On Frequency Split Analysis For Hemispherical Resonator And Error Restraint Method For The Hemispherical Resonator Gyroscope

HRG has a promising application in the inertial navigation of long-life spacecraft due to its advantages, such as longevity, high precision, high reliability, low noise, low power and free of nuclear radiation. So it is meaningful to analyze the HRG’s error and to explore the methods of raising HRG’s accuracy under current technical conditions. In this paper, the error analysis for HRG is based on the resonator with defects in the circular direction. The dynamics equations of resonator with error are established, then the relationship between the frequency split and the density nonuniformity error is deeply analyzed. The error restraint method is researched from the following three aspects: control different parts of the resonator’s vibration displacement, adjust the position of the excitation electrode relative to the resonator, balance the resonator’s nonuniformity error. Moreover, the methods of angular rate calculation and error compensation are deeply researched, which give the guidance for raising HRG’s accuracy. The specific tasks of this dissertation are as follows:The dynamics equations of resonator are established. At first, the inertia forces of an arbitrary point in the hemispherical thin shell are deduced, then the force equilibrium equations of the thin shell element which is sectioned from the medium plane are gained. On the basis of it, the dynamics equations of the resonator are established by way of Bubonov–Galerkin method, and the accurate expression of the angular precession factor is deduced. All those lay a foundation for further analyzing the error mechanism and error restraint method of HRG.Analysis on the frequency split and the error analysis for HRG under open-loop control mode are achieved. Firstly, the dynamics equations of resonator with density distributed nonuniformity are established. According to the dynamics equations, the expressions of natural frequency of hemispherical resonator are solved. The frequency split mechanism caused by density distribution nonuniformity error of the hemispherical resonator is achieved. Secondly, under open-loop mode, the steady-state solutions of the antinode’s azimuth and the expression of the angular rate calculation are given. By simulation calculating, the tolerance towards the fourth harmonic of density nonuniformity is determined to guarantee the accuracy of HRG under open-loop mode.Under force-rebalance mode, the method that different parts of the resonator’s vibration displacement are controlled by different modes to restrain density nonuniformity error is researched, and the method of angular rate calculation is given. Firstly, the expression of the angular rate calculation is given under general control. By simulation calculating, the influence of the fourth harmonic of density nonuniformity on angular rate calculation is analyzed. Secondly, the expression of the angular rate calculation is given under quadrature control. The quasi quadrature control is put forward to solve the problems of open-loop control, general control and quadrature control. The expression of the angular rate calculation is deduced under quasi quadrature control. By simulation and analyzing, the quasi quadrature control has more advantages in the aspects of error restraint and practical application. In addition, under the quasi quadrature control, the expression of the azimuth of radial vibration antinode is deduced, and the steady state model of amplitude-control is established.The methods of enhancing HRG’s accuracy and balancing the density nonuniformity error are put forward. At first, according to the characteristics of the inherent toughness axis, the azimuth of inherent toughness axis is given. Then the methods of raising HRG’s accuracy are given by adjusting the angle between the excitation electrode and the azimuth of inherent toughness axis under open-loop control and quasi quadrature control modes, and the method’s effectiveness is proved by simulating. To counteract density nonuniformity error and raise the accuracy of HRG, the dynamics equations of resonator with the 1st~4th harmonic of density nonuniformity are established. The identification model of density nonuniformity error is established through the dynamics equations, and then the amplitude and phase of each density nonuniformity harmonic are identified. After that, the process of balancing the density nonuniformity error by removing the micro mass out of resonator is analyzed and deduced.The establishment of error model and error analysis for HRG are conducted. Firstly, the dynamics equations of resonator with the nonuniformity errors of inherent parameters, dimension parameters and excitation parameters are established. The method of identifying the errors is given. The anisoelasticity and damping nonuniformity are given through the dynamics equations. And the method of balancing the errors except damping nonuniformity error is also given. Secondly, the maximum values of errors are calculated under the requirement of frequency split, and the tolerances towards errors are determined to guarantee the accuracy of HRG under open-loop control and quasi quadrature control modes. Finally, the method of increasing the tolerance towards damping nonuniformity error is given, so the processing and machining difficulty is reduced.