Rotation measuring apparatus and associated rotation measuring method
Patent Information
- Application Number
- FR2023000967
- Authority / Receiving Office
- FR · FR
- Patent Type
- Patents
- Current Assignee / Owner
- Filing Date
- 2023-02-02
- Publication Date
- 2025-02-14
- Estimated Expiration
- 2043-02-02
Smart Images
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Abstract
Description
Title of the invention: Rotation measuring apparatus and associated rotation measuring method Technical field
[0001] The invention relates to the field of inertial sensors, such as vibrating gyroscopic sensors or resonators, used to measure rotations.
[0002] The invention also relates to a method for measuring rotations. Previous techniques
[0003] Vibrating gyroscopic sensors are commonly used in many fields due to their robustness, low power consumption and speed of implementation.
[0004] Such vibrating gyroscopic sensors comprise a resonator which can take various forms, such as a bell or a tuning fork.
[0005] For example, US patent 4,644,793 describes a resonator structure composed of a cylindrical shell associated with a plate positioned on a plane of symmetry of the cylindrical shell and allowing a connection with a support.
[0006] Furthermore, resonators with two nested masses having a common center of gravity are known, in particular from document US 9,631,929, in order to obtain a symmetrical and flat structure.
[0007] Documents FR 2 692 349 and FR 2 705 147 disclose vibrating gyroscopes comprising four identical metal beams arranged on a common base using linear or planar vibration modes to measure a rotation around a single sensitive axis corresponding to the axis of the gyrometer.
[0008] Furthermore, a gyrometer-type device capable of measuring the three components of rotational speed is known from document US 5,625,145.
[0009] Finally, document US 9,863,770 describes a gyroscope whose resonator comprises eight suspended masses connected to each other by springs.
[0010] Such a configuration has several advantages residing in the possibility of measuring rotations around three orthogonal axes, thus completely describing the rotational movement in three dimensions, an isotropic distribution of the masses in motion relative to the center of gravity leading to an overall cancellation of the external forces during acceleration and also during rotation.
[0011] Nevertheless, the set of eight masses presents numerous degrees of freedom capable of being excited, which creates a certain complexity in controlling the movements of the resonator, taking into account the number of parasitic vibration modes. Presentation of the invention
[0012] In view of the above, the aim of the invention is to propose a device for measuring rotations in a three-dimensional frame of reference based on a compact, precise resonator having strong symmetry.
[0013] The subject of the invention is a rotation measuring apparatus comprising a mechanical resonator comprising at least four identical and rigid masses, capable of exhibiting translational vibration modes. According to a general characteristic, said resonator comprises control means comprising measuring means capable of measuring a relative displacement between each pair of masses in at least two directions and application means capable of applying inter-mass forces for each pair of masses in said at least two directions. According to another general characteristic, the resonator further comprises a rotation calculation module, and a vibration regulation module receiving data from the measuring means and issuing instructions for controlling said application means as a function of said data.
[0014] The resonator has cubic symmetry and said masses are nested together and each have a plane of symmetry and a ternary axis of symmetry oriented along a ternary axis of symmetry of a cube. Said masses are connected to each other by first springs and / or are connected to an external support of the resonator by second springs.
[0015] According to one characteristic, the masses each comprise two bases connected by at least three rods.
[0016] Advantageously, the first springs are positioned perpendicular to each other along the twelve edges of the cube.
[0017] Preferably, the first springs are rectilinear rods stressed axially and / or in bending.
[0018] Preferably, the second springs are arranged at each end of the masses, in particular in symmetrical extension of the first springs.
[0019] Preferably, the second springs are rectilinear rods stressed axially and / or in bending.
[0020] According to one characteristic, the second springs have an axial stiffness and / or a bending stiffness different from an axial stiffness and / or a bending stiffness of the first springs.
[0021] Advantageously, the masses are each made of at least two assembled parts, in order to facilitate construction.
[0022] According to one characteristic, the control means are transducers, in particular electrostatic or piezoelectric transducers, making it possible to measure deformations and / or to apply forces.
[0023] Preferably, the transducers are arranged parallel to a first and / or a second bisector plane of the ternary symmetry axes of each pair of two masses and make it possible to measure a displacement and to apply forces following a normal respectively to the first and / or the second bisector plane of the ternary symmetry axes of each pair of two masses.
[0024] According to one characteristic, the transducers are in the form of plates and are arranged on the rods of the masses, so that each plate placed on the rod of a mass corresponds to another associated plate which is parallel to it and arranged nearby on the rod of another mass.
[0025] According to one characteristic, the control means are transducers of the microelectromechanical system (MEMS) type.
[0026] Advantageously, the transducers are glued to the masses on the six faces of the cube and integrate the first springs, the second springs and means of fixing to a housing which envelops them, the transducers being capable of carrying out measurements of relative deformation between two masses and of applying inter-mass forces.
[0027] Advantageously, translational vibration modes are generated by the vibration regulation module from three initial elementary vibration patterns, understood as bases for modal decomposition of any vibration, having the property of creating a zero overall vibration at the frequency of the natural modes.
[0028] Preferably, the vibration regulation module maintains a relative phase between a distribution of the patterns on three orthogonal axes, in particular the quaternary symmetry axes of the resonator, an amplitude of each of the patterns and a relative orientation of each of the patterns between them.
[0029] Advantageously, the vibration regulation module positions at predetermined values, according to a time law, amplitudes, phases and orientations of each of said elementary patterns, the time law being capable of exploiting the symmetries of the defects of the resonator in order to average them.
[0030] For example, resonator defects are identified using an angular reference external to the resonator, used continuously or punctually.
[0031] According to another aspect, the invention relates to a method for measuring rotation of a rotation measuring device as described above.
