JP2020204506A - Vibration gyroscope - Google Patents

Abstract

To provide a vibration gyroscope using a single crystal piezoelectric material.SOLUTION: A vibration gyroscope includes: (a) a piezoelectric substrate 12 having a pair of main surfaces 12s, 12t opposed to each other, and having a shape line-symmetrical with each of two drive shafts in parallel to the main surfaces 12s and 12t and orthogonal to each other and two detection shafts that equally divide a space between the drive shafts being a center; (b) drive electrodes 21 to 28, 31 to 38 for applying an electric field for vibrating the piezoelectric substrate 12 in a drive axis direction to the piezoelectric substrate 12; and (c) detection electrodes 41 to 28, 51 to 58 for detecting electric charges excited in the piezoelectric substrate 12 by vibration in a detection shaft direction of the piezoelectric substrate 12. The piezoelectric substrate 12 is made of a single crystal piezoelectric material classified into a point group 3m of a trigonal system, and is cut out so that elastic compliance in a direction of the main surfaces 12s and 12t of the piezoelectric substrate 12 becomes substantially constant regardless of an orientation in the main surfaces 12s and 12t.SELECTED DRAWING: Figure 5

Description

The present invention relates to a vibration gyro, and more particularly to a vibration gyro driven and detected by a wine glass vibration in a degenerate mode or a ring spreading vibration.

In recent years, technologies such as automatic driving of automobiles and automatic steering bogies of railways have attracted attention. For these controls, an angular velocity sensor (gyroscope, hereinafter referred to as "gyro") capable of sensing the attitude of the own vehicle with high accuracy is indispensable. Conventionally, optical types such as an optical fiber gyro and a ring laser gyro that realize a bias stability of about 0.01 to 1 ° / h have been used for such applications, but they are very expensive. Therefore, it is expected that the performance of the relatively inexpensive MEMS vibrating gyro having a bias stability of about 10 to 1,000 ° / h will be improved.

There are electrostatic type and piezoelectric type as the drive detection method of the MEMS vibration gyro, and the higher the electromechanical coupling coefficient and the Q value, the better the performance. The electrostatic type, which can use a single crystal material that can be expected to have a high Q value, and the piezoelectric type, which uses quartz, have a low coupling coefficient. On the other hand, a perovskite-type piezoelectric material such as lead zirconate titanate (hereinafter referred to as "PZT") having a high bonding coefficient is polycrystalline and has a low Q value of about several hundreds.

Therefore, a tuning fork type vibration gyro using lithium niobate (LiNbO ₃ , hereinafter referred to as "LN"), which is an ilmenite type single crystal piezoelectric material having a high coupling coefficient and a high Q value of 10,000 or more, was developed. Has been done. However, LN, which is a brittle material, is difficult to machine and has a very high etching resistance, so that the degree of freedom in design is low and its performance has reached a plateau.

In addition to the tuning fork type, the MEMS vibrating gyro includes a plate type and a ring disc type. In these, it is possible to improve the performance by matching the resonance frequency of the drive vibration and the detection vibration, driving and detecting in the degenerate mode, and lowering the driving and detection frequency, and by making it a symmetrical structure, the sensitivity of other axes can be increased. Reduction is also possible. Currently, electrostatic plate type and electrostatic ring type have been reported, and the bias stability is in the 0.1 ° / h range.

For example, FIG. 24 is a cross-sectional view of a disc-type vibrating gyro made of PZT polycrystalline piezoelectric ceramic. As shown in FIG. 24, electrodes 105 to 112 divided into eight in the circumferential direction are formed on the main surface 103 of the disc-type piezoelectric substrate 101. Electrodes 105 and 106 facing each other are connected to _one terminal T ₁ of the vibration circuit and the active gain control system 117, and electrodes 107 and 108 facing each other are connected to the other terminal T ₂ . Further, electrodes 109 and 110 facing each other are connected to one terminal T ₃ of the feedback system 18, and electrodes 111 and 112 facing each other are connected to the other terminal T ₄ . An electric field of opposite phase is applied in the thickness direction by the electrodes 105, 106 and the electrodes 107, 108 to drive the piezoelectric substrate 101, and the charges between the electrodes 109, 110 and the electrodes 111, 112 are detected (for example, Patent Document 1). reference).

FIG. 25 is a perspective view of a tuning fork type gyro made of a single crystal piezoelectric material. As shown in FIG. 25, this tuning fork type gyro asymmetrically forms drive electrodes and / or detection electrodes on the inside and outside of the arm and on the front and back surfaces of the arm to reduce irregular vibration and leakage output. It is configured in. That is, the drive electrode 211 provided inside the front and back surfaces of one arm 202 is smaller than the drive electrode 213 provided outside the front and back surfaces thereof. The length of the detection electrode 224 provided on the outer side surface of the other arm 203 is short by the dimension indicated by the reference numeral x. The drive electrodes 211 and 213 provided on the front and back surfaces of the arm 202 extend from the boundary position between the arm 202 and the base 204 to the base 204 side by the dimension indicated by the reference numeral f. The detection electrodes 221 provided on the front and back surfaces of the arm 203 extend from the boundary position between the arm 203 and the base 204 to the base 204 side by the dimension indicated by the reference numeral g (see, for example, Patent Document 2).

U.S. Pat. No. 4,650,081 Japanese Patent No. 3336451

In the vibrating gyro of Patent Document 1, since PZT used for the PZT ceramic plate 107 is polycrystalline, mechanical loss due to variations in grain boundaries and orientation is large. The gyro 210 of Patent Document 2 requires high processing accuracy. In addition, leakage vibration to out-of-plane (detection) vibration is always an issue for high accuracy.

As described above, the vibration gyro of the type that drives the inverse piezoelectric effect and uses the piezoelectric effect for detection generally has a high electromechanical coupling coefficient, and is most suitable for high performance. Further, since the loss inside the single crystal material is smaller than that of the polycrystalline material, a high vibration Q value can be expected. Therefore, a vibrating gyro using a single crystal piezoelectric material is required.

The structure of the gyro includes a tuning fork type, a disc type, and a hemispherical type, but in order to improve the performance of the gyro, a disc type and a hemispherical type having high structural symmetry and being able to support in the center are preferable. Further, in order to improve the performance, the contour vibration mode is preferable as the drive method.

Conventionally, capacitance detection type single crystal silicon disk structures, quartz hemispheres, and donut-shaped devices have been studied. However, capacitance detection has a problem that the electromechanical coupling coefficient is small.

