Mechanical resonator comprising four nested masses, each possessing a ternary axis of symmetry oriented along a ternary axis of symmetry of a cube, and associated method for calculating rotational speed
Patent Information
- Authority / Receiving Office
- FR · FR
- Patent Type
- Patents
- Current Assignee / Owner
- SAFRAN ELECTRONICS & DEFENSE (FR)
- Filing Date
- 2024-06-10
- Publication Date
- 2026-06-12
Abstract
Description
Title of the invention: Mechanical resonator comprising four nested masses, each having a ternary axis of symmetry oriented along a ternary axis of symmetry of a cube, and associated method for calculating rotational speed. Technical field
[0001] The invention relates to the field of inertial sensors, such as vibrating or resonating gyroscopic sensors, used in particular to measure rotations.
[0002] The invention also relates to a method for calculating rotational speed. Prior techniques
[0003] Vibrating gyroscopic sensors are commonly used in many fields because of their robustness, low power consumption and speed of implementation.
[0004] Such vibrating gyroscopic sensors include 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 consisting 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, it is known, in particular from US document 9,631,929, of resonators with two nested masses having a common center of gravity, in order to obtain a symmetrical and planar 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 gyroscope.
[0008] In addition, a gyroscope-type device capable of measuring the three components of the rotational speed is known from US document 5,625,145.
[0009] Finally, US document 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 motion in three dimensions, an isotropic distribution of the masses in motion with respect to the center of gravity leading to a global cancellation of external forces during an acceleration.
[0011] Nevertheless, the set of eight masses has many degrees of freedom that can be excited, which creates a certain complexity in control
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[0023] movements of the resonator, taking into account the number of parasitic vibration modes. Description of the invention In view of the above, the aim of the invention is to provide a compact, precise resonator with strong symmetry and simple implementation that allows the measurement of rotations in a three-dimensional frame of reference. The invention relates to a mechanical resonator comprising at least four masses, each having its center of mass positioned at the center of a cube. The masses are nested together and each possesses a ternary axis of symmetry oriented along a ternary axis of symmetry of the cube. The masses are each connected by elastic supports to a frame of the resonator. The resonator includes control means comprising measurement means capable of measuring a relative displacement between each pair of masses along at least two directions and application means capable of applying inter-mass forces for each pair of masses along at least two directions. The resonator includes a vibration control module that receives data from the measuring means and issues instructions to control the application means according to the data received. The vibration control module is configured to implement a radial vibration mode of the resonator corresponding to a vibration of each mass in the direction of its ternary axis of symmetry at a vibration amplitude of predetermined value and identical between the masses. Such a radial vibration mode is frequency-separated from other vibration modes. Using such a radial vibration mode simplifies the implementation of the resonator, particularly when the resonator is used as a gyroscope. For example, the vibration control module implements the radial vibration mode of the resonator using time-varying laws of mass positions expressed by the following equations: T P2a = P 1 P^ = P .1. where P — pcoswz with, -r -i i. p: amplitude of the vibration expressed in pm, and : vibration frequency expressed in rad / s ' 1 ' p^=p -1 .P» According to one feature, the resonator further includes a rotational speed calculation module configured to calculate, in an orthonormal coordinate system of the resonator, the speed of a rotation applied to the resonator from a difference in relative displacement between each pair of masses compared to the relative displacement between each pair of masses due to the radial mode of vibration.
[0024] During rotation applied to the resonator, internal forces with zero sum appear, inducing displacements between each pair of masses. These displacements are different from the displacements due solely to the radial mode of vibration. It thus becomes possible to calculate the 3D rotational speed from the observed displacement differences.
[0025] According to one embodiment, the rotational speed calculation module is configured to calculate acceleration differences for each mass pair based on the time variation of the relative displacements between each mass pair, and to calculate the rotational speed of the resonator in a three-dimensional frame associated with the resonator from a system of linear equations for the acceleration differences calculated for each mass pair. For example, the three-dimensional frame associated with the resonator corresponds to the orthonormal frame of the resonator.
