基于索力优化的FAST柔索牵引并联机构的静力学分析

EQUILIBRIUM ANALYSIS OF FAST ROPE-DRIVE PARALLEL MANIPULATOR BASED ON ROPE FORCE OPTIMIZATION

FAST望远镜的馈源支撑是一个跨度巨大的柔索牵引并联机构,其中可承载用于收集射电波信号的馈源接收机的馈源舱由六根并联的支撑钢索悬挂于空中,并随着6索的协调收/放可在空中大范围缓慢运动。由于支撑钢索的截面尺寸较大,在机构平衡状态下其自重不能忽略。其中一部分钢索还需要悬挂入舱的动力电缆和通讯光缆,因此馈源舱运动范围、馈源舱姿态、各索的张力和索的几何构形均存在着复杂的耦合关系。该文建立了支撑钢索和馈源舱的静力平衡方程,通过引入各索张力均衡分配的优化原则,对舱静力平衡方程进行了优化求解,并获得了各索张力和馈源舱姿态角在轨迹球冠面内的优化计算结果。从各索张力的优化计算结果可推导出各索张力的最大值、最小值和变化趋势。基于馈源舱姿态角的优化计算结果,并结合馈源接收机在焦点位置所必须达到的姿态角控制要求,估算了舱内的AB转轴机构所需要的最小姿态角补偿范围。该文最后分析了支撑塔高度和馈源舱的重心位置对于索张力和馈源舱姿态角在轨迹球冠面内的优化分布计算结果的影响。分析结果表明最大索张力对于支撑塔高度较为敏感且成反比,而舱姿态角对馈源舱的重心位置较为敏感。这两项重要参数均应在未来FAST的设计中进行优化。

The feed support of the FAST telescope is a rope-driven parallel manipulator with huge spans.In such mechanism,an airborne focus cabin carrying the feed receiver searching for radio waves is suspended by six parallel steel ropes and can move slowly in a large range,a spherical focus surface,through the continuously coordinated coiling/uncoiling of the six ropes.Because of the large sectional areas of the steel ropes,the gravity cannot be neglected in the equilibrium analysis of the mechanism.Moreover the power supply cables and optical communication cables also have to be suspended on the ropes for the electronic equipments in the cabin.So there are quite complicate interactions among the workspace of the parallel manipulator,how the airborne focus cabin poses itself,the rope forces and rope geometries.The equilibrium equations are formulated in the paper for the steel ropes and the focus cabin respectively.The equations of the focus cabin are solved by introducing an optimization principle of intending a uniform allocation among the six rope forces.As result,the optimal rope forces and the optimal pose of the cabin are computed along the whole focus surface.The maximal and minimal rope forces are therefore deduced from the optimization solutions of the six rope forces as well as their variations in the focus surface.Combining the optimization solutions of the cabin pose with the required tilt of the cabin at a focus point,we calculate the minimal workspace of the AB rotator,a tilt compensator in the focus cabin.Finally,the tower height and the gravity center of the cabin are studied on how their changes influence the optimization solutions of the rope forces and cabin tilt.The investigation proves that the maximal rope force is sensitive and inversely proportional to the tower height,whereas the cabin tilt is sensitive to gravity center of the cabin.They both should be optimized in the future design of the FAST telescope.