基于叶片几何特征的精加工刀具轨迹生成

doi:10.11996/JG.j.2095-302X.2026020402

摘要/Abstract

摘要：

航空发动机叶片作为航空制造领域的核心零件，其复杂几何特征与高精度要求导致精加工过程中面临切削力波动大、刀具磨损严重等挑战。为在复杂曲面加工中实现切削力稳定控制，提出一种融合叶片几何特征分析与切削参数优化的刀具轨迹规划方法。首先，基于微元切削理论建立切削力计算模型，分析叶片曲面特征、切削参数和切削力之间的关系；然后，针对传统等参数轨迹中切削参数固定导致力波动的问题，采用变尺度混沌算法对刀轴倾角、进给速度和切削深度3个切削参数进行协同优化，建立了以最小化切削力波动为目标的参数优化模型；最后，基于叶片几何特征计算走刀步长和走刀行距，采用等参数线法规划刀触点轨迹，通过切削力计算和切削参数优化确定每个加工路径点的刀轴倾角等切削参数，生成完整的叶片精加工刀具轨迹。结果表明，该刀具轨迹生成方法通过优化切削力的分布，实现了加工过程中切削力平滑，可以降低刀具的疲劳损伤和磨损，保证刀具使用寿命。该研究为复杂曲面零件的精密加工提供了一种基于力控的轨迹规划新思路。

关键词: 叶片几何特征, 刀具轨迹生成, 切削力计算, 切削参数优化, 混沌优化

Abstract:

As a core component in aerospace manufacturing, aero-engine blades face challenges of significant cutting-force fluctuations and severe tool wear during finishing due to their complex geometries and high precision requirements. To achieve stable cutting-force control in complex-surface machining, a toolpath-planning method integrating blade geometric-feature analysis and cutting-parameter optimization was proposed. First, a cutting-force model based on micro-element cutting theory was developed to analyze the relationship among surface features, cutting parameters, and cutting forces. Subsequently, to address force fluctuations caused by fixed parameters in traditional paths, a variable-scale chaotic algorithm was used co-optimize tool-axis inclination, feed rate, and cutting depth, establishing an optimization model to minimize force fluctuation. Finally, step length and row spacing were calculated based on blade geometry, and the isoparametric-line method plans tool-contact-point trajectories. Optimal cutting parameters for each point were determined by integrating the force model with the optimization results, generating the complete finishing toolpath. Results showed that this method optimized cutting-force distribution, achieved smooth machining forces, reduced tool fatigue and wear, and extended tool life. This work provided a new force-control-based approach for precision machining of complex surfaces.

Key words: blade geometric features, tool path generation, cutting-force calculation, cutting-parameter optimization, chaotic optimization

中图分类号:

TG547
V263

涂艺豪, 马文扬, 闫光荣. 基于叶片几何特征的精加工刀具轨迹生成[J]. 图学学报, 2026, 47(2): 402-410.

TU Yihao, MA Wenyang, YAN Guangrong. Toolpath generation for finishing machining of blades based on geometric features[J]. Journal of Graphics, 2026, 47(2): 402-410.

图/表 16

图1 球头铣刀模型

Fig. 1 Ball-end milling cutter model

图2 刀具球头刃线解析

Fig. 2 Cutting edge analysis of ball-end milling cutter

图3 切削刃微元受力分析

Fig. 3 Cutting edge micro-element force analysis

图4 刀具-工件啮合区域积分限计算流程

Fig. 4 Tool-workpiece engagement zone integration limit calculation process

图5 变尺度混沌优化流程

Fig. 5 Variable-scale chaotic optimization process

图6 切削力分布优化前后对比((a) 优化前；(b) 优化后)

Fig. 6 Comparison of cutting forces before and after optimization ((a) Before optimization; (b) After optimization)

表1 切削参数优化结果分析

Table 1 Analysis of cutting parameter optimization results

参数	优化前/N	优化后/N	改善幅度/%
平均值	57.358 0	57.700 2	+0.6
标准差	11.50	0.03	-99.7
最大值	80.642 0	57.756 0	-28.3
最小值	38.124 1	57.619 4	+51.2

