JP2005077290A - Elastic surface wave gyroscope - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To obtain a means for generating Coriolis force only at one desired axis that generates when torque is applied to a gyroscope. <P>SOLUTION: A plurality of IDT electrodes are arranged on the main surface of a piezoelectric substrate LiNbO<SB>3</SB>, and then, under the condition that an elastic surface wave W is excited, the Euler angles of the piezoelectric substrate LiNbO<SB>3</SB>are set to (0°, 43.2°, 0°) or (0°, 158.9°, 0°) in an elastic surface wave gyroscope using the difference in speed between the speed of an elastic wave C generated with the Coriolis force that is produced by applying the torque to the piezoelectric substrate and the speed of elastic surface wave W. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a surface acoustic wave gyroscope, and more particularly to a surface acoustic wave gyroscope that detects only the rotational angular velocity of a desired axis among three orthogonal axes by cutting a piezoelectric substrate at a specific angle. Is.

Piezoelectric vibratory gyroscopes are used as angular velocity sensors in various fields such as camera shake compensation for VTR images, attitude control systems, car navigation systems, etc., and their applications are becoming increasingly widespread due to improved performance, lower prices, and smaller size. Yes.
The piezoelectric vibration gyroscope is an angle sensor that drives one vibration mode of two vibration modes and that the other vibration mode is excited by Coriolis force when a rotational angular velocity is applied. When configuring such a piezoelectric vibration gyroscope, it is desirable that the vibrator can electrically drive and detect two vibration modes independently, and that their resonance frequencies are close to each other.

FIG. 4 is a schematic plan view showing the configuration of a surface acoustic wave gyroscope disclosed in Japanese Patent Application Laid-Open No. 9-264745. The gyroscope 11 includes a detection element 12, a high frequency power supply 13, a delay circuit 14, an electronic circuit 15 and the like. The detection element 12 has an IDT electrode 17 (for driving) disposed on the main surface of the piezoelectric substrate 16, for example, 128 ° Y-cut LiNbO ₃ , along the X-axis direction shown in FIG. An IDT electrode 18 (for detection) is disposed with a predetermined gap L therebetween. Each of the IDT electrodes 17 and 18 is composed of a pair of comb-shaped electrodes having a plurality of electrode fingers interleaved with each other, and the electrode pitch λ of each IDT electrode is the same. Further, the gap L is set such that the detection IDT electrode 18 is spatially shifted by 90 ° with respect to the driving IDT electrode 17. That is, the IDT electrodes 17 and 18 are placed at positions where the phase difference between the high-frequency phase input to the driving IDT electrode 17 and the phase of the AC signal detected by the detection IDT electrode 18 is 90 °. Deploy.

  When a high frequency voltage is applied to the comb electrode of the driving IDT electrode 17 from the high frequency power supply 13, a surface acoustic wave W (Rayleigh wave) is excited, the surface acoustic wave W propagates in the X-axis direction, and the detection IDT electrode 18 The elastic vibration is received as an electrical signal. Since the voltage waveform of this signal is based on the surface acoustic wave W, it becomes an AC waveform. When a rotational motion is applied to the piezoelectric substrate 16 in a state where the piezoelectric substrate 16 is vibrated by the surface acoustic wave W, a Coriolis force vector F acts. It is well known that this Coriolis force vector F is related to the particle density ρ of the piezoelectric substrate 16, the vibration velocity vector v of the elliptically moving particles, and the rotational angular velocity vector Ω of the piezoelectric substrate 16 and is expressed by the following equation. Yes.

  Here, bold indicates a vector.

When the orthogonal coordinate system (X, Y, Z) is set as shown in FIG. 4, the particles of the surface acoustic wave W (Rayleigh wave) make an elliptical motion opposite to the traveling direction in the XZ plane as is well known. This particle velocity vector v can be separated into a component v _x (P wave) in the X-axis direction and a component v _z (SV wave) in the Z-axis direction. Here, it is assumed that a rotational motion with a rotational angular velocity Ωz is applied to the piezoelectric substrate 16 around the Z axis. Because there is a rotation axis direction to the direction of the vibration velocity component v _z of the particles is parallel, only the velocity components v _x, the Coriolis force _{Fy (= 2ρ · v x ·} Ωz) as shown in FIG. 5 is applied . Since the Coriolis force Fy is generated based on the surface acoustic wave W, the Coriolis force Fy becomes an acoustic wave that propagates in synchronization with the surface acoustic wave W as shown in FIG.

