空间可展开索网天线的机构构型综合与形面设计方法研究

发布时间：2018-10-29 08:13

【摘要】：空间可展开索网天线是卫星通信、环境探测、载人航天以及探月工程的关键设备之一。为了实现其大口径、轻质量和高精度的设计,本文系统地研究了支撑桁架的广义机构自由度分析与构型综合问题,提出了索网结构的几何设计、预张力设计及不确定性索网结构设计方法。主要工作及创新点如下：(1)对广义机构自由度进行了分析。广义机构包括传统刚性构件和运动副,还包括柔性构件、弹簧和绳索等广义构件,以及预紧移动副、预紧转动副等广义运动副。基于螺旋理论,对广义构件的运动空间和广义运动副的约束空间进行了分析,得到了广义构件的最大／最小自由度和广义运动副的最大／最小约束度。考虑公共约束、冗余约束和局部自由度,建立了广义机构自由度的三种计算公式。分析结果表明：广义机构的自由度并不一定存在唯一值,而是落在最小与最大自由度的区间内,自由度的具体值与机构组成、几何以及所受外力(矩)的大小和方向有关。(2)提出了广义机构构型的逆运动综合方法。通过螺旋对广义构件和广义运动副的描述构造广义机构支链的运动螺旋系,由组合运算得到输出构件的运动类型,建立了广义机构的运动学特征分析方法。继而通过对运动学特征分析方法的逆向展开,建立了广义机构构型的逆运动综合方法。根据指定的运动类型,通过旋量描述并进行互易运算,得到输出运动的约束螺旋系,进一步分解和互易得到广义机构支链的运动螺旋系,得到对应的广义构件和广义运动副集合,形成广义机构的运动支链,最后通过对运动支链的排列组合,得到满足指定运动功能的广义机构构型。(3)提出了可展开天线的测地线索网生成方法。基于微分几何测地线理论,分析了旋转抛物面上曲线的测地曲率,推导了曲面上任意两点的通用测地线微分方程组,结合松弛法和牛顿迭代法,形成了方程组的数值求解方法。为了使抛物面上的测地线按照指定的拓扑连接关系生成数学意义上的测地线索网,建立了边界节点调整的优化模型,形成了测地线索网结构几何设计的动态边界调整方法。通过与其他索网结构相比,测地线索网结构的长度短、有效面积大。(4)研究了索网预张力设计的平面投影法和等张力设计方法。对于几何坐标已知的抛物曲面索网结构,研究了预张力设计的平面投影方法。首先将其投影到口径平面上,建立平面索网的预张力优化模型,计算平面张力分布并将其反投影到抛物曲面上,得到抛物曲面索网结构的张力,提高了索网预张力计算效率。对于几何与张力均未知的索网结构,提出了索网结构的等张力设计方法。基于非线性方程组求解的不动点理论,将索网张力设定为同一值,以力密度作为迭代变量,根据索网力密度、索长和张力三者之间的耦合关系,建立了等张力的迭代数学模型。研究结果表明：通过平面投影法计算测地线索网结构的预张力,可以得到较好的张力均匀性和较高的形面精度,而等张力方法可实现部分索网内部张力完全相等。(5)考虑不确定性因素情况下,对索网的预张力设计进行了研究。通过分析结构、材料与环境等不确定因素对索网张力的影响,将不确定性因素等效为索网张力的不确定性。对于几何坐标已知的索网结构,引入反优化策略,建立不确定性索网结构的张力优化模型,得到了不确定性对形面精度影响最小的索网预张力。对于几何与张力均未知的索网结构,提出了区间力密度的概念,推导了不确定性索网结构的形面精度区间表达式,建立了不确定性索网结构的区间力密度优化模型,有效降低了不确定性因素对索网形面精度的影响。
[Abstract]:Space deployable cable network antenna is one of the key equipment of satellite communication, environment detection, manned space and lunar month engineering. In order to realize the design of large aperture, light quality and high precision, this paper systematically studies the general mechanism degree of freedom analysis and configuration synthesis problem of supporting frame, and puts forward the geometric design, pre-tensioning force design of cable net structure and design method of uncertain cable net. The main work and innovation points are as follows: (1) The degree of freedom of the generalized mechanism is analyzed. the generalized mechanism comprises a traditional rigid component and a moving pair, and also comprises a generalized component such as a flexible component, a spring and a rope, and a generalized motion pair such as a pre-tightening moving pair, a pre-tightening rotating pair and the like. Based on the theory of helix, the constrained space of the motion space and the generalized motion pair of the generalized component is analyzed, and the maximum/ minimum degree of freedom and the maximum/ minimum constraint degree of the generalized motion pair are obtained. Considering the common constraints, redundancy constraints and local degrees of freedom, three formulas for calculating the degree of freedom of the generalized mechanism are established. The results show that the degree of freedom of the generalized mechanism does not necessarily have a unique value, but falls within the interval between the minimum and the maximum degree of freedom, and the specific value of the degree of freedom is related to the structure, the geometry and the magnitude and direction of the external force (moment). (2) The generalized mechanism configuration inverse motion synthesis method is proposed. The motion type of the output member is obtained by combining the description of the generalized component and the generalized motion pair through the spiral, and the kinematics characteristic analysis method of the generalized mechanism is established by combining the motion type of the output member. In turn, the inverse motion synthesis method of generalized mechanism configuration is established by reverse expansion of the kinematic analysis method. according to the specified motion type, performing reciprocal operation on the rotation quantity to obtain a constrained spiral system for outputting motion, further decomposing and reciprocal obtaining the moving