表2 曲面曲率特征分析

Table 2 Surface curvature characteristic analysis

高斯曲率	平均曲率
高斯曲率	H>0	H=0	H<0
K>0	凹椭圆点		凸椭圆点
K=0	凹抛物点	平面	凸抛物点
K<0	双曲点	双曲点	双曲点

图7 叶片曲面凹凸性分析((a) 叶盆曲面特征分析；(b) 叶背曲面特征分析)

Fig. 7 Blade surface convexity-concavity analysis ((a) Pressure-side (concave) surface characterization; (b) Suction-side (convex) surface characterization)

图8 叶盆曲面曲率分析与行距计算

Fig. 8 Pressure-side surface curvature analysis and stepover calculation

图9 叶盆曲面行距规划

Fig. 9 Pressure-side surface stepover planning

表3 刀轨曲率区间划分与步长选取

Table 3 Toolpath curvature interval partitioning and step length selection

主曲率区间	走刀步长	特点
(0，0.000 2)	5.0	平坦区域，大走刀步长
(0.000 2，0.001 0)	2.5	轻微弯曲，适中步长
(0.001 0，0.002 0)	1.2	中等弯曲，较小步长
(0.002 0，∞)	0.6	较陡弯曲，精细步长

图10 叶盆曲面一条刀轨曲率区间划分

Fig. 10 Curvature interval partitioning for a single toolpath on pressure-side surface

图11 该刀轨优化前后切削力对比

Fig. 11 Comparison of cutting forces before and after toolpath optimization

图12 优化后该刀轨切削参数取值

Fig. 12 Optimized cutting parameter values for the toolpath

图13 叶片曲面轨迹规划((a) 叶盆曲面；(b) 叶背曲面)

Fig. 13 Blade surface cutter contact point trajectory planning ((a) Pressure-side surface; (b) Suction-side surface)

