Abstract
Due to complicated processing technology, the mass distribution of a hemispherical resonator made of fused silica is not uniform, which can affect the azimuth of the standing wave of a resonator under the linear vibration excitation. Therefore, the analysis of standing wave evolution of a resonator with mass imperfection under linear vibration excitation is of significance for the improvement of the output accuracy of a gyroscope. In this paper, it is assumed that the resonator containing the first–third harmonics of mass imperfection is excited by horizontal and vertical linear vibration, respectively; then, the equations of motion of an imperfect resonator under the second-order vibration mode are established by the elastic thin shell theory and Lagrange mechanics principle. Through error mechanism analysis, it is found that, when the frequency of linear vibration is equal to the natural frequency of resonator, the standing wave is bound in the azimuth of different harmonics of mass imperfection with the change in vibration excitation direction. In other words, there are parasitic components in the azimuth of the standing wave of a resonator under linear vibration excitation, which can cause distortion of the output signal of a gyroscope. On the other hand, according to the standing wave binding phenomenon, the azimuths of the first–third harmonics of mass imperfection of a resonator can also be identified under linear vibration excitation, which can provide a theoretical method for the mass balance of an imperfect resonator.
Highlights
Hemispherical resonators composed of fused quartz were studied extensively by researchers all over the world, especially for their engineering applications, such as a hemispherical resonance gyroscope (HRG)
Wang et al [11] investigated a chemical etching procedure to remove the fourth harmonic of mass nonuniformity of a hemispherical resonator, which resulted in a frequency split, and the experimental results indicated that the frequency split of the resonator could be reduced to 0.05 Hz
The standing wave binding phenomenon of a hemispherical resonator containing the first–third harmonics of mass imperfection and the location identification method of mass imperfection are verified using a numerical simulation model of the vibration system, which is based on the equations of motion and radial vibration displacement of a resonator
Summary
Hemispherical resonators composed of fused quartz were studied extensively by researchers all over the world, especially for their engineering applications, such as a hemispherical resonance gyroscope (HRG). When is in aDue linear vibration environment, the trigonometric function system and the second-order vibration of a resonator, the first–third influence of the first–third harmonics of mass imperfection on the azimuth of a standing wave cannot harmonics of mass imperfection cannot appear in the equations of motion of an imperfect resonator. Based on the equations of motion, the binding wave, phenomenon an identification theislocation of On the the first–third harmonics of mass is of a method standing for wave analyzed.
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