中文摘要：

在涡旋压缩机涡旋型线设计研究中，针对单一涡旋型线受其固定数学模型固有特性的限制，并研究出通用涡旋型线的共轭啮合特征型线，分析平面曲线的啮合理论，研究共轭啮合型线的解析包络原理。对可取函数类基于泛函的涡旋型线的共轭啮合特性进行研究，建立基于泛函的涡旋型线的笛卡尔坐标表达式及其共轭型线的啮合条件，推导出基于泛函的涡旋型线的共轭啮合型线，动静涡旋型线特征几何中心距为r。根据通用涡旋型线的型线组合特性及级数系数收敛原则，给出具体算例，得到基于Matlab的涡旋型线及其共轭型线图形。基于泛函的涡旋型线共轭啮合研究为采用泛函理论的涡旋压型线研究提供了机会，拓宽了涡旋压缩机型线设计理论与方法研究的思路。

英文摘要：

Abstract： In the design study of scroll profiles, aiming at the restriction of single profile and its ameliorate or parameter op- timization presently, for studying conjugation meshing scroll profiles of the general scroll profiles, the meshing theory of planar curve is analyzed and the analysis envelope method to seek conjugation meshing profiles is studied. The unified gen- eral functional equation of scroll profiles represents the admis- sible function scrolls, the conjugation meshing characteristic of which is studied. Then the meshing condition of conjugation profiles and the Cartesian coordinate expression of general functional integrate scroll profiles is educed. It is also general functional scroll profiles. Distance between characteristic geo- metric centers is r. Based on the combination characteristics of the general scroll profiles the example is given. And the plan of the scroll profiles and its conjugation profiles is gained based on the Matlab technology. The conjugation profiles of general func- tional integrate scrolls is obtained finally. It offers an opportunity for studying scrolls adopting the fimctional theory and the design theory and the method study of scrolls profiles is widen.