Squeeze-film air damping of a torsion mirror at a finite tilting angle

Abstract

This paper proposes an analytical model for calculating the squeeze-film air damping of a rectangular torsion mirror at finite normalized tilting angles. The general Reynolds equation is first modified to a nonlinear equation for the condition. Based on the nonlinear equation, the damping pressure, the damping torque and the coefficient of the damping torque are derived as functions of the tilting angle and the aspect ratio of the mirror plate. To show the relation clearly and for the ease of application, the coefficient of the damping torque is given in curves in addition to complicated analytical expressions. The results show that the damping torque coefficient is a highly nonlinear function of the tilting angle and basically a linear function of the aspect ratio of the mirror. The coupling between the two factors is appreciable but not very strong. When the tilting angle is reduced to zero, the result of this paper agrees perfectly well with those of previous papers, which have been verified by experiments and/or numerical calculation. The analytical results are effective for normalized tilting angles up to 0.7.