Prediction of Micro-milling Forces Considering Flank Wear with Cutting Edge Radius

doi:10.3969/j.issn.1004-132X.2026.05.013

Abstract

Abstract:

To accurately predict cutting forces in the micro-milling processes， a micro-milling force mechanism model was proposed that comprehensively considering the cutting edge radius， tool flank wear and tool runout. A precise analytical relationship between flank wear of micro-milling tools and the cutting edge radius was established and the trochoidal trajectory of the cutting edge was accurately analyzed under tool runout. An analytical model was constructed for instantaneous undeformed chip thickness and entry-exit angles， along with a tool-workpiece contact area and cutting force coefficient model that accounted for flank wear. Consequently， a generalized micro-milling force model was developed， incorporating critical factors such as cutting edge radius， flank wear and tool runout. The effectiveness of the proposed model was validated through micro-milling experiments and statistical analysis of cutting force results. When flank wear is considered， the average prediction errors of forces in three directions are reduced by 35%， 27% and 58%， respectively. Furthermore， the case studies were conducted to investigate the effects of flank wear on cutting force coefficients， mean force error and root mean square error， demonstrating the necessity of considering flank wear in micro-milling force modeling.

Key words: micro-milling, cutting force, tool edge radius, flank wear, tool runout

摘要：

为精确预测微铣削过程中的切削力，提出综合考虑切削刃钝圆半径、后刀面磨损与刀具跳动的微铣削力机理模型，建立了微铣刀后刀面磨损与切削刃钝圆半径之间的精确解析关系，并对刀具跳动下的切削刃余摆线轨迹进行了精确分析，构建了瞬时未变形切屑厚度和切入切出角的解析模型，确定了考虑后刀面磨损的刀具-工件切触区域和切削力系数模型，进而构建了同时涵盖切削刃钝圆半径、后刀面磨损及刀具跳动等关键因素的微铣削力通用模型。通过微铣削实验与切削力结果的统计分析，当考虑后刀面磨损时，3个方向平均力预测误差分别减小了35%、27%和58%，验证了该模型的有效性。进一步通过案例分析探讨了后刀面磨损对切削力系数、平均力误差和均方根误差的影响，证明了在微铣削力建模中考虑后刀面磨损的必要性。

关键词: 微铣削, 切削力, 切削刃钝圆半径, 后刀面磨损, 刀具跳动

CLC Number:

V261.97

GAO Shuaishuai, DUAN Xianyin, ZHANG Yu, ZHU Kunpeng. Prediction of Micro-milling Forces Considering Flank Wear with Cutting Edge Radius[J]. China Mechanical Engineering, 2026, 37(5): 1132-1140.

高帅帅, 段现银, 张宇, 朱锟鹏. 考虑切削刃钝圆半径后刀面磨损的微铣削力预测[J]. 中国机械工程, 2026, 37(5): 1132-1140.

Figures/Tables 16

Fig.1 Schematic diagram of the micro-milling process

Fig.2 Relationship among the actual tool radius， cutting edge radius， and flank wear

Fig.3 Instantaneous undeformed chip thickness and cutting contact area

Fig. 4 Micro-milling experimental setup

Tab.1 Micro-milling experimental parameters

实验编号	主轴转速 n/（r·min $- 1$ ）	轴向切深 a_p/μm	每齿进给量 f_z/μm
1	18 000	60	2
2	18 000	80	4
3	18 000	100	6
4	24 000	80	6
5	30 000	60	6
6	24 000	60	4
7	24 000	100	2
8	30 000	80	2
9	30 000	100	4

Tab.1 Micro-milling experimental parameters

实验编号	主轴转速 n/（r·min $- 1$ ）	轴向切深 a_p/μm	每齿进给量 f_z/μm
1	18 000	60	2
2	18 000	80	4
3	18 000	100	6
4	24 000	80	6
5	30 000	60	6
6	24 000	60	4
7	24 000	100	2
8	30 000	80	2
9	30 000	100	4

Fig.5 Images of tool wear

Fig.6 Micro-milling cutting force prediction process

Fig.7 Error of the predicted average force

Fig.8 Mean absolute error of the predicted cutting forces

Fig.9 Root mean square error of the predicted cutting forces

Tab.2 Determination coefficient of milling force model

实验编号	R $x 2$	R $y 2$
1	0.79	0.77
2	0.83	0.80
3	0.77	0.74
4	0.82	0.84
5	0.84	0.82
6	0.76	0.81
7	0.72	0.76
8	0.85	0.80
9	0.84	0.75

Tab.2 Determination coefficient of milling force model

实验编号	R $x 2$	R $y 2$
1	0.79	0.77
2	0.83	0.80
3	0.77	0.74
4	0.82	0.84
5	0.84	0.82
6	0.76	0.81
7	0.72	0.76
8	0.85	0.80
9	0.84	0.75

Fig.10 Entry/Exit angles of the 4th group experiments

Fig.11 The fitting results of the cutting force coefficients

Fig.12 Comparison between measured and predicted micro-milling forces

Fig.13 Average cutting force error throughout the micro-milling process

Fig.14 Root mean square error of the predicted cutting forces throughout the micro-milling process

