大变形空间柔顺机构的几何精确建模与高效仿真方法研究

Compliant mechanisms, which use the large deformation of flexure hinges and compliant rods to accomplish the transmission of motion and force, have a broad application prospect in many engineering fields, because of their many advantages, such as part-count reduction, reduced weight, no friction and wear, reduced assembly time, simplified manufacturing processes, and so on. At present, the researches on structure and kinematics of the planar compliant mechanism have gotten a lot of achievements. However, there are still few researches on spatial problems and dynamics, which has become a bottleneck restricting the development of compliant mechanisms. Based on the spatial compliant mechanism, a depth research on the theory of geometric modeling of the flexible hinge and complaint rod with large deformation and high efficient and stable numerical simulation method has been made in this research project. The main contents include:.1. A precise mechanical model of flexible hinge with large deformation, which accounts for deformation coupling and variable cross section characteristics, is proposed;.2. Based on the consideration of the initial bending, a spatial geometrically exact Euler-Bernoulli beam element for discretization the slender complaint rod is constructed;.3. According to the characteristics of the dynamic equation of compliant mechanism, a new method which can remove the high frequency of the equations and improve the simulation efficiency is proposed..This research subject has not only important application value in the field of compliant mechanism, but also an important academic value to the development of flexible multibody system dynamics theory.

柔顺机构主要依靠柔性铰链和柔顺杆件的大变形来传递运动和力，因其结构简单、质量轻、无摩擦磨损、容易制造和装配等优点而在众多工程领域应用前景广泛。目前，平面柔顺机构的结构学和运动学研究已取得大量成果，但在涉及空间问题和动力学方面的研究仍然开展较少，已成为制约柔顺机构发展的瓶颈。本课题以空间柔顺机构为背景，对大变形柔性铰链和柔顺杆件的几何精确建模理论及高效稳定数值仿真方法进行深入研究。主要内容包括：1. 提出一种计及大变形空间柔性铰链变形耦合与变截面特征的精确力学模型；2. 在考虑初始弯曲基础上，构造一种用于离散细长柔顺杆件的几何精确空间Euler-Bernoulli梁单元；3. 结合柔顺机构动力学方程特点，提出可从方程层面滤除系统高频、大幅提高仿真计算效率的新方法，并通过实验予以验证。本课题的研究不仅在柔顺机构相关工程领域有重要应用价值，也对柔性多体系统动力学理论的发展有着重要学术价值。

柔顺机构是一类利用弹性大变形传递运动、力和能量的新型机构形式，具有质量轻、易装配、无摩擦、精度高、可实现微型化等优点，在微机电系统、微纳制造等工程领域有着广泛的应用前景。柔顺杆件和柔性铰链的几何非线性问题是对此类机构进行分析与设计所面临的最主要困难。被广泛应用于柔顺机构运动学分析的伪刚体模型方法主要针对平面问题提出，且模型精度较低，不适于推广到空间柔顺机构的刚柔偶合动力学分析研究。本课题围绕空间柔顺机构的精确动力学建模理论与高效数值求解方法，结合柔性多体系统动力学领域最新研究成果开展了系统性研究。基于大转动矢量方法和绝对节点坐标方法，研究了空间大变形柔顺杆件的精确建模问题；并针对绝对节点坐标动力学方程的刚性问题，提出了从建模层面滤出系统高频分量的求解策略。项目执行期间所取得的主要研究成果可以归结如下：1. 针对大转动参数奇异性问题所引发的数值积分困难，提出了一种可有效避开转动矢量奇异点的角速度矢量数值积分方法；2. 基于绝对节点坐标方法框架，开发了适用于柔顺杆件和柔顺铰链建模的三角形板/壳单元；3. 在充分发掘绝对节点坐标单元几何描述优势基础上，针对小变形问题提出了一种适用于包含初始复杂几何构型梁类部件建模的绝对节点坐标-浮动坐标梁单元；4. 考察了绝对节点坐标梁单元和几何精确梁单元对于空间柔顺机构动力学问题的适用性；5. 基于在模型层面滤出系统高频分量的思想，提出了绝对节点坐标方法的模型降噪列式，大幅提高了系统动力学方程的仿真求解效率。本项目的研究成果为空间柔顺机构动力学特性分析、疲劳寿命计算和机构优化设计提供了有力计算工具，同时也丰富和发展了大变形柔性多体系统建模和仿真计算理论。