[0026] For example, the control means are transducers, in particular electrostatic or piezoelectric transducers, allowing deformations to be measured and / or forces to be applied.
[0027] For example, the control means are microelectromechanical systems (MEMS) type transducers allowing the measurement of deformations and / or the application of forces.
[0028] Preferably, the elastic supports are oriented along quaternary axes of symmetry of the resonator. Such a configuration improves the overall symmetry of the resonator.
[0029] Advantageously, each mass comprises two bases connected to each other by at least three rods. Such a configuration facilitates the manufacture of the masses.
[0030] According to another aspect, the invention relates to a method for calculating the speed of a rotation applied to a resonator as defined above. The method comprises at least: - a step of implementing a radial vibration mode of the resonator corresponding to a vibration of each mass in the direction of its ternary axis of symmetry at a vibration amplitude of predetermined value and identical between the masses, - 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 measurements of relative displacements; - a step of decomposing the calculated movements of each mass by distinguishing a first part corresponding to the effects of the radial mode of vibration and a second part corresponding to the effects of the Coriolis forces induced by the applied rotation; and - a step of constructing a first rotation speed matrix from the decomposition obtained and according to a first calculation method.
[0031] Advantageously, the method includes an additional step of constructing a second rotation speed matrix from the decomposition obtained and according to a second calculation method different from the first calculation method.
[0032] Preferably, the method further includes a step of comparing the first and second rotation speed matrices followed by a step of issuing an alert message if a discrepancy found between the first and second rotation speed matrices exceeds a predetermined alert threshold value.
[0033] According to another aspect, the invention relates to a transport device equipped with a resonator and implementing a calculation method as defined above. Brief description of the drawings
[0034] Other objects, features and advantages of the invention will become apparent from the following description, given solely by way of non-limiting example, and made with reference to the accompanying drawings in which:
[0035] [Fig-1] illustrates a general construction of a resonator according to an example of realization of the invention;
[0036] [Fig.2] illustrates a mass of the resonator of the [Fig.1] considered separately;
[0037] [Fig.3] illustrates ternary and quaternary axes of symmetry of a cube;
[0038] [Fig.4] illustrates the resonator of [Fig.1] without a frame or elastic supports and with two control plates;
[0039] [Fig.5] schematically illustrates the resonator of [Fig.1] and,
[0040] [Fig.6] is a flowchart of a method for calculating the rotational speed of a resonator of the [Fig.1] according to an example of an embodiment of the invention. Detailed description of at least one embodiment
[0041] Figures 1 to 3 respectively illustrate a general construction of a resonator 1 according to an example of an embodiment of the invention, a mass of the resonator 1 considered separately and the ternary and quaternary axes of symmetry of a cube.
[0042] According to the embodiment illustrated in [Fig. 1], the resonator 1 comprises four identical, rigid masses 2a, 2b, 2c, 2d, nested together. The masses 2a, 2b, 2c, 2d are connected to a frame 3 of the resonator 1 by elastic supports 4.
[0043] Each mass 2a, 2b, 2c, 2d has a ternary axis of symmetry 5, as shown in [Fig. 2]. Thus, the mass is invariant under a rotation of 120° around of the ternary axis of symmetry 5. It should be noted that identical or similar elements carry the same numerical references from one figure to another.
[0044] Each mass 2a, 2b, 2c, 2d comprises two bases 6 connected to each other by at least three rods 7.
[0045] Here, the bases 6 have a surface defined by three orthogonal planes and a portion of a sphere. Alternatively, the bases 6 may have the shape of a disk with a circular or polygonal cross-section, a chamfered cube, or a truncated cone. Other base shapes are conceivable provided the symmetry conditions are met.
[0046] The ternary symmetry axes 5 of the masses 2a, 2b, 2c, 2d are oriented along the four ternary symmetry axes 8, or of order three, of a cube 9, as illustrated in [Fig.3], having twelve edges 10. The four ternary symmetry axes 8 of the cube 9 are concurrent at the center of symmetry O of the cube 9.
