平面曲线端铣加工过程铣削力的建模与预测

doi:10.3969/j.issn.1000-1093.2015.09.018

摘要/Abstract

摘要： 针对平面曲线端铣加工过程，提出一种考虑瞬时进给方向的铣削力预测方法。铣削加工时每齿进给量、切入/切出角以及瞬时切屑厚度等铣削参量随着曲线曲率的改变而变化，将单个频齿周期内的曲线加工过程看做是一系列铣削条件恒定的微小稳态加工过程，建立了等效进给量、切入/切出角的矢量计算模型，通过计算每一微小阶段的铣削参量，推导了平面曲线端铣中基于傅里叶级数展开的铣削力模型。以PCrNi3MoVA钢为工件材料，分别进行圆弧和Bezier曲线端铣加工试验，试验结果表明，预测的铣削力在幅值和变化趋势上与试验测量结果吻合良好，验证了该铣削力预测方法的有效性。

关键词: 机械制造工艺与设备, 铣削力, 矢量模型, 平面曲线端铣, 傅里叶级数展开

Abstract: A novel mechanistic cutting force model is presented for end milling of curved surfaces, including the effect of instantaneous feed direction. In machining of curved geometries where the curvature varies continuously along tool path, the cutting parameters, such as feed per tooth, entry/exit angle, and instantaneous undeformed chip thickness, vary along tool path. The cutting process of curved surface is discretized into a series of steady-state cutting processes at intervals of feed per tooth, and a vector model for these parameters of each segmented cutting process is presented. The Fourier series expansion is used for deriving the cutting force model. Combined with the milling force coefficients fitted by a series of slot milling tests, the predicted cutting forces in machining PCrNi3MoVA workpiece with circular and Bezier curve geometries are achieved, respectively. The prediction accuracy of the model is validated experimentally and the predicted and measured results correspond well with each other.

Key words: manufaturing technolgy and equipment, cutting force, vector model, end milling of curved surfaces, Fourier series expansion

中图分类号:

TG506

罗智文，赵文祥，焦黎，王西彬，谭方浩，刘志兵，梁志强. 平面曲线端铣加工过程铣削力的建模与预测[J]. 兵工学报, 2015, 36(9): 1727-1735.

LUO Zhi-wen, ZHAO Wen-xiang, JIAO Li, WANG Xi-bin, TAN Fang-hao, LIU Zhi-bing, LIANG Zhi-qiang. Modeling and Prediction of Cutting Forces in End Milling of Curved Surfaces[J]. Acta Armamentarii, 2015, 36(9): 1727-1735.

参考文献

［1］ Kline W A, Devor R E, Lindberg J R. The prediction of cutting forces in end milling with application to cornering cuts[J]. International Journal of Machine Tool Design and Research, 1982, 22(1): 7-22.
［2］ Zhang L, Zheng L. Prediction of cutting forces in milling of circular corner profiles[J]. International Journal of Machine Tools and Manufacture, 2004, 44(2/3): 225-235.
［3］李忠群，刘强. 圆角铣削颤振稳定域建模与仿真研究[J]. 机械工程学报， 2010,46(7): 181-186.
LI Zhong-qun, LIU Qiang. Modeling and simulation of chatter stability for circular milling[J].Journal of Mechanical Engineering，2010,46(7): 181-186. (in Chinese)
［4］ Wu B, Yan X, Luo M, et al. Cutting force prediction for circular end milling process[J]. Chinese Journal of Aeronautics， 2013,26(4): 1057-1063.
［5］ Han X, Tang L. Precise prediction of forces in milling circular corners[J]. International Journal of Machine Tools and Manufacture， 2015, 88: 184-193.
［6］ Banerjee A, Feng H, Bordatchev E V. Geometry of chip formation in circular end milling[J]. The International Journal of Advanced Manufacturing Technology， 2012, 59(1): 21-35.
［7］ Rao V S, Rao P V M. Modelling of tooth trajectory and process geometry in peripheral milling of curved surfaces[J]. International Journal of Machine Tools and Manufacture， 2005, 45(6): 617-630.
［8］ Desai K A, Agarwal P K, Rao P V M. Process geometry modeling with cutter runout for milling of curved surfaces[J]. International Journal of Machine Tools and Manufacture， 2009, 49(12/13): 1015-1028.
［9］ Desai K A, Rao P V M. Effect of direction of parameterization on cutting forces and surface error in machining curved geometries[J]. International Journal of Machine Tools and Manufacture， 2008, 48(2): 249-259.
［10］ Sun Y, Guo Q. Numerical simulation and prediction of cutting forces in five-axis milling processes with cutter run-out[J]. International Journal of Machine Tools and Manufacture, 2011, 51(10/11): 806-815.
［11］ Yang Y, Zhang W, Wan M. Effect of cutter runout on process geometry and forces in peripheral milling of curved surfaces with variable curvature[J]. International Journal of Machine Tools and Manufacture, 2011, 51(5): 420-427.
［12］ Wei Z C, Wang M J, Han X G. Cutting forces prediction in generalized pocket machining[J]. The International Journal of Advanced Manufacturing Technology, 2010, 50(5/6/7/8): 449-458.
［13］ Wei Z C, Wang M J, Ma R G, et al. Modeling of process geometry in peripheral milling of curved surfaces[J]. Journal of Materials Processing Technology, 2010, 210(5): 799-806.
［14］ Qi H, Tian Y, Zhang D. Machining forces prediction for peripheral milling of low-rigidity component with curved geometry[J]. The International Journal of Advanced Manufacturing Technology, 2013, 64(9/10/11/12): 1599-1610.
［15］戚厚军，张大卫，蔡玉俊，等. 摆线轮轮廓高速周铣工艺系统的弹性铣削力预测方法[J]. 机械工程学报, 2009, 45(9): 164-172.
QI Hou-jun, ZHANG Da-wei, CAI Yu-jun, et al. Modeling methodology of flexible milling force for cycloid gear on high speed peripheral milling process system[J]. Journal of Mechanical Engineering, 2009,45(9): 164-172. (in Chinese)
［16］ Lotfi B, Zhong Z W, Khoo L P. Prediction of cutting forces along Pythagorean-hodograph curves[J]. The International Journal of Advanced Manufacturing Technology, 2009, 43(9/10): 872-882.
［17］ Ferry W B, Altintas Y. Virtual five-axis flank milling of jet engine impellers—part Ⅰ: mechanics of five-axis flank milling[J]. Journal of Manufacutring Science and Engineering, 2008, 130(1): 11005.
［18］ Lu L, Liu X, Tang Y, et al. FEM analysis of workpiece curvature influence on groove deformation during plough process[J]. Transactions of Nonferrous Metals Society of China, 2012, 22(7): 1738-1743.
［19］ Davim J P. Machining:fundamentals and recent advances[M]. London: Springer Science & Business Media, 2008.
［20］ Martellotti M E. An analysis of the milling process[J]. Transactions of the ASME, 1941(65): 677-700.
［21］ Wan M, Lu M S, Zhang W H, et al. A new ternary-mechanism model for the prediction of cutting forces in flat end milling[J]. International Journal of Machine Tools and Manufacture, 2012, 57: 34-45.
［22］ Wang M, Gao L, Zheng Y. An examination of the fundamental mechanics of cutting force coefficients[J]. International Journal of Machine Tools and Manufacture, 2014, 78: 1-7.

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