[0032] Said rotation measurement method comprises at least: • a step of measuring the relative displacements between the masses for each pair of masses; • a step of calculating the movement of each mass based on the measurements of the relative displacements; • a step of decomposing the calculated movements of each mass according to the initial elementary vibration patterns; and • a step of constructing a rotation matrix from the decom- position obtained, preferably taking into account the defects of the resonator by corrective terms.
[0033] For example, the method comprises a step of providing rotation speed information from the forces calculated by the vibration regulation module, in particular by excluding forces resulting from monitoring the predetermined values according to the time law.
[0034] For example, the method provides rotation information from the integral, performed using rotation matrices or quaternions, of the rotation speed information. Brief description of the drawings
[0035] Other aims, characteristics and advantages of the invention will appear on reading the following description, given solely by way of non-limiting example, and made with reference to the appended drawings in which: • [Fig.l] illustrates a general constitution of a resonator according to the invention; • [Fig.2] illustrates a mass of the resonator of [Fig.l] considered separately; • [Fig.3] illustrates the ternary and quaternary symmetry axes of a cube; • [Fig.4] illustrates a placement of control means arranged between two masses; • [Fig.5] is a perspective view of one embodiment of the resonator according to the invention; • [Fig.6] is a perspective view of the embodiment of [Fig.5] without re presentation of a mass; • [Fig.7] is a detail view of [Fig.6]; • [Fig.8], [Fig. 10] and [Fig. 11] are perspective views of another mode of production of the resonator according to the invention; • [Fig.9] illustrates MEMS structures used in the embodiment of the resonator illustrated in [Fig.8], [Fig. 10] and [Fig. 11]; • [Fig. 12] illustrates mass vibration patterns; and • [Fig. 13] schematically illustrates a rotation measuring device according to the invention. Detailed description of at least one embodiment
[0036] Figures 1 to 3 respectively illustrate a general constitution of a resonator 1 of a rotation measuring device according to the invention, a mass of the resonator 1 considered separately and ternary and quaternary axes of symmetry of a cube.
[0037] The invention finds a useful application in any technical field where it is necessary to measure rotations along one or more axes, in relation to a space inertial, including, in particular, aiming and stabilization systems and inertial units.
[0038] According to an embodiment illustrated in [Fig.l], the resonator 1 comprises four identical, rigid, nested masses 2a, 2b, 2c, 2d connected to each other by first springs 3.
[0039] Each mass 2a, 2b, 2c, 2d has a plane of symmetry 4 and an axis of ternary symmetry 5, as shown in [Fig.2]. Thus, the mass is invariant during a rotation of 120° around the axis of ternary symmetry 5.
[0040] In addition, each mass 2a, 2b, 2c, 2d comprises two bases 6 connected by at least three rods 7.
[0041] For example, the bases 6 may be in the form of a disc with a circular or polygonal section.
[0042] According to another embodiment, as illustrated in [Fig.6], the bases 6 can have more complex shapes of the chamfered cube type.
[0043] The axes of ternary symmetry 5 of the masses 2a, 2b, 2c, 2d are oriented along the four axes of ternary symmetry 8, or of order three, of a cube 9, as illustrated in [Fig.3], having twelve edges 10. The four axes of ternary symmetry 8 of the cube 9 are concurrent with the center of symmetry O of the cube 9.
[0044] Axes X, Y and Z, forming an orthonormal reference frame centered on the center of symmetry O, constitute axes of quaternary symmetry, or of order four, of the cube 9. These axes X, Y and Z also constitute normals to the first bisector planes of the axes of ternary symmetry. Straight lines, passing through the center of symmetry O and having as direction vectors (JL, J-,0), (0, -L, J_), (-1-,0, _L), (--L, -1,0), (0, J_,- J_) and (_L # # fi fi fi ,0,- i) in the X, Y and Z reference frame, constitute normals to the second planes bis sectors of the ternary symmetry axes.
[0045] According to one embodiment, the first springs 3 are rectilinear rods stressed axially and in bending. The first springs 3 are arranged perpendicular to each other along the twelve edges 10 of the cube 9.
[0046] The first springs 3 make it possible to create, in the absence of vibration, an equilibrium for which the centers of masses 2a, 2b, 2c, 2d are positioned at the center of symmetry O of the cube 9.
[0047] In vibration, the centers of gravity of the masses 2a, 2b, 2c, 2d have a relative movement, while maintaining a global center of gravity of the masses 2a, 2b, 2c, 2d, constant and merged with the center of symmetry O of the cube 9.
[0048] It should be noted that the relative movement of the centers of gravity of the masses 2a, 2b, 2c, 2d is small in comparison with the dimensions of the resonator 1. The relative movement of the centers of gravity of masses 2a, 2b, 2c, 2d can be about Ipm relative to a length of about 1cm of edge 10 of cube 9.
[0049] In such a configuration, the hypothesis of small displacements is applicable and it is thus possible to neglect the changes in geometry to write equations describing an operation of the system.
[0050] The resonator 1 is connected to an external support, not shown in the figures, by means of second springs 11, in particular identical in shape to the first springs 3. Thus, the second springs 11 are of the rectilinear rod type arranged at each end of the masses 2a, 2b, 2c, 2d, preferably in symmetrical extension of the first springs 3. The symmetrical extension of the first springs 3 by the second springs 11 makes it possible to preserve the balance of the overall center of gravity of the masses 2a, 2b, 2c, 2d.
[0051] According to one embodiment, the second springs 11 more particularly connect the base 6 to the external support.
[0052] More particularly, the second springs 11 are three in number for each base. Thus configured, the twenty-four second springs 11 may have a section and / or a stiffness different from that of the first springs 3 connecting the masses 2a, 2b, 2c, 2d together.
