螺杆转子型线正向设计中的曲线连续性研究
Exploring Curve Continuity in Forward Design of Screw Rotor Profile

螺杆转子是双螺杆压缩机的核心，而传统规则曲线的构造自由度越来越不能满足螺杆转子型线的设计要求，由此本文提出了利用自由曲线代替传统规则曲线来获得更高自由度和曲线连续性的型线。对自由曲线的转子型线设计深入研究，利用几何解析法实现对规则曲线的控制点及权因子的获取，实现只由控制点、权因子和节点矢量决定的一段式自由曲线典型型线设计，减少了传统分段设计型线的步骤，大幅提高了设计效率。提出利用控制型线段端点矢量的方法设计曲线连续级别为G0、G1和G2的自由曲线型线，利用控制点与次数对曲率变化规律研究，得到了曲率平稳且与典型型线误差低于0.1 μm的自由曲线型线。
A screw rotor is the core of a twin screw compressor, but the construction degree of the traditional rule curve cannot meet the design requirements of the screw rotor profile. Therefore, this paper proposes using the free curve to replace the traditional rule curve so as to obtain the profile with a higher degree of freedom and curve continuity. The design of the rotor curve of the free curve is studied deeply, and the control point of the regular curve and its weighting factor are obtained through geometric analysis. The control point determines the typical curve design with the free curve, the weight factor and the node vector, thus reducing the steps of the traditional segmental design line and greatly improving design efficiency. In this paper, the free curve lines with continuous curves G0, G1 and G2 are designed by controlling the end point vector of a profile segment. The curvature change rule is studied by using various numbers of control points and various powers, and a smooth curvature and the profile whose error is less than 0.1μm are obtained