高速铣削稳定性预测及软件开发
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摘要
高速铣削加工技术是先进制造技术中重要的基础技术之一,己成为21世纪先进制造技术中的重要组成部分,已经被广泛应用于航空航天、汽车、模具、能源、等众多领域。铣削过程中的颤振是高速铣削实现高速、高效和高精度加工的关键限制因素之一,因此高速铣削系统的稳定性预测问题是机械加工迫切需要解决的技术难题之一。本文以高速铣削稳定性预测及颤振抑制为研究目标,借助理论分析和有限元仿真等手段,对高速铣削过程中,主轴／刀具系统陀螺效应的动态特性、工件系统的动态特性,以及稳定性进行系统、深入地研究,并基于研究结果进行软件开发。
基于建立的高速铣削动态铣削力模型,建立了高速铣削系统动力学模型,方面,针对高速铣削的特点,建立了考虑高速旋转主轴引起的陀螺效应影响的二自由度动力学模型；另一方面,当工件刚度和刀具刚度在同一数量级时,建立了考虑刀具和工件系统的高速铣削四自由度动力学模型。
基于所建的动力学模型,深入研究铣削稳定性的解析分析方法,采用稳定性极限图作为对铣削稳定性分析的表示方法,并以此作为对高速切削稳定性进行预测、评价和优化的理论依据。同时,基于二维稳定性极限图,建立三维稳定性极限图及曲面图,通过三维稳定性图,可以直观、清晰地分析稳定性极限图坐标变量对铣削稳定性的影响规律,并全面、准确地选择稳定铣削条件下的最优铣削参数。
将刀具系统简化为梁模型,通过有限元方法,建立主轴／刀具系统的有限元模型,研究陀螺效应对系统动态特性及稳定性的影响规律：另外,建立工件的有限元模型,研究不同工况对工件系统的动态特性及其对稳定性的影响。
在上述建立的的稳定性预测方法基础上,编译开发稳定性预测软件,探讨高速切削的振动和失稳机制、特征及演变发展规律,以便于应用于实际生产中,实现工程应用。
As an important basic technology, high speed milling has become an important part of the advanced manufacturing technology in the 21st century, which has been widely used in aerospace, automotive, mold, energy, and many other fields. Chatter in milling process is the main constraints of realizing high-speed, efficient and accurate processing high speed milling, so the problem of stability prediction under high-speed milling machining is urgency. Taking the stability prediction of high-speed milling and Chatter as the background, the prediction of high-speed milling stability as object, the dynamic and stability characteristics of spindle and tool system and gyroscopic effect and also that of workpiece in the high speed milling is studied by the method of theoretical analysis and finite element simulation, and some of the results developed by the form of software.
Based on the force model of the instantaneous cutting force, the dynamic milling model is established considering two aspects. First, the dynamic model is established considering that the gyroscopic effects of the high speed rotating shaft. Second, the dynamic model is also established considering that the stiffness of workpiece and that of the tool is at the same magnitude.
Based on the dynamic model setup, the method of the analytical stability analysis and the stability limit diagram used as a representation of milling stability is proposed, which is the theoretical basis of prediction, evaluation and optimization. Based on two-dimensional stability limit diagram, the establishment of three-dimensional stability limit diagram is studied, by which the direct and clear analysis of milling parameters on milling stability, comprehensive, and accurately selection of the optimal cutting conditions and stability milling parameters can be made.
By simplifying the tool system to beam model, the numerical method for solving differential equations is proposed, and the gyroscopic effect of the tool system and its natural frequency is analyzed. By the finite element method, the finite element model of the tool and spindle system is established, gyroscopic effect on the dynamics and stability is analyzed. The finite element model of the workpiece is established, respectively, dynamic characteristics of different conditions and its stability are also analyzed.
On the base of achieved method in the stability limit diagram prediction, the software compiler development is proposed, which probes into the the vibration and instability mechanisms, characteristics and evolution discipline of high speed milling and make it easy to apply to actual production and realization of engineering applications.
