曲面高速铣削加工动态分析和仿真研究
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摘要
本文在球头铣刀理论铣削力模型基础上，考虑高速加工切屑惯性力，建立了单元铣削力模型，并针对深型腔的加工铣刀变形，建立了球头铣刀变形铣削力模型，给出了曲面曲率变化的切入提前角和切出滞后角的切削区间模型。
在许多模具和复杂零件中的曲面型腔加工需要采用细长杆球头铣刀，因此在铣刀变形铣削力模型基础上，针对动态铣削中细长杆球头铣刀振动和工件表面波纹对切削厚度的再生反馈建立了动态铣削力模型，并在ANSYS中进行模态分析，得出铣削刀具的模态固有振动频率，为球头铣刀截面系数的求解提供必要的数据。
铣刀在铣削时的振动位移是影响工件加工质量的重要因素之一。本文利用MATLAB／GUI工具对动态铣削力模型和振动位移模型进行了仿真分析，研究了铣削参数对铣刀在曲面高速铣削时动态铣削力和振动位移的影响。论文通过曲面高速铣削实验实测铣削力，并与仿真结果对比，仿真与实测结果之间的相对误差较小，证明了模型的正确性。
论文利用动态铣削力模型和振动位移模型对高速铣削加工中振动进行了预测研究，进而可以优化切削参数，并可为曲面高速加工中刀具运动轨迹优化提供参考，以延长刀具寿命，并提高加工工件的表面质量。
Considering the inertial force of high speed milling, the elemental force componentsare established based on the cutting force model of ball end milling, and the cutting forcemodel of ball end milling which is used to mill the deep contour with considering springdeflection is established. In view of the feature of ball end milling process, the model ofaccurate cutting area is presented which considers the advance angle of cutting in and thelag angle of cutting off with considering the curvature of machined surface.
Considering the feedback of dynamic deflection of the cutter and vibration mark onthe milled surface on the transient chip thickness, the dynamic model of the regenerativemilling force is constructed based on the cutting force model of ball end milling which isused to mill the deep contour with considering spring deflection. Carrying on modelanalyze through ANSYS software to milling cutter, study the natural frequency of ball endmilling,and provide some data for the cutter effective cross section coefficient.
The milling cutter's vibration displacement in the milling process is one of the mainelements which influence the accuracy of the work piece. The MATLAB/GUI is used tothe dynamic model of the regenerative milling force and the model of vibrationdisplacement; we can research the influence of the high speed surface machining processparameters for the vibration displacement and the regenerative dynamic milling force ofhigh speed surface machining. In the high speed milling experiment research, a series ofexperiment shave have been carried out to get milling force data. By comparison with thepredicted milling force, it is shown that the simulation errors is small, which proves thecorrectness of the model.
The vibration displacement of the high speed milling based on the dynamic model ofthe regenerative milling force and the model of vibration displacement has been researched,then the optimized parameter choices has been offered, and these establish the basis forchoosing the tool path of high-speed cutting, these are advantageous in strengthening thecutting tool life, and enhance the high speed surface machining process quality.
在许多模具和复杂零件中的曲面型腔加工需要采用细长杆球头铣刀，因此在铣刀变形铣削力模型基础上，针对动态铣削中细长杆球头铣刀振动和工件表面波纹对切削厚度的再生反馈建立了动态铣削力模型，并在ANSYS中进行模态分析，得出铣削刀具的模态固有振动频率，为球头铣刀截面系数的求解提供必要的数据。
铣刀在铣削时的振动位移是影响工件加工质量的重要因素之一。本文利用MATLAB／GUI工具对动态铣削力模型和振动位移模型进行了仿真分析，研究了铣削参数对铣刀在曲面高速铣削时动态铣削力和振动位移的影响。论文通过曲面高速铣削实验实测铣削力，并与仿真结果对比，仿真与实测结果之间的相对误差较小，证明了模型的正确性。
论文利用动态铣削力模型和振动位移模型对高速铣削加工中振动进行了预测研究，进而可以优化切削参数，并可为曲面高速加工中刀具运动轨迹优化提供参考，以延长刀具寿命，并提高加工工件的表面质量。
Considering the inertial force of high speed milling, the elemental force componentsare established based on the cutting force model of ball end milling, and the cutting forcemodel of ball end milling which is used to mill the deep contour with considering springdeflection is established. In view of the feature of ball end milling process, the model ofaccurate cutting area is presented which considers the advance angle of cutting in and thelag angle of cutting off with considering the curvature of machined surface.
Considering the feedback of dynamic deflection of the cutter and vibration mark onthe milled surface on the transient chip thickness, the dynamic model of the regenerativemilling force is constructed based on the cutting force model of ball end milling which isused to mill the deep contour with considering spring deflection. Carrying on modelanalyze through ANSYS software to milling cutter, study the natural frequency of ball endmilling,and provide some data for the cutter effective cross section coefficient.
