考虑柔索垂度影响的索支撑系统静刚度

Static Stiffness of a Cable-supporting System with the Cable Sag Effects Considered

大射电望远镜的索支撑系统由于工作空间巨大,刚度分析时必须考虑柔索垂度的影响。为此,基于弹性悬链线方程推导出柔索的索端张力与索长之间的关系,建立索支撑系统的静力学模型。在此基础上,根据索端张力与舱体位移之间的非线性关系推导出作用在舱体上的柔索合力与舱体位移之间的增量关系,从而获得系统静刚度矩阵的解析表达式。利用数值算例证明分析方法的正确性,在算例中给出索支撑系统在某点处的刚度矩阵及其在工作空间内的刚度分布。分析结果表明索支撑系统绕舱体中轴的转动刚度相对薄弱。

Because of the huge workspace of the cable-supporting system for the large radio telescope,sag of cables needs to be considered in the stiffness analysis. Therefore,the relationship between cable end tension and cable length is deduced by using elastic catenary equation. The static model of the cable-supporting system is constructed with this relationship. Based on the nonlinear relationship between the cable end tension and the cabin displacement,the incremental expression of the resultant force on the cabin exerted by cables is formulated in terms of the cabin displacement. Then the analytical expression of the static stiffness matrix is obtained. Numerical examples are presented to validate the method. Stiffness matrix is reported at a point and the stiffness distribution is depicted within the workspace. The results show that the rotational stiffness about the cabin central axis is relatively weak.