基于铣削系统动力学响应的球头铣刀铣削表面形貌建模

doi:10.12382/bgxb.2021.0472

摘要/Abstract

摘要： 基于系统动力学响应完成弱刚度球头铣刀铣削系统中铣削表面形貌建模，对于提高表面质量具有重要的理论价值。为此，借助齐次坐标变换原理建立球头铣刀刀齿的运动学轨迹，按照机械建模法提出铣削力的求解方法，根据再生振动理论建立柔性刀具-柔性工件铣削系统的动力学模型，基于全离散法提出考虑变时滞效应的工艺系统动态位移求解方法，并采用线性插值法修正刀齿运动轨迹；综合Z-MAP法和数值法提出球头铣刀铣削表面形貌仿真方法，在完成加工轨迹驱动的表面形貌几何仿真的基础上，实现考虑振动诱导下工艺系统动态位移的表面形貌物理仿真；以硬质合金球头铣刀铣削7050-T6进行验证性实验。实验和仿真结果具有较高的一致性，表明该仿真方法是有效的，可以为实际加工参数的选择和优化提供理论依据。

关键词: 球头铣刀铣削, 表面形貌, 动态位移, 建模与仿真

Abstract: Milling surface topography modeling based on the dynamic response of the weak-stiffness ball-end milling system has an important theoretical value for improving surface quality. To do this, first of all, the kinematic trajectory of the ball-end milling cutter teeth is established by homogeneous coordinate transformation, and a solution for the milling force is put forward according to the mechanical modeling method. A dynamic model for the flexible cutter-flexible workpiece milling system is established based on the regenerative vibration theory. A method for solving dynamic displacement of processes based on the full discrete method with the effect of variable time delay considered is proposed. And a linear interpolation method is adopted to modify the cutter tooth trajectory. Then, a simulation method for the surface topography under ball-end milling is proposed by combining Z-MAP method and numerical method. After completing geometric simulation of the surface topography generated by the machining path, a physical simulation considering the dynamic displacement of the process system induced by vibration is carried out. Lastly, a validation experiment is conducted by milling material 7050-T6 using a carbide ball-end milling cutter. The experiment and simulation results are consistent, indicating that the modeling method is effective and can provide theoretical basis for selecting and optimizing actual machining parameters.

Key words: ball-endmilling, surfacetopography, dynamicdisplacement, modelingandsimulation

中图分类号:

TH161
TG54

董永亨，李淑娟，张倩，李鹏阳，李旗，贾祯，李言. 基于铣削系统动力学响应的球头铣刀铣削表面形貌建模[J]. 兵工学报, 2022, 43(8): 1977-1989.

DONG Yongheng， LI Shujuan， ZHANG Qian， LI Pengyang， LI Qi， JIA Zhen， LI Yan. Modeling and Simulation of Surface Topography under Ball-end Milling Based on Dynamic Response of Milling System[J]. Acta Armamentarii, 2022, 43(8): 1977-1989.