Disc-type and hemispherical-type gyros using single crystal piezoelectric materials have not been realized so far. The reason is that the crystal anisotropy of the physical properties (rigidity, piezoelectric characteristics, etc.) of the single crystal material becomes an issue. In order to obtain high performance, not only the structure but also the asymmetry of physical properties becomes a problem.

In view of such circumstances, an object to be solved by the present invention is to provide a vibrating gyro using a single crystal piezoelectric material.

The present invention provides a vibrating gyro configured as follows in order to solve the above problems.

The vibrating gyro is a vibrating gyro that is driven and detected by wine glass vibration or ring spreading vibration in a contraction mode, and (a) a piezoelectric substrate having a pair of main surfaces facing each other, and (b) the piezoelectric substrate. The drive electrodes for applying an electric field vibrating in the directions of the two drive shafts parallel to the main surface and orthogonal to each other to the piezoelectric substrate and (c) the drive shafts of the piezoelectric substrate are equally divided. A detection electrode for detecting the electric charge excited by the piezoelectric substrate by vibration in the directions of the two detection axes is provided. The piezoelectric substrate is made of a single-crystal piezoelectric material classified into a trigonal point group of 3 m, and the Z-axis of the single-crystal crystal axes X, Y, and Z is the polarization direction, and the crystal axis X, According to the definition of the right-handed Euler angle, the crystal XYZ coordinate system by Y and Z is rotated by an angle of ψ around the Z axis, and the X'Y'Z'coordinate system is further rotated by an angle of θ around the X'axis. Assuming that the "Z" coordinates are the wafer coordinate system of the piezoelectric substrate, one of the two drive axes and the two detection axes is parallel to the X "axis or the Y" axis. The other of the two drive shafts and the two detection shafts is parallel to one or the other of the two straight lines equally dividing between the X ″ axis and the Y ″ axis, and the piezoelectric substrate. The elastic compliance in the main surface direction is substantially constant regardless of the orientation in the main surface.

In the above configuration, an electric field is applied to the piezoelectric substrate using the drive electrode to vibrate the piezoelectric substrate in the direction of the drive axis in the degenerate mode, and the electric charge excited by the vibration in the degenerate mode in the direction of the detection axis is detected. Detect using electrodes.

According to the above configuration, since the piezoelectric substrate is substantially isotropic, the mechanical characteristics are substantially constant in the orientation corresponding to the operation mode, and a vibration gyro that is driven and detected in the degenerate mode can be configured. ..

It should be noted that "the elastic compliance of the piezoelectric substrate in the main surface direction is substantially constant regardless of the orientation in the main surface" means that the difference in the elastic compliance in the main surface direction of the piezoelectric substrate depends on the orientation in the main surface. It means that it is practically negligible, and means that the coefficient of variation CV (ψ, θ) described later is less than 1%.

Preferably, the piezoelectric substrate is made of a single crystal of lithium niobate (LN) and has -4 ° <ψ <4 ° and 63 ° <θ <67 °.

In the case of this piezoelectric substrate, the coefficient of variation C.V. (ψ, θ) in the main plane of elastic compliance is less than 1%.

Preferably, the piezoelectric substrate is a Y-cut plate having a cut angle of 155 ° or more and 156 ° or less.

In this case, the coefficient of variation is almost 0, and the resonance frequencies in the drive shaft and the detection shaft directions are substantially the same.

As described above, the piezoelectric substrate has a line-symmetrical shape centered on each of the two drive shafts and the two detection shafts.

Preferably, the shape of the piezoelectric substrate is circular or regular polygon.

In this case, the piezoelectric substrate can be easily processed.

In a preferred embodiment, the drive electrode or detection electrode is divided by four virtual planes that include two drive shafts and each of the two detection shafts and are perpendicular to the main surface of the piezoelectric substrate. Of the eight regions of at least one of the main surfaces of the piezoelectric substrate, two adjacent to each other with the virtual surface parallel to the straight line equally dividing between the X ″ axis and the Y ″ axis. The region comprises at least a pair of 45 ° mode electrodes arranged in pairs. When voltages of opposite phases are applied to the 45 ° mode electrodes arranged in pairs, the 45 ° mode vibrations occur in the facing region of the piezoelectric substrate facing the 45 ° mode electrodes. Due to the strain generated in the direction parallel to the main surface for excitation, or to generate the strain in the direction parallel to the main surface when vibrating in the facing region in the piezoelectric substrate in 45 ° mode. It is configured so that charges of opposite phases are detected.

In another preferred embodiment, the drive electrode or the detection electrode includes the drive shaft or the detection shaft and is parallel to the X ″ axis and the Y ″ axis, respectively, and perpendicular to the main surface of the piezoelectric substrate. At least one of the four regions of the main surface of at least one of the piezoelectric substrates divided by the two virtual planes is equally divided between the two boundaries with the adjacent region of the region. Includes at least one set of 45 ° mode electrodes arranged in pairs facing each other at intervals in the direction. When a voltage is applied, the 45 ° mode electrodes arranged in pairs vibrate in the 45 ° mode in an intermediate region between the facing regions facing the 45 ° mode electrodes in the piezoelectric substrate. Charges are detected by the strain generated in the direction parallel to the main surface so as to generate a strain in the direction parallel to the main surface for exciting, or by the vibration in the 45 ° mode in the intermediate region in the piezoelectric substrate. It is configured to be.

In yet another preferred embodiment, the drive electrode or detection electrode is divided by four virtual planes that include each of the two drive shafts and the two detection shafts and are perpendicular to the main surface of the piezoelectric substrate. Of the eight regions of the main surface of at least one of the piezoelectric substrates, the virtual surfaces parallel to the straight line equally dividing the X ″ axis and the Y ″ axis are adjacent to each other. The two said regions include at least one set of 45 ° mode electrodes arranged so as to face each other at a distance. When a voltage is applied, the 45 ° mode electrodes arranged in pairs vibrate in the 45 ° mode in an intermediate region between the facing regions facing the 45 ° mode electrodes in the piezoelectric substrate. Charges are detected by the strain generated in the direction parallel to the main surface so as to generate a strain in the direction parallel to the main surface for exciting, or by the vibration in the 45 ° mode in the intermediate region in the piezoelectric substrate. It is configured to be.

According to the present invention, it is possible to provide a vibrating gyro using a single crystal piezoelectric material.

