Abstract
A resonator is suitable for reducing or suppressing a force transmitted by a vibrating portion of the resonator to a support part. To this end, the vibrating portion includes two extensions which are each meander shaped such that two segments of each extension have respective speed components that are oriented in opposite directions. Such a resonator, which is balanced, can advantageously be used within a rate gyro or a force sensor.
Claims
1. A resonator comprising: a portion of a wafer having two opposite faces which are flat and parallel, the wafer portion being intended to vibrate flexurally during use of the resonator, and referred to as the vibrating portion; and a support part, which is external to the vibrating portion and connected thereto by an intermediate segment of the wafer referred to as a foot, said foot being integral with the vibrating portion and forming a rigid connection between the support part and said vibrating portion, the vibrating portion having a first plane of symmetry, referred to as the midplane, which is parallel to both faces of the wafer and equidistant from said two faces, and a second plane of symmetry, referred to as the plane of symmetry orthogonal to the wafer, which is perpendicular to the midplane and which passes longitudinally through the connection formed by the foot between the support part and the vibrating portion, an intersection between the midplane and the plane of symmetry orthogonal to the wafer constituting a center axis of the vibrating portion, the vibrating portion comprising two extensions which are each intended to vibrate flexurally, said two extensions extending symmetrically from the foot on each side of the plane of symmetry orthogonal to the wafer, wherein each extension is provided with a longitudinal slot which passes through the vibrating portion perpendicularly to the midplane, from the plane of symmetry orthogonal to the wafer towards a distal end of said extension but without reaching said distal end, so that each extension is meander shaped, the respective slots of the two extensions being symmetrical relative to the plane of symmetry orthogonal to the wafer, and meeting at said plane of symmetry orthogonal to the wafer, so that the vibrating portion comprises two primary segments which each connect the foot to the distal end of one of the extensions, and two secondary segments which are interconnected at the plane of symmetry orthogonal to the wafer by respective proximal ends of said secondary segments, and which each extend to the distal end of one of the extensions so as to connect to one of the primary segments at said distal end, such that for a mode of vibration of the vibrating portion which comprises only movements parallel to the midplane, and which is symmetrical relative to the plane of symmetry orthogonal to the wafer, both primary segments have instantaneous velocity components, parallel to the center axis, which at each instant during vibration, are in the opposite direction to that of instantaneous velocity components of the secondary segments, also parallel to the center axis.
2. The resonator of claim 1, wherein the vibrating portion has a distribution of mass such that the mode of vibration, which only comprises movements parallel to the midplane and which is symmetrical relative to the plane of symmetry orthogonal to the wafer, does not cause movement of the foot parallel to the center axis.
3. The resonator of claim 1, wherein a material of the wafer is monocrystalline and of trigonal class and piezoelectric, and wherein: the center axis of the vibrating portion is parallel to an axis Xc of said material, and both primary segments as well as both secondary segments of the vibrating portion are parallel to axes Yc of said material.
4. The resonator of claim 3, wherein both extensions of the vibrating portion form an angle between them which is equal to 60? or 180?.
5. The resonator of claim 3, further comprising: excitation means, adapted for generating flexural deformations of the vibrating portion, said excitation means comprising first and second electrodes which are electrically insulated from each other, said first electrode comprising, on each face of the wafer and for each primary or secondary segment, a strip of electrically conducting material which is arranged longitudinally on said segment, centrally within a width of said segment, and the second electrode comprising, also on each face of the wafer and for each primary or secondary segment, two strips on said segment which are arranged on two opposite sides of the strip of the first electrode; and detection means, adapted for measuring an amplitude of flexural deformations of the vibrating portion which are generated by the excitation means during use of the resonator, said detection means comprising a circuit for detecting an electrical current which appears in the first and second electrodes.
6. The resonator of claim 1, wherein each extension comprises, at its distal end and parallel to the midplane, a widening relative to the outer longitudinal edges of the primary and secondary segments of said extension.
7. The resonator of claim 1, further comprising an additional portion of the wafer, in the form of a segment and referred to as a stem, which extends from the interconnected proximal ends of the secondary segments, parallel to the center axis and in a direction away from the foot.
8. The resonator of claim 7, comprising two vibrating portions formed in the same wafer, provided with respective stems, said two vibrating portions being interconnected by said stems, and oriented opposite to each other so that the respective center axes of said two vibrating portions are superimposed.
9. The resonator of claim 1, comprising two vibrating portions formed in the same wafer, both vibrating portions being interconnected by the respective feet of said two vibrating portions, and oriented opposite to each other so that the respective center axes of said two vibrating portions are superimposed.
10. A force sensor, comprising the resonator of claim 8, and adapted for measuring a tensile force which is applied between the respective feet of both vibrating portions and which is parallel to the center axes of said two vibrating portions.
