基于Coons重新参数化的整体叶盘组合曲面叶片螺旋精加工路径生成方法研究

doi:10.3969/j.issn.1004-132X.2026.08.017

摘要/Abstract

摘要：

为提高叶片加工质量和解决现有叶片螺旋加工轨迹生成方法无法用于裁剪曲面的问题，提出了一种新的针对有裁剪曲面存在的组合曲面造型叶片的螺旋精加工轨迹生成方法。首先使用基于Coons重参数化的方式计算螺旋加工轨迹生成所依赖的控制线，适用于有裁剪曲面的叶片。然后根据组合曲面叶片造型，给出组合曲面叶片螺旋加工刀位轨迹生成方法和切触点的计算公式，通过引入敏感度分析来修正刀触点。最后通过引入球面插值，最小化旋转轴的加速度来优化刀轴矢量。开发了基于所提方法的自动编程软件，仿真和实验结果表明，所提方法相较于UG/NX叶片轮廓精度得到了提高，压力面粗糙度减小了11.28%，吸力面减小了20.32%。刀轴矢量优化后旋转轴加速度最大减小了88.72%。

关键词: 叶片, 组合曲面, 裁剪曲面, Coons面片, 刀位轨迹生成

Abstract:

In order to improve the blade processing quality and solve the problems that the existing blade spiral machining trajectory generation method might not be used for trimmed surfaces， a new spiral finishing trajectory generation method was proposed for combined curved surface modeling blades with cutting surfaces. Firstly， using the Coons reparameterization method to calculate the control lines relied on for spiral machining trajectory generation， suitable for blades with trimmed surfaces. Then， based on the model of blade with compound surfaces， a method for generating tool path and the spiral cutter contact point’s calculation formula were proposed. The cutter contact point is modified by introducing sensitivity analysis. Finally， the tool axis vector is optimized by introducing spherical interpolation to minimize the acceleration of the rotation axis. An automatic programming software based on this method was developed to generate a continuous and smooth blade spiral finishing tool path. Simulation and experimental results show that the proposed method improves the blade profile accuracy compared to UG/NX， the pressure surface roughness is reduced by 11.28%， and the suction surface is reduced by 20.32%. After the optimization of the tool axis vector， the acceleration of the rotation axis is reduced by 88.72 %.

Key words: blade, compound surface, trimmed surfaces, Coons patch, tool path generation

中图分类号:

TG54

韩江, 杜豪, 田晓青, 夏链. 基于Coons重新参数化的整体叶盘组合曲面叶片螺旋精加工路径生成方法研究[J]. 中国机械工程, 2026, 37(8): 1976-1988.

HAN Jiang, DU Hao, TIAN Xiaoqing, XIA Lian. Research on Tool Path Planning of Spiral Finishing Processes Based on Coons Reparameterization for Blades with Blisk Compound Surfaces[J]. China Mechanical Engineering, 2026, 37(8): 1976-1988.

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链接本文: https://www.cmemo.org.cn/CN/10.3969/j.issn.1004-132X.2026.08.017

https://www.cmemo.org.cn/CN/Y2026/V37/I8/1976

图/表 30

图1 控制线相交示意图

Fig.1 Control line intersection diagram

图2 等参数线与曲面边界相交示意图

Fig.2 A schematic diagram of the intersection of isoparametric curves and surface boundaries

图3 开式整体叶盘叶片螺旋精加工流程图

Fig.3 Open blisk blade spiral finishing flow chart

图4 典型的开式整体叶盘结构

Fig.4 Typical open blisk structure

图5 吸力面重新参数化示意图

Fig.5 Suction surface reparameterization schematic diagram

图6 Coons曲面参数域等s/t线示意图

Fig.6 Coons patch parameter domain iso s/t curves diagram

图7 曲面参数域上的等t线

Fig.7 The iso t curve on the parameter domain of the suction surface

图8 弦高约束下曲面参数域上的等s线

Fig.8 The iso s curves on the parameter domain of the suction surface under chord height constraint

图9 欧氏空间中曲面的控制线

Fig.9 The control curves in Euclidean space

图10 顺铣加工点链排序示意图

Fig.10 Sorting diagram of climb milling processing point chain

图11 线性插值出螺旋点链原理

Fig.11 The principle of spiral point chain is linearly interpolated

图12 第i条刀触曲线上刀触点生成原理

Fig.12 The principle of cutter contact point generation on the i th cutter contact curve is drawn.

图13 第i条刀触曲线上刀触点修正原理

Fig.13 The principle for modification of cutter contact point correction on the i th cutter contact curve

图14 修正前后刀位点对比

Fig.14 Comparison of tool location points before and after correction

图15 加工行距为1.0 mm时的刀具路径

Fig.15 The tool paths when the machining row spacing is 1.0 mm

图16 刀位点刀轴矢量规划示意图

Fig.16 Schematic diagram of tool orientation planning for tool location points

图17 UG/NX和所提方法的铣削路径

Fig.17 Toolpaths for UG/NX and proposed methods

图18 UG/NX和所提方法仿真结果

Fig.18 Simulation results of UG/NX and the proposed method

图19 叶片实际加工结果

Fig.19 Results of blade processing

图20 所提方法和UG/NX 的叶片表面轮廓精度

Fig.20 Blade surface profile accuracy of the proposed method and UG/NX

表1 所提方法和UG/NX 的叶片表面轮廓精度对比分析

Tab.1 Comparative analysis of the blade surface profile accuracy between the proposed method and UG/NX

	平均值/mm	标准差	偏度	峰度	最小值/mm	最大值/mm
所提方法	0.042	0.010	0.762	$-$ 0.330	$-$ 0.065	0.067
UG/NX	0.046	0.016	1.197	0.757	$-$ 0.082	0.086

表1 所提方法和UG/NX 的叶片表面轮廓精度对比分析

Tab.1 Comparative analysis of the blade surface profile accuracy between the proposed method and UG/NX

	平均值/mm	标准差	偏度	峰度	最小值/mm	最大值/mm
所提方法	0.042	0.010	0.762	$-$ 0.330	$-$ 0.065	0.067
UG/NX	0.046	0.016	1.197	0.757	$-$ 0.082	0.086

图21 所提方法加工压力面粗糙度测量结果

Fig.21 Measurement results of the roughness of the pressure surface machined by the proposed method

图22 UG/NX加工压力面粗糙度测量结果

Fig.22 Measurement results of the roughness of pressure surface machined by the UG/NX

图23 所提方法加工吸力面表面粗糙度测量结果

Fig.23 Measurement results of the roughness of the suction surface machined by the proposed method

图24 UG/NX加工吸力面表面粗糙度测量结果

Fig.24 Measurement results of the roughness of suction surface machined by the UG/NX

图25 刀轴矢量优化前后对比

Fig.25 Comparison of tool axis vector before and after optimization

图26 A轴位移优化前后对比

Fig.26 Comparison of A-axis displacement before and after optimization

图27 C轴位移优化前后对比

Fig.27 Comparison of C-axis displacement before and after optimization

图28 A轴优化前后加速度对比

Fig.28 Comparison of acceleration before and after A-axis optimization

图29 C轴优化前后加速度对比

Fig.29 Comparison of acceleration before and after C-axis optimization

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