Abstract:
Diapason type gyrometers using a micro-mechanical structure of vibrating beams. The gyrometer includes a micro-machined sensitive element with at least two symmetrically positioned excitation beams on each side of and parallel to a sensitive Oy axis of the gyrometer. The two beams are connected at their ends through at least one transverse element fixed in its central part to the sensitive Oy axis, to a frame through an elastic torsion return element acting in opposition to the rotation of the transverse element about the Oy axis. The elastic return elements are sized such that the variation of their resonant natural frequency in torsion with temperature is similar to the variation of the resonant natural frequency in bending of the beams with temperature. Such a device may find particular application in the measurement of the angular velocity of a mobile.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The invention relates to machined micro-mechanisms comprising return elements in the form of beams subjected to simultaneous bending and torsion deformations. More precisely, the invention relates to diapason type gyrometers using a micro-mechanical structure of vibrating beams. 
     2. Description of the Related Art 
     In some machined micro-mechanisms, it is sometimes necessary to have resonance modes in translation and other resonance modes in rotation simultaneously. The sensitive element of a diapason gyrometer is one of these micro-mechanisms. 
     FIG. 1 shows a simplified drawing of a sensitive micro-machined element  10  of a diapason type gyrometer with a symmetrical double beam structure. The sensitive element has two degrees of freedom about the Ox and Oz axes perpendicular to a reference coordinate system Oxyz. The purpose of the gyrometer is to measure the angular velocity Ω of the reference Oxz rotating about the Oy axis perpendicular to this reference. 
     The sensitive element of the gyrometer comprises a first pair of two excitation beams  12  and  14 , and a second pair of two other excitation beams  16  and  18 . The excitation beams in the first pair and the second pair are located in the same Oxy plane of the reference coordinate system and are parallel to a sensitive axis YY′ coincident with the Oy axis. The first and the second pairs are located on opposite sides of the YY′ axis and at approximately equal distances from it. 
     Each pair of excitation beams comprises a central mass connecting the two beams in the pair at their center, a mass ml at the middle of the first pair and a mass m 2  at the middle of the second pair. 
     The ends of the beams  12 ,  14 ,  16 ,  18  located on one side are connected to a first transverse element  20  and to a second transverse element  22  located in the same Oxy plane as the excitation beams and approximately perpendicular to these beams. 
     The first  20  and second  22  transverse elements comprise a first return beam  24  and a second return beam  26  (or return element) respectively, that have torsion axes collinear with the sensitive axis YY′ of the gyrometer. The ends of the first and the second return beams are connected to a first frame  28  and a second frame  30  respectively, rigidly fixed to the gyrometer. 
     In order to measure the angular velocity during one rotation of the gyrometer, an electrostatic device  32  creates deliberate excitations E 1  and E 2  respectively on masses m 1  and m 2  respectively at the resonant natural frequency of the excitation beams and the return beams. These excitation forces E 1  and E 2  have the same amplitude but opposite directions, and are applied to masses m 1  and m 2  parallel to an XX′ axis coincident with the Ox axis of the reference coordinate system. The excitations E 1  and E 2  produce displacements of masses m 1  and m 2  in two opposite directions at instantaneous velocities v 1  and v 2  respectively. One rotation of the gyrometer with a sensitive element  10  subject to excitations E 1  and E 2  produces a pair of Coriolis forces F 1  and F 2  about the sensitive axis YY′ on masses m 1  and m 2  respectively, causing a rotation of the transverse elements  20 ,  22  and torsion of the return beams  24  and  26  about this axis. 
     The angular rotation velocity Ω of the sensitive element  10  is determined by a measurement of the position of masses m 1  and m 2 . The Coriolis moment at masses m 1  and m 2  is calculated as follows:          Mcor          /     y       =               t            (     J   ·   Ω     )                              
     where J≈J 0 +J 1 sin ωt 
     Mcor/ y : Coriolis moment applied on masses m 1  and m 2 ; 
     Ω: angular velocity of the sensitive element  10  about the sensitive axis YY′; 
     ω: natural angular frequency of masses m 1  and m 2 ; 
     J: moment of inertia of masses m 1  and m 2  about the YY′ axis; 
     Jo: constant part of the moment of inertia J; 
     J 1 : oscillating part of the moment of inertia generated by movement of the masses about the XX′ axis at the natural angular frequency ω. 