[0047] Axes X, Y, and Z, forming an orthonormal coordinate system centered on the center of symmetry O, constitute quaternary, or fourth-order, axes of symmetry of the cube 9. These axes X, Y, and Z also constitute normals to the first bisecting planes of the ternary axes of symmetry. Lines passing through the center of symmetry O and having direction vectors (-L, -L, 0), (0, -L, -L), (-L, 0 ... & fi ^2 y2 ^2 y2 fi fi 72 _L) and (-^,0,- -L) in the X, Y and Z coordinate system, constitute normals to the second p ,12 p bisecting planes of the axes of ternary symmetry.
[0048] According to the example illustrated in [Fig. 1], the elastic supports 4 are straight rods subjected to axial and bending stress. The elastic supports 4 are arranged perpendicular to each other along the twelve edges 10 of the cube 9.
[0049] The elastic supports 4 make it possible to create, in the absence of vibration, an equilibrium for which the centers of mass 2a, 2b, 2c, 2d are positioned at the center of symmetry O of the cube 9.
[0050] In vibration, the centers of gravity of the masses 2a, 2b, 2c, 2d have a relative motion, while maintaining a global center of gravity of the masses 2a, 2b, 2c, 2d, constant and coincident with the center of symmetry O of the cube 9.
[0051] It should be noted that the relative motion 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 motion of the centers of gravity of the masses 2a, 2b, 2c, 2d can be of about Ipm with respect to a length of about 1cm of the edge 10 of the cube 9.
[0052] In such a configuration, the assumption of small displacements is applicable and it is thus possible to neglect changes in geometry to write equations describing the operation of the system.
[0053] For example, the resonator 1 is connected to an external support, not shown in the figures, by means of springs not shown, in particular identical in shape to the elastic supports 4. For example, the springs are of the straight rod type arranged at each end of the masses 2a, 2b, 2c, 2d, preferably in symmetrical extension of the elastic supports 4. Alternatively, the springs can be arranged directly on the frame 3.
[0054] According to one embodiment, the springs more particularly connect the base 6 to the outer support.
[0055] More specifically, there are three springs for each base. Thus configured, the twenty-four springs can have a cross-section and / or stiffness different from that of the elastic supports 4.
[0056] In all embodiments, the resonator 1 has cubic symmetry.
[0057] To allow the nesting of masses 2a, 2b, 2c, 2d, these masses can be made in at least two assembled parts. Alternatively, masses 2a, 2b, 2c, 2d can be made by additive manufacturing methods that allow the production of nested parts.
[0058] The resonator 1 is equipped with control means 12 comprising: - measuring means 19, capable of measuring a relative displacement between each pair of masses along at least two directions, and - 20 application means, capable of applying inter-mass forces for each pair of masses along at least two directions.
[0059] The overall resultant of the applied forces is zero.
[0060] According to a particular embodiment, the resonator 1 is equipped with control means 12 configured to operate successively or simultaneously as means for measuring 19 the relative displacement between each pair of masses and as means for applying inter-mass forces 20 for each pair of masses.
[0061] Alternatively, the resonator 1 can be equipped with first control means dedicated to measuring the relative displacement between each pair of masses and second control means dedicated to applying inter-mass forces for each pair of masses. In this case, the first control means are different from the second control means.
[0062] The control means 12 can be electrostatic, piezoelectric or microelectromechanical system type transducers, also designated by the acronym MEMS for "MicroElectroMechanical Systems" in English.
[0063] According to one embodiment, the control means 12 comprise six plates 13 glued to the masses 2a, 2b, 2c, 2d on the six faces of the cube 9 ([Fig.4]).
[0064] Figure 4 illustrates the resonator of Figure 1 without the frame 3 or the elastic supports 4, and on which only two of the six plates 13 are shown to facilitate the understanding. The plates 13 are suitable for performing relative deformation measurements between two masses 2a, 2b, 2c, 2d and for applying inter-mass forces.
