Abstract:
The present disclosure relates to a vibrating element which is planar parallelly to an electrical crystallographic axis of a piezoelectric material such as quartz. The element comprises a beam holding electrodes, a stationary portion rigidly connected to one end of the beam, and a solid portion rigidly connected to the other end of the beam. The structure with facets from the chemical machining of the element has an axis of symmetry parallel to the electrical axis, and the solid portion has a center of gravity on the axis of symmetry. The useful vibration modes of the vibrating element, according to which the solid portion is reciprocatingly rotated about the axis of symmetry and reciprocatingly moved parallel to the plane of the element, are uncoupled. The measurement of an angular speed by a rate gyroscope including said vibrating elements is more precise.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This is a national phase application under 35 U.S.C. §371 of PCT Application No. PCT/EP2010/054443, filed Apr. 1, 2010, which claims the benefit of French application No. 09/52172 filed Apr. 3, 2009, the contents of which are expressly incorporated herein by reference. 
     
    
     FIELD OF ART 
       [0002]    The present disclosure relates generally to vibratory gyrometers used for measuring the rotation of a vehicle in the space. 
         [0003]    More particularly, the present disclosure concerns a vibrating element configuration made in a piezoelectric material for such a gyrometer. 
       BACKGROUND 
       [0004]    The operating principle of a vibratory gyrometer is based on the sensing of Coriolis accelerations acting on an element vibrating according to a first useful mode of vibration, referred to as drive mode, when this element is subjected to a rotation with angular velocity Ω referenced with respect to an inertial frame of reference, referred to as Galilean frame of reference. The Coriolis accelerations are alternating at the frequency of the first useful mode and excite a second transversal useful mode of vibration, referred to as a sense mode and the vibration amplitude of which is proportional to Ω. The vibration amplitude is generally converted into the shape of electric signals and measured to determine Ω. 
         [0005]    It is known (EP-A2-1 962 055; EP-A2-0 844 461) that the vibrating element can be a tuning fork formed of two identical and parallel branches facing each other and each fixed each at one end to a common part, as shown in  FIG. 1 . The drive mode is a flexional resonance vibration of the two branches in phase opposition therebetween parallel to the plane XY of the tuning fork. When the tuning fork is subjected to rotation about an axis parallel to the longitudinal axis of the tuning fork, the sense mode is a flexional resonance vibration of the two branches in phase opposition therebetween perpendicularly to the plane XY of the tuning fork. 
         [0006]    The tuning fork is made through chemical machining of a quartz plate of a uniform thickness in an etching bath comprising hydrofluoric acid, as it is implemented for clock resonators. The tuning fork first takes advantage of the excellent dimensional definition of the photolithographic methods, secondly, of the easy piezoelectric excitation and sensing of both useful modes by means of electrodes deposited on the quartz, and third, of a very reduced industrial manufacture cost. 
         [0007]    The quartz plate with a uniform thickness is parallel to the electric and mechanical crystallographic plane XY of the quartz to facilitate the chemical machining. The branches of the tuning fork are oriented following a mechanical crystallographic axis Y to allow for a good efficiency of the piezoelectric excitation and sensing. 
         [0008]    As a result of the advantages thereof the chemical machining of the quartz inevitably results in oblique facets occurring with respect to the main crystallographic axes X and Y of the tuning fork, as shown in a simplified way on  FIG. 1 . First oblique facets fo are located at the foot of the branches of the tuning fork, at the start of the common part, and second oblique facets shaped as dihedron fd are located on each of the branches along a machined flank, the other machined flank being nearly planar and perpendicular to the plane of the plate. These facets, having quite large dimensions, are very well defined and reproducible from one machining to another, and do not have any drawback when the tuning fork operates according to a single vibratory mode, as it is the case with clock resonators, as they can be easily taken into account for the geometric definition of photolithographic tools. 
         [0009]    In contrast, when the tuning fork is used as a vibrating element of a gyrometer operating according to two useful vibration modes, the oblique facets have the drawback of creating a mechanical coupling between these useful vibration modes within each beam forming a branch of the tuning fork. Such a mechanical coupling results on the sense electrodes in the occurrence of an electric signal that is in quadrature with the Coriolis signal and that should be removed so as to be able to determine the angular velocity Ω. 
         [0010]    Two means are known for removing such a quadrature signal. 
         [0011]    The first known means implements electronic circuits for signal processing aiming at removing the quadrature signal through synchronous demodulation. The first means is however unsatisfactory when low rotational velocities are to be measured, as the Coriolis signal is then very small with respect to the quadrature signal and it becomes difficult to control with a sufficient accuracy the phase of the electric signals for taking advantage of the synchronous demodulation. 
         [0012]    The second known means for removing the quadrature signal consists in directly acting on the vibrating element, for instance carrying a trimming using a mechanical tool until obtaining a sufficient reduction of the electric quadrature signal present on the sense electrodes, as disclosed in U.S. Pat. No. 6,101,878. The second means significantly increases the measurement accuracy for the gyrometer, but has the drawback of increasing the manufacturing cost, as each gyrometer copy being manufactured should be submitted to a specific trimming operation. 
         [0013]    In order to reduce the mechanical coupling without carrying out a trimming, it seems interesting to orient the branches of the tuning fork according to another axis than the axis Y in the plane XY of the plate, for example following an electric crystallographic axis X, as shown on  FIG. 2 . Indeed, the chemical machining of a thus oriented tuning fork produces significantly reduced oblique facets at the foot of the branches and does not produce any oblique facet along the machined flanks of the branches. The mechanical coupling achieved within each beam of such a tuning fork is more significant than the previous embodiment with the branches oriented following the axis Y. This is due to the mechanical anisotropy of the quartz which, for branches oriented following the axis X, prevents that the vibrations of the two useful modes are independent from each other. 