FIG. 1 is an explanatory diagram of wine glass vibration. (Example 1) FIG. 2 is an explanatory diagram of the wafer. (Example 1) FIG. 3 is an explanatory diagram of vibration of the piezoelectric substrate in the 0 ° mode. (Example 1) FIG. 4 is an explanatory diagram of vibration of the piezoelectric substrate in the 45 ° mode. (Example 1) FIG. 5 is an explanatory diagram of the vibrating body. (Example 1) FIG. 6 is an enlarged plan view of a main part of the vibrating body. (Example 1) FIG. 7 is an explanatory view of Euler angles. (Analysis Example of Example 1) FIG. 8 is a distribution diagram of the coefficient of variation. (Analysis Example of Example 1) FIG. 9 is an enlarged view of FIG. (Analysis Example of Example 1) FIG. 10 is a distribution diagram of the electromechanical coupling coefficient. (Analysis Example of Example 1) FIG. 11 is a diagram showing a vibration simulation result. (Analysis Example of Example 1) FIG. 12 is an explanatory diagram of a manufacturing process of the vibrating body. (Prototype example of Example 1) FIG. 13 is a photograph of the vibrating body. (Prototype example of Example 1) FIG. 14 is a cross-sectional view of the vibrating gyro. (Prototype example of Example 1) FIG. 15 is a photograph of a vibrating gyro. (Prototype example of Example 1) FIG. 16 is a graph of impedance characteristics. (Prototype example of Example 1) FIG. 17 is a graph of the velocity at the resonance end. (Prototype example of Example 1) FIG. 18 is a plan view of the piezoelectric substrate. (Modification example 1) FIG. 19 is a plan view of the vibrating body. (Modification 2) FIG. 20 is a plan view of the vibrating body. (Modification 3) FIG. 21 is a cross-sectional view of the vibrating body. (Modification 3) FIG. 22 is a plan view of the vibrating body. (Modification example 4) FIG. 23 is a cross-sectional view of the vibrating body. (Modification example 4) FIG. 24 is an explanatory diagram of a disc type vibrating gyro. (Conventional example 1) FIG. 25 is an explanatory diagram of a tuning fork type vibrating gyro. (Conventional example 2)

Hereinafter, embodiments of the present invention will be described with reference to the drawings.

<Example 1> The vibration gyro of Example 1 driven and detected by the wine glass vibration or the ring spreading vibration in the degenerate mode will be described with reference to FIGS. 1 to 17.

First, the driving principle of the vibration gyro will be described. FIG. 1 is an explanatory diagram of wine glass vibration. As shown in FIG. 1, two axes parallel to the surface including the circular contour 90a of the vibrating body 90 and orthogonal to each other are defined as the first axis and the second axis, and are perpendicular to the surface including the contour 90a of the vibrating body 90. Axis is the third axis. The first axis, the second axis, and the third axis pass through the center of the vibrating body 90.

FIG. 1A is an explanatory diagram of a 0 ° −90 ° mode (hereinafter referred to as “0 ° mode”). As shown in FIG. 1A, in the vibration in the 0 ° mode, the contour 90a of the vibrating body 90 spreads in the first axial direction (the direction of 0 ° with respect to the first axis) as shown by the chain line, and the second The deformation that contracts in the axial direction (90 ° with respect to the first axis) and the deformation that contracts in the first axial direction and spreads in the second axial direction as shown by the broken line are repeated.

FIG. 1B is an explanatory diagram of a 45 ° −135 ° mode (hereinafter referred to as “45 ° mode”). As shown in FIG. 1 (b), in the vibration in the 45 ° mode, the contour 90a of the vibrating body 90 spreads in the direction of 45 ° counterclockwise with respect to the first axis as shown by the chain line, and becomes the second axis. On the other hand, the deformation that contracts counterclockwise in the direction of 135 ° and the direction that contracts in the direction of 45 ° counterclockwise with respect to the first axis and the direction of 135 ° counterclockwise with respect to the second axis as shown by the broken line. Repeat the transformation that spreads to.

If the vibrating body 90 is isotropic, the vibrating body 90 deforms symmetrically with respect to the first axis and the second in the 0 ° mode, and becomes a vibration node in the 45 ° and 135 ° directions, so that the vibration in the 45 ° mode Does not occur. When the angular velocity Ω acts around the third axis when vibrating in the 0 ° mode, the symmetric vibration of the vibrating body 90 is distorted by the Coriolis force, and the vibration in the 45 ° mode is excited. By detecting the excited vibration in the 45 ° mode, the angular velocity Ω around the third axis can be measured.

In this way, when driving in 0 ° mode and detecting in 45 ° mode, the first axis and the second axis are the drive axes, and the axis that equally divides between the first axis and the second axis is the detection axis. is there. It is also possible to drive in 45 ° mode and detect in 0 ° mode. In this case, the first axis and the second axis are the detection axes, and the axis that equally divides the first axis and the second axis is the drive axis.

The piezoelectric substrate that vibrates in the 0 ° mode and the 45 ° mode has a line-symmetrical shape centered on each of the two drive shafts and the two detection shafts.

3 and 4 are explanatory views when the piezoelectric substrates 92 and 94 vibrate. In FIGS. 3 and 4, the first axis and the second axis are parallel to the main surfaces 92s, 92t; 94s, 94t of the piezoelectric substrates 92, 94, and are orthogonal to each other. The third axis is perpendicular to the main surfaces 92s, 92t; 94s, 94t of the piezoelectric substrates 92,94.

FIG. 3 is an explanatory diagram of the 0 ° mode. As shown in FIG. 3A, when a voltage is applied between the electrodes 96 formed on the main surfaces 92s and 92t of the piezoelectric substrate 92, the voltage extends in the first axial direction as shown by arrows 81a and 81b, and arrows 82a, As shown by 82b, it contracts in the second axial direction. As shown in FIG. 3B, when a voltage is similarly applied to the disc-shaped piezoelectric substrate 94, the eight-divided regions of the piezoelectric substrate 94 expand and contract in the same direction as indicated by the arrows. The contour 94a of the piezoelectric substrate 94 is deformed as shown by the chain wire 94p. When a periodically fluctuating electric field is applied between the main surfaces 92s, 92t; 94s, 94t, the piezoelectric substrates 92, 94 can be vibrated in 0 ° mode. On the contrary, when the piezoelectric substrates 92 and 94 vibrate in the 0 ° mode, a charge that fluctuates periodically is generated between the main surfaces 92s and 92t; 94s and 94t of the piezoelectric substrates 92 and 94.