Similarly, when a rotational angular velocity Ωx around the X axis and a rotational angular velocity Ωy around the Y axis are applied to the piezoelectric substrate 16, Coriolis forces Fx, Fy, and Fz are generated, respectively. The relationship between the rotational angular velocity components (Ωx, Ωy, Ωz) around the X, Y, and Z axes and the generated Coriolis force vector F (Fx, Fy, Fz) is expressed by the unit vectors (i _x , i _y , i _z ), it can be expressed as:

    As shown in FIG. 7, the elastic wave C caused by the Coriolis force vector F is generated 90 ° out of phase with the surface acoustic wave W, and the Coriolis force is generated at the moment when the amplitude of the surface acoustic wave W becomes zero. The amplitude of the elastic wave resulting from is maximized.

In order to function as a surface acoustic wave gyroscope, a signal received by the detection IDT electrode 18 is electrically processed by an electronic circuit added to the outside of the detection element 12 to detect the rotation angular velocity and rotation angle of each axis. It is what I did.
Japanese Patent Laid-Open No. 9-264745 `` A Method for Estimating Optical Crystal Cuts and Propagation Directions for Excitation of Piezoelectric Waves '' JJ Campbell, IEEE Transaction on Sonics and Ultrasonics, vol.su-15, no.4, Oct. '68

The problem to be solved is that, as described above, in the conventional example, each Coriolis force is generated according to the rotational motion in the three-axis (X, Y, Z) directions, and these are separated into components in the respective axial directions. For processing, an electronic circuit added to the outside becomes complicated, and the cost cannot be reduced.

In the present invention, a plurality of IDT electrodes are arranged on the main surface of the piezoelectric substrate LiNbO _{3 and} a surface acoustic wave W is excited, and a rotational force is applied to the piezoelectric substrate to obtain a particle velocity and a rotational angular velocity of the piezoelectric substrate. In a surface acoustic wave gyroscope using a speed difference between the velocity of the elastic wave C generated by the generated Coriolis force and the velocity of the surface acoustic wave W, the Euler angles of the piezoelectric substrate LiNbO ₃ are set to (0 °, θ, 0 )), Θ is set to 43.2 ° and 158.9 °.

  Since the piezoelectric substrate for detecting element of the present invention is cut at a specific angle, only the rotational angular velocity around a desired axis can be detected, so that an electronic circuit for signal processing to be added to the outside can be easily obtained. There is an advantage that the cost can be reduced.

FIG. 1 is a schematic plan view of a detection element of a surface acoustic wave gyroscope according to the present invention, and is along the X-axis direction of orthogonal coordinates (X, Y, Z) shown in the figure on the main surface of a piezoelectric substrate 1. The IDT electrode 2 (for driving) is disposed so that the excited surface acoustic wave propagates, and the IDT electrode 3 (for detection) is disposed with a predetermined gap L from the IDT electrode 2. Each of the IDT electrodes 2 and 3 is composed of a pair of comb-shaped electrodes having a plurality of electrode fingers interleaved with each other, and the electrode pitch λ of each IDT electrode is the same. Furthermore, the gap L is set so that the detection IDT electrode 3 is spatially 90 ° out of phase with the driving IDT electrode 2.

FIG. 2 uses lithium niobate (LiNbO ₃ ) as the piezoelectric substrate 1 and represents the Euler angles of the piezoelectric substrate 1 as (0, θ, 0). When θ is changed, each axis (X, Y, The Coriolis force sensitivity is shown when rotating at a rotational angular velocity Ωi around Z). Coriolis force sensitivity S _F was defined as the following equation.
S _F = (ΔV / V) · ω / Ωi
Here, V is the phase velocity of the surface acoustic wave excited on the piezoelectric substrate 1, ω is the angular frequency, Ωi (i = X, Y, Z) is the rotational angular velocity around each axis, and ΔV is generated by the Coriolis force. The velocity difference between the velocity of the elastic wave C and the V.

