Dynamic analysis of gimbaled and gimbal-less MEMS biaxial micromirrors in omnidirectional scanning
摘要
The scanning dynamics and the motion nonlinearity of gimbaled and gimbal-less MEMS micromirrors are studied using Euler’s equations of motion for the application to omnidirectional scanning of light detection and ranging. The motion interaction between the rotations around the two axes is dependent intricately on moments of inertia, rotation angles, and angular velocities. The magnitudes of the interaction terms of the equations increase with the increase of the difference of the moments of inertia along the orthogonal axes of mirrors. Solving the motion equations by Runge–Kutta method, we investigate comparatively the omnidirectional trajectories of a gimbaled micromirror and a gimbal-less micromirror with the same moment of inertia. The models of the mirrors are based on the fabricated MEMS micromirror having the resonant frequency of 5336 kHz. The circular trajectory is obtained in a wide range of actuator torque in vacuum at quality factor of 1000 for the gimbaled mirror, while for the gimbal-less mirror, the circular trajectory tends to deform elliptically. The trajectory is stable but occasionally become uncontrollable by the actuator torque. Decreasing the quality factor to 100 corresponding to atmospheric pressure, the elliptical deformations are suppressed although the scan angles decreased. The minimization of the motion nonlinearity is discussed from the viewpoints of damping and actuator torque.