Dynamic response-based characterization of ring-based vibratory angular rate sensors

Dynamic response behaviour of a rotating ring is investigated in order to better understand the achievable performance improvements as well as system limitations. For this purpose, the governing equations that represent the transverse as well as the tangential in-plane motion of a rotating ring are derived via the Hamilton’s principle. These equations are then discretized to represent a two-degree-of-freedom time-varying gyroscopic system. The asymmetry effects are considered important and are included by considering mass mismatch in the system mass matrix. In order to predict dynamic behaviour of a ring system subjected to external excitation and body rotation, time and frequency response analyses are performed. The natural frequency variations due to the gyroscopic coupling presented in the system are first characterized for varying input angular rates. The effects of system parameters such as damping and mass mismatch on the sensor sensitivity and operating range are quantified via suitable time and frequency response analyses.