基于NURBS啮合线的高效双螺杆转子自适应设计方法

doi:10.3969/j.issn.1004-132X.2025.12.004

摘要/Abstract

摘要：

为解决压缩机转子型线设计过程繁琐以及性能难以评判的问题，对双螺杆压缩机转子型线的反向设计进行了研究。利用NURBS曲线对转子啮合线进行分段拟合，求解出各段啮合线的控制点，并建立转子型线的优化模型，利用单纯形法调整啮合线控制点坐标实现对转子型线的自适应优化设计。将优化前后的转子型线与原始型线比较分析并进行流体仿真，结果显示，优化后的转子型线综合性能提高了11.38%，优化后的压缩机转子表面压力数值在三种工况下分别提高了5.16%、5.00%、4.93%，证明了双螺杆压缩机转子型线自适应优化设计的有效性。

关键词: 转子型线, 反向设计, 啮合线, 优化设计, 非均匀有理B样条曲线

Abstract:

To address the issues of cumbersome design processes and challenging performance evaluation in compressor rotor profile design， a reverse design approach for twin-screw compressor rotor profiles was investigated. The rotor meshing line was segmented and fitted using NURBS curves， the control points of each meshing line segment were solved， and an optimization model for the rotor profiles was established. An adaptive optimization design of the rotor profile was achieved by adjusting the coordinates of the meshing line control points using the simplex method. A comparative analysis between the optimized rotor profiles and the original profiles was conducted， along with fluid simulation. The results demonstrate that the comprehensive performance of the optimized rotor profiles is improved by 11.38%. Under three operating conditions， the surface pressure values of the optimized compressor rotors are increased by 5.16%， 5.00%， and 4.93%， respectively， which verify the effectiveness of the adaptive optimization design for twin-screw compressor rotor profiles.

Key words: rotor profile, reverse design, meshing line, optimization design, NURBS curve

中图分类号:

TP182

耿宇航, 何雪明, 高宗. 基于NURBS啮合线的高效双螺杆转子自适应设计方法[J]. 中国机械工程, 2025, 36(12): 2837-2845.

Yuhang GENG, Xueming HE, Zong GAO. Adaptive Design Method of Efficient Twin Screw Rotors Based on NURBS Mesh Lines[J]. China Mechanical Engineering, 2025, 36(12): 2837-2845.

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链接本文: https://www.cmemo.org.cn/CN/10.3969/j.issn.1004-132X.2025.12.004

https://www.cmemo.org.cn/CN/Y2025/V36/I12/2837

图/表 18

图1 反向设计坐标系

Fig.1 Reverse design coordinate system

图2 反向设计流程图

Fig.2 Reverse design flowchart

图3 复盛型线及其啮合线

Fig.3 Fusheng profile and meshing line

表1 复盛型线各段齿曲线类型

Tab.1 Types of tooth curves for each section of the Fusheng profile

阳转子		阴转子3		啮合线段标
齿曲线段标	曲线类型	齿曲线段标	曲线类型	啮合线段标
A₁B₁	圆弧	A₂B₂	圆弧包络线	12
B₁C₁	椭圆弧	B₂C₂	椭圆包络线	23
C₁D₁	圆弧	C₂D₂	圆弧包络线	34
D₁E₁	圆弧包络线	D₂E₂	圆弧	41

图4 原始啮合线分段

Fig.4 Segmentation of the original meshing line

表2 优化前后性能参数对比

Tab.2 Comparison of performance parameters before and after optimization

性能参数	接触线长度L/mm	泄漏三角形面积S/mm²	面积利用系数M	综合性能指标K
原始	177.3729	12.4898	0.4320	3.4089
优化后	177.0004	11.2158	0.4384	3.0209
差值	$-$ 0.3725	$-$ 1.2740	0.0064	$-$ 0.388
变化比例/%	$-$ 0.21	$-$ 10.2	1.49	$-$ 11.38

表2 优化前后性能参数对比

Tab.2 Comparison of performance parameters before and after optimization

性能参数	接触线长度L/mm	泄漏三角形面积S/mm²	面积利用系数M	综合性能指标K
原始	177.3729	12.4898	0.4320	3.4089
优化后	177.0004	11.2158	0.4384	3.0209
差值	$-$ 0.3725	$-$ 1.2740	0.0064	$-$ 0.388
变化比例/%	$-$ 0.21	$-$ 10.2	1.49	$-$ 11.38

图5 优化前后啮合线对比

Fig.5 Comparison of meshing lines before and after optimization

图6 优化前后型线对比

Fig.6 Comparison of profiles before and after optimization

图7 三维几何模型

Fig.7 Three-dimensional geometrical modeling

图8 流体域网格划分

Fig.8 Fluid domain mesh division

图9 2940 r/min转速下优化前后转子表面压力分布

Fig.9 Surface pressure distribution of rotor before and after optimization at 2940 r/min speed

图10 3480 r/min转速下优化前后转子表面压力分布

Fig.10 Surface pressure distribution of rotor before and after optimization at 3480 r/min speed

图11 4020 r/min转速下优化前后转子表面压力分布

Fig.11 Surface pressure distribution of rotor before and after optimization at 4020 r/min speed

图12 三组工况下转子表面的压力值对比

Fig.12 Comparison of pressure values on rotor surfaces under three operating conditions

图13 压缩机实验平台示意图

Fig.13 Schematic diagram of compressor experimental platform

图14 监测点位置示意图

Fig.14 Schematic diagram of detection hole position

图15 流体域监测点位置

Fig.15 Location of fluid domain monitoring points

图16 监测点压力实验值与仿真值对比

Fig.16 Comparison between experimental and simulated pressure values at monitoring points

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