Vibration gyrometer with planar structure

Abstract

The inertial angular position sensor comprises at least three equivalent resonators (R1 to R3) arranged symmetrically around the sensitive axis (AA) of the sensor. As a result, a gyrometer constituted by said sensor has an integrating function. Said sensor further comprises a connecting element (Ec) connecting the vibrating part of each resonator to the vibrating parts of all other resonators of the sensor. The preferred configuration of the inertial angular position sensor makes it possible to obtain an integrating gyrometer with high sensitivity and low manufacturing costs.

Description

Detailed Description of the Invention

[0001] [Technical field] The present invention relates to an inertial angular position sensor and a gyrometer comprising said sensor. The present invention provides several models of gyrometers with planar structures, which can be manufactured by an integral etching process, each of which provides the functionality of an integrated gyrometer. The present invention applies to both piezoelectric materials, such as quartz crystals, and to other crystalline materials (e.g. silicon) common in the field of microsystems.

[0002] [Prior art] As is known, it is possible to form a gyrometer from at least one vibrating part having at least two distinct vibration modes, which can be coupled to each other by a rotation applied to the at least one vibrating part. The gyrometer then comprises, in addition to the (at least one) vibrating part, (i) means for exciting one of the two vibration modes (called pilot mode) and (ii) means for detecting the amplitude of the vibration in the other mode (called sensing mode).

[0003] In the objects called integrating gyrometers, the value measured directly is not the rotation rate, but the value corresponding to the angle of rotation of the gyro with respect to the Galilean reference frame. This principle of operation is known as the "inertia of oscillating bodies" and was demonstrated in 1851 by Léon Foucault using a pendulum. It concerns the resulting expression of the inertial forces revealed by Gustave Coriolis when they act on one or more resonators that do not have any preferred axis of oscillation. The direct measurement of the result of the time integral of the angular velocity can be very useful in highly dynamic applications and when information on the angular deviation is essential. This is the case, for example, especially in inertial navigation applications.

[0004] As theorized by Lord Bryan in his 1892 paper "On a revolving cylinder or bell", Proceedings of the Cambridge Philosophical Society, Volume VII, October 28, 1889 - May 30, 1892, the well-known integrating gyrometer uses a hemispherical resonator or bell. In this resonator configuration, rotation produces a partial entrainment of the resonator vibration due to partial transfer of vibrational energy between two degenerate modes in the resonator.

[0005] As is known, two vibration modes are said to be degenerate if they (i) correspond to distinct categories of geometric distortions (deformations) of the resonator, but (ii) have the same vibration frequency value. Throughout this specification, a vibration mode of a resonator or an inertial angular position sensor is simply referred to as one of its natural vibration modes. That is, in the absence of external interference, the vibrations in the process in this mode continue without mixing with another natural vibration mode of the resonator or sensor. In the case of a gyrometer, it is the Coriolis force that causes the coupling between the two natural modes. As a result, the vibrations excited according to one of the two natural modes are partially or completely transmitted to the other natural mode. The intensity of this transmission of vibration energy gives a measure of the rotation rate, or, in the case of an integrating gyrometer, a measure of the rotation angle.

[0006] Another example of an integrating gyrometer is based on a beam that is designed (intended) to oscillate in bending. This beam is made of an isotropic material and has a cross section such that its bending inertia is equivalent in at least two different bending directions. This is especially true if the cross section of the beam is a circle, a square or an isosceles triangle, and more generally if the beam does not have a preferred axis of bending vibration, in contrast to a beam with a rectangular cross section. The reader will understand that (i) any asymmetry in the beam or in the embeddings in the support may destroy the desired effect, and (ii) in order to obtain the inertia of the vibration, the vibrating part must be considered isolated from the outside world. This means that the vibration does not depend on the mounting of the vibrating part. Furthermore, the material of the vibrating part may need to have a symmetry suitable for the vibration considered.

[0007] For a resonator in the form of a microsystem, a planar structure is required, which allows it to be easily realized by a wafer-based monolithic manufacturing process of the material chosen to form the resonator(s) in the gyrometer. Traditionally, this material is silicon, either monocrystalline or polycrystalline, or quartz crystal.

[0008] In silicon-based resonators, the movement of the mass is usually set by using electrostatic forces, and the movement thus caused is usually detected by capacitance measurements made on at least one capacitor formed between a moving part and a fixed part.

[0009] In the case of resonators made of piezoelectric materials, the useful excitation of vibrations due to the piezoelectric effect, and the useful signals to be detected, no longer come from motion, but from mechanical stress or strain. As a result, resonator structures in which the stresses and strains are distributed over the extended area of ​​the resonator are more suitable for piezoelectric materials than structures in the form of non-deformable inertial masses associated with springs, where the stresses and strains are present only in the parts of the material acting as said springs.

[0010] In the paper "The theory of a piezoelectric disc gyroscope", JS Burdess et al., IEEE Transactions on Aerospace And Electronic Systems, 1986, Volume: AES-22, issue 4, an integrating gyrometer is proposed, which has a planar structure and is made of piezoelectric material. The resonator considered in the paper has a disk shape. The two degenerate modes of vibration of the resonator are selected by the design of the excitation and detection electrodes. The vibration electronics allow to follow the natural precession of the vibration when the resonator is subjected to an axial rotation orthogonal to the disk. The main drawback of this gyro arises from the great sensitivity of the resonator to the mounting conditions: the mounting area, located in the center of the disk, must be large enough to allow an effective mounting of the resonator. However, the mounting area strongly changes the frequency and the damping of the two useful modes of vibration. In most cases, the mounting area causes losses in the degeneracy of the two modes, making it difficult or even impossible to function as an integrating gyrometer. For example, in FR 2,723,635, improvements are proposed by using higher order modes, but sufficient isolation of the resonator from the environment is not achieved.

[0011] A disk shape according to the resonator has also been used with silicon material, by proposing an apertured disk that allows the insertion of means for excitation by electrostatic forces and for capacitive detection of the vibration modes, as described in US 7,040,163. However, as is the case with disks made of piezoelectric material, a central mounting does not allow a sufficient degeneracy of the vibration modes, and requires the use of complex and expensive balancing and / or electronic compensation techniques.

