On Error Mechanism Analysis And Error Restraint Method For The Hemispherical Resonator Gyroscope

HRG has a promising application in the inertial navigation of long-lifespacecraft 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 analyzethe HRG’s error and to explore the methods of raising HRG’s accuracy under currenttechnical conditions. In this paper, the error analysis for HRG is based on theresonator with defects in the circular direction. The dynamics equations of resonatorwith error are established, then the relationship between the frequency split and thedensity nonuniformity error is deeply analyzed. The error restraint method isresearched from the following three aspects: control different parts of theresonator’s vibration displacement, adjust the position of the excitation electroderelative to the resonator, balance the resonator’s nonuniformity error. Moreover, themethods of angular rate calculation and error compensation are deeply researched,which give the guidance for raising HRG’s accuracy. The specific tasks of thisdissertation are as follows:The dynamics equations of resonator are established. At first, the inertia forcesof an arbitrary point in the hemispherical thin shell are deduced, then the forceequilibrium equations of the thin shell element which is sectioned from the mediumplane are gained. On the basis of it, the dynamics equations of the resonator areestablished by way of Bubonov–Galerkin method, and the accurate expression of theangular precession factor is deduced. All those lay a foundation for further analyzingthe error mechanism and error restraint method of HRG.Analysis on the frequency split and the error analysis for HRG under open-loopcontrol mode are achieved. Firstly, the dynamics equations of resonator with densitydistributed nonuniformity are established. According to the dynamics equations, theexpressions of natural frequency of hemispherical resonator are solved. Thefrequency split mechanism caused by density distribution nonuniformity error of thehemispherical resonator is achieved. Secondly, under open-loop mode, thesteady-state solutions of the antinode’s azimuth and the expression of the angularrate calculation are given. By simulation calculating, the tolerance towards thefourth harmonic of density nonuniformity is determined to guarantee the accuracy ofHRG under open-loop mode.Under force-rebalance mode, the method that different parts of the resonator’svibration displacement are controlled by different modes to restrain densitynonuniformity error is researched, and the method of angular rate calculation isgiven. Firstly, the expression of the angular rate calculation is given under general control. By simulation calculating, the influence of the fourth harmonic of densitynonuniformity on angular rate calculation is analyzed. Secondly, the expression ofthe angular rate calculation is given under quadrature control. The quasi quadraturecontrol is put forward to solve the problems of open-loop control, general controland quadrature control. The expression of the angular rate calculation is deducedunder quasi quadrature control. By simulation and analyzing, the quasi quadraturecontrol has more advantages in the aspects of error restraint and practicalapplication. In addition, under the quasi quadrature control, the expression of theazimuth of radial vibration antinode is deduced, and the steady state model ofamplitude-control is established.The methods of enhancing HRG’s accuracy and balancing the densitynonuniformity error are put forward. At first, according to the characteristics of theinherent toughness axis, the azimuth of inherent toughness axis is given. Then themethods of raising HRG’s accuracy are given by adjusting the angle between theexcitation electrode and the azimuth of inherent toughness axis under open-loopcontrol and quasi quadrature control modes, and the method’s effectiveness isproved by simulating. To counteract density nonuniformity error and raise theaccuracy of HRG, the dynamics equations of resonator with the1st~4thharmonic ofdensity nonuniformity are established. The identification model of densitynonuniformity error is established through the dynamics equations, and then theamplitude and phase of each density nonuniformity harmonic are identified. Afterthat, the process of balancing the density nonuniformity error by removing the micromass 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 ofinherent parameters, dimension parameters and excitation parameters are established.The method of identifying the errors is given. The anisoelasticity and dampingnonuniformity are given through the dynamics equations. And the method ofbalancing the errors except damping nonuniformity error is also given. Secondly, themaximum values of errors are calculated under the requirement of frequency split,and the tolerances towards errors are determined to guarantee the accuracy of HRGunder open-loop control and quasi quadrature control modes. Finally, the method ofincreasing the tolerance towards damping nonuniformity error is given, so theprocessing and machining difficulty is reduced.