具有时变模态的多级柔性伸缩臂滑动耦合动力学建模方法研究

With the increment of telescopic boom number, the decrease of component rigidity and the growth of payload, the conflicts among rapidity, stability and reliability of the boom motion become more and more serious. To deal with the problem, this study focuses on the theoretical investigation and modeling analysis on the dynamic feature of the boom extending and retracting process. The methodology for modeling the two-stage flexible telescopic boom coupling with double sliding joints is investigated. The differential and algebraic equations of the specific model are then derived and obtained. In view of the extensive degrees of freedom and the difficulties in numerical solution of the differential and algebraic equations, the component mode synthesis method suiting for the specific flexible multi-body system is explored and studied to reduce the dimensions of the aforementioned equations. The mathematical model for the typical motions of the telescopic boom is constructed and the numerical calculation for the motion equations is implemented. The virtual prototype model of the multiple-stage telescopic mechanism is created on the simulation software platform. The corresponding typical motions of the mechanism are calculated by the simulation model and the results are mutually verified with those obtained by the theoretical model. The modeling theory and methodology for the telescopic boom are verified by the testing platform of a compact telescopic crane with multi-stage telescopic booms. The achievement of the study can offer theoretical references and methodological support for the dynamic design and analysis of the system with time-varying mode and sliding boundary, such as the operating system of space station, the automatic transferring system of mechanic arm and the launching system of rocket missile.

随着大型空间站和转载机器人机械伸缩臂的臂节数增多、结构件柔性化与负载质量增加，其运动快速性、稳定性与安全性之间的矛盾越发突出。为解决该问题，本项目基于绝对节点坐标法，对机械臂伸缩过程动力学特性开展理论研究与建模分析。研究双滑移铰-双柔性伸缩臂的动力学建模方法，推导系统的微分-代数方程组。针对方程自由度多、数值求解困难的问题，探索适于该多柔体系统的模态综合理论，实现对方程自由度的压缩。构建多级伸缩臂典型运动过程的数学模型，并进行数值计算。基于软件仿真平台，组建多级伸缩臂机构的虚拟样机模型，实现对机构典型运动过程的仿真验算。利用小型起重机多级伸缩臂试验平台，实现对建模理论及方法的试验验证。本项目的研究成果可为大型空间站操作系统、机械臂自动转载系统、火箭弹发射系统等具有“变模态、动边界”类系统的动力学设计和分析提供理论依据与方法支持。

针对转载机器人机械伸缩臂的臂节数增多、结构件柔性化与负载质量增加，其运动快速性、稳定性与安全性之间的矛盾越发突出的问题。本项目基于绝对节点坐标法，对机械臂伸缩过程动力学特性开展理论研究、建模分析及试验验证等工作。主要研究内容如下：.（1）从若丹速度变分形式的单个未约束柔性梁单元动力学变分方程出发，利用速度约束方程的速度变更关系，将拉格朗日乘子引入未约束单元的动力学方程，推导出了基于若丹速度变分原理的第一类拉格朗日方程形式的柔性多体约束系统动力学方程的广义表达式。.（2）提出了非光滑滑移铰的建模方法。定义了低维物理空间与高维向量空间之间的映射变换矩阵，实现了从广义约束力到实际约束力不同维数力向量之间的映射变换；利用映射变换矩阵和相对速度变换矩阵，推导了非光滑滑移铰广义摩擦力的一般表达式，从而将摩擦力引入滑移铰模型。.（3）基于浮动节点坐标法的小变形弹性体建模理论，结合三维实体建模软件Pro/E、有限元分析软件ANSYS和动力学分析软件ADAMS，建立了多级柔性伸缩臂动力学仿真模型。通过Pro/E构建了起重机和伸缩臂实体模型，将伸缩臂视为弹性体，通过ANSYS生成了弹性体的模态中性文件，导入ADAMS后生成柔性体，并在柔性伸缩臂与滑块之间添加碰撞接触及摩擦力，仿真分析了臂节接触及摩擦力的影响及伸缩端的动学响应。.（4）以HIAB033T-2型轻质折臂吊为试验平台，针对其机械、液压与控制系统进行了改造，以开展电液比例位置闭环控制试验、电液比例速度闭环控制试验与电液比例力闭环控制试验，充分验证本项目所提出的多级柔性伸缩臂伸缩过程动力学模型的正确性，以及所构建的多级柔性伸缩臂伸缩过程虚拟样机模型的正确性。.本项目的研究成果可为大型空间站操作系统、机械臂自动转载系统、火箭弹发射系统等具有“时变结构、滑动边界、非光滑约束”类系统的动力学设计和分析提供理论依据与方法支持。