Study On The Nonlinear Behavior Of Clustered Laminated Sub-mirrors Deployment And Primary Mirror Posture Adjustment For Space Telescope

Space telescope is a prolonged observation equipment working in space for observe space phenomena,its imaging effect is affected by the accuracy of mirrors surface and pointing.However,limited by the effective transportation capacity of the rocket,large aperture primary mirror is designed as deployable mechanism and a lightweight flexible laminated composites is selected as the mirrors substrate materials.During the sub-mirrors deployment and primary mirror posture adjustment progress,the coupling of elastic deformation and rotational motion excited the oscillation of the mirrors.Oscillation is difficult to dissipate in a low-damping and gravity-free environment,which affect the imaging effect of the primary mirror and the attitude stability of the telescope system.Therefore,the dynamic modeling and nonlinear behavior characteristics of the flexible laminated sub-mirrors deployment and primary mirror posture adjustment are studied in this paper.The dynamic modeling of the sub-mirrors deployment primary mirror adjustment progress for the space telescope belongs to the problem of large-scale motion and large deformation of the flexible clustered multi-body system.In order to accurately describe the constitutive relation of flexible mirrors,the mi rror is discretized into the equal thickness shell elements considering shell curvature by using the absolute nodal coordinate formula(ANCF).Then,the Lagrangian strain of the element is expressed by continuum mechanics,and the stress-strain relationship is obtained considering structural characteristics of laminated mirror.Furthermore,the deployable primary mirror is equivalent to a flexible clustered multi-body system,its dynamic model during sub-mirrors deployment and primary mirror posture adjustment are established based on principle of virtual work.The fine dynamic model contains the geometric structure and material nonlinearity of the laminated paraboloidal mirror.It overcomes the problems of divergence and fitting shell structure accurately in solving the large deformation problem by traditional models.This method is especially suitable for solving the large rotation problem of flexible laminated thin shells with variable curvature.Based on the established mirror model of ANCF shell elements and the coupling dynamic equations,the effects of driving parameters,shell curvature and laminated structure on the dynamic behavior of the primary mirror system are analyzed.ANCF shell element accurately fits the structure of paraboloidal mirror to improve the accuracy of describing elastic deformation for mirrors,geometric structure and material nonlinearity have great influence on the dynamic behavior of mirrors.The precise dynamics behavior prediction of the primary mirror system under the multi-factor coupling provide a theoretical basis for improving the vibration control,attitude stability adjustment and image quality of the primary mirror.The equivalent physical model of the deployable laminated primary mirror was built,and the process of sub-mirrors deployment and primary mirror posture adjustment are analyzed by experiment.The comparison between experimental and simulation results shows that the present model can effectively solve the dynamic problems of flexible laminated parabolic mirrors clustered system.Experiments of sub-mirrors deployment with different laminated structure and driving strategies verify the prediction of sub-mirror dynamic behavior using the present model.It provides a reference for dynamic behavior analysis and defor mation control of deployable primary mirror,and is helpful for mirrors structure design and material selection.