构架式可展开天线工作表面母线拟合方法

Fitting method of working surface generatrix for deployable truss antennas

针对由六棱柱单元组成的构架式可展开天线工作表面与球面背部支撑桁架形状差异的问题,基于微分几何和最小二乘法,提出了一种构架式可展开天线工作表面母线的拟合方法.通过对构架式天线的类型、组成模块的结构以及球面背架与工作表面关系的分析,将工作表面由空间状态转换成平面状态,用矩形将其包络,给出了母抛物面母线方程的求解步骤.根据偏距,得到了工作表面母线的端点坐标,将待拟合曲线离散化,应用最小二乘法分析推导了拟合圆弧的计算公式.通过算例对口径相同的3种组合的天线进行了拟合,比较了3种组合的优劣,结果表明各条曲线的最大的拟合误差均小于各自的许用误差,不需要进行修正,该方法对构架式可展开天线工作表面母线的拟合具有较好的效果.

The difference between the shape of the working surface and the spherical truss structure of a deployable truss antenna with hexagonal prism modules causes problems.To resolve them,a fitting method of working surface generatrix based on differential geometry and the least square method was proposed.After analyzing the types of deployable truss antenna,module structures and the relationship between the truss structure and the mesh surface,the working surface was transformed from a space state into a plane state enveloped by a rectangle.The steps for solving the mother paraboloid＇s generatrix equation were analyzed.Based on offset distances,the endpoint coordinates of a working surface generatrix were obtained.The fitting curve was discretized,and calculation formulas of fitting arc were derived by the least square method.Using this method,three assembled antennas which have the same diameters were calculated.The results were then evaluated.They showed that the maximum fitting error of any curve was less than the allowable error,so it was not necessary to correct the fitting curve.This method proved to be an effective working surface generatrix.