11. A rate gyro, comprising at least one resonator according to claim 1.
Description
BRIEF DESCRIPTION OF FIGURES
[0034] The features and advantages of the invention will become more clearly apparent from the following detailed description of some non-limiting embodiments, with reference to the appended figures which include:
[0035] FIG. 1a, already discussed, is a reminder of a first possible electrode configuration suitable for piezoelectric coupling which can be used for the excitation and detection of flexural vibrations of a beam within the plane, in the case of a beam material which is piezoelectric and belonging to the trigonal system of symmetry class 32, such as ?-quartz;
[0036] FIG. 1b, already discussed, corresponds to FIG. 1a for a second possible electrode configuration that can be used for the excitation and detection of out-of-plane vibrations;
[0037] FIG. 2a, already discussed, is a reminder of trigonal symmetry;
[0038] FIG. 2b, already discussed, shows a resonator in the form of a tuning fork as known from the prior art and obtained by chemically etching a quartz crystal, using a mixture of ammonium fluoride and hydrofluoric acid, with the breaks in symmetry that result when the two beams (tines) of the tuning fork are parallel to the Y axis;
[0039] FIG. 3a shows the momentum involved for a tuning fork with parallel beams as known from the prior art;
[0040] FIG. 3b corresponds to FIG. 3a for a tuning fork with non-parallel beams;
[0041] FIG. 3c corresponds to FIG. 3b for a double-ended tuning fork with non-parallel tines, which allows globally compensating for imbalanced momentums within each tuning fork;
[0042] FIG. 4a is a plan view of a first resonator made of trigonal piezoelectric material, which is in accordance with the invention;
[0043] FIG. 4b corresponds to FIG. 4a, showing deformations of the useful mode of vibration of the first resonator, and of the associated momentums;
[0044] FIG. 4c corresponds to FIG. 4a, showing its electrodes which allow exciting and detecting the vibration of the useful mode, in the case of a resonator made of trigonal piezoelectric crystal of symmetry class 32, such as quartz;
[0045] FIG. 4d is a section view of the first resonator, corresponding to FIG. 4c;
[0046] FIG. 5a corresponds to FIG. 4a when two possible improvements of the invention are used;
[0047] FIG. 5b corresponds to FIG. 5a, showing deformations of the useful mode of vibration;
[0048] FIG. 6a is a plan view of a second resonator made of piezoelectric material, which is also in accordance with the invention;
[0049] FIG. 6b corresponds to FIG. 6a, showing deformations of the useful mode of vibration of the second resonator;
[0050] FIG. 6c corresponds to FIG. 6a, when a possible improvement of the invention is used;
[0051] FIG. 6d corresponds to FIG. 6b for the resonator of FIG. 6c;
[0052] FIG. 7a is a perspective view of a first gyrometer in accordance with the invention, and shows deformations which are associated with a pilot mode of this first gyrometer;
[0053] FIG. 7b corresponds to FIG. 7a but shows deformations generated from the pilot mode of FIG. 7a by rotation around a first axis;
[0054] FIG. 7c corresponds to FIG. 7b for a second axis of rotation;
[0055] FIG. 7d corresponds to FIG. 7b for a third axis of rotation;
[0056] FIG. 8a shows deformations of a second gyrometer also in accordance with the invention, which are generated in a first pilot mode;
[0057] FIG. 8b corresponds to FIG. 8a, showing deformations of a first sensing mode of the second gyrometer which are generated by rotation about a first axis, starting from the first pilot mode;
[0058] FIG. 8c shows other deformations of the second gyrometer which are generated in a second pilot mode;
[0059] FIG. 8d corresponds to FIG. 8b, showing deformations of a second sensing mode of the second gyrometer which are generated by rotation about a second axis, starting from the second pilot mode;
[0060] FIG. 9a is a perspective view of the second gyrometer, showing its electrodes;
[0061] FIG. 9b is a first section view of the second gyrometer, corresponding to FIG. 9a;
[0062] FIG. 9c is a second section view of the second gyrometer, also corresponding to FIG. 9a;
[0063] FIG. 10a is a plan view of first force e sensor which is in accordance with the invention;
[0064] FIG. 10b corresponds to FIG. 10a, showing deformations associated with a useful mode of vibration of the first force sensor;
[0065] FIG. 10c corresponds to FIG. 10a, showing a static deformation of the first force sensor when subjected to an axial tensile force;
[0066] FIG. 11a corresponds to FIG. 10a for a second force sensor which is also in accordance with the invention;
[0067] FIG. 11b corresponds to FIG. 10b for the second force sensor; and
[0068] FIG. 11c corresponds to FIG. 10c for the second force sensor.
DETAILED DESCRIPTION OF THE INVENTION
[0069] For clarity sake, the dimensions of the elements shown in these figures correspond neither to actual dimensions nor to actual dimensional ratios. In particular, all the resonator deformations which are represented are enlarged to an exaggerated extent for better visibility. Furthermore, identical references indicated in different figures designate elements or measurements which are identical or which have identical functions.