       SUMMARY 
       [0014]    The object of the present method, system and device is to overcome these drawbacks linked to the chemical machining of a tuning fork in quartz by providing other configurations of the piezoelectric vibrating element of a gyrometer so that the oblique facets issued from the chemical machining do not create nearly any mechanical coupling between the two useful modes of vibration within a beam of the vibrating element, which is favorable to the measurement accuracy of the gyrometer. 
         [0015]    Accordingly, a vibrating element made in a piezoelectric material machinable through a chemical way, having first and second modes of vibration and having a monolithic structure with a uniform thickness and being planar parallelly to an electric crystallographic axis of the material, and including a substantially parallelepipedic beam supporting electrodes able to take part in one of the two modes of vibration, a fixed part fastened to one of the ends of the beam, and a mass part fastened to the other end of the beam, the mass part being able to move with an alternating displacement parallel to the plane of the monolithic structure following the second mode of vibration, is characterized in that the structure has a symmetry axis parallel to the electric crystallographic axis, and the mass part has a center of gravity located on the symmetry axis and is able to move with an alternating rotation about the symmetry axis following the first mode of vibration. 
         [0016]    The symmetry of the structure of the vibrating element, including the facets due to the chemical machining of the vibrating element, with respect to an axis parallel to an electric crystallographic axis of the piezoelectric material belonging, like quartz, to the crystal symmetry class  32  with a trigonal crystal system provides the mechanical decoupling between the first and the second useful modes of vibration in the vibrating element. The position of the gravity center of the mass part on the symmetry axis can lead to the two useful modes having substantially equal resonant frequencies, which enhances the measurement accuracy of a component of the angular velocity of the rotation to which the vibrating element is able to be subjected. 
         [0017]    The electrodes of the vibrating element are all supported by the beam, whatever the mode of vibration according to which the mass part moves. The electrodes are able to take part in one of the useful modes of vibration of the vibrating element for a particular gyrometer configuration of the present method, system and device, although, in another configuration, the beam of the vibrating element supports both electrodes for exciting the first vibration mode of the vibrating element, according to which the mass part is able to move with an alternating rotation about the symmetry axis, and electrodes for sensing the second vibration mode of the vibrating element according to which the mass part is able to move with an alternating displacement parallel to the plane of the monolithic structure. 
         [0018]    As will be described in the remainder of the description, two embodiments of a vibrating element according to the present method, system and device are set forth. According to a first embodiment, the mass part includes two branches symmetric about the symmetry axis and having ends fastened to said other end of the beam, and the gravity center of the mass part is located on the symmetry axis between the ends of the beam. According to a second embodiment, the vibrating element includes another beam supporting other electrodes, the two beams being substantially parallelepipedic, symmetric about the symmetry axis and having ends fastened therebetween and to the fixed part and other ends fastened to the mass part; the beams can form an angle of approximately 60°. 
         [0019]    The present method, system and device also relate to a gyrometer including four vibrating elements according to the present method, system and device, thus protecting the vibration quality of the two useful modes against the influences of the fastening of the gyrometer. The gyrometer includes two first substantially identical vibrating elements according to the first or the second embodiment and supporting electrodes for taking part in the first mode of vibration, and two substantially identical second vibrating elements according to the first or the second embodiment and supporting electrodes for taking part in the second mode of vibration. In the gyrometer, the fixed parts of the vibrating elements include together a central common part connecting ends of the beams of the first vibrating elements and ends of the beams of the second vibrating elements, and flexible arms connecting the common part to a fastening part. 
         [0020]    Although according to an alternative, the gyrometer is able to only include two substantially identical vibrating elements according to the first or the second embodiment and supporting both electrodes for taking part respectively in the first mode of vibration and the second mode of vibration, the separation of vibrating elements in two pairs, the electrodes of which are respectively allocated to the excitation of the first mode of vibration and to the sensing of the second mode of vibration, provides a better decoupling between the two modes by means, more specifically, of the common part remaining substantially stationary for both modes of vibration, imparting more accuracy to the measurement of the angular velocity of the rotation. 
         [0021]    When the vibrating elements are implemented according to the first embodiment and have each a beam collinear to that of another vibrating element, electrodes able to take part in the first mode of vibration and supported by each of the faces of the beam of each first vibrating element are first and second longitudinal electrodes respectively superposed to second and first electrodes on the other face of the beam and respectively collinear to first and second electrodes on the other first vibrating element, the four first electrodes being connected therebetween and the four second electrodes being connected therebetween, and electrodes able to take part in the second mode of vibration and supported by each of the faces of the beam of each second vibrating element are third and fourth longitudinal electrodes respectively superposed to the third and fourth electrodes on the other face of the beam and respectively collinear to the fourth and third electrodes on the other second vibrating element, the four third electrodes being connected therebetween and the four fourth electrodes being connected therebetween. 
         [0022]    When the gyrometer includes two first substantially identical vibrating elements being implemented according to the second embodiment and have each two beams, the beams of the first vibrating elements being two to two substantially collinear and supporting electrodes for taking part in the first mode of vibration, and two second substantially identical vibrating elements being implemented according to the second embodiment and have each two beams, the beams of the second vibrating elements being two to two substantially collinear and supporting electrodes for taking part in the second mode of vibration, the electrodes are distributed in first and second electrodes able to take part in the first mode of vibration and third and fourth electrodes able to take part in the second mode of vibration. 
         [0023]    The faces of a beam of each first vibrating element longitudinally support first parallel electrodes and second parallel electrodes. A first electrode on a face of the beam of each first vibrating element is superposed to a second electrode on the other face of the beam. The first electrodes on two substantially collinear beams of the first vibrating elements are substantially collinear two to two. The second electrodes on two substantially collinear beams of the first vibrating elements are substantially collinear two to two. The eight first electrodes are connected therebetween and the eight second electrodes are connected therebetween. 