基于建立的高速铣削动态铣削力模型,建立了高速铣削系统动力学模型,方面,针对高速铣削的特点,建立了考虑高速旋转主轴引起的陀螺效应影响的二自由度动力学模型；另一方面,当工件刚度和刀具刚度在同一数量级时,建立了考虑刀具和工件系统的高速铣削四自由度动力学模型。
基于所建的动力学模型,深入研究铣削稳定性的解析分析方法,采用稳定性极限图作为对铣削稳定性分析的表示方法,并以此作为对高速切削稳定性进行预测、评价和优化的理论依据。同时,基于二维稳定性极限图,建立三维稳定性极限图及曲面图,通过三维稳定性图,可以直观、清晰地分析稳定性极限图坐标变量对铣削稳定性的影响规律,并全面、准确地选择稳定铣削条件下的最优铣削参数。
将刀具系统简化为梁模型,通过有限元方法,建立主轴／刀具系统的有限元模型,研究陀螺效应对系统动态特性及稳定性的影响规律：另外,建立工件的有限元模型,研究不同工况对工件系统的动态特性及其对稳定性的影响。
在上述建立的的稳定性预测方法基础上,编译开发稳定性预测软件,探讨高速切削的振动和失稳机制、特征及演变发展规律,以便于应用于实际生产中,实现工程应用。
As an important basic technology, high speed milling has become an important part of the advanced manufacturing technology in the 21st century, which has been widely used in aerospace, automotive, mold, energy, and many other fields. Chatter in milling process is the main constraints of realizing high-speed, efficient and accurate processing high speed milling, so the problem of stability prediction under high-speed milling machining is urgency. Taking the stability prediction of high-speed milling and Chatter as the background, the prediction of high-speed milling stability as object, the dynamic and stability characteristics of spindle and tool system and gyroscopic effect and also that of workpiece in the high speed milling is studied by the method of theoretical analysis and finite element simulation, and some of the results developed by the form of software.
Based on the force model of the instantaneous cutting force, the dynamic milling model is established considering two aspects. First, the dynamic model is established considering that the gyroscopic effects of the high speed rotating shaft. Second, the dynamic model is also established considering that the stiffness of workpiece and that of the tool is at the same magnitude.
Based on the dynamic model setup, the method of the analytical stability analysis and the stability limit diagram used as a representation of milling stability is proposed, which is the theoretical basis of prediction, evaluation and optimization. Based on two-dimensional stability limit diagram, the establishment of three-dimensional stability limit diagram is studied, by which the direct and clear analysis of milling parameters on milling stability, comprehensive, and accurately selection of the optimal cutting conditions and stability milling parameters can be made.
By simplifying the tool system to beam model, the numerical method for solving differential equations is proposed, and the gyroscopic effect of the tool system and its natural frequency is analyzed. By the finite element method, the finite element model of the tool and spindle system is established, gyroscopic effect on the dynamics and stability is analyzed. The finite element model of the workpiece is established, respectively, dynamic characteristics of different conditions and its stability are also analyzed.
On the base of achieved method in the stability limit diagram prediction, the software compiler development is proposed, which probes into the the vibration and instability mechanisms, characteristics and evolution discipline of high speed milling and make it easy to apply to actual production and realization of engineering applications.
引文
[1]艾兴.高速切削加工技术[M].北京：国防工业出版社,2003.
[2]J. Tlusty. High-speed milling [J]. Annals of the CIRP,1993,42(2):733-728.
[3]G. Byrne, D. Dornfeld, and B. Denkena. Advanced cutting technology [J]. Annals of the CIRP, 2003,52(2):483-507.
[4]张伯霖.高速切削技术及应用[M].北京：机械工业出版社,2002.
[5]J.P. Davim. Machining-Fundamentals and recent advances [M]. Springer-Verlag London Limited,2008.