[0012] Other vibrating structures implement non-deformable masses connected to (i) rigid bodies and (ii) connection means between the masses, as described in the paper "Flat is not dead: current and future performance of Si-MEMS Quad Mass Gyro (QMG) system", AA Trusov et al., DOI: 10.1109 / PLANS.2014.6851383. The structure described in that paper consists of four masses connected to each other in pairs by a system of levers to enforce anti-phase motion. However, these levers are complex to manufacture and require a high level of manufacturing precision to obtain symmetry between the vibration modes in the plane of the structure. This structure therefore requires the introduction of auxiliary systems to balance the useful modes, in particular by adding electrostatic rigid bodies.

[0013] Document CN 106,441,261A describes a micromechanical gyro with four seismic masses connected to an inner and an outer ring. The connections to the inner ring are made by levers. The whole gyro is invariant to a rotation of 90°.

[0014] [Technical issues] Based on this situation, it is an object of the present invention to provide a novel inertial angular position sensor for an integrating gyrometer, which, as mentioned above, improves on at least some of the drawbacks of conventional sensors.

[0015] A secondary object of the present invention is to provide a sensor in which the vibration energy loss to the outside is reduced, resulting in an increased quality factor value and making it easier to obtain the two degenerate modes.

[0016] Another secondary object of the present invention is to reduce symmetry defects that may affect the shape of the sensor when it is fabricated by a wet chemical etching process, which is a low cost manufacturing process due to the difference in etch rates that exist between different crystal orientations of the material used to form the sensor.

[0017] [Summary of the Invention] To achieve at least one of these or other objects, a first aspect of the invention proposes a novel inertial angular position sensor, said sensor comprising at least three identical resonators arranged symmetrically around an axis called the sensitive axis, said resonators being invariant to a rotation of 2π / n around this sensitive axis, n being the number of resonators of the sensor. The n resonators are connected to each other such that the sensor has at least two degenerate modes of vibration, which makes it possible to characterize the rotation of the sensor around the sensitive axis.

[0018] According to a first configuration of the sensor of the invention, each resonator comprises a respective part of a wafer having two flat and parallel opposing faces. The part of the wafer dedicated to each resonator is designed to vibrate when the sensor is in use and is called the vibrating part of that resonator. Moreover, the wafer is common to the n resonators of the sensor.

[0019] According to a second configuration of the sensor of the invention, each vibrating portion is designed to vibrate in bending when the sensor is in use.

[0020] Finally, according to a third configuration of the sensor of the invention, the sensor further comprises a connecting element, which connects the oscillating part of each resonator to all other oscillating parts of the n resonators of the sensor. The connecting element is also invariant to a rotation of 2π / n about the sensing axis. The oscillating parts of the n resonators are angularly distributed around the connecting element.

[0021] The sensor of the present invention can be manufactured industrially at low cost using wafer-based monolithic manufacturing processes designed to form the vibrating portions of each of the n resonators.

[0022] In addition, the inertial angular position sensor of the present invention is suitable to be part of an integral gyrometer, since it has two degenerate modes of vibration, in which vibration energy is likely to be transferred from one mode to another by a rotation about a sensitive axis relative to the Galilean reference frame to which the sensor is subjected. More precisely, the value of the number of individual resonators forming the sensor (3 or more) allows the existence of a pair of degenerate modes of vibration to be combined with the possibility of a rotation about a sensitive axis transferring energy between the degenerate modes. As mentioned above, the two degenerate modes have a common vibration frequency value. However, the sensor may have several vibration frequency values, respectively associated with the two degenerate modes of vibration.

[0023] Finally, the connection elements of the sensor of the invention are invariant to a rotation of 2π / n about the sensitive axis of the sensor, so that for a rotation about the sensitive axis to be measured, the degeneracy between the two modes of vibration of the set of resonators can be maintained while ensuring good efficiency when transferring vibration energy between the two degenerate modes of vibration, thus providing the sensor with high detection and measurement sensitivity for the gyrometer in which it is incorporated.

[0024] Preferably, the number n of resonators in the sensor is eight or less.

[0025] Preferably, each vibrating portion may be designed to vibrate in flexure parallel to the plane of the wafer when the sensor is in use.

[0026] Preferably, the connection elements may consist of a pattern formed in a wafer integral with (integral with) the respective vibrating parts of the resonators of the sensor.

[0027] According to a fourth configuration of the invention, the vibrating part of each resonator is connected to the support of the sensor, located outside the vibrating part and the connection element, by intermediate segments of the wafer called feet, which are integrated with the vibrating part and form the connection between the vibrating part and the support, and for each resonator:

[0028] The vibrating part of this resonator has (i) a first plane of symmetry (called the mid-plane) parallel to both faces of the wafer and equidistant from these two faces, and (ii) a second plane of symmetry (called the plane of symmetry orthogonal to the wafer) perpendicular to the mid-plane and passing longitudinally through the connection formed by the feet located between the support part and the vibrating part: The intersection of (i) the mid-plane and (ii) the plane of symmetry perpendicular to the wafer defines the central axis of the vibrating part: The vibrating part has two extensions, each of which is designed to vibrate in bending, which extend symmetrically from the foot on either side of a plane of symmetry perpendicular to the wafer: Each extension is provided with a longitudinal slot which runs from the plane of symmetry perpendicular to the wafer towards the distal end of the extension, but does not reach the distal end, passing through the vibrating portion perpendicular to the mid-plane, so that each extension has a serpentine shape: The slots of both extensions are symmetrical with respect to a plane of symmetry perpendicular to the wafer and intersect in this plane of symmetry perpendicular to the wafer. As a result, the vibrating part comprises two primary segments and two secondary segments. The two primary segments each connect a foot to a distal end of one of the extensions. The two secondary segments are interconnected by their respective proximal ends in the plane of symmetry perpendicular to the wafer. Each of the two secondary segments extends to a distal end of one of the extensions and is connected at its distal end to one of the segments of the primary segment.