         [0024]    Each one of the faces of a beam of a second vibrating element supports three parallel electrodes extending longitudinally. Said three electrodes of a beam are two third electrodes adjacent to the flanks of the beam and a fourth electrode is arranged between the third electrodes. The four third electrodes on the faces of a beam are superposed two to two. The two fourth electrodes on the faces of a beam are superposed. The eight third electrodes on two first substantially collinear beams of the second vibrating elements are connected and respectively substantially collinear two to two. The four fourth electrodes on the two first beams of the second vibrating elements are connected and respectively substantially collinear two to two. Eight third electrodes and four fourth electrodes on two second substantially collinear beams of the second vibrating elements are arranged in the same manner as the eight third electrodes and the four fourth electrodes on the first beams of the second vibrating elements. 
         [0025]    The eight third electrodes on the first beams of the second vibrating elements are connected to four fourth electrodes of the second beams of the second vibrating elements. The eight third electrodes on the second beams of the second vibrating elements are connected to the four fourth electrodes of the first beams of the second vibrating elements. 
         [0026]    Practically, the allocation of the first mode to one of the pairs of substantially identical vibrating elements can result from differences between the dimensions and consequently, between the resonant frequencies of the first vibrating elements and the second vibrating elements. The excitation of the first mode by the electrodes of the first vibrating elements does not produce any vibration of the second vibrating elements. 
         [0027]    The operation of the gyrometer according to the first mode of vibration, for instance as a drive mode excited by the electrodes of the first vibrating elements, generates Coriolis accelerations for the operation according to the second mode of vibration of the first vibrating elements, as a sense mode, when the gyrometer is biased by the rotation to be measured. When the second modes of vibration of the first and second vibrating elements have substantially equal resonant frequencies, the operation according to the second mode of vibration of the first vibrating elements is communicated to the second vibrating elements, the electrodes of which can sense the second mode of vibration. 
     
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         [0028]    Other features and advantages of the present method, system and device will be become more clearly apparent on reading the following description of several embodiments of the present method, system and device given by way of non-limiting examples and with reference to the corresponding appended drawings, in which: 
           [0029]      FIG. 1  is a perspective view of a prior art tuning fork already commented on; 
           [0030]      FIG. 2  is a perspective view of another tuning fork derived from the prior art and already commented on; 
           [0031]      FIG. 3A  is a perspective view of a vibrating element according to a first embodiment of the present method, system and device, achieved through chemical machining in a piezoelectric plate; 
           [0032]      FIGS. 3B and 3C  are perspective views showing exaggeratedly enlarged deformations of the vibrating element respectively for both useful modes of vibration; 
           [0033]      FIG. 4  is a perspective view of a gyrometer according to the present method, system and device, including four vibrating elements similar to that of  FIG. 3A ; 
           [0034]      FIGS. 5A and 5B  are perspective views showing exaggeratedly enlarged deformations of the vibrating elements of the gyrometer of  FIG. 4  respectively for the drive mode and the sense mode; 
           [0035]      FIG. 5C  is a perspective view showing exaggeratedly enlarged deformations of the vibrating elements of the gyrometer of  FIG. 4  for another particular mode of vibration of interest to be taken into account in the dimensioning of the gyrometer; 
           [0036]      FIG. 6  is a front view of the vibrating elements of the gyrometer of  FIG. 4  showing an arrangement of the selective excitation electrodes of the drive mode and the selective sense electrodes of the sense mode; 
           [0037]      FIG. 7A  is a perspective view of a vibrating element according to a second embodiment of the present method, system and device; 
           [0038]      FIGS. 7B and 7C  are perspective views showing exaggeratedly enlarged deformations of the vibrating element respectively for both useful modes of vibration; 
           [0039]      FIG. 8  is a perspective view of a gyrometer according to the present method, system and device, including four vibrating elements similar to that of  FIG. 7A ; 
           [0040]      FIGS. 9A and 9B  are perspective views showing exaggeratedly enlarged deformations of the vibrating elements of the gyrometer of  FIG. 8  respectively for the drive mode and the sense mode; 
           [0041]      FIG. 9C  is a perspective view showing exaggeratedly enlarged deformations of the vibrating elements of the gyrometer of  FIG. 8  for another particular mode of interest to be taken into account in the dimensioning of the gyrometer; and 
           [0042]      FIG. 10  is a front view of the vibrating elements of the gyrometer of  FIG. 8  showing an arrangement of the selective excitation electrodes of the drive mode and the selective sense electrodes of the sense mode. 
       
    
    
     DETAILED DESCRIPTION 
       [0043]      FIG. 3A  shows a first embodiment of a monolithic vibrating element  10  according to the present method, system and device, machined in a planar plate made in a piezoelectric material such as quartz, having a uniform thickness e. The vibrating element  10  includes a substantially parallelepipedic beam  1 , a fixed part PF fastened to one of the ends of the beam and a mass part  2  fastened to the other end of the beam. The vibrating element  10  is symmetric about the longitudinal axis  3  of the beam  1 . The mass part  2  is dimensioned so that its center of gravity is located on the longitudinal symmetry axis  3  of the beam between the two ends of the beam. According to  FIG. 3A , the mass part has a U shape, the web of which is fastened to the beam and perpendicular to the latter and the parallel branches of which are arranged on both faces of the beam  1 . More generally, the mass part includes two branches symmetric about the symmetry axis  3  and having ends fastened to the end of the beam not fastened to the fixed part PF. According to other examples, the mass part has a C or a V shape, the ends of which are oriented to the fixed part. 
         [0044]    The cross-sectional dimension  1  of the beam  1  taken in the plane of the plate is substantially larger than its other cross-sectional dimension e. Preferably the dimension  1  lies between about 1.3 times and about twice the dimension e. Preferably, the length dimension L of the beam  1  lies between about 4 times and about 5 times the dimension e. 
