泛函多维空间理论在动态设计中的应用  

NORM FUNCTIONAL MULTIDIMENSIONAL SPACE THEORY USED FOR DYNAMIC MECHANICAL DESIGN

作　　者：蒋勇敏[1] 许明恒[1] 

机构地区：[1]西南交通大学机械工程学院,成都610031

出　　处：《机械工程学报》2006年第B05期165-169,共5页Journal of Mechanical Engineering

基　　金：四川省教育厅自然科学基金重点资助项目(2004A163)。

摘　　要：多于三维空间的动态设计问题是机械设计的难题,原因是对多维空间没有恰当的认识方法和分析方法,因此,动态设计需要更抽象、更全面的分析方法。泛函空间理论是成熟的多维空间数学理论,是多维空间分析和表达的有力工具。用泛函处理动态设计问题,如多变量系统的描述,关系建模和优化处理等。物理意义完全不同的变量系统可能具有相同的范函结构,便于简化复杂问题的抽象和分析;设计内容是根据物理本质建模和对模型的分析计算,而不是传统的几何分析;设计方法不是类比,而是精确计算;设计结果是系统范函最优解。离心调速系统是一个典型的机械动力系统,根据动态要求,建立和求解该系统的能量泛函,完成系统的机械结构设计。实例表明:泛函设计方法是可行的、数字化的动态设计方法。A dynamic design method using functional analysis is described. Lacking of proper realization and analyses method, it is difficult to deal with dynamic design problem in more than three-dimensional space. Therefore, more abstractive and comprehensive design method is needed to solve the problem. Functional analysis theory is a mature hyperspace mathematics theory. It is a potent tool for multidimensional space analysis and expression. It can be used to solve the dynamic design problem such as multivariate system description, relation model establishment, optimization treatment etc. The variables which have dissimilar physics signification may have similar norm functional expression, so it is benefit for the simplification and abstract of complicated question. The content of design is to establish the model and to analyse the model. The way of design is rigorous calculation rather than geometric analogy, the result of design is optimal solution of system functional. Centrifugal velocity modulation system is a typical mechanical dynamical system. According to the dynamic requirement, the energy norm function of the system has been built-up and calculated. In this way, the mechanical structure design be worked out. The results demonstrate that this design method is feasible and accurate digitizing dynamic design methods.

关 键 词：多维空间 路径规划 动态设计 泛函空间 

分 类 号：TH122[机械工程—机械设计及理论] TH123.1