Dynamic modeling and performance evaluation of a vibrating beam microgyroscope under general support motion

A general modeling framework is presented for the development of the frequency equation of a microgyroscope, which is modeled as a suspended cantilever beam with a tip mass under general base excitation. Specifically, the beam is considered to vibrate in all the three directions, while subjected to a base rotational motion around its longitudinal direction. This is a common configuration utilized in many vibrating beam gyroscopes and well drilling systems. The governing equations are derived by using the Extended Hamiltonʹs Principle with a general 6-dof base motion. The natural frequency equation is then extracted in a closed-form for the case where the beam support undergoes longitudinal rotation. The effect of substrate motions on the performance of microgyroscopes is also discussed, along with the effects of a beam-distributed mass, a tip mass, angular accelerations, centripetal accelerations and Coriolis accelerations. The response of the system to different inputs is studied and the response sensitivity to input parameter variations is examined. Finally, the sources of error in the measurement of input rotational speed are investigated and identified. The results of the study demonstrate the importance of errors, caused by cross axes inputs, on the gyroscope output measurements.