Xc, the pilot mode is the two resonators vibrating synchronously in opposite directions, as shown in Figure 8a. To limit the capacitive coupling between the pilot mode and the sensing mode, the teachings of commonly filed U.S. Patent Application No. 2012 / 279303 can then be applied.

[0152] According to these teachings, strip el 3-A , el 103-A , el 4-A , el 104-A , el 9-A , el 109-A , el 10-A , el 110-A , el 3-B , el 103-B , el 4-B , el 104-B , el 9-B , el 110-B , and el 110-Bare used to excite the pilot modes by electrically connecting them to a source of AC voltage V. To detect the amplitude of the pilot mode, 2-A , el 102-A , el 5-A , el 105-A , el 8-A , el 108-A , el 11-A , and el 111-A is used.

[0153] In this way, strip el 1-A , el 101-A , el 6-A , el 106-A , el 7-A , el 107-A , el 12-A , el 112-A , el 1-B , el 101-B , el 6-B , el 106-B , el 7-B , el 107-B , el 12-B , and el 112-B can be used to detect the motion generated by rotation around the X axis, while the strip el 1-A , el 6-A , el 7-A , el 12-A , el 1-B , el 6-B , el 7-B , and el 12-B is connected to the input terminal of the differential amplifier, which is part of the current detector, and on the other hand, the strip el 101-A , el 106-A , el 107-A , el 112-A , el 101-B , el 106-B , el 107-B , and el 112-B is connected to the input terminal of a differential amplifier that is part of the current detector.

[0154] The sensitive axis is perpendicular to the crystal axis Xc and is perpendicular to the axis Xc, Y C+ , and Y C-The pilot mode of the gyrometer, whose Y axis is in the common plane of the gyrometer, is due to the two resonators whose vibrations are synchronized as shown in Figure 8c. 1-A , el 101-A , el 6-A , el 106-A , el 7-A , el 107-A , el 12-A , el 112-A , el 1-B , el 101-B , el 6-B , el 106-B , el 7-B , el 107-B , el 12-B , and el 112-B It is possible to excite this pilot mode by connecting them to a source of alternating voltage V. Also, strip el 2-A , el 102-A , el 5-A , el 105-A , el 8-A , el 108-A , el 11-A , el 111-A , el 2-B , el 102-B , el 5-B , el 105-B , el 8-B , el 108-B , el 11-B , and el 111-B is used to detect the amplitude of this pilot mode.

[0155] In this case, strip el 3-A , el 103-A , el 4-A , el 104-A , el 9-A , el 109-A , el 10-A , el 110-A , el 3-B , el 103-B , el 4-B , el 104-B , el 9-B , el 109-B , el 10-B , and el 110-Bcan be used to detect the motion generated by rotation around the Y axis, while the strip el 3-A , el 4-A , el 9-A , el 10-A , el 103-B , el 104-B , el 10-B , and el 110-B is connected to the input terminal of the differential amplifier, which is part of the current detector, and on the other hand, the strip el 103-A , el 104-A , el 109-A , el 110-A , el 3-B , el 4-B , el 9-B , and el 10-B is connected to the input terminal of a differential amplifier that is part of the current detector.

[0156] Another application of the resonator according to the invention is as a force sensor. As shown in FIG. 10a, the force sensor is based on two identical vibrating sections, fabricated on the same wafer and facing oppositely, but joined by their stems Pc. Each of the two vibrating sections is sized to be individually balanced. The beams P1 and P2 of one of the two vibrating sections form an angle of 60° between them, and the beams P3 and P4 of the other of the two vibrating sections form an angle of 60° between them.

[0157] As shown in Figure 10b, for a vibration mode in which the two vibrating parts vibrate synchronously in opposite directions, the coupling of the two vibrating parts results in a dual resonator in which the two ends formed by the legs of the individual vibrating parts have no or almost no residual motion. When this sensor is subjected to axial tension, the static deformation applied to the dual resonator modifies its bending inertia. Figure 10c shows the static deformation under axial tension T.

