Dynamic Analysis And Mathematical Model Of Silicon Micromechanical Vibration Gyroscope

Silicon micromechanical vibration gyroscopes are a new kind of sensors for measuring the inertial angular velocity and they have been developed with the microelectronic technology and micromaching technology. Owning to using of the microamplitude vibration instead of high-speed rotation, the new sensors have many advantages over the conventional gyroscopes, such as smaller size, less weight, lower cost, higher reliability, being able to be produced in batch and to be integrated with electronic circuits, and so on. With the coming years, this type of sensors-silicon micromechanical vibration gyroscopes-can be widely used in military and civil scopes as stable equipments.The use scope of gyroscopes is bound with their accuracy and sensitivity. So we must improve its accuracy and sensitivity before we can put silicon micromechanical vibration gyroscope in the markets. However, in order to improve its accuracy and sensitivity, first of all we must know its working laws. Just for this, in this paper we have presented our dissertations on the fundamental motion laws of some kinds of silicon micromechanical vibration gyroscopes, and have established mathematical models of these gyroscopes and analyzed their fundament working laws. The main results and news ideas are as following. 1. We have studied the basic structure of the lateral comb drive micromechanical silicon gyroscopes and discussed its working laws in details. First, by the composition theorem of acceleration of influence move, strict mechanical analysis and accurate mathematical computations, we have acquired the presentation formula of acceleration of the movable mass of the gyroscope rotating in a constant angular velocity in an inertia coordinate system. And, by Newton's mechanics laws, we have also acquired the accurate differential equation that presents the working of the lateral comb drive micromechanical silicon gyroscopes. And, under the different circumstances we have solved the models and by the solutions we have analyzed the basic working laws. With the modeland the analytical working formula, we have also gotten the known properties of the gyroscope. So we have theoretically revealed the mechanism of those properties, and the results have tested the accuracy of the mathematical model. For example, in an inertia space, the rotating angular velocity mainly influences the amplitude of the vibration of the frequency (in the direction perpendicular to the gyroscope plane, namely in z-axis direction) of the same with the drive frequency ω. With an ω enough big, the influence on the amplitude mainly comes from the angular velocity in the y-axis direction of the gyroscope, and they are approximately in direct ratio. The angular velocities in x-axis and z-axis directions can also give influences, but the influences are less. Finally, in order to provide basic theory for analyzing the gyroscope more accurately, we have presented the mathematical model of accounting in the angular velocities of the gyroscopes.2. By the Euler's dynamics equation of rigid body rotation, we have deduced in detais the accurate differential equation models of the micromechanical vibratory wheel gyroscopes, the micromechanical gyroscopes transducer with improved drive and the frame vibratory micromechanical gyroscopes. And we have simplified the differential equation models by using its basic working properties and also discussed the rationality of the simplification. And, under the different circumstances we have solved the models, by the solutions we have analyzed the basic working laws of the micromechanical vibratory wheel gyroscopes and theoretically revealed the mechanism of those properties and tested the accuracy of the mathematical models.3. Because the two vibrations of the micromechanical comb drive tuning fork rate gyroscopes for driving and testing are libration and angle vibrations respectively, so the studies of its are different from the gyroscopes mentioned above. By using Newton's mechanics laws and the Euler's dynamics equation of rigid body r...