Mechanical resonator optimised to operate in a fluid

Abstract

A resonator includes a prong of which the width between edges is close to /2. The pressure variation at one edge is then in phase opposition with that at the other edge. Acoustic coupling with an incident wave having the wavelength is thus improved. The ratio between the width between edges and the height of the prong is chosen so that only the fundamental mode with bending oscillation of the prong is present. It to prongs of a tuning fork embedded in a solid shared base optimized to contain the energy in the tuning fork while avoiding energy losses in the support. Finally, the tuning fork is advantageously combined with a unit for containing acoustic energy including a rigid reflecting screen.

Claims

1. A mechanical resonator (100), comprising: a flat plate of a material of thickness T, said plate having a shared portion (2) on which is embedded at least one parallelepipedic prong (1) of length Lb and width Wb, said length Lb and width Wb being measured parallel to the plate, said prong having a resonance mode with bending in a plane of the plate at a frequency f, at which an acoustic wave is emitted of wavelength in a fluid in contact with and surrounding the prong, wherein electrodes are arranged on said prong, and wherein the width Wb is correspondent to the wavelength in the fluid such that the width Wb is between
/4+n
and
3/4+n, n being a positive integer or zero, wherein the prong is embedded at both ends thereof, and wherein the resonance mode is the fundamental mode with bending, a ratio of the length Lb of the prong to the width Wb of the prong being between 2 and 5.

2. The resonator according to claim 1, wherein the width Wb is equal to /2+n.

3. A device comprising a mechanical resonator (100) according to claim 1, and an acoustic containment means arranged near the resonator and arranged to reflect acoustic energy emitted by the resonator.

4. A device comprising a mechanical resonator (100) according to claim 2, and an acoustic containment means arranged near the resonator and arranged to reflect acoustic energy emitted by the resonator.

5. A mechanical resonator (100), comprising: a flat plate of a material of thickness T, said plate having a shared portion (2) on which is embedded at least one parallelepipedic prong (1) of length Lb and width Wb, said length Lb and width Wb being measured parallel to the plate, said prong having a resonance mode with bending in a plane of the plate at a frequency f, at which an acoustic wave is emitted of wavelength in a fluid in contact with and surrounding the prong, wherein electrodes are arranged on said prong, and wherein the width Wb is correspondent to the wavelength in the fluid such that the width Wb is between
/4+n
and
3/4+n, n being a positive integer or zero, wherein the prong is embedded at only one end thereof, and wherein the resonance mode is the fundamental mode with bending, a ratio of the length Lb of the prong to the width Wb of the prong being between 1.2 and 3.2.

6. The resonator according to claim 5, wherein the prong is a first prong arranged in parallel with a second prong having a same form as the first prong, said first and second prongs together forming a tuning fork, embedded in the shared portion (2), the shared portion (2) having a mass comprised between 2 and 4 times that of said first and second prongs.

7. The resonator according to claim 6, wherein the shared portion (2) has a shape of a rectangular parallelepiped 22 with a length W that is more than twice the width Wb of each of said first and second prongs (1) and with a height (L22) that is greater than the length Lb of each of said first and second prongs, two isosceles trapezoids (21, 23) arranged one on either side of the parallelepiped, large bases of each of said two isosceles trapezoids having a length equal to the length of the shared portion, the first and second prongs (1) arranged in parallel at a distance Ws' between 0.5 and 2 times the thickness T of the plate being embedded in a small base of a first of the isosceles trapezoids (21), outer edge faces of the first and second prongs being coincident with ends of said small base of the first isosceles trapezoid, a small base of a second isosceles trapezoid (23) supporting an intermediate connection member (24) connecting the resonator to a support, a length of said small base of the second isosceles trapezoid being less than half the width Wb of one of the first and second prongs.

8. The resonator according to claim 7, wherein the electrodes are arranged on faces of each of said first and second prongs (1) and of the shared portion (2) which are parallel to the plane of the plate, of which the electrodes occupy an entire surface except for inter-electrode insulation areas, said insulation areas occupying less than 20% of a total surface area of said faces parallel to the plane of the plate.