[0070] A first resonator according to the invention is now described with reference to [FIG. 4a]-[FIG. 4d]. This first resonator comprises a support part or fixed part, designated by the reference Pf, a vibrating portion, and a foot Pd which connects the vibrating portion to the fixed part Pf. Preferably, the fixed part Pf, the vibrating portion, and the foot Pd are formed simultaneously by chemical etching in a wafer having parallel faces, such that the material of these three resonator portions is continuous. The wafer used can have a thickness of between several micrometers and several millimeters, when this thickness is measured perpendicularly to its faces. The vibrating portion of the resonator of [FIG. 4a]-[FIG. 4d] comprises two extensions P.sub.1 and P.sub.2 which extend from the foot Pd and which between them form a non-zero angle ?. The two extensions P.sub.1 and P.sub.2 extend symmetrically to either side of a center axis which is coincident with the longitudinal direction of the foot Pd. This center axis corresponds to the intersection between a first plane of symmetry which is parallel to the faces of the wafer and located at the mid-thickness thereof, and a second plane of symmetry which is orthogonal to the faces of the wafer and in which the two extensions P.sub.1 and P.sub.2 correspond via reflective symmetry. In the remainder of this description, and by analogy with a tuning fork resonator as described in U.S. Pat. No. 3,683,213, the two extensions P.sub.1 and P.sub.2 are also called beams P.sub.1 and P.sub.2. According to the invention, a longitudinal slot is provided in each beam P.sub.1, P.sub.2, and respectively designated by the reference FL.sub.1, FL.sub.2. These two longitudinal slots FL.sub.1 and FL.sub.2 meet at the center axis of the resonator. Each beam P.sub.i, the index i being equal to 1 or 2, is thus composed of two blades L.sub.iext and L.sub.iint. In the general part of this description, blade L.sub.1ext (respectively L.sub.2ext) was referred to as the primary segment of extension P.sub.1 (resp. P.sub.2), and blade L.sub.1int (respectively L.sub.2int) was referred to as the secondary segment of extension P.sub.1 (rasp. P.sub.2). Thus, the two blades L.sub.1ext and L.sub.2ext are connected to the foot Pd, and extend to the respective distal ends of extensions P.sub.1 and P.sub.2, where they are connected one-on-one to the two blades L.sub.1int and L.sub.2int. Each extension P.sub.1, P.sub.2 thus is meander shaped between the center axis and its distal end. In addition, blades L.sub.1int and L.sub.2int are interconnected at the center axis by respective proximal ends of these two blades L.sub.1int and L.sub.2int. The two longitudinal slots FL.sub.1 and FL.sub.2 of the respective beams P.sub.1 and P.sub.2 also meet at the center axis, such that the joining of the respective proximal ends of the two blades L.sub.1int and L.sub.2int is separated from blades L.sub.1ext and L.sub.2ext and from the foot Pd. As is shown in [FIG. 4b], when, during vibration of the resonator, the distal ends of beams P.sub.1 and P.sub.2 symmetrically move away from the center axis in opposite directions, blades L.sub.1ext and L.sub.2ext have respective momentums MV.sub.1 and MV.sub.2 which are oriented towards the same side of the resonator as the foot Pd, obliquely but symmetrically, and the joint connection of blades L.sub.1int and L.sub.2int has a momentum MV.sub.12 which is parallel to the center axis while being oriented away from the foot Pd. As a result, blades L.sub.1int and L.sub.2int have respective momentums which are oriented, obliquely but symmetrically, towards the side of the resonator which is opposite to the foot Pd. Then, according to an optimization proposed by the invention, a distribution of mass in the vibrating portion, between all the blades L.sub.1ext, L.sub.2ext, L.sub.1int and L.sub.2int, can be done such that movement of the foot Pd resulting from these momentums is zero or almost zero. Due to this lack of movement of the foot Pd, the transmission of vibrational energy from the vibrating portion to the support part Pf is zero or very low, so the quality factor of the resonator can be high. The optimized distribution of mass between the four blades of the vibrating portion is still symmetrical relative to the center axis, and can be obtained by assigning a common thickness e.sub.ext to the two blades L.sub.1ext and L.sub.2ext which is different from that of the two blades L.sub.1int and L.sub.2int, denoted e.sub.int. When such optimization is applied, the resonator is said to be balanced. The blade thicknesses e.sub.ext and e.sub.int are measured parallel to the faces of the wafer.
[0071] According to two improvements of the invention which are shown together in [FIG. 5a] but which can be used independently of each other, the vibrating portion of the resonator can be supplemented by two inertial masses MI.sub.1 and MI.sub.2 for the first improvement, and by a stem Pc for the second improvement. Preferably, the two inertial masses MI.sub.1 and MI.sub.2 are located at the distal ends of the two beams P.sub.1 and P.sub.2, and are identical. They can each be formed by widening the corresponding beam P.sub.1, P.sub.2 at its distal end. The stem Pc can be formed by an additional blade which extends from the joining of the proximal ends of blades L.sub.1int and L.sub.2int, parallel to the center axis and superimposed thereon, in a direction away from the foot Pd. Advantageously, the stem Pc is also symmetrical relative to the center axis. The addition of the two inertial masses MI.sub.1 and MI.sub.2, and/or of the stem Pc, to the vibrating portion of the resonator makes it possible to obtain balance of the resonator with additional degrees of freedom. [FIG. 5b] shows the movements of the inertial masses MI.sub.1 and MI.sub.2 as well as that of the stem Pc at the same instant during vibration of the resonator. The two inertial masses MI.sub.1 and MI.sub.2 then have momentum components along the center axis which are opposite to that of the stem Pc. These momentum components of the inertial masses MI.sub.1 and MI.sub.2 and of the stem Pc combine with those of the four blades L.sub.1ext, L.sub.2ext, L.sub.1int and L.sub.2int to produce a movement of the foot Pd which is zero or substantially zero, by applying the invention.
[0072] It should be noted that such resonator balance is naturally obtained for a tuning fork with parallel beams as known from the prior art and represented in [FIG. 3a], since the two beams P.sub.1 and P.sub.2 are identical. The momentums of the two beams P.sub.1 and P.sub.2 are again respectively denoted MV.sub.1 and MV.sub.2. Such a resonator in accordance with [FIG. 3a] does not cause movement of its foot Pd in parallel to its center axis X during its vibrations, because the momentums MV.sub.1 and MV.sub.2 are perpendicular to this center axis. Moreover, for the mode of vibration where the two beams P.sub.1 and P.sub.2 move in phase opposition, the momentums MV.sub.1 and MV.sub.2 of the two beams compensate if both beams P.sub.1 and P.sub.2 are identical. The tuning fork resonator is then balanced. There is therefore no transmission of vibrational energy by the beams P.sub.1 and P.sub.2 to the foot Pd, ignoring the deformations of this foot at the embedded ends of the two beams P.sub.1 and P.sub.2, which produce bending moments Mf.sub.1 and Mf.sub.2 and shear forces T.sub.1 and T.sub.2, all the more so when the gap separating the two beams P.sub.1 and P.sub.2 is narrow. However, as mentioned above, such a resonator with parallel and symmetrical beams cannot be produced solely by chemically etching a wafer of trigonal class 32 crystalline material, because of the etching facets which will appear and break the symmetry of shape between the two beams P.sub.1 and P.sub.2. To obtain two beams which have symmetrical shapes, it is possible to produce the resonator with its two beams P.sub.1 and P.sub.2 being parallel to axes Yc+ and Yc? of trigonal class 32 crystalline material, and with the center axis of the resonator being parallel to crystallographic axis Xc. But then the two beams P.sub.1 and P.sub.2 of the tuning fork are no longer parallel, and for this reason it becomes impossible to achieve resonator balance. Thanks to the use of longitudinal slots FL.sub.1 and FL.sub.2 according to the invention in the resonator of [FIG. 4a]-[FIG. 4d], resonator balance is again possible although its beams P.sub.1 and P.sub.2 are not parallel to each other.
