矩阵算子法构建切削滑移线场的分析

周里群; 胡中翔; 刘毅; 王俊文; 汪振南

doi:10.13433/j.cnki.1003-8728.20220177

矩阵算子法构建切削滑移线场的分析

doi: 10.13433/j.cnki.1003-8728.20220177

湘潭大学机械工程与力学学院，湖南湘潭　411105

基金项目: 湖南省自然科学湘潭联合基金项目（2021JJ50127）

详细信息

作者简介:
周里群（1965−），教授，硕士生导师，研究方向为先进制造技术，johnzlq@163.com

中图分类号: TG501.3
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- 文章访问数: 74
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- PDF下载量: 9
- 被引次数: 0
出版历程
- 收稿日期: 2021-11-16
- 刊出日期: 2023-12-25

Analysis of Cutting Slip-line Field Constructed by Using Matrix-operator Method

School of Mechanical Engineering and Mechanics, Xiangtan University, Xiangtan 411105, Hu'nan, China

摘要

摘要: 刀具与切屑接触的摩擦因数呈不均匀分布增加了正交切削分析的难度，缺少一个完善的解析模型。针对于此，本文采用矩阵算子法构建了一种考虑在刀−屑接触面上变摩擦因数的滑移线场。通过Oxley的剪切切削理论找出工件表面材料塑性剪切变形的位置，为滑移线场的添加几何约束条件，从而求解滑移线参数。根据滑移线场，导出刀−屑接触长度，推算出切削力的解析式。模型计算结果与GH4169切削有限元仿真结果对比发现：刀−屑接触长度误差在9.8%内，两者的切削力在变化趋势上一致且数值上相近，验证了滑移线场的准确性。上述研究成果为变摩擦因数的正交切削分析刀−屑接触长度和切削力提供了理论方法。
- 金属切削 /
- 矩阵算子法 /
- 滑移线场 /
- 刀-屑接触长度 /
- 切削力
Abstract: The friction coefficient between the tool and the chip is unevenly distributed which increases the difficulty of orthogonal cutting analysis and lacks an analytical model. A slip-line field with variable friction coefficient on the tool-chip contact surface is constructed with matrix operator method. Geometric constraints, which obtain from the position of plastic shear deformation of workpiece surface found in terms of the Oxley's shear cutting theory, are added to the slip-line field to determine the parameters in the slip-line field. According to the above model, the tool-chip contact length is derived and the analytical formula of the cutting force is deduced. By comparing with the model and the finite element results in the cutting of GH4169, it is found that the error of tool-chip contact length is within 9.8%, the change in cutting force is slight, which verifies the accuracy of the model via slip line field method. The above results provide a theoretical method for orthogonal cutting with variable friction coefficient analysis of tool chip contact length and cutting force.
- metal cutting /
- matrix-operator method /
- slip-line field /
- tool-chip contact length /
- cutting force

HTML全文

图 1 切削滑移线场

Figure 1. The cutting slip-line field model

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图 2 滑移线场速矢图

Figure 2. Holograph for the slip-line field model

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图 3 滑移线场的约束条件

Figure 3. Constraints for the slip line field

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图 4 K点静水压力

Figure 4. K-point hydrostatic pressure

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图 5 K点受力分析

Figure 5. K-point force analysis

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图 6 Mises应力云图

Figure 6. Mises stress nephogram

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图 7 仿真切削力

Figure 7. Simulated cutting force

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图 8 不同切削深度下刀−屑接触长度对比

Figure 8. Comparison of tool-chip contact length under different cutting depths

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图 9 不同刀具前角下刀−屑接触长度对比

Figure 9. Comparison of tool-chip contact length under different tool rake angles

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图 10 不同切削深度下X向切削力对比

Figure 10. Comparison of X-direction cutting forces at different cutting depths

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图 11 不同切削深度下Y向切削力对比

Figure 11. Comparison of Y-direction cutting forces at different cutting depths

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图 12 不同刀具前角下X向切削力对比

Figure 12. Comparison of X-direction cutting forces under different tool rake angles

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图 13 不同刀具前角下Y向切削力对比

Figure 13. Comparison of Y-direction cutting forces under different tool rake angles

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表 1 GH4169J-C本构模型参数

Table 1. GH4169 J-C constitutive model parameters

A/MPa B/MPa C m n

963 937 0.022 1.3 0.333

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表 2 仿真加工参数表

Table 2. Processing parameters for simulation

组数切削深度t_u/mm 刀具前角φ/（°）切削速度v/（m·min⁻¹）

1 0.1 15 100
2 0.2 15 100
3 0.3 15 100
4 0.4 15 100
5 0.2 5 100
6 0.2 10 100
7 0.2 20 100

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