[0053] Resonator 1 thus has cubic symmetry.
[0054] In order to allow the masses 2a, 2b, 2c, 2d to be nested, these can be made in at least two assembled parts. Alternatively, the masses 2a, 2b, 2c, 2d can be made by additive manufacturing methods allowing the manufacture of nested parts.
[0055] The resonator 1 is equipped with control means 12, 13, 14 comprising: - measuring means 19, capable of measuring a relative displacement between each pair of masses in at least two directions, and - application means 20, capable of applying inter-mass forces for each pair of masses in at least two directions.
[0056] The overall resultant of the applied forces is zero.
[0057] According to a particular embodiment, the resonator 1 is equipped with control means 12, 13, 14 configured to operate successively as means 19 for measuring the relative displacement between each pair of masses and as means 20 for applying inter-mass forces for each pair of masses.
[0058] Alternatively, the resonator 1 may be equipped with control means 19 dedicated to measuring the relative displacement between each pair of masses and control means 20 dedicated to applying inter-mass forces for each pair of masses.
[0059] The control means 12, 13, 14 may be electrostatic, piezoelectric or microelectromechanical system type transducers, also designated by the acronym MEMS for “MicroElectroMechanical Systems” in English.
[0060] For example, in the case of electrostatic transducers, each pair of masses is equipped with two pairs of electrodes 12, as control means 12, making it possible to measure the displacement and to apply electrostatic forces along the normal to the first bisector plane of the two masses.
[0061] Figure 4 illustrates a placement of control means 12, as electrodes 12, arranged between two masses 2a and 2b forming an angle of value equal to COS'^-t / ?), or approximately 109°28'.
[0062] The electrodes 12 may be in the form of plates and are arranged parallel to the first and / or second bisector plane of the ternary symmetry axes 5 of the two masses and make it possible to measure the displacement and to apply electrostatic forces along the normal respectively to the first and / or second bisector plane of the ternary symmetry axes 5 of the two masses.
[0063] Alternatively, the electrodes 12 can be replaced by piezoelectric elements positioned on the first springs 13 and making it possible to measure their deformations and / or to apply forces.
[0064] Figures 5 to 7 illustrate another illustrated embodiment, in which, respectively, [Fig.5] is a perspective view of the resonator 1, [Fig.6] a perspective view of the resonator 1 of [Fig.1] in which a mass is not shown and [Fig.7] a detail view of [Fig.6].
[0065] In the embodiment illustrated in Figures 5 to 7, electrostatic type transducers, in the form of plates, are placed on the rods 7 of the masses 2a, 2b, 2c, 2d.
[0066] In [Fig.6], mass 2a is not shown for the sake of clarity. The plates are placed on the rods 7 of the masses 2a, 2b, 2c, 2d so that each plate placed on the rod 7 of a mass corresponds to another associated plate, which is parallel to it, and arranged nearby on the rod 7 of another mass.
[0067] According to the example presented, [Fig.7] illustrates pairs of plates 13ca and 13ac, 13ba and 13ab, 13da and 13ad. According to the notation used, the first index indicates the mass on which the plate is arranged, the second index corresponds to the mass on which the associated plate is arranged. Thus, the plate 13ca is arranged on a rod 7 of the mass 2c and is associated with the plate 13ac which is arranged nearby on the rod 7 of the mass 2a.
[0068] Figures 8, 10 and 11 are perspective views of another embodiment of the resonator 1 according to the invention.
[0069] In such another embodiment, the transducers comprise six MEMS type planar structures 14 bonded to the masses 2a, 2b, 2c, 2d on the six faces of the cube 9.
[0070] In Figures 8 and 9, only three of the six structures 14 are shown to facilitate understanding. References a, b, c, d in [Fig.9] indicate the bonding areas
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[0083] corresponding to masses 2a, 2b, 2c, 2d, respectively. The MEMS structures 14 integrate the first springs 3, the second springs 11 and means of attachment to a housing 15 which envelops them. The MEMS structures 14 are capable of carrying out relative deformation measurements between two masses 2a, 2b, 2c, 2d and of applying inter-mass forces. In all embodiments, resonator 1 has cubic symmetry. In the embodiments presented, the resonator 1 comprises four masses 2a, 2b, 2c, 2d. However, the invention is not limited to the embodiments described and it is possible in particular to vary the number N of masses that the resonator 1 comprises provided that the constraints linked to the symmetry of the resonator are respected and this without departing from the scope of the invention. Indeed, the number N of masses that the resonator 1 comprises could exceed four, if the arrangement of these N masses respects the same symmetry constraints along the N axes of symmetry associated with each of the N masses, as for the embodiments described above. Alternatively, the presence of the second springs 11 could make it possible to dispense with the first springs 3. In such a configuration, the masses 2a, 2b, 2c, 2d then vibrate relative to the housing 15 operating as a neutral point and the measurement of the displacements and the application of the forces can be carried out relative to the housing 15. Cubic symmetry implies that, for each of the masses 2a, 2b, 2c, 2d taken individually, a stiffness of the translational links is identical in all directions. Under the effect of rotations, assuming zero damping, the initial translational vibrations of each of the masses propagate on the three axes of where x' z are respectively the positions of each mass along the X, Y, Z axes of quaternary symmetry of the resonator, XXZ are respectively the speeds of each mass along the X, Y, Z axes of quaternary symmetry of the resonator, XX < are respectively the accelerations of each mass along the X, Y, Z axes of quaternary symmetry of the resonator, Qx, LL. EL are respectively the rotation speeds of the resonator, in an inertial space, according to the X, Y, Z axes of quaternary symmetry of the resonator, and are respectively the resonance pulsations along the X, Y, Z axes of quaternary symmetry of the resonator corresponding to the triplet of degenerate modes corresponding to the type of vibration pattern considered (see below) with, in the case of perfect cubic symmetry, = = 6?z.
