Analysis of Manufacture Errors for Space Truss With Bolted Spherical Joints Base on Monte Carlo Method

Abstract

The active reflector of the five-hundred-meter aperture sphere radio telescope (FAST) is constituted by about 4600 triangular reflector elements, whose surface error will determine the telescope’s antenna efficiency. One solution is a grid structure backup with the bolted spherical joints, in which the surface accuracy is dominated mainly by the length accuracy of the rods in it. In this paper, an accuracy analysis based on Monte Carlo method is proceeded to predict the surface error. Random errors are input the rods, and the surface errors in root mean square (rms) are output. After the calculations, the final accuracy’s probability distribution charts are given for the different error inputs. And a relationship chart between rod length error and final accuracy is given to help determining the most reasonable rod length error. To solve the position of the grid structure, an iteration method is deduced. The relationship between joints and rods in the frame structure which is described as a graph, is presented by adjacency list. Forces on joints are balanced at the beginning, but when rod length errors are input, forces to pull or push the joints are yielded. The process of moving their positions to make the forces balance again is the process to solve the surface accuracy. An existing reflector element model was measured. The measurement verified the analysis. Finally, the proper accuracy of rods length error is given. It is useful for cost controlling and time keeping in FAST design, for the possibility to achieve a qualified surface by controlling the manufacture error of rods reveals that the reflector elements maybe avoid adjustment and can be mounted to the telescope directly. The method to predict accuracy can be generalized for the other grid structures.