Study On The Reflective Surface Accuracy And The Deployable Motion Of Space Mesh Antennas

The space mesh antenna is an important component of spacecrafts and satellites.Meanwhile,it is also the key equipment of mobile communications,electronic reconnaissance and deep space exploration.The reflective surface accuracy determines the working band,bandwidth and gain of antennas,and is an important technical indicator.Space mesh antennas are statically indeterminate structures that consist of deployable trusses and flexible cable networks,and the surface accuracy is influenced by the interactions between trusses and cable networks.Meanwhile,a smooth and stable deployable motion should be achieved to ensure the normal service of mesh antennas.At present,the antenna design method and technical means have lagged behind the demand,researches on the reflector surface accuracy and the deployable motion of space mesh antennas are urgently required.This paper studies these problems systematically,and the main works and results are as follows.The compatible deformation between the deployable truss and the flexible cable network is studied,and the modified force density method is proposed.This method keeps the force density method’s advantages of solving nonlinear equations,and meanwhile overcomes the disadvantages of its inability to consider the flexibility of the supporting structure in the form finding and optimal design process.Euler-Bernoulli beams are adopted to consider the axil strain,bending and torsion of the supports.The rotation coordinates of beam nodes are eliminated by applying boundary conditions,so that the degree of freedom(DOF)of cable nodes and beam nodes are the same.Deformation compatibility conditions are used to couple the truss and the cable network.The modified force density method avoids deviations of the form finding caused by the assumption of rigid truss.Therefore,it is meaningful to the prestress design of cable networks and the improvement of the antenna’s surface accuracy.The flexible hinge model is established and coupled with the truss and the cable network to obtain the integrated form finding method for mesh antennas.By combing the gradient based optimization method,the optimal design of the cable network’s prestress can be achieved according to the requirements for the surface accuracy and cable tensions.The stiffness coefficients of three kinds of hinges in six DOFs are obtained by experimental measurement and curve fitting.The influences of the flexibility of rods and hinges on the form finding and prestress design is studied through several numerical case studies.The static analysis by ABAQUS is used to verify the proposed method.In order to calculate the time varying cable tensions during the deployment of mesh antennas,the parameterized deployment analysis for space cable network structures considering geometric nonlinearity,topological diversity and the cable’s sag is presented.The cable network is discretized into finite cable elements,and the serial numbering rule is proposed to obtain the corresponding topological matrix.Equilibrium equations are formulated and further assembled by matrix transformation theory,and trust-region algorithm is used to solve the system equations.In the calculating,the cable’s stiffness is determined by its slack or tensional state,and the coupling between the deployment of trusses and the deformation of cable networks are considered by updating the coordinate values of boundary nodes in each time step.The variation of cable tensions during the deployment is analyzed by case studies,and the “selfstretching” process is discussed.The dynamic modeling and analysis for the deployment of mesh reflector antennas considering the rigid body rotation of rods,the geometric nonlinearity of the cable network,and the rigid-flexible coupling of the truss and the cable network are presented.The mass of hinges is concentrated on their centroids and the longerons,battens,and diagonals are regarded as homogeneous rods.The kinematics analysis of the truss is conducted and the kinetic energy during the deployment is derived.Then,the cable network is discretized into multiple cable elements that are modeled by springs.The elastic energy of the cable network is derived by solving systematic equilibrium equations.The dynamic model is established by using Lagrange equation and then the driving force under the predesigned motion is derived.The feasibility of the deployment motion is discussed through numerical case studies.Through the above researches about the form finding method,optimal design of the cable network’s prestress and the dynamics analysis of the deployment process,the method to ensure both the deployment performance and the surface accuracy was formed.These researches enriched and developed the multi-body system theory and the knowledge of cable-beam structures,improved the analytical methodology on the active control of deformation field for the flexible body,and provided technical knowledge to guarantee the mesh antennas’ surface accuracy and dynamic behavior.