The properties of small size, low noise, high performance and no wear-out have made the hemispherical resonator gyroscope a good choice for high-value space missions. To enhance the precision of the hemispherical resonator gyroscope for use in tasks with large angular velocities and angular accelerations, this paper investigates the standing wave precession of a non-ideal hemispherical resonator under nonlinear high-intensity dynamic conditions. Based on the thin shell theory of elasticity, a dynamic model of a hemispherical resonator is established by using Lagrange\'s second kind equation. Then, the dynamic model is equivalently transformed into a simple harmonic vibration model of a point mass in two-dimensional space, which is analyzed using a method of averaging that separates the slow variables from the fast variables. The results reveal that taking the nonlinear terms about the square of the angular velocity and the angular acceleration in the dynamic equation into account can weaken the influence of the 4th harmonic component of a mass defect on standing wave drift, and the extent of this weakening effect varies with the dimensions of the mass defects, which is very important for steering the development of the high-precision hemispherical resonator gyroscope.

The MEMS gyroscope is one of the basic units of inertial navigation, whose performance and accuracy is noteworthy. Because of the limitations of processing technology and other factors, the relative manufacturing error of MEMS gyroscopes is usually large. Errors directly lead to a frequency mismatch of resonant structures and consequently restrict the performance improvement of the gyroscope. This study proposes a mechanical trimming technique combining the addition and removal of gold in a ring MEMS gyroscope. Firstly, the analysis of the gyroscope dynamics and error model and trimming theory provides theoretical guidance for the trimming process. Secondly, the method of adjusting the mass is investigated, and the ablation threshold of femtosecond laser parameters on gold is analyzed, which provides the process with parameters for the trimming experiment. Finally, the frequency trimming process is conducted in three steps, including the addition of gold spheres and the removal of gold spheres and gold film, which are applicable to the trimming process at different rates of frequency split. The results shows that the proposed method can reduce the frequency split of the gyroscope from 4.36 to 0.017 Hz.

As an inertial sensor with excellent performance, the hemispherical resonator gyro is widely used in aerospace, weapon navigation and other fields due to its advantages of high precision, high reliability, and long life. Due to the uneven distributions of material properties and mass of the resonator in the circumferential direction, the frequencies of the two 4-antinodes vibration modes (operational mode) of resonator in different directions are different, which is called frequency splitting. Frequency splitting is the main error source affecting the accuracy of the hemispherical resonator gyro and must be suppressed. The frequency splitting is related to the structure of the resonator. For the planar-electrode-type hemispherical resonator gyro, in order to suppress the frequency splitting from the structure, improve the accuracy of the hemispherical resonator gyro, and determine and optimize the equivalent bottom angle parameters of the hemispherical resonator, this paper starts from the thin shell theory, and the 4-antinodes vibration mode and waveform precession model of the hemispherical resonator are researched. The effect of the equivalent bottom angle on the 4-antinodes vibration mode frequency value under different boundary conditions is theoretically analyzed and simulated. The simulation results show that the equivalent bottom angle affects the 4-antinodes vibration mode of the hemispherical resonator through radial constraints. The hemispherical resonator with mid-surface radius R=15 mm and shell thickness h=1 mm is the optimization object, and the stem diameter D and fillet radius R1 are experimental factors, with the 4-antinodes vibration mode frequency value and mass sensitivity factor as the response indexes. The central composite design is carried out to optimize the equivalent bottom angle parameters. The optimized structural parameters are: stem diameter D=7 mm, fillet radii R1=1 mm, R2=0.8 mm. The simulation results show that the 4-antinodes vibration mode frequency value is 5441.761 Hz, and the mass sensitivity factor is 3.91 Hz/mg, which meets the working and excitation requirements wonderfully. This research will provide guidance and reference for improving the accuracy of the hemispherical resonator gyro.

In practical engineering, the frequency splitting of Hemispherical Resonator Gyro (HRG) caused by uneven mass distribution seriously affects the precision of HRG. So, the inherent frequency is an important parameter of micro-Hemispherical Resonator Gyro (m-HRG). In the processing of hemispherical resonator, there are some morphological errors and internal defects in the hemispherical resonator, which affect the inherent frequency and the working mode of m-HRG, and reduce the precision and performance of m-HRG. In order to improve the precision and performance of m-HRG, the partial differential equation of the hemispherical resonator is solved, and the three-dimensional model using ANSYS software accurately reflected the actual shape is established in this paper. Then, the mode of hemispherical resonator in ideal state and uneven mass distribution state are simulated and analyzed. The frequency splitting mechanism of the hemispherical resonator is determined by calculation and demonstration, and the frequency splitting of the hemispherical resonator is suppressed by partial mass elimination. The results show that the absolute balance of energy can ensure the high-quality factor and the minimum frequency splitting of the hemispherical resonator. Therefore, during the processing of hemispherical resonator, the balance of mass should be achieved as much as possible to avoid various surface damage, internal defects and uneven mass distribution to guarantee the high-quality factor Q and minimum frequency splitting of hemispherical resonator.

Inductive powering for implanted medical devices, such as implantable biosensors, is a safe and effective technique that allows power to be delivered to implants wirelessly, avoiding the use of transcutaneous wires or implanted batteries. Wireless powering is very sensitive to a number of link parameters, including coil distance, alignment, shape, and load conditions. The optimum drive frequency of an inductive link varies depending on the coil spacing and load. This paper presents an optimum frequency tracking (OFT) method, in which an inductive power link is driven at a frequency that is maintained at an optimum value to ensure that the link is working at resonance, and the output voltage is maximised. The method is shown to provide significant improvements in maintained secondary voltage and system efficiency for a range of loads when the link is overcoupled. The OFT method does not require the use of variable capacitors or inductors. When tested at frequencies around a nominal frequency of 5 MHz, the OFT method provides up to a twofold efficiency improvement compared to a fixed frequency drive. The system can be readily interfaced with passive implants or implantable biosensors, and lends itself to interfacing with designs such as distributed implanted sensor networks, where each implant is operating at a different frequency.