Mechanics of micro capacitive accelerometer with u-shape cantilever beam

Abstract

Due to an increasing in industrial micromation need in recent years, the use of micro accelerometers has been highly increased. Consecutively, this has promoted research activities in this field; capacitive accelerometers also have got high concern at large. As a research project of the Kentron in South Africa, this thesis deals with a theoretical model for a one-dimensional micro capacitive accelerometer with U-shape cantilever beam. The properties of the small angle tilted-plate capacitor have been analyzed; the capacitance equation and electrostatic force equation of this kind capacitor have been derived. The sensing element of this accelerometer consists of an inertial mass connected with two cantilever beams. The vibration modes analysis to the sensing element was accomplished by using CoventorWare2004's MemMech module, the result indicates that the main vibration mode can cause the capacitance change observably and the effect of the other modes to the capacitance can be ignored, which satisfied the purpose of the design. In the process of deriving the linearizing acceleration equation, the angle of the inertial mass caused by the deformation of the U-shape cantilever beam was taken into account as well as the electrostatic force between the two electrodes, thus the more precise acceleration linear equation was obtained. The sensitivity equation was derived through the acceleration linear equation, the relationship between the main parameters of the system and the sensitivity has been analyzed. The differential structure of this micro capacitive accelerometer was also analyzed; the linearizing acceleration equation and sensitivity equation of this kind structure were derived, it has been proven that the sensitivity of this structure is twice than the normal structure approximately. The maximum detectable signal was obtained in terms of the fracture strength of the cantilever beam and the maximum displacement of the inertial mass. The minimum detectable signal was obtained in terms of the thermal noise analysis. In the process of the dynamic analysis, the forced vibration produced by the sinusoidal periodic force and sinusoidal periodic moment was analyzed and the transient capacitance equation was derived, this proved the system has good dynamic character in theory. The system was simulated and analyzed by using CoventorWare2004's Saber module. The initial capacitance analysis indicates the relationship between the voltage and the initial capacitance, the result is close to the analytic model. The resonance frequencies analysis indicates that the main dimensions of the sensing element can determine the resonance frequencies and each vibration mode's sequence, the initial dimensions of the sensing element was proved reasonable by analyzing. Sensitivity analysis and Monte Carlo analysis indicate the effect of the sensing element's normal manufacturing tolerance to the system's frequency is small. Impact of plate curvature analysis indicates the effect of the inertial mass's deformation caused by the surface stress to the capacitance is small. Transient analysis obtained the system's transient displacement curve of six directions and transient capacitance curve in normal terms; this proved the system has good dynamic character in the simulating environment.