     The positions of the masses m 1  and m 2  are calculated by capacitive effect, and the angular velocity Ω of the gyrometer is calculated using known methods making use of the masses m 1  and m 2  and the torsion and the bending constants of the beams of the sensitive element. 
     Coriolis forces exerted on the element during one rotation of the gyrometer create a torsion in the return elements at the oscillation frequency of the excitation, while the deliberate excitation of masses m 1  and m 2  causes bending of the excitation beams. 
     The resulting bending force and amplitude of bending on a beam are related to each other by Young&#39;s modulus for the material used, while the torsion forces and the resulting torsion angle for the same material are related by Poisson&#39;s ratio for the mechanical behavior that varies depending on the geometry of the beam subjected to torsion. 
     In gyrometers according to known practice, an attempt is made to make two systems of beams (excitation beams and detection beams) that have the closest possible resonant natural frequencies to amplify the two movements (the excitation vibration movement and the detection vibration movement) produced by the Coriolis force on the sensitive element  10 . On gyrometers according to known practice, the excitation vibration takes place on a bending mode, whereas the detection vibration takes place on a torsion mode. 
     These two resonance modes have different behaviors in terms of frequency variation 
     as a function of beam machining uncertainties: the stiffness of a beam with a rectangular cross-section in bending depends mainly on its thickness and length, whereas the stiffness in torsion depends mainly on the thickness and the width. The two types of stiffness are expressed by: 
     Stiffness in bending: Kbending proportional to E.W.(H 3 /L 3 ) 
     Stiffness in torsion: Ktorsion proportional to [E./2(1−ν)].W 3 .H 3 /[L.(W 2 +H 2 )] 
     where L, W, and H are the length, width and depth of the beams, 
     E and ν are the Young&#39;s modulus and the Poisson&#39;s ratio for the material. 
     as a function of the temperature: the bending mode being related only to the Young&#39;s modulus for the material, while the torsion is dependent on Young&#39;s modulus and Poisson&#39;s ratio; these two parameters do not have the same thermal behavior and therefore do not vary in the same way to temperature fluctuations applied to the gyrometer. 
     These disadvantages cause a change in the resonant frequencies between beams operating in different modes (bending and torsion), that limit the performance and stability of the gyrometers. 
     SUMMARY OF THE INVENTION 
     In order to overcome the disadvantages of angular velocity measurement systems according to prior art, the invention proposes m gyrometer comprising a micro-machined sensitive element with at least two symmetrically positioned excitation beams on each side of and parallel to a sensitive Oy axis of the gyrometer, excited in bending about an Ox axis perpendicular to the sensitive Oy axis, and connected through their ends to at least one transverse element fixed in its central part to the sensitive Oy axis, to a frame through an elastic torsion return element acting in opposition to the rotation of the transverse element about the Oy axis, characterized in that elastic return element(s) are sized such that the variation of their resonant natural frequency in torsion with temperature is similar to the variation of the resonant natural frequency in bending of the beams with temperature. 
     According to a first embodiment of the gyrometer according to the invention, the elastic return element of a transverse element comprises at least one beam elongated in a direction perpendicular to the Oy axis such that the torsion return force due to this elastic return element is essentially due to the resistance of this elongated beam to bending. 
     In a second embodiment of the gyrometer according to the invention, the elastic return element comprises two elongated beams approximately parallel to each other and attached to each other at their ends on the same side, the central part of one of the beams being attached to the transverse element and the central part of the other beam being attached to the central part of the frame. 
     In another embodiment of the gyrometer according to the invention, the elastic return element comprises three approximately parallel elongated beams, a first beam attached through one of its end to the transverse element, a second beam attached through one of its ends to the frame, and a third beam attached through one of its ends to the other end of the first beam and through its other end to the other end of the second beam. 