[6]汤爱君,马海龙.铣削颤振的线性和非线性理论研究[J].工具技术,2007,41(6)：48-51.
[7]吴雅.机床铣削系统的颤振及其控制[M].北京：科学出版社,1993：85.
[8]黄仁贵,郑艳萍,孙炎,董红霞.机械加工振型耦合颤振研究[J].郑州大学学报(工学版),2002(3)：67-69.
[9]C.J. Hook, S.A. Tobias. Finite amplitude instability-a new type of chatter [J]. Pro.4th MTDR: 1963:97-109.
[10]汤爱军,马海龙.机床再生颤振系统研究现状的综述[J].机床与液压,2007,35(8)：223-225.
[11]E. Budak, A. Ert(?), H.N. Ozgi(?)en. A modeling approach for analysis and improvement of spindle-holder-tool assembly dynamics [J]. Annals of the CIRP,2006,55:369-372.
[12]E. Budak. Analytical models for high performance milling, part II:process dynamic and stability [J]. International Journal of Machine Tools and Manufacture,2006,46:1489-1499.
[13]M. Namazi, Y. Altintas, T. Abe, et al. Modeling and identification of tool holder-spindle interface dynamics [J]. International Journal of Machine Tools and Manufacture,2007,47: 1333-1341.
[14]K. Ahmadi, H. Ahmadian. Modeling machine tool dynamics using a distributed parameter tool-holder joint interface [J]. International Journal of Machine Tools and Manufacture,2007,47: 1916-1928.
[15]X.H. Long, B. Balachandran, B.P. Mann. Dynamics of milling processes with variable time delays [J]. Nonlinear Dynamics,2007,47:49-63.
[16]X.H. Long. Loss of contact and time delay dynamics of milling processes [D]. University of Maryland,2006:15.
[17]T. Insperger, B.P. Mann, T. Surmann, et al. On the chatter frequencies of milling processes with runout [J]. Journal of Machine Tools and Manufacture,2008,48:1432-1443.
[18]R.P.H. Faassen, N. Wouw, H. Nijmeijer, et al. An improved tool path model including periodic delay for chatter prediction in milling [J]. Journal of Computational and Nonlinear Dynamics, 2007,2(2):167-179.
[19]汪通悦,何宁,李亮.薄壁零件铣削加工的振动模型[J].机械工程学报,2007,43(8)：22-25.
[20]李沪曾,王逸,张冲等.薄壁大型整体薄壁件的高速铣削[J].同济大学学报(自然科学版),2007,35(4)：522-525.
[21]G.L. Xiong, J.M. Yi, C. Zeng, et al. Study of the gyroscopic effect of the spindle on the stability characteristics of the milling system [J]. Journal of Materials Processing Technology,2003,138: 379-384.
[22]M.R. Movahhedy, P. Mosaddegh. Prediction of chatter in high speed milling including gyroscopic effects [J]. International Journal of Machine Tools and Manufacture,2006,46: 996-1001.
[23]W.X. Tang, X. Ai, S. Zhang, et al. Dynamic modeling for high-speed milling system with centrifugal force & gyroscopic effect [J]. Key Engineering Materials,2004,259-260:848-852.
[24]W.X. Tang, X. Ai, S. Zhang, et al. An algorithm for dynamic characteristics of high-speed machining tool system with rotating symmetry [J]. Key Engineering Materials,2004,259-260: 137-140.
[25]W.X. Tang, Q.H. Song, S.S. Sun, et al. Stability and its influence factors for high-speed milling [C]. Proc.of Int.Conference on Advanced Design and Manufacture (ICADM),2008:513-520.
[26]W.X. Tang, Q.H. Song, S.Q. Yu, et al. Prediction of chatter stability in high-speed finishing end milling considering multi-mode dynamics characteristics [J]. Journal of Materials Processing Technology,2009,209:2585-2591.