         [0045]    Still with reference to  FIG. 3A , the plate is perpendicular to the optical crystallographic axis Z of the quartz and thus parallel to the crystallographic plane XY of the quartz including the three “electric” crystallographic axes and the three “mechanical” crystallographic axes respectively perpendicular to the electric axes. In  FIG. 3A , only one electric crystallographic axis designated to as X and one mechanical crystallographic axis referred to as Y are shown. The longitudinal axis  3  of the beam  1  is oriented following the electric crystallographic axis X. The chemical machining of the vibrating element  10  in an etching bath comprising hydrofluoric acid causes the occurrence of oblique facets  4  and  4 ′ at the end of the beam  1  fastened to the fixed part PF, and oblique facets  5  and  5 ′ at the other end fastened to the web of the U-shaped mass part  2 . No dihedron-shaped facet appears on the machine flanks of the beam, as it is oriented according to the axis X. The facets  4  and  4 ′ are respectively symmetric to each other with respect to the longitudinal axis  3  of the beam, and the facets  5  and  5 ′ are respectively symmetric to each other with respect to the longitudinal axis  3  of the beam. The symmetry between the facets is due to the orientation of the beam according to the axis X of the quartz and to the nature of the etching bath comprising hydrofluoric acid. The vibrating element  10  made through chemical machining thus has a symmetry axis confused with the longitudinal axis  3  of the beam and parallel to the axis X. If the longitudinal axis  3  of the beam were oriented according to a mechanical crystallographic axis Y of the quartz, or more generally according to any other different direction of an electric crystallographic axis X in the crystallographic plane XY of the plate, the flanks of the beam would comprise dissymmetric facets. 
         [0046]      FIGS. 3B and 3C  show excessively enlarged deformations of the vibrating element  10  for the two useful modes of vibration respectively and associated with appropriate positions of electrodes on the faces of the beam, as will be seen hereinafter with reference to  FIG. 6 . The oblique facets are not shown on  FIGS. 3B and 3C . 
         [0047]    For the first useful mode of vibration shown on  FIG. 3B , the beam  1  undergoes an alternating torsional deformation around the longitudinal symmetry axis  3 . The mass part  2  moves with an alternating rotation about said longitudinal symmetry axis and does not practically undergo any deformation. 
         [0048]    For the second useful mode of vibration shown on  FIG. 3C , the beam  1  undergoes an alternating flexional deformation parallel to the plane XY of the plate. The mass part  2  moves with an alternating displacement parallel to said plane and does not undergo practically any deformation. 
         [0049]    Each of the two useful modes of vibration may be used as a drive mode, the other useful mode then being used as a sense mode. For instance, according to the embodiments as illustrated on  FIGS. 3B and 3C , when an angular velocity Ω to which the vibrating element  10  is subjected, or a component of the angular velocity, is parallel to the plane XY of the plate and perpendicular to the symmetry axis  3 , and when the first useful mode is the drive mode that generates alternating velocities V perpendicular to the plane XY of the plate, said velocities V are combined with the rotational velocity Ω for creating the Coriolis accelerations Γ c  exciting the second useful mode. In this example, the vibrating element according to the present method, system and device is sensitive to a rotation with a velocity Ω around an axis parallel to the plane of the plate and perpendicular to the longitudinal axis of the beam. 
         [0050]    The choice of these two useful modes of vibration combined with the symmetry of the vibrating element with respect to an axis parallel to the axis X of the quartz, generates practically a mechanical decoupling between the two modes. The two useful modes of vibration would not be independent if for one of them, the mass part moved for instance with an alternating motion perpendicularly to the plane of the plate, or if the vibrating element did not have said symmetry. 
         [0051]    Furthermore, the position of the gravity center of the mass part  2  on the longitudinal axis  3  of the beam and the above mentioned intervals of the 1/e and L/e ratios contribute to the resonant frequencies of the two useful modes being close to each other, deviated, for instance, by about 1% in relative value, i.e. they are substantially equal, which is beneficial to the accuracy of the gyrometric measurement. 
         [0052]    The present method, system and device are not restricted to the first above described embodiment of vibrating element  10  achieved through chemical machining a quartz plate parallel to the crystallographic plane XY, and combining a low manufacturing cost and the quasi absence of mechanical coupling between the two useful modes. The scope of the present method, system and device covers other types of machining operations, piezoelectric materials and crystallographic orientations, as explained hereinafter. 
         [0053]    As far as machining is concerned, this should respect the symmetry of the structure of the vibrating element with respect to the longitudinal axis  3  of the structure, namely that of the beam  1 . For instance, machining is carried out through ultrasound or through plasma etching. 
         [0054]    As far as the piezoelectric material is concerned, the latter should belong to the same crystal symmetry class as the quartz, i.e. the symmetry class  32  with a trigonal crystal system. For instance, the piezoelectric material can be a synthesis material such as gallium orthophosphate GaPO 4 , or belonging to the family of the langasites (LGS) or to that of the langanites (LGN) or to that of the langatates (LGT). All these piezoelectric materials have at least one pair of electric X and mechanical Y crystallographic axes perpendicular to an optical crystallographic axis Z. 
         [0055]    As far as the orientation of the plate with respect to the crystallographic axes is concerned, the plane of the plate should be parallel to the axis X. The orientation of the plate can thus be considered as being derived from the orientation XY by a rotation of an angle θ about the axis X. The angle θ can be selected to optimize the behavior of the frequencies of both useful modes upon variations of temperature. 
         [0056]    The present method, system and device also relate to a gyrometer including four vibrating elements according to the present method, system and device to protect the vibration quality of both useful modes against the influences of the fastening of the gyrometer. An exemplary embodiment of said gyrometer is explained with reference to  FIGS. 4 ,  5 A,  5 B,  5 C and  6  in which the oblique facets are not shown. 