FIG. 4 is an explanatory diagram of the 45 ° mode. As shown in FIG. 4A, when voltages of opposite phases are alternately applied between the electrodes 98 formed in eight on the main surfaces 92s and 92t of the piezoelectric substrate 92, as shown by arrows 83a and 83b. It extends in the direction of 45 ° with respect to the first axis and contracts in the direction of 135 ° with respect to the first axis as shown by arrows 84a and 84b. As shown in FIG. 4B, when a voltage is similarly applied to the disc-shaped piezoelectric substrate 94, the piezoelectric substrate 94 expands and contracts in the direction indicated by the arrow in each region corresponding to the electrode, and the expansion and contraction directions alternate. The contour 94a of the piezoelectric substrate 94 is deformed as shown by the chain line 94q. When a voltage that fluctuates periodically is applied to the piezoelectric substrates 92 and 94, the piezoelectric substrates 92 and 94 can be vibrated in the 45 ° mode. On the contrary, when the piezoelectric substrates 92 and 94 vibrate in the 45 ° mode, the charge of the piezoelectric substrates 92 and 94 fluctuates.

When measuring the angular velocity using vibration in 0 ° mode and vibration in 45 ° mode, the piezoelectric substrates 92 and 94 are isotropic, and the elastic compliance of the piezoelectric substrates 92 and 94 is the main surface 92s, 92t; 94s, Ideally, it should be the same in all directions within 94t.

As described above, the single crystal piezoelectric material has crystal anisotropy, but the inventor of the present application considers that it may be isotropic in the main plane direction depending on the cutting direction, and the crystal becomes isotropic in the main plane direction. I searched for the direction. As will be described in detail later, for example, in the 155 ° Y-cut LN plate, the first axis component and the second axis component of elastic compliance are substantially constant in any direction in the main surface.

FIG. 2 is an explanatory diagram of the wafer. FIG. 2A shows a Z-cut wafer 2a. FIG. 7B shows a wafer 2b with a 155 ° Y cut.

3 (a) and 4 (a) show the crystal axes X, Y, and Z when the piezoelectric substrate 92 is a 155 ° Y-cut LN plate. As shown in FIGS. 3 (a) and 4 (a), the first axis coincides with the Y axis. The polarization direction is the Z axis.

Next, the configuration of the vibrating body 11 used for the vibrating gyro will be described.

5 (a) is a plan view of the vibrating body 11, and FIG. 5 (b) is a cross-sectional view of the vibrating body 11. As shown in FIG. 5, in the vibrating body 11, inner electrodes 21 to 28 and outer electrodes 41 to 48 are formed on one main surface 12s of the circular plate-shaped piezoelectric substrate 12, and the other main surface 12t of the piezoelectric substrate 12 is formed. The inner electrodes 31 to 38 and the outer electrodes 51 to 58 are formed therein. One inner electrode 21 to 28 and the other inner electrode 31 to 38 face each other with the piezoelectric substrate 12 interposed therebetween. Similarly, one outer electrode 41 to 48 and the other outer electrode 51 to 58 face each other with the piezoelectric substrate 12 interposed therebetween.

A center hole 12b is formed in the center of the piezoelectric substrate 12 so as to penetrate between the main surfaces 12s and 12t of the piezoelectric substrate 12. The inner electrodes 21 to 28 and 31 to 38 are arranged at a pitch of 45 ° along the center hole 12b at a distance from each other. The outer electrodes 41 to 48, 51 to 58 are arranged on the radial outer side (opposite to the center hole 12b) of the inner electrodes 21 to 28, 31 to 38 at a pitch of 45 ° along the outer peripheral surface 12a of the piezoelectric substrate 12. They are arranged at intervals from each other.

That is, the first and second axes of the piezoelectric substrate 12 are parallel to the two axes that equally divide the first and second axes of the piezoelectric substrate 12, and the main surface 12s of the piezoelectric substrate 12 is parallel to each other. , Inner electrodes 21 to 28, 31 to 38 are formed on the center side (center hole 12b side) of the main surfaces 12s and 12t, respectively, in eight regions divided by four virtual lines passing through the center of 12t, respectively. The outer electrodes 41 to 48 and 51 to 58 are formed on the side opposite to the center of 12s and 12t (the outer peripheral surface 12a side), respectively.

FIG. 6 is an enlarged view of a main part of the vibrating body 11. As shown in FIG. 6, eight inner electrode terminal portions 21x to 28x and eight outer electrode terminal portions 41x to 48x are formed on one main surface 12s of the piezoelectric substrate 12 along the center hole 12b. Has been done. The terminal portions 21x to 28x for the inner electrodes are formed integrally with the inner electrodes 21 to 28. The outer electrode terminal portions 41x to 48x are formed with a gap between the inner electrodes 21 to 28 and the inner electrode terminal portions 21x to 28x. As shown in FIGS. 5 and 6, wirings 41a to 48a for electrically connecting the outer electrodes 41 to 48 and the outer electrode terminal portions 41x to 48x are formed between the inner electrodes 21 to 28 adjacent to each other. ing. The inner electrode terminal portions 21x to 28x and the outer electrode terminal portions 41x to 48x are electrically connected to a rod terminal 64 (see FIG. 14) described later.

Although not shown, on the other main surface 12t of the piezoelectric substrate 12, the inner electrode terminal portions 21x to 28x, the outer electrode terminal portions 41x to 48x, and the wiring 41a to 48a of one main surface 12t of the piezoelectric substrate 12 Similarly, the terminal portion for the inner electrode, the terminal portion for the outer electrode, and the wiring are formed. The inner electrode terminal portion and the outer electrode terminal portion formed on the other main surface 12t of the piezoelectric substrate 12 are electrically connected to a rod terminal 66 (see FIG. 14) described later.

The vibrating body 11 may be vibrated in 0 ° mode to detect the electric charge generated by the vibration in 45 ° mode, or the vibrating body 11 may be vibrated in 45 ° mode to detect the electric charge generated by the vibration in 0 ° mode. You may.

When driving in 0 ° mode and detecting in 45 ° mode, for example, the inner electrodes 21 to 28, 31 to 38 vibrate the piezoelectric substrate 12 in the direction of the first axis or two drive axes parallel to the second axis. The electric field to be generated is used as a drive electrode for applying the electric field to the piezoelectric substrate 12, and the outer electrodes 41 to 48, 51 to 58 are excited to the piezoelectric substrate 12 by vibration in the directions of the two detection axes that equally divide the drive shafts. It is used as a detection electrode for detecting the electric charge to be generated. It is also possible to use the inner electrodes 21 to 28 and 31 to 38 as detection electrodes and the outer electrodes 41 to 48 and 51 to 58 as drive electrodes.

