含不确定性区间参数的刚柔耦合多体系统动力学建模与分析

Based on the Absolute Coordinate Based method (Absolute Nodal Coordinate Formulation + Natural Coordinate Formulation) for studying the dynamics of deterministic rigid-flexible coupling multibody system, and using the interval arithmetic, affine arithmetic and computational continuum mechanics, the project aims at the accurate modeling and efficient computation algorithm for rigid-flexible coupling multibody system with uncertain interval parameters so as to reveal the effects of the uncertain interval parameters on the system dynamic responses. The results of numerical simulation and those of ground experiments will be validated and amended mutually. These researches can be considered as a new theoretical framework for the dynamics of the uncertain rigid-flexible coupling multibody system, and can develop the mutlibody system dynamics theory. The major studies of the project include: the accurate modeling method of the rigid-flexible coupling multibody system with uncertain interval parameters( for example, the anti-expansion description of the interval parameters and the interval finite element of the Absolute Nodal Coordinate Formulation), the efficient non-intrusive interval parallel algorithm for solving the equations of motions of the multibody system with uncertain interval parameters, the effect of the uncertain interval parameters (inertia parameters, material parameters, and joint clearance size) on the system's dynamic responses, and the verification experiments of the above modeling and computational algorithms. The project will focus on solving the following key problems: how to describe interval parameters without interval expanding, how to accurately and efficiently solving the interval equations of motion, and how to model and compute the dynamics of rigid-flexible coupling multibody system with uncertain uncertain joint clearance size.

基于确定性刚柔耦合多体系统动力学研究的绝对坐标方法（绝对节点坐标方法+自然坐标方法）并利用区间算术，仿射算术以及计算连续介质力学理论，深入研究含不确定性区间参数的刚柔耦合多体系统动力学精确建模与高效计算方法，揭示不确定性区间参数对系统动响应的影响规律，通过数值模拟和地面实验的相互引证和补充，形成一个不确定性刚柔耦合多体系统动力学研究新理论框架，发展多体系统动力学理论。主要研究内容包括：含区间不确定性参数的刚柔耦合多体系统动力学精确建模方法，如：区间参数的防扩张描述、绝对节点坐标区间有限单元等；不确定性刚柔耦合多体系统动力学方程的高效非侵入式区间并行算法；不确定性区间参数（如：惯量、材料参数、运动副间隙尺寸等）对系统动力学性态的影响分析；建模与计算方法的验证实验。重点解决如下关键问题：区间参数的防扩张表达问题；区间动力学方程的精确、高效求解问题；运动副间隙尺寸不确定性问题的建模与计算问题。

由于各种原因，如制造、测量误差、使用材料的不均匀性、环境变化等均会导致模型参数具有不确定性。研究表明：如果硬将这些不确定性的参数当成确定性参数来处理，是对真实物理模型的极大简化与粗糙化，有时会得出不合理或矛盾的结果。因此，发展预测具有不确定性参数的多柔体系统动力学建模与高效计算方法，对于实际系统的工程设计具有重要的指导意义。通过本项目研究发展了基于不确定性多柔体系统动力学理论，取得的主要研究成果为：提出求解含区间参数的多柔体系统动力学建模与分析方法；提出含有区间运动副间隙尺寸的多柔体系统动力学建模方法与分叉控制策略；搭建了柔性机械臂半物理仿真实验系统；发现了含有混合不确定性参数的多柔体系统动力学新现象；提出弹性流体润滑球铰的新模型, 为研究其不确定性参数影响奠定了基础；在国际著名期刊《Mechanism and Machine Theory》发表57页长综述论文。通过研究在著名期刊上共发表SCI文章9篇（包括2篇ESI高被引论文），中文期刊文章1篇，完成了课题拟定的研究内容，实现了研究目标。