[0084] Equation Eq.l is the consequence of maintaining, in an isotropic medium, the direction of vibration in an inertial frame or, in other words, the consequence of the Coriolis forces in the frame of resonator 1.
[0085] In the case of perfect cubic symmetry, when the resonator 1 is subjected to rotation, an orientation of the vibration of each of the masses 2a, 2b, 2c, 2d remains fixed in an inertial space. Such orientations can then be used as an orientation reference.
[0086] If the cubic symmetry is not perfect and the damping is not zero, the equation Eq. 1 must be completed by error terms and it is necessary to apply forces in order to compensate for the losses and the differences between the pulsations and
[0087] The system has (Nl)*6 degrees of freedom, where N is the number of masses in the system. Thus, for resonator 1 with four masses 2a, 2b, 2c, 2d, there are theoretically eighteen balanced degrees of freedom: nine translational vibration modes and nine rotational vibration modes.
[0088] The distribution of the rotational vibration modes can be complex because they cannot be grouped into triplets at the same frequency. Indeed, given the shape of the masses 2a, 2b, 2c, 2d, their moment of inertia is not equal along the three axes of space.
[0089] On the other hand, for translational vibration modes, cubic symmetry makes it possible to guarantee isotropic behavior along the three dimensions of space.
[0090] [Fig. 12] illustrates translational vibration patterns of masses 2a, 2b, 2c, 2d.
[0091] A vibration pattern corresponds to a basis of modal decomposition of any vibration in translation, which has the property of creating a global vibration of the system, of four masses 2a, 2b, 2c, 2d in the present case, zero at the frequency of the natural modes.
[0092] There are, for the system of four masses 2a, 2b, 2c, 2d, a total of nine translational vibration modes including - first three degenerate modes, that is to say of the same frequency concerning a three-dimensional pattern, - three second degenerate modes, of frequency concerning a plane pattern, - three third degenerate modes, of frequency concerning a pattern linear.
[0093] The six degenerate modes of the plane and linear patterns are generally of almost identical frequency ~ -'A
[0094] The resonator is used with only one type of these patterns, either linear, planar, or three-dimensional.
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[0107] In the linear pattern, the translations are carried out along the same straight line, with two masses, corresponding to 2a and 2c, in one direction and two other masses, corresponding to 2b and 2d, in the other direction. At initialization, this line can be arbitrarily positioned along the X axis of quaternary symmetry. In the plane pattern, two masses, corresponding to 2a, 2b, are in translation in opposite directions to each other along a first straight line and two other masses, corresponding to 2c and 2d, are in translation in opposite directions to each other along a second straight line intersecting and perpendicular to the first straight line. At initialization, these lines can be chosen arbitrarily according to the bisectors of the X and Y axes of quaternary symmetry. In the three-dimensional pattern, at initialization, the translations of each of the masses 2a, 2b, 2c and 2d are carried out arbitrarily along their ternary symmetry axis 5 which merges by construction with one of the four ternary symmetry axes 8 of the cube 9. As a result, during the rotations of the resonator, the vibration axes of each of the patterns evolve according to equation Eq.l while maintaining their relative orientations. The total rotation, from initialization to the current time, can be represented by a rotation matrix as follows: 1 0 0 ' ■ COS / ) 0 sin / î ' 'cosy -siny 0' Mfjÿy 0 cosa -sina 0 1 0 siny cozy 0 .0 sina cosa. . - sin / i 0 cos / J. . 0 0 1. Or : a is an angle of rotation around the X axis of quaternary symmetry of the resonator, P is an angle of rotation around the Y axis of quaternary symmetry of the resonator, and V is an angle of rotation around the Z axis of quaternary symmetry of the resonator. In the case of the linear pattern, the vibrations of the positions of each of the masses 2a, 2b, 2c, 2d, can therefore be described, up to a permutation of masses, by the following relations, describing the vibrations of the four masses 2a, 2b, 2c, 2d in a single direction: ■M p^COSuV there is —Mapy 0 (Eq.2A) -*b yh A,. - v x cosw L you 0 0 (Eq.2B)
[0108]
[0109]
[0110] [YES] *d > x COSüVl (Eq.2C) 0 . 0 . ' - i^cosaVl (Eq.2D) are the coordinates of groups 2a, 2b, 2c, 2d, œL is the pulsation corresponding, in the case of perfect cubic symmetry, to linear pattern, — a\ — û;>'—
[0112] t is time, and
[0113] Vv is the amplitude of the vibration initially positioned along the x axis.
[0114] In the case of the plane pattern, the vibrations of the positions of each of the masses 2a, 2b, 2c, 2d, can therefore be described, up to a permutation of masses, by the relations following, describing the vibrations of the four masses 2a, 2b, 2c, 2d according to two di orthogonal sections:
[0115]
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[0120] Go . <ja . yh yd 'V^COSO^q (Eq.3A) 0 . '-V x COSW P q (Eq.3B) = Mafjy -Vvcoswpt 0 ' V^COS^ (Eq.3C) - VyCOSCOpZ 0 ' -v v œsa>q (Eq.3D) V y COS(Vpt 0 where x\ are the coordinates of the masses 2a, 2b, 2c, 2d, is the pulsation corresponding, in the case of perfect cubic symmetry, to the plan pattern, œ P ~ ~ a) y —
[0121] test the time,
[0122] is the amplitude of the vibration initially positioned along the x axis, and
[0123] Vy is the amplitude of the vibration initially positioned along the y axis.
