Deployment dynamics for flexible deployable primary mirror of space telescope with paraboloidal and laminated structure by using absolute node coordinate method

Abstract

A nonlinear dynamic modeling method for primary mirror of Flower-like Deployable Space Telescope (F-DST) undergoing large deployment motion is proposed in this paper. To ensure pointing accuracy and attitude stability of the paraboloidal primary mirror, the mirror is discretized into equal thickness shell elements by considering shell curvature. And the material nonlinear constitutive relation of flexible mirror is acquired using Absolute Nodal Coordinate Formulation (ANCF). Furthermore, the primary mirror of F-DST can be regarded as a clustered multi-body system, and its dynamic equations of elastic deformation and deployment motion are established by virtual work principle. Finally, the deployment motion of primary mirror by different driving conditions are simulated, the results show that the vibrations of mirrors that driven by elastic hinge device are more than that driven by servo motor. In addition, single sub-mirror deployment process will perturb the pointing accuracy of primary mirror, and the multiple sub-mirrors simultaneously deploying will seriously affect all the sub-mirrors surface accuracy because of the coupling effect. Thus, there are theoretical value and practical significance for the controlling surface accuracy and attitude accuracy of space telescope.