Eşlenik modlu jiroskopların analizi

The aim of this thesis is to characterize the mode matched vibratory gyroscopes in terms of noise and stability. Furthermore, the mode matched wave coupling in rotating rod systems due to the Coriolis Effect is explored in order to provide a basis for novel gyroscope structures. This thesis is composed of two parts. In the first part, the noise analysis of the mode matched vibratory gyroscope is discussed with emphasis on MEMS gyroscope. MEMS (Micro-electromechanical System) vibratory gyroscopes have attracted a lot of interest recently and these gyroscopes made their way through portable devices and smart phones. However, their performance is not enough to cope with the demanding requirements of applications such as dead reckoning. Mode-matched gyroscopes are considered to be a solution for this problem. Various mode-matched gyroscope architectures have been proposed and their noise performances have been analyzed in the literature. However, in most of these analyses zero-rate output was considered and the noise analysis for dynamic cases were ignored. In the first part, we demonstrate the noise analysis of mode-matched vibratory gyroscope using the power spectral density (PSD) and the Allan deviation methods while non-zero rate is applied to the gyroscope. We show that for mode-matched gyros the noise performance of a rotating gyro can be significantly different from that of a gyro that does not experience any rotation. We also show that this difference is due to the coupling between the drive and sense systems via Coriolis force. This sets a fundamental limit for the noise performance of mode-matched vibratory gyroscopes where ARW (Angle Random Walk) increases proportionally with the rotation rate for the open loop and the force to rebalance operation modes. In the second part, vibration analysis of rods that are subjected to rotation is presented. It is shown that flexural-flexural, longitudinal-flexural and torsional-flexural wave coupling occur due to the Coriolis Effect. First, we carried out our analysis for thin rods where the wavelength is much larger than the radius. It is shown that the wavenumbers change due to the Coriolis Effect. Then, we characterize the 3-D wave propagation in rotating rods by using the Finite Element Method (FEM) in order to determine the corresponding wavenumber shifts for each type of wave. We show that for different drive frequency (ω0) and rotation rate (Ω), wave couplings exhibit different characteristics. For flexural-flexural wave coupling, the wavenumber increases for the primary flexural wave whereas the wave number decreases for the coupled flexural wave where Ω < ω0. For the Coriolis coupling between flexural-longitudinal waves, the wavenumber increases for the flexural wave and decreases for the longitudinal wave where Ω < ω0. For the Coriolis coupling between flexural-torsional waves, the wavenumber increases for both flexural and torsional waves. Based on the several case studies, it is found that the sizes of the rod structures are not suitable enough for the sensor applications, except for the case of flexural-flexural wave coupling. Thus, the flexural wave that couples with its conjugate flexural mode can be used to measure the rotation rate applied about the direction of propagation, where the gyro structure can be miniaturized in small scales by the MEMS technology. Based on this observation, we proposed a novel cylindrical rod gyroscope using the coupled flexural-flexural wave propagation. The new gyroscope will consist of a straight circular rod waveguide and piezoelectric transducers; one of which will excite the flexural wave from one end of the rod and the other will receive the corresponding signal. When the waveguide is subjected to a rotational motion, due to the Coriolis force the flexural wave is modulated by its conjugate flexural mode. This causes phase change in the transmitted signal and the relative phase change will increase in proportional to the angular velocity of the waveguide. In other words, by measuring the phase difference in the modulated signal, one can monitor the rate of rotational motion.