基于泛函的制冷压缩机通用涡旋型线几何理论研究  

Research on Geometric Theories for Scroll Profiles Based on Functional Theory

作　　者：张贤明[1] 陈国强[1] 王立存[1,2] 牟瑛[1] 陈彬[1] 

机构地区：[1]重庆工商大学废油资源化技术与装备教育部工程研究中心,重庆400067 [2]西安交通大学流体机械及压缩机国家工程研究中心,西安710049

出　　处：《中国机械工程》2011年第3期265-268,共4页China Mechanical Engineering

基　　金：国家自然科学基金资助项目(50805149);中国博士后科学基金资助项目(20090450166);重庆市教委科技资助项目(KJZH08212);重庆市科技攻关重点项目(CSTC;2009AB3234)

摘　　要：在涡旋压缩机型线设计研究中,针对单一型线的限制性,提出以泛函理论为基础的新型涡旋型线设计思路,利用Taylor级数思想,得出通用涡旋型线的新形式,就涡旋型线的压缩行程容积、型线方程、曲率(半径)以及型线长度等基本几何性质,在笛卡尔坐标系下做了较详尽的阐述和推导,得出了坐标、向量和Taylor级数等三种形式下的涡旋型线的完整几何表达形式。给出算例予以说明,得到基于MATLAB的涡旋型线及其共扼型线图形。研究结果为研究基于泛函理论的通用涡旋压缩机型线设计理论奠定了基础,同时拓宽了涡旋压缩机型线设计的研究思路。In the design of scroll profiles,aiming at the restriction of single profile,we proposed new design ideas,which were based on functional theory.The Taylor series was used to draw a new expression of scroll profiles.Basic geometric properties were detailed exposition and derivation in the Cartesian coordinate system such as the compressed volume-based equation,the curvature（radius of curvature） and type length.The integrated geometric expression of scroll profiles was obtained in three forms of Coordinate,vector and the Taylor series.Some examples were given to explain,and graphics of the scroll profiles and its conjugate contour line which were based on MATLAB were obtained.Research results of geometric theories for scroll profiles based on functional theory are as basis and will expand related research ideas.

关 键 词：涡旋型线 泛函理论 行程容积 几何理论 共轭型线 

分 类 号：TH45[机械工程—机械制造及自动化]