[27]汤爱军,马海龙.机床再生颤振系统研究现状的综述[J].机床与液压,2007,35(8)：223-225.
[28]赵学智,陈统坚,叶邦彦.基于奇异值分解的铣削力信号处理与铣床状态信息分离[J].机械工程学报,2007,43(6)：169-1 74.
[29]唐委校,艾兴,姜华,宋清华.高速切削稳定性数据库研究[J].制造技术与机床,2005,6：75-78.
[30]宋清华,艾兴,唐委校.铣削系统稳定性判定新方法研究[J].机械强度,2008,30(5)：718-722.
[31]I. Mane, V. Gagnol, B.C. Bouzgarrou, P. Ray. Stability-based spindle speed control during flexible workpiece high-speed milling, Interantional Journal of Machine Tools and Manufacture, 2008,48:184-194.
[32]E. Budak, Y. Altintas, E.J.A. Armarego. Prediction of milling force coefficients from orthogonal cutting data [J]. Transactions of the ASME Journal of Manufacturing Science and Engineering,1996,118(2):216-224.
[33]E. Budak, Y. Altintas. Analytical prediction of chatter stability in milling. Part 1:general formulation [J]. Proceedings of the ASME, Dynamic Systems and Control Division,1995, 57(1):545-556.
[34]Y. Altintas, E. Budak. Analytical prediction of stability lobes in milling [J]. Annals of CIRP, 1995,44(1):357-362.
[35]R. Sridhar, R. EHohn, G. W. Long. A stability algorithm for the general milling process [J]. Transactions on ASME Journal of Engineering for Industry,1968,90:300-334.
[36]T.L. Schmitz, J.C. Stanislaus, C. Stanislaus. A method for predicting chatter stability for systems with speed-dependent spindle dynamics [C]. Proceedings of NAMARC32, Charlotte, North Carolina, US,2004.
[37]J. Tian. Self-excited vibrations of rotating disks and shafts with applications in sawing and milling [D]. University of British Columbia,1998.
[38]H.D. Nelson, J.M. Mcvough. The dynamics of rotor bearing system using finite element [J]. Transactions on ASME Journal of Engineering for Industry,1976,98:593-600.
[39]H.D. Nelson. A finite rotating shaft element using Timoshenko beam theory [J]. ASME Journal of Mechanical Design,1980,102:793-803.
[40]郭厚焜,熊国良,伊俊敏.旋转主轴的陀螺效应对铣削系统稳定性的影响.华东交通大学学报,2000,17(4)：1-6.
[41]刘强,尹力.一种面向数控工艺参数优化的铣削过程动力学仿真系统研究[J].中国机械工程,2005,16(13)：1146-1150.
[42]刘战强,万熠,艾兴.刀具材料智能选择系统的研究与开发[J].中国机械工程,2003,14(21)：1871-1874.
[43]王太勇,王晓斌,王国锋等.数控切削过程仿真系统的研究[J].组合机床与自动化加工技术,2004(1)：63-66.
[44]钟一愕等.转子动力学[M].北京：清华大学出版社,1987.
[45]闻邦椿等.高等转子动力学：理论、技术及应用[M].北京：机械工业出版社,2000.
[46]P.T. Mativenga, K.K.B. Hon. An experimental study of cutting forces in high-speed end milling and implications for dynamic force modeling [J]. Journal of Manufacturing Science and Engineering,2005,127(2):251-261.
[47]刘希珠.雷天玉.陀螺力学基础.北京：清华大学出版社,1987.
[48]R.M. Mohammad, M. Peiman. Prediction of chatter in high speed milling including gyroscopic effects [J]. International Journal of Machine Tools & Manufacture,2006,46:996-1001.
[2]J. Tlusty. High-speed milling [J]. Annals of the CIRP,1993,42(2):733-728.
[3]G. Byrne, D. Dornfeld, and B. Denkena. Advanced cutting technology [J]. Annals of the CIRP, 2003,52(2):483-507.
