柔性多体系统非连续动力学模型降阶与仿真技术研究

The hybrid coordinate formulation is the most widely used in the modeling of the flexible multibody system dynamics, in which the motion of the flexible body is decomposed into the large overall motion of rigid body and the elastic deformation relative to the floating frame. The finite element method is commonly used to describe the element deformation of the complex flexible body, and the degree of freedom is very large. How to reduce the degree of freedom of the system, and to improve the computational efficiency of the dynamic simulation is a huge challenge of the current flexible multibody system dynamics. Therefore, the dynamic model reduction of flexible multibody systems is required to be investigated. A research strategy of the global simulation of flexible multibody system dynamics is proposed in this project. Firstly, rigid-flexible coupling dynamic mechanism is analyzed, and the advantages of Krylov subspace methods and Gram control matrix method are taken into account respectively. Then the accuracy, efficiency and validity of the mixture of the two methods are investigated to deal with the dynamic model reduction of flexible multibody systems from time domain and frequency domain. Secondly, the two method are proposed to deal with the model reduction technique of the non-continuous dynamic of flexible multibody systems, one uses the subarea model reduction method, in which the contact/impact flexible body is divided into collision region and non-collision region; another is investigated the model reduction technique of the non-continuous dynamic process of the system directly. Lastly, the validity of the propose method are explored according to experiments, and the effects of the model reduction on the global dynamic characters of flexible multibody systems are analyzed.

混合坐标法是柔性多体系统动力学最常用的建模方法，将柔性体的运动分解为大范围刚体运动和相对浮动基的弹性变形。复杂柔性体的弹性变形大多采用有限单元法描述，其自由度非常庞大。如何降低系统的自由度，提高动力学仿真的计算效率，是当前柔性多体系统动力学面临的一个巨大挑战。这就需要对柔性多体系统动力学模型降阶进行研究。本项目提出一种柔性多体系统动力学全局仿真的研究策略。首先分析刚柔耦合动力学机理，考虑Krylov子空间方法和Gram控制矩阵方法的优点，分别从时域和频域方面，研究二者混合方法处理柔性多体系统连续动力学模型降阶的精度、效率和有效性；其次提出两种策略研究非连续动力学模型降阶技术，一是将碰撞柔性体分为碰撞区和非碰撞区，采用分区模型降阶方法；二是系统整个非连续过程直接模型降阶技术研究。结合实验，探讨所提方法的有效性，并分析模型降阶对柔性多体系统动力学全局特性的影响。

复杂柔性体的弹性变形大多采用有限单元法描述，其自由度非常庞大。作大范围运动的柔性体，其大范围刚体运动和小幅弹性变形相互耦合，动力学行为更加复杂。如何降低系统的自由度，提高动力学仿真的计算效率，是当前柔性多体系统动力学面临的一个巨大挑战。这就需要对柔性多体系统动力学模型降阶进行研究。本项目提出一种柔性多体系统动力学全局仿真的研究策略。首先针对柔性体连续动力学问题，借鉴内平衡截断的思想，提出了一种基于Krylov子空间模型降阶方法的阶数控制方法，从而大幅度降低了柔性多体系统的自由度。接触碰撞是一种非连续的边界非线性问题，当前线性模型降阶技术无法直接应用。本项目基于柔性多体系统接触碰撞动力学的多变量方法，提出一种柔性多体系统非连续动力学分区模型降阶研究方法。将发生碰撞的柔性体分为碰撞区和非碰撞区。碰撞区采用全有限元模型以保留其局部非线性信息；而对非碰撞区采用模型降阶技术来降低其自由度。最后针对柔性体的碰撞问题，已经采用模态截断方法、模态价值分析方法、内平衡方法和Krylov子空间方法等进行模型降阶研究。并把降阶模型的仿真结果和实验结果计算的碰撞力进行对比研究，发现吻合较好，从而验证了本项目所提方法的正确性。表明所提方法能够有效的降低了系统的自由度，提高柔性多体系统动力学全局仿真的效率。