When driving in the 45 ° mode and detecting in the 0 ° mode, for example, the inner electrodes 21 to 28, 31 to 38 are used as driving electrodes, and the outer electrodes 41 to 48, 51 to 58 are used as detection electrodes. It is also possible to use the inner electrodes 21 to 28 and 31 to 38 as detection electrodes and the outer electrodes 41 to 48 and 51 to 58 as drive electrodes.

Next, an analysis example of Example 1 will be described with reference to FIGS. 7 to 11.

First, the analysis of the crystal orientation of the piezoelectric substrate 12 which is isotropic in the main plane direction, that is, isotropic in the plane will be described. The constants of various materials of the piezoelectric material are determined by the XYZ coordinate system (hereinafter referred to as the crystal XYZ coordinate system) with the polarization direction as the Z axis. When the crystal orientation of the wafer is different from the orientation based on this polarization direction, it is necessary to consider various material constants re-expressed in the coordinate system based on the wafer (hereinafter referred to as the wafer coordinate system).

Here, the crystal XYZ coordinate system is rotated by an angle of ψ around the Z axis according to the definition of Euler angles shown in FIG. 7, and the X'Y'Z' coordinate system is further rotated by an angle of θ around the X'axis. Let the Y''Z'' coordinate system be the wafer coordinate system.

The stress T-strain S relational expression belonging to the crystallographic point group 3m in the crystal XYZ coordinate system can be expressed by the following equation (1).
Here, S _i : strain, T _i : stress, and S _ij : elastic compliance.

When the equation (1) is re-expressed in the wafer X''Y''Z'' coordinate system, the following equation (2) is obtained.
However, assuming that the piezoelectric substrate 12 is sufficiently thin, it is in a plane stress state (T ₃ '' = 0, T ₄ '' = 0, T ₅ '' = 0), and components that are not related to strain in the plane direction are It is omitted.

Wafer X''Y''Z''coordinate system further angled around Z''axis to investigate elastic properties due to in-plane orientation
Considering the elastic compliance in the rotated X'''Y'''Z'''coordinate system s ₁₁ ''', s ₁₂ ''', s ₁₆ ''', s ₆₆ ''', the following equation It can be represented by (3).

These equations (3) are
These equations (3) are functions of
If it is constant regardless of, elastic compliance s ₁₁ ″, s ₁₂ ″, s ₁₆ ″, s ₆₆ ″ can be said to be in-plane isotropic. Note that s ₂₂ '' and s ₂₆ '''' are equivalent to s ₁₁ '' and s ₁₆ '', respectively, and therefore need not be considered. For this purpose, all the coefficients of the cos term and the sin term in the equation (3) should be close to 0. From equation (3), there are the following four coefficients.

Since s ₁₁ ″ includes all of these, constant s ₁₁ ″ ″ is a sufficient condition. So, of s ₁₁ ''''
The coefficient of variation CV (ψ, θ) with respect to the above was defined by the following equation (5), and the wafer orientation in which the value of the coefficient of variation CV (ψ, θ) was close to 0 was searched.

FIG. 8 is a distribution diagram of the coefficient of variation C.V. (ψ, θ). As shown in FIG. 8, (ψ, θ) = (0 °, 0 °), (0 °, 65 °), that is, the Z cut or the 155 ° Y cut is in-plane isotropic. Since LN belongs to the point cloud 3m of the trigonal system, there are two crystal structure equivalent points for (0 °, 0 °) and six points for (0 °, 65 °).

FIG. 9 is a distribution map showing the calculation results in the vicinity of (0 °, 65 °). As can be seen from FIG. 9, the coefficient of variation C.V. (ψ, θ) is less than 1% in approximately -4 ° <ψ <4 ° and 63 ° <θ <67 °.

FIG. 10 is a distribution diagram of electromechanical coupling coefficients k ₃₁ and k _{32 in} the vicinity of (0 °, 65 °). From FIG. 10, the electromechanical coupling coefficient is about 0.3.

In the vicinity of (0 °, 0 °), the electromechanical coupling coefficient k ₃₁ is close to 0 in any in-plane direction, so (0 °, 65 °) is adopted.

FIG. 11 shows the result of simulating the vibration of the wine glass of the 155 ° Y-cut LN plate by the finite element method. FIG. 11A shows vibration in 0 ° mode, and FIG. 11B shows vibration in 45 ° mode. The resonance frequency in the 0 ° mode was 96.8 kHz, and the resonance frequency in the 45 ° mode was 95.0 kHz.

When the piezoelectric substrate is composed of a single crystal classified into a trigonal point cloud group of 3 m, a piezoelectric substrate other than LN, for example, a piezoelectric substrate such as lithium tantalate (LT) or langasite may be used.

Next, a prototype example of Example 1 will be described with reference to FIGS. 12 to 17.

FIG. 12 is a schematic view showing a manufacturing process of the vibrating body 11. As shown in FIG. 12 (a), a 4-inch 155 ° Y-cut LN wafer 12w was prepared, and as shown in FIG. 12 (b), on both sides 12p and 12q of the wafer 12w by electron beam deposition under chromium. The strata 70 and 71 are formed, and the gold electrode layers 72 and 73 are formed on the strata 70 and 71. Next, as shown in FIG. 12 (c), photoresist is applied to both surfaces, mask patterns 74 and 75 are formed by photolithography, and then wet etching is performed as shown in FIG. 12 (d) to perform an electrode pattern. To form. Finally, the disc piece and its center hole are cut out using a core drill, the outer peripheral surface 12a and the center hole 12b of the piezoelectric substrate 12 are processed, washed, and the mask pattern 74, as shown in FIG. 12 (e). When 75 is removed, the vibrating body 11 is completed.

FIG. 13 is a photograph of the prototype vibrating body 11. The prototype vibrating body 11 has a thickness of 330 μm, a diameter of 25.8 mm, and a center hole 12b having a diameter of 4 mm. The thickness of each of the chrome base layers 70 and 71 is 50 nm, and the thickness of each of the gold electrode layers 72 and 73 is 200 nm.

