# Vibrating structure gyroscope

A vibrating structure gyroscope is a type of gyroscope that functions much like the halteres of an insect. The underlying physical principle is that a vibrating object tends to continue vibrating in the same plane as its support rotates. In the engineering literature, this type of device is also known as a Coriolis vibratory gyro because as the plane of oscillation is rotated, the response detected by the transducer results from the Coriolis term in its equations of motion ("Coriolis force").

Vibrating structure gyroscopes are simpler and cheaper than conventional rotating gyroscopes of similar accuracy. Miniaturized devices using this principle are a relatively inexpensive type of attitude indicator.

## Theory of operation

Consider two proof masses vibrating in plane (as in the MEMS gyro) at frequency $\scriptstyle\omega_r$. Recall that the Coriolis effect induces an acceleration on the proof masses equal to $\scriptstyle a_c = -2(v\times\Omega)$, where $\scriptstyle v$ is a velocity and $\scriptstyle\Omega$ is an angular rate of rotation. The in-plane velocity of the proof masses is given by: $\scriptstyle X_{ip} \omega_r \cos(\omega_r t)$, if the in-plane position is given by $\scriptstyle X_{ip} \sin(\omega_r t)$. The out-of-plane motion $\scriptstyle y_{op}$, induced by rotation, is given by:

$y_{op} = \frac{F_c}{k_{op}} = \frac{2m\Omega X_{ip} \omega_r \cos(\omega_r t)}{k_{op}}$

where

$\scriptstyle m$ is a mass of the proof mass,
$\scriptstyle k_{op}$ is a spring constant in the out of plane direction,
$\scriptstyle\Omega$ is a magnitude of a rotation vector in the plane of and perpendicular to the driven proof mass motion.

In application to axi-symmetric thin-walled structures like beams and shells, the Coriolis forces cause a precession of vibration pattern about the axis of rotation. For such shells, it causes a slow precession of a standing wave about this axis with an angular rate which differs from input one. It is so-called "wave inertia effect" discovered in 1890 by British scientist George Hartley Bryan (1864–1928).[1]

If we consider a polarization of a shear (transverse) elastic wave propagating along an acoustic axis in a solid, a polarization rotation effect due to rotation of the body as a whole (so-called, "polarization inertia effect") can be observed too (it was noted by Ukrainian scientist Sergii A. Sarapuloff in the early 1980s,[2] as well as a corresponding modification of Green-Christoffel's tensors in Acoustics[3]).

## Implementations

### Piezoelectric gyroscope

A piezoelectric material can be induced to vibrate, and lateral motion due to centrifugal force can be measured to produce a signal related to the rate of rotation.[4]

### Wine glass resonator

Also called a hemispherical resonator gyro or HRG, a wine glass resonator makes use of a hemisphere driven to resonance, the nodal points of which are measured to detect rotation. There are two basic variants of the system, one based on a rate regime of operation and one based on an integrating regime of operation, usually in combination with a controlled parametric excitation. It is possible to use both regimes with the same hardware, which is a feature unique to this type of gyroscope. Engineers and researchers in several countries have been working on the technology.[5]

### Cylindrical Vibratory Gyroscope (CVG)

This type of gyroscope was developed by GE Marconi and GE Ferranti in 80s using alloys with attached piezoelectri elements and single-piece piezoceramic design, then, in 90s, CRGs with magneto-electric excitation and readout were produced by Inertial Engineering, Inc. (CA, USA), and piezo-ceramic variants by Watson Industries, and a recently-patented variant by Innalabs uses alloy-based cylindrical design resonator with excitation and pickoff at its perforated bottom. This breakthrough technologies allowed substantially increase product life of the gyroscopes (MTBF > 500,000 hours) and their shock resistance (>300g) that looks enough for "tactical" (mid-accuracy) applications. The resonator is operated on its second order resonant modes. Standing waves are therefore elliptical shape oscillations with four antinodes and four nodes located circumferentially along the rim, angle between two adjacent antinode – node being 45 deg. One of the elliptical resonant modes is excited to a prescribed amplitude. When the device rotates about its sensitive axis (along its inner stem), the resulting Coriolis forces acting on the resonator’s vibrating mass elements excite the second resonant mode. Angle between major axis of the two modes is 45 deg. A closed-loop drives the second resonant mode to zero and the force required to null this mode is proportional to the input rotation rate. Corresponding control loop system is called force-rebalanced mode. In order to provide forces and to sense induced motions, piezo-electric elements placed on the resonator are used. This electromechanical system is particularly effective and leads to low output noise and large dynamic range as required in case of demanding applications.

### Tuning fork gyroscope

This type of gyroscope uses a pair of test masses which are driven to resonance. Their displacement from the plane of oscillation is then measured to produce a signal related to the system's rate of rotation.

F.W. Meredith registered a patent for such a device in 1942 while working at the Royal Aircraft Establishment. Further development was carried out at the RAE in the late 1950s by G.H. Hunt and A.E.W. Hobbs, who demonstrated drift of less than 1 °/h (3.6×10−4 °/s).[6]

Modern variants of tactical gyros use doubled tuning forks such as those produced by Systron Donnel (CA, USA) and SAGEM Défence Securité / Safran Group (France).[7]

### Vibrating wheel gyroscope

A wheel is driven to rotate a fraction of a full turn about its axis. The tilt of the wheel is measured to produce a signal related to the rate of rotation.[8]

### MEMS gyroscope

Inexpensive vibrating structure gyroscopes manufactured with MEMS technology have become widely available. These are packaged similarly to other integrated circuits and may provide either analog or digital outputs. In many cases, a single part includes gyroscopic sensors for multiple axes. Some parts incorporate both a gyroscope and an accelerometer, in which case the output has six full degrees of freedom. Panasonic, Robert Bosch GmbH, InvenSense, Seiko Epson, STMicroelectronics, and Analog Devices are major manufacturers.

