串联机械系统运动方案设计的状态空间理论与方法的研究
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摘要
本论文在国家自然科学基金(No．50075012，50275016)的资助下，结合工程设计实际，对机器创新方案的机构与结构并行设计理论与方法进行了研究。
本文首先从运动变换的角度定义了广义单自由度机械运动基本变换单元，归纳总结了常用的基本变换单元。其次，在基本坐标系中，通过建立状态方程来描述基本变换单元输入、输出特征矢量(统称状态特征矢量)及状态变换矩阵之间的相互关系。其中，前者按照输入输出端的不同运动类型、速度矢量的大小及方向特征，以6维矢量形式表示；而后者作为输入、输出特征矢量之间的纽带，描述了基本变换单元的功能与特征。再次，阐述了状态变换矩阵的形成过程，通过泰勒级数展开，提取其非零元素的特征，并按照传递特征值对基本变换单元加以分类，归纳了状态变换矩阵的性质。为了解决方案设计过程中知识表达问题，建立了基本变换单元的状态变换矩阵信息存储模型。本文接着引入状态空间的概念，并在状态空间中进一步讨论并获得了基本变换单元特征矢量对及其集合的性质。基于状态空间理论，本文深入研究了机械运动基本变换单元的组合方法。获得状态变换矩阵在基本坐标系及系统坐标系下的转换规律、机械系统的传递函数特征值及其性质。按照状态空间中对偶特征矢量的运算规则，在已知系统的输入输出特征矢量的情况下，通过数学推导求解，将形成的系统状态变换矩阵分解为多个状态变换矩阵的乘积，再通过各状态变换矩阵到数据库中寻找相应的基本变换单元集合，然后进行按序组合，进而从理论上获得相应的方案设计可行解。
根据建立的数学模型，本文提出了相应的按位存储数据结构以及树型递归分解算法，实现了状态变换矩阵(包括类型、方向及变换特征)的自动分解。同时，结合关系型数据库系统对运动方案设计知识库的组织管理(包括基本变换单元信息的存储、提取操作及数据流间的复杂关系建立)，提出了方案设计的综合求解算法，实现了在计算机上进行方案设计的可计算自动求解。
本文对机械运动设计方案的可视化方法进行了探索，实现了基于Solidworks特征造型系统的寄生式三维模型表达目的。此外，对方案设计获得的诸多可行解优选问题，还运用模糊综合评价方法进行了简单评价，明确了针对轻工业服装机械行业所必须考虑的评价因素。
本文最后综述并实现了机械运动方案设计系统的开发。概括了方案设计系统的体系结构，分析了数据库的组织结构，描述了系统的实现功能。将本文提
出的状态变换矩阵方法应用于生产实际中，进行多个设计实例的可计算自动求
解，实践表明该方法可行、有效。
The approaches of conceptual design of mechanical system, based on state space model, is researched for mechanism and machine creative scheme in the paper, which is supported by National Natural Science Foundation of China (No.50075012 and 50275016).
At first, a generalized basic mechanical unit with single-degree of freedom is defined from the point of view of motion transformation. The input and output state vectors are defined, which are a 6×1 column vector including motion types, the magnitude and spatial orientation, respectively. The state matrices (SMs) can be deduced by vectors operation, that is, the output state vectors multiplied by the input state vectors. And then, a state equation is set up by the relationship among the input and output characteristic vectors as well as the state matrices (SMs). The non-zero element in the SMs characteristic is taken according to Taylor series expansion, which is a transfer function of the basic mechanical unit. The properties of the SMs are discussed and 44 basic mechanical units are listed. The storage models of the basic mechanical units are presented to describe the vast sources and types of knowledge at the conceptual design stage. And a database diagram is created to manage the associated data relations. As a result, the concept of state space for conceptual design of mechanical system is presented, which is new to the literature, based on the set of all state vectors. Meanwhile, the properties of state vectors, which are vectors addition, constant multiplying, reversible driving, zero vectors, are discussed in state space.
Secondly, the dual-vector is introduced to descript the essential relation among the input and output characteristic vectors as well as SMs. The coordinate transformation rules, the combination characteristic of the transfer function are discussed. The solution procedure of series mechanical system is deduced by applying dual-vector addition and matrix multiplication. And the mathematical models are obtained. The SMs representation scheme allows a given specification to be decomposed into an ordered sequence of sub-SMs, and attempts to match each sub-SMs with one or more stored basic mechanical units. Thus, the possible solutions are generated.
The data structures, the decomposing and the synthesis algorithm are presented according to the established mathematical models and the data base system. Thereby, for a given design specification, the possible solutions can be successfully obtained in computer by means of state space method presented in this paper.
In additional, the 3-dimension assembly models based on SolidWorks system are explored to aid designers to conceive the schemes by decomposing direction matrices. Evaluation method is also discussed in order to select the optimal one from the possible solutions. The factors of
evaluation involved in the sewing machine industry are discussed. And the fuzzy synthetical decision method is adopted in the paper.