[0073] However, the inventors point out that it is possible to achieve balancing of the resonator of [FIG. 3b] with its non-parallel beams, by making its vibrating portion symmetrical relative to plane Y-Z. The vibrating portion thus comprises four beams P.sub.1, P.sub.2, P.sub.3 and P.sub.4 which can have symmetrical shapes such as those resulting from chemical etching of a trigonal class 32 crystalline material. The foot Pd of the resonator is then located where the four beams intersect. In this case, the resonator is balanced for a mode of vibration in which the two tuning forks vibrate in phase. However, the double-ended tuning fork resonator configuration which is thus obtained, as represented in [FIG. 3c], is more bulky and may be poorly suited for applications where significant miniaturization is required. For such applications, the resonator of [FIG. 4a]-[FIG. 4d] or [FIG. 5a]-[FIG. 5b] may be preferred.
[0074] For the resonator of [FIG. 4a]-[FIG. 4d] or [FIG. 5a]-[FIG. 5b], the angle ? between the two beams P.sub.1 and P.sub.2 is equal to 60?. In this manner, it is possible to obtain symmetrical implementations by chemically etching a wafer having parallel faces which is made of a trigonal class 32 crystalline material, by longitudinally orienting the beams P.sub.1 and P.sub.2 to be parallel to crystallographic axes Yc+ and Yc?, and the center axis to be parallel to crystallographic axis Xc, the faces of the wafer being perpendicular to axis Z. For example, the material of the wafer can be monocrystalline ?-quartz, which is piezoelectric. In this case, the resonator can be provided with two electrodes as shown in [FIG. 4c] and [FIG. 4d]. In a known manner, these electrodes can be used both as means for exciting the symmetrical vibration mode, and as means for detecting the vibration amplitude in this same mode. The references in these two figures have the meanings listed below: [0075] for the first electrode, which can be connected to an electrical ground: [0076] PC.sub.1 segment of the first electrode which is carried by the support part Pf of the resonator [0077] el.sub.1-PC1 segment of the first electrode which is carried by the foot Pd of the resonator [0078] el.sub.1 segment of the first electrode which is carried by blade L.sub.1ext along an outer edge thereof, on a first of the two faces of the wafer [0079] el.sub.3 segment of the first electrode which is carried by blade L.sub.1ext along an internal edge thereof, on the first face of the wafer [0080] el.sub.4 segment of the first electrode which is carried by blade L.sub.1int along an internal edge thereof, on the first face of the wafer [0081] el.sub.6 segment of the first electrode which is carried by blade L.sub.1int along an outer edge thereof, on the first face of the wafer [0082] el.sub.7 and el.sub.9 respectively correspond to el.sub.6 and el.sub.4, for blade L.sub.2int [0083] el.sub.10 and el.sub.12 respectively correspond to el.sub.3 and el.sub.1, for blade L.sub.2ext [0084] el.sub.1-6 electrical connection segment between segments el.sub.1 and el.sub.6 at the distal end of beam P.sub.1, on the first face of the wafer [0085] el.sub.3-4 electrical connection segment between segments el.sub.3 and el.sub.4 at the distal end of beam P.sub.1, on the first face of the wafer [0086] el.sub.7-9 electrical connection segment between segments el.sub.7 and el.sub.9 at the distal end of beam P.sub.2, on the first face of the wafer [0087] el.sub.10-12 electrical connection segment between segments el.sub.10 and el.sub.12 at the distal end of beam P.sub.2 and on the first face of the wafer.
First electrode segments el.sub.6 and el.sub.7 are interconnected at the center axis, as are segments el.sub.4 and el.sub.9, and as are segments el.sub.3 and el.sub.10. [0088] for the second electrode, which can be connected to a source of alternating voltage V: [0089] PC.sub.2 and el.sub.2-PC2 respectively correspond to PC.sub.1 and el.sub.1-PC1, and for the second electrode [0090] el.sub.2 segment of the second electrode which is carried by blade L.sub.1ext in a central part thereof, on the first face of the wafer [0091] el.sub.5, el.sub.8 and el.sub.11 correspond to el.sub.2 for blades L.sub.1int, L.sub.2int and L.sub.2ext respectively [0092] el.sub.2-5 electrical connection segment between segments el.sub.2 and el.sub.5 at the distal end of beam P.sub.1, on the first face of the wafer.
Second electrode segments el.sub.5 and el.sub.8 are interconnected at the center axis, as are segments el.sub.2 and el.sub.11.
Electrode segments el.sub.10n, the integer index n varying from 1 to 12, respectively correspond to segments el.sub.n for the second face of the wafer, with electrical connection segments which are similar to those described for the first face of the wafer. Lastly, the segments of a same electrode of the two electrodes which are located on each of the two faces of the wafer are electrically interconnected, either by an electrical connection carried by the resonator, or by an external electrical connection.