     In these embodiments according to the invention, the various return elements are subject to forces that essentially produce deformations in bending and very small deformations in torsion, unlike machined micro-mechanical devices according to prior art (sensitive element  10  in FIG. 1) comprising excitation beams subjected to forces causing deformation by bending and return beams subjected to forces causing deformation by torsion (rotation torque about the YY′ sensitive axis). 
     During vibrational excitation of excitation beams of the sensitive element  10  in FIG. 1, the resonant frequencies of beams deformed in bending and beams deformed in torsion are expressed differently, and in this case the dimensions of the excitation beams and the return beams will be very different if it is required to make these beams vibrate at the same resonant frequency. The return beam to which torsion forces are applied will be shorter than the excitation beam to which bending forces are applied. 
     The geometric manufacturing uncertainties affect these two resonance modes very differently (in bending and in torsion) and it is difficult to obtain two superposed resonant frequencies. Furthermore in the sensitive element  10  in FIG. 1, the return beam has a rectangular section instead of a round section, therefore the torsion mode is not pure and consequently is difficult to predict precisely. Finally, the frequencies of the torsion and bending modes do not vary with temperature in the same way, possibly creating thermal instabilities in resonance. 
     Another disadvantage of the sensitive element  10  in FIG. 1 is the appearance of a shift between resonant natural frequencies of the excitation beams and return beams due to manufacturing dispersions. The same geometric variation in the excitation beams and in the return beams will modify the corresponding natural frequencies in bending and torsion differently. 
     In the micro-mechanical device according to the invention machined from the same material (normally silicon), the elongated beams are essentially subjected to bending forces and therefore deformations are determined as a function of the Young&#39;s modulus. The attachments of the elongated beams of a return element are composed of beams that are short in the direction of the Oy sensitive axis in order to have good resistance to torsion. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Other characteristics of the invention will become clear after reading the detailed description of the following embodiments with reference to the attached drawings in which: 
     FIG. 1, already described, shows a simplified drawing of the sensitive element  10  of a diapason gyrometer according to prior art; 
     FIG. 2 shows a first embodiment of the sensitive element of a diapason gyrometer according to the invention; 
     FIG. 3 a  shows a partial view of the sensitive element of the gyrometer in FIG.  2 . 
     FIG. 3 b  shows a top view along AA′ of the partial view in FIG. 3 a.    
     FIG. 4 shows a second embodiment of the sensitive element of a diapason gyrometer according to the invention; 
     FIG. 5 a  shows a partial view of the sensitive element of the gyrometer in FIG. 4; 
     FIG. 5 b  shows a bottom view along BB′ of the partial view in FIG. 5 a.    
     FIGS. 6 and 7 show two simplified embodiments of the diapason gyrometer according to the invention, for which the sensitive element comprises a single transverse element. 
     FIG. 8 shows a partial view of a sensitive element of a gyrometer according to the invention, comprising a cascade of return elements. 
     FIG. 9 shows a partial view of a sensitive element around attachments comprising small beams. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     FIG. 2 shows a first embodiment of a sensitive element  40  of a diapason gyrometer according to the invention with a sensitive element comprising two transverse elements, a first transverse element connecting the ends of the excitation beams located on the same side and a second transverse element connecting the other ends of these same excitation beams. The sensitive element  40  has a symmetric double beam structure like that of the sensitive element  10  shown in FIG.  1 . 
     The sensitive element  40  of the gyrometer comprises the first pair of two excitation beams  12  and  14  and the second pair of two other excitation beams  16  and  18 . The excitation beams of the first and second pairs are located in the same Oxy plane of the reference coordinate system and are parallel to a YY′ sensitive axis coincident with the Oy axis. The first and second pairs are located on each side and at approximately equal distances from the YY′ axis. 
     Each pair of excitation beams comprises a central mass connecting the two beams of one pair at their middle, the mass m 1  at the middle of the first pair and the mass m 2  at the middle of the second pair 
     The ends of the beams  12 ,  14 ,  16 ,  18  located on the same side are connected to the first transverse element  20  and to the second transverse element  22  located in the same Oxy plane of the excitation beams and approximately perpendicular to these beams. 