[0029] According to the above configuration of the vibration parts of each of the resonators of the sensor, for both degenerate modes of vibration of the sensor that allow to characterize the rotation around the sensitive axis, the vibration parts only involve a movement that is parallel to the midplane and symmetrical with respect to a plane of symmetry perpendicular to the wafer. Moreover, both primary segments have, at each instant during the vibration, an instantaneous velocity component that is parallel to the central axis, the direction of which is opposite to that of the instantaneous velocity component of the secondary segments, which is also parallel to the central axis. These opposite velocity orientations allow some of the momentum components associated with them to at least partially compensate each other for each resonator. The movement transmitted by the vibration parts to the feet of this resonator is therefore reduced. As a result, the resonator has low vibration energy losses. Its quality factor can therefore be high. For this reason, the quality factor of the sensor effective for each of the two degenerate vibration modes is also high.

[0030] Advantageously, for each resonator, each degenerate mode of vibration of the sensor, which only involves a movement parallel to the midplane and symmetrical to the symmetry plane perpendicular to the wafer, may have a mass distribution such that the resonator considered does not experience any movement of the feet parallel to the central axis. In other words, the compensation of the momentum component of each vibrating part parallel to the central axis of the resonator considered may be precise or nearly precise. In this case, the vibration energy loss through the feet of the resonator is zero or nearly zero. Thus, the quality factor of the sensor for the two degenerate modes of vibration may be very high. In addition, the lack of said movement of the feet makes the sensor insensitive to symmetry defects, which may occur during mounting to an external base and may eliminate the degeneracy between the vibration modes.

[0031] Each extension of each resonator may include an extension at its distal end, parallel to the mid-plane, to the outer longitudinal edges of the primary and secondary segments of the extension. The extension provides an additional degree of freedom, which can provide compensation of the momentum component parallel to the central axis within each vibrating portion. This facilitates the design of resonators that do not transmit motion through the feet.

[0032] Advantageously, in a preferred embodiment of the invention, a connecting element may be connected to the vibrating part of each resonator at the interconnected proximal end of the secondary segment, parallel to the central axis of the resonator and on the side of the vibrating part opposite the foot. The above configuration of the sensor increases the transmission of the vibration energy caused by the rotation to be measured in the two degenerate modes of vibration. Thus, the sensitivity of the sensor is further increased.

[0033] Advantageously, the wafer material may be monocrystalline, belong to the trigonal crystal system and have piezoelectric properties. In this case, for each resonator of the preferred embodiment of the present invention described above, the central axis of the vibrating part may be parallel to the axis Xc of the material. And both the primary and secondary segments of this vibrating part may be parallel to the axis Yc of the material. In other words, one of both extensions of each vibrating part may be parallel to the crystal axis Yc+ and the other may be parallel to the crystal axis Yc-. Thus, the extensions make an angle between them equal to 60° (degrees). Each sensor resonator may therefore be symmetrical, since it is directly manufactured using a wet chemical etching process for etching the sensor pattern into the wafer. In particular, the wafer may be made of (i) alpha-quartz crystal (alpha-SiO2), (ii) any other crystal of the trigonal crystal class 32, such as gallium orthophosphate (GaPO4), germanium oxide (GeO2), gallium arsenate (GaAsO4), or (iii) crystal of the LGX family, i.e., langasite (LGS, i.e., La3Ga5SiO2). 14 ), Langatate (LGT, i.e., La3Ga5,5TaO,5O 14 ), or langhanite (LGN, i.e. La3Ga5,5NbO,5O 14 )

[0034] Alternatively, both extensions of each vibrating portion may have an angle between them equal to 90° or 180°.

[0035] Generally, the sensor according to the invention comprises: - excitation means adapted to produce a bending distortion of the vibrating parts of the n resonators according to a first mode of a plurality of degenerate modes of vibration of the sensor; - detection means adapted to measure a vibration amplitude of the sensor according to another degenerate mode of vibration different from the first degenerate mode of vibration; It further has:

[0036] Finally, a second aspect of the invention relates to a gyrometer comprising a sensor according to the first aspect of the invention, the functioning of which uses the coupling caused by the Coriolis force between two degenerate modes of vibration, and which is of the type integrating gyrometer.

[0037] [Brief description of the drawings] The features and advantages of the present invention will become more apparent from the following detailed description of several non-limiting exemplary embodiments, taken in conjunction with the accompanying drawings, in which: FIG. 1a is a plan view of a first inertial angular position sensor according to the present invention; FIG. 1b corresponds to FIG. 1a and shows a first degenerate mode of vibration in the first inertial angular position sensor; FIG. 1c corresponds to FIG. 1b and shows a second degenerate mode of vibration in the first inertial angular position sensor; FIG. 2a corresponds to FIG. 1a and relates to a second inertial angular position sensor according to the invention; FIG. 2b corresponds to FIG. 1b and relates to a second inertial angular position sensor; FIG. 2c corresponds to FIG. 1c, but for a second inertial angular position sensor; FIG. 3a corresponds to FIG. 1a and relates to a third inertial angular position sensor according to the invention; FIG. 3b corresponds to FIG. 1b and relates to a third inertial angular position sensor; FIG. 3c corresponds to FIG. 1c, but for a third inertial angular position sensor; FIG. 4a corresponds to FIG. 1a and relates to a fourth inertial angular position sensor according to the invention; FIG. 4b corresponds to FIG. 1b and relates to a fourth inertial angular position sensor; FIG. 4c corresponds to FIG. 1c and relates to a fourth inertial angular position sensor; FIG. 5a is a plan view showing a first resonator model usable in a preferred embodiment of the present invention; Figure 5b corresponds to Figure 5a and shows the distortions in the vibrational modes of the first resonator model together with the associated momenta; FIG. 5c corresponds to FIG. 5a and relates to a second resonator model that can be used in another preferred embodiment of the invention; Figure 5d corresponds to Figure 5b, but for the second resonator model; FIG. 6a corresponds to FIG. 1a and relates to a fifth inertial angular position sensor according to the invention using the first resonator model of FIGS. 5a-5b; FIG. 6b corresponds to FIG. 1b and relates to a fifth inertial angular position sensor; FIG. 6c corresponds to FIG. 1c and relates to a fifth inertial angular position sensor; FIG. 7a corresponds to FIG. 1a and relates to a sixth inertial angular position sensor according to the invention using the second resonator model of FIGS. 5c-5d; FIG. 7b corresponds to FIG. 1b and relates to a sixth inertial angular position sensor; FIG. 7c corresponds to FIG. 1c and relates to a sixth inertial angular position sensor; FIG. 8a corresponds to FIG. 1a and relates to a seventh inertial angular position sensor according to the invention; FIG. 8b corresponds to FIG. 1b and relates to a seventh inertial angular position sensor; FIG. 8c corresponds to FIG. 1c and relates to a seventh inertial angular position sensor; FIG. 9 shows a possible electrode configuration suitable for piezoelectric coupling that can be used to excite and detect bending vibrations of a beam for a beam material that has piezoelectric properties and belongs to the trigonal crystalline system and symmetry class 32 (e.g., alpha-quartz).

