Multi-Objective Optimization Design of Natural Frequency of Two-Degree-of-Freedom Fast Steering Mirror System

In the design of two-degree-of-freedom (2-DOF) fast steering mirror (FSM) system, in order to improve the control bandwidth of the system, the low-order natural frequency in the working direction should be reduced as much as possible, and the high-order natural frequency in the non-working direction should be increased. In this paper, a deep-cut flexure hinge mirror system was studied. Firstly, the motion direction of the first to third order natural vibration mode of the system was analyzed. Next, the working stiffness in the third vibration mode direction was deduced to solve the problem that the traditional stiffness calculation method is not suitable for the third vibration mode direction. Then, the energy method and the Castigliano’s second theorem were used to analyze the working stiffness of the deep-cut flexure hinge. Next, the formula for calculating the relationship between the thickness of the mirror and the moment of inertia in the direction of the vibration mode was derived. Combined with the calculation formula of working stiffness in the vibration mode direction, the formula of the first to third order natural frequencies was derived, and the finite element verification and sensitivity analysis of structural parameters were carried out. Finally, by using NSGA-II, a multi-objective optimization design was carried out on the first to third natural frequencies of the system with hinge structure parameters and reflector thickness as independent variables, and the optimization results were analyzed by theoretical calculation and finite element simulation verification. The results show that the first and second-order natural frequencies of fast steering mirror system are reduced by 7.8% and 7.11%, and the third-order natural frequencies are increased by 139.8%. It proves that the optimized structure is much better than the original structure, and the optimal calculation can effectively increase the control bandwidth of the system