Reviews

An original design of vibrating gyro is the vibrating string gyro, which was described by Quick [19] in 1964. The string vibrates in a plane and the plane of vibration tends to stay fixed in space without extra applied. With the string lying along the z-axis and vibrating in xz-plane, a pickoff positioned along y-axis is used to measure the induced vibration.

The Coriolis acceleration induced by the rotation causes the string vibration to be coupled into the y-axis, and the amplitude is positive proportional to the rotation rate. In order to avoid the environment noise, the implying frequency is usually above 10kHz. Anisoelasticity and geometric asymmetry cause large drift errors; bias torques arisen form

asymmetry damping and end attachment. There is no successful marketed vibrating string gyro.

A similar design to the vibrating string gyro is the vibrating beam gyro. Due to square or rectangular cross section, the beam vibrates with its two identical bending modes as shown in Fig. 2.1[20]. The beam, which is lying along with the z-axis, vibrates in the xz-plane of the primary mode, and the Coriolis force induced vibration on the secondary mode. Typically, the primary mode amplitude is driven to be fixed. The output amplitude of secondary mode is proportional to the rotation rate.

Beam actuation and detection usually uses piezo-electric transducer;

capacitively actuation and detection are also available. There are other kinds of cross section such as triangular and etc [21], which still works with two identical modes. The problem of this kind of design is the large temperature drift. It usually comes from the piezo-electric material and their cement layers. The other one is mounting problem. Moreover, the flexibility along the beam axis causes the device to be sensitive to the environmental vibration.

To solve the mounting problem, the structure is transformed into the symmetry design as shown in Fig. 2.2[22,23]. The principle for the tuning fork likes that for the vibrating beam gyroscope. For balanced system made from two bars oscillating anti-phase, it has no net torque at the junction and can obtain stable mounting condition. It leads to low energy loss and obtain higher Q factor. The symmetry design usually forms as tuning fork or trident. The balance structure is less sensitive to the linear acceleration with respect to the vibrating beam gyro. But it has large zero bias error for its open loop operation. Besides, the misalignment for individual tines that makes a vibration torque also leads to the bias error.

The bending and torsional elastic moduli of the metal material vary dramatically over temperature; the crystalline quartz or silicon made

structure allows the device overcome this problem. It also makes them small, inexpensive, and requiring few powers [24].

A further modification form the tuning fork gyro is the double fork gyro or the dual accelerometer gyro as shown in Fig. 2.3[25]. Similar to the tuning fork, the opposite proof masses vibrate in anti-phase on xz-plane and the Coriolis acceleration induced vibration appears in y-axis.

The output amplitude of out plane vibration in y-axis is proportional to the rotation rate. The seismic masses are supported by beam-type suspension like accelerometer. The structure is usually driven electro-statically, piezoelectrically or electromagnetically. The out plane vibration is detected capacitively for the large area form the roof masses.

Because of the similarity to the tuning fork gyroscope, they share many of the same advantages and disadvantages.

There are several types of micro-machined vibrating gyroscope that are conceptually similar to the conventional gyroscope. The first one is double gimbals vibrating gyroscope [26]. This device is fabricated with bulk micromachining to form the double gimbals as shown in Fig. 2.4.

The outer gimbals is electro-statically driven at constant amplitude using the drive electrodes, and the inner gimbals synchronously vibrates along the stiff axis of the inner gimbals. When exposed to a rotation normal to the plane of the device, Coriolis force causes the inner gimbals to oscillate about its weak axis with a frequency equal to the drive frequency.

The vibration of inner gimbals is detected by using the variable capacitance. Therefore, maximum resolution is obtained when the outer gimbals is driven at the resonant frequency of the inner gimbals, causing the signal to be amplified by the mechanical quality factor of the sense resonance mode of the structure. The out plane motion is strongly damped due to squeeze film effect and the Q factor decreases. Moreover,

the capacitively driving and detection may result in nonlinear motion form the gimbals frames.

Those above reported in the literatures are bulk-micromachined silicon-on-glass vibrating beams [27], vibrating membranes [28], and double-gimbaled structures [29] as demonstrated. Since the Young’s modulus of single-crystal silicon changes with crystallographic orientation, symmetric vibrating structures made of single-crystal silicon may show excessive mechanical coupling between drive and sense modes due to the anisotropy, resulting in a large error with unacceptable drift characteristics [27]. Surface-micromachined vibratory gyroscopes have also been demonstrated. Some have been integrated with the readout electronic circuitry on a single silicon chip, reducing parasitic capacitances and hence increasing the signal-to-noise ratio. In addition, the vibrating structure is made of polysilicon, which has a high quality factor and an orientation-independent Young’s modulus.