As apparent from FIG. 2, Euler angles (0, θ, 0) be set how theta is, Coriolis force sensitivity S _F for rotation about the X axis is zero. Setting θ to 43.2 ° or 158.9 °, the Coriolis force sensitivity S _F around the Z axis can be detected only the rotation angular velocity of zero next, Y-axis. If θ is set to 130.3 ° or 167.7 °, only the rotational angular velocity of the Z axis can be detected. Thus, by setting θ to one of the above four, only the Coriolis force around a single axis can be detected, so a circuit that separates the rotational angular velocity component of each axis in the partial electronic circuit is provided. There is no need to add, the external electronic circuit can be simplified, and the cost can be reduced.
Desirably, the sensitivity around the Y axis is maximized when θ is set to 43.2 °.

Here, the method for obtaining the Coriolis force sensitivity shown in FIG. 2 will be described in detail. The paper “A Method for Estimating Optical Crystal Cuts and Propagation Directions for Excitation of Piezoelectric Waves”, Campbell et. Al, examines in detail the propagation velocity of surface acoustic waves in the absence and presence of electrodes on LiNbO ₃ . . However, since the Coriolis force is not taken into account, it is not described how the propagation speed is affected when the Coriolis force is generated. Therefore, we examined an equation in which Coriolis force F was added to Campbell's equation and tried this solution.

The differential equations that are fundamental when considering the high-coupled piezoelectric vibration theory as a boundary value problem are equations of motion in mechanical systems and Maxwell's equations in electrical systems, and there are piezoelectric basic equations related to material constants that connect them.
The relation between strain vector S and displacement vector u is

  The relational expression between electric field vector E and electrostatic potential Φ is

  The relationship between strain vector S, electric field vector E, and stress vector T is

  The relational expression between the electric displacement vector D, the electric field vector E, and the distortion vector S is

Here, “:” in Equation 4 represents a matrix product.
The equation of motion by external force vector F, particle velocity vector v, and stress vector T is

  The charge equation is

  The relational expression of particle velocity vector v, rotational angular velocity vector Ω and Coriolis force vector F is

Here, c ^E , e, ε ^s and ρ are an elastic constant, a piezoelectric constant, a dielectric constant, and a mass density, respectively. However, the rotational angular velocity vector Ω by the external force vector F and the angular frequency ω of the surface acoustic wave have the following relationship.

Therefore, the centrifugal force was ignored and only the Coriolis force was considered.
Considering the coordinate system shown in FIG. 3, since the region I (x ₃ > 0) is in the piezoelectric medium, the particle displacement ui of the surface wave and the electrostatic potential Φ ^I are expressed as follows.

On the other hand, since the region II (x ₃ <0) is a vacuum (or in the air), there is no displacement, and only the electrostatic potential should be considered as in the following equation.

Next, in the piezoelectric medium (region I) shown in FIG. 3, the equation 11 is substituted into the equations 3 to 6 to obtain the stress vector T and the electric displacement vector D, and these are substituted into the equations 7 and 8. When the amplitude coefficients A _{1 to} A ₄ are arranged, they are expressed as follows.

Here, each element of the matrix X _ij is expressed as follows.

Since c = c ^t due to crystal symmetry, the rotational angular velocity is zero, i.e.

  If there is

And symmetric. Here, “t” in c ^t and X ^t represents a transposed matrix.
In order to have non-zero solutions A _{1 to} A _{4 in} Equation 13,

Must.
Solving this quaternary equation gives eight solutions represented by the following real or complex equations.

However, the solution that decays in the depth direction of the substrate is the four roots of α = b-ja. Therefore, the displacement vector u and the electrostatic potential Φ are a linear sum of Expression 11 using these four roots.
Since only the ratio of A _{1 to} A ₄ can be found from Equation 13, the ratio of each root is defined as follows.

If always a _4j = 1,

Is obtained.
Next, since the region II (x ₃ <0) is in a vacuum, only the electrostatic potential Φ ^II needs to be considered. In vacuum, Φ ^II is Laplace's equation

Is satisfied, γ ² = 1 is obtained by substituting Equation (1) into this. Here, when a root satisfying the condition for concentrating energy on the surface (γ> 1) is selected, Φ ^II is expressed by the following equation.

Here, mechanically free at x ₃ = + 0, that is, the stress becomes zero. Here, the symbol on the x ₃ represents the unit vector in the x ₃ direction.