The milling cutter's vibration displacement in the milling process is one of the mainelements which influence the accuracy of the work piece. The MATLAB/GUI is used tothe dynamic model of the regenerative milling force and the model of vibrationdisplacement; we can research the influence of the high speed surface machining processparameters for the vibration displacement and the regenerative dynamic milling force ofhigh speed surface machining. In the high speed milling experiment research, a series ofexperiment shave have been carried out to get milling force data. By comparison with thepredicted milling force, it is shown that the simulation errors is small, which proves thecorrectness of the model.
The vibration displacement of the high speed milling based on the dynamic model ofthe regenerative milling force and the model of vibration displacement has been researched,then the optimized parameter choices has been offered, and these establish the basis forchoosing the tool path of high-speed cutting, these are advantageous in strengthening thecutting tool life, and enhance the high speed surface machining process quality.
引文
1 M. E. Martellotti. An Analysis of the Milling Process. ASME, 1941, 63:677～700
2 M. E. Martellotti. An Analysis of the Milling Process, Part2-Dawn Milling. ASME, 1945, 67: 233～251
3 T.Hosoi. Cutting Action of Ball End Mill with a Spiral Edge. Annals of the CIRP, 1977, 26(1-2): 49～53
4 S.Jain, K.C.Yang. A Systematic Force Analysis of the Milling Operation. in Proceedings of ASME Winter Annual Meeting, San Francisco, 1989, 55～63
5 His-Yung Feng. Prediction of cutting forces in the ball-end milling process. Journal of Materials Processing Technology, 1995, 54(1-4): 286～301
6 K.Nakayama, M.Arai. On the Storage of Data on Metal Cutting Forces. Annals of the CIRP, 1976, 25(1): 13～18
7 N.Ueda, T.Matsuo. Investigation of Some Shear Angle Theories. Annals of the CIRP, 1986, 35(1): 27～30
8 H.Y.Feng, C.H.Menq. Prediction of Cutting Force in the Ball-End Milling Process-1. Model Formulation and model Building Procedure. Int. J. Mach. Tools & Manuf, 1994, 34(5): 698～710
9 H. Y. Feng, C. H. Menq. Flexible Ball-End Milling System Model for Cutting Force and Machining Error Prediction. Journal of Manufacturing Science and Engineering, Transactions of the ASME, 1996, 118(4): 461～469
10 P. Lee, Y. Altintas. Prediction of Ball End Milling Forces From Orthogonal Cutting Data. Int. J. Mach. Tools.Manuf, 1996, 36(9): 1059～1072
11 Li Zheng, Yun Shun Chiou, S. Y. Liang. Three Dimensional Cutting Force Analysis in End Milling. International Journal of Mechanical Sciences, 1996, 38(3): 259～269
12 A. E. Bayoumi, G. Yucesan, L. A. Kendall. Analytic Mechanistic Cutting Force Model for Milling Operations. Journal of Engineering for Industry, Transactions of the ASME, 1994, 116: 324～330
13 A.E.Bayoumi, G.Yucesan, L.A.Kendall. An Analytic Mechanistic Cutting Force Model for Milling Operations. A Theory and Methodology ASME Journal of Engineering for Industry, 1994, 116(3): 331～339
14 冯志勇．数控环境下广义铣削力建模理论及参数识别方法的研究[博士论文]．天津：天津大学，1998，9：41～44
15 冯志勇，张大卫，黄田，曾子平．一种新型的广义铣削力模型．中国机械工程，1998，9：41～44
16 W.A.K line, R.E.Devor. Effect of Runout on Cutting Geometry and Forces in End Milling. ASME Journal of Engineering for Industry, 1983, 23(2-3): 123～140
