Analysis Of Multi-source Errors Of Cable Net-frame Combination Structure

Cable net–frame combination structure has been widely used in deployable antenna. However, some significant drawbacks to these antennas including the complex structure, limited deployed surface accuracy of reflectors and the low deployment reliability have imposed a restriction on the ability to reflect RF communications at shorter wavelengths. Thus it is essential to analyze the multisource errors of a cable net–frame structure at its design stage.First of all, as a deployable mechanism, the presence of joint clearance and the error of dimensional tolerance must be considered. This study presents an effective method for error analysis of planar linkage with joint clearances and manufacturing errors. In this paper, the joint clearance is treated as virtual link, and the motion freedom caused by the joint clearance is modeled by equivalent kinematical pairs. The externally applied wrench is applied on the actuating link to guarantee the multi-freedom mechanism with equivalent joint clearances being in equilibrium. In addition, uncertainties due to manufacture tolerance and friction lead to positional deviation and thus, random dimensional errors are taken into account based on the mechanism with equivalent joint clearances. Eventually, two planar four-bar linkages and a spatial four-bar linkages are taken as example, and its positional error caused by joint clearance and random dimensional errors is compared with that of ideal mechanisms.Then, an analysis to the systematic surface figure error influenced by three factors including errors of faceted paraboloids, fabrication imperfection and random thermal strains is performed. The computational formulas for root-mean-square surface deviations caused by these factors are presented respectively. The stochastic finite element method is applied to derive the computational formulas of fabrication imperfection and random thermal strains, by which the sensitivity of surface accuracy to component imperfection can be revealed. Then the Monte Carlo simulation method is introduced to obtain the surface figure by sampling test on random errors. And the analytical method is applied to the research on the surface figure error of Astro Mesh reflector.Finally,this paper presents a new approach to study the mechanical relaxation behavior, caused by the viscoelastic material, of a large cable net–frame combination. Based onthe theory of Schapery, one-dimensional nonlinear viscoelastic constitutive model, whose instantaneous compliance is approximated by Prony series, has been arrived. The Schapery nonlinear viscoelastic material model parameters and Prony series coefficients of the structure’s material has been determined by the nonlinear least squares method for curve fitting the experimental data. In addition, the finite element model of the cable net structure in time domain has been established based on the cable segment mechanical relaxation model. And the large cable net structure mechanical relaxation behavior analysis has been carried out eventually.