[0158] If such a force sensor is made of quartz, two configurations are possible, corresponding either to an angle α equal to 60° as shown in Figures 10a-10c, or to an angle α equal to 180° as shown in Figures 11a-11c.

[0159] Thus, Figure 11a shows a configuration with two vibrating sections. In one of the two sections, beams P1 and P2 form a 180° angle between them, while in the other, beams P3 and P4 form a 180° angle between them. Figure 11b shows the instantaneous deformation of the dual-resonator structure of Figure 11a for a given vibration mode in which the two vibrating sections vibrate in phase. Figure 11c shows the static deformation of the same force sensor when subjected to an axial attractive force T.

[0160] For an angle α equal to 180°, the variation of the relative frequency F of the considered mode of vibration caused by an axial tension T is proportional to (equation 8):

[0161]

number

[0162] Using Equation 8, one skilled in the art can determine the dimensions of the force sensor depending on the application and the measurement sensitivity appropriate for the application.

[0163] It will be appreciated that the present invention may be reproduced by modifying secondary aspects of the embodiments detailed above while retaining at least some of the aforementioned advantages. In particular, the material of the wafer does not necessarily have to be a piezoelectric single crystal material. For example, the wafer may be made of single crystal or polycrystalline silicon, or the wafer may be a piezoelectric ceramic, or a combination of metal and piezoelectric ceramic.

[0164] The means of vibration excitation and detection must be adapted to each material. For example, excitation can be achieved using electrostatic forces, magnetic forces, or by implementing the photothermal effect, etc. Detection can also be achieved by measuring the variation in capacitance of a capacitor formed between the moving part of the resonator and the stationary part, or by using the piezoresistive effect, or by measuring using optical interferometry, etc. Finally, all the values ​​mentioned above are provided for illustrative purposes only and may be modified depending on the application considered. [Brief explanation of the drawings]

[0165] [Figure 1a] As already discussed, in the case of beam materials that are piezoelectric and belong to the trigonal symmetry class 32, such as α-quartz, we recall a first possible electrode configuration suitable for piezoelectric coupling, which can be used to excite and detect bending vibrations of the beam in the plane. [Figure 1b] Although already discussed, this corresponds to Figure 1a of a second possible electrode configuration that can be used for excitation and detection of out-of-plane vibrations. [Figure 2a] As already discussed, this is reminiscent of trigonal symmetry. [Figure 2b] As already discussed, the figure 2b shows a resonator in the form of a tuning fork known from the prior art and obtained by chemically etching quartz crystal with a mixture of ammonium fluoride and hydrofluoric acid. The tuning fork in figure 2b has a breaking of symmetry that occurs when the two beams (tines) of the tuning fork are parallel to the Y axis. [Figure 3a] 1 shows the momentum associated with a tuning fork with parallel beams, as known from the prior art. [Figure 3b] Corresponds to Figure 3a for a tuning fork with non-parallel beams. [Figure 3c] This corresponds to Figure 3b of a double-ended tuning fork with non-parallel tines, which allows for overall compensation of the unbalanced momentum within each tuning fork. [Figure 4a]1 is a plan view of a first resonator made of a trigonal piezoelectric material according to the present invention; [Figure 4b] 4a and shows the beneficial modes of vibration of the first resonator and the associated momentum deformations. [Figure 4c] Corresponding to FIG. 4a, electrodes are shown which make it possible to excite and detect useful modes of vibration in the case of a resonator made of a trigonal piezoelectric crystal of symmetry class 32, such as quartz. [Figure 4d] FIG. 4b is a cross-sectional view of the first resonator corresponding to FIG. 4c; [Figure 5a] This corresponds to FIG. 4a when two possible refinements of the invention are used. [Figure 5b] This corresponds to Figure 5a and shows the deformation of useful vibration modes. [Figure 6a] 1 is a plan view of a second resonator according to the invention made of piezoelectric material; [Figure 6b] 6a and shows the deformation of the useful vibration modes of the second resonator. [Figure 6c] This corresponds to FIG. 6a when a possible refinement of the invention is used. [Figure 6d] This corresponds to Figure 6b for the resonator of Figure 6c. [Figure 7a] 1 is a perspective view of a first gyrometer according to the present invention, showing the variants associated with the pilot mode of the first gyrometer; [Figure 7b] 7a, but showing the deformation resulting from the pilot mode of FIG. 7a by rotation about a first axis. [Figure 7c] Corresponds to FIG. 7b for the second axis of rotation. [Figure 7d] Corresponds to FIG. 7b for the third axis of rotation. [Figure 8a] 10 shows the deformation of a second gyrometer according to the invention, produced in a first pilot mode. [Figure 8b] Corresponding to FIG. 8a, starting from the first pilot mode, the deformation of the first sensing mode of the second gyrometer produced by rotation about the first axis is shown. [Figure 8c] 10 shows another variation of the second gyrometer generated in the second pilot mode. [Figure 8d] Corresponding to FIG. 8b, starting from the second pilot mode, the deformation of the second sensing mode of the second gyrometer produced by rotation about the second axis is shown. [Figure 9a] FIG. 1 is a perspective view of a second gyrometer showing the electrodes of the second gyrometer. [Figure 9b] FIG. 9b is a first cross-sectional view of a second gyrometer corresponding to FIG. 9a. [Figure 9c] FIG. 9b is a second cross-sectional view of the second gyrometer corresponding to FIG. 9a. [Figure 10a] FIG. 1 is a plan view of a first force sensor according to the present invention; [Figure 10b] 10a and shows the deformations associated with useful modes of vibration of the first force sensor. [Figure 10c] 10a and corresponds to FIG. 10b, which shows the static deformation of the first force sensor when subjected to axial tension. [Figure 11a] FIG. 2 is a plan view of a second force sensor according to the present invention. [Figure 11b] 11a and shows the deformations associated with useful modes of vibration of the second force sensor. [Figure 11c] 11a and corresponds to FIG. 11b, showing the static deformation of the second force sensor when subjected to axial tension.