17 W. A. Kline, R. E. Devor. Prediction of Cutting Force in End Milling with Application to Cornering Cuts. International Journal of Machine Tools & Manufacture, 1982, 22(1): 7～22
18 C. Sim, M. Yang. Prediction of Cutting Force in Ball-End Milling with a flexible cutter. International Journal of Machine Tools & Manufacture, 1993, 33(2): 267～284
19 Gyu Man Kin, Chong Nam Chu. Mean cutting force prediction ball end milling using force map method. Journal of Material Processing Technology, 2004, 146(3): 303～310
20 Y. Altintas, P. Lee. General Mechanics and Dynamics Model for Helical End Mills. Annals of the CIRP, 1996, 45(1): 59～64
21 Tlusty, F. Ismail. Special Aspects of Chatter in Milling. ASME Journal of Vib. Aco. Str. & Relia. in Design, 1983, 105(1): 24～32
22 S. Smith, J.Tlusty. Efficient Simulation Programs for Chatter in Milling. Annals of the CIRP, 1993, 42(1): 463～466
23 H. El Mounayri, A.D.Spence, M.A.Elbestawi. Milling Process Simulation-A Generic Solid Modeller Based Paradigm. Journal of Manufacturing Science and Engineering, Transactions of the ASME, 1998, 120(2): 213～221
24 F.Abrari, M.A.Elbestawi, A.D.Spence. On the Dynamics of Ball End Milling: Modeling of Cutting Forces and Stability Analysis. International Journal of Machine Tools & Manufacture, 1998, 38(3): 215～237
25 艾兴．高速切削加工技术[M]．北京：国防工业出版社，2003，26～76
26 黄雪梅．切削加工过程动态模型的研究．制造业自动化，2000，22(1)
27 王素玉，王来，彭朋，李明艳．高速铣削力建模技术研究进展．煤矿机械，2004，11
28 李洪江，庄海军．球头铣刀铣削力仿真技术研究．航空精密制造技术，2006，42(1)
29 张智海，郑力，李志忠，张伯鹏．波形刃铣刀铣削力的预报数值模型．清华大学学报(自然科学版)，2002，42(6)：766～768
30 闫兵．螺旋刃球头铣刀铣削过程的物理建模与仿真及实验研究[博士论文]．天津：天津大学，1999，11：21～23
31 阎兵，徐安平．球头铣刀铣削过程的物理建模与仿真．天津职业技术师范学院学报，2001，11(4)
32 倪其民，李从心，吴光琳，阮雪榆．考虑刀具变形的球头铣刀铣削力建模与仿真．机械工程学报，2002，38(3)
33 倪其民．曲面加工过程切削负载自适应新策略及其关键技术研究[博士论文]．上海：上海交通大学，2001，3(1)：74～75
34 马万太，王宁生．考虑弹性变形时的球头铣刀切削力模型的研究．南京航空航天大学学报， 1998，30(6)
35 阎兵，徐安平，张大卫，黄田，曾子平．一种新的螺旋刃球头铣刀铣削力模型．中国机械工程，2002，13(2)
36 吕佩珊．用李亚普诺夫直接法拟定切削过程的动态稳定性．华中工学院学报，1987，15(3)：103～180
37 [加]奥廷塔思．数控技术与制造自动化．北京：化学工业出版社，2002，11
38 胡少伟，苗同臣．结构振动理论及其应用．北京：中国建筑工业出版社，2005：108～109
39 清华大学工程力学系固体力学教研组振动组．机械振动(上册)．北京：机械工业出版社，1980
40 邵蕴秋．ANSYS8.0有限元分析实例导航．北京：中国铁道出版社，2004
41 张朝晖．ANSYS工程应用范例入门与提高．北京：清华大学出版社，2004
42 李良福．用计算机计算立铣刀螺旋容屑槽的法向截形．工具技术，1996，30(5)
2 M. E. Martellotti. An Analysis of the Milling Process, Part2-Dawn Milling. ASME, 1945, 67: 233～251
3 T.Hosoi. Cutting Action of Ball End Mill with a Spiral Edge. Annals of the CIRP, 1977, 26(1-2): 49～53
4 S.Jain, K.C.Yang. A Systematic Force Analysis of the Milling Operation. in Proceedings of ASME Winter Annual Meeting, San Francisco, 1989, 55～63
5 His-Yung Feng. Prediction of cutting forces in the ball-end milling process. Journal of Materials Processing Technology, 1995, 54(1-4): 286～301
6 K.Nakayama, M.Arai. On the Storage of Data on Metal Cutting Forces. Annals of the CIRP, 1976, 25(1): 13～18
7 N.Ueda, T.Matsuo. Investigation of Some Shear Angle Theories. Annals of the CIRP, 1986, 35(1): 27～30
8 H.Y.Feng, C.H.Menq. Prediction of Cutting Force in the Ball-End Milling Process-1. Model Formulation and model Building Procedure. Int. J. Mach. Tools & Manuf, 1994, 34(5): 698～710
9 H. Y. Feng, C. H. Menq. Flexible Ball-End Milling System Model for Cutting Force and Machining Error Prediction. Journal of Manufacturing Science and Engineering, Transactions of the ASME, 1996, 118(4): 461～469
