メッシュ式宇宙リフレクタの表面精度の検討 円及び正三角形膜要素の鏡面誤差

Abstract

In this paper, effects of configuration, boundary deflection, position, etc. of circular and equilateral triangular membrane elements subject to isotropic tension, upon root-mean-square (rms) surface error in a faceted reflector surface are analyzed. Boundaries of the membranes are assumed to coincide with elliptic or hyperbolic paraboloidal surfaces (including a plane surface), or paraboloidal curves. Exact solutions for the deflection of circular and triangular membranes are obtained based on the linear membrane theory. These solutions are used to calculate the rms errors between the approximate parabolic surface (APS) which approximate the ideal parabolic surface and the membrane surfaces. Different kinds of rms error optimizations according to constraints of parameters which determine the boundary deflections of membrane elements are carried out, from which corresponding optimum membranes are obtained and compared. Rms errors of the optimum membranes calculated reduce as the distance of the membranes from the axis of the reflector becomes large. The rms error of the optimum membrane which gives minimum surface error among others is found to be 0.5 (circular membrane) and 0.46 (equilateral triangular membrane) of that of the membrane whose boundary coincides with the approximate parabolic surface, and 1-0.577 (circular membrane) and 0.28-0.43 (equilateral triangular membrane) of that of the best fit flat membrane. Comparison of the rms errors of a circular and triangular membrane with the same area is also made.