Internally, MEMS gyroscopes use lithographically constructed versions of one or more of the mechanisms outlined above (tuning forks, vibrating wheels, or resonant solids of various designs).[9]

## Applications

### Spacecraft orientation

The oscillation can also be induced and controlled in the vibrating structure gyroscope for the positioning of spacecraft such as Cassini-Huygens. These small Hemispherical Resonator Gyroscopes made of quartz glass operate in vacuum. There are also prototypes of elastically-decoupled Cylindrical Resonator Gyroscopes (CRG)[10][11] made from high-purity single-crystalline sapphire. They provide accurate 3 axis positioning of the spacecraft and are highly reliable over the years as they have no moving parts.

### Automotive

Automotive yaw sensors can be built around vibrating structure gyroscopes. These are used to detect error states in yaw compared to a predicted response when connected as an input to electronic stability control systems in conjunction with a steering wheel sensor.[12] Advanced systems could conceivably offer rollover detection based on a second VSG but it is cheaper to add longitudinal and vertical accelerometers to the existing lateral one to this end.

### Entertainment

The Nintendo Game Boy Advance game WarioWare: Twisted! uses a piezoelectric gyroscope to detect rotational movement. The Sony SIXAXIS PS3 controller uses a single MEMS gyroscope to measure the sixth axis (yaw). The Nintendo Wii MotionPlus accessory uses multi-axis MEMS gyroscopes provided by InvenSense to augment the motion sensing capabilities of the Wii Remote.[13] The iPhone, iPad, iPod Touch, Nintendo 3DS, Nexus S and HTC Titan also feature gyroscopes.

### Photography

Many Image stabilization systems on video and still cameras employ vibrating structure gyroscopes.

### Hobbies

Vibrating structure gyroscopes are commonly used in radio-controlled helicopters to help control the helicopter's tail rotor and in radio-controlled airplanes to help keep the attitude steady during flight.

### Industrial Robotics

Epson Robots uses a Quartz MEMS Gyroscope called QMEMS to detect and control vibrations on their robots, in order to attain high precision in positioning the Robot end effector in high speed and fast deceleration motion.[14]

### Other

The Segway Human Transporter employs a vibrating structure gyroscope made by Silicon Sensing Systems to maintain stability of the operator platform.[15]

## References

1. ^ Bryan G.H. On the Beats in the Vibrations of a Revolving Cylinder or Bell //Proc. of Cambridge Phil. Soc. 1890, Nov. 24. Vol.VII. Pt.III. - P.101-111.
2. ^ Sarapuloff S.A. General Solution of Problem of Elasticity Theory of a Rotated Medium //Mechanics of Gyroscopic Systems. Issue 8. – Kyiv. 1989. – P.57-61. (In Russian.)
3. ^ Sarapuloff S.A., and Ulitko I.A. Rotation Influence upon Bulk Waves in an Elastic Medium and their Usage in Solid-State Gyroscopy // VIII International Conference on Integrated Navigation Systems. – St. Petersburg. St.-Petersburg. The State Research Center of Russia - Central Scientific & Research Institute "ElektroPribor". RF. 2001. – P.127-129.
4. ^ "NEC TOKIN's ceramic piezo gyros". Retrieved 2009-05-28.
5. ^ Sarapuloff S.A. 15 Years of Solid-State Gyrodynamics Development in the USSR and Ukraine: Results and Perspectives of Applied Theory //Proc. of the National Technical Meeting of Institute of Navigation (Santa Monica, Calif., USA. January 14–16, 1997). – P.151-164.
6. ^ Collinson, R.P.G. Introduction to Avionics, Second edition, Kluwer Academic Publishers: Netherlands, 2003, p.235
7. ^ QuapasonTM
8. ^ "Inertial Sensors - Angular Rate Sensors". Retrieved 2009-05-28.
9. ^ Bernstein, Jonathan. "An Overview of MEMS Inertial Sensing Technology", Sensors Weekly, February 1, 2003.
10. ^ Sarapuloff S.A. High-Q Sapphire Resonator of Solid-State Gyroscope CRG-1 http://www.stcu.int/documents/reports/distribution/tpf/MATERIALS/Sapphire_Gyro_Sarapuloff_ATSU.pdf
11. ^ Sarapuloff S. A., Lytvynov L.A., et al. Particularities of Designs and Fabrication Technology of High-Q Sapphire Resonators of CRG-1 Type Solid-State Gyroscopes //XIVth International Conference on Integrated Navigation Systems (28–30 May 2007. St.-Petersburg, RF.). – St.-Petersburg. The State Research Center of Russia - Central Scientific & Research Institute "ElektroPribor". RF. 2007. – P.47-48.
12. ^ "The Falling Box (Video)". Retrieved 2010-07-01.
13. ^ "InvenSense IDG-600 Motion Sensing Solution Showcased In Nintendo's New Wii MotionPlus Accessory" (Press release). InvenSense. 15 July 2008. Retrieved 2009-05-28.
14. ^ "Epson Quartz Crystal Device - About QMEMS". Retrieved 2013-03-12.
15. ^ Steven Nasiri. "A Critical Review of MEMS Gyroscopes Technology and Commercialization Status". Retrieved 2010-07-01.