Robust micromachined gyroscopes with two degrees of freedom sense-mode oscillator

• US 20070034005A1
• Filed: 08/15/2005
• Published: 02/15/2007
• Est. Priority Date: 08/15/2005
• Status: Active Grant

• Current Assignee: Regents of the University of California (University of California)
• Original Assignee: Regents of the University of California (University of California)
• Inventors: Shkel, Andrei, Acar, Cenk
• Granted Patent: US 7,284,430 B2
• Time in Patent Office: Days
• US Class Current: 73/504.20
• CPC Class Codes: G01C 19/5719 using planar vibrating masses driven in a translation vibration along an axis

Abstract

A three-degrees of freedom (DOF) MEMS inertial micromachined gyroscope with nonresonant actuation with a drive direction, sense direction and a direction perpendicular to the drive and sense directions comprises a planar substrate, a 2-DOF sense-mode oscillator coupled to the substrate operated at a flattened wide-bandwidth frequency region, and a 1-DOF drive mode oscillator coupled operated at resonance in the flattened wide-bandwidth frequency region to achieve large drive-mode amplitudes.

Claims

1. A three-degrees of freedom (DOF) MEMS inertial micromachined gyroscope with nonresonant actuation with a drive direction, sense direction and a direction perpendicular to the drive and sense directions comprising:

a planar substrate;

a 2-DOF sense-mode oscillator coupled to the substrate operated at a wide-bandwidth frequency region; and

a 1-DOF drive mode oscillator coupled operated at resonance to achieve large drive-mode amplitudes.

2. The gyroscope of claim 1 where the 2-DOF sense mode oscillator is comprised of a second mass, m₂, which is free to vibrate in two dimensions relative to the substrate.

3. The gyroscope of claim 1 where the 1-DOF drive mode oscillator is comprised of a second mass, m₂, which is free to vibrate in a sense direction and drive direction and a first mass, m₁, which is constrained with respect to the second mass to vibrate relative to the second mass, m₂, only in the drive direction, the first and second masses vibrating together in the drive direction at a single peak resonance.

4. The gyroscope of claim 3 where the 2-DOF sense mode oscillator is comprised of the second mass, m₂, which is free to vibrate in two dimensions with respect to the substrate.

5. The gyroscope of claim 1 further comprising a frame structure coupled to the substrate and constrained to vibrate only in the drive direction relative to the substrate where the first mass is coupled to the frame structure and is constrained to vibrate only in the sense direction with respect to the frame structure to minimize quadrature error and undesired electrostatic forces in the sense-mode due to drive-mode actuator imperfections.

6. The gyroscope of claim 1 where the first and second masses are stiff in the direction perpendicular to the plane of the substrate.

7. The gyroscope of claim 5 where the 2-DOF sense mode oscillator is comprised of a second mass, m₂, which is free to vibrate in two dimensions relative to the substrate, and where the 1-DOF drive mode oscillator is comprised of a second mass, m₂, which is free to vibrate in a sense direction and drive direction and a first mass, m₁, which is constrained with respect to the second mass to vibrate relative to the second mass, m₂, only in the drive direction, the first and second masses vibrating together in the drive direction at a single peak resonance.

8. The gyroscope of claim 5 where equations of motion of the first and second masses, m₁ and m₂, are decomposed into the drive and sense directions, according to

(m₁+m₂+m_j){umlaut over (x)}₁+c_1x{dot over (x)}₁+k_1xx₁=(m₁+m₂+m_f)Ω

_z²x₁+F_d(t) 

 

(1)
m₁ÿ

₁+c_1y{dot over (y)}₁+k_1yy₁=k_2y(y₂−

y₁)+m₁Ω

_z²y₁−

2m₁Ω

_z{dot over (x)}₁−

m₁{dot over (Ω

)}_zx₁  

 

(2)
m₂ÿ

₂+c_2y{dot over (y)}₂+k_2yy₂=k_2yy₁m+2Ω

_z²y₂−

2m₂Ω

_z{dot over (x)}₂−

m₂{dot over (Ω

)}_zx₂. 

 

(3)

where z is the z-axis angular rate, m_f is the mass of the decoupling frame, F_d(t) is the driving electrostatic force applied to the active mass at the driving frequency ω

_d and where the subscripts refer to the masses and position coordinates (x, y) and their derivatives of the first and second masses, m₁ and m₂, respectively.

9. The gyroscope of claim 1 where the 2 DOF sense-mode oscillator is arranged and configured to have a generally flat operation region between two resonance peaks in the frequency response curves of the 2-DOF sense-mode oscillator to ensure that the drive-mode oscillation amplitude is insensitive to parameter fluctuations in the operation frequency band resulting in robustness to fluctuations in residual stresses, variations in elastic modulus from run to run in MEMs fabrication, and also insensitivity to thermal fluctuations throughout operation time.