spiral system of the branched chain of the generalized mechanism, obtaining the corresponding generalized component and the generalized motion pair set, forming the motion branched chain of the generalized mechanism, finally, a generalized mechanism configuration meeting the specified motion function is obtained through the combination of the chains of the moving branched chains. (3) A method for generating ground lead network of deployable antenna is proposed. Based on the theory of differential geometry geodesy, the measured curvature of the curve on the rotating paraboloid is analyzed, and the general geodynamic differential equation set of arbitrary two points on the curved surface is derived, and the numerical solution method of the equations is formed by combining the relaxation method and the Newton iteration method. In order to make the geosynchronous line on the parabolic curve to generate the geodetic clue net in mathematical sense according to the specified topological connection relation, the optimization model of the boundary node adjustment is established, and the dynamic boundary adjusting method of the geometric design of the ground thread net structure is formed. Compared with other cable net structures, the length of the wire net structure is short and the effective area is large. (4) Plane projection method and isotonic force design method of cable net pre-tensioning force design are studied. In this paper, the plane projection method of the pre-tensioning force design is studied for the parabolic surface cable net structure known by geometric coordinates. firstly, projecting it onto a caliber plane, establishing a pre-tensioning force optimization model of the plane cable net, calculating the plane tension distribution and reversely projecting the plane tension force to the parabolic curved surface to obtain the tension force of the parabolic curved surface cable net structure, and improving the pre-tension calculation efficiency of the cable net. For the cable net structure with unknown geometry and tension force, the isotension design method of cable net structure is put forward. Based on the fixed point theory for solving the nonlinear equations, the cable network tension is set to the same value, the force density is used as the iteration variable, and the iterative mathematical model of equal tensioning force is established according to the coupling relation between the cable net force density, the cable length and the tension force. The results show that the pre-tension force of the wire net structure can be calculated by the planar projection method, which can obtain better force uniformity and higher surface accuracy, while the isotonic force method can realize the full equality of the tension force inside the partial cable net. (5) Considering the uncertainty factors, the pre-tension design of the cable net is studied. By analyzing the influence of uncertain factors such as structure, material and environment on the tension force of cable net, the uncertainty factor is equivalent to the uncertainty of cable net tension. For the cable net structure known by the geometric coordinates, an anti-optimization strategy is introduced, and a tension optimization model of the uncertain cable net structure is established, and a cable net pre-tensioning force with minimal impact on the shape surface accuracy is obtained. For the cable net structure with unknown geometry and tension force, the concept of interval force density is put forward, the expression of the shape surface precision interval of uncertain cable net structure is deduced, and the interval force density optimization model of uncertain cable net structure is established. and the influence of the uncertainty factors on the accuracy of the cable net-shaped surface is effectively reduced.
【学位授予单位】：西安电子科技大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TN820

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