Motion equations of hemispherical resonator and analysis of frequency split caused by slight mass non-uniformity

The mass non-uniformity of hemispherical resonator is one of reasons for frequency split,and frequency split can cause gyroscope to drift.Therefore,it is of great significance to analyze the relationship between mass non-uniformity and frequency split,which can provide a theoretical basis for mass balance of imperfect resonator.The starting point of error mechanism analysis for gyroscope is the motion equations of resonator.Firstly,based on the Kirchhoff-Love hypothesis in the elastic thin shell theory,the geometric deformation equations of resonator are deduced.Secondly,the deformation energy equation of resonator is derived according to the vibration mode and relationship between the stress and strain of hemispherical thin shell.Thirdly,the kinetic energy equation of resonator is deduced by the Coriolis theorem.Finally,the motion equations of resonator are established by the Lagrange mechanics principle.The theoretical values of precession factor and natural frequency are calculated by the motion equations,which are substantially consistent with the ones by the finite element method and practical measurement,the errors are within a reasonable range.Simultaneously,the varying trend of natural frequency with respect to the geometrical and physical parameters of resonator by the motion equations is consistent with that by the finite element analysis.The above conclusions prove the correctness and rationality of motion equations.Similarly,the motion equations of resonator with mass non-uniformity are established by the same modeling method in case of ignoring the input angular rate and damping,and the state equations with respect to the velocity and displacement of vibration system are derived,then twonatural frequencies are solved by the characteristic equation.It is concluded that one of reasons for frequency split is the 4 th harmonic of mass non-uniformity,and thus much attention should be paid to minimizing the 4 th harmonic of mass non-uniformity in the course of mass balancing for imperfect resonator.

Precision Balance Method for Cupped Wave Gyro Based on Cup-bottom Trimming

The mechanical balance process is the key process to eliminate the quadrature error and improve the performance of the cupped wave gyro. The conventional mechanical balance method for cupped wave gyro based on cup-wall trimming requires high control accuracy of trimming quantity, which increases the production cost and decreases the fabrication efficiency in large extent. However, it is hard to reach the high balance accuracy with the natural frequency split of mHz grade by using the conventional method. In this paper, the lumped mass dynamic model of the cupped wave gyro is built by discretization method, and the effects of different position trimming on the natural frequency are analyzed. It is pointed out that trimming off a tiny quantity of material from cup-wall causes large variation of the natural frequency is the main reason for the low accuracy of the conventional mechanical balance method. Then, a precision balance method for cupped wave gyro based on cup-bottom trimming is presented and the entire procedures of this method are given. The static balance process and dynamic balance process of the precision balance method are simulated by the finite element software. The simulation result shows that the precision balance method based on cup-bottom trimming brings less additional natural frequency split in the static balance process, minimizes the natural frequency split to mHz grade and rectify the angle of mode offset to 0.1° grade in the dynamic balance process, furthermore, the method decreases the requirement for control accuracy of trimming quantity evidently. The research work provides references for structure optimization design and balance process plan of the cupped wave gyro.

Intensity modulation characters of orthogonally polarized HeNe lasers with different optical feedback level

This paper demonstrates the intensity modulation characters of orthogonally polarized HeNe lasers with different optical feedback level generated by the variable reflectivity of external reflector. The modulation depths of the orthogonally polarized frequencies are increased when the optical feedback level becomes strong. It also observes that the modulation amplitudes are different for different external cavity length. Based on the vectorial extension of Lamb＇s semi-classical theory, it finds that the calculations are consistent with the experimental results.

Design and Analysis of a Wireless Power Transmission System with Magnetic Coupling Resonance in the Weak-coupling Region

The magnetically coupled resonant wireless power transfer(MCR-WPT)system for implantable medical devices has gradually become one of the research hotspots.The transmission characteristics of the system in weak-coupling regions are of research significance.The mathematical model of the system's transmission characteristics is established by equivalent circuit theory.Several key factors that affect the transmission characteristics of the system are obtained,to include the self-inductance of the coil,the mutual inductance between the coils,and the load resistance.A magnetically coupled resonant wireless power transfer system is designed.A method of coil design is proposed.The transmission efficiency of the system in the weak-coupling region is improved by optimizing the design of the coil.Simulation and experimental results exhibited good consistency.The results show that the transmission performance of the system in the weak-coupling area is improved.This work provides guidance and practical significance for the research of the MCR-WPT system with implantable medical equipment.