9. The resonator according to claim 8, wherein the electrodes of a face parallel to the plane of the plate comprise: a Y-shaped central electrode (41) having two symmetrical arms running alongside inner edge faces of the prongs (1) that face one another, and having a tail connecting a central point of the intermediate connection member (24), two symmetrical external electrodes (42) which each cover at least 25% of a portion of the face parallel to the plane of the plate that is part of the shared portion (2), each in a lateral area opposite to said shared portion, and which each connect a respective external point of the intermediate connection member, and two symmetrical intermediate electrodes (51), each having an arm running alongside an outer edge face of one of the prongs, a return portion which surrounds an end of one of the external electrodes opposite to the intermediate connection member, and a tail connecting a respective intermediate point of the intermediate connection member, between the central point and one of the external points.

10. A device comprising a mechanical resonator (100) according to claim 6, and an acoustic containment means arranged near the resonator and arranged to reflect acoustic energy emitted by the resonator.

11. The device according to claim 10, wherein the acoustic containment means is an acoustic cavity resonating at the mechanical resonance frequency of the tuning fork, the acoustic resonance mode of the cavity having nodes and antinodes such that each of the two inner edge faces of the prongs of the resonator is located at a central antinode and such that each of the two outer edge faces of the prongs is located at antinodes in phase opposition to the central antinode.

12. A device comprising a mechanical resonator (100) according to claim 7, and an acoustic containment means arranged near the resonator and arranged to reflect acoustic energy emitted by the resonator.

13. A device comprising a mechanical resonator (100) according to claim 8, and an acoustic containment means arranged near the resonator and arranged to reflect acoustic energy emitted by the resonator.

14. A device comprising a mechanical resonator (100) according to claim 5, and an acoustic containment means arranged near the resonator and arranged to reflect acoustic energy emitted by the resonator.

15. The resonator according to claim 5, wherein the width Wb is equal to /2+n.

16. A device comprising a mechanical resonator (100) according to claim 15, and an acoustic containment means arranged near the resonator and arranged to reflect acoustic energy emitted by the resonator.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 illustrates a resonator of the prior art: a timepiece tuning fork.

(2) FIG. 2A illustrates the pressure variation P existing between the two edges of a prong of width Wb of the resonator of FIG. 1.

(3) FIG. 2B illustrates the pressure variation P existing between the two edges of a prong of width Wb of a resonator according to the invention.

(4) FIG. 3A illustrates a tuning fork according to the invention, comprising two prongs of width Wb.

(5) FIG. 3B illustrates an optimized conformation of electrodes for detecting a tuning fork optimized according to the invention.

(6) FIG. 4A illustrates the principle of a tuning fork equipped with its acoustic containment means, with a stationary pressure wave shown in 1D.

(7) FIGS. 4B and 4C illustrate one of the possible shapes for the acoustic containment means, namely a cylindrical cavity viewed from the front and from above.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

(8) The underlying idea of the invention is to define a simple object having high acoustic coupling in the usage conditions of resonators: shape, nature of the component material of the object, vibration mode, and nature of the fluid.

(9) The selected object is an adapted parallelepipedic prong of length Lb, width Wb, and thickness T, of the type constituting a tuning fork prong of the prior art. It is made of a rigid material, for example quartz or silicon. The resonance vibration of the prong is a bending vibration in the plane defined by its length and width. The vibration modes are the fundamental mode and, optionally, the harmonic modes. The fluids are gases or mixtures of gases such as oxygen, nitrogen, carbon dioxide, carbon monoxide, hydrogen, helium.

(10) The two faces defined by the length Lb and the thickness T of the prong are called edges.

(11) The energy losses of a prong resonating under the usage conditions of the invention are of three types: acoustic losses, viscous losses, and losses into the support, the latter type of loss essentially being the only one encountered in timepiece resonators encapsulated in a vacuum if we ignore thermoelastic losses (Frederick Lochon, Isabelle Dufour, Dominique Rebiere, A microcantilever chemical sensors optimization by taking into account losses. Sensors and Actuators B: Chemical, Elsevier, 2006, 118, pp 292-296).

(12) The quality factor is a convenient means for expressing the influence of resonator losses. The quality factor of a resonator is defined as the ratio between the energy stored in the resonator in the form of kinetic energy and deformation potential, and the energy lost during an oscillation cycle.

