考虑切削刃钝圆半径后刀面磨损的微铣削力预测

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

摘要/Abstract

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

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

中图分类号:

V261.97

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.

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.

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链接本文: https://www.cmemo.org.cn/CN/10.3969/j.issn.1004-132X.2026.05.013

https://www.cmemo.org.cn/CN/Y2026/V37/I5/1132

图/表 16

图1 微铣削过程示意图

Fig.1 Schematic diagram of the micro-milling process

图2 实际刀具半径与切削刃半径和后刀面磨损的关系

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

图3 瞬时未变形切屑厚度和切触区域

Fig.3 Instantaneous undeformed chip thickness and cutting contact area

图4 微铣削实验设置

Fig. 4 Micro-milling experimental setup

表1 微铣削实验参数

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

表1 微铣削实验参数

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

图5 刀具磨损图像

Fig.5 Images of tool wear

图6 微铣削切削力预测流程

Fig.6 Micro-milling cutting force prediction process

图7 平均力预测值的误差

Fig.7 Error of the predicted average force

图8 切削力预测值的平均绝对误差

Fig.8 Mean absolute error of the predicted cutting forces

图9 切削力预测值的均方根误差

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

表2 铣削力模型的决定系数

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

表2 铣削力模型的决定系数

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

图10 第4组实验的切入角和切出角

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

图11 切削力系数的拟合结果

Fig.11 The fitting results of the cutting force coefficients

图12 微铣削力测量值和预测值对比

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

图13 整个微铣削过程中的平均切削力误差

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

图14 整个微铣削过程中切削力预测值的均方根误差

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

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