[0124] In the case of the three-dimensional pattern, the vibrations of the positions of each of the masses 2a, 2b, 2c, 2d, can therefore be described, up to a permutation of masses, by the following relations, describing the vibrations of the four masses 2a, 2b, 2c, 2d along isotropic directions in three dimensions:
[0125]
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[0141] X a yh zb ■vxCOSWrq (Eq.4A) = M ap . Y V z COSü) T t ' -v^savq (Eq.4B) V z COSüJ T t ■ V x COS«' T t (Eq.4C) - VyCOSO?rf - V,COSWrZ. ■ -VxCOStorq (Eq.4D) , v y cosœ T t - VjCGs^r. ~d are the coordinates of the groups 2a, 2b, 2c, 2d, is the pulsation corresponding, in the case of perfect cubic symmetry, to the three-dimensional pattern, WT = OJX ~ ~ t is the time, is the amplitude of the vibration initially positioned along the x axis, Vv is the amplitude of the vibration initially positioned along the y axis, and vz is the amplitude of the vibration initially positioned along the z axis. Remarkably, all these motions can be described using the Map-y matrix, a pulsation M and by a linear combination of the following initial elementary vibrations, corresponding to " = P = y = 0 : ' <W1 (Eq.5A) xd L 0 'œWI (Eq.5C) 0 . 0 . '-cosmH (Eq.5D) 0 0 . xb» ^xc, Pxd are the initial vibrations of the positions of the masses a, b, c and d along the x axis and are affected by the coefficient vx. 0 (Eq.6A) COSWf 0 .
[0142] Pyb = 0 -COSûY 0 (Eq.6B)
[0143] Pyc — 0 - COSttY 0 ' (Eq.6C)
[0144] Pyd = • 0 coswf . 0 (Eq.6D)
[0145] WHERE Pya. P yc, Pyd are the initial vibrations of the positions of the masses a, b, c and d along the y axis and are affected by the coefficient L; and
[0146] P^ = 0 ' 0 .coswr. (Eq.7A)
[0147] P^ 0 ' 0 .cosmL (Eq.7B)
[0148] P^ = 0 ' 0 (Eq.7C) -COSOtL
[0149] P^ ■ 0 0 . -COSWf ' (Eq.7D)
[0150] where P^a, p^ P. æ» are the initial vibrations of the positions of the masses a, b, c and d along the z axis and are affected by the coefficient L.
[0151] The pulsation corresponding to the type of pattern considered: • for a linear pattern, w ~ • for a flat pattern, • for a three-dimensional pattern, ~ a,r
[0152] The three initial elementary vibration patterns retain the overall center of gravity. Indeed, they group together, at the initial instant, for each of the quaternary symmetry axes X, Y, Z, two pairs of masses 2a, 2b, 2c, 2d having opposite vibrations. The following property is then observed:
[0153] + *4 = - XB = + xc = - XD = VXCOSW? (Eq.8A)
[0154] + = - yB ~ -yc - + yD = (Eq.8B)
[0155] + Za= =
[0156] where XA, are the coordinates of the masses 2a, 2b, 2c, 2d, and
[0157] L', L and L are the amplitudes corresponding to each of the elementary vibrations initials.
[0158] The initial vibrations are distributed in all directions under the effect of the rotations. However, each of the vibration patterns retains the properties of re partition on the different masses 2a, 2b, 2c, 2d corresponding to the equations Eq.8A, Eq.8B and Eq.8C, thus allowing the initial vibrations to be distinguished.
[0159] The measure of the distribution (v^ rw, 1¾¾ t'a» vzy, Lx) these vi initial brations can then be carried out from the vibration present on each masses 2a, 2b, 2c, 2d and corresponding to each of the patterns according to the equation next:
[0160] I *a 1 v 1 L« 1 '1 0 0 -1 0 0 1 0 0 -1 0 0 1 a Vvy 0 1 0 0 -1 0 0 1 0 0 -1 0 xb 0 0 1 0 0 -1 0 0 1 0 0 -1 yh 1 0 0 -1 0 0 -1 0 0 1 0 0 b COSWÏ Vyy -1 “ 4 0 1 0 0 -1 0 0 -1 0 0 1 0 b xc Vy? 0 0 1 0 0 -1 0 0 -1 0 0 1 V Vx 1 0 0 1 0 0 -1 0 0 -1 0 0 - c Ey 0 1 0 0 1 0 0 -1 0 0 -1 0 1 ^<7 1 .0 0 1 0 0 1 0 0 -1 0 0 -L Xd y 1 Z'd 1 (Eq.9)
[0161] where vji is the consequence, under the effect of rotation, on an axis 'i' of the vibration initially present, for a = 0 = y = 0, on an axis 'j',
[0162] In the case of perfect cubic symmetry and zero damping, the parameters respect the following theoretical properties: [°163] ^Vx2 + Vxy2 + Vx.2 - Vx
[0164] = Vy
[0165]
[0166] and it is then possible to arbitrarily choose: - for a linear vibration pattern: vx = 1 and vy = L = 0 - for a plane vibration pattern: vv = vy = 1 and Vj - 0 - for a three-dimensional vibration pattern: = vy = = 1
[0167] [Fig. 13] schematically illustrates a rotation measuring device 16 comprising a resonator 1 as described previously, a vibration regulation module 17, and a rotation calculation module 18.
[0168] The regulation module 17 makes it possible to generate and maintain the vibrations of the re sonator 1.
[0169] The regulation module 17 comprises a measurement module 17a, a module calculation 17b and a control module 17c.
[0170] More specifically, the measurement module 17a makes it possible to calculate data representative of amplitude and phases of vibrations. vxz, vzy, vzz from the deformation measurements of the re sonator 1 provided by measuring means 19.