[4]张伯霖.高速切削技术及应用[M].北京：机械工业出版社,2002.
[5]J.P. Davim. Machining-Fundamentals and recent advances [M]. Springer-Verlag London Limited,2008.
[6]汤爱君,马海龙.铣削颤振的线性和非线性理论研究[J].工具技术,2007,41(6)：48-51.
[7]吴雅.机床铣削系统的颤振及其控制[M].北京：科学出版社,1993：85.
[8]黄仁贵,郑艳萍,孙炎,董红霞.机械加工振型耦合颤振研究[J].郑州大学学报(工学版),2002(3)：67-69.
[9]C.J. Hook, S.A. Tobias. Finite amplitude instability-a new type of chatter [J]. Pro.4th MTDR: 1963:97-109.
[10]汤爱军,马海龙.机床再生颤振系统研究现状的综述[J].机床与液压,2007,35(8)：223-225.
[11]E. Budak, A. Ert(?), H.N. Ozgi(?)en. A modeling approach for analysis and improvement of spindle-holder-tool assembly dynamics [J]. Annals of the CIRP,2006,55:369-372.
[12]E. Budak. Analytical models for high performance milling, part II:process dynamic and stability [J]. International Journal of Machine Tools and Manufacture,2006,46:1489-1499.
[13]M. Namazi, Y. Altintas, T. Abe, et al. Modeling and identification of tool holder-spindle interface dynamics [J]. International Journal of Machine Tools and Manufacture,2007,47: 1333-1341.
[14]K. Ahmadi, H. Ahmadian. Modeling machine tool dynamics using a distributed parameter tool-holder joint interface [J]. International Journal of Machine Tools and Manufacture,2007,47: 1916-1928.
[15]X.H. Long, B. Balachandran, B.P. Mann. Dynamics of milling processes with variable time delays [J]. Nonlinear Dynamics,2007,47:49-63.
[16]X.H. Long. Loss of contact and time delay dynamics of milling processes [D]. University of Maryland,2006:15.
[17]T. Insperger, B.P. Mann, T. Surmann, et al. On the chatter frequencies of milling processes with runout [J]. Journal of Machine Tools and Manufacture,2008,48:1432-1443.
[18]R.P.H. Faassen, N. Wouw, H. Nijmeijer, et al. An improved tool path model including periodic delay for chatter prediction in milling [J]. Journal of Computational and Nonlinear Dynamics, 2007,2(2):167-179.
[19]汪通悦,何宁,李亮.薄壁零件铣削加工的振动模型[J].机械工程学报,2007,43(8)：22-25.
[20]李沪曾,王逸,张冲等.薄壁大型整体薄壁件的高速铣削[J].同济大学学报(自然科学版),2007,35(4)：522-525.
[21]G.L. Xiong, J.M. Yi, C. Zeng, et al. Study of the gyroscopic effect of the spindle on the stability characteristics of the milling system [J]. Journal of Materials Processing Technology,2003,138: 379-384.
[22]M.R. Movahhedy, P. Mosaddegh. Prediction of chatter in high speed milling including gyroscopic effects [J]. International Journal of Machine Tools and Manufacture,2006,46: 996-1001.
[23]W.X. Tang, X. Ai, S. Zhang, et al. Dynamic modeling for high-speed milling system with centrifugal force & gyroscopic effect [J]. Key Engineering Materials,2004,259-260:848-852.
[24]W.X. Tang, X. Ai, S. Zhang, et al. An algorithm for dynamic characteristics of high-speed machining tool system with rotating symmetry [J]. Key Engineering Materials,2004,259-260: 137-140.
[25]W.X. Tang, Q.H. Song, S.S. Sun, et al. Stability and its influence factors for high-speed milling [C]. Proc.of Int.Conference on Advanced Design and Manufacture (ICADM),2008:513-520.
