A vibrating structure gyroscope (VSG), defined by the IEEE as a Coriolis vibratory gyroscope (CVG), is a gyroscope that uses a vibrating (as opposed to rotating) structure as its orientation reference. A VSG functions much like the halteres of flies (insects in the order Diptera). The underlying physical principle is that a vibrating object tends to continue vibrating in the same plane even if its support rotates. The Coriolis effect causes the object to exert a force on its support, and by measuring this force the rate of rotation can be determined. Vibrating structure gyroscopes are simpler and cheaper than conventional rotating gyroscopes of similar accuracy. Inexpensive VSGs manufactured with micro-electromechanical systems (MEMS) technology are widely used in smartphones, gaming devices, cameras and many other applications.
Theory of operation Consider two proof masses vibrating in plane (as in a MEMS gyro) at frequency ω r {\displaystyle \omega _{r}} . The Coriolis effect induces an acceleration on the proof masses equal to a c = 2 ( Ω × v ) {\displaystyle a_{\mathrm {c} }=2(\Omega \times v)} , where v {\displaystyle v} is the velocity and Ω {\displaystyle \Omega } is the angular rate of rotation. The in-plane velocity of the proof masses is given by v = x ip ω r cos ( ω r t ) {\displaystyle v=x_{\text{ip}}\omega _{r}\cos(\omega _{r}t)} , if the in-plane position at time t {\displaystyle t} is given by x ip = sin ( ω r t ) {\displaystyle x_{\text{ip}}=\sin(\omega _{r}t)} . The out-of-plane motion y op {\displaystyle y_{\text{op}}} , induced by rotation, is given by:
y op = F c k op = 1 k op 2 m Ω x ip ω r cos ( ω r t ) {\displaystyle y_{\text{op}}={\frac {F_{c}}{k_{\text{op}}}}={\frac {1}{k_{\text{op}}}}2m\Omega x_{\text{ip}}\omega _{r}\cos(\omega _{r}t)}
where
F c {\displaystyle F_{c}} is the Coriolis force,
k op {\displaystyle k_{\text{op}}} is the spring constant in the out-of-plane direction,
m {\displaystyle m} is the mass of a proof mass, and
Ω {\displaystyle \Omega } is the magnitude of a rotation vector in the plane of and perpendicular to the driven proof mass motion. By measuring y op {\displaystyle y_{\text{op}}} , the rate of rotation Ω {\displaystyle \Omega } can thus be determined.
Implementations
Cylindrical resonator gyroscope (CRG)
This type of gyroscope was developed by GEC-Marconi and Ferranti in the 1980s using metal alloys with attached piezoelectric elements and a single-piece piezoceramic design. In the 1990s, CRGs with magneto-electric excitation and readout were produced by American-based Inertial Engineering, Inc. in California, and piezoceramic variants by Watson Industries. A recently-patented variant by Innalabs uses a cylindrical resonator design made from Elinvar alloy with piezoceramic elements for excitation and pickoff at its bottom. This technology gave a substantially increased product life (MTBF > 500,000 hours); its shock resistance (>300g) should qualify it for tactical (mid-accuracy) applications. The resonator is operated in its second-order resonant mode. The Q factor is usually about 20,000; that predetermines its noise and angular random walks. Standing waves are elliptically-shaped oscillations with four antinodes and four nodes located circumferentially along the rim. The angle between two adjacent antinode–node pairs is 45 degrees. 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. The angle between major axes of the two modes is also 45 degrees. 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. This control loop is designated the force-rebalanced mode. Piezoelectric elements on the resonator produce forces and sense induced motions. This electromechanical system provides the low output noise and large dynamic range that demanding applications require, but suffers from intense acoustic noises and high overloads.
Piezoelectric gyroscopes A piezoelectric material can be induced to vibrate, and lateral motion due to Coriolis force can be measured to produce a signal related to the rate of rotation.
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