[0093] Each electrode segment may be composed of a strip of conducting material such as gold (Au), for example deposited using a thin film deposition technique, and have a width equal to 200 ?m (micrometers). In accordance with the list just provided, three parallel strips are arranged on each blade face, meaning a total of twelve conducting strips per face of the wafer, el.sub.1 to el.sub.12 on the first face and el.sub.101 to el.sub.112 on the second face. As already explained with reference to [FIG. 1a], the three conducting strips on each blade face enable excitation and detection which are effective for flexural vibrations of the blade that are parallel to plane Xc-Yc, when this blade extends longitudinally along crystallographic axis Yc+ or Yc?. For increased efficiency of the piezoelectric coupling, it is advantageous for the strips of the first electrode to be relatively thin, with strip widths that are between 1/10 and ? of the thickness e.sub.ext or e.sub.int of the blades L.sub.1ext, L.sub.2ext, L.sub.1int and L.sub.2int. For the strips of the second electrode, their widths can be between two and five times those of the strips of the first electrode.
[0094] Such a layout for electrodes for vibration excitation and detection by piezoelectric effect is suitable for the mode of flexural vibration where the two beams P.sub.1 and P.sub.2 move in phase opposition, as shown in [FIG. 4b]. However, other electrode configurations are alternatively possible, for example by depositing strips of conducting material on the sides of the blades which are perpendicular to the faces of the wafer. In this case, strips el.sub.1 and el.sub.101 are replaced by a single strip on the side of blade L.sub.1ext, and similarly for the pairs of strips of the first electrode which are separately carried by the other strips L.sub.1int, L.sub.2int and L.sub.2ext. Each blade side then carries two strips which are each close to the edge of the side that is opposite to that of the other strip, with one of the two strips belonging to the first electrode, and the other strip belonging to the second electrode. This other electrode configuration is more efficient than that of [FIG. 4c]-[FIG. 4d] for piezoelectric coupling, but at the cost of greater complexity in its production.
[0095] The resonator can thus be associated with an electronic oscillator loop, which is connected to the input of segments PC.sub.1 of the first electrode on the support part Pf of the resonator, and to the output of segments PC.sub.2 of the second electrode, also on the support part Pf. The mode of vibration in which the two beams P.sub.1 and P.sub.2 move in phase opposition is thus excited by the alternating voltage V applied by the electronic oscillator loop between the two electrodes, and the vibration amplitude of the resonator for this same mode is detected by the electrical current generated in the two electrodes by the vibrations 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.
[0096] The inventors now provide some rules which allow balancing, according to the invention, of a resonator in accordance with [FIG. 4a]-[FIG. 4d], i.e. without the inertial masses MI.sub.1, MI.sub.2 or the stem Pc. The resonator frequency F for the mode of flexural vibration, where the two beams P.sub.1 and P.sub.2 move symmetrically in phase opposition, can be approximated using the following equation (equation 1):
[00001]
with the following meanings, some of which have already been provided: [0097] e.sub.int: common thickness of blades L.sub.int1 and L.sub.2int, measured parallel to the faces of the wafer and expressed in meters [0098] e.sub.ext: common thickness of blades L.sub.1ext and L.sub.2ext, measured parallel to the faces of the wafer and expressed in meters [0099] L.sub.int: common length of blades L.sub.1int and L.sub.2int, expressed in meters [0100] L.sub.ext: common length of blades L.sub.1ext and L.sub.2ext, expressed in meters [0101] F.sub.l: common width of longitudinal slots FL.sub.1 and FL.sub.2 in extensions P.sub.1 and P.sub.2, measured parallel to the faces of the wafer and expressed in meters [0102] E: Young's modulus of the wafer material, expressed in newtons per square meter (N/m.sup.2) [0103] ?: density of the wafer material, expressed in kilograms per cubic meter (kg/m.sup.3).
[0104] To allow compensation at the foot Pd for the momentum components that are parallel to axis Xc, it is also necessary for dimensions e.sub.int, e.sub.ext, L.sub.1int and L.sub.ext to satisfy the following condition (equation 2):
[00002]
However, this condition means that slenderness L.sub.ext/e.sub.ext of each of blades L.sub.1ext, L.sub.2ext is greater than slenderness L.sub.int/e.sub.int of each of blades L.sub.1int, L.sub.2int. Equation 2 can also be written in the following form (equation 3):
[00003]
Positivity of 1?k makes it possible to give a first bound for quotient e.sub.ext/e.sub.int: this quotient is greater than 0.4.
Moreover, by construction, the following equation links the lengths of blades L.sub.ext and L.sub.int, via the angle ? which separates the two beams P.sub.1 and P.sub.2 (equation 4):
[00004]
These last three equations, with the five unknowns e.sub.ext, e.sub.int, L.sub.ext, L.sub.int and F.sub.l, allow the person skilled in the art to choose the dimensions of the resonator according to the intended applications and the technological constraints, in particular according to the space available for the resonator in each application.
[0105] For example, with a crystal wafer of the trigonal system of symmetry class 32, such as ?-quartz which is piezoelectric, and for an angle ? of 60? between the two beams P.sub.1 and P.sub.2, each oriented parallel to a crystallographic axis Yc, one parallel to Yc+ and the other to Yc?, to guarantee symmetry of the resonator as obtained by chemical etching as has already been explained, it is possible to calculate the dimensions of a balanced resonator with a slenderness P.sub.int=L.sub.int/e.sub.int common to blades L.sub.1int and L.sub.2int which is between 3 and 10, and another slenderness P.sub.ext=L.sub.ext/e.sub.ext common to blades L.sub.1ext and L.sub.2ext which is between 8 and 30, and with a quotient e.sub.int/e.sub.ext which is between 1 and 5. For example, L.sub.1int?2.5 mm (millimeters), e.sub.int?0.24 mm, L.sub.ext?3.3 mm, e.sub.ext?0.15 mm, and F.sub.l?0.27 mm, producing a vibration frequency F of the resonator which is equal to 32 kHz (kilohertz). This same value of 32 kHz for the frequency F can also be obtained with L.sub.int?4.95 mm, e.sub.int?1.5 mm, L.sub.ext?8.9 mm, e.sub.ext?1.7 mm, and F.sub.l?0.7 mm, which shows the extent of the dimensional possibilities for obtaining a balanced resonator when using the invention.