References 18

[1]	商鹏，黄思硕，刘晓鹏，等. 二维振动辅助微细铣削切削力建模与试验研究［J］. 中国机械工程，2021，32（6）：648-657.
	SHANG Peng， HUANG Sishuo， LIU Xiaopeng， et al. Modeling and Experimental Study on Cutting Forces of 2D Vibration Assisted Micro-milling［J］. China Mechanical Engineering， 2021，32（6）：648-657.
[2]	CAPPELLINI C， ABENI A. An Analytical Micro-milling Force Model Based on the Specific Cutting Pressure-feed Dependence， in Presence of Ploughing and Tool Run-out Effects［J］. Journal of Manufacturing Processes， 2024， 116： 224-245.
[3]	SAHA S， DEB S， BANDYOPADHYAY P P. Precise Measurement of Worn-out Tool Diameter Using Cutting Edge Features during Progressive Wear Analysis in Micro-milling［J］. Wear， 2022， 488/489： 204169.
[4]	马廉洁，杜文豪，赵镇，等. 刀具偏心跳动下侧铣硬脆材料的瞬时铣削力模型［J］. 航空学报， 2024， 45（4）： 428925.
	MA Lianjie， DU Wenhao， ZHAO Zhen， et al. Instantaneous Milling Force Model of Side Milling Hard and Brittle Materials in the State of Tool Eccentricity and Runout［J］. Acta Aeronautica et Astronautica Sinica， 2024， 45（4）： 428925.
[5]	MA K， LIU Z， WANG B， et al. How Does the Uncut Chip Thickness Affect the Deformation States within the Primary Shear Zone during Metal Cutting？［J］. International Journal of Machine Tools and Manufacture， 2024， 199： 104161.
[6]	LIU Z， SHI Z， WAN Y. Definition and Determination of the Minimum Uncut Chip Thickness of Microcutting［J］. The International Journal of Advanced Manufacturing Technology， 2013， 69（5/8）： 1219-1232.
[7]	ZHANG X， YU T， XU P， et al. In-process Stochastic Tool Wear Identification and Its Application to the Improved Cutting Force Modeling of Micro Milling［J］. Mechanical Systems and Signal Processing， 2022， 164： 108233.
[8]	WOJCIECHOWSKI S， MATUSZAK M， POWAŁKA B， et al. Prediction of Cutting Forces during Micro End Milling Considering Chip Thickness Accumulation［J］. International Journal of Machine Tools and Manufacture， 2019， 147： 103466.
[9]	ZHANG X W， EHMANN K F， YU T B， et al. Cutting Forces in Micro-end-milling Processes［J］. International Journal of Machine Tools and Manufacture， 2016， 107： 21-40.
[10]	WAN M， WEN D Y， ZHANG W H， et al. Prediction of Cutting Forces in Flexible Micro Milling Processes by Considering the Change of Instantaneous Cutting Direction［J］. Journal of Manufacturing Processes， 2023， 90： 180-195.
[11]	DING Pengfei， HUANG Xianzhen， LI Shangjie， et al. Real-time Reliability Analysis of Micro-milling Processes Considering the Effects of Tool Wear［J］. Mechanical Systems and Signal Processing， 2023， 200： 110582.
[12]	JING X， LYU R， CHEN Y， et al. Modelling and Experimental Analysis of the Effects of Run Out， Minimum Chip Thickness and Elastic Recovery on the Cutting Force in Micro-end-milling［J］. International Journal of Mechanical Sciences， 2020， 176： 105540.
[13]	DAMBLY V， RIVIÈRE-LORPHÈVRE É， DUCOBU F， et al. Tri-dexel-based Cutter-workpiece Engagement： Computation and Validation for Virtual Machining Operations［J］. The International Journal of Advanced Manufacturing Technology， 2024， 131（2）： 623-635.
[14]	ZHANG Yu， LI Si， ZHU Kunpeng. Generic Instantaneous Force Modeling and Comprehensive Real Engagement Identification in Micro-milling［J］. International Journal of Mechanical Sciences， 2020， 176： 105504.
[15]	DOU Jianming， JIAO Shengjie， XU Chuangwen， et al. Unsupervised Online Prediction of Tool Wear Values Using Force Model Coefficients in Milling［J］. The International Journal of Advanced Manufacturing Technology， 2020， 109（3）： 1153-1166.
[16]	MAMMADOV B， MOHAMMADI Y， FARAHANI N D， et al. A Unified FFT-based Mechanistic Force Coefficient Identification Model for Isotropic and Anisotropic Materials［J］. CIRP Journal of Manufacturing Science and Technology， 2024， 49： 216-229.
[17]	朱锟鹏，李刚. 基于刀具磨损映射关系的微细铣削力理论建模与试验研究［J］. 机械工程学报， 2021， 57（19）： 246-259.
	ZHU Kunpeng， LI Gang. Theoretical Modeling and Experimental Study of Micro Milling Force Based on Tool Wear Mapping［J］. Journal of Mechanical Engineering， 2021， 57（19）： 246-259.
[18]	李刚，张宇，李斯，等. 基于运动学的高速高精密铣削力建模：综合模型与试验［J］. 航空学报， 2023， 44（8）： 427261.
	LI Gang， ZHANG Yu， LI Si， et al. Modeling of High Speed and High Precision Milling Forces Based on Kinematics： Comprehensive Modeling and Experimental［J］. Acta Aeronautica et Astronautica Sinica， 2023， 44（8）： 427261.