     The first transverse element  20  and the second transverse element  22  are attached to a first element  42  and a second element  44  of a torsion return element, each of the elastic return elements comprising a first elongated beam  46  and a second elongated beam  48  along a direction perpendicular to the sensitive axis TT′, a first elongated beam  46  being attached to a transverse element and a second elongated beam  48  being attached to a frame, the first and second elongated beams being attached to each other through its ends on the same side. 
     FIG. 3 a  shows an enlarged partial view of the sensitive element  40  of the gyrometer according to the invention, showing the first return element  42 . 
     The first transverse element  20  is attached to the first elongated beam  46  of the first elastic return element  42  by a first rigid element  50  located along the sensitive axis YY′ at a central part of this first elongated beam  46 . The second elongated beam of the same return element  42  is attached to the first frame  28  through a second rigid element  52  located on the YY′ axis at the central part of the second elongated beam  48 . The two ends located on the same side of the two elongated beams are attached through a third rigid element  54  and a fourth rigid element  56  respectively. 
     FIG. 3 b  shows a top view along AA′ of the return element  42  in FIG. 3 a  during a rotation R around the YY′ axis in the transverse element driven by a pair of forces Fg and Fd applied on this element. 
     Rotation of the transverse element  20  about the sensitive axis YY′ causes deformations in S by bending of the first elongated beam  46  and the second elongated beam  48 , the first elongated beam  46  being driven in rotation by the first rigid element  50  fixed to the first transverse element  20  and the second elongated beam  48  being driven in rotation by the third rigid element  54  and the fourth rigid element  56  fixed to the ends of these two elongated beams  46  and  48 . The bending forces and deformations in these elongated beams created by the rotation of the transverse element  20  are related through Young&#39;s modulus. 
     In the same way (see FIG. 2) the second transverse element  22  is attached to the first elongated beam  46  through the first rigid element  50  located in the sensitive axis YY′ at the central part of the first elongated beam  46 , the second elongated beam  48  being attached to the second frame  30  to the second rigid element  52  located in the YY′ sensitive axis at the central part of the second elongated beam  48 . The two ends located on the same side of the elongated beams are attached through the third rigid element  54  and the fourth rigid element  56 , respectively. 
     The elastic return elements  42  and  44  must be correctly sized in order to obtain the required effect, either a rotation about a given axis (YY′ sensitive axis) preferred over the other movements and mainly causing bending movements. This is done by making the rigid elements  50 ,  52 ,  54 ,  56  with torsion axes parallel to the sensitive axis TT′, very stiffen and consequently very short along the YY′ axis and wide along the perpendicular XX′ and ZZ′ axes. The elongated beams  46  and  48  can then be sized to determine a rotation stiffness. The length of these beams elongated in a direction perpendicular to the YY′ sensitive axis must also be chosen to give priority to rotation about the YY′ axis rather than bending about the ZZ′ axis perpendicular to the beams and the YY′ axis of rotation. 
     The rotation stiffness Kt about the YY′ axis, calculated for the first embodiment of the return element in FIG. 3 a  and assuming that the rigid elements  50 ,  52 ,  54 ,  56  are very stiff compared with the elongated beams, is expressed as follows: 
     
       
           Kt 1=2 .E. I/L   
       
     
     Where I=b.t 3 /12; 
     E: Young&#39;s modulus; 
     L: half-length of beams  42 ,  44 ; 
     b: dimension of beams parallel to the YY′ axis; 
     t: dimension of beams parallel to the ZZ′ axis. 
     In order to limit the bending movement about the ZZ′ axis, the natural frequency of this mode f Z  about ZZ′ must be greater than the natural frequency in torsion f t . The half-length of the beams determines the ratio between these two frequencies. 