10 P. Lee, Y. Altintas. Prediction of Ball End Milling Forces From Orthogonal Cutting Data. Int. J. Mach. Tools.Manuf, 1996, 36(9): 1059～1072
11 Li Zheng, Yun Shun Chiou, S. Y. Liang. Three Dimensional Cutting Force Analysis in End Milling. International Journal of Mechanical Sciences, 1996, 38(3): 259～269
12 A. E. Bayoumi, G. Yucesan, L. A. Kendall. Analytic Mechanistic Cutting Force Model for Milling Operations. Journal of Engineering for Industry, Transactions of the ASME, 1994, 116: 324～330
13 A.E.Bayoumi, G.Yucesan, L.A.Kendall. An Analytic Mechanistic Cutting Force Model for Milling Operations. A Theory and Methodology ASME Journal of Engineering for Industry, 1994, 116(3): 331～339
14 冯志勇．数控环境下广义铣削力建模理论及参数识别方法的研究[博士论文]．天津：天津大学，1998，9：41～44
15 冯志勇，张大卫，黄田，曾子平．一种新型的广义铣削力模型．中国机械工程，1998，9：41～44
16 W.A.K line, R.E.Devor. Effect of Runout on Cutting Geometry and Forces in End Milling. ASME Journal of Engineering for Industry, 1983, 23(2-3): 123～140
17 W. A. Kline, R. E. Devor. Prediction of Cutting Force in End Milling with Application to Cornering Cuts. International Journal of Machine Tools & Manufacture, 1982, 22(1): 7～22
18 C. Sim, M. Yang. Prediction of Cutting Force in Ball-End Milling with a flexible cutter. International Journal of Machine Tools & Manufacture, 1993, 33(2): 267～284
19 Gyu Man Kin, Chong Nam Chu. Mean cutting force prediction ball end milling using force map method. Journal of Material Processing Technology, 2004, 146(3): 303～310
20 Y. Altintas, P. Lee. General Mechanics and Dynamics Model for Helical End Mills. Annals of the CIRP, 1996, 45(1): 59～64
21 Tlusty, F. Ismail. Special Aspects of Chatter in Milling. ASME Journal of Vib. Aco. Str. & Relia. in Design, 1983, 105(1): 24～32
22 S. Smith, J.Tlusty. Efficient Simulation Programs for Chatter in Milling. Annals of the CIRP, 1993, 42(1): 463～466
23 H. El Mounayri, A.D.Spence, M.A.Elbestawi. Milling Process Simulation-A Generic Solid Modeller Based Paradigm. Journal of Manufacturing Science and Engineering, Transactions of the ASME, 1998, 120(2): 213～221
24 F.Abrari, M.A.Elbestawi, A.D.Spence. On the Dynamics of Ball End Milling: Modeling of Cutting Forces and Stability Analysis. International Journal of Machine Tools & Manufacture, 1998, 38(3): 215～237
25 艾兴．高速切削加工技术[M]．北京：国防工业出版社，2003，26～76
26 黄雪梅．切削加工过程动态模型的研究．制造业自动化，2000，22(1)
27 王素玉，王来，彭朋，李明艳．高速铣削力建模技术研究进展．煤矿机械，2004，11
28 李洪江，庄海军．球头铣刀铣削力仿真技术研究．航空精密制造技术，2006，42(1)
29 张智海，郑力，李志忠，张伯鹏．波形刃铣刀铣削力的预报数值模型．清华大学学报(自然科学版)，2002，42(6)：766～768
30 闫兵．螺旋刃球头铣刀铣削过程的物理建模与仿真及实验研究[博士论文]．天津：天津大学，1999，11：21～23
31 阎兵，徐安平．球头铣刀铣削过程的物理建模与仿真．天津职业技术师范学院学报，2001，11(4)
32 倪其民，李从心，吴光琳，阮雪榆．考虑刀具变形的球头铣刀铣削力建模与仿真．机械工程学报，2002，38(3)
33 倪其民．曲面加工过程切削负载自适应新策略及其关键技术研究[博士论文]．上海：上海交通大学，2001，3(1)：74～75
34 马万太，王宁生．考虑弹性变形时的球头铣刀切削力模型的研究．南京航空航天大学学报， 1998，30(6)
35 阎兵，徐安平，张大卫，黄田，曾子平．一种新的螺旋刃球头铣刀铣削力模型．中国机械工程，2002，13(2)
36 吕佩珊．用李亚普诺夫直接法拟定切削过程的动态稳定性．华中工学院学报，1987，15(3)：103～180
37 [加]奥廷塔思．数控技术与制造自动化．北京：化学工业出版社，2002，11
38 胡少伟，苗同臣．结构振动理论及其应用．北京：中国建筑工业出版社，2005：108～109
39 清华大学工程力学系固体力学教研组振动组．机械振动(上册)．北京：机械工业出版社，1980
40 邵蕴秋．ANSYS8.0有限元分析实例导航．北京：中国铁道出版社，2004
41 张朝晖．ANSYS工程应用范例入门与提高．北京：清华大学出版社，2004
42 李良福．用计算机计算立铣刀螺旋容屑槽的法向截形．工具技术，1996，30(5)