[0171] The calculation module 17b uses the data from the measurement module 17a to determine forces to be applied to the masses 2a, 2b, 2c and 2d along the quaternary symmetry axes X, Y and Z, / if ? f ■> f ,•> fff ■> fif ■> fvfs? f , in order to obtain J x <? J w J z» J xh J yb J zb ' xx J yc’ J ze J xd J ycP J z<d consignes d’amplitudes, de phases et des orientations relatives des motifs de vibration du résonateur 1.
[0172] According to an alternative embodiment, the calculation module 17b can also use the data from the measurement module 17a to determine the forces necessary for the orientation of the vibration patterns relative to the quaternary symmetry axes X, Y, Z.
[0173] The control module 17c controls the application means 20 as a function of the amplitudes, phases and orientations of forces from the calculation module 17b.
[0174] The rotation calculation module 18 is configured to calculate a rotation R performed by the rotation measuring device 16 from data representative of amplitude and vibration phases from the measurement module 17a.
[0175] In practice, cubic symmetry is never perfect (EL E'y 0½) and vibration damping is never zero. Thus, in order to compensate for these imperfections, the calculation module 17b calculates the necessary forces xa' ya' za' fxb' zP xJ yc' f xJ ycF AJ the maintenance of the properties of the vibration, from the measurement of the distributions (vxv tLy, vxz, Vy.Y, Vyy, Vv& Vzv, v^) of the initial vibration patterns (vv, on the three axes of the Quaternary symmetry X, Y and Z.
[0176] This thus makes it possible to maintain the relative phase between the distribution of the patterns on the three quaternary symmetry axes X, Y and Z. The distributions of the patterns on the quaternary symmetry axes X, Y and Z are respectively + + Ery + Vyy + vy and vxz +1¼ + v.
[0177] It is therefore a question of ensuring that the following conditions are respected:
[0178] Phase( v xx + + v^, he y + v vv + v zy ) = 0
[0179] Phase ( î\ v + Vyy + v zy , v xz + +v zz ) = 0
[0180] Phase ( v xz + v yz + v zz , v xx + r + v zx ) = 0
[0181] This also allows the amplitude of each of the vibration patterns to be maintained in enforcing the following conditions: - for a linear vibration pattern, । ;
[0182] for a plane vibration pattern, Jy +1^^ 4- — ] ;
[0183] This also makes it possible to maintain the relative geometric orientation of each of the vibration patterns by imposing the following conditions: for a plane vibration pattern, for a three-dimensional vibration pattern,
[0184] In a variant, this also makes it possible to maintain the geometric orientation of each of the vibration patterns relative to the quaternary symmetry axes X, Y and Z, by controlling forces compensating the Coriolis forces, represented by the second term of the equation Eq.l:
[0185] ■ 0 Qz -Qy' 'X -^Z 0 y -A 0 .Z.
[0186] From the forces to be applied to each of the masses 2a, 2b, 2c, 2d, the control module 17c calculates the inter-mass forces, namely two inter-mass forces for each of the six pairs of masses 2a, 2b, 2c, 2d.
[0187] For example, it may be chosen to direct the inter-mass forces according to the normal to the second bisector planes of the ternary symmetry axes 5 of the masses 2a, 2b, 2c, 2d, from six forces (y । y । J, one per pair of masses.
[0188] For example, it may be chosen to direct the inter-mass forces according to the normal to the first bisector planes of the ternary symmetry axes 5 of the masses, from six forces / ^2 f2 Y a Pæ" pair of masses. ab " ' ' ~cd}
[0189]
[0190] In this case, the relationships between the forces applied to the masses 2a, 2b, 2c, 2d and the inter-mass forces can be collected according to the following matrix equation: 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 -1 0 0 0 0 1 0 0 0 0 1 0 - 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 -1 -1 -1 0 0 0 0 0 0 0 0 -1 0 -1 0 -1 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 -1 0 -1 0 0 0 1 0 0 0 1 0 0 0 0 -1 1 0 0 0 0 0 0 -1 0 0 0 0 -1 -1 0 0 0 -1 0 0 0 0 0 -1 0 1 0 0 0 0 -1 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 0 1 0 1 0 £ fx J a fya f^a fxh A,. fyh ■^bd. fx — J fyc fl J ac fxd f2 J ad fyd 0 0 (Eq.10)
[0191]
[0192]
[0193]
[0194] It should be noted that the last three rows of matrix Eq.10 are necessary to guarantee the pseudo-inversion of the latter. They are therefore arbitrary. In the example of equation Eq.10, they are chosen so as to distribute the forces to be applied to the different application means 20. Furthermore, it is possible to delete up to three other rows without impacting the pseudo-inversion of the matrix. This allows to compare the forces applied by each pair of masses and to correct their relative differences by observing the differences appearing during cyclic deletions of rows. The control module 17c calculates the inter-mass forces to be applied to each of the masses 2a, 2b, 2c, 2d by classical methods of solving linear systems such as, for example, the following classical pseudo-inverse of least squares: masses in the case where there are means of applying forces relative to the housing.
[0197] We will now describe how to measure the displacements of the masses 2a, 2b, 2c, 2d.
[0198] For example, the measuring means 19 can use the measurements of relative displacements between two masses according to the normal to the second bisector plane of their ternary symmetry axes 5, from six measurements (mesi h... mesl one per pair of masses.
[0199] For example, the measuring means 19 can use the measurements of relative displacements between two masses according to the normal to the first bisector plane of the ternary symmetry axes 5 of the masses, from six measurements (me$2ah ... mes2r^ one per pair of masses.