At last, a computer program, based on state space method, the algorithm and database techniques, is implemented. The whole design flow is analyzed, the database structure is described and the system function is introduced. Some practical examples are given to show the capabilities of the approach in a series mechanical system.
本文首先从运动变换的角度定义了广义单自由度机械运动基本变换单元，归纳总结了常用的基本变换单元。其次，在基本坐标系中，通过建立状态方程来描述基本变换单元输入、输出特征矢量(统称状态特征矢量)及状态变换矩阵之间的相互关系。其中，前者按照输入输出端的不同运动类型、速度矢量的大小及方向特征，以6维矢量形式表示；而后者作为输入、输出特征矢量之间的纽带，描述了基本变换单元的功能与特征。再次，阐述了状态变换矩阵的形成过程，通过泰勒级数展开，提取其非零元素的特征，并按照传递特征值对基本变换单元加以分类，归纳了状态变换矩阵的性质。为了解决方案设计过程中知识表达问题，建立了基本变换单元的状态变换矩阵信息存储模型。本文接着引入状态空间的概念，并在状态空间中进一步讨论并获得了基本变换单元特征矢量对及其集合的性质。基于状态空间理论，本文深入研究了机械运动基本变换单元的组合方法。获得状态变换矩阵在基本坐标系及系统坐标系下的转换规律、机械系统的传递函数特征值及其性质。按照状态空间中对偶特征矢量的运算规则，在已知系统的输入输出特征矢量的情况下，通过数学推导求解，将形成的系统状态变换矩阵分解为多个状态变换矩阵的乘积，再通过各状态变换矩阵到数据库中寻找相应的基本变换单元集合，然后进行按序组合，进而从理论上获得相应的方案设计可行解。
根据建立的数学模型，本文提出了相应的按位存储数据结构以及树型递归分解算法，实现了状态变换矩阵(包括类型、方向及变换特征)的自动分解。同时，结合关系型数据库系统对运动方案设计知识库的组织管理(包括基本变换单元信息的存储、提取操作及数据流间的复杂关系建立)，提出了方案设计的综合求解算法，实现了在计算机上进行方案设计的可计算自动求解。
本文对机械运动设计方案的可视化方法进行了探索，实现了基于Solidworks特征造型系统的寄生式三维模型表达目的。此外，对方案设计获得的诸多可行解优选问题，还运用模糊综合评价方法进行了简单评价，明确了针对轻工业服装机械行业所必须考虑的评价因素。
本文最后综述并实现了机械运动方案设计系统的开发。概括了方案设计系统的体系结构，分析了数据库的组织结构，描述了系统的实现功能。将本文提
出的状态变换矩阵方法应用于生产实际中，进行多个设计实例的可计算自动求
解，实践表明该方法可行、有效。
The approaches of conceptual design of mechanical system, based on state space model, is researched for mechanism and machine creative scheme in the paper, which is supported by National Natural Science Foundation of China (No.50075012 and 50275016).
At first, a generalized basic mechanical unit with single-degree of freedom is defined from the point of view of motion transformation. The input and output state vectors are defined, which are a 6×1 column vector including motion types, the magnitude and spatial orientation, respectively. The state matrices (SMs) can be deduced by vectors operation, that is, the output state vectors multiplied by the input state vectors. And then, a state equation is set up by the relationship among the input and output characteristic vectors as well as the state matrices (SMs). The non-zero element in the SMs characteristic is taken according to Taylor series expansion, which is a transfer function of the basic mechanical unit. The properties of the SMs are discussed and 44 basic mechanical units are listed. The storage models of the basic mechanical units are presented to describe the vast sources and types of knowledge at the conceptual design stage. And a database diagram is created to manage the associated data relations. As a result, the concept of state space for conceptual design of mechanical system is presented, which is new to the literature, based on the set of all state vectors. Meanwhile, the properties of state vectors, which are vectors addition, constant multiplying, reversible driving, zero vectors, are discussed in state space.
Secondly, the dual-vector is introduced to descript the essential relation among the input and output characteristic vectors as well as SMs. The coordinate transformation rules, the combination characteristic of the transfer function are discussed. The solution procedure of series mechanical system is deduced by applying dual-vector addition and matrix multiplication. And the mathematical models are obtained. The SMs representation scheme allows a given specification to be decomposed into an ordered sequence of sub-SMs, and attempts to match each sub-SMs with one or more stored basic mechanical units. Thus, the possible solutions are generated.
The data structures, the decomposing and the synthesis algorithm are presented according to the established mathematical models and the data base system. Thereby, for a given design specification, the possible solutions can be successfully obtained in computer by means of state space method presented in this paper.
In additional, the 3-dimension assembly models based on SolidWorks system are explored to aid designers to conceive the schemes by decomposing direction matrices. Evaluation method is also discussed in order to select the optimal one from the possible solutions. The factors of
evaluation involved in the sewing machine industry are discussed. And the fuzzy synthetical decision method is adopted in the paper.
At last, a computer program, based on state space method, the algorithm and database techniques, is implemented. The whole design flow is analyzed, the database structure is described and the system function is introduced. Some practical examples are given to show the capabilities of the approach in a series mechanical system.
引文
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