Claims

1. a portion of the wafer having two flat, parallel, opposing faces, which is intended to vibrate in flexure during use of the resonator, said portion of the wafer being called the vibrating portion; a support (Pf) located outside the vibrating part and connected to it by intermediate segments of the wafer called feet (Pd), the feet are integral with the vibrating part and form a rigid connection between the support part and the vibrating part; the vibration part has a first plane of symmetry, called the mid-plane (M), parallel to both sides of the wafer and equidistant from the faces of the two wafers, and a second plane of symmetry, called the mid-plane (P), perpendicular to the wafers and passing longitudinally through the connection formed by the legs between the support (Pf) and the vibration part; a common portion of the central plane (M) and a plane of symmetry (P) perpendicular to the wafer constitutes a central axis of the vibration part; The vibrating part has two extension parts (P １ , P ２ ) wherein the two extensions extend symmetrically from the foot (Pd) on either side of a plane of symmetry (P) perpendicular to the wafer, Each extension part (P １ , P ２ ) is a longitudinal groove (FL １ , F.L. ２ ) wherein the longitudinal grooves penetrate the vibration part in a direction perpendicular to the mid-plane (M) and extend from a plane of symmetry (P) perpendicular to the wafer towards the distal end of the extension, but do not reach said distal end, so that each extension has a serpentine shape; The two extension parts (P １ , P ２ ) each groove (FL １ , F.L. ２ ) are symmetrical with respect to a plane of symmetry (P) perpendicular to the wafer, and intersect at the plane of symmetry perpendicular to the wafer, so that the vibration part is divided into two primary segments (L １ｅｘｔ , L ２ｅｘｔ ) and two secondary segments (L １ｉｎｔ , L ２ｉｎｔ ), and the two primary segments (L １ｅｘｔ , L ２ｅｘｔ ) each connects the foot (Pd) to the distal end of one of the extensions and the two secondary segments (L １ｉｎｔ , L ２ｉｎｔ ) are interconnected by their respective proximal ends in a plane of symmetry perpendicular to the wafer and extend toward the distal end of one of the extensions such that each secondary segment connects to one of the primary segments at the distal end; If the vibration mode of the vibration part includes only motion parallel to the mid-plane (M) and is symmetrical with respect to a plane of symmetry (P) perpendicular to the wafer, the two primary segments (L １ｅｘｔ , L ２ｅｘｔ ) has an instantaneous velocity component parallel to the central axis at each moment during vibration, and the directions of the instantaneous velocity components of the two primary segments are parallel to the secondary segment (L １ｉｎｔ , L ２ｉｎｔ ) in the opposite direction to the instantaneous velocity component of the resonator.