[0106] For resonators intended for flexural vibration, the intrinsic quality factor of the resonator is limited by the thermoelastic losses generated by heat exchange between the fibers of each blade which are compressed and stretched during vibration, as has been theorized in the article by C. Zener, entitled Internal friction in solids, Physical Review 52, August 1937, pp. 230-235. In the case of quartz and for a simple beam having flexural vibration at a frequency 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 vibrating thickness: Q.sub.thermoelastic(quartz)?F.Math.e.sup.2. In the case of silicon and for the same frequency interval, this thermoelastic factor is proportional to the frequency F of the resonator divided by the square of the vibrating thickness e: Q.sub.thermoelastic(silicon)?F/e.sup.2, which leads to very different dimensional determinations for the resonators, between these two crystals. Thus, in the case of quartz and when frequency stability performance is desired for the resonator, dimensional determinations which correspond to significant values for the thicknesses e.sub.int and e.sub.ext are preferred, and conversely for silicon.
[0107] In comparison to a resonator configuration in accordance with [FIG. 4a], adding the stem Pc modifies the momentum which is generated along axis Xc by the vibration: a momentum component of the stem Pc is added to those of the blades L.sub.1int and L.sub.2int. It thus makes it possible to increase the possibilities for dimensional determinations which produce resonator balance. In particular, the addition of the stem Pc allows increasing thickness e.sub.ext of blades L.sub.1ext and L.sub.2ext in comparison to the configuration of [FIG. 4a] which has no stem.
[0108] Again in comparison to a resonator configuration in accordance with [FIG. 4a], the addition of inertial masses MI.sub.1 and MI.sub.2 to the distal ends of beams P.sub.1 and P.sub.2 also makes it possible to modify the distribution of momentum between all parts of the vibrating portion. In particular, the addition of inertial masses MI.sub.1 and MI.sub.2 allows increasing thickness e.sub.int of blades L.sub.1int and L.sub.2int for an equal value of their length L.sub.int.
[0109] The resonator of [FIG. 6a] or [FIG. 6c] corresponds to that of [FIG. 5a] but with angle ? being equal to 180? instead of 60?, with no stem for [FIG. 6a] and with a stem Pc for [FIG. 6c]. The lengths of blades L.sub.ext and L.sub.int then become equal, and the condition of equation 3 for balance of the resonator, previously provided for a resonator with no stem Pc and no inertial masses MI.sub.1 and MI.sub.2, can no longer be satisfied. The inertial masses MI.sub.1 and MI.sub.2 are necessary when angle ? is equal to 180?, in order to compensate for the momentums. The mode of vibration shown in [FIG. 6b] when the resonator has no stem, or in [FIG. 6d] when the resonator includes the stem Pc, corresponds primarily to a continuous flexural vibration of the blade which is the union of the above two blades L.sub.1int and L.sub.2int, with a total length equal to the sum of their individual lengths, and again with thickness e.sub.int. The frequency F of the resonator for this mode of vibration can be approximated by the following equation (equation 5):
[00005]
where: [0110] L.sub.int: total blade length measured between the two inertial masses MI.sub.1 and MI.sub.2, and expressed in meters [0111] e.sub.int: width of the blade which is opposite to the foot Pd, measured parallel to the faces of the wafer and expressed in meters [0112] L.sub.c: length of the stem Pc, measured parallel to the faces of the wafer and expressed in meters [0113] e.sub.c: width of the stem Pc, measured parallel to the faces of the wafer and expressed in meters. [0114] E: Young's modulus of the wafer material, expressed in newtons per square meter (N/m.sup.2) [0115] ?: density of the wafer material, expressed in kilograms per cubic meter (kg/m.sup.3).
[0116] To allow compensating for the momentums along axis Xc, it is also necessary that dimensions e.sub.int, e.sub.ext, L.sub.int, e.sub.Mi, L.sub.c and e.sub.c satisfy the following double inequality (equation 6):
[00006]
with the following additional meanings: [0117] e.sub.ext: width of the blade that is connected to the foot Pd, measured parallel to the faces of the wafer and expressed in meters [0118] e.sub.Mi: common width of inertial masses MI.sub.1 and MI.sub.2, measured parallel to the blades and expressed in meters [0119] L.sub.Mi: common length of inertial masses MI.sub.1 and MI.sub.2, measured parallel to axis Xc and expressed in meters [0120] J: moment of inertia per unit surface area of inertial masses MI.sub.1 and MI.sub.2, which is equal to (equation 7):
J=L.sub.Mi.Math.e.sub.Mi.Math.(L.sub.Mi.sup.2+e.sub.Mi.sup.2)
The double inequality of equation 6 makes it possible to determine the dimensions of the resonators of [FIG. 6a]-[FIG. 6d] so that they are balanced, based on certain values which are initially chosen according to the desired characteristics of these resonators,
[0121] It is possible that the dimensional determination for each of the resonators presented above, using the rules provided above, could be continued using numerical simulations such as finite element calculations, to achieve more precise balancing of these resonators.
