Principles of a three-axis vibrating gyroscope

Gyroscope sensing and self-calibration architecture based on signal phase shift

“…This relationship can be used to extract the value of λ from the simulation results, which in this case yield λ ≈ 0.6174 (using f 0 = 10.41 MHz, Q = 56, 000). This is close to the value λ = 2n/(n 2 + 1) = 0.6 obtained from the theoretical analysis of the resonance modes of an ideal ring gyroscope [23]. Figure 7 plots the simulated outputs of the sensor and calibration architectures of Figs.…”

“…where x 1 and x 2 are generalized coordinates [23], ω 1 and ω 2 the resonance frequencies of the two resonance modes of the system, Q 1 and Q 2 their respective quality factors, and d 12 and ω 12 are coefficients that model the coupling between the two resonance modes caused by non-ideal behavior of the physical device. The right-hand side of (1) represents the external excitations applied to each resonance mode, while the effect of the Coriolis force is modeled by terms 2λΩ zẋ1 and 2λΩ zẋ2 , where Ω z is the angular rotation velocity around the sensitive axis of the gyroscope, and λ a constant that depends on the gyroscope type and on the index of the resonance modes of the device [23]. If the system is in sinusoidal steady-state at a given frequency ω, then (1) is equivalent to the following set of equations where F I , F Q and X 1 , X 2 are the phasors of the applied excitations and of the generalized coordinates, respectively, and…”

Investigation of the ring resonator parameters influence on the characteristics of the three-axis optoelectronic angular velocity transducer

“…1, б и в). Во вторых режимах движение кольцевого резонатора пропорционально измеряемой угловой скорости, поэтому величины амплитуд вторых движений определяют измеряемую величину угловой скорости относительно соответст-вующей оси [2]. При существующей угловой скорости (Ω Z ) точ-ки в плоскости кольца (45, 135, 225 и 315° относи-тельно главных осей) показывают величину изме-ряемой угловой скорости.…”

“…Для частоты собственных колебаний второго режима «на плоскости» частота собственных коле-баний определяется как     Для правильного функционирования КР необ-ходимо, чтобы частота собственных колебаний ре-жима «в плоскости» и режима «на плоскости» име-ли одинаковую резонансную частоту [2]. Разностная частота собственных колебаний(F = f 1 -f 2 ) зависит от значений толщины и ширины кольца (рис.…”

Design and Development of a 3-axis Micro Gyroscope with Vibratory Ring Springs

“…The vibrating ring gyroscope is immune to the spurious vibration and temperature change, and has the symmetric structure which also shows outstanding rotational detection [5]. The ring gyroscope have been studied for a single axis device at [6] and a 3 axis silicon ring gyroscope using in-plane & out-of-plane operation at [7], etc. 3 axis angular velocity is measured using the in-plane and out of plane structure to contain into same die.…”