[0038] [Detailed Description of the Invention] For the sake of clarity, the dimensions of the elements shown in these figures do not correspond to the actual dimensions or to the actual dimensional ratios. In particular, the distortions of all the illustrated resonators are enlarged to an exaggerated extent for the purposes of better visibility. Moreover, identical reference signs shown in different figures denote identical elements or measurements, or elements or measurements with the same function.

[0039] All figures except for Figure 9 show inertial angular position sensors or resonators etched into a wafer of solid material having two flat parallel faces. The figures are in a plane parallel to, located between and equidistant from the two faces of the wafer. This plane is the plane of symmetry of each sensor or resonator and is called the mid-plane. For miniature sensors made by an integral etching process, the thickness of the wafer used (measured perpendicular to the plane) can be from a few micrometers to a few millimeters.

[0040] 1a to 1c, 2a to 2c, 3a to 3c, and 4a to 4c do not correspond to the inventions according to the claims, and the parts shown as explanations regarding these figures are intended to facilitate understanding of the present invention and the advantages of the present invention.

[0041] FIG. 1a shows a first inertial angular position sensor 101 according to the invention, with four resonators (i.e. n=4). The sensor comprises a support in the form of a square peripheral frame, indicated by the reference Pf and also called fixed part. This fixed part Pf is designed to fix the sensor 101 to a base (not shown) and to establish electrical contact between the electrodes (not shown) carried by the resonators and an electronic excitation and detection circuit (not shown). Four beams P are arranged inside the frame of the fixed part Pf, parallel to and spaced apart from the four sides of the frame. Each of the beams P is connected at its two opposite ends to the fixed part Pf by two feet Pd located at the corners of the fixed part Pf. Each foot Pd is thus shared by two adjacent beams P. Each of the beams P can then flexurally vibrate between its two ends parallel to the mid-plane. Thus, each beam P constitutes an individual resonator. The four resonators are individually indicated by the references R1, R2, R3, and R4. Thus, each beam P constitutes a vibrating part of each resonator. The sensor 101 further comprises a cross-shaped connection element indicated as Ec. The connection element Ec is also etched inside the wafer, as are the beams P and the feet Pd. The ends of the arms of the connection element Ec are connected one-to-one to the centers of each of the beams P. Thus, the entire sensor 101, including the fixed part Pf, the feet Pd, the beams P, and the connection element Ec, is orthogonal to the mid-plane and invariant to a π / 2 rotation about an axis passing through the center of the sensor. The sensor has two degenerate modes corresponding to the vibration displacement of the center point of the connection element Ec. In the first mode, the vibration displacement is parallel to the X-axis, as shown in FIG. 1b. And in the second mode, the vibration displacement is parallel to the Y-axis, as shown in FIG. 1c. Due to symmetry, these two modes are degenerate since they have the same vibration frequency values, and furthermore, the Coriolis force applied to the connecting element Ec, caused by the rotation of the sensor about an axis AA perpendicular to the wafer and passing through its center, leads to a coupling of these two degenerate modes.Thus, rotation of the sensor 101 causes a transfer of vibration energy from one mode to the other. This first inertial angular position sensor 101 is therefore suitable for creating an integrating gyrometer having the axis AA as the sensitive axis.

[0042] FIG. 2a shows a second inertial angular position sensor 102 according to the invention, with three resonators (i.e. n=3). The design of this second sensor is similar to that of the first sensor of FIG. 1a, but the square shape of the frame of the fixed part Pf is replaced by an equilateral triangle shape. The second sensor therefore comprises (i) three separate resonators R1-R3 and (ii) a connection element Ec with three arms. Each of the resonators R1-R3 is formed by two opposite ends of a beam P connected to the fixed part Pf. Each of the three arms is spaced apart by 120° from its neighboring arm. Each arm of the connection element Ec is still connected to the center of one of the three beams P. This second sensor 102 still has two degenerate modes of vibration, the first mode and the second mode. As shown in FIG. 2b, in the first mode, the center point of the connection element Ec undergoes a vibratory motion parallel to the X-axis. 2c, in the second mode, the center point of the connection element Ec undergoes an oscillatory motion parallel to the Y-axis. Therefore, this second inertial angular position sensor 102 is also suitable for creating an integrating gyrometer.

[0043] However, in the two sensors of Figs. 1a-c and 2a-c, the momentum involved in each of both degenerate modes of vibration is not compensated. The fixed part Pf is therefore moved by a movement in the opposite direction to the movement of the set of resonators and the connecting element Ec. The transmission of this movement to the fixed part Pf occurs via the feet Pd. This results in the sensor having a very high sensitivity to the mounting conditions of the fixed part Pf to the external base. In particular, the loss of symmetry between the X-axis and the Y-axis caused by these mounting conditions has the consequence that the degeneracy in the two eigenmodes of vibration of the sensor is prevented. In this case, the gyro no longer functions as an integrator. However, it is common that the conditions for mounting the fixed part Pf to the external base are not sufficiently controllable (especially if this mounting is performed by adhesive). In addition, the movements transmitted to the fixed part Pf cause losses of vibration energy in several modes of vibration. This gives rise to resonant overvoltages and reduces the sensitivity of the gyro. The improvements of the invention described hereafter overcome this drawback.