[0122] A resonator as described above can be used to form a gyrometer with one or more sensitive axes. A sensitive axis of a gyrometer is an axis of rotation for which the gyrometer allows measuring the rotational speed about this axis. To obtain a gyrometer with three sensitive axes, making it possible to measure rotational speed components respectively along axes X, Y, and Z, a resonator is necessary for which the angle ? is different from 0? and from 180?. Such a resonator for which the angle ? is equal to 60? is preferred. During rotation of the resonator, Coriolis acceleration produces additional displacement of each blade of the resonator, which is perpendicular to the displacement of this blade for pilot mode. [FIG. 7a] recalls the simultaneous displacements of beams P.sub.1 and P.sub.2, as well as of stem Pc, for a resonator in accordance with the invention where a is equal to 60?, and when the mode of vibration which is excited by electrodes, i.e. pilot mode, is the one where the two beams P.sub.1 and P.sub.2 move in phase opposition parallel to the faces of the wafer, in the manner of a tuning fork. MV.sub.1, MV.sub.2, and MV.sub.c designate the respective momentums of beams P.sub.1, P.sub.2 and of stem Pc. [FIG. 7b] shows the corresponding Coriolis accelerations, denoted ?.sub.C, which are produced by rotation about axis X, with rotational speed ?.sub.y; [FIG. 7c] shows those produced by rotation about axis Y, with rotational speed ?.sub.y; and [FIG. 7d] shows those produced by rotation about axis Z, with rotational speed ?.sub.z. These Coriolis accelerations are perpendicular to the wafer for rotations about axes X and Y, with the symbol of a dot surrounded by a circle representing a Coriolis acceleration directed towards the reader, and a cross surrounded by a circle representing a Coriolis acceleration oriented in the direction of the reader's gaze. However, the inertial forces which result from these Coriolis accelerations do not compensate at the foot Pd, so it is preferable to provide additional means to limit the losses of vibrational energy occurring through the foot Pd of the resonator. For example, a decoupling structure as described in U.S. Pat. No. 6,414,416, filed by the Applicant, could be used for a gyrometer having a single sensitive axis which is axis X (see [FIG. 7b]), since this decoupling structure is effective in reducing or avoiding a transmission of torsional moments to the attachment part of the resonator via its foot Pd. For a gyrometer with only one sensitive axis which is axis Y (see [FIG. 7c]), the mode of vibration coupled to the pilot mode of [FIG. 7a] by rotational speed ?y is a mode where the two beams P.sub.1 and P.sub.2 undergo out-of-plane bending in phase, and the stem Pc undergoes out-of-plane bending in phase opposition to beams P.sub.1 and P.sub.2. But the resulting forces do not compensate at the foot Pd of the resonator, and a residual moment is transmitted to the attachment part of the resonator via its foot Pd. The forces generated during rotation about axis Z (see [FIG. 7d]) from the pilot mode of [FIG. 7a] are parallel to the wafer, but also do not compensate.
[0123] To achieve compensation of the forces and moments transmitted to the attachment part Pf of the resonator, a new pyrometer is proposed by the invention, which comprises two vibrating portions each similar to that of [FIG. 7a], facing away from each other and with a common foot Pd. Both vibrating portions are fabricated from the same wafer, so their material is continuous across the foot Pd. Such a gyrometer, which is shown in [FIG. 8a]-[FIG. 8d], is effective for measuring rotations about axis X or about axis Y. Two excitation modes of vibration are possible as pilot modes, each of them preserving the balance provided by the double-resonator structure: a phase-opposition mode, in which the two beams P.sub.1 and P.sub.2 of one of the vibrating portions move apart and move towards each other in phase opposition relative to beams P.sub.3 and Pd of the other vibrating portion, as shown in [FIG. 8a], and an in-phase mode, in which the two beams P.sub.1 and P.sub.2 of one of the vibrating portions move apart and move towards each other in phase with beams P.sub.3 and P.sub.4 of the other vibrating portion, as shown in [FIG. 8c]. In these two figures, each MV label designates the momentum of the beam or of the stem on which it is superimposed. [FIG. 8b] shows the compensation in the inertial forces which result from Coriolis accelerations ?.sub.C for the excitation mode of vibration of [FIG. 8a] used as pilot mode, and [FIG. 8d] for the excitation mode of vibration of [FIG. 8c] used as pilot mode. One of these two excitation modes is selected as the pilot mode via the configuration of the electrodes on the two vibrating portions. For example, in the case of piezoelectric quartz crystal or any other piezoelectric crystal in the same symmetry class, the gyrometer can be composed of two vibrating portions located head to tail, each with two beams forming an angle of 60? between them, such that these beams are parallel to crystallographic axes Yc+ and Yc?. [FIG. 9a]-[FIG. 9c] show a set of strips of conducting material which are arranged on the faces of all segments of the two vibrating portions. The two vibrating portions are respectively designated by the letters A and B, and correspond to the section view of [FIG. 9b] for vibrating portion A, and to the section view of [FIG. 9c] for vibrating portion B.
[0124] For a gyrometer in which the sensitive axis is axis X, parallel to crystallographic axis Xc, the pilot mode is the one where the two resonators vibrate in phase opposition, as illustrated by [FIG. 8a]. It is then possible to apply the teachings of US Pat. No. 2012/279303, filed by the Applicant, to limit the capacitive couplings between pilot mode and sensing mode. According to these teachings, strips el.sub.3-A, el.sub.103-A, el.sub.4-A, el.sub.104-A, el.sub.9-A, el.sub.109-A, el.sub.10-A, el.sub.110-A, el.sub.3-B, el.sub.103-B, el.sub.4-B, el.sub.104-B, el.sub.9-B, el.sub.110-B, el.sub.110-B are used to excite pilot mode by electrically connecting them to a source of alternating voltage V, and el.sub.2-A, el.sub.102-A, el.sub.5-A, el.sub.105-A, el.sub.8-A, el.sub.108-A, el.sub.11-A and el.sub.1110-A are used to detect the amplitude of the pilot mode. Thus, strips el.sub.1-A, el.sub.101-A, el.sub.6-A, el.sub.106-A, el.sub.7-A, el.sub.107-A, el.sub.12-A, el.sub.112-A, el.sub.1-B, el.sub.101-B, el.sub.6-B, el.sub.106-B, el.sub.7-B, el.sub.107-B, el.sub.12-B and el.sub.112-B can be used to detect movements which are generated by rotation about axis X, but by connecting strips el.sub.1-A, el.sub.6-A, el.sub.7-A, el.sub.12-A, el.sub.1-B, el.sub.6-B, el.sub.7-B and el.sub.12-B on the one hand, and strips el.sub.101-A, el.sub.106-A, el.sub.107-A, el.sub.112-A, el.sub.101-B, el.sub.107-B and el.sub.112-B on the other hand, respectively to the input terminals of a differential amplifier which is part of an electrical current detector.
