Exploring Curve Continuity in Forward Design of Screw Rotor Profile
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摘要: 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。Abstract: 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.
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Key words:
- screw rotor profile /
- NURBS free curve /
- curvature /
- curve continuity
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表 1 复盛型线各段参数取值
曲线 r或a, b c1 c2 参数t范围 圆弧A2B2 1.65 41.99 -15.28 [-0.349, 1.601] 圆弧B1C1 3.992 28.047 0 [3.142, 3.838] 椭圆弧
C1D1(30.032, 24.967) 54.117 0 [1.571, 3.142] 圆弧D1E1 6 54.117 30.967 [4.712, 5.445] 
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表 2 复盛型线设计相关数据
阴转子齿曲线 阳转子齿曲线 啮合线对应齿曲线 圆弧A2B2 圆弧包络线A1B1 A0B0 圆弧包络线B2C2 圆弧B1C1 B0C0 椭圆弧包络线C2D2 椭圆弧C1D1 C0D0 圆弧包络线D2E2 圆弧D1E1 D0E0 注:阴阳转子齿数比为6/5;H=82 mm。
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表 3 NURBS曲线型线设计数据
NURBS曲线阴转子型线 NURBS曲线的包络线 齿曲线 次数 控制点数 精度误差/
μm齿曲线 精度误差/
μm圆弧
A2B2三 4 4.33×10-4 圆弧
包络线
A1B14.41×10-4 四 5 5.00×10-6 5.00×10-6 五 9 9.23×10-4 9.02×10-4 六 8 5.19×10-4 2.74×10-4 圆弧
包络线
B2C2三 13 0.066 圆弧
B1C10.069 四 11 0.062 0.068 五 10 0.077 0.072 六 10 0.084 0.074 椭圆弧
包络线
C2D2三 27 0.070 椭圆弧
C1D10.068 四 22 0.064 0.051 五 21 0.066 0.053 六 24 0.024 0.012 圆弧
包络线
D2E2三 8 0.060 圆弧
D1E10.058 四 7 0.055 0.059 五 7 0.041 0.040 六 7 0.030 0.029
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表 4 改进优化前后性能参数对比
改进状况 泄漏三角形面积/mm2 接触线长度/mm 阳转子齿间面积/mm2 阴转子齿间面积/mm2 面积利用系数 改进前 4.259 147.732 600.742 618.982 0.454 改进后 4.236 152.140 633.420 602.770 0.460
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