Frequency trimming of a vibrating ring-based multi-axis rate sensor

A recently proposed concept for a ring-based multi-axis rate sensor requires that two in-plane modes of vibration and two out-of-plane modes of vibration of a ring each have identical natural frequencies. This work proposes a practical mass trimming approach for eliminating the frequency splits between these four natural frequencies for an initially imperfect ring. Given that the modes of an imperfect ring are unlikely to consist of pure in-plane and pure out-of-plane modes, the proposed trimming approach takes account of the cross-coupling that exists between the in-plane and out-of-plane modes. The proposed approach consists of three stages: (i) eliminate the frequency split between a pair of predominantly in-plane modes and a pair of predominantly out-of-plane modes; (ii) eliminate the cross-coupling between the in-plane and out-of-plane modes; (iii) match the in-plane and out-of-plane natural frequencies. Numerical examples demonstrating and validating the approach are provided.