[0065] 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 the number N of masses comprising the resonator 1 can be varied in particular provided that the constraints related to the symmetry of the resonator are respected and this without departing from the scope of the invention.
[0066] Fig. 5 schematically illustrates the architecture of a resonator 1 comprising a vibration control module 17 and a rotation speed calculation module 18, according to an example embodiment.
[0067] Alternatively, it remains possible that the vibration control module and / or the rotation speed calculation module are not integrated into the resonator 1. In this case, the vibration control module and / or the rotation speed calculation module are associated with the resonator 1 within a rotation speed measuring device.
[0068] The control module 17 includes a measurement module 17a, a calculation module 17b and a control module 17c.
[0069] More specifically, the measurement module 17a is configured to calculate representative amplitude and phase vibration data from resonator 1 deformation measurements provided by measurement means 19.
[0070] The calculation module 17b uses data from the measurement module 17a to determine forces to be applied to the masses 2a, 2b, 2c, and 2d in order to induce a radial vibration mode corresponding to a vibration of each mass in the direction of its ternary axis of symmetry 5 at a vibration amplitude of predetermined value, identical for all masses. The radial vibration mode will be described in more detail, in particular by equations 3 below. It should be noted that the radial vibration mode is unique, this mode being generally separated from other modes in terms of frequency. Thus, the 90° rotation of its displacement field does not correspond to the displacement field of another mode, which results in the vibration.In other words, the radial mode of vibration follows the movement of the resonator during rotation, whereas generally the vibration maintains its orientation in an inertial frame of reference by switching from one mode to another within a triplet of translational modes having the same frequency and rotated 90° relative to each other. The predetermined value of the amplitude can be stored in a memory of the computing module 17b.
[0071] The control module 17c controls the application means 20 according to the amplitude, phases, orientations and values of the forces from the calculation module 17b.
[0072] The rotation speed calculation module 18 is configured to calculate a speed Q of a rotation R applied to the resonator 1 from data from the measurement module 17a. More specifically, the module 18 calculates the rotation speed Q from a relative displacement difference between each mass pair calculated with respect to the relative displacement between each mass pair due to the radial mode of vibration alone.
[0073] According to one embodiment, the rotation speed calculation module 18 is configured to calculate acceleration differences for each mass pair from the time variation of the relative displacements between each mass pair and to calculate the rotation speed of the resonator in a three-dimensional frame associated with the resonator from a system of linear combinations of the acceleration differences calculated for each mass pair.
[0074] The laws governing the variation over time of the position P and the velocity Q are defined by the following relations:
[0075] P = pcoswf (Eq. 1)
[0076] Q = - pwsinwf (Eq. 2)
[0077] with,
[0078] : amplitude of the vibration (generally on the order of 1 pm)
[0079] (V: vibration frequency (generally on the order of 50,000 rad / s)
[0080] Neglecting imperfections in resonator 1 and in the absence of rotation and global acceleration of resonator 1, the positions of the masses are expressed during the radial mode of vibration induced by the control module 17 by the following equations:
[0081] he rr Pa=P 1 Pb = P -1 1J L 1
[0082] where PA, PB, Pc, Posont respectively represent the positions of masses 2a, 2b, 2c and 2d in the
[0083] orthonormal XYZ coordinate system of the resonator. With these assumptions, the accelerations of the masses can be obtained by the second derivative with respect to time t of the position of each mass and are expressed by the following equations:
[0084] A0 = -Poe 2 1,y BQ ^ -Pw 2 -i ,r co - . i 11 F - 11 (Eq. 4)
[0085] If we now consider a rotational speed Q- imposed on FQ resonator and in the absence of global resonator acceleration, the Coriolis accelerations add up perpendicularly to the direction of the radial mode vibrations.
