利用Frenet活动标架构建涡旋压缩机型线的新方法

A new method of constructing scroll compressor profile using frenet moving frame

摘要:

针对涡旋齿型线设计中缺乏简洁有效的通用几何模型、在实际工程应用中未考虑型线几何性能倾向性的问题,提出一种利用Frenet活动标架构建涡旋齿型线的新方法. 首先在构成涡旋齿型线的曲线上依附一个Frenet活动标架,让该标架取代固定的笛卡尔直角坐标系. 然后利用平面曲线的曲率和Frenet活动标架表示涡旋齿型线的内在特征,建立以曲率和Frenet活动标架为参数的涡旋齿型线的通用几何模型. 最后建立了控制系数与涡旋齿型线几何性能的映射关系,在此基础上,以考虑涡旋压缩机工程应用为设计目标,在涡盘圆周大径和涡旋齿齿厚分别确定的条件下,利用映射关系,依据设计需求的倾向性来优选出一系列控制系数,进而构造出满足要求的涡旋齿型线. 研究结果表明:利用Frenet活动标架构建的涡旋齿型线,不但涵盖了当前所有类型的涡旋齿型线,而且能按预期的几何性能对型线进行重构,从而设计出具有最佳性能的涡旋齿型线,该方法为实现涡旋压缩机型线的柔性化设计打下理论基础.

Abstract:

In the design of scroll wrap profiles, aiming at the problem of lacking of simple and effective general geometric model and the preference of scroll profile geometric performance is not taken into consideration in practical engineering applications, a new method of constructing scroll wrap profiles applying the frenet moving frame was proposed. Firstly, a frenet moving frame was attached to the curve of scroll wrap profile to replace the fixed Cartesian Coordinate System. Then, using the curvature of the plane curve and frenet moving frame to express the intrinsic characteristics of the scroll wrap profiles, a general geometric model of scroll wrap profiles with curvature and frenet moving frame as parameters was established. Finally, the mapping relationship between the control coefficients and the geometric performance of the scroll wrap profiles was set up. On this basis, taking the engineering application of scroll compressor as the design goal, under the condition that the circumferential diameter of scroll plate as well as the tooth thickness were known respectively, by using the mapping relationship, a series of control coefficients were selected according to the preferences of the design requirements, then the scroll wrap profiles that satisfy the requirements were constructed. The results show that the scroll wrap profile constructed by frenet moving frame not only includes all types of scroll wrap profiles at present, but also reconstructs them according to the expected geometric performance, so as to design the scroll wrap profiles with the best performances. This method lays a theoretical foundation for the flexible design of scroll compressor profile.