参考文献

［1］ WANG H X, ZONG W J, SUN T, et al. Modification of three dimensional topography of the machined KDP crystal surface using wavelet analysis method[J]. Applied Surface Science, 2010, 256(16): 5061-5068.
[2］ AIT-SADI H, HEMMOUCHE L, HATTALI L, et al. Effect of nanosilica additive particles on both friction and wear performance of mild steel/CuSn/SnBi multimaterial system[J]. Tribology International, 2015,90:372-385.
[3］梁鑫光, 姚振强. 基于动力学响应的球头刀五轴铣削表面形貌仿真[J]. 机械工程学报, 2013, 6(6):171-178.
LIANG X G, YAO Z Q. Dynamic-based simulation for machined surface topography in 5-axis ball-end milling[J]. Journal of Mechanical Engineering, 2013, 6(6): 171-178. (in Chinese)
[4］ ALTINTAS Y, ENGIN S. Generalized modeling of mechanics and dynamics of milling cutters[J]. CIRP Annals-Manufacturing Technology, 2001, 50(1):25-30.
[5］阎兵, 张大卫. 球头铣刀铣削表面形貌建模与仿真[J]. 计算机辅助设计与图形学学报, 2001,13(2):135-140.
YAN B, ZHANG D W. Modeling and Simulation of ball end milling surface topology[J]. Journal of Computer Aided Design and Graphics, 2001,13(2): 135-140. (in Chinese)
[6］ QUINSAT Y, SABOURIN L, LARTIGUE C. Surface topography in ball end milling process: description of a 3D surface roughness parameter[J]. Journal of Materials Processing Technology, 2008, 195(1/2/3):135-143.
[7］ QUINSAT Y, LAVERNHE S, LARTIGUE C. Characterization of 3D surface topography in 5-axis milling[J]. Wear, 2011,271(3/4):590-595.
[8］ LIU X, SOSHI M, SAHASRABUDHE A, et al. A geometrical simulation system of ball end finish milling process and its application for the prediction of surface micro features[J]. Journal of Manufacturing Science and Engineering, 2006,128(1):74.
[9］范思敏, 肖继明, 董永亨, 等. 球头铣刀铣削球面的表面形貌建模与仿真研究[J]. 中国机械工程, 2020, 31(24): 2924-2930, 2936.
FAN S M, XIAO J M, DONG Y H, et al. Study on modeling and simulation of surface topography of spherical milling with ball-end milling cutters[J]. China Mechanicl Engneering, 2020, 31(24): 2924-2930, 2936. (in Chinese)
[10］赵厚伟, 张松, 赵斌, 等. 球头铣刀加工表面形貌仿真预测[J]. 计算机集成制造系统, 2014, 20(4):880-889.
ZHAO H W, ZHANG S, ZHAO B, et al. Simulation and prediction of surface topography machined by ball-nose end mill[J]. Computer Integrated Manufacturing System, 2014, 20(4): 880-889. (in Chinese)
[11］赵厚伟, 张松, 王高琦, 等. 球头铣刀加工倾角对表面形貌的影响[J]. 计算机集成制造系统, 2013, 19(10):2438-2444.
ZHAO H W, ZHANG S, WANG G Q, et al. Effect of machining inclination angle of ball-nose end mill on surface topography[J]. Computer Integrated Manufacturing System, 2013, 19(10): 2438-2444. (in Chinese)
[12］王仁伟, 张松, 葛人杰, 等. 改进的球头铣刀加工表面形貌建模方法[J]. 计算机集成制造系统, 2021, 27(4): 973-980.
WANG R W, ZHANG S, GE R J, et al. Modified machined surface topography modeling in ball-end milling process[J]. Computer Integrated Manufacturing System, 2021, 27(4): 973-980. (in Chinese)
[13］ ANTONIADIS A, SAVAKIS C, BILALIS N, et al. Prediction of surface topomorphy and roughness in ball-end milling[J]. International Journal of Advanced Manufacturing Technology, 2003, 21(12):965-971.
[14］ GAO T, ZHANG W H, QIU K P, et al. Numerical simulation of machined surface topography and roughness in milling process[J]. Journal of Manufacturing Science and Engineering, 2006, 128(1):96.
[15］谭刚, 张卫红, 万敏, 等. 球头刀多轴铣削表面形貌建模仿真研究[J]. 昆明理工大学学报(理工版), 2007, 32(3):23-29.
TAN G,ZHANG W H, WAN M, et al. Modeling and smiulation study on multi-axis milled surface topography with round head cutter[J]. Journal of Kunming University of Science and Technology (Science and Technology), 2007, 32(3):23-29. (in Chinese)
[16］ ZHANG W-H, TAN G, WAN M, et al. A new algorithm for the numerical simulation of machined surface topography in multiaxis ball-end milling[J]. Journal of Manufacturing Science and Engineering, 2008, 130(1):011003.
[17］ CHEN J S, HUANG Y K, CHEN M S. A study of the surface scallop generating mechanism in the ball-end milling process[J]. International Journal of Machine Tools and Manufacture, 2005, 45(9):1077-1084.
[18］ MIZUGAKI Y, HAO M, KIKKAWA K, et al. Geometric generating mechanism of machined surface by ball-nosed end milling[J]. CIRP Annals-Manufacturing Technology, 2001, 50(1): 69-72.
[19］ ARIZMENDI M, FERNNDEZ J, LACALLE L N L D, et al. Model development for the prediction of surface topography generated by ball-end mills taking into account the tool parallel axis offset. experimental validation[J]. CIRP Annals-Manufacturing Technology, 2008, 57(1):101-104.
[20］董永亨, 李淑娟, 李言, 等. 基于改进Z-MAP算法的球头铣刀加工表面形貌仿真与试验研究[J]. 机械工程学报, 2017, 53(23):197-208.
DONG Y H, LI S J, LI Y, et al. Simulation and experimental study of ball-end milling surface topography based on an improved Z-MAP algorithm[J]. Chinese Journal of Mechanical Engineering, 2017, 53(23):197-208. (in Chinese)
[21］董永亨, 李淑娟, 李言, 等. 球头铣刀余摆线加工表面形貌的建模与仿真研究[J]. 机械工程学报, 2018, 54(19):212-223.
DONG Y H, LI S J, LI Y, et al. Research on modeling and simulation of surface topography obtained by trochoidal milling mode with ball end milling cutter[J]. Chinese Journal of Mechanical Engineering, 2018, 54(19):212-223.(in Chinese)
[22］ TOH C K. Surface topography analysis in high speed finish milling inclined hardened steel[J]. Precision Engineering, 2004, 28(4):386-398.
[23］ CHIANG S T, TSAI C M, LEE A C. Analysis of cutting forces in ball-end milling[J]. Journal of Materials Processing Technology, 1995, 47(3/4):231-249.
[24］ BUDAK E, ALTINTAS?瘙塁 Y, ARMAREGO E J A. Prediction of milling force coefficients from orthogonal cutting data[J]. Journal of Manufacturing Science and Engineering, 1996, 118(2):216-224.
[25］ ALTINTAS Y, WECK M. Chatter stability of metal cutting and grinding[J]. CIRP Annals-Manufacturing Technology, 2004, 53(2): 619-642.
[26］ MONTGOMERY D, ALTINTAS Y. Mechanism of cutting force and surface generation in dynamic milling[J]. Journal of Manufacturing Science and Engineering, 1991, 113(2):160-168.
[27］ DING Y, ZHU L M, ZHANG X J, et al. A full-discretization method for prediction of milling stability[J]. International Journal of Machine Tools & Manufacture, 2010, 50(5):502-509.

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