[0125] For a gyrometer whose sensitive axis is axis Y, perpendicular to axis Xc of the crystal and in the common plane of axes Xc, Yc+, and Yc?, the pilot mode is the one with the two resonators which vibrate in phase, as illustrated by [FIG. 8c], el.sub.1-A, el.sub.101-A, el.sub.6-A, el.sub.106-A, el.sub.7-A, el.sub.107-A, el.sub.12-A, el.sub.112-A, el.sub.1-B, el.sub.101-B, el.sub.6-B, el.sub.106-B, el.sub.7-B, el.sub.107-B, el.sub.12-B and el.sub.112-B then make it possible to excite this pilot mode by connecting them to the source of alternating voltage V, and strips el.sub.2-A, el.sub.102-A, el.sub.5-A, el.sub.105-A, el.sub.8-A, el.sub.108-A, el.sub.11-A, el.sub.111-A, el.sub.2-B, el.sub.102-B, el.sub.5-B, el.sub.105-B, el.sub.8-B, el.sub.108-B, el.sub.11-B and el.sub.111-B are used to detect the amplitude of the pilot mode. In this case, strips el.sub.3-A, el.sub.103-A, el.sub.4-A, el.sub.104-A, el.sub.9-A, el.sub.109-A, el.sub.10-A, el.sub.110-A, el.sub.3-B, el.sub.103-B, el.sub.4-B, el.sub.104-B, el.sub.9-B, el.sub.109-B, el.sub.10-B and el.sub.110-B can be used to detect movements which are generated by rotation about axis Y, but connecting by strips el.sub.3-A, el.sub.4-A, el.sub.9-A, el.sub.10-A, el.sub.103-B, el.sub.104-B, el.sub.10-B and el.sub.110-B on the one hand, and strips el.sub.103-A, el.sub.104-A, el.sub.109-A, el.sub.110-A, el.sub.3-B, el.sub.4-B, el.sub.9-B et el.sub.10-B on the other hand, respectively to the input terminals of the differential amplifier which is part of the electrical current detector.
[0126] Another application of resonators according to the invention is the implementation of a force sensor. The force sensor, as shown in [FIG. 10a], is based on two identical vibrating portions which are again produced in a same wafer, again oriented to be opposite to each other but which are joined by their stems Pc. Each of the two vibrating portions is sized to be individually balanced. Beams P.sub.1 and P.sub.2 of one of the two vibrating portions, and beams P.sub.3 and P.sub.4 of the other vibrating portion, between them form angles of 60?. This association of the two vibrating portions makes it possible to obtain a double-resonator whose two ends, formed by the respective feet of the individual vibrating portions, are without or almost without residual motion, as shown by [FIG. 10b], for a mode of vibration where the two vibrating portions vibrate in phase opposition. When this sensor is subjected to an axial tensile force, the static deformation imposed on the double-resonator modifies its flexural inertia. [FIG. 10c] shows this static deformation for axial tensile force T.
[0127] If such a force sensor is made of quartz crystal, two configurations are possible, which correspond either to an angle ? which is equal to 60?, as shown in [FIG. 10a]-[FIG. 10c], or to an angle ? which is equal to 180?, as shown in [FIG. 11a]-[FIG. 11c]. Thus, [FIG. 11a] shows the configuration with two vibrating portions for which beams P.sub.1 and P.sub.2 on the one hand, and P.sub.3 and P.sub.4 on the other hand, form an angle of 180? between them. [FIG. 11b] shows an instantaneous deformation of the double-resonator structure of [FIG. 11a], for the mode of vibration of interest where the two vibrating portions vibrate in phase. [FIG. 11c] shows the static deformation of the same force sensor when it is subjected to axial tensile force T. For the case where the angle ? is equal to 180?, the variation in relative frequency F of the mode of vibration considered, induced by axial tensile force T, is proportional to (equation 8):
[00007]
Using Equation 8, those skilled in the art can determine the dimensions of the force sensor according to each application and to the measurement sensitivity that is appropriate for it.
[0128] It is understood that the invention can be reproduced by modifying secondary aspects of the embodiments described in detail above, while retaining at least some of the cited advantages. In particular, the material of the wafer is not necessarily a piezoelectric monocrystalline material. For example, the wafer can be made of monocrystalline or polycrystalline silicon, or it can be a piezoelectric ceramic, or a combination of a metal and piezoelectric ceramics. The means for vibration excitation and detection must then be adapted according to each material. For example, excitation can be achieved using electrostatic forces, magnetic force, or by implementing a photo-thermal effect, etc., and detection can be achieved by measuring a variation in the capacitance of a capacitor formed between a portion of the resonator which is moving and a portion which is stationary, or by using a piezoresistive effect, or by measuring with optical interferometry, etc. Finally, all the numerical values that have been cited have been provided for illustration purposes only, and may be changed according to the application considered.