[0044] According to this improvement, each resonator in the sensor is individually balanced. As a result, each of the resonators is dynamically isolated from the fixed part Pf. Therefore, the vibration of each resonator does not cause the movement of the foot(s) to which it is connected. As a result, there is no loss of vibration energy through the foot. Therefore, the degenerate modes of vibration in the sensor have low sensitivity to symmetry defects in the mounting of the fixed part Pf to the external base. As a result, a gyrometer incorporating the sensor may have a high-performance integration function. In other words, this improvement in the present invention includes the use of an inherently balanced resonator model in addition to an n-th order axisymmetric arrangement of the inertial angular position sensor.

[0045] Resonators separated from the fixed part as described above are known from the prior art, examples of which include (i) the double-ended tuning fork described in particular in US 4,215,570 and (ii) the simple double-ended blade with inertial masses at both ends described in FR 8,418,587.

[0046] In other words, this improvement of the present invention involves using an inherently balanced resonator model in an nth order axisymmetric arrangement of an inertial angular position sensor.

[0047] The third inertial angular position sensor 103 of FIG. 3a still uses the fourth-order (n=4) axial symmetry of the sensor of FIG. 1a. However, it uses a resonator model based on a double-ended tuning fork. Each of the resonators R1-R4 is therefore constituted by two beams P1 and P2 parallel to each other and extending respectively between the two legs Pd to which the resonator is connected. Preferably, each of the resonators R1-R4 has an intermediate area ZI between the beams P1 and P2 and the respective leg Pd. Inside the intermediate area ZI, the two beams are embedded. The intermediate area ZI eliminates residual forces that would otherwise be transmitted by the beams P1 and P2 to the legs Pd. Furthermore, an additional inertial mass MI is rigidly connected to the beam P2 of the respective resonator in order to balance the inertial contribution caused by the connection element Ec to the beam P1 of this resonator. Preferably, each of the additional inertial mass MI may be constituted by a wafer segment. The center of the wafer segment is connected to the center of the beam P2. As a result, the stiffness of the wafer segment is not modified. Or the symmetry in the resonator is not broken. Then, Fig. 3b and Fig. 3c show two degenerate modes of vibration effective for the sensor, with a movement of the connection element Ec parallel to the X-axis or Y-axis, respectively. For each of these degenerate modes of vibration, the two beams P1 and P2 vibrate in antiphase, moving away from each other and then moving towards each other by respective bending parallel to the mid-plane. Thus, no resulting forces are transmitted to each foot Pd of the sensor 103. The fixed part Pf of the sensor 103 therefore remains stationary during each of the two degenerate modes of vibration. Thus, the gyro can have a high-performance integration function.

[0048] The fourth inertial angular position sensor 104 of FIG. 4a still uses the fourth order (n=4) axial symmetry of the sensor of FIG. 1a. However, in this example, the sensor uses the resonator model described in FR8,418,587 to form each of the resonators R1-R4. Each resonator thus comprises two inertial masses MI1 and MI2. Each of these inertial masses is connected to a fixed part Pf by a respective foot Pd acting as a hinge. In addition, the inertial masses MI1 and MI2 are connected to each other by a flexible segment S. When each of the resonators R1-R4 vibrates, the two inertial masses MI1 and MI2 move parallel to the plane of the wafer towards the same side and rotate in opposite directions. Meanwhile, the center of the flexible segment S moves towards the opposite side. Each arm of the connection element Ec is connected to the center of the flexible segment S of one of the resonators R1-R4. Thus, by adopting dimensions according to the inertial masses MI1 and MI2 that take into account the mass of the connection element Ec, and possibly by adding an additional inertial mass at the center of the connection element Ec, each resonator R1-R4 appears to be individually balanced in the sensor 104. Figures 4b and 4c show two degenerate modes of vibration of the sensor 104 with the movement of the connection element Ec parallel to the X-axis or Y-axis, respectively. A gyrometer incorporating this fourth inertial angular position sensor 104 can have a high-performance integration function.

[0049] However, the two sensor configurations of Figures 3a and 4a are bulky and therefore not well suited for applications requiring a high level of miniaturization. Figures 5a and 5c show two novel resonator models according to the improvements of the present invention that can still be balanced and used in an inertial angular position sensor. Furthermore, these two novel resonator models can be made with smaller dimensions compared to the resonator models shown in Figures 3a and 4a.

[0050] The resonators of Fig. 5a and Fig. 5c differ from conventional resonators in that they are connected to the fixed part Pf by only one foot Pd. Moreover, each resonator is individually constituted by a vibrating part having two extensions (denoted P1 and P2, respectively) extending longitudinally along respective axes A1 and A2. In the resonator of Fig. 5a, the axes A1 and A2 form an angle α between the axes A1 and A2 equal to 60°. In the resonator of Fig. 5c, the angle α between the axes A1 and A2 is equal to 180°. The two extensions P1 and P2 extend symmetrically from the foot Pd on either side of a central axis Xm coinciding with the longitudinal direction of said foot Pd. This central axis Xm corresponds to the intersection of (i) the mid-plane already described and (ii) another symmetry plane perpendicular to the plane of the wafer. The two extensions P1 and P2 correspond to mirror symmetry with respect to said symmetry plane. In the remainder of this specification, by analogy with the tuning fork resonator described in US 3,683,213, the two extensions P1 and P2 are also referred to as beams P1 and P2. According to the inherent characteristics of the resonators of Fig. 5a and Fig. 5c, each beam P1, P2 is provided with a longitudinal slot, respectively indicated by the references FL1, FL2. These two longitudinal slots FL1 and FL2 intersect at the central axis Xm of the resonator. Thus, for index i equal to 1 or 2, each beam Pi is constituted by two blades Liext and Liint. In the general part of this specification, the blade L1ext (or L2ext) is referred to as the primary segment of the extension P1 (or P2), and the blade L1int (or L2int) is referred to as the secondary segment of the extension P1 (or P2). Thus, the two blades L1ext and L2ext are connected to the foot Pd and extend towards the distal ends of the beams P1 and P2, respectively, at which the two blades L1ext and L2ext are connected one-to-one to the two blades L1int and L2int, respectively, so that each beam or extension P1, P2 has a serpentine shape between the central axis Xm and its distal end.In addition, the blades L1int and L2int are interconnected by their respective proximal ends at the central axis Xm. Also, the two longitudinal slots FL1 and FL2 of each beam P1 and P2 intersect at the central axis Xm. Thus, the junction of the proximal ends of each of the two blades L1int and L2int is separated from the blades L1ext and L2ext and from the foot Pd.

