Advances in Engineering Advances in Engineering features breaking research judged by Advances in Engineering advisory team to be of key importance in the Engineering field. Papers are selected from over 10,000 published each week from most peer reviewed journals.
Vib. Acoust.136(3), 034502 (Mar 18, 2014) (5 pages).
K.Y. Narasimhan.
Lockheed Martin Space Systems, Sunnyvale, CA 94088-3504, e-mail: [email protected]
Abstract
This article derives closed form expressions of the Bryan’s Factor (BF) for truncated spherical and conical shells useful in the design and calibration of resonator gyroscopes. It is shown that Bryan’s factor depends only on the shape of the structure and the modes of vibration and does not depend on the physical properties of the material of the shell. The material properties are needed to determine the resonating frequency and the Q-factor.
Hemispherical Resonator Gyroscopes (HRGs) are in use now for satellite attitude determination. Micro-scale gyroscopes are in development, (Figure 1) and do not as yet satisfy the accuracy requirements for satellite applications. Required accuracies of micro-scale resonator gyroscopes for satellite applications may be attained in the future. Until such time, methods of reducing weight, volume and cost of resonator gyroscopes are of interest. The Bryan’s factor for conical shell gyroscopes (Figure 2) includes the cylindrical shell as a special case. Cylindrical shell resonators rather than HRGs are simpler to manufacture and lead to larger gain factors resulting in better accuracies. Better accuracies of cylindrical shell gyroscopes also aid in the development of microscale resonator gyroscopes. Further, cylindrical shell gyroscopes can be made smaller than HRGs, together with more compact electronic packaging resulting in reduced weight, volume, and cost. Hence it is advantageous to consider manufacturing cylindrical resonator gyroscopes for satellite as well as other applications until micro-scale resonator gyroscopes attain required accuracies.
Figure 1. Micro scale HRG made of Polycrystalline Diamond
Figure 2. Truncated Conical Shell Parameters (Note: For alpha = 0 we obtain a cylindrical shell gyroscope with higher accuracy and gain factor)
