Analysis Of Frequency-Solit Elimination And Whole-Angle Control Theory Analysis Of Hemispherical Resonator Gyroscope

The Hemispherical Resonator Gyro(HRG)is usually used as an inertial sensing component together with the accelerometer to measure and calculate the position,velocity,attitude and other navigation parameters of the moving carrier.It has a broad application prospect in the military and civil fields.How to correct the frequency difference caused by the quality defects and how to measure the precession Angle of the hemispherical shell by full Angle control in the presence of damping defects has always been the difficulty and focus of HRG production and research.Due to its axisymmetric structure the ideal hemispherical shell possesses degenerated pairs of flexibly bending resonant modes,the two modes of each degenerated pair have the same resonant frequency.The inevitable mass imperfection results in the frequency splitting of the two degenerated modes,which,in turn,seriously damages the measuring performance of the gyroscope.Based on Niordson’s thin shell theory and Rayleigh’s displacement model on the assumption that the middle surface of the shell is inextensible to derive the equations of motion with the amplitudes of the two degenerated modes as variables(generalized coordinates).Taking single point,two point and multiple point mass defects as examples,this paper proves that for the case of a single point-mass imperfection the obtained exact solution gives the explicit expressions of the two split natural frequencies and the corresponding eigenvectors,which represents the orientations of the two degenerated modes,one of the two eigenvectors is proved to pass through the mass-imperfection point and therefore the orientations of the resonant modes are no longer located arbitrarily as are the resonant modes of the ideal hemispherical shell.Finally,multiple-point imperfection is proved to be equivalent to a single-point imperfection,and the correctness of the theory is verified by simulation.The equations of motion are independent if the coordinate axes are rotated to coincide by the two eigenvectors,removing the mass of the shell by pulse-laser ablation does not change the directions of the eigenvectors if the etching point is located at the intersection between the eigenvector and the great circle of the hemispherical shell.The proper amount of the removed mass for eliminating the frequency split is obtained exactly,and in the meanwhile the cross-coupling of the three components of angular velocity in the equations of motion is also simultaneously to eliminate.Damping defects are unavoidable and the control force in generalized coordinates is converted to voltage.Then,the voltage is distributed through the proper configuration of electrode pairs,and the damping of the hemispherical shell is offset by the electrostatic force generated by the potential difference between the metal electrode plated on the spherical shell and the inner electrode of the driving seat,so as to obtain the HRG under the ideal condition and realize the full Angle control of the hemispherical shell to measure the precession Angle.