FIG. 14 is a cross-sectional view of the vibrating gyro 10 in which the vibrating body 11 is housed in the socket. As shown in FIG. 14, the vibrating body 11 is arranged between the pair of socket plates 60 and 62. The vibrating body 11 is supported in a state where the protrusion 63 of one of the socket plates 60 is inserted into the center hole 12b of the piezoelectric substrate 12 and the inner peripheral surface of the center hole 12b is in contact with the outer peripheral surface of the protrusion 63 of the socket plate 60. Will be done. Rod terminals 64 and 66 are attached to the socket plates 60 and 62, and the tips of the rod terminals 64 and 66 are formed in the vicinity of the center hole 12b of the piezoelectric substrate 12 for the inner electrode terminal portion and the outer electrode terminal portion. Is in contact with.

FIG. 15 is a photograph of the prototype vibrating gyro 10, showing a state in which the vibrating body 11 is housed in a socket.

In order to evaluate the vibration characteristics of the prototype vibration gyro 10, an impedance analyzer (4294A, manufactured by KeySight Technologies, Inc.) was connected to the rod terminals 64 and 66, and the impedance characteristics were measured.

In the 0 ° mode, the positive electrode terminal of the impedance analyzer is electrically connected to the inner electrodes 21 to 28 of one main surface 12s of the piezoelectric substrate 12, and the negative electrode terminal is connected to the inner electrode of the other main surface 12t of the piezoelectric substrate 12. Electrically connect to 31-38. In the 45 ° mode, the outer electrodes 41 to 48, 51 to 58 are alternately electrically connected to the positive electrode terminal and the negative electrode terminal. For example, the positive electrode terminals are electrically connected to the outer electrodes 41, 43, 45, 47, 52, 54, 56, 58, and the negative electrode terminals are connected to the outer electrodes 42, 44, 46, 48, 51, 53, 55, 57. Connect electrically. In both cases, electrodes not used for measurement are short-circuited.

FIG. 16 is a graph showing the measurement results of the impedance characteristics in the 0 ° mode and the 45 ° mode, and shows the frequency response in the vicinity of the wine glass mode. From FIG. 12, it can be seen that the vibration occurs at the resonance frequencies of the 0 ° mode and the 45 ° mode. The measured resonance frequency is 95.7 kHz in 0 ° mode and 95.5 kHz in 45 ° mode. The resonance frequency is in good agreement with the simulation with finite elements. In order to increase the detection sensitivity, it is preferable to detect the 0 ° mode and use the 45 ° mode for driving.

FIG. 17 is a graph showing the results of measuring the velocity at the resonance end using an optical heterodyne micro-vibration measuring device (MLD-230D-200K, manufactured by NeoArc Co., Ltd.). The vibration amplitude calculated from the velocity measured in 0 ° mode was 80 nm at a voltage amplitude of 200 mV. The vibration amplitude calculated from the velocity measured in 45 ° mode was 25 nm at a voltage amplitude of 500 mV.

The impedance at the resonance frequency was low enough to oscillate the vibrating body 11 in both modes using a self-excited oscillation circuit. The electromechanical coupling coefficient calculated from the impedance measurement results was 30.0% in the 0 ° mode and 4.3% in the 45 ° mode, which was in good agreement with the finite element simulation. The Q value calculated from the measured impedance is 920 in 0 ° mode and 1300 in 45 ° mode, and the Q value calculated from the measured velocity is 960 in 0 ° mode and 45 °. It was 880 in mode.

As described above, even if the piezoelectric substrate of the vibrating body is made of an anisotropic material such as LN, mode matching can be achieved by using the optimally oriented wafer. Therefore, it is possible to realize a vibrating gyro using a single crystal piezoelectric material.

Next, a modified example of the first embodiment will be described.

<Modification Example 1> FIG. 18 is a plan view of a piezoelectric substrate used for a vibrating body. As shown in FIGS. 18A to 18C, the shapes of the piezoelectric substrates 91a to 91c may be circular, square (not shown), regular polygons such as regular octagons and regular hexadecagons. In this case, the piezoelectric substrates 91a to 91c can be easily processed.

Further, as shown in FIGS. 18 (d) to 18 (f), even if the center holes 91p to 91r are provided in the center of the piezoelectric substrates 91a to 91c, they are not provided as shown in FIGS. 18 (a) to 18 (c). May be good. When the center holes 91p to 91r are not provided, for example, the center point of the piezoelectric substrate is supported, or the piezoelectric substrate is held by elastically pulling a plurality of points on the outer periphery of the piezoelectric substrate in the radial direction to improve the elasticity. A piezoelectric substrate is sandwiched between the members to be held.

<Modification 2> As shown in the plan view of FIG. 19, 0 ° mode electrodes 96a to 96c and 45 ° mode electrodes 98a to 98c are arranged in various modes on the same main surface 94s of the piezoelectric substrate 94. It is possible.

In FIG. 19A, of the main surfaces 94s of the piezoelectric substrate 94, one 0 ° mode electrode 96a is arranged on the right side, and two sets of 45 ° mode electrodes 96a are arranged in pairs on the left side. 98a and 98s are arranged so as to be offset by 90 °. The electrodes 96a and the two sets of electrodes 98a and 98s may be arranged upside down.

The 45 ° mode electrodes 98a and 98s can be used to drive the 45 ° mode vibration or detect the 45 ° mode vibration. FIG. 19A illustrates the case where two sets of 45 ° mode electrodes 98a, 98s are arranged in pairs, but if there is at least one set of 45 ° mode electrodes 98a, 98s. , 45 ° mode vibration can be detected.

That is, the drive electrode or the detection electrode includes at least one main surface 94s of the piezoelectric substrate 94 including the drive shaft and the detection shaft and is divided by four virtual surfaces 86 to 89 perpendicular to the main surface 94s of the piezoelectric substrate 94. Of the eight regions of, adjacent to each other with virtual surfaces 87 and 89 parallel to the straight line equally dividing between the first axis and the second axis (that is, the X ″ axis and the Y ″ axis described above). The two mating regions include at least one pair of 45 ° mode electrodes 98a, 98s arranged in pairs. The 45 ° mode electrodes 98a, 98s arranged in pairs are (a) opposite regions facing the 45 ° mode electrodes 98a, 98s in the piezoelectric substrate 94 when voltages having opposite phases are applied. In order to generate strain in the direction parallel to the main surface 94s for exciting the vibration in the 45 ° mode, or (b) in the region facing the electrodes 98a, 98s for the 45 ° mode in the piezoelectric substrate 94, 45. It is configured so that charges in opposite phases are detected by the strain generated in the direction parallel to the main surface 94s when oscillating in the ° mode.