[0200] The relative displacement measurements indicated above can be gathered according to the following matrix equation:
[0201] H 1 0 -1 -1 0 0 0 0 0 0 0' yf2jnes%c 0110 0 0 0-1-1 0 0 0 IAJ ^Jneslad 1 0 1 0 0 0 0 0 0 -1 0 -1 y fêjnesl 0 0 0 0 0 0 -1 1 0 y a 1 -! 0 Za 0 0 0 0 1 -1 0 0 0 0 -1 1 0 ^ = mes2ab 0 1 0 0 0 0 0 0 0 0 -1 0 v mes2ac 000000 00 1 oo-i 7 zc mes2 000 1 00000 -10 0 Y 0 0 0 0 1 0 0 -1 0 ooo mes2cd 1 0 0 1 0 0 1 0 0 10 0 d 0 1 0 0 1 0 0 1 0 0 1 o mes2hc 10 0 1 0 0 1 0 0 1 0 0 11 0 0 1 0 1 (Eq.ll)
[0202] It should be noted that the last three lines of the matrix Eq. 11 are necessary to guarantee the pseudo-inversion of the latter and correspond to the hypothesis that the movements are globally zero-mean. This is the case when inter-mass forces having a globally zero sum are applied, as described above.
[0203] Furthermore, it is possible to delete up to three other rows without affecting the pseudo-inversion of the matrix. This makes it possible to correct for differences between the different measurement channels by observing the differences occurring during cyclic deletions of rows.
[0204] According to the notation used, xa are the coordinates of the masses 2a, 2b, 2c, 2d.
[0205] The measurement module 17a calculates from the equation Eq. 11 the movement of each mass 2a, 2b, 2c, 2d.
[0206] For the calculation of the movements of the masses 2a, 2b, 2c, 2d, the measurement module 17a uses classical methods for solving linear systems such as, for example, the following classical pseudo-inverse of least squares:
[0207] J2mesl 'ah ■L A , , ^xy^abcd y. Xc yc Zc xd yd zd v / 2 jnesl v bd J2mesl * bc mes2ab mes2ac mes2ad mes2cd mes2bd mes2hc 0 0 0 ypjnesl^ mes 1m-#■ mes lad fëjnesl^ >pmeslM J2 jnesl V bc mes2ah mes2ae mes2ad me^cd mes2bd mes2bc 0 0 0
[0208] It is also possible to measure directly ( rrv , v _ r \ in case there are means The ±a> y & y cd, j
[0209] measuring displacements relative to the housing. In this case, the measurements will be corrected for the overall movement of the four masses. The measuring module 17a then distributes the calculated movements ( Y v -, y i' 7 v A! 7 yv 7 1 based on elementary patterns X c? 2 y Zy, yc, Ad, dd: ) initial vibration using equation Eq.9 recalled below:
[0210] ' R™ ' '1 0 0 -1 0 1½ 0 1 0 0 -1 VÏZ 0 0 1 0 0 1 0 0 -1 0 COSûJf Vyy = 1 4 0 1 0 0 -1 V.V4 0 0 1 0 0 1 0 0 1 0 VZy 0 1 0 0 1 i । .0 0 1 0 0 1 Xa 1 y " a 0 1 0 0 -1 0 0 ' 0 0 1 0 0 -1 0 Xc Zc 0 0 -1 0 0 -1 0 xd । zd । (Eq.9)
[0211] In the case of using a three-dimensional pattern, the distributions Vxw Vyx, v^ vy& v?A, vx>y V??) of the initial vibration patterns ( Vy, allow to reconstruct a rotation matrix Rp accounting for the transformation of the initial vibration, during the rotations, according to the equation Eq.l. In the case of an absence of defect, this matrix represents the rotation of the resonator 1 since the initial instant:
[0212] Vyx Vx' Rr = Vyy Vyy Vzy Vyz sX. J
[0213] In the case of a plane pattern, only the first two columns are measurable, so the third column is completed by the vector product of the first two columns:
[0214] 'Ux' Uy —— •Vvx- Vxy A 'Vyx' Vyy . Es. Vxz. .¾.
[0215] We then obtain a rotation matrix Rp representing the rotation of resonator 1 from the initial moment: 'VAx Vyx He Vyv Vyy. Tri Vyz
[0216] In the case of a linear pattern, only the first column is measured. This vector is representative of the rotation of the vibration initially positioned along the X axis of quaternary symmetry of the resonator. We then obtain a rotation matrix Rp representing the component, perpendicular to the X axis, of the rotation of resonator 1 since the initial instant:
[0218] Such a resonator 1 is therefore a gyroscope, because it makes it possible to measure the rotation that it undergoes (only two components of the rotation in the case of a linear vibration pattern).
[0219] The calculation module 18 constructs a rotation matrix R (Rp, Rp or Rp), according to the relations above, from a decomposition obtained by the measurement module 17a and, preferably, taking into account the defects of the resonator 1 by corrective terms.
[0220] First of all, because of measurement noise and the partial achievement of the objectives of the calculation module 17b, the matrices Rp, Rp or Rp can be ortho-normalized in order to calculate the matrices R^, Rpv or RT\
[0221] Otherwise, at any time, measurement noise, angular bias and drift appear. The bias and drift are dependent on these matrices which are representative of the state of the vibration distribution within the resonator 1. The faults are taken into account, for example, by a calibration carried out periodically in the laboratory making it possible to obtain an additional rotation matrix, Rcorr, corrective and representative of the angular bias and the integral of the drift since the initial time.
[0222] We then obtain the matrix R, constituting the corrected measurement of the rotation of resonator 1, by the following calculation: for a three-dimensional vibration pattern: R = R Corr R T \ (Eq.l2.A) for a plane vibration pattern: R = RCmrRp, (Eq.l2.B) for a linear vibration pattern: R = R Corr R L \ (Eq.l2.C)
Claims
1.
