| The piezoelectric fast steering mirror(PFSM)with large aperture and high resonant frequency is regarded as an important development direction of fast steering mirror(FSM).However,there are some technical challenges need to be solved,such as with the increase of optical aperture and resonant frequency,the serious reaction force/rotary torque generated by PFSM will lead coupling disturbance to optical platform.Then,for adaptive optics(AO)system,the beam stabilization accuracy and the tilting aberration correction ability will be severely interfered.In this paper,a mechanical-piezoelectric coupling model of PFSM is proposed to analyze the reaction force characteristics based on the working principle of traditional PFSM drivied by four actuators.The coupling mathematical equation of dynamic reaction force is established combined with the inverse piezoelectric effect and mechanical dynamic balance relationship.The generation mechanism of PFSM reaction force is analyzed,the reaction force compensation system is designed based on Newton’s third law,and the dynamic balance condition to eliminate PFSM reaction force is established.To verify the design idea of reaction force compensation system for large aperture PFSM,the main line of researches is carried out from reaction force characteristic analysis to experimental test.The researches follow the method that single PFSM reaction force analys is carried out firstly and then the PFSM with reaction force compensation system is developed.The related researches are mainly carried out from the following aspects.Firstly,in order to explain the great significance of analyzing and eliminating the reaction force for large aperture PFSM,the research on dynamic coupling disturbance of large aperture PFSM reaction force to effective components on optical platform is carried out.The basic components of PFSM,the principle of beam stability adjustment,the dynamic model and the generating mechanism of reaction force are introduced.The numerical simulation method is used to verify the jitter interference caused by PFSM reaction force,and the results show that the phase and amplitude of disturbance are different for components at different positions on optical platform.In the verification experiment,the classical control algorithm is used to suppress the beam jitter caused by PFSM reaction force;the results show that it is difficult to suppress the coupling disturbance caused by PFSM reaction force in AO system.Then the research on reaction force characteristics is introduced to provide reference for the design of reaction force compensation system for large aperture PFSM.A mechanical-piezoelectric coupling model for PFSM reaction force analysis is established firstly.Then the coupling mathematical relationship model of PFSM reaction force is deduced theoretically based on the Lagrange and piezoelectric constitutive equations,and the coupling characteristics among PFSM reaction force,PFSM internal components parameters and driving voltage parameters are discussed in depth.To solve the problem that the coupling mathematical model is complex and difficult to calculate,two numerical analysis methods based on piezoelectric coupling theory and rigid-flexible coupling dynamics of multi-body system are proposed.To verify the appropriateness of the established coupling mathematical model,three large aperture PFSMs(Φ250mm,Φ320mm and Φ400mm)are designed,and the relationships among the reaction force characteristics,the tilting angle of mirror,the amplitude and frequency of driving voltage,and the equivalent stiffness of central flexure hinge are numerically analyzed.Finally,the two numerical reaction force analysis methods are compared,and the results show that the piezoelectric coupling numerical analysis can calculate reaction force more accurately and the reaction force characteristics of can be better demonstrated.The research on the reaction force compensation system design for large aperture PFSM is carried out,when the analysis of reaction force characteristics are accomplished.The generation mechanism of PFSM reaction force is analyzed firstly,and the PFSM reaction force compensation structure is designed based on Newton’s third law.Then the dynamic balance condition of the designed PFSM reaction force compensation structure is studied,and the dynamic relationship model for completely eliminating the reaction force is deduced and established theoretically based on the deflection balance equation of Newton’s second law.The numerical analysis of the reaction force based on the piezoelectric coupling theory shows that the reaction force elimination rate can reach up to 99%,which indicates that the designed reaction force compensation system is effectiveness and the established dynamic equilibrium conditions is appropriate.Finally,the relationships among the shear stress and tensile stress of the PFSM,the equivalent bending stiffness of flexure hinge on the top piezoelectric actuator,the driving voltage frequency and amplitude are preliminarily explored,which show that the optimal design of the top flexure hinge can effectively avoid the shear damage of the piezoelectric actuator.A 320 mm aperture PFSM equipped with reaction force compensation system is developed finally,and the test platform for performance characteristics and reaction force of PFSM is built,the elimination ratio of reaction force can reach 90.45%.The experimental research results show that mounting the reaction force compensation system for large aperture PFSM is an effective way to eliminate the reaction force,and the coupling disturbance caused by large PFSM reaction force can be effectively prevented. |
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