Research on Tool Path Planning of Spiral Finishing Processes Based on Coons Reparameterization for Blades with Blisk Compound Surfaces

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

Abstract

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

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

CLC Number:

TG54

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.

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.

Figures/Tables 30

Fig.1 Control line intersection diagram

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

Fig.3 Open blisk blade spiral finishing flow chart

Fig.4 Typical open blisk structure

Fig.5 Suction surface reparameterization schematic diagram

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

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

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

Fig.9 The control curves in Euclidean space

Fig.10 Sorting diagram of climb milling processing point chain

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

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

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

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

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

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

Fig.17 Toolpaths for UG/NX and proposed methods

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

Fig.19 Results of blade processing

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

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

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

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

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

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

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

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

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

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

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

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

References 33

[1]	SHEN Moqi， LIU Jia， WANG Jingtao， et al. Design Method and Experimental Study of a Cathode Tool with an Extremely High Leveling Ratio for Electrochemical Machining of Blisk［J］. Chinese Journal of Aeronautics， 2024， 37（4）： 593-608.
[2]	ASCHENBRUCK J， ADAMCZUK R， SEUME J R. Recent Progress in Turbine Blade and Compressor Blisk Regeneration［J］. Procedia CIRP， 2014， 22： 256-262.
[3]	YAO Zequan， SHEN Jingyuan， WU Ming， et al. Position-dependent Milling Process Monitoring and Surface Roughness Prediction for Complex Thin-walled Blade Component［J］. Mechanical Systems and Signal Processing， 2023， 198： 110439.
[4]	WANG Jingtao， XU Zhengyang， ZHU Di. Improving Profile Accuracy and Surface Quality of Blisk by Electrochemical Machining with a Micro Inter-electrode Gap［J］. Chinese Journal of Aeronautics， 2023， 36（4）： 523-537.
[5]	WU Dongbo， WANG Hui， ZHANG Kaiyao， et al. Research on Formation Mechanism and Optimization Method of Surface Waviness of TC4 Blisk Blade［J］. Journal of Manufacturing Processes， 2019， 39： 305-326.
[6]	LIANG Jiawei， WU Dongbo， LIU Shibo， et al. Research on Hybrid Remanufacturing Process Chain of Laser Cladding， CNC Machining and Ultrasonic Rolling for Aero-engine Blades［J］. Journal of Manufacturing Processes， 2024， 110： 331-349.
[7]	LI Xiangyu， REN Junxue， TANG Kai， et al. Optimization of Cutter Profile for Achieving Maximum Stiffness in Five-axis Milling of Deep and Narrow Channel Parts［J］. Journal of Manufacturing Processes， 2019， 37： 541-555.
[8]	LI Xiangyu， LI Zhaoyu， HE Dong， et al. Efficient Machining of a Complex Blisk Channel Using a Disc Cutter［J］. Chinese Journal of Aeronautics， 2024， 37（1）： 414-437.
[9]	DAI Xing， QI Qi， YANG Jixiang， et al. A Trochoidal Toolpath Planning Method for 5-axis Milling of Blisks with Equal Radial Cutting Depth［J］. Journal of Manufacturing Processes， 2024， 123： 128-141.
[10]	LEE E. Contour Offset Approach to Spiral Toolpath Generation with Constant Scallop Height［J］. Computer-Aided Design， 2003， 35（6）： 511-518.
[11]	ZHANG Ke， TANG Kai. An Efficient Greedy Strategy for Five-axis Tool Path Generation on Dense Triangular Mesh［J］. The International Journal of Advanced Manufacturing Technology， 2014， 74（9）： 1539-1550.
