基于Frenet标架的涡旋始端型线重构与几何特性分析

Reconstruction and Geometrical Property of Top Scroll Profile Based on Frenet Frame

针对当前型线研究中尚未建立表征修正型线和主体型线固有特性统一模型的问题,建立了基于Frenet标架曲率半径函数的涡旋型线通用方程,分别采用零次曲线和一次曲线对涡旋始端型线进行重构。定量分析了型线参数对涡旋始端齿厚的影响,构建了基于母线曲率半径函数方程的涡旋压缩腔面积几何模型,研究了曲率半径函数参数对面积特性的影响。结果表明:以曲率半径函数构成涡旋母线的连续性方程,在设计阶段即能得到完全啮合型线和完整涡旋齿廓,无需再进行齿端修正;一次曲线重构较大的设计自由度可以使其兼顾涡旋端部齿厚和内容积比要求,获得较零次曲线重构综合性能更为优越的涡旋齿。

According to the situation that there is no general model to express both main profile and modified top profile,a general integration equation expressed in tangential angle series was established for scroll profile.The start part of profile was reconstructed with zeroth-order curve and first-order curve,respectively.The influence of parameters of top profile on thickness of scroll tooth was analyzed quantitatively.Furthermore,the geometrical models of area of compression chamber were set up based on curvature radius function of base line.The effect of curvature radius parameters on area property was explored.This study showed that first-order curve construction of top scroll could achieve higher performance by improving volume ratio while maintain reasonable tooth strength.With continuity equation of scroll baseline in form of radius of curvature,a fully-meshed profile and complete tooth profile could be obtained in the stage of machine design,so that there was no need to modify top scroll in later stages.The results could be applied in the scroll profile design.