Balancing of hemispherical resonator gyros by chemical etching

Decreasing Frequency Splits of Hemispherical Resonators by Chemical Etching

“…Basarab et al [ 29 ] put up the chemical etching method. In his research, the resonator’s mass distribution M ( φ ) can be expressed in Fourier series with respect to the circumferential angle φ : where M 0 is the uniformly distributed mass in the circumferential angle; k is the harmonic number of the Fourier series; M k is the k -th harmonic of the resonator mass, while φ k is the corresponding orientation of M k with respect to the defined zero direction.…”

“…This paper mainly focuses on reducing M 4 , which is the cause of the frequency split of the resonator and the main sources of bias and random errors in HRGs. According to Basarab et al [ 29 ], the fourth harmonic error of mass M 4 can be decreased by chemical etching at four antinodes along the lower frequency axis of n = 2 resonant mode, as is shown in Figure 2 a. The spherical coordinate ( r , θ , φ ) is used to describe the resonator.…”

“…However, he also pointed out that this method consumed a large amount of time and energy, and was only able to adjust the frequency split within a small range. The conception and procedure of tuning resonators by chemical etching was first proposed by Basarab et al [ 29 ]. However, until now there have been no reports of experimental results on reducing frequency splits of hemispherical resonators by chemical etching, because some technical difficulties still exist in conducting chemical etching experiments, such as temperature stability, small changes of chemical etching solution concentration, position accuracy of the four antinodes, the precise control of the etching height and inclined angle, etc.…”

“…In this paper, decreasing frequency splits of hemispherical resonators by chemical etching is realized. Section 2 gives theoretical analyses on the relationship between mass errors and frequency splits of hemispherical resonators, and briefly presents the theoretical aspects of chemical balancing method according to Basarab et al [ 29 ]. Section 3 shows the simulation results on an imperfect hemispherical resonator model obtained by the COMSOL Multiphysics.…”

Standing Wave Binding of Hemispherical Resonator Containing First–Third Harmonics of Mass Imperfection under Linear Vibration Excitation

“…Choi and Kim [ 9 ] pointed out that the effect of point masses on a hemispherical resonator can be expressed by functions for the frequency split and shift angle of the vibration mode, while the dynamic model of an imperfect resonator with multiple point masses can be represented by the model of an imperfect resonator with an equivalent single-point mass. Basarab et al [ 10 ] proposed a chemical etching method to remove the first–fourth harmonics of mass nonuniformity of an imperfect resonator and gave the rotation angle about the axis of symmetry of resonator, the depth and inclination of resonator immersion into a chemical bath, and the duration time of chemical etching of resonator. 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.…”