         [0057]    With reference to  FIG. 4 , a monolithic gyrometer  100  according to the present method, system and device includes four vibrating elements  11 ,  12 ,  21  and  22  similar to that 10 shown on  FIG. 3A . The fixed parts of the vibrating elements are gathered into one set including a central common part PC in the shape of a bar extending parallel to the longitudinal axes of the beams of the four vibrating elements and connecting ends fastened to the beams of the first vibrating elements  11  and  12  at ends fastened to the beams of the second vibrating elements  21  and  22 , two sets of flexible T-shaped arms BS, the legs of which are coaxial longitudinally to the common part and connected to the ends of the latter, and a fastening frame CF connected to the common part with the flexible arms. The common part PC is not fastened, as opposed to the fixed part PF of the vibrating element  10  shown on  FIG. 3A . However, as will be explained later on, the common part PC remains spontaneously practically stationary for the useful modes of vibration of the gyrometer  100 . Like the vibrating element  10  illustrated on  FIG. 3A , the gyrometer  100  is made in a planar plate made in a piezoelectric material, such as quartz, parallel to the electric crystallographic axis X, in the present case parallel to the crystallographic plane XY, and having a uniform thickness for instance via chemical machining. 
         [0058]    The first vibrating elements  11  and  12  are arranged on either sides of the common part PC and the longitudinal axes of their beams are collinear. The vibrating elements  11  and  12  are substantially identical and have, accordingly, a common frequency F 1  for their first useful mode and a common frequency F 2  for their second useful mode. The oblique facets (not shown) achieved through chemical machining the piezoelectric material not being identical for the elements  11  and  12 , it can be advantageous to modify slightly the photolithographic tools so as to obtain a sufficient symmetry of the vibrating elements  11  and  12  with respect to the longitudinal axis of the common part PC perpendicular to the axis X and therefore a sufficient identity of the dynamic behaviors of the vibrating elements  11  and  12  and a balance of the latter with respect to the longitudinal axis of the common part. This situation is similar for the balance of the second vibrating elements  21  and  22  with respect to the longitudinal axis of the common part PC. Furthermore, the vibrating elements  11  and  12  are dimensioned so that the frequencies F 1  and F 2  are close to each other, deviating, for instance, by about 1% in relative value. 
         [0059]    The vibrating elements  21  and  22  are arranged on either sides of the common part PC and the longitudinal axes of their beams are collinear. The vibrating elements  21  and  22  are substantially identical therebetween, but can be different from the elements  11  and  12 . For instance as shown on  FIG. 4 , the elements  21  and  22  have beams of a length different from that of the beams of the elements  11  and  12 , as well as U-shaped mass parts of dimensions different from those of the mass parts of the elements  11  and  12 . The vibrating elements  21  and  22  are dimensioned so that the common frequency F′I of their first useful mode is significantly different from F 1 , i.e. so that F 1  and F′ 1  deviate by at least about 10% in relative value and that the common frequency F′2 of their second useful mode is substantially equal to F 2 . Such relationships between frequencies are achieved for instance acting both on the three dimensional parameters of the vibrating elements: the length of the beam, the length of the branches of the mass part, and the cross-sectional width of a portion of said mass part taken in the plane of the plate, such as the cross-sectional width of the web of a U. 
         [0060]    Thus, the gyrometer  100  has three particular modes of vibration, as shown in  FIGS. 5A ,  5 B and  5 C limited to the four vibrating elements and to their common part PC. 
         [0061]    The first particular mode of vibration shown on  FIG. 5A  is the drive mode of the gyrometer  100  and only practically sets in motion the two first elements  11  and  12  vibrating in phase opposition therebetween according to their first useful mode at the frequency F 1 . The alternating torsional stresses produced by the beams of the vibrating elements  11  and  12  are mutually equilibrating in the area of the common part PC fastened to the beams of the elements  11  and  12  that do not communicate any displacement to the second vibrating elements  21  and  22 , the frequencies F 1  and F′ 1  being significantly different. 
         [0062]    The second particular mode of vibration shown on  FIG. 5B  is the sense mode of the gyrometer  100  and sets in motion the four vibrating elements on their second useful mode at the frequency F 2  close to F 1 , the elements  11  and  12  vibrating in phase opposition respectively with the elements  21  and  22 . The alternating flexional stresses produced by the four beams of the vibrating elements  11  and  12  are mutually equilibrating in the portion of the common part located between the fastened ends of the beams of the elements  11  and  12  and the fastened ends of the beams of the elements  21  and  22 . 
         [0063]    Like what was previously explained for one single vibrating element according to the present method, system and device with reference to  FIGS. 3A ,  3 B and  3 C, the gyrometer  100  including four vibrating elements is sensitive to a rotation with an angular velocity Ω to which the gyrometer is subjected, around an axis parallel to the plane of the plate and perpendicular to the longitudinal axes of the beams. Furthermore, there is practically no mechanical coupling between the drive mode and the sense mode of the gyrometer  100 , as the two useful modes of each one of the four vibrating elements are practically decoupled. In contrast, the action of the Coriolis accelerations is less direct than for the single vibrating element shown on  FIGS. 3B and 3C . In the case of the gyrometer  100 , the alternating velocities generated by the drive mode are only relative to the elements  11  and  12 , and therefore the Coriolis accelerations induced by the rotation to be measured only apply to such single elements  11  and  12  that are thereby vibrated. Because the four vibrating elements have substantially the same common frequency F 2  for their second useful mode, the vibration of the elements  11  and  12  spontaneously causes the vibration in phase opposition of the elements  21  and  22 , as well as, as far as it is a tuning fork with two branches, the excitation of one single branch in the vicinity of the tuning fork resonance spontaneously vibrates the two branches. 
         [0064]    Finally, the third particular mode of vibration, as shown on  FIG. 5C , practically sets in motion only the second elements  21  and  22  vibrating in phase opposition therebetween at the frequency F′ 1  significantly different from F 1 . This third particular mode is not a useful mode of the gyrometer  100 , but is nevertheless of interest to be taken into account in dimensioning the gyrometer  100  as the more the frequency F′ 1  deviates from the frequency F 1  of the drive mode of the gyrometer  100 , the more the first and third particular modes are independent from each other. A deviation of at least about 10% in relative value between F 1  and F′ 1  allows a sufficient independence to be reached so that the vibrations of each one of the first and third particular modes only practically relate to two of the four elements, as represented on  FIGS. 5A and 5C . 