10. The gyroscope of claim 1 where the drive oscillator is arranged and configured to operate at resonance in a frequency band in a drive direction for optimal response, while the 2 DOF sense-mode oscillator is arranged and configured to have a sensitivity which is relatively flat within the same frequency band in which the drive oscillator is at resonance.

11. A method of operating a three-degrees of freedom (DOF) MEMS inertial micromachined gyroscope comprising:

driving a 1-DOF drive mode oscillator operated at resonance to achieve large drive-mode amplitudes; and

sensing with a 2-DOF sense-mode oscillator simultaneously operated at a wide-bandwidth frequency region.

12. The method of claim 11 where sensing with the 2-DOF sense-mode oscillator comprises oscillating a second mass, m₂, in two dimensions relative to a substrate to which the sense-mode oscillator is coupled.

13. The method of claim 11 where driving the 1-DOF drive mode oscillator comprises oscillating a second mass, m₂, and oscillating a first mass, m₁, which first mass is constrained with respect to the second mass to oscillate relative to the second mass only in the drive direction, the first and second masses oscillating together in the drive direction at a single peak resonance.

14. The method of claim 13 where sensing with the 2-DOF sense-mode oscillator comprises oscillating a second mass, m₂, in two dimensions relative to a substrate to which the sense-mode oscillator is coupled.

15. The method of claim 11 further comprising:

oscillating a frame structure only in the drive direction relative to a substrate to which the frame is coupled;

where driving the 1-DOF drive mode oscillator comprises oscillating a second mass, m₂, and oscillating a first mass, m₁, which first mass is constrained with respect to the second mass to oscillate relative to the second mass only in the drive direction, the first and second masses oscillating together in the drive direction at a single peak resonance, and

where oscillating the first mass coupled to the frame structure only in the sense direction with respect to the frame structure to minimize quadrature error and undesired electrostatic forces in the sense-mode due to drive-mode actuator imperfections.

16. The method of claim 11 where the first and second masses are stiff in the direction perpendicular to a plane which defines a substrate to which the drive mode and sense-mode oscillators are coupled, so that driving the 1-DOF drive mode oscillator and sensing with a 2-DOF sense-mode oscillator are substantially all in a plane parallel to the substrate.

17. The method of claim 15 where sensing with a 2-DOF sense-mode oscillator comprises oscillating a second mass, m₂ in two dimensions relative to the substrate.

18. The gyroscope of claim 15 where driving the drive mode oscillator and sensing with the sense-mode oscillator is described by the equations of motion of the first and second masses, m₁ and m₂, which motions are decomposed into the drive and sense directions, according to

(m₁+m₂+m_j){umlaut over (x)}₁+c_1x{dot over (x)}₁+k_1xx₁=(m₁+m₂+m_f)Ω

_z²x₁+F_d(t) 

 

(1)
m₁ÿ

₁+c_1y{dot over (y)}₁+k_1yy₁=k_2y(y₂−

y₁)+m₁Ω

_z²y₁−

2m₁Ω

_z{dot over (x)}₁−

m₁{dot over (Ω

)}_zx₁  

 

(2)
m₂ÿ

₂+c_2y{dot over (y)}₂+k_2yy₂=k_2yy₁m+2Ω

_z²y₂−

2m₂Ω

_z{dot over (x)}₂−

m₂{dot over (Ω

)}_zx₂. 

 

(3)

where z is the z-axis angular rate, m_f is the mass of the decoupling frame, F_d(t) is the driving electrostatic force applied to the active mass at the driving frequency ω

_d and where the subscripts refer to the masses and position coordinates (x, y) and their derivatives of the first and second masses, m₁ and m₂, respectively.

19. The method of claim 11 where sensing with a 2-DOF sense-mode oscillator comprises operating the sense-mode oscillator with a generally flat region between two resonance peaks in the frequency response curves of the 2-DOF sense-mode oscillator to ensure that the drive-mode oscillation amplitude is insensitive to parameter fluctuations in the operation frequency band resulting in robustness to fluctuations in residual stresses, variations in elastic modulus from run to run in MEMs fabrication, and also insensitivity to thermal fluctuations throughout operation time.

20. The method of claim 11 where driving a 1-DOF driving a 1-DOF drive mode oscillator mode oscillator comprises operating driving the drive mode oscillator at resonance in a frequency band in a drive direction for optimal response, while operating the sense-mode oscillator with a generally flat region between two resonance peaks in the frequency response curves of the 2-DOF sense-mode oscillator within the same frequency band in which the drive oscillator is at resonance.