Single-axis polysilicon surface-micromachined vibrating gyroscopes have been realized at Berkeley [30,31] and Samsung [32–34]. Figure 2.6 depicts the schematic diagram for the z-axis vibrating gyroscope. The structure is compliant in two identical directions and driven to vibrate in sensing mode. When exposed to a rotation normal to the plane of the device, Coriolis force causes the vibration in sensing mode that is proportional to the rotation rate. Berkeley’s z–axis vibratory rate gyroscope resembles a vibrating beam design and consists of an oscillating mass that is electrostatically driven into resonance using comb drives. Any detection that resulted from Coriolis acceleration is detected differentially in the sense mode using comb fingers. This device was integrated with a trans-resistance amplifier on a single die using the Analog Devices BiMEMS process. The remaining control and signal-processing electronics were implemented off-chip. Samsung has also

reported a very similar surface-micromachined z-axis device, shown in Fig. 2.5, with polysilicon resonating mass supported by four fishhook-shaped springs [33]. Hybrid attachment of the sensor chip to a CMOS application-specific integrated circuit (ASIC) chip used for readout and closed-loop operation of the device was done in a vacuum-packaged ceramic case.

The x-axis vibrating gyroscope, which is similar to z-axis vibrating gyroscope, has been demonstrated and reported at HSG-IMIT. It is a surface-micromachined precision x-axis vibratory gyroscope (MARS-RR) with a very small zero-rate output achieved by mechanical decoupling of the drive and sense vibration modes [35]. Figure 2.7 depicts the schematic diagram for the x-axis vibrating gyro. The structure is driven electro-statically with comb fingers to vibrate in rotary mode. When exposed to the rotation about x-axis, Coriolis force tilts the structure to vibrate along y-axis and the rotation is detected. This device, shown in Fig. 2.8, was fabricated through the standard Bosch foundry process featuring a 10-µm-thick structural polysilicon layer in addition to the buried polysilicon layer, which defines the sense electrodes.

The dual-axis vibrating gyroscope is reported at Berkeley [36], that a surface-micromachined dual-axis gyroscope based on the rotational resonance of a 2-µm-thick polysilicon rotor disk, as shown in Fig. 2.10 and the schematic diagram in Fig. 2.9. Since the disk is symmetric in two orthogonal axes, the sensor can sense rotation equally about these two axes. Also reported in this literature is a cross-shaped nickel-on-glass two-axis micromachined gyroscope [37].

The vibrating ring gyroscope is one subject of this proposal. General Motors and the University of Michigan have developed a vibrating ring gyroscope [38] as shown in Fig. 2.11. This device consists of a ring, semicircular support springs, and drive, sense, and balance electrodes,

which are located around the structure. Symmetry considerations require at least eight springs to result in a balanced device with two identical flexural modes that have equal natural frequencies [39]. The first micromachined version of the vibrating ring gyroscope was fabricated by electroforming nickel into a thick polyimide mold on a silicon substrate in a post circuit process [38-40]. To improve performance further, a new polysilicon ring gyroscope (PRG) [41] was recently fabricated through a single-wafer, all-silicon, high-aspect-ratio polysilicon trench-refill technology [42] at the University of Michigan. A similar design is developed by British Aerospace Systems & Equipment(BASE) as shown in Fig. 2.12 [43-45].

The vibrating ring structure has some important features compared to other types of vibratory gyroscopes. First, the symmetry of the structure makes it less sensitive to spurious vibrations. Only when the ring has mass or stiffness asymmetries induce a spurious response from the environmental vibrations. Second, two identical flexural modes of the structure with nominally equal resonant frequencies are used to sense rotation, and the detected signal is amplified by the quality factor of the structure, that resulting in higher sensitivity. Third, the vibrating ring is less temperature sensitive since the vibration modes are affected equally by temperature. Last, electronic balancing of the structure is possible.

Any frequency mismatch due to mass or stiffness asymmetry that occurs during the fabrication process can be electronically compensated by use of the balancing electrodes that are located around the structure.