In FIG. 19B, of the main surface 94s of the piezoelectric substrate 94, one 0 ° mode electrode 96b is arranged inside, and four sets of 45 ° mode electrodes 96b are arranged so as to be paired outside. 98b and 98t are arranged every 90 °.

In FIG. 19C, eight electrodes 98c for 45 ° mode are arranged inside every 45 °, and one electrode 96c for 0 ° mode is arranged outside.

In FIG. 19D, eight inner electrodes 97a are arranged at intervals of 45 ° on the inner side and eight outer electrodes 97b are arranged at intervals of 45 ° on the outer side of the main surface 94s of the piezoelectric substrate 94. The aspect of FIG. 19 (d) is highly versatile because it is equivalent to FIGS. 19 (a) to 19 (c) depending on the combination of the phases of the electrodes 97a and 97b. For example, for the inner electrode 97a, the electrode with "A" and the electrode with "B" are in phase, and for the outer electrode 97b, the electrode with "A" and "B" are in phase. When the attached electrodes are out of phase with each other, it becomes equivalent to FIG. 19B.

<Modification Example 3> The electrodes may be arranged so as to combine the 3-axis electric field in the 0 ° mode and the in-plane electric field in the radial direction in the 45 ° mode. FIG. 20 is a plan view of the vibrating body. FIG. 20 is a partial cross-sectional view cut along the line RR'of FIG. 20 (b).

FIG. 20A is an explanatory diagram of the 0 ° mode. The four electrodes 45x marked with “0” in FIG. 20A are 0 ° mode electrodes 45x, and as indicated by the symbol P, their electric fields are in phase.

FIG. 20B is an explanatory diagram of the 45 ° mode. The electrodes 45a and 45b marked with "45" in FIG. 20B are 45 ° mode electrodes 45a and 45b arranged in pairs, and the 0 ° mode electrodes 45x adjacent to each other in the circumferential direction. They are arranged so as to face each other with a radial interval between them and form a pair.

As shown in FIG. 21 (a), the 45 ° mode electrodes 45a and 45b may be formed apart from the outer peripheral surface 94a and the inner peripheral surface 94b of the piezoelectric substrate 94, or as shown in FIG. 21 (b). In addition, it may be formed so as to be continuous from the main surfaces 94s and 94t of the piezoelectric substrate 94 to the inner peripheral surface 94b or the outer peripheral surface 94a.

An electric field in the direction indicated by the arrow in FIGS. 20 (b) and 21 is generated between the 45 ° mode electrodes 45a and 45b facing each other in the radial direction.

The 45 ° mode electrodes 45a and 45b can be used to drive the 45 ° mode vibration or detect the 45 ° mode vibration. FIG. 20 shows four pairs of 45 ° mode electrodes 45a and 45b arranged in pairs, but at least one pair of 45 ° mode electrodes 45a and 45b is arranged. When assembled, vibration in 45 ° mode can be detected.

That is, the drive electrode or the detection electrode includes the drive shaft or the detection shaft and is parallel to the first axis and the second axis (that is, the X ″ axis and the Y ″ axis described above) and the main surface of the piezoelectric substrate 94. At least one of four regions of at least one main surface 94s of the piezoelectric substrate 94 divided by two virtual surfaces 86,88 perpendicular to 94s, 94t has two boundaries with adjacent regions of the region. It includes at least one set of 45 ° mode electrodes 45a, 45b that are spaced apart from each other in a direction that equally divides the lines and are arranged so as to face each other. The 45 ° mode electrodes 45a and 45b arranged in pairs are intermediate between the facing regions facing the 45 ° mode electrodes 45a and 45b in the piezoelectric substrate 94 when the voltage (a) is applied. To generate strain in the direction parallel to the main surfaces 94s, 94t for exciting 45 ° mode vibrations in the region, or (b) facing the 45 ° mode electrodes 45a, 45b in the piezoelectric substrate 94. In the intermediate region between the regions, the charge is detected by the strain generated in the direction parallel to the main surfaces 94s and 94t by the vibration in the 45 ° mode.

<Modification Example 4> A 3-axis electric field in the 0 ° mode and an in-plane electric field in the circumferential direction in the 45 ° mode may be combined. FIG. 22 is a plan view of the vibrating body. FIG. 23 is a cross-sectional view taken along the line SS'of FIG. 22 (b).

FIG. 22A is an explanatory diagram of the 0 ° mode. The four electrodes 45y marked with “0” in FIG. 22A are 0 ° mode electrodes 45y, and as indicated by the symbol P, their electric fields are in phase.

FIG. 22B is an explanatory diagram of the 45 ° mode. The electrodes 45p and 45q marked with “45” in FIG. 22B are 45 ° mode electrodes 45p and 45q, and are located between the 0 ° mode electrodes 45y adjacent to each other in the circumferential direction. They are arranged so as to face each other and form a pair. An electric field in the direction indicated by the arrow in FIGS. 22 (b) and 23, for example, is generated between the 45 ° mode electrodes 45p and 45q facing each other in the circumferential direction.

The 45 ° mode electrodes 45p and 45q can be used to drive the 45 ° mode vibration or detect the 45 ° mode vibration. FIG. 22 shows four sets of 45 ° mode electrodes 45p and 45q arranged in pairs, but at least one of the 45 ° mode electrodes 45a and 45b arranged in pairs. When assembled, vibration in 45 ° mode can be detected.

That is, the drive electrode or the detection electrode is at least one main of the piezoelectric substrate 94 including the drive shaft and the detection shaft and is divided by four virtual surfaces 86 to 89 perpendicular to the main surfaces 94s and 94t of the piezoelectric substrate 94. Of the eight regions of the surface 94s, the virtual surfaces 87 and 89 parallel to the straight line equally dividing between the first axis and the second axis (that is, the X ″ axis and the Y ″ axis described above) are sandwiched. Two regions adjacent to each other include at least one set of 45 ° mode electrodes 45p, 45q that are spaced apart from each other and are arranged in pairs. The 45 ° mode electrodes 45p and 45q arranged in pairs are intermediate between the facing regions facing the 45 ° mode electrodes 45p and 45q in the piezoelectric substrate 94 when the voltage (a) is applied. To generate strain in the direction parallel to the main surfaces 94s, 94t for exciting 45 ° mode vibrations in the region, or (b) opposite the 45 ° mode electrodes 45p, 45q in the piezoelectric substrate 94. It is configured so that the charge is detected by the strain generated in the direction parallel to the main surfaces 94s and 94t when vibrating in the 45 ° mode in the intermediate region between the regions.