(13) The overall quality factor Q.sub.g of the resonator is defined by the formula:
1/Q.sub.g=1/Q.sub.a+1/Q.sub.v+1/Q.sub.s

(14) where

(15) Q.sub.a=acoustic quality factor

(16) Q.sub.v=viscous quality factor

(17) Q.sub.s=support quality factor

(18) This formula emphasizes that it is the lowest quality factor that degrades the overall quality factor, the optimal configuration being achieved when the quality factors are equal and as high as possible.

(19) In contrast to this approach, the invention aims at define the dimensions of the prong in order to increase it acoustic coupling with the surrounding fluid. Consequently, the acoustic losses are significant, which goes against the teachings of the prior art.

(20) The characterizing dimension of the invention is the width Wb of the prong. In the prior art there is no relation between the width of the prong and the wavelength of the wave emitted at the resonance frequency f of the prong.

(21) In FIG. 2, the wavelength is on the abscissa and the pressure is on the ordinate. In these figures, the width Wb or Wb of the prong, shown in gray, is superimposed on the sinusoidal acoustic wave at the resonance frequency f of the prong. The acoustic wave represented is flat, to facilitate understanding. If the wave comes from an outside source, the source is far away from the prong and within its bending plane of vibration. If the acoustic wave is generated by the prong in motion, its movements are ignored.

(22) In the general case shown in FIG. 2A, the pressure variation P between the edges of the prong in relation to its width is small. In contrast, in the case of the invention, illustrated in FIG. 2B, the pressure variation P between the edges of the prong, separated by a distance equal to half the wavelength, is maximized because the pressure variations on each edge are in phase opposition.

(23) In the case of an external source, the incident wave creates a force on an edge of equal amplitude and of opposite sign to the force applied to the other edge, which results in the two forces being additive in an optimum manner for exciting the bending vibration mode of the prong.

(24) Generally, the acoustic wave is not flat and it is not possible to obtain forces in phase opposition on the surface of the two edges of the prong. Under these conditions, the width Wb is between /4+ and 3/4+, n being a positive integer or zero.

(25) These dimensions also apply in the case where it is the prong which generates the acoustic wave. The width dimension so defined increases the acoustic coupling of the prong with the surrounding fluid.

(26) Moreover, the performance of a resonator according to the invention has been improved by limiting the energy losses of the other two types: viscous losses and losses into the support.

(27) To limit the viscous losses of an optimized prong resonator of the invention, the length Lb of the prong is an important parameter because it determines the resonance frequency. The fundamental bending mode makes it possible to obtain one of the best quality factors.

(28) For an embedded prong, the slenderness ratio varies with the component material and the surrounding fluid.

(29) The optimized slenderness ratios for a prong embedded at one of its ends, as shown in FIG. 3A, for quartz and silicon in air, helium, hydrogen, oxygen, and carbon dioxide are shown in the table below:

(30) TABLE-US-00001 CO.sub.2 O.sub.2 Air He H.sub.2 Quartz 2.6 2.4 2.3 1.4 1.2 Silicon 3.2 2.9 2.8 1.7 1.45

(31) The thickness T of the prong is about a quarter of the width Wb of the prong.

(32) For a prong embedded at both ends, the slenderness ratio is between 2 and 5 depending on the material and the nature of the fluid.

(33) To limit losses into the support, it is known that the performance of a single prong is not as good as that of a tuning fork. The latter type of resonator has therefore been analyzed for use in the context of the invention.

(34) The low slenderness ratio of the prongs according to the invention alters the nature of the stresses at the embedding area on the shared portion fixed to the support.

(35) In particular, there are high shear stresses in the embedding area.

(36) This results in a specific conformation of the tuning fork of the invention, illustrated in FIG. 3A, which significantly increases the contribution of the shared portion to the vibration of the resonator and to the detection of said vibration.

(37) For this embodiment, the frequency is 42,500 Hz, which is a wavelength of 8 mm in air under normal pressure conditions, the material used being quartz in the form of a machined flat plate of dimensions L=23.75 mm, meaning 2.97, by W=13.8 mm, meaning 1.72, and of thickness T=1 mm, meaning /8.

