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.

scroll, functional theory, volume, geometry theory, conjugation meshing profile

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。

涡旋型线, 泛函理论, 行程容积, 几何理论, 共轭型线