[0051] In the resonator of FIG. 5a, when the distal ends of the extensions P1 and P2 move symmetrically away from the central axis Xm in opposite directions during vibration of the resonator, as shown in FIG. 5b, the blades L1ext and L2ext have momenta MV1 and MV2, respectively. MV1 and MV2 are diagonally and symmetrically oriented and towards the same side as the foot Pd. Thus, the common junction of the blades L1int and L2int has a momenta MV12, which is parallel to the central axis Xm and points away from the foot Pd. As a result, the blades L1int and L2int each have a momenta that is diagonally and symmetrically oriented towards the side of the resonator opposite the foot Pd. Thus, the distribution of mass in the vibrating part between all the blades L1ext, L2ext, L1int and L2int can be such that the movement of the foot Pd due to these momenta is zero or nearly zero. By eliminating the movement of the feet Pd in ​​this way, the transfer of vibration energy from the vibrating part to the support Pf can be zero or very low. The quality factor of the resonator can therefore be high. The optimized distribution of mass between the four blades of the vibrating part is still symmetrical with respect to the central axis. Said distribution can be obtained by assigning a common thickness eext to the two blades L1ext and L2ext, eext being different from the thicknesses (denoted eint) of the two blades L1int and L2int. By applying such an optimization, the resonator is balanced. The blade thicknesses eext and eint are measured parallel to the plane of the wafer. The values ​​of the resonator dimensions that provide said balancing can be determined according to several methods, in particular by using finite element calculations.

[0052] According to two refinements of the resonator, shown together in FIG. 5a but which can be used independently of each other, the vibration part of the resonator can be supplemented by (i) two inertial masses MI1 and MI2 according to the first refinement and (ii) a stem Pc according to the second refinement. Preferably, the two inertial masses MI1 and MI2 are located at the distal ends of two beams P1 and P2 and are identical. The two inertial masses can each be formed by widening the corresponding beam P1, P2 at its distal end. The stem Pc can be formed by an additional blade that extends from the junction of the proximal ends of the blades L1int and L2int parallel to the central axis Xm and away from the foot Pd so as to overlap with said central axis Xm. Advantageously, the stem Pc is also symmetrical with respect to the central axis Xm. By adding two inertial masses MI1 and MI2 and / or a stem Pc to the vibrating part of the resonator, the balancing of the resonator can be realized with additional degrees of freedom. Thus, the balancing can be further facilitated. FIG. 5b shows the motion of the inertial masses MI1 and MI2 together with the motion of the stem Pc at the same time during the vibration of the resonator. The two inertial masses MI1 and MI2 have momentum components MV1 and MV2 along the central axis Xm that are opposite (opposite) to the momentum component MV12 of the stem Pc. These momentum components of the inertial masses MI1 and MI2 and the stem Pc, combined with the momentum components of the four blades L1ext, L2ext, L1int and L2int, result in a motion of the foot Pd that is zero or nearly (substantially) zero.

[0053] In the resonator of FIG. 5c, as shown in FIG. 5d, the two inertial masses MI1 and MI2 move in phase parallel to the central axis Xm when the resonator oscillates. The junction of the blades L1int and L2int also moves parallel to the central axis Xm, but in antiphase with respect to the inertial masses MI1 and MI2. This results in at least partial compensation of the momentum involved. As a result, the movement of the foot Pd can be reduced or eliminated by determining the appropriate dimensions depending on the resonator. The inertial masses MI1 and MI2 are necessary to achieve an accurate balancing of the resonator. On the other hand, the stem Pc is optional, although it gives an additional degree of freedom in the dimensions that lead to the balancing of the resonator.

[0054] The fifth inertial angular position sensor 105 of Fig. 6a is obtained from the second sensor of Fig. 2a by using the resonator model of Fig. 5a instead of the single beam resonator model held by its two ends for each of the resonators R1-R3. The foot Pd of each of the three resonators R1-R3 is connected to a fixed part Pf at one of the corners of the triangular frame formed by said fixed part Pf. Fig. 6b and Fig. 6c then show two degenerate modes of vibration valid for said fifth sensor, with the movement of the connecting element Ec parallel to either the X-axis or the Y-axis.

[0055] The sixth inertial angular position sensor 106 of Fig. 7a is also derived from the second sensor of Fig. 2a. However, in this example, instead of the single beam resonator model held by its two ends, the resonator model of Fig. 5c is used for each of the resonators R1-R3. The foot Pd of each of the three resonators R1-R3 is connected to a fixed part Pf at the centre of one of the sides of the frame formed by said fixed part Pf. Figs. 7b and 7c then show two degenerate modes of vibration available to said sixth sensor, with the movement of the connection element Ec parallel to either the X-axis or the Y-axis.

[0056] Finally, the seventh inertial angular position sensor 107 of FIG. 8a is obtained from the first sensor of FIG. 1a. However, in this example, instead of the single beam resonator model held by the two ends, for each of the resonators R1 to R4, the resonator model of FIG. 5a is used, with the angle α equal to 90°. The foot Pd of each of the four resonators R1 to R4 is connected to a fixed part Pf at one of the corners of the square frame formed by said fixed part Pf. Figures 8b and 8c then show two degenerate modes of vibration valid for said seventh sensor, with a movement of the connection element Ec parallel to either the X-axis or the Y-axis.

[0057] Since the fifth, sixth and seventh inertial angular position sensors are made by individually balanced resonators, it is possible to obtain high-performance integral gyrometers with high or very high quality factor values, especially in pilot and sensing modes. The gyro thus obtained can be very sensitive.

