基于线性图理论的可扩展单元复合仿真方法
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摘要
复杂的工程系统涉及多个学科领域,是由机械、液压、控制等多个子系统融合的有机整体,其性能是各学科领域技术的综合体现,如重载锻压操作机是典型的复杂机液耦合系统。针对这类多领域系统的仿真,统一的建模表达是核心问题之一。而现有的多领域统一建模方法,还存在以下不足:难以应用到矢量表达的机械系统;对于柔性体、间隙等精细模型的描述有很大限制;有的建模方法难于实现计算机程序自动建模。因此,发展和完善多领域统一建模的理论方法,对于解决复杂工程系统的整体性能仿真具有重要意义。
图论方法是多领域统一建模方法之一,本文基于线性图建模方法,研究和发展了一种模块化的多领域建模方法——可扩展单元线性图复合仿真方法,以实现跨能量域的统一模型表达。论文对可扩展单元线性图建模的基本原则、拓扑结构的封装和标准化组件的定义等方面进行研究。建立了通过端口连接,将单元线性图拼装成系统整体线性图模型的复合建模方法。借助Modelica语言开发了标准化组件库,利用Dymola平台进行求解计算。本文采用可扩展单元线性图统一表达了机械刚柔体动力学、含间隙机械动力学、机液耦合系统的仿真模型,并在重载锻压操作机的仿真计算中得以应用。
论文的主要研究成果与特色如下:
(1)将传统线性图理论与面向对象、模块化封装技术相结合,研究建立可扩展单元线性图模型,并且基于该模型实现复合建模方法:通过单元拓扑矩阵与变量矩阵的运算,自动获取组件的单元方程;再由连接方程联立所有单元方程,并通过耦合组件的方程实现跨学科域能量的交互,以形成整个多领域系统的状态方程。
(2)定义了转动矢量边线,使得机械转动与平动合并在同一个单元线性图中进行分析,从而简化建模过程。针对运动副组件的模块化,提出了机构功能点、开口边线、自封闭边线等概念,对传统线性图的工具元素进行了扩充;依据复杂机械组合件的独立性,把它们作为整体建立独立的模块,以取代传统环境中的基本元件连接建模。
(3)将线性图方法应用到间隙、含柔性构件的机构动力学分析建模中。引入间隙矢量边线以及与间隙相关的机构功能点,并结合的Dubowsky二状态机构间隙模型,创建含间隙机构的复合单元模型;通过定义柔性位移矢量边线、柔性转角矢量边线,以及运用牛顿欧拉方程和三次曲线拟合方法,分析表达了柔性组件的复合单元模型。
(4)定义了液压端口、液压功能点与液压矢量边线等图论要素,创建了液压组件的可扩展单元线性图,以及液压单元拓扑矩阵,并着重以图解形式表达了机液耦合系统,从而成功地把线性图建模理论拓展到含有复杂平面机构的机液系统。
(5)针对锻造操作机的结构和作业特点,运用可扩展单元线性图方法建立了该系统的复合模型,通过仿真计算模拟了操作机锻造顺应过程的受载状况,揭示了操作机缓冲锻件变形冲击载荷的作用规律。
理论分析和应用研表明,本文提出的基于可扩展单元线性图模型的复合建模方法在多领域统一建模理论上取得了一些进展,扩展了应用范围,提高了建模效率,为复杂的多领域系统整体性能仿真提供了有效的建模方法和工具。
The complicated engineering system will be involved in the multidiscipline fileds, including mechanical, hydraulic, and controlling system, etc., and is intergreted into an organic whole with those subsystems. Then the characteries of such system should be realized with the technologies belonged to every discipline field, i.e., the heaven forging manipulator is a typical mechano-hydraulic coupling system. It is a kernel question to realize modelling with an unified tool for simulating multidiscipline system. However, there are three main disadvantages in the achieved approaches of unified modelling now, and they are follows: it is difficult to express the mechanical multibody system described with vector variables; the moldeling range is limited in a large extent, such as joint clearences, flexible bar, etc. specific mold; some unified methods could not be realized automatically by computer.
Therefore, the development and complement of unified modelling method is a beneficial topic for simulating the whole functions of multidisciplinary system. Graph theory is one of the unified modelling methods. Based on the traditional linear graph theory, the paper proposed the Extensible Elementary Linear Graph method (EELG), which could realize composable simulation for multidiscipline system, and perform inter-energy domain expression in a unified way. We focused on the research of modelling rules, encapsulating topology, and standardizing multidisciplinary components, etc. By connecting the modules’port successively, the system linear graph will be obtained by assemblizing modules’elementary linear graphs. Some librarys of standard multidisciplinary components were developed with Modelica lauguage, and then the system equations will be solved on Dymola platform. With EELG method, it can be simulated that the system can include mechanical rigid and flexible dynamics, joint clearences dynamics, mechano-hydraulic coupling analysis, and so on.