[26]W.X. Tang, Q.H. Song, S.Q. Yu, et al. Prediction of chatter stability in high-speed finishing end milling considering multi-mode dynamics characteristics [J]. Journal of Materials Processing Technology,2009,209:2585-2591.
[27]汤爱军,马海龙.机床再生颤振系统研究现状的综述[J].机床与液压,2007,35(8)：223-225.
[28]赵学智,陈统坚,叶邦彦.基于奇异值分解的铣削力信号处理与铣床状态信息分离[J].机械工程学报,2007,43(6)：169-1 74.
[29]唐委校,艾兴,姜华,宋清华.高速切削稳定性数据库研究[J].制造技术与机床,2005,6：75-78.
[30]宋清华,艾兴,唐委校.铣削系统稳定性判定新方法研究[J].机械强度,2008,30(5)：718-722.
[31]I. Mane, V. Gagnol, B.C. Bouzgarrou, P. Ray. Stability-based spindle speed control during flexible workpiece high-speed milling, Interantional Journal of Machine Tools and Manufacture, 2008,48:184-194.
[32]E. Budak, Y. Altintas, E.J.A. Armarego. Prediction of milling force coefficients from orthogonal cutting data [J]. Transactions of the ASME Journal of Manufacturing Science and Engineering,1996,118(2):216-224.
[33]E. Budak, Y. Altintas. Analytical prediction of chatter stability in milling. Part 1:general formulation [J]. Proceedings of the ASME, Dynamic Systems and Control Division,1995, 57(1):545-556.
[34]Y. Altintas, E. Budak. Analytical prediction of stability lobes in milling [J]. Annals of CIRP, 1995,44(1):357-362.
[35]R. Sridhar, R. EHohn, G. W. Long. A stability algorithm for the general milling process [J]. Transactions on ASME Journal of Engineering for Industry,1968,90:300-334.
[36]T.L. Schmitz, J.C. Stanislaus, C. Stanislaus. A method for predicting chatter stability for systems with speed-dependent spindle dynamics [C]. Proceedings of NAMARC32, Charlotte, North Carolina, US,2004.
[37]J. Tian. Self-excited vibrations of rotating disks and shafts with applications in sawing and milling [D]. University of British Columbia,1998.
[38]H.D. Nelson, J.M. Mcvough. The dynamics of rotor bearing system using finite element [J]. Transactions on ASME Journal of Engineering for Industry,1976,98:593-600.
[39]H.D. Nelson. A finite rotating shaft element using Timoshenko beam theory [J]. ASME Journal of Mechanical Design,1980,102:793-803.
[40]郭厚焜,熊国良,伊俊敏.旋转主轴的陀螺效应对铣削系统稳定性的影响.华东交通大学学报,2000,17(4)：1-6.
[41]刘强,尹力.一种面向数控工艺参数优化的铣削过程动力学仿真系统研究[J].中国机械工程,2005,16(13)：1146-1150.
[42]刘战强,万熠,艾兴.刀具材料智能选择系统的研究与开发[J].中国机械工程,2003,14(21)：1871-1874.
[43]王太勇,王晓斌,王国锋等.数控切削过程仿真系统的研究[J].组合机床与自动化加工技术,2004(1)：63-66.
[44]钟一愕等.转子动力学[M].北京：清华大学出版社,1987.
[45]闻邦椿等.高等转子动力学：理论、技术及应用[M].北京：机械工业出版社,2000.
[46]P.T. Mativenga, K.K.B. Hon. An experimental study of cutting forces in high-speed end milling and implications for dynamic force modeling [J]. Journal of Manufacturing Science and Engineering,2005,127(2):251-261.
[47]刘希珠.雷天玉.陀螺力学基础.北京：清华大学出版社,1987.
[48]R.M. Mohammad, M. Peiman. Prediction of chatter in high speed milling including gyroscopic effects [J]. International Journal of Machine Tools & Manufacture,2006,46:996-1001.