2. 2. The resonator of claim 1, wherein the vibrating part has a mass distribution such that the vibration modes, which include only motions parallel to the central plane (M) and are symmetrical with respect to a plane of symmetry (P) perpendicular to the wafer, do not cause motions of the legs (Pd) parallel to the central axis.

3. The material of the wafer is single crystal, trigonal crystal class, and piezoelectric; the central axis of the vibrating part is parallel to the axis Xc of the material; The two primary segments (L １ｅｘｔ , L ２ｅｘｔ ) and two secondary segments (L １ｉｎｔ , L ２ｉｎｔ 3. A resonator according to claim 1, wherein the Yc axis of the material is parallel to the Yc axis of the material.

4. The two extensions (P １ , P ２ ) is the extension part (P １ ) and the extension part (P ２ 4. A resonator according to claim 3, which forms an angle (α) between the first and second electrodes equal to 60° or 180°.

5. further comprising excitation means adapted to generate a bending deformation of the vibrating portion; and detection means adapted to measure the amplitude of the bending deformation of the vibrating portion generated by the excitation means during use of the resonator; the excitation means comprises first and second electrodes electrically insulated from each other; The first electrode has a first segment (L １ｅｘｔ , L ２ｅｘｔ ) or secondary segment (L １ｉｎｔ , L ２ｉｎｔ ) a strip of conductive material on each side of the wafer, the strip of conductive material being longitudinally disposed at the center of the width of the segment; The second electrode is connected to each primary segment (L １ｅｘｔ , L ２ｅｘｔ ) or secondary segment (L １ｉｎｔ , L ２ｉｎｔ ) two strips on each side of the wafer, the two strips being disposed on either side of the first electrode strip; 5. A resonator according to claim 3 or 4, wherein the detection means comprises a circuit for detecting the current appearing in the first and second electrodes.

6. Each extension part (P １ , P ２ ) at its distal end, the primary segment (L) of the extension parallel to the central plane (M) １ｅｘｔ , L ２ｅｘｔ ) and the secondary segment (L １ｉｎｔ , L ２ｉｎｔ 6. A resonator according to claim 1, comprising an extension to the outer longitudinal edge of said first and second electrodes.

7. It further comprises an additional part of the wafer in the form of a segment, called stem (Pc), which additional part is connected to the secondary segment (L １ｉｎｔ , L ２ｉｎｔ 7. A resonator according to claim 1, wherein a pair of legs (Pd) extend from the interconnected proximal ends of the legs (Pd) parallel to the central axis and in a direction away from the legs (Pd).

8. 8. The resonator of claim 7, comprising two vibrating parts formed from the same wafer, each having a stem (Pd), the two vibrating parts being interconnected by the stem and oriented opposite to each other so that the central axes of the two vibrating parts overlap.

9. 8. A resonator according to claim 1, comprising two vibration parts formed from the same wafer, the two vibration parts being interconnected by their respective legs (Pd) and oriented opposite to each other so that the respective central axes of the two vibration parts overlap.

10. A force sensor comprising a resonator according to claim 8 and adapted to measure tension applied between the respective legs (Pd) of said two vibrating parts and parallel to the central axis of said two vibrating parts.

11. A gyrometer comprising at least one resonator according to any one of claims 1 to 9.

Images