The main thesis research results and characteristics are as follows:
(1) Combining the conventional linear graph theory with the technologies of modularization, encapsulation and object-oriented, we researched the extensible elementary linear graph and composable modeling based on the former. In the EELG framework, the component-level dynamic equations would be automatically generated by matrixes operation of topology matrixes and vector variables. Furthermore, the connection of variables between two components could be created by the relational expressions of linking two ports, and the inter-energy transformation can be realized by coupling components. Then the sate equations of the whole multidisciplinary system could be formed by collecting these terminal equations.
(2) By defining the rotation vector in modelling of mechanical members, one can analyze rotational and translational motion in a same elementary linear graph, and then both of the modelling process and fainal results became simpler. For kinematic pairs modularizing, the kinematic function vertices, opening edges and self-closed edges were introduced to the elementary linear graph, and enrich the symbols of the linear graph theory. The various combinations consisted of mechanical members were dealt with as a whole module separativly, instead of being assembled with many basic modules belonged to conventional package.
(3) We extended the linear graph theory to the dynamic analysis of kinematic clearances and flexible beams. With firstly introdcing clearance vectors edges and the kinematic function vertices related to clearance, we combined it with the Dubowsky classical models in two state motions, and created the elementary composable model of kinematic clearances. By originally defining the elastic rotational vectors edges, elastic transational vectors edges, we adopted Newton-Euler equations and cubic polynomial fitting curve, and analyzed the elastic component for expressing elementary composable model.
(4) With the definition of hydraulic ports, hydraulic function points, and hydraulic vectors edges, we established the elementary encapsulation linear graph of hydraulic members, and elementary topology vectors. We also solved the key issue of mechano-hydraulic coupling in the form of linear graph. Finally, we successfully applied the linear graph theory to mechano-hydraulic systems, which are the association of planar mechanism in rotation, general motion, or translation and hydraulic devices.
(5) According to the structure and working, we created the composable model for heaven forging manipulator with EELG method. By simulating the load condition in forging process, the relation of manipulator acting and deformation shock would be obtained.
By summarizing theorical analysis and application, it is validated that the proposed approach of the extensible elementary linear graph made some achievements in multidisciplinary composable simulation. And then the modelling range was enlarged, and the simulating efficient was improved. So the effective method and tool were provided for simulating multidisciplinary system.
图论方法是多领域统一建模方法之一,本文基于线性图建模方法,研究和发展了一种模块化的多领域建模方法——可扩展单元线性图复合仿真方法,以实现跨能量域的统一模型表达。论文对可扩展单元线性图建模的基本原则、拓扑结构的封装和标准化组件的定义等方面进行研究。建立了通过端口连接,将单元线性图拼装成系统整体线性图模型的复合建模方法。借助Modelica语言开发了标准化组件库,利用Dymola平台进行求解计算。本文采用可扩展单元线性图统一表达了机械刚柔体动力学、含间隙机械动力学、机液耦合系统的仿真模型,并在重载锻压操作机的仿真计算中得以应用。
论文的主要研究成果与特色如下:
(1)将传统线性图理论与面向对象、模块化封装技术相结合,研究建立可扩展单元线性图模型,并且基于该模型实现复合建模方法:通过单元拓扑矩阵与变量矩阵的运算,自动获取组件的单元方程;再由连接方程联立所有单元方程,并通过耦合组件的方程实现跨学科域能量的交互,以形成整个多领域系统的状态方程。
(2)定义了转动矢量边线,使得机械转动与平动合并在同一个单元线性图中进行分析,从而简化建模过程。针对运动副组件的模块化,提出了机构功能点、开口边线、自封闭边线等概念,对传统线性图的工具元素进行了扩充;依据复杂机械组合件的独立性,把它们作为整体建立独立的模块,以取代传统环境中的基本元件连接建模。
(3)将线性图方法应用到间隙、含柔性构件的机构动力学分析建模中。引入间隙矢量边线以及与间隙相关的机构功能点,并结合的Dubowsky二状态机构间隙模型,创建含间隙机构的复合单元模型;通过定义柔性位移矢量边线、柔性转角矢量边线,以及运用牛顿欧拉方程和三次曲线拟合方法,分析表达了柔性组件的复合单元模型。
(4)定义了液压端口、液压功能点与液压矢量边线等图论要素,创建了液压组件的可扩展单元线性图,以及液压单元拓扑矩阵,并着重以图解形式表达了机液耦合系统,从而成功地把线性图建模理论拓展到含有复杂平面机构的机液系统。
(5)针对锻造操作机的结构和作业特点,运用可扩展单元线性图方法建立了该系统的复合模型,通过仿真计算模拟了操作机锻造顺应过程的受载状况,揭示了操作机缓冲锻件变形冲击载荷的作用规律。
理论分析和应用研表明,本文提出的基于可扩展单元线性图模型的复合建模方法在多领域统一建模理论上取得了一些进展,扩展了应用范围,提高了建模效率,为复杂的多领域系统整体性能仿真提供了有效的建模方法和工具。
The complicated engineering system will be involved in the multidiscipline fileds, including mechanical, hydraulic, and controlling system, etc., and is intergreted into an organic whole with those subsystems. Then the characteries of such system should be realized with the technologies belonged to every discipline field, i.e., the heaven forging manipulator is a typical mechano-hydraulic coupling system. It is a kernel question to realize modelling with an unified tool for simulating multidiscipline system. However, there are three main disadvantages in the achieved approaches of unified modelling now, and they are follows: it is difficult to express the mechanical multibody system described with vector variables; the moldeling range is limited in a large extent, such as joint clearences, flexible bar, etc. specific mold; some unified methods could not be realized automatically by computer.