2.
3. Claims Rotation measuring device (16) comprising a mechanical resonator (1) comprising - at least four identical and rigid masses (2a, 2b, 2c, 2d), capable of exhibiting translational vibration modes, - control means (12,13,14) comprising • measuring means (19), capable of measuring a relative displacement between each pair of masses in at least two directions, and • application means (20), capable of applying inter-mass forces for each pair of masses in said at least two directions, - a vibration regulation module (17) receiving data from said measuring means (19) and issuing instructions for controlling said application means (20) as a function of said data, and - a rotation calculation module (18) configured to calculate a rotation (R) of said device from data representative of amplitude and phases of vibrations from said vibration regulation module (17); characterized in that the resonator (1) has cubic symmetry, in that the masses (2a, 2b, 2c, 2d) are nested between them, the masses each having a plane of symmetry (4) and a ternary axis of symmetry (5) oriented along a ternary axis of symmetry (8) of a cube (9), and in that the masses are connected to each other by first springs (3), and / or are connected to an external support of the resonator (1) by second springs (11). Rotation measuring device (16) according to claim 1, in which the masses (2a, 2b, 2c, 2d) each comprise two bases (6) connected by at least three rods (7). Rotation measuring device (16) according to claim 1 or 2, wherein the first springs (3) are positioned perpendicular to each other along the twelve edges (10) of the cube (9).
4. Rotation measuring apparatus (16) according to any one of claims 1 to 3, in which the first springs (3) are rectilinear rods stressed axially and / or in bending.
5. Rotation measuring apparatus (16) according to any one of the preceding claims, in which the second springs (11) are arranged at each end of the masses (2a, 2b, 2c, 2d), in particular in symmetrical extension of the first springs (3).
6. Rotation measuring apparatus (16) according to claim 5, in which the second springs (11) are rectilinear rods stressed axially and / or in bending.
7. Rotation measuring apparatus (16) according to claim 5 or 6, wherein the second springs (11) have an axial stiffness and / or a bending stiffness different from an axial stiffness and / or a bending stiffness of the first springs (3).
8. Rotation measuring apparatus (16) according to any one of the preceding claims, in which the masses (2a, 2b, 2c, 2d) are each made of at least two assembled parts.
9. Rotation measuring apparatus (16) according to any one of the preceding claims, in which the control means (12, 13) are transducers, in particular electrostatic or piezoelectric transducers, making it possible to measure deformations and / or to apply forces.
10. Rotation measuring apparatus (16) according to claim 9, in which the transducers are arranged parallel to a first and / or a second bisector plane of the ternary symmetry axes of each pair of two masses (2a, 2b, 2c, 2d) and make it possible to measure a displacement and to apply forces along a normal respectively to the first and / or to the second bisector plane of the ternary symmetry axes of each pair of two masses (2a, 2b, 2c, 2d).
11. Rotation measuring apparatus (16) according to claim 9 or 10, dependent on claim 2, in which the transducers are plate-shaped and are arranged on the rods (7) of the masses (2a, 2b, 2c, 2d), so that each plate placed on the rod (7) of one mass (2a, 2b, 2c, 2d) corresponds to another associated plate which is parallel to it and arranged nearby on the rod (7) of another mass (2a, 2b, 2c, 2d).
12. Rotation measuring apparatus (16) according to any one of claims 1 to 9, in which the control means (14) are trans- micro electromechanical system (MEMS) type drivers.
13. Rotation measuring apparatus (16) according to claim 12, in which the transducers are glued to the masses (2a, 2b, 2c, 2d) on the six faces of the cube (9) and integrate the first springs (3), the second springs (11) and means of fixing to a housing (15) which encloses them, the transducers being capable of carrying out measurements of relative deformation between two masses (2a, 2b, 2c, 2d) and of applying inter-mass forces.
14. Rotation measuring apparatus (16) according to any one of the preceding claims, in which translational vibration modes are generated by the vibration regulation module (17) from three initial elementary vibration patterns, understood as modal decomposition bases of any vibration, having the property of creating a zero overall vibration at the frequency of the natural modes.
15. Rotation measuring apparatus (16) according to claim 14, in which the vibration regulation module (17) maintains a relative phase between a distribution of the patterns on three orthogonal axes, in particular the quaternary symmetry axes (X, Y, Z) of the resonator (1), an amplitude of each of the patterns and a relative orientation of each of the patterns between them.
16. Rotation measuring apparatus (16) according to claim 14 or 15, in which the vibration regulation module (17) positions at predetermined values, according to a time law, amplitudes, phases and orientations of each of said elementary patterns, the time law being capable of exploiting the symmetries of the defects of the resonator (1) in order to average them.
17. Rotation measuring apparatus (16) according to claim 16, in which the defects of the resonator (1) are identified using an angular reference external to the resonator (1), used continuously or punctually.
18. Method for measuring rotation of a rotation measuring device (16) according to any one of claims 14 to 17, characterized in that it comprises at least: • a step of measuring the relative displacements between the masses (2a, 2b, 2c, 2d) for each pair of masses; • a step of calculating the movement of each mass (2a, 2b, 2c, 2d) as a function of the measurements of the relative displacements; • a step of decomposing the calculated movements of each mass (2a, 2b, 2c, 2d) as a function of the initial elementary vibration patterns; and • a step of constructing a rotation matrix (R) from the decomposition obtained, preferably taking into account the defects of the resonator (1) by corrective terms.
19. Rotation measurement method according to claim 18, characterized in that it comprises a step of providing rotation speed information from the forces calculated by the vibration regulation module (17).
20. Rotation measurement method according to claim 19, characterized in that it provides rotation information from the integral, carried out using rotation matrices or quaternions, of the rotation speed information.