Integrated Form-Finding And Error Analysis Of Umbrella Antenna Based On Equivalent Radiating Rib

With the continuous development of aerospace technology,space network deployable antennas are becoming larger and more accurate.The umbrella antennas have been widely concerned due to simple structure,high gain and high precision.In this paper,the shape finding analysis,the optimization design under thermal load and the influence of rib spread angle error on the shape accuracy of cable net deployable umbrella antenna are studied.(1)An integrated form-finding optimization design method for cable net umbrella antenna based on equivalent radiating ribs is proposed.Firstly,in view of the complex structure of the existing digging ribs and the difficulty of integrating the stiffness matrix,the equivalent of digging rib structure to the radiating rib structure is completed by optimizing the cross section of the radiating rib unit.Secondly,the stiffness matrix of umbrella antenna support rib structure is transformed accordingly and the force balance equation of rib structure containing only the rigid body displacement is established.According to the balance coordination condition between the cable net and the support rib and the force density,the overall balance equation of net nodes and rib nodes is established,the cable net pretension optimization model is given and the optimization calculation is carried out.Finally,according to the designed geometric parameters of cable net umbrella antenna,a finite element model is established,the static analysis under pretension is carried out,and the shape accuracy after deformation is calculated.The results show that the optimization design method of cable net umbrella antenna given has good applicability.(2)Aiming at the influence of space thermal load on the accuracy of umbrella antenna shape,an optimization design method of umbrella antenna cable net pretension based on equivalent radiating ribs and considering the space thermal effect is proposed.Firstly,the force balance analysis of cable net nodes under thermal load is carried out and the method of solving the force density under thermal load is derived.Secondly,based on the establishment process of the balance equation between cable nets node and rib nodes in the second chapter.the balance equation between cable net nodes and rib nodes considering the rib deformation and thermal load is established.According to the requirements of shape accuracy,an optimization model considering rib deformation and pretension of cable net under thermal load is established.Finally,based on the designed geometric structure model of umbrella antenna,the integrated optimization design of umbrella antenna under thermal load is completed.The thermal load and calculated pretension are applied to the finite element model for verification.This method provides a reference for the optimization design of the prestress of cable net umbrella antenna under the space thermal load.(3)Aiming at the problem of the influence of the random error of the rib spread angle caused by manufacturing and assembly on the surface accuracy and gain loss,a calculation method between the average value of the surface accuracy and antenna gain loss and the random error of the rib spread angle is proposed.Firstly,based on the condition of small deformation and without considering the rib deformation,the calculation formula between the mean value of the surface accuracy and the random error of the spread angle is established.Secondly,the Monte Carlo method is used to verify the correctness of the expression.Finally,the standard deviation of the rib spread angle error is given.The deduced formula and the Monte Carlo method are used to calculate the average value of surface accuracy and the gain loss value.The results show that the average shape accuracy and gain loss calculated by the derived calculation formula are similar to those calculated by the Monte Carlo method within a certain error angle range and the calculation efficiency is relatively high.