基于斜角切削的球头铣刀铣削力建模

靳淇超, 李军, 叶子银, 等

doi:10.12141/j.issn.1000-565X.250053

华南理工大学学报(自然科学版) >

2026 , Vol. 54 >Issue 1: 134 - 141

DOI: https://doi.org/10.12141/j.issn.1000-565X.250053

机械工程

基于斜角切削的球头铣刀铣削力建模

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1. 长安大学道路施工技术与装备教育部重点实验室，陕西西安 710064；

2. 中国航发西安航空发动机有限公司，陕西西安 710021；

3. 西安交通大学精密微纳制造技术全国重点实验室，陕西西安 710054

网络出版日期: 2025-06-17

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Modeling of Milling Force for Ball End Milling Cutter Based on Oblique Cutting

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1. Key Laboratory of Road Construction Technology and Equipment of MOE, Chang’an University, Xi’an 710064, Shaanxi, China；

2. AECC Xi’an Aero-engine Ltd., Xi’an Shaanxi 710021, Shaanxi, China；

3. National Key Laboratory of Precision Micro/Nano Manufacturing Technology, Xi’an Jiaotong University, Xi’an Shaanxi 710054, Shaanxi, China

Online published: 2025-06-17

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摘要

针对球头铣刀变刃倾角切削时三维力场分布复杂、未变形切屑厚度动态变化显著等特点，为实现球头铣刀多轴加工中切削力的高精度预测，本研究提出了一种融合斜角切削理论与动态运动学仿真的铣削力建模方法。首先，基于等效平面法建立斜角切削力学解析框架，通过坐标变换将三维切削问题转化为二维平面，推导包含剪切效应与耕犁效应的复合力学模型，重点表征刃倾角对材料流动方向及应力分布的调控机制；其次，建立球头铣刀刃线几何特征，结合刀具-工件运动学耦合模型，求解刀齿运动微分方程，并通过改进型Z-MAP算法实现动态加工表面形貌仿真，提取时变未变形切屑厚度分布；进而提出多尺度力学映射策略，将刀具离散为微元切削刃，基于斜角切削解析模型迭代积分求解各微元的切向力、径向力与轴向力分量，最终合成三维铣削力时域信号。结果表明：轴向、进给方向与切宽方向的铣削力预测最大误差分别为18.3%、10.8%与22.4%，验证了模型在复杂几何刀具受力分析中的适用性。该研究通过融合运动学仿真与微观力学解析，为球头铣刀工艺参数优化与加工稳定性提升提供了理论支撑。

关键词： 斜角切削; 球头铣刀; TANH本构模型; 刀具-工件接触区域; 铣削力模型

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靳淇超, 李军, 叶子银, 等 . 基于斜角切削的球头铣刀铣削力建模[J]. 华南理工大学学报(自然科学版), 2026 , 54(1) : 134 -141 . DOI: 10.12141/j.issn.1000-565X.250053

Abstract

In order to address the challenges of complex three-dimensional force distributions under varying cutting edge angles and significant dynamic variations in undeformed chip thickness in ball-end milling, this study proposed a milling force prediction model integrating oblique cutting theory and dynamic kinematic simulation for high-precision cutting force analysis in multi-axis machining. First, an oblique cutting mechanical framework was established based on the equivalent plane method. The three-dimensional cutting problem was transformed into a two-dimensional plane through coordinate transformation, and a composite mechanical model incorporating shear and ploughing effects was derived, specifically characterizing the regulatory mechanisms of cutting edge angles on material flow direction and stress distribution. Subsequently, the geometric features of the ball-end cutter’s cutting edges were precisely reconstructed. A coupled tool-workpiece kinematic model was developed to solve the differential equations governing tooth motion trajectories, and dynamic machining surface morphology simulation was implemented via an improved Z-MAP algorithm to extract time-varying undeformed chip thickness distributions. Furthermore, a multi-scale mechanical mapping strategy was proposed, where the tool was discretized into micro-element cutting edges. The tangential, radial, and axial force components of each element were iteratively integrated based on the oblique cutting analytical model, ultimately synthesizing three-dimensional milling force time-domain signals. Experimental results demonstrated that the maximum prediction errors for axial , feed-direction , and cutting-width-direction milling forces were 18.3%, 10.8%, and 22.4%, respectively, validating the model’s applicability in force analysis for complex geometric tools. By integrating kinematic simulation and microscopic mechanical analysis, this study provided theoretical support for optimizing process parameters and enhancing machining stability in ball-end milling operations.

Key words： oblique cutting; ball-end Mill; TANH constitutive model; tool-workpiece contact area; milling force model

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