参考文献 20

[1]	王辉, 郑洋, 吴动波. 航空发动机叶片精密加工工艺及装备[J]. 金属加工(冷加工), 2023(10): 1-9.
	WANG H, ZHENG Y, WU D B. Precision machining technology and equipment for aeroengine blades[J]. Metal Working (Metal Cutting), 2023(10): 1-9 (in Chinese).
[2]	MERCHANT M E. Mechanics of the metal cutting process. II. Plasticity conditions in orthogonal cutting[J]. Journal of Applied Physics, 1945, 16(6): 318-324. DOI URL
[3]	LEE E H, SHAFFER B W. The theory of plasticity applied to a problem of machining[J]. Journal of Applied Mechanics, 1951, 18(4): 405-413. DOI URL
[4]	YANG M Y, PARK H. The prediction of cutting force in ball-end milling[J]. International Journal of Machine Tools and Manufacture, 1991, 31(1): 45-54. DOI URL
[5]	ALTINTAS Y, LEE P. Mechanics and dynamics of ball end milling[J]. Journal of Manufacturing Science and Engineering, 1998, 120(4): 684-692. DOI URL
[6]	吴石, 杨琳, 刘献礼, 等. 覆盖件模具曲面曲率特征对球头刀铣削力的影响[J]. 机械工程学报, 2017, 53(13): 188-198. DOI
	WU S, YANG L, LIU X L, et al. Influence of curvature characteristics of sculptured surface on milling force in ball-end milling of panel moulds[J]. Journal of Mechanical Engineering, 2017, 53(13): 188-198 (in Chinese). DOI
[7]	张双德. 基于改进型模拟退火算法的数控加工切削参数优化[J]. 煤矿机械, 2004(6): 76-78.
	ZHANG S D. Application of improved simulated annealing algorithm in NC machining parameter optimization[J]. Coal Mine Machinery, 2004(6): 76-78 (in Chinese).
[8]	刘长清. 数控铣削过程离线优化技术研究[D]. 哈尔滨: 哈尔滨工业大学, 2007.
	LIU C Q. Research on off-line optimization technology of NC milling process[D]. Harbin: Harbin Institute of Technology, 2007 (in Chinese).
[9]	姜彬, 郑敏利, 李振加, 等. 数控铣削用量多目标优化[J]. 哈尔滨理工大学学报, 2002, 7(3): 67-70.
	JIANG B, ZHENG M L, LI Z J, et al. The optimization of the multi—goal cutting parameters in the NC milling process[J]. Journal of Harbin University of Science and Technology, 2002, 7(3): 67-70 (in Chinese).
[10]	MONTGOMERY D, ALTINTAS Y. Mechanism of cutting force and surface generation in dynamic milling[J]. Journal of Manufacturing Science and Engineering, 1991, 113(2): 160-168.
[11]	沈小艺. 大尺寸叶片曲面分区数控加工轨迹规划[D]. 北京: 北京交通大学, 2021.
	SHEN X Y. NC machining toolpath planning for large size blade surface with partition[D]. Beijing: Beijing Jiaotong University, 2021 (in Chinese).
[12]	席晓琳. 基于刚度匹配的叶盘加工变形控制技术研究[D]. 北京: 北京交通大学, 2022.
	XI X L. Research on machining deformation control technology of blisk based on stiffness matching[D]. Beijing: Beijing Jiaotong University, 2022 (in Chinese).
[13]	鞠楠. 基于切削力分析的叶片加工刀具轨迹规划[D]. 北京: 北京交通大学, 2019.
	JU N. NC machining tool path planning of the blade based on cutting force analysis[D]. Beijing: Beijing Jiaotong University, 2019 (in Chinese).
[14]	葛立才, 黄涛, 顾梦沁, 等. 基于高斯过程回归的复杂曲面加工切削力高效预测[J]. 航空制造技术, 2023, 66(21): 84-94.
	GE L C, HUANG T, GU M Q, et al. Cutting forces prediction for complex surface machining based on Gaussian process regression[J]. Aeronautical Manufacturing Technology, 2023, 66(21): 84-94 (in Chinese).
[15]	潘永智, 艾兴, 唐志涛, 等. 基于切削力预测模型的刀具几何参数和切削参数优化[J]. 中国机械工程, 2008, 19(4): 428-431.
	PAN Y Z, AI X, TANG Z T, et al. Optimization of tool geometry and cutting parameters based on a predictive model of cutting force[J]. China Mechanical Engineering, 2008, 19(4): 428-431 (in Chinese).
[16]	张彤, 王宏伟, 王子才. 变尺度混沌优化方法及其应用[J]. 控制与决策, 1999, 14(3): 94-97.
	ZHANG T, WANG H W, WANG Z C. Mutative scale chaos optimization algorithm and its application[J]. Control and Decision, 1999, 14(3): 94-97 (in Chinese).
[17]	徐翔宇, 闫光荣, 雷毅. 基于变尺度混沌算法的曲面品质优化[J]. 北京航空航天大学学报, 2023, 49(12): 3328-3334.
	XU X Y, YAN G R, LEI Y. Surface quality optimization based on mutative scale chaos algorithm[J]. Journal of Beijing University of Aeronautics and Astronautics, 2023, 49(12): 3328-3334 (in Chinese).
[18]	周纯江. 基于特征的曲面高速加工方法的研究[J]. 制造业自动化, 2011, 33(10): 52-55.
	ZHOU C J. Research on feature based high speed, surface machining method[J]. Manufacturing Automation, 2011, 33(10): 52-55 (in Chinese).
[19]	董佳琦, 张平. 基于曲面分片的五轴刀具轨迹规划[J]. 机床与液压, 2013, 41(15): 50-53.
	DONG J Q, ZHANG P. Tool path planning for five-axis tool based on surface subdivision[J]. Machine Tool & Hydraulics, 2013, 41(15): 50-53 (in Chinese).
[20]	陈龙. 自由曲面加工轨迹规划方法及解释器关键技术的研究与应用[D]. 合肥: 中国科学技术大学, 2013.
	CHEN L. Research and applications of the tool path planning method of sculptured surface machining and the key technology of interpreter[D]. Hefei: University of Science and Technology of China, 2013 (in Chinese).