薄壁多框结构件高效铣削稳定性研究
摘要
整体薄壁框体结构件具有重量轻、强度高、动力性能好等一系列优点,广泛应用于航空、电子、模具等工业领域。由于其具有薄壁、变厚度、曲面曲线结构多、加工余量大等特点,加工过程容易发生颤振,加工质量很难保证,加工效率难以提高。研究整体薄壁框体结构件切削加工颤振问题与稳定性问题具有重要意义。本文对薄壁多框结构件铣削加工颤振机理及其稳定性机