[0058] Beneficially, all of the above-mentioned inertial angular position sensors may be fabricated from (i) single crystal wafers of alpha-quartz (alpha-SiO2), (ii) any other single crystal of the trigonal crystal class 32 such as gallium orthophosphate (GaPO4), germanium oxide (GeO2), gallium arsenate (GaAsO4), or (iii) crystals of the LGX family, i.e., langasite (LGS, i.e., La3Ga5SiO2). 14 ), Langatate (LGT, i.e., La3Ga5,5TaO,5O 14 ), or langhanite (LGN, i.e. La3Ga5,5NbO,5O 14), these materials have piezoelectric properties. In this case, when the resonators of the model of FIG. 5a or the model of FIG. 5c are used, the orientation of the beams P1 and P2 of each resonator of the sensor (i.e. their longitudinal axes A1 and A2) is advantageously chosen to be parallel to the crystal axes Yc, Yc+ and Yc-. The plane of the wafer is parallel to the crystal plane Xc-Yc. This orientation of the sensor pattern with respect to the crystal of the wafer makes it possible to benefit from an optimal piezoelectric coupling to excite the pilot modes and to detect the sensing modes according to their respective bending vibrations in the crystal plane Xc-Yc. As a matter of fact, the piezoelectric tensor of the trigonal class of crystals provides an optimal coupling according to the strain Syy along the axis of each beam with the electric field Exx. This makes it possible (i) to excite the bending vibrations of the pilot modes by the direct piezoelectric effect with the electrodes arranged along the blades, resulting in the electric field Exx, and (ii) to detect the strain Syy with the charges generated by the indirect piezoelectric effect on these same electrodes. For this purpose, several different electrode configurations are known. According to a first of these configurations, as shown in FIG. 9, three electrode segments are arranged on each of the two sides of each blade that coincide with one of the faces of the wafer. The electrodes of this first configuration are easily manufactured by a process of conductive material deposition. According to another possible configuration, two electrode segments are arranged on each side of each blade perpendicular to the faces of the wafer. This other configuration is more effective but more difficult to realize, as described for example in US 4,524,619. Also, the same orientation of the sensor pattern with respect to the crystal of the wafer allows the wet chemical etching rate to benefit from the crystal axis Z, i.e. the wet chemical etching rate along the crystal axis Z is faster. This axis Z is perpendicular to the face of the wafer used. In this case, the sensor can be manufactured at low cost by a wet chemical etching process, in particular using a mixture of ammonium fluoride (NH4F) and hydrofluoric acid (HF).Moreover, resonators according to Figure 5a or 5c, which are produced in a wafer of trigonal monocrystalline material of symmetry class 32 and have the above-mentioned orientation with respect to the crystal axes, are obtained directly at the end of the wet-chemical etching step without symmetry defects. Thus, the resonators in the inertial angular position sensors of Figures 6a and 7a are strictly equivalent, since they are directly balanced.

[0059] The ability to manufacture the pattern of the sensor using only wet chemical etching processes as described above is particularly beneficial due to the low cost obtained by this integrated manufacturing process according to microdevices. In addition, wet chemical etching processes preserve the intrinsic quality factor of the crystal. As a matter of fact, chemical etching is based on local reactions that cause the dissolution of the crystal atom by atom. Due to this fact, chemical etching does not change the crystal lattice of the remaining wafer material forming the sensor. This is not the case in the case of etching based on local abrasion, such as ultrasonic machining using fine abrasive particles excited by ultrasonic waves generated between the probe (sonotrode) and the surface to be etched, or ion bombardment using the kinetic energy of ions. These last two techniques change the crystal lattice at the edge of the etching over characteristic distances ranging from tens of nanometers to several micrometers for the highest energy etching. For this reason, the intrinsic quality factor of the resonator is increasingly reduced if a significant miniaturization of the sensor is desired.

[0060] It is understood that the invention is not limited to trigonal piezoelectric materials of symmetry class 32. The principle of equivalent resonators separated with respect to the mounting, arranged in an axially symmetric configuration and connected to each other by connecting elements that are also axially symmetric may be combined with the use of other materials, in particular silicon crystals. Considering the cubic crystal structure of monocrystalline silicon, arrangements based on four resonators such as those in Fig. 1a, Fig. 3a, Fig. 4a and Fig. 8a are preferred. In this case, the excitation of the pilot mode can be realized by applying an electrostatic force. The amplitude in the sensing mode can be determined by measuring the capacitance between the fixed part of the sensor and the movable part of said sensor. [Brief description of the drawings]

[0061] [Figure 1a] FIG. 2 is a plan view of a first inertial angular position sensor according to the present invention. [Figure 1b] FIG. 1 corresponds to FIG. 1a and shows a first degenerate mode of vibration in the first inertial angular position sensor; [Figure 1c] 1b corresponds to FIG. 1b and shows a second degenerate mode of vibration in the first inertial angular position sensor; [Figure 2a] 1a and relates to a second inertial angular position sensor according to the invention; [Figure 2b] 1b and relates to a second inertial angular position sensor. [Figure 2c] 1c and relates to a second inertial angular position sensor. [Figure 3a] 1a and relates to a third inertial angular position sensor according to the invention; [Figure 3b] 1b and relates to a third inertial angular position sensor. [Figure 3c] 1c and relates to a third inertial angular position sensor. [Figure 4a] 1a and relates to a fourth inertial angular position sensor according to the invention; [Figure 4b] 1b and relates to a fourth inertial angular position sensor. [Figure 4c] 1c and relates to a fourth inertial angular position sensor. [Figure 5a] FIG. 2 is a plan view showing a first resonator model that can be used in a preferred embodiment of the present invention. [Figure 5b] 5a and 5b show the distortions in the vibrational modes of the first resonator model together with the associated momenta. [Figure 5c] 5a and relates to a second resonator model which can be used in another preferred embodiment of the invention. [Figure 5d] 5b and for the second resonator model. [Figure 6a] 1a and relates to a fifth inertial angular position sensor according to the invention which uses the first resonator model of FIGS. 5a-5b. [Figure 6b] 1b and relates to the fifth inertial angular position sensor. [Figure 6c] 1c and relates to the fifth inertial angular position sensor. [Figure 7a] 1a and relates to a sixth inertial angular position sensor according to the present invention which uses the second resonator model of FIGS. 5c-5d. [Figure 7b] 1b and relates to the sixth inertial angular position sensor. [Figure 7c] 1c and relates to the sixth inertial angular position sensor. [Figure 8a] 1a and relates to a seventh inertial angular position sensor according to the present invention; [Figure 8b] 1b and relates to the seventh inertial angular position sensor. [Figure 8c] 1c and relates to the seventh inertial angular position sensor. [Figure 9] For beam materials that have piezoelectric properties and belong to the trigonal crystalline system and symmetry class 32 (e.g., alpha-quartz), we show possible electrode configurations suitable for piezoelectric coupling that can be used to excite and detect bending vibrations of the beam.

