通用涡旋型线理论研究与深入分析

涡旋压缩机型线设计研究中,对于任意简单平滑规则曲线至少二阶连续可导,此处型线采用极角、瞬时曲率中心和曲率半径来表征更为简单,基于此建立了涡旋型线啮合理论。针对通用涡旋型线设计存在的问题,深入研究了涡旋型线啮合理论、共轭型线节线、通用控制方程、通用方程和行程容积、内容积比、型线长度与曲率半径等关键几何公式。总结了通用涡旋型线,涡旋型线节线方程和通用型线控制方程等理论,分析了现有通用型线的一些缺陷及其通用型线控制方程理论的片面性。提出了基于泛函理论的通用涡旋型线统一数学模型理论,利用泛函理论,建立能表征任意几何形状且能集成现有各种涡旋型线数学模型的可取曲线类涡旋型线广义泛函方程, 进而可研究涡旋型线广义泛函的光滑性、一次变分二次变分及高次变分等解析特性,并利用变分法理论分析其泛函极值条件。为在不同阶空间利用泛函理论研究涡旋型线提供了机会,为通用涡旋型线研究拓宽了思路。

STUDY AND PROFOUND ANALYSIS ON GENERAL PROFILE THEORY OF SCROLLS

In the mechanism study of scroll profile, for the continuity of its derivatives is at least up to the second order for a regular curve, the scroll profile is expressed in terms of its instantaneous center of curvature, radius of curvature and polar angle. The engagement theory of scroll profiles is established under this situation. Aiming at existed problems of general profile designed for scrolls, it carries through deep study and analysis on scroll profile engagement theory, conjugate profile pitch line theory, general control equation and general equation. And the geometry equation of stroke volume, inner volume ratio, length of profile and radius of curvature etc. are also studied. Summarization on general scroll profile, conjugate profile pitch line and its control equation are given. The shortage of general scroll profile in existence and the theoretic one sidedness of control equation are analyzed. A new methodology based on functional theory to study scroll profile that widening method for general profile design of scroll compressor is developed. Using functional analysis theory, general functional equation that can represent random geometry and integrate all mathematical models of scroll profile in exiting is established.Then using variation method and functional extreme condition, the analytic character of gliding property, first variation, second variation and high order variation, etc. can be studied. It offers an opportunity for studying scroll profile theory adopting functional theory and analyzing scroll profile in different ranks metric space.