         [0065]    It should be noticed that for the three particular modes of vibration, the common part remains spontaneously practically stationary. In such conditions, with reference to  FIG. 4 , the flexible arms BS allow small residual alternating motions of the common part to be efficiently filtered and thereby only practically negligible alternating stresses to be transmitted to the fastening frame CF. As a result, the fastening frame CF remains spontaneously stationary and its fastening on a casing base does not impair the vibration quality of the useful modes of the gyrometer  100 . As an example, it is possible to make such a gyrometer according to the present method, system and device in a quartz pellet of a diameter of 9 mm and a thickness of 0.4 mm, and the two useful modes of vibration of which have frequencies close to 35 kHz and quality coefficients higher than 200,000. 
         [0066]    It can seem interesting, for putting further apart the frequency F′ 1  of the third particular mode shown on  FIG. 5C  from the frequency F 1  of the first mode of vibration illustrated on  FIG. 5A , that the mass parts of the vibrating elements  21  and  22  do not include two symmetric branches, but are more compact, for instance with a square or rectangular shape, the mass parts of the vibrating elements  11  and  12  only keeping their two symmetric branches. Theoretically, this would not prevent from dimensioning the four vibrating elements so as the common part remains spontaneously practically stationary for the second particular mode. In practice, such a balance would be difficult to achieve, as the manufacturing tolerances would be more stringent than in the case illustrated on  FIG. 4  where the four vibrating elements have similar shapes. 
         [0067]    As far as the piezoelectric excitation and sensing of the two useful modes of vibration of the gyrometer  100  are concerned, electrodes adhering to the piezoelectric material are arranged on the two large faces of the plate. As shown on  FIG. 6 , the electrodes are distributed in two systems of excitation electrodes  61  and  62  mainly on the beams of the vibrating elements  11  and  12  and two systems of sense electrodes  63  and  64  mainly on the beams of the vibrating elements  21  and  22 . The branches of the U-shapes of the mass parts  2  of the vibrating elements support no electrode.  FIG. 6  shows an arrangement of the electrodes on one of said large faces, the arrangement of the electrodes on the other large face being geometrically identical but being able, depending on the useful mode considered, to be different through different electric polarities, as will be explained herein below. In order to better understand the drawing, the electrodes designated by a reference dashed line are located on the other large face. 
         [0068]    On each one of the two large faces and for each one of the vibrating elements  11  and  12 ,  21  and  22 , the electrodes  61  and  62 ,  63  and  64  have the shape of two substantially identical conductive strips extending parallel to the longitudinal axis of the beam of the vibrating element and covering the whole large face of the beam with the exception of a median band separating said two strips. Preferably, as shown on  FIG. 6 , the two strips extend on the web of the U-shaped mass part of the vibrating element. Preferably, the width of the median band separating the two strips is lower than 10% of the cross-sectional dimension of the beam taken in the plane of the plate. 
         [0069]    For each one of the two large faces, four electric connections (not shown) respectively connect the collinear electrodes  61  of the vibrating elements  11  and  12 , the collinear electrodes  62  of the vibrating elements  11  and  12 , the misaligned electrodes  63  of the vibrating elements  21  and  22 , and the misaligned electrodes  64  of the vibrating elements  21  and  22 . 
         [0070]    For each one of the vibrating elements  11  and  12 , two electric connections (not shown), respectively connect the collinear electrodes  61  not superposed on the large faces and the electrodes  62  not superposed on the large faces. For each one of the vibrating elements  21  and  22 , two electric connections (not shown), respectively connect the collinear electrodes  63  superposed on the large faces and the electrodes  64  superposed on the large faces. 
         [0071]    The systems of the excitation electrodes  61  and  62  arranged on the vibrating elements  11  and  12  are able to selectively excite the drive mode of the gyrometer  100  illustrated on  FIG. 5A  relying on the distribution of the shear constraint T XY  specific to the torsion of the beams of the vibrating elements  11  and  12  around their longitudinal axis and linked through piezoelectric effect to opposite components E Y  of an alternative electric field on the main faces of the beams, when the electrodes  61  and  62  are respectively connected to terminals of an electronic oscillating circuit (not shown). For the drive mode, the constraint T XY  relied on is the main constraint of the torsional vibration, and a minimum of electric voltage applied between the electrodes  61  and  62  acts optimally for exciting the drive mode. 
         [0072]    The systems of the electrodes  63  and  64  arranged on the vibrating elements  21  and  22  are able to selectively sense the sense mode of the gyrometer  100  shown on  FIG. 5B  relying on the distribution of the shear constraint T XY  specific to the flexion of the beams of the vibrating elements  21  and  22  parallel to the plane XY of the plate and linked through piezoelectric effect to components E Y  of an alternative electric field having the same direction on the main faces of the beams, when the electrodes  63  and  64  are respectively connected to opposite polarity terminals of a capacitive circuit sensing an electric voltage (not shown). For the sense mode, the used constraint T XY  is several times lower than the main mechanical tensile-compression constraint T XX  of the alternatively stretched and compressed longitudinal fibers of the beams vibrating flexionally, said main mechanical constraint T XX  being difficult to use because of the tensor of the piezoelectric coefficients of the quartz and the orientation of the beams following the axis X. 
         [0073]    The selectivity of the excitation of the drive mode and the sensing of the sense mode, combined with the mechanical decoupling between these two modes of vibration, allows that, in the absence of a rotation Ω applied to the gyrometer  100 , the vibration of the drive mode does not generate through piezoelectric effect the occurrence of electric loads on the sense electrodes  63  and  64 . 
         [0074]    Furthermore, the quite important distance between the excitation electrodes  61  and  62  and the sense electrodes  63  and  64  allows an alternative electrical excitation potential present on at least one of the electrodes  61  and  62  almost not to generate, via an electrostatic effect, the occurrence of electric loads on the electrodes  63  and  64 . 