<Modification 5> The piezoelectric substrate does not have to have a uniform thickness. For example, the thickness of the region near the outer circumference of the piezoelectric substrate is made larger than the thickness of the other regions to form a weight. By partially changing the thickness of the piezoelectric substrate, it is possible to compensate for the difference in resonance frequency between the 0 ° mode and the 45 ° mode.

Further, as a modification of the ring type in which the thickness of the region near the outer circumference is increased, a wine glass (hemispherical shape) type or a cup (cylindrical) type is also possible by changing the thickness of the piezoelectric substrate. In this case, it is possible to lower the resonance frequency as compared with the disc type.

<Summary> As described above, a vibrating gyro using a single crystal piezoelectric material can be constructed by selecting an appropriate cutting angle.

The present invention is not limited to the above embodiment, and can be implemented with various modifications.

For example, the dimensions such as the thickness and outer diameter of the piezoelectric substrate, the dimensions, shape, and arrangement of the electrodes may be appropriately selected.

1 1st axis (drive axis or detection axis)
2 2nd axis (detection axis or drive axis)
10 Vibrating gyro 11 Vibrating body 12 Piezoelectric substrate 12w Wafer 21-28, 31-38 Inner electrode (driving electrode or detection electrode)
41-48, 51-58 outer electrodes (detection electrodes or drive electrodes)
45a, 45b, 45p, 45q 45 ° mode electrode 86-89 Virtual surface 92,94 Piezoelectric substrate 96, 96a, 96b, 96c Electrode 97a, 97b Electrode 98 Electrode 98a, 98b 45 ° mode electrode 98c Electrode 98s, 98t 45 ° Mode electrode

Claims (7)

A vibration gyro that is driven and detected by wine glass vibration or ring spreading vibration in degenerate mode.
A piezoelectric substrate having a pair of main surfaces facing each other,
A drive electrode for applying an electric field that vibrates the piezoelectric substrate in the directions of two drive shafts parallel to the main surface and orthogonal to each other, and
A detection electrode for detecting the electric charge excited by the piezoelectric substrate due to vibration in the direction of the two detection shafts that equally divide the drive shafts of the piezoelectric substrate.
With
The piezoelectric substrate is
It consists of a single crystal piezoelectric material classified into a trigonal point cloud of 3 m.
Of the crystal axes X, Y, and Z of the single crystal, the Z axis is the polarization direction.
The X'Y'Z'coordinate system obtained by rotating the crystal XYZ coordinate system based on the crystal axes X, Y, Z by an angle ψ around the Z axis according to the definition of right-handed Euler angles, and further rotating the angle θ around the X'axis. Assuming that the X''Y''Z''coordinates are the wafer coordinate system of the piezoelectric substrate,
One of the two drive shafts and the two detection shafts is parallel to the X ″ axis or the Y ″ axis.
The other of the two drive shafts and the two detection axes is parallel to one or the other of the two straight lines that equally divide between the X ″ axis and the Y ″ axis.
A vibration gyro, characterized in that the elastic compliance of the piezoelectric substrate in the main surface direction is substantially constant regardless of the orientation in the main surface. The piezoelectric substrate is made of a single crystal of lithium niobate.
-4 ° <ψ <4 ° and 63 ° <θ <67 °
The vibrating gyro according to claim 1, wherein the vibration gyro is characterized by the above. The vibration gyro according to claim 2, wherein the piezoelectric substrate is a Y-cut plate having a cut angle of 155 ° or more and 156 ° or less. The vibration gyro according to any one of claims 1 to 3, wherein the shape of the piezoelectric substrate is circular or a regular polygon. The drive electrode or the detection electrode is
Of the eight regions of at least one of the main surfaces of the piezoelectric substrate, each of which includes the two drive shafts and the two detection axes and is divided by four virtual surfaces perpendicular to the main surface of the piezoelectric substrate. At least one set of pairs arranged in two adjacent regions across the virtual plane parallel to the straight line that equally divides between the X'axis and the Y'axis. Includes electrodes for 45 ° mode
When voltages of opposite phases are applied to the 45 ° mode electrodes arranged in pairs, the 45 ° mode vibrations occur in the facing region of the piezoelectric substrate facing the 45 ° mode electrodes. Due to the strain generated in the direction parallel to the main surface for excitation, or to generate the strain in the direction parallel to the main surface when vibrating in the facing region in the piezoelectric substrate in 45 ° mode. The vibration gyro according to any one of claims 1 to 4, wherein charges of opposite phases are detected. The drive electrode or the detection electrode is
At least one of the piezoelectric substrates divided by two virtual planes including the drive shaft or the detection shaft, parallel to each of the X'axis and the Y'axis and perpendicular to the main surface of the piezoelectric substrate. At least one of the four regions of the main surface is arranged so as to face each other and form a pair at least one of the four regions of the main surface at intervals in a direction that equally divides the two boundaries with the adjacent regions of the region. Includes at least one set of 45 ° mode electrodes
When a voltage is applied, the 45 ° mode electrodes arranged in pairs vibrate in the 45 ° mode in the intermediate region between the facing regions facing the 45 ° mode electrodes in the piezoelectric substrate. Charges are detected by the strain generated in the direction parallel to the main surface so as to generate a strain in the direction parallel to the main surface for exciting, or by the vibration in the 45 ° mode in the intermediate region in the piezoelectric substrate. The vibrating gyro according to any one of claims 1 to 4, wherein the vibration gyro is configured to be the same. The drive electrode or the detection electrode is
Of the eight regions of at least one of the main surfaces of the piezoelectric substrate, each of which includes the two drive shafts and the two detection axes and is divided by four virtual surfaces perpendicular to the main surface of the piezoelectric substrate. The two regions that are adjacent to each other with the virtual surface parallel to the straight line that equally divides the X ″ axis and the Y ″ axis are spaced apart from each other so as to be paired with each other. Includes at least one set of 45 ° mode electrodes arranged in
When a voltage is applied, the 45 ° mode electrodes arranged in pairs vibrate in the 45 ° mode in the intermediate region between the facing regions facing the 45 ° mode electrodes in the piezoelectric substrate. Charges are detected by the strain generated in the direction parallel to the main surface so as to generate a strain in the direction parallel to the main surface for exciting, or by the vibration in the 45 ° mode in the intermediate region in the piezoelectric substrate. The vibrating gyro according to any one of claims 1 to 4, wherein the vibration gyro is configured to be the same.