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工程设计学报
Chinese Journal of Engineering Design  2024, Vol. 31 Issue (5): 575-584    DOI: 10.3785/j.issn.1006-754X.2024.03.183
Theory and Method of Mechanical Design     
Five-axis flank milling tool positioning method based on spiral contact line
Zhongpeng LI1(),Liqiang ZHANG1(),Gang LIU1,2,3
1.School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai 201620, China
2.Key Laboratory of Machinery Industry for Intelligent Manufacturing of Large Complex Thin-Walled Parts, Shanghai 201620, China
3.Institute of Chengdu Zhiyuan Advanced Manufacturing Technology, Chengdu 610511, China
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Abstract  

A tool positioning method based on spiral contact line is proposed to address the problem of mutual interference between tool and design surface during five-axis flank milling of undevelopable ruled surfaces. Firstly, an analytical error model under a single tool position was established based on the Z-buffer method to evaluate the advantages and disadvantages of the tool positioning method. Secondly, a mathematical model of the tool axis vector was constructed based on the torsional characteristics of the undevelopable ruled surfaces, and the properties and parametric expressions of the tool-workpiece contact line were analyzed. Thirdly, considering the non-linear machining errors in actual machining, the path interpolation optimization for the global tool position was carried out by kinematics transformation. Finally, the simulation analysis was conducted based on the improved two-point offset method, the least square method and the proposed method, and the errors generated by the three methods were compared, with the latter two methods being used for experimental verification. The simulation and experimental results show that the proposed method can effectively reduce the principle error in flank milling, which can provide a certain reference for five-axis flank milling of undevelopable ruled surfaces.

Key words： five-axis flank milling      undevelopable ruled surface      spiral contact line      path optimization      principle error     
Received: 30 June 2023      Published: 30 October 2024
CLC:  TH 161.1  
Corresponding Authors: Liqiang ZHANG     E-mail: M310121104@sues.edu.cn;zhanglq@sues.edu.cn
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Zhongpeng LI
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Gang LIU
Cite this article:

Zhongpeng LI,Liqiang ZHANG,Gang LIU. Five-axis flank milling tool positioning method based on spiral contact line. Chinese Journal of Engineering Design, 2024, 31(5): 575-584.

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https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2024.03.183     OR     https://www.zjujournals.com/gcsjxb/Y2024/V31/I5/575


基于螺旋接触线的五轴侧铣刀具定位方法

针对五轴侧铣加工非可展直纹面时刀具与设计曲面相互干涉的问题，提出了一种基于螺旋接触线的刀具定位方法。首先，基于Z-buffer法建立单个刀位下的误差解析模型，以评估刀具定位方法的优劣。其次，根据非可展直纹面的扭转特性，构造刀轴矢量的数学模型，同时分析刀具-工件接触线的性质及参数表达式。再次，考虑实际加工中的非线性加工误差，通过运动学变换对全局刀位进行路径插补优化。最后，基于改进两点偏置法、最小二乘法及所提出的方法进行仿真分析并对比3种方法所产生的误差，同时基于后2种方法进行实验验证。仿真和实验结果表明，所提出的方法能够有效减小侧铣加工中的原理误差，可为非可展直纹面的五轴侧铣加工提供一定的参考依据。


关键词： 五轴侧铣,  非可展直纹面,  螺旋接触线,  路径优化,  原理误差 
Fig.1 Error model based on Z-buffer method
Fig.2 Schematic of Boolean quadrature for line and surface
Fig.3 Schematic of tool positioning
Fig.4 Schematic of tool axis position determination
Fig.5 Schematic of actual tool-workpiece contact line
Fig.6 Kinematics transformation for five-axis flank milling
Fig.7 Global tool position diagram based on spiral contact line
 
Fig.8 Torsion angle variation curve of undevelopable ruled surface
Fig.9 Distribution law of maximum machining error under different tool positions
误差改进两点偏置法最小二乘法本文方法
极差0.102 70.078 20.028 9
eo, max-0.080 8-0.058 8-0.028 9
eu, max0.021 90.019 40
Table 2 Comparison of maximum machining error under different methods
Fig.10 Distribution law of maximum overcut error under the method in this paper
Fig.11 Distribution law of machining error under a single tool position
Fig.12 Five-axis machining center and three-coordinate measuring instrument
Fig.13 Machining error distribution nephogram under least square method
Fig.14 Machining error distribution nephogram under the method in this paper
Fig.15 Comparison between simulated and measured machining error values under the method in this paper （v=0.45）
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