[12]	MONREAL M， RODRIGUEZ C A. Influence of Tool Path Strategy on the Cycle Time of High-speed Milling［J］. Computer-Aided Design， 2003， 35（4）： 395-401.
[13]	PAVANASKAR S， PANDE S， KWON Y， et al. Energy-efficient Vector Field Based Toolpaths for CNC Pocketmachining［J］. Journal of Manufacturing Processes， 2015， 20： 314-320.
[14]	PARK S C， CHUNG Y C， CHOI B K. Contour-parallel Offset Machining without Tool-retractions［J］. Computer-Aided Design， 2003， 35（9）： 841-849.
[15]	RAUCH M， DUC E， HASCOET J Y. Improving Trochoidal Tool Paths Generation and Implementation Using Process Constraints Modelling［J］. International Journal of Machine Tools and Manufacture， 2009， 49（5）： 375-383.
[16]	WU Shixiong， MA Wei， LI Bin， et al. Trochoidal Machining for the High-speed Milling of Pockets［J］. Journal of Materials Processing Technology， 2016， 233： 29-43.
[17]	HUANG Nuodi， JIN Yongqiao， LU Yaoan， et al. Spiral Toolpath Generation Method for Pocket Machining［J］. Computers & Industrial Engineering， 2020， 139： 106142.
[18]	单晨伟，张定华，刘维伟. 组合曲面叶片的螺旋加工刀位轨迹生成［J］. 计算机集成制造系统， 2008， 14（11）： 2243-2247.
	SHAN Chenwei， ZHANG Dinghua， LIU Weiwei. Spiral Machining Tool Path Generation for Blade with Compound Surfaces［J］. Computer Integrated Manufacturing Systems， 2008， 14（11）： 2243-2247.
[19]	GONG Hu， WANG Yi， SONG Le， et al. Spiral Tool Path Generation for Diamond Turning Optical Freeform Surfaces of Quasi-revolution［J］. Computer-Aided Design， 2015， 59： 15-22.
[20]	HAUTH S， LINSEN L. Double-spiral Tool Path in Configuration Space［J］. The International Journal of Advanced Manufacturing Technology， 2011， 54（9）： 1011-1022.
[21]	XU Jinting， SUN Yuwen， ZHANG Lei. A Mapping-based Approach to Eliminating Self-intersection of Offset Paths on Mesh Surfaces for CNC Machining［J］. Computer-Aided Design， 2015， 62： 131-142.
[22]	BIETERMAN M B， SANDSTROM D R. A Curvilinear Tool-path Method for Pocket Machining［J］. Journal of Manufacturing Science and Engineering， 2003， 125（4）： 709-715.
[23]	ZHOU Bo， ZHAO Jibin， LI Lun. CNC Double Spiral Tool-path Generation Based on Parametric Surface Mapping［J］. Computer-Aided Design， 2015， 67/68： 87-106.
[24]	BANERJEE A， FENG H Y， BORDATCHEV E V. Process Planning for Floor Machining of 2½D Pockets Based on a Morphed Spiral Tool Path Pattern［J］. Computers & Industrial Engineering， 2012， 63（4）： 971-979.
[25]	SUN Yuwen， GUO Dongming， JIA Zhenyuan. Spiral Cutting Operation Strategy for Machining of Sculptured Surfaces by Conformal Map Approach［J］. Journal of Materials Processing Technology， 2006， 180（1/2/3）： 74-82.
[26]	REN Fei， YUWEN Sun， GUO Dongming. Combined Reparameterization-based Spiral Toolpath Generation for Five-axis Sculptured Surface Machining［J］. The International Journal of Advanced Manufacturing Technology， 2009， 40（7）： 760-768.
[27]	SUN Yuwen， XU Jinting， JIN Chunning， et al. Smooth Tool Path Generation for 5-axis Machining of Triangular Mesh Surface with Nonzero Genus［J］. Computer-Aided Design， 2016， 79（C）： 60-74.
[28]	SHEN Changqing， MAO Sihao， XU Bingzhou， et al. Spiral Complete Coverage Path Planning Based on Conformal Slit Mapping in Multi-connected Domains［J］. The International Journal of Robotics Research， 2024， 43（14）： 2183-2203.
[29]	XU Jinting， JI Yukun， SUN Yuwen， et al. Spiral Tool Path Generation Method on Mesh Surfaces Guided by Radial Curves［J］. Journal of Manufacturing Science and Engineering， 2018， 140（7）： 071016.
[30]	吴江盛，柴兴亮，薄其乐，等. 基于离散点云构造径向线的螺旋加工轨迹规划方法［J］. 中国机械工程， 2025， 36（4）： 697-702.
	WU Jiangsheng， CHAI Xingliang， BO Qile， et al. Spiral Machining Trajectory Planning Method Based on Discrete Point Cloud Construction of Radial Lines［J］. China Mechanical Engineering， 2025， 36（4）： 697-702.
[31]	HELD M， de LORENZO S. On the Generation of Spiral-like Paths within Planar Shapes［J］. Journal of Computational Design and Engineering， 2018， 5（3）： 348-357.
[32]	白瑀，张定华，刘维伟，等. 叶片类零件四坐标高效螺旋数控编程方法研究［J］. 机械科学与技术， 2003， 22（2）： 177-179.
	BAI Yu， ZHANG Dinghua， LIU Weiwei， et al. An Efficient Method for Four-axis Spiral NC Programming of Blade Parts［J］. Mechanical Science and Technology， 2003， 22（2）： 177-179.
[33]	单晨伟，张定华，刘维伟，等. 带边界约束叶片的螺旋加工轨迹规划［J］. 中国机械工程， 2005， 16（18）： 1629-1632.
	SHAN Chenwei， ZHANG Dinghua， LIU Weiwei， et al. Track Programming for the Spiral Machining of the Blade with Boundaries［J］. China Mechanical Engineering， 2005， 16（18）： 1629-1632.