Instability analysis of bi-axial micro-scanner under electromagnetic actuation including small scale and damping effects

Abstract

The objective of this work is to create an analytical framework to study the problem of instability and squeezed film damping in bi-axial micro-scanners under electromagnetic actuation considering Casimir effects and size dependence, simultaneously. Also, the concept of Eulerian angles has also been used to achieve this idea. The novelty of this work is analytical solution of squeeze film damping considering changes of pressure distribution for micro-mirror in the horizontal and vertical rotations. Moreover, the modified couple stress theory is employed to assess the effect of the small-scale on the dynamic instability of a biaxial micro-scanner, and the governing equations are derived based on the concept of Eulerian angles. This study addresses the nonlinear effect of air squeeze film damping on the stability of the micro-scanner according to its geometry. Then, the influence of magnetic field, Casimir force, and size are examined, followed by the generation of phase portrait and plot of parametric analysis. Based on the obtained results, the Casimir force accounts for the instability threshold of the system. Moreover, the phase portrait diagrams indicates that small size and air squeeze film damping improves the rotational stability of the micro-scanner. AC voltage is applied to induce electromagnetic actuation, and the graphs of nonlinear frequency response are plotted versus the micromirror rotation amplitudes considering various effects of magnetic field actuation and air squeeze film damping. Furthermore, increasing the magnetic field diminishes the instability threshold, and augmentation of the air squeeze film damping enhances the system stability and decreases the maximum rotation amplitude of the micro-scanner. The obtained results are validated against the empirical/theoretical results in the literature.