     If it is assumed that point masses M are placed at the ends of a transverse element (see FIG. 3 a ) with length Lm, and that the mass of this transverse element is negligible, and that the rigid elements  50 ,  52 ,  54 ,  56  are very stiff compared with the elongated beams, the relation between the length of the transverse element supporting these masses, the length of the beams in the return element and the natural frequencies of the torsion and bending modes about ZZ′ are given by: 
     
       
           L =(f t   /f   z ). Lm . {square root over (3)} 
       
     
     FIG. 4 shows another embodiment of a sensitive element  60  of a gyrometer according to the invention with the same symmetric double beam structure as the sensitive elements  10 ,  40 FIGS. 1 and 2. 
     In this other embodiment, the first transverse element  20  and the second transverse element  22  are attached to a first elastic return element  62  and a second elastic return element  64  respectively. Each return element comprises three beams elongated in a direction perpendicular to the YY′ sensitive axis, a first elongated beam  66  being attached at one of its ends to a transverse element, a second elongated beam  68  being attached at one of its ends to a frame and a third elongated beam  70  being attached at one of its two ends to the other end of the first elongated beam  66  and at the other end to the other end of the second elongated beam  68 . 
     FIG. 5 a  shows a partial enlarged view of the sensitive element  60  of the gyrometer according to the invention showing the first elastic return element  62 . 
     The first transverse element  20  is attached to one of the ends of the first elongated beam  66  through a first rigid element  72  located in the YY′ sensitive axis of the sensitive element  60 . The second elongated beam  68  is attached by one of its ends to the first frame  28  through a second rigid element  74  located in the YY′ sensitive axis. The third elongated beam  70  is attached through its two ends through a third rigid element  76  to the other end of the first elongated beam  72  and through a fourth rigid element  78  to the other end of the second elongated beam  68 . 
     FIG. 5 b  shows a top view along BB′ of the machined micro-mechanical return element  62  in FIG. 5 a  during rotation R around the sensitive axis YY′, of the mobile element  20  driven by the pair of forces Fg and Fd applied to this element. Rotation of the first transverse element  20  about the YY′ axis causes a deformation in S by bending of the first elongated beam  66 , the second elongated beam  68  and the third elongated beam  70 . The first elongated beam  66  is driven in rotation and is deflected by the first rigid element  72  rigidly attached to the first transverse element  20 , the movement of this first elongated beam in turn causing a rotation in bending of the third elongated beam  70  and the second elongated beam  68 , through the third rigid element  76  and fourth rigid elements  78  respectively. 
     Similarly, (see FIG. 4) the second transverse element  22  is attached to one of the ends of the first elongated beam  66  of the second elastic return element  64 , through the first rigid element  72  located in the YY′ axis of the return element, the second elongated beam  68  being attached through one of its ends to the second frame  30  through the second rigid element  72  located in the YY′ sensitive axis. The third elongated beam  70  is attached at its two ends through the third rigid element  76  to the other end of the first elongated beam  72 , and through the fourth rigid element  78  to the other end of the second elongated beam  68 . 
     As in the case of the first embodiment in FIG. 2, the rotation movement about the sensitive axis YY′ of the transverse elements  20 ,  22  creates bending deformations of the three elongated beams of the return element, the stiffness of which is related to the Young&#39;s modulus. 
     In this second embodiment of the sensitive element in FIG. 4, the rotation stiffness is given by: 
     
       
           Kt 2 =E.I /3 .L   
       
     
     In gyrometers according to the invention, the return element creates a sort of decoupling by transmitting the rotation of the transverse element through rigid beams parallel to the YY′ sensitive axis to flexible beams perpendicular to this axis. Rotation thus causes bending of beams perpendicular to the sensitive axis whereas beams parallel to the sensitive axis are more rigid, and are affected by only a small amount of torsion. This return element thus gives priority to rotation compared with other movements. 
     In the case of machined micro-mechanical systems such as the sensitive element in FIG. 1, the rotating masses may be carried by high stiffness lever arms in order to limit deflection movements of masses by bending of these arms. The return element itself may be designed to be stiffer in translation movements than for the required rotation. Thus, in the embodiments described with reference to FIGS. 3 a ,  3   b ,  4   a  and  4   b , the elongated beams are attached through rigid elements that have very little torsion. 
