Analytical investigation of air squeeze film damping for bi‐axial micro‐scanner using eigenfunction expansion method

Squeeze film damping is an important factor in the dynamic stability of the bi‐axial microelectromechanic systems. The purpose of this article is to provide an analytical solution for calculating the air squeeze film damping in bi‐axial torsional micro‐mirrors, considering the changes of pressure distribution in rotation around different axes. This is the first time that has been done for a circular micro‐mirror. One of the advantages of bi‐axis micro‐scanners compared to single‐axis types is the larger space covered by the scan in different axes. To calculate the pressure distribution in different rotation of micro‐mirror and also to achieve the squeeze film damping torque, Reynolds nonlinear equations have been used in polar coordinates, which have been solved by Taylor series expansion and also by eigenfunction expansion method. The results are verified with previous research in single‐axis mode. The results also show that with increasing gap between the micro‐mirror and the scanner substrate, the coefficient squeeze film damping will be less, but if the air gap is not changed, increasing the micro‐mirror radius will increase the damping coefficient. When the radius of micro‐mirror decrease, in order for the damping coefficient to be higher, the angle of rotation of the micro‐mirror must be greater too. The results of this article can be used for accurate modeling of squeeze film damping in micro‐scanners, control of dual‐axis torsion micro‐mirrors, and improvement of their efficiency.