(38) The plane of the plate is substantially parallel to the crystallographic XY plane of the quartz, and the longitudinal axes of the arms 1 are substantially parallel to the crystallographic X-axis of the quartz (unlike the timepiece tuning fork shown in FIG. 1A, in which the arms are substantially parallel to the crystallographic Y-axis of the quartz). The tuning fork 100 is symmetrical about a plane perpendicular to the plane of the plate.

(39) The tuning fork 100 is formed of two identical and substantially parallelepipedic arms 1 of length Lb=6.8 mm, meaning 0.85, and width Wb=4 mm, meaning 0.5, each integral at one end with a shared portion 2 consisting of four areas 21, 22, 23, 24 bounded by dotted lines.

(40) The shared portion 2 is integral with a mounting arm 3 at the area 24 opposite to the area 21 integral with the two arms.

(41) The connection area 21 between the arms 1 and the main portion 22 of the shared portion 2 has an isosceles trapezoidal shape in which the outwardly facing edges 211 connect the outer edges of the arms to the edges of the main shared portion 22 with an inclination of angle A substantially equal to 120 relative to the X axis (which, in the case where the tuning fork is created by chemical machining, prevents the formation of oblique facets on said edges). The height of this trapezoid is about 1.4 mm.

(42) Similarly, area 23 which connects areas 22 and 24 of the shared portion 2, has an angle of 120 relative to the crystallographic X-axis of the quartz. The height of the trapezoid is about 3.5 mm.

(43) The tuning fork 100 is fixed to a housing base B (not shown), for example by bonding, at surfaces 31 (indicated with hatching) of the mounting arm 3.

(44) The thickness T of the plate and the width of the slot Ws are substantially equal to 1 mm, which is /8. In general, the thickness T and the distance W are close, meaning that the distance Ws may be comprised between 0.5 and 2 times the thickness T of the plate.

(45) The shared portion 2 is integral with the two arms at the connection area 21 which connects the arms to the area 22 of rectangular shape, and its dimension W perpendicular to plane is greater than the width (2Wb+Ws) containing the two arms: W is substantially 1.5 times (2Wb+Ws). Furthermore, dimension L22 of area 22 taken parallel to the X axis is substantially half the length Lc of the shared portion 2. For example, Lc is 15.45 mm, which is 1.93, and L22 is 7.6 mm, which is 0.95.

(46) The width W24 of area 24 is much less than W: W24 is substantially equal to 1.6 mm, which is /5.

(47) Under these conditions, the surface area of the shared portion 2 is about three times the total surface area 2.Math.Lb.Math.Wb of the two arms 1. For the tuning fork of the invention, the mass of material in the shared portion is therefore significantly greater than that in the two arms, unlike the case of the timepiece tuning fork.

(48) FIG. 3B shows a front view of the electrodes equipping the resonator 100 of FIG. 3A and enabling, by piezoelectric effect, detection of the vibration of the resonator. The electrodes are in the form of conductive pads 41, 42, and 51, represented by hatched areas, arranged on the two large faces of the plate, and acting in the arms 1 and in the shared portion 2. Electrodes 41 and 42 have the same electrical polarity, different from the polarity of electrode 51. The electrodes 41, 42, and 51 arranged on one of the large faces are directly opposite the electrodes 41, 42 and 51 arranged on the other large face (indicated with a reference dotted line), and each of the electrodes has the same electrical polarity as the electrode arranged directly opposite on the other large face.

(49) The relatively complex shapes of the electrodes 41, 42 and 51 result from numerical simulations with finite elements and are related to the relatively complex distribution of mechanical stresses generated by the vibration of the tuning fork, these stresses being of three types: expansion/compression stress T.sub.XX along the X axis, expansion/compression stress T.sub.YY along the Y axis, and shear stress T.sub.XY in the XY plane. The conformation of the electrodes is characteristic in that they concern the prongs equally in the conventional manner, but the shared portion 2 as well. Electrodes 41, 42 of the same polarity and electrodes 51 are connected to respective connecting pads 70 and 71 located on the mounting arm 3, by means of connecting tracks of the type denoted 60.