         [0075]    Thus, the electric loads occurring on the electrodes  63  and  64  are practically only generated by the rotation to be measured, leading the gyrometer  100  to deliver an accurate measurement of the vibration amplitude of the sense mode proportional to the angular rotational velocity Ω. In addition, the gyrometer  100  is easy to make through chemical machining as it does not require any trimming, as opposed to the known gyrometer described in the preamble of the description. 
         [0076]      FIG. 7A  shows a second embodiment of a monolithic vibrating element  30  according to the present method, system and device, allowing the electric loads induced by the rotation to be measured to be increased so as to further improve the accuracy of the gyrometric measurement. Such increase of electric loads will be explained later on in relationship with the description of a gyrometer including four vibrating elements being similar to the vibrating element  30 . 
         [0077]    The vibrating element  30 , machined in a planar plate made in a piezoelectric material, such as quartz, having a uniform thickness e, includes two parallelepipedic beams  1   a  and  1   b  having substantially identical dimensions and having ends fastened therebetween, the longitudinal axes  3   a  and  3   b  of which form an angle of about 60°, a fixed part PF′ fastened to fastened ends of the beams at the apex of said angle, and a mass part  2 ′ fastened to the other ends of the beams  1   a  and  1   b  and having the general shape of a bar with sharp ends oriented to the fixed part. The vibrating element  30  is symmetric about a longitudinal axis  3 ′ bisecting the angle between the longitudinal axes  3   a  and  3   b  of the beams. The mass part  2 ′ and the two beams  1   a  and  1   b  form the outline of a substantially equilateral triangle. Thus, the two beams  1   a  and  1   b  can be regarded as substituting the beam  1  in the vibrating element  10  shown on  FIG. 3A . Similarly to the first embodiment, the mass part  2 ′ can be conformed with several shapes of symmetric branches at the ends of a bar rectilinear or symmetrically curved with respect to the axis  3 ′. 
         [0078]    Still referring to  FIG. 7A , the cross-sectional dimension  1 ′ of each one of the beams  1   a  and  1   b  taken in the plane of the plate is substantially larger than its other cross-sectional dimension e. Preferably, the dimension  1 ′ lies between about 1.1 times and about 1.5 times the dimension e. Preferably, the length dimension L′ of each one of the beams lies between about 4 times and about 6 times the dimension e. 
         [0079]    As for the vibrating element  10  shown on  FIG. 3A , the plate is parallel to the crystallographic plane XY of the quartz and the symmetry axis  3 ′ is oriented following one of the electric crystallographic axes of the quartz designated as X. Taking into account the ternary symmetry of the quartz expressing that the crystalline pattern of the latter is repeated every 120° around the optical axis Z in the plane XY of the plate, the longitudinal axes  3   a  and  3   b  of the beams  1   a  and  1   b  are respectively oriented parallel to the two mechanical crystallographic axes other than the shown axis Y orthogonal to the axis X parallel to the symmetry axis  3 ′ and, as shown on  FIG. 7A , one  1   b  of the beams is facing the positive direction of the axis Y and the other beam  1   a  is facing the negative direction of the axis Y. Chemically machining the vibrating element  30  in an etching bath comprising hydrofluoric acid causes the occurrence of oblique facets  6  and  6 ′ and facets having the shape of dihedrons  7 . The oblique facets  6  are located at the apexes of 60° dihedrons at internal in a triangular opening between the beams  1   a  and  1   b  and the mass part  2 ′. The oblique facets  6 ′ are located at the apexes of 60° dihedrons between the beams  1   a  and  1   b  and the fixed part PF′ and between the beams  1   a  and  1   b  and the sharp ends of the mass part  2 ′. The facets  7  are located along flanks of the beams  1   a  and  1   b  and of the mass part  2 ′ located outside the equilateral triangle formed by said beams and said mass part. The arrangement of such oblique facets and such dihedrons is symmetric about the axis  3 ′. The symmetry between the facets is due to the orientation of the axis  3 ′ following the axis X of the quartz and to the nature of the etching bath comprising hydrofluoric acid. 
         [0080]      FIGS. 7B and 7C  show excessively enlarged deformations of the vibrating element  30  for the two useful modes of vibration respectively and associated with appropriate positions of electrodes on the faces of the beam, as will be seen hereinafter with reference to  FIG. 10 . The oblique facets are not shown on  FIGS. 7B and 7C . 
         [0081]    For the first useful mode of vibration shown on  FIG. 7B , the beams  1   a  and  1   b  mainly undergo alternating flexional deformations perpendicularly to the plane of the plate and, in a lesser extent, alternating torsional deformations around their longitudinal axes. The mass part  2 ′ moves with an alternating rotation about the symmetry axis  3 ′ of the vibrating element and thus of alternating velocities V perpendicular to the plane XY of the plate and does not practically undergo any deformation. 
         [0082]    For the second useful mode of vibration shown on  FIG. 7C , the beams  1   a  and  1   b  undergo alternating flexional deformations parallel to the plane XY of the plate. The mass part  2 ′ moves with an alternating displacement parallel to said plane and does not undergo practically any deformation. 
         [0083]    As for the vibrating element  10  shown on  FIGS. 3B and 3C , the vibrating element  30  is sensitive to a rotation with an angular velocity Ω about an axis parallel to the plane of the plate and perpendicular to the symmetry axis  3 ′ of the vibrating element. 
         [0084]    As for the vibrating element  10 , the choice of these two useful modes of vibration of the vibrating element  30 , combined with the symmetry of the vibrating element about an axis parallel to the axis X of the quartz, allows for practically no mechanical coupling between the two modes. If the angular velocity Ω is nil, the excitation of the vibrating element  30  according to the first mode does not generate the second mode. 
         [0085]    As for the vibrating element  10 , the position of the gravity center of the mass part  2 ′ on the symmetry axis  3 ′ and the above-mentioned intervals of the 1′/e and L′/e ratios contribute to the resonant frequencies of the two useful modes being close to each other, deviated, for instance, by about 1% in relative value, that is they are substantially equal, which is beneficial to the accuracy of the gyrometric measurement. 