[0086] The accelerations of the masses are then expressed by the following relation:
[0087] on a dP> (Eq- 5)
[0088] By hypothesis, the variation in the position of the center of mass of the resonator is zero and therefore Pa + ?b + + H results from the global acceleration applied to the The resonator is also zero as expressed by the following equation:
[0089] '0] (Eq. 6) L
[0090] In one embodiment, the rotation speed calculation module 18 is configured to calculate acceleration differences for each mass pair from the time variation of the relative displacements between each mass pair.
[0091] The calculation of the rotational speed of the resonator in the orthonormal XYZ coordinate system of the resonator is carried out by the rotational speed calculation module 18 from the following system of linear equations:
[0092] 11 0 (Eq. 7A) ^Pa-b+cd , An 7 ~^a-b+cd~^a~^b + ^c~^d~ 0 -8g 01 -Qy r0 r-Qz (Eq. 7B) ^Pa-C+DB , An ~ dp ~ A-C+DB “ JA '?
[0093] 01 Qyl (Eq. 7C) ^PPbCaAD, An 3 0 -8g dP “ ^B-C+AD ~^B"^C + ^A~^D IJ 0 J
[0094] Thus for each equation above corresponding to the differential inter-mass accelerations we obtain on one of the axes X, Y or Z the acceleration due to the radial mode of vibration (term in - 4 / W ) while on the other two axes we obtain an acceleration proportional to two components of the velocity of the imposed rotation (term in QQ ) corresponding to the effects of the Coriolis forces.
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[0108] It should be noted that there are several ways to calculate the components Üx, Qy and of the rotation speed Q as expressed by the following relations 0' (Eq. 8A) -8QQX= (rA-rc+vD~rBy 0 . 1. 0 (Eq. 8B) (vB-rc+rA-vD)- -1 0 T (Eq. 9A) -8QQ,= (rB-vc+rA-rDy 0 .0. 0 (Eq. 9B) -SQa,= (rrrB+rc-re 0 -1 0' (Eq. 10A) -8Q^= (rA-rB+rc-rD) This gives us two different calculation methods for each component of the rotational speed Q, which can be used for redundancy, verification, or simplification. It thus becomes possible to construct a first rotation speed matrix Q1 from a first calculation method, for example by considering equations 8A, 9A and 10A and a second rotation speed matrix Q2 from a second calculation method, for example by considering equations 8B, 9B and 10B. Figure 6 illustrates the different steps of a method for calculating a rotational speed applied to a resonator 1 according to an example of an embodiment of the invention. The process is implemented in particular using the rotation speed calculation module 18. The process begins with a step 21 of implementation of a radial vibration mode of the resonator 1 carried out by the vibration control module 17. The process continues with a step 22 of measuring the relative displacements between the masses 2a, 2b, 2c, 2d for each pair of masses of the resonator 1. After step 22 of measuring relative displacements, the rotation speed calculation module 18 calculates the movement of each mass 2a, 2b, 2c, 2d as a function of the relative displacement measurements (step 23).
[0109] After step 23 of calculating the motion of each mass, the rotation speed calculation module 18 performs a decomposition of the calculated motions by distinguishing a first part corresponding to the effects of the vibration of the radial mode of vibration and a second part corresponding to the effects of the Coriolis forces induced by the applied rotation (step 24).
[0110] The process continues with a step 25 of constructing a first rotation speed matrix Ql from the decomposition obtained and according to a first calculation method.
[0111] After step 25 of constructing the first rotation speed matrix Q1, the process continues with a step 26 of constructing a second rotation speed matrix Q2 from the decomposition obtained and according to a second calculation method, different from the first calculation method.
[0112] In the next comparison step 27, the first rotational velocity matrix Q1 and the second rotational velocity matrix Q2 are compared.
[0113] If a discrepancy observed between the first Q1 and second Q2 rotation speed matrices exceeds a predetermined alert threshold value, the rotation speed calculation module 18 issues an alert message (step 28).
