Research On Differential Equations Model Of Mocro Gyroscope And Its Disturbances

Micro silicon vibration gyroscopes are a new kind of angular rate sensor with the development of microelectronic technology and micromachining technology .Owing to using 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 produced in batch easily and integrated with electronic circuits, etc. .It is predictable that this type of sensors- Silicon micromechanical vibration gyroscopes can be widely used in military and civil scopes as stable equipments in the next few years.The uses gyroscope is bound with its accuracy and sensitivity .So we must improve its accuracy and sensitivity before we can put silicon micromechanical vibration gyroscopes on the market. In order to improve its accuracy and sensitivity, we must know its working mechanism firstly. Therefore, we study the micromechanical comb drive tuning rate gyroscopes and establish mathematical models of the gyroscopes and analyze its fundament working regulation in this paper. And we utilize Euler dynamical equations of rigid body rotation to deduce the accurate differential equation model of the micromechanical comb drive tuning rate gyroscopes in details.Because the two vibrations of the micromechanical comb drive tuning fork rate gyroscopes for driving and testing are libration and angle vibration respectively, we deduce the accurate differential equation of the micromechanical comb drive tuning fork rate gyroscopes by Newton's mechanics laws and the Euler's dynamics equation of rigid body rotation respectively. And we simplify the differential equation model by using its basic operating features and try to find the solutions of reduced equation on some special occasions.In order to obtain more information of the model, this paper analyzes the line vibration and solutions in details by solving equation to obtain the distribution of solution interference amplitude, and controls the model parameters by the relationships between distribution and palstance to get better optimization. The method of studying amplitude distribution borrows ideas from other similar situations.