【作者】 王中双；

【导师】 陆念力；

【作者基本信息】 哈尔滨工业大学 ， 机械设计及理论， 2007， 博士

【摘要】 对于复杂的多体机械系统,许多学者相继提出了不同形式的以分析力学原理为基础的计算机辅助建模与仿真方法。但是,这些方法及软件多数仅限于单一能量形式的系统(例如,机械系统)的局部动力学,对于多种能量形式耦合的多体机械系统(例如:机、电、液、气及刚柔性耦合的系统),无法以统一的方式在计算机上自动地建立系统正、逆动力学方程及运动副约束反力方程,并进行有效的全局动态性能分析,使得分析结果与实际工况差别较大。另外,其仿真效率也有待于进一步地提高。上述问题已成为多种能量形式集成的多体机械系统的分析、研究及开发应用的根本障碍,使键合图理论在多能域耦合系统全局动力学的研究中占有重要的地位。本文的研究工作解决了基于键合图理论的多能域耦合多体系统全局动力学建模与仿真研究领域的一系列重要问题,为功能更加完备的动力学分析软件系统的研制提供有力的理论支持。这对进一步提高该类工作的自动化和实用化程度颇具意义,在车辆系统、数控机床、工程机械、机器人、一般机械、航天机械等领域具有广泛的应用前景。本文系统地阐述了基于键合图理论的多体系统耦合动力学建模与仿真方法。从能量守恒的基本原理出发,讨论了键合图中的多通口元件MTF所具有的的性质:只要知道其输入流和输出流间的关系,就可以通过简单的矩阵变换确定输入势和输出势间的关系,反之亦然。以此为基础阐述了建立平面多刚体系统、非惯性系平面多刚体系统、平面柔性多体系统、非惯性系平面柔性多体系统及空间多刚体系统键合图模型的一般方法及其动力学原理。多体系统构件间的运动几何约束,使其键合图模型产生微分因果环;构件上任意一点与其质心的非线性速度关系,使其键合图模型具有非线性结型结构。这给用传统标准的键合图法进行计算机自动建模与仿真带来了非常困难的代数问题。本文提出两种各具特色的解决策略:(1)在标准键合图理论框架下,将运动副约束反力视作未知外界势源,加在系统键合图模型相应的0-结处;(2)利用键合图基本元件间的等效转换关系,将标准键合图转换成回转键合图(Gyrobondgraph)。上述两种策略在多能域范围内,实现了对微分因果环及所产生的非线性结型结构的解耦,解决了其给系统全局耦合动力学计算机辅助建模与仿真所带来的代数困难。对于多体系统动力学逆问题,分别在标准键合图及回转键合图理论框架下,推导出不同形式的便于计算机自动生成的系统状态方程、运动副约束反力方程的统一公式。所述方法特别适用于多种能量形式并存的复杂系统的计算机自动建模与仿真。对于多体系统动力学正问题,分别在标准键合图及回转键合图理论框架下,严格推导出不同形式的便于计算机自动生成的多体系统驱动力矩(或驱动力)及运动副约束反力的统一公式。所述方法特别适用于多种能量形式并存的复杂系统的计算机辅助动态静力分析。同时,无需进行系统加速度分析,可以提高复杂多体系统动态静力分析的效率及可靠性。此外,基于MATLAB研制了相应的系统动态分析软件,实现了计算机自动建模与仿真。通过典型应用实例说明所述方法及软件的有效性。更多还原

【Abstract】 To complicated multibody systems, different kinds of computer aided modeling and simulation procedure based on analytic mechanics have been proposed. As a result, some representative system dynamic analysis softwares with powerful function are developed. But these procedures and softwares are only suitable for the partial dynamic analysis of systems with single energy domain such as mechanical system. For the system with the coupling of multi-energy domains, such as the systems with the coupling of machine, electricity, hydraulics, pneumatics, rigidity and flexibility, they can not be used for deriving the forward and inverse system dynamic equations and constraint force equations in a unified manner automatically on a computer. So that the global dynamic analysis of systems can not be carried out. These result in larger error in dynamic analysis. In addition to these, the simulation efficiency of system should be increased further. The above problems have become the ultimate obstacle of analysis, study, development and application for the multibody mechanical systems with the integration of multi-energy domains, and made bond graph theory become very important to the global dynamics of systems with multi-energy domains.By the research work in this dissertation,a series of important problems of global dynamic modelling and simulation for multibody systems with the coupling of multi-enegy domains based on bond graph theory are solved. As a result, the dynamic analysis software with more powerful function are supported theoretically, and the automatic and reliable level of this kind of work can be raised greatly. The research work in this dissertation can be widely used in the fields such as vehicle system, numerical control machine, engineering machine, robot, general machine,and space machine, etc.In this dissertation, the modeling and simulation procedure based on bond graph theory for the coupling dynamics of multibody systems is described systematically. From the viewpoint of enegy conservation, the properties of bond graph multiport element MTF are discussed. Thus knowledge of the flow vector relationship across the MTF dictates the effort vector relationship through a simple matrix transposition, and vice versa. Based on this, the generic procedures of modeling planar rigid multibody system, planar rigid multibody system in non-inertial coordinate system, planar flexible multibody system, planar flexible multibody system in non-inertial coordinate system and spatial multibody system by bond graphs and their dynamic principles are described.The kinematic and geometric constraints between bodies of multibody system result in differential causality loop, and the nonlinear velocity relationship between the mass center and an arbitrary point on a body leads to the nonlinear junction strcture. These bring very difficult algebraic problem for automatic modeling and simulation on a computer by traditional standard bond graph method. To solve this problem, two strategies with different characteristic are proposed in this dissertation. First, in the frame of standard bond graph theory, the constraint forces at joints can be considered as unknown effort sources and added to the corresponding 0-junctions of system bond graph model. Second, by means of the equivalent transformation between basic elements of bond graph, the standard bond graph can be transformed into gyrobondgraph. By means of the two above strategies, the decoupling to differential causality loop and nonlinear junction structure can be realized. As a result, the algebraic difficulty brought by them for computer aided modelling and simulation of system global coupling dynamics can be solved.For inverse dynamic problem of multibody system, the different form of unified formulae of system state-space equations and constraint force equations at joints are derived in the frame of bond graph and gyrobondgraph theory respectively, they are very suitable for the automatic modeling and simulation on a computer for complex multibody systems with multi-energy domains. For forward dynamic problem, the different form of unified formulae of balancing moments and constraint forces at joints are derived in the frame of bond graph and gyrobondgraph theory respectively, they are very suitable for computer aided static analysis for dynamic of complex multibody systems with multi-energy domains. By these procedure, the acceleration analysis of system is not needed, so that the efficiency and reliability of static analysis for dynamic of complex multibody systems is increased.In addition to above work, the corresponding system dynamic analysis software is developed based on MATLAB. As a result, the automatic dynamic modeling and simulation on a computer are realized. The validity of the procedures are illustrated by a lot of typical examples of application.更多还原