Claims

1. An inertial angular position sensor (101-107), It comprises at least three identical resonators (R1 to R3; R1 to R4) arranged symmetrically around an axis called the sensitive axis (A-A) and invariant to a rotation of 2π / n around said sensitive axis, n is the number of resonators in the sensor; the n resonators (R1 to R3; R1 to R4) are connected to one another so that the sensor has at least two degenerate modes of vibration, making it possible to characterize the rotation of the sensor around the sensitive axis (A-A); Each resonator (R1-R3; R1-R4) includes a respective portion of a wafer having two opposing flat and parallel surfaces; the portion of the wafer dedicated to each resonator is referred to as the vibrating portion of said resonator and is designed to vibrate in bending when said sensor is in use; the wafer is common to the n resonators (R1 to R3; R1 to R4) of the sensor; the sensor further comprises a connecting element (Ec) connecting the vibrating portion of each resonator (R1 to R3; R1 to R4) to the vibrating portions of all the other n resonators of the sensor, the connecting element is also invariant to a rotation of 2π / n about the sensitive axis (A-A), the vibrating portions of the n resonators are angularly arranged around the connecting element; the vibrating part of each resonator (R1 to R3; R1 to R4) is connected to a support (Pf) of the sensor located outside the vibrating part and the connecting element (Ec) by an intermediate segment of the wafer called a foot (Pd) dedicated to the resonator; The foot portion is integrated with the vibration portion and forms a foot portion (Pd) between the support portion and the vibration portion, For each resonator (R1 to R3; R1 to R4), The vibrating portion of the resonator a first plane of symmetry parallel to and equidistant from both surfaces of the wafer; a second plane of symmetry that is perpendicular to the first plane of symmetry and that passes through the foot (Pd) located between the support portion and the vibrating portion in the longitudinal direction; The common portion of the first plane of symmetry and the second plane of symmetry forms a central axis (Xm) of the vibration portion, the vibrating portion includes two extensions (P1, P2) each designed to vibrate in bending; The two extension portions extend symmetrically from the foot portion (Pd) on both sides of the second plane of symmetry, each extension (P1, P2) is provided with a longitudinal slot (FL1, FL2) which runs from the second plane of symmetry towards the distal end of the extension but does not reach said distal end and passes through the vibrating part perpendicular to the first plane of symmetry, Each extension portion has a bent shape, the slots (FL1, FL2) of each of the extensions (P1, P2) are symmetrical with respect to the second plane of symmetry and intersect in the second plane of symmetry; The vibration portion includes two primary segments (L1ext, L2ext) and two secondary segments (L1int, L2int), Each of the two primary segments connects the foot (Pd) to a distal end of one of the extensions; two of the secondary segments are interconnected by their respective proximal ends in the second plane of symmetry; each of the two secondary segments extends toward a distal end of one of the extensions and is connected to one of the primary segments at the distal end; For both degenerate modes in the sensor that allow to characterize the rotation around the sensitive axis (A-A), the vibrating part of each resonator is parallel to the first plane of symmetry and only moves symmetrically with respect to the second plane of symmetry; Both primary segments (L1ext, L2ext) have instantaneous velocity components parallel to the central axis (Xm) at each time during vibration, A sensor wherein the direction of the instantaneous velocity component is opposite to the direction of the instantaneous velocity component of the secondary segment (L1int, L2int) parallel to the central axis (Xm).

2. 2. The sensor according to claim 1, wherein the connecting element (Ec) is constituted by a pattern formed on the wafer and is integrated with the vibrating part of each resonator (R1-R3; R1-R4).

3. For each resonator (R1 to R3; R1 to R4), 3. A sensor according to claim 1 or 2, wherein the vibrating part has a mass distribution such that each degenerate mode of vibration of the sensor which is parallel to the first plane of symmetry and which involves only movements symmetrical with respect to the second plane of symmetry does not cause the sensor to produce any movements of the feet (Pd) parallel to the central axis (Xm).

4. 4. The sensor according to claim 1, wherein each extension (P1, P2) of each resonator (R1-R3) has, at its distal end, an extension parallel to the first plane of symmetry to the outer longitudinal edges of the primary (L1ext, L2ext) and secondary (L1int, L2int) segments of the extension.

5. 5. The sensor according to claim 1, wherein the connecting element (Ec) is connected to the vibrating part of each resonator (R1-R3; R1-R4) at the interconnected proximal ends of the secondary segments (L1int, L2int), parallel to the central axis (Xm) of the resonator and on the side of the vibrating part opposite the feet (Pd) of the resonator.

6. the material of the wafer is single crystal, belongs to the trigonal crystal system, and has piezoelectric properties; For each resonator (R1 to R3; R1 to R4), the central axis (Xm) of the vibrating part is parallel to the axis Xc of the material; 6. The sensor according to claim 1, wherein both primary segments (L1ext, L2ext) and both secondary segments (L1int, L2int) of the vibrating part are parallel to the axis Yc of the material.

7. 7. The sensor according to claim 1, wherein both extensions (P1, P2) of the vibrating part of each resonator (R1-R3; R1-R4) make an angle (α) between them equal to 60°, 90° or 180°.

8. an excitation means for generating bending distortions in the vibrating portions of the n resonators (R1 to R3; R1 to R4) according to a first degenerate mode of vibration; 8. The sensor of claim 1, further comprising detection means for measuring a vibration amplitude of the sensor according to another degenerate mode of vibration different from the first degenerate mode of vibration.

9. 1. A gyrometer comprising an inertial angular position sensor, A gyrometer, wherein the sensor is a sensor according to any one of claims 1 to 8.

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