     The stiffness of these rigid elements may be a result of their dimensions. These rigid elements are wider and shorter beams than the elongated beams. 
     In simplified embodiments of the diapason gyrometer according to the invention, the sensitive elements  80  and  90  shown in FIGS. 6 and 7 respectively comprise a single transverse element. 
     The structure of the sensitive element  80  in FIG. 6 is the same as the structure of the top part of the sensitive element  40  in FIG. 2 located only on the side of the XX′ axis comprising the first transverse element  20 . A first pair of excitation beams  82  and  84  and a second pair of excitation beams  86  and  88  are fixed at their ends located on the same side through the sole first transverse element, the other ends of the first and second pair of beams being connected to masses m 1  and m 2  respectively. The sensitive element  80  comprises the sole elastic return element  42  connecting a central part of the first transverse element  20  to the frame  28 . 
     Similarly, the structure of the sensitive element  90  in FIG. 7 is the same as the structure of the upper part of the sensitive element  60  in FIG. 4 located on the one side of the XX′ axis comprising the first transverse element  20 . The first pair of excitation beams  82  and  84  and the second pair of excitation beams  86  and  88  are fixed at their ends located on the same side through the sole first transverse element  20 , the other ends of the first and second pair of beams being connected to masses m 1  and m 2  respectively. The sensitive element  90  comprises the sole elastic return element  62  connecting a central part of the first transverse element  20  to the frame  28 . 
     In other variant embodiments of the diapason gyrometer according to the invention, the sensitive element comprises two excitation beams located on each side of the sensitive axis YY′ connected at their ends on the same side through the first transverse element  20  and the second transverse element  22  respectively. 
     The elastic return elements shown in FIGS. 3 a  and  5   a  may be cascaded, which gives a greater rotation amplitude of the resulting return element. 
     FIG. 8 shows a partial view of a sensitive element  100  with the same double beam structure as the sensitive element  40  in FIG.  2 . The sensitive element  100  comprises a cascade  102  of return elements, each of the elastic return elements being as shown in FIG. 3 a , comprising two elongated beams  46 ,  48 . The first transverse element  20 , and the first frame  28  are connected through a cascade  102  of elastic return elements, a first return element  104  being connected to the first transverse element  20  of the sensitive element  100  through the first rigid element  50 , a next elastic return element  106  being connected to the first elastic return element  104  through an intermediate rigid element  108 , and so on until a last elastic return element  110  connected to the frame  28  through a second rigid element  52 . 
     In another embodiment of the gyrometer, the cascade of return elements in the sensitive element may be made using return elements  72  in FIG. 5 a  comprising three elongated beams  66 ,  68 ,  70 . 
     In other variant embodiments of the sensitive element of the diapason gyrometer, the elastic return element ( 42 ,  44 ,  62 ,  64 ) is attached firstly to the transverse element ( 20 ,  22 ) through a first pair of small beams  120 ,  122  and secondly to the frame ( 28 , 30 ) through a second pair of small beams  124 ,  126  with dimensions along the sensitive axis YY′ and along the XX′ axis that are very small compared with the length of the elongated beams, the two small beams in one pair being located close to and on each side of the sensitive axis YY′. 
     FIG. 9 shows a partial view of a sensitive element around the attachments of a first elastic return element  118  with the same structure as the elastic return element  42  shown in FIG. 3 a  comprising the first pair of small beams  120  and  122  and the second pair of small beams  124  and  126 . These small beams further facilitate bending compared with torsion of the sensitive element. 
     Gyrometers according to the state of the art can give measurement precisions for the angular velocity of the order of 1 degree per second. 
     The invention makes it possible to superpose the two resonance modes of the sensitive element of a diapason gyrometer precisely during manufacture, and then in operation particularly during thermal fluctuations. 
     Therefore the gyrometer according to the invention has a better signal to noise ratio and a better thermal stability. Therefore, it can achieve measurement precisions of angular velocities of the order of ten times greater than what is possible with gyrometers according to prior art.