Claims
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2. Demands Mechanical resonator (1) comprising: - at least four masses (2a, 2b, 2c, 2d), each having a center of mass positioned at the center of symmetry (O) of a cube (9), the masses (2a, 2b, 2c, 2d) being nested among themselves and each possessing a ternary axis of symmetry (5) oriented along a ternary axis of symmetry (8) of the cube (9), the masses each being connected by elastic supports (4) to a frame (3) of the resonator (1), - control means (12) comprising • measuring means (19), capable of measuring a relative displacement between each pair of masses along at least two directions, and • application means (20), capable of applying inter-mass forces for each pair of masses along said masses in at least two directions, a vibration control module (17) receiving data from said measuring means (19) and issuing instructions to control said application means (20) according to said data, characterized in that the vibration control module (17) is configured to implement a radial vibration mode of the resonator corresponding to a vibration of each mass in the direction of its ternary symmetry axis (5) at a vibration amplitude of predetermined value and identical between the masses (2a, 2b, 2c, 2d). Resonator (1) according to claim 1, wherein the vibration control module (17) implements the radial vibration mode of the resonator using time variation laws of the positions of the masses (2a, 2b, 2c, 2d) expressed by the following equations: T ■ -r ■ i ' -r aJ [1 1 ^2.= P p^p -ii .
1. . i. .-i. where P = pcoset with, p: amplitude of the vibration expressed in pm, and w: angular frequency of the vibration expressed in rad / s
3. Resonator (1) according to claim 1 or 2, further comprising a rotation speed calculation module (18) configured to calculate in an orthonormal (XYZ) frame of the resonator (1) the speed of a rotation applied to the resonator (1) from a relative displacement difference between each pair of masses compared to the relative displacement between each pair of masses due to the radial mode of vibration.
4. Resonator (1) according to claim 3, wherein the rotation speed calculation module (18) is configured to calculate acceleration gaps for each mass pair from the time variation of the relative displacements between each mass pair and to calculate the rotation speed of the resonator (1) in a three-dimensional frame associated with the resonator (1) from a system of linear equations of the acceleration gaps calculated for each mass pair.
5. Resonator according to any one of claims 1 to 4, wherein the control means (12) are electrostatic or piezoelectric transducers, enabling the measurement of deformations and / or the application of forces.
6. Resonator according to any one of claims 1 to 4, wherein the control means (12) are microelectromechanical systems (MEMS) type transducers for measuring deformations and / or applying forces.
7. Resonator according to any one of claims 1 to 6, wherein the elastic supports (4) are oriented along quaternary symmetry axes (X, Y, Z) of the resonator (1).
8. Resonator according to any one of claims 1 to 7, wherein the masses (2a, 2b, 2c, 2d) each comprise two bases (6) connected to each other by at least three rods (7).
9. Method for calculating the speed of a rotation applied to a resonator (1) according to any one of claims 1 to 8, characterized in that it comprises at least: - a step of implementing a radial mode of vibration of the resonator corresponding to a vibration of each mass in the direction of its ternary axis of symmetry (5) at a vibration amplitude of predetermined value and identical between the masses (2a, 2b, 2c, 2d),
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12. - 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 motions of each mass (2a, 2b, 2c, 2d) by distinguishing a first part corresponding to the effects of the radial mode of vibration and a second part corresponding to the effects of the Coriolis forces induced by the applied rotation; and - a step of constructing a first rotation speed matrix (Ql) from the decomposition obtained and according to a first calculation method. Calculation method according to claim 9, comprising an additional step of constructing a second rotation speed matrix (Q2) from the decomposition obtained and according to a second calculation method different from the first calculation method. Calculation method according to claim 10, further comprising a step of comparing the first (Q1) and second (Q2) rotation speed matrices followed by a step of issuing an alert message if a discrepancy found between the first (Q1) and second (Q2) rotation speed matrices exceeds a predetermined alert threshold value. Transport device equipped with a resonator (1) according to any one of claims 1 to 8 and implementing a calculation method according to any one of claims 9 to 11.