Therefore, the development and complement of unified modelling method is a beneficial topic for simulating the whole functions of multidisciplinary system. Graph theory is one of the unified modelling methods. Based on the traditional linear graph theory, the paper proposed the Extensible Elementary Linear Graph method (EELG), which could realize composable simulation for multidiscipline system, and perform inter-energy domain expression in a unified way. We focused on the research of modelling rules, encapsulating topology, and standardizing multidisciplinary components, etc. By connecting the modules’port successively, the system linear graph will be obtained by assemblizing modules’elementary linear graphs. Some librarys of standard multidisciplinary components were developed with Modelica lauguage, and then the system equations will be solved on Dymola platform. With EELG method, it can be simulated that the system can include mechanical rigid and flexible dynamics, joint clearences dynamics, mechano-hydraulic coupling analysis, and so on.
The main thesis research results and characteristics are as follows:
(1) Combining the conventional linear graph theory with the technologies of modularization, encapsulation and object-oriented, we researched the extensible elementary linear graph and composable modeling based on the former. In the EELG framework, the component-level dynamic equations would be automatically generated by matrixes operation of topology matrixes and vector variables. Furthermore, the connection of variables between two components could be created by the relational expressions of linking two ports, and the inter-energy transformation can be realized by coupling components. Then the sate equations of the whole multidisciplinary system could be formed by collecting these terminal equations.
(2) By defining the rotation vector in modelling of mechanical members, one can analyze rotational and translational motion in a same elementary linear graph, and then both of the modelling process and fainal results became simpler. For kinematic pairs modularizing, the kinematic function vertices, opening edges and self-closed edges were introduced to the elementary linear graph, and enrich the symbols of the linear graph theory. The various combinations consisted of mechanical members were dealt with as a whole module separativly, instead of being assembled with many basic modules belonged to conventional package.
(3) We extended the linear graph theory to the dynamic analysis of kinematic clearances and flexible beams. With firstly introdcing clearance vectors edges and the kinematic function vertices related to clearance, we combined it with the Dubowsky classical models in two state motions, and created the elementary composable model of kinematic clearances. By originally defining the elastic rotational vectors edges, elastic transational vectors edges, we adopted Newton-Euler equations and cubic polynomial fitting curve, and analyzed the elastic component for expressing elementary composable model.
(4) With the definition of hydraulic ports, hydraulic function points, and hydraulic vectors edges, we established the elementary encapsulation linear graph of hydraulic members, and elementary topology vectors. We also solved the key issue of mechano-hydraulic coupling in the form of linear graph. Finally, we successfully applied the linear graph theory to mechano-hydraulic systems, which are the association of planar mechanism in rotation, general motion, or translation and hydraulic devices.
(5) According to the structure and working, we created the composable model for heaven forging manipulator with EELG method. By simulating the load condition in forging process, the relation of manipulator acting and deformation shock would be obtained.
By summarizing theorical analysis and application, it is validated that the proposed approach of the extensible elementary linear graph made some achievements in multidisciplinary composable simulation. And then the modelling range was enlarged, and the simulating efficient was improved. So the effective method and tool were provided for simulating multidisciplinary system.
引文
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