Standing wave drift of hemispherical resonator with quality factor non-uniformity under a ring electrode excitation

Hemispherical Resonator Gyroscope(HRG) is a classical high precision Coriolis Vibration Gyroscope(CVG), which performs attitude estimation of carrier by detecting the precession of standing wave of resonator, thus, the drift of standing wave of resonator has a great influence on the output accuracy of gyroscope, where the quality factor nonuniformity of resonator is one of main error sources. Ring electrode is a classical excitation structure of HRG because the standing wave can precess freely under its excitation, which makes the gyroscope have more accurate scale factor, larger measurement range and better dynamic characteristics. In this paper, the equations of motion of an ideal resonator excited by a ring electrode are derived by the elastic thin shell theory and Lagrange mechanical principle, then the corresponding equivalent mechanical model is established. According to the ‘‘average method", it can be seen that the ideal resonator excited by the ring electrode works in integral mode, and any position in the circumferential direction of resonator can be a working point, which means that the quality factor non-uniformity has a great effect on the drift of standing wave. Therefore, the equations of motion of resonator with quality factor nonuniformity under the ring electrode excitation are deduced by the equivalent mechanical model,and the drift model of standing wave is established by the ‘‘average method", it can be found that both the amplitude of quality factor non-uniformity and angle between the ‘‘inherent damping axis" and antinode axis of standing wave can affect the drift rate of standing wave.Moreover, the drift model indicates that if the input angular rate does not reach the threshold,the precession angular rate of standing wave will appear ‘‘self-locking" phenomenon, that is,the gyroscope will lose the integral effect.