绳索驱动多体系统动力学建模与求解方法研究

In multibody systems driven by ropes, motion of bodies can be controlled by their embedded pulley-rope systems. Such systems have being applied in many industrial mechanisms such as large-scale space deployable structures, aircraft arresting systems, robots and hoisting machines. The rapid development of modern industry has higher and higher demands for their performance. However, the researches on dynamics of rope-pulley mechanisms are not mature enough to provide solid theoretical support for satisfying such high demands. In current methods, ropes are modeled by finite elements whose nodes are fixed at material points on ropes, and forces of contacts between pulleys and ropes are calculated by virtue of the traditional contact-impact force model. As a result, constraints of the shape of the rope contacting with a pulley are always be violated, and the obtained contact forces are not in accord with the real ones. In this project, a new kind of rope element whose nodes are no longer fixed at material points will be studied in order to remove these obstacles. A new method of modeling multibody systems driven by ropes is to be presented, after deep studies on the behaviors of contacts between pulleys and ropes. A large-scale deployable antenna system will be numerically simulated, to reveal the insight reasons behind the possible malfunction during the deploying process, as well as to improve the design of such mechanical systems.

绳索驱动多体系统是一类可利用内嵌于其中的滑轮绳索控制物体运动的多体系统，广泛应用于大型空间可展结构、飞机拦阻系统、机器人、起重机等机械系统中。很多领域对这类机械系统的精确性和可靠性提出越来越高的要求。但现有方法还不足以为实现这些高性能指标提供足够的理论支撑。绝大部分现有方法采用节点与绳索物质点固结的绳索单元描述绳索的运动，采用传统的接触碰撞模型计算滑轮绳索间的接触力。它们都无法精确满足接触段绳索的形状约束，也不能高精度地求解相应的接触力。本项目拟构造一种允许节点物质坐标变化的空间描述绳索单元。利用这种单元可精确满足绳索的形状约束，并将接触力归结为形状约束反力。在此基础上，通过对滑轮绳索间接触状态的深入研究，提出一种高效稳定的绳索驱动多体系统动力学分析方法；利用所得结果对大型周边桁架式可展天线系统进行动力学仿真，深入研究天线展开过程中的故障产生机理，为改进这些系统的设计提供技术储备。

滑轮绳索系统中，描述系统运动的关键点为绳索与滑轮接触边界点（出入绳点），这些关键点是在绳索中不断移动的空间点，它们不与绳索上物质点固结。传统有限元法中单元节点都是与物质点固结的点，引起滑轮-绳索系统建模和求解的诸多困难。课题组通过对滑轮绳索系统的深入研究，提出了一种单元节点不与物质点固结的有限元方法，具体构造了动态节点绳索单元、动态节点梁单元。这类单元的节点可在介质中移动，更能体现系统的特性。在解决具有动态系统边界、移动载荷等问题时具有明显优势。在此基础上，提出了滑轮-绳索系统动力学建模与求解方法，与传统方法相比，所提方法所需单元较少、不需要绳索-滑轮间的接触碰撞分析、避免了传统方法经常遇到的数值发散等问题、可高精度地求解绳索出入绳点的位置、弧长坐标、绳索在运动过程中形状和所受拉力，以及整个系统在绳索作用下的位置、速度、加速度等重要物理量的变化。所提方法可用于带有滑轮绳索系统的机械系统，具有十分广阔的应用前景。