  As an electrical boundary condition, it is electrically open.

  In case of electrical short

  From equation (3)

  Is derived, and the following expression is derived from Expression (2) and Expression (4) or Expression (5).

Here, each element of the matrix Y _ij is expressed as follows. In case of electrical opening

  In case of electrical short

To have non-zero solutions F _{1 to} F ₄ in equation (6)

Must hold. Therefore, in order to obtain the propagation velocity Vs of the surface acoustic wave, Vs that satisfies Equation (7) may be obtained by numerical calculation using the Newton method or the like.
The diagram shown in FIG. 2 is a plot of the numerical analysis results in this way. From FIG. 2, it was found that a gyroscope showing Coriolis force sensitivity on only one axis, which is a feature of the present invention, can be realized. . Since FIG. 2 shows the result of the numerical analysis described above, it is expected that deviation from the actual gyroscope detection element will occur. Is estimated to be about ± 2 °.

It is the schematic plan view which showed the structure of the detection element of the surface acoustic wave gyroscope which concerns on this invention. Euler angles (0, θ, 0) is a diagram showing the relationship between the rotational axis sensitivity S _F of the square shaft. It is a figure which shows the coordinate axis setting on a piezoelectric substrate. It is a figure which shows the structure of the conventional surface acoustic wave gyroscope. It is a figure which shows the relationship between particle velocity and Coriolis force when a rotation angular velocity is added around the Z-axis. It is a figure which shows propagation of Coriolis force. The elasticity generated by the surface acoustic wave W and the Coriolis force is a diagram showing a relationship with C.

Explanation of symbols

Gap _x 1 between the first piezoelectric substrate 2,3 IDT electrode λ wavelength L IDT electrodes 2 and 3 of the surface acoustic waves excited from the IDT electrodes _2, x 2, _{x 3} orthogonal axes

Claims (4)

A plurality of IDT electrodes are arranged on the main surface of the piezoelectric substrate and generated by the Coriolis force generated by the particle velocity and the rotational angular velocity of the piezoelectric substrate by applying a rotational force to the piezoelectric substrate while exciting the surface acoustic wave W. In the surface acoustic wave gyroscope using the speed difference between the velocity of the acoustic wave C and the velocity of the surface acoustic wave W,
A surface acoustic wave gyroscope using LiNbO ₃ as the piezoelectric substrate, wherein θ is set to 43.2 ° when Euler angles are (0 °, θ, 0 °). A plurality of IDT electrodes are arranged on the main surface of the piezoelectric substrate and generated by the Coriolis force generated by the particle velocity and the rotational angular velocity of the piezoelectric substrate by applying a rotational force to the piezoelectric substrate while exciting the surface acoustic wave W. In the surface acoustic wave gyroscope using the speed difference between the velocity of the acoustic wave C and the velocity of the surface acoustic wave W,
A surface acoustic wave gyroscope in which LiNbO ₃ is used as the piezoelectric substrate and θ is set to 158.9 ° when its Euler angles are (0 °, θ, 0 °). A plurality of IDT electrodes are arranged on the main surface of the piezoelectric substrate and generated by the Coriolis force generated by the particle velocity and the rotational angular velocity of the piezoelectric substrate by applying a rotational force to the piezoelectric substrate while exciting the surface acoustic wave W. In the surface acoustic wave gyroscope using the speed difference between the velocity of the acoustic wave C and the velocity of the surface acoustic wave W,
A surface acoustic wave gyroscope wherein LiNbO ₃ is used as the piezoelectric substrate, and θ is set to 130.3 ° when the Euler angles are (0 °, θ, 0 °). A plurality of IDT electrodes are arranged on the main surface of the piezoelectric substrate and generated by the Coriolis force generated by the particle velocity and the rotational angular velocity of the piezoelectric substrate by applying a rotational force to the piezoelectric substrate while exciting the surface acoustic wave W. In the surface acoustic wave gyroscope using the speed difference between the velocity of the acoustic wave C and the velocity of the surface acoustic wave W,
A surface acoustic wave gyroscope characterized in that LiNbO ₃ is used as the piezoelectric substrate, and θ is set to 167.7 ° when its Euler angles are (0 °, θ, 0 °).

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