(50) Thus, the connecting pads 70 and 71 respectively connect the two polarities of all the electrodes, the tuning fork equipped with its electrodes constituting a dipole piezoelectrically linked to vibration.

(51) It is possible to detect the vibration of the tuning fork, for example by connecting the pads 70 and 71 to a differential charge amplifier (not shown) which generates for example a voltage representative of the amplitude of the vibration. Note that the electrodes shown in FIG. 3B, arranged only on the two large faces of the plate, are well suited for low-cost manufacturing. For example, when the resonator structure is obtained by chemical etching of a quartz wafer, the electrodes can easily be created by etching metal masks on the front and back which were previously used for etching chemically the quartz.

(52) The invention aims to provide a resonator for use in a fluid. However, the resonator described has significant acoustic losses, which is not favorable in this state for obtaining a high overall quality factor.

(53) To obtain a device optimized according to the invention and having a high quality factor, a means must be added to the resonator described above which is able to restore substantially all acoustic energy losses due to its coupling with the fluid.

(54) The role of the means able to restore the acoustic energy or the containment means is to return to the resonator the acoustic waves emitted by the resonator in order to create a new excitation force which then contributes to the vibration.

(55) The containment means of the invention is a resonant acoustic cavity. The resonator is placed at the heart of the resonant acoustic cavity, which is in the form of a hollow cavity. It is known that any hollow cavity offers the phenomenon of acoustic resonance. Therefore natural acoustic resonance modes exist within the cavity, and each is associated with a resonance frequency and a quality factor. These three parameters can for example be calculated for any shape by finite-element simulation software.

(56) The acoustic cavity according to the invention, associated with the mechanical resonator in bending, is characterized in that: it has a natural frequency of acoustic resonance near or equal to the natural frequency of mechanical resonance of the tuning fork. the natural acoustic resonance mode, corresponding to the natural frequency of acoustic resonance of the preceding paragraph, has nodes and antinodes according to the position within the cavity. The antinodes can correspond either to overpressures (+) or underpressures (). Most of the surface area of the two inner edges must be within antinodes of the same sign, meaning either an overpressure or an underpressure. Most of the surface area of the two outer edges must also be located within antinodes of the same sign, but of a sign opposite to those of the inner edges. the acoustic quality factor of the mode described above must be maximized. For example, the material used to make the walls of the cavity must be rigid.

(57) A mechanical resonator according to our invention is therefore coupled quite well to this acoustic mode in that its dimensions are compatible with the acoustic wavelength, and therefore with the spatial distribution of the pressure mode (where the distance between successive antinodes is precisely equal to /2).

(58) A simplified illustration is shown in FIG. 4A, where the overpressure antinodes (+) and the underpressure antinodes () of the resonant acoustic mode are plotted. The wave represented does indeed possess this property of having an underpressure for the two inner edges of the tuning fork, and an overpressure for the two outer edges.

(59) Another illustration in FIG. 4B shows the same principle for a cylindrical cavity formed with a circular directrix of radius , in a front view at the same scale as that of the sensor. The acoustic mode is then radial and one can clearly see that the edges mostly occupy areas with the appropriate signs.

(60) FIG. 4C shows a top view of the same cavity.

(61) The typical quality factors of tuning fork resonators in a fluid, respectively of the timepiece type, of the type according to the invention alone, and of the optimized type, are summarized in the following table with the corresponding overall quality factors:

(62) TABLE-US-00002 Q.sub.s Q.sub.v Q.sub.a Q.sub.g Timepiece 80 000 10 000 2 000 000 8850 Invention 400 000 100 000 7 000 6437 Optimized 400 000 100 000 400 000 66 667

(63) The quality factor that penalizes timepiece resonators is the viscous damping related to the small dimensions required for such applications. The quality factor is proportional to the surface area/volume ratio.

(64) The tuning fork resonator of the invention offers many improved viscous and support quality factors compared to timepiece tuning forks, but as desired its acoustic quality factor is greatly degraded.

(65) The acoustic quality factor of the optimized device comprising a resonator of the invention is very high due to the cooperation between resonator and resonant cavity.

(66) The optimized device has, as is desirable, high quality factors of similar values, meaning within a range of 1 to 4 compared to a range of 1 to 200 for a timepiece tuning fork of the prior art.