         [0086]    As for the vibrating element  10 , the scope of the present method, system and device further covers types of machining allowing the symmetry of the vibrating element  30  to be respected about its symmetry axis  3 ′, piezoelectric materials belonging to the same crystal symmetry class  32  as the quartz, and the orientations of the plate derived from the crystallographic orientation XY by a rotation of an angle θ about the axis X. 
         [0087]    The present method, system and device also relate to a monolithic gyrometer including four vibrating elements  31 ,  32 ,  41  and  42  similar to the vibrating element  30  according to the second embodiment, to protect the vibration quality of both useful modes against the influences of the fastening of the gyrometer. The arrangement of such a gyrometer  200 , shown on  FIG. 8 , is similar to that of the gyrometer  100  illustrated on  FIG. 4  as far as the arrangement of the four vibrating elements  31 ,  32 ,  41  and  42 , the common part PC′, the flexible arms BS′ and the fastening frame CF′ is concerned. The vibrating elements  31  and  32  are substantially identical therebetween, but can be different from the elements  41  and  42  which are substantially identical. The beams of the elements  31  and  32  are substantially collinear longitudinally two to two and together form a cross. Similarly, the beams of the elements  41  and  42  are substantially collinear longitudinally two to two and together form a cross. 
         [0088]    Similarly to the gyrometer  100 , the gyrometer  200  has three particular modes of vibration, as illustrated on  FIGS. 9A ,  9 B and  9 C limited to the four vibrating elements and to their common part PC′. 
         [0089]    The drive mode of the gyrometer  200  only sets in motion two elements  31  and vibrating in phase opposition therebetween according to their first useful mode such as represented on  FIG. 9A . The sense mode sets in motion the four elements vibrating according to their second useful mode, the elements  31  and  32  vibrating in phase opposition respectively with the elements  41  and  42 , as shown on  FIG. 9B . The frequencies of the drive mode and the sense mode are close to each other. The third particular mode of vibration shown on  FIG. 9C  practically sets in motion only the two elements  41  and  42  vibrating in phase opposition at a frequency deviated by at least 10% from the frequency of the drive mode. 
         [0090]    As for the gyrometer  100 , electrodes adhering to the piezoelectric material are arranged on the two large faces of the plate. As shown on  FIG. 10 , the electrodes are distributed in two systems of excitation electrodes  71  and  72  on the beams of the vibrating elements  31  and  32  and two systems of sense electrodes  73  and  74  on the beams of the vibrating elements  41  and  42 . The mass parts  2 ′ of the vibrating elements support no electrode.  FIG. 10  shows an arrangement of the electrodes on one of said large faces, the arrangement of the electrodes on the other large face being geometrically identical but being able, depending on the useful mode being considered, to be different through different electric polarities. 
         [0091]    Each one of the beams of the vibrating elements of the gyrometer  200  being oriented according to a respective mechanical axis of the quartz and mainly operating in flexion, the faces of the beams of the elements  31  and  32  support a known electrode arrangement with two conductive strips  71  and  72 , so as to selectively excite the drive mode for which the beams of the elements  31  and  32  vibrate perpendicularly to the plane of the plate. The faces of the beams of the elements  41  and  42  support a known arrangement of electrodes with three conductive strips  73  and  74  so as to selectively sense the sense mode for which the beams of the elements  41  and  42  vibrate parallelly to the plane of the plate. In order to better understand  FIG. 10 , it should be understood that electrodes designated with the same reference numeral are connected therebetween by electric connections (not shown). 
         [0092]    For the known two-strip arrangement, two electrodes  71 , or  72 , not superposed on the faces of a beam of an element  31 ,  32  are connected. Two excitation electrodes  71  or  72  extending longitudinally on a large face of two substantially collinear beams of the elements  31  and  32  are substantially collinear and connected. 
         [0093]    For the known three-strip arrangement, each one of the faces of a beam supports three parallel sense electrodes extending longitudinally. These three electrodes are two edge electrodes adjacent to the flanks of the beam and a central electrode located between the edge electrodes. The four edge electrodes on the faces of the beam are superposed two to two. The two central electrodes on the faces of the beam are also superposed. The eight edge electrodes  73  on two first substantially collinear beams of the elements  41  and  42  are connected and respectively substantially collinear two to two. The four central electrodes  74  on the two first beams of the elements  41  and  42  are connected and respectively substantially collinear two to two. Eight edge electrodes  74  and four central electrodes  73  on two second substantially collinear beams of the elements  41  and  42  are arranged in the same manner as the eight edge electrodes  73  and the four central electrodes  74  on the first beams of the elements  41  and  42 . The eight edge electrodes  73  on the first beams are connected to the four central electrodes  73  of the second beams, and the eight edge electrodes  74  on the second beams are connected to the four central electrodes  74  of the first beams. 
         [0094]    The gyrometer  200  allows, compared to the gyrometer  100 , the electric loads induced by the rotation to be measured to be increased, thereby improving the accuracy of the gyrometric measurement, i.e. the measurement of the vibration amplitude of the sense mode proportional to the angular rotational velocity Ω. For the drive mode and the sense mode of the gyrometer  200 , the main mechanical constraint is the tensile-compression constraint T XY  of the alternately stretched and compressed longitudinal fibers of the beams vibrating flexionally. The known electrode systems with two strips and three strips allow to use piezoelectrically this constraint in an optimal way, i.e. the electrodes  71  and  72  supported by the vibrating elements  31  and  32  allow the drive mode to be excited with a low electric voltage therebetween, as for the gyrometer  100 , and the sense electrodes  73  and  74  supported by the vibrating elements  41  and  42  allow many more loads induced by the Coriolis accelerations to be sensed, as compared to the sensing by means of the gyrometer  100 . The amount of loads induced by the Coriolis accelerations and thus the accuracy of the gyrometric measurement with the gyrometer  200  are thus several times higher than those with the gyrometer  100 .