A variable-capacitance micromotor where the rotor is supported electrostatically in five degrees of freedom was designed, fabricated and tested in order to study the behavior of this electrostatic motor. The micromachined device is based on a glass/silicon/glass stack bonding structure, fabricated by bulk micromachining and initially operated in atmospheric environment. The analytical torque model is obtained by calculating the capacitances between different stator electrodes and the rotor. Capacitance values in the order of 10 −13 pF and torque values in the order of 10 −10 N m have been calculated from the motor geometry and attainable drive voltage. A dynamic model of the motor is proposed by further estimating the air-film damping effect in an effort to explain the experimental rotation measurements. Experimental results of starting voltage, continuous operation, switching response and electric bearing of the micromotor are presented and discussed. Preliminary measurements indicate that a rotor rotating speed of 73.3 r min −1 can be achieved at a drive voltage of 28.3 V, equivalent to a theoretical motive torque of 517 pN m. Starting voltage results obtained from experimental measurement are in agreement with the developed dynamic model.

An electric bearing used to support a micromachined rotor of variable-capacitance motors was designed and tested in order to study the characteristics of this frictionless bearing. Electrostatic suspension of a ring-shaped rotor in five degrees of freedom is required to eliminate the mechanical bearing and thus the friction and wear between the rotor and the substrate. Bulk microfabrication-based glass/silicon/glass bonding is chosen for this device, allowing the fabrication of large area sense capacitors and rotor, which make the device potentially suitable for the development of an electrostatically suspended micromachined gyroscope. The device and its basic operating principle are described, as well as the dynamics of the rotor and basic design considerations of the electric bearing system. A theoretical relationship to relate the characteristics of a classical lag–lead compensator to the stiffness properties of the electric bearing is developed to explain the experimental bearing measurements. The experimental results of closed-loop frequency response, suspension stiffness and drive voltage effects are presented and discussed for the bearing operated initially in the atmospheric environment. The performance of a tri-axial electrostatic accelerometer has also been experimentally investigated on the prototype of the electric bearing system.

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The gravity disturbance vector is one of the major error sources in high-precision and long-term inertial navigation applications. Specific to the inertial navigation systems (INSs) with high-order horizontal damping networks, analyses of the error propagation show that the gravity-induced errors exist almost exclusively in the horizontal channels and are mostly caused by deflections of the vertical (DOV). Low-frequency components of the DOV propagate into the latitude and longitude errors at a ratio of 1:1 and time-varying fluctuations in the DOV excite Schuler oscillation. This paper presents two gravity compensation methods using the Earth Gravitational Model 2008 (EGM2008), namely, interpolation from the off-line database and computing gravity vectors directly using the spherical harmonic model. Particular attention is given to the error contribution of the gravity update interval and computing time delay. It is recommended for the marine navigation that a gravity vector should be calculated within 1 s and updated every 100 s at most. To meet this demand, the time duration of calculating the current gravity vector using EGM2008 has been reduced to less than 1 s by optimizing the calculation procedure. A few off-line experiments were conducted using the data of a shipborne INS collected during an actual sea test. With the aid of EGM2008, most of the low-frequency components of the position errors caused by the gravity disturbance vector have been removed and the Schuler oscillation has been attenuated effectively. In the rugged terrain, the horizontal position error could be reduced at best 48.85% of its regional maximum. The experimental results match with the theoretical analysis and indicate that EGM2008 is suitable for gravity compensation of the high-precision and long-term INSs.