Nodal vibration and pattern angle error analysis of the imperfect resonators for vibratory cylinder gyroscopes

In this paper, vibration of imperfect resonators for vibratory cylinder gyroscopes is investigated. A model of the vibration based on the wave superposition is established. For an imperfect resonator, the principal stiffness axis does not coincide with the driving electrodes, so the primary mode and the secondary mode of the resonator are both excited. Superposition of these two pattern components produces the resultant pattern, which leads to a complicated vibration near the nodes and the pattern angle error. The influence of the frequency split and the driving vector orientation on the nodal vibration and the pattern angle error is particularly analyzed. Theoretical results show that the amplitude and phase of the nodal vibration are affected by the frequency split and the driving vector orientation. The pattern angle error has a positive correlation with the frequency split, and this angle also has a positive proportion with sin(8α), where α is the angle between the drive electrodes and the principal stiffness axis of the primary mode. Experiments are also included in this work to validate these influence factors. The theoretical and measured results are in close agreement. These results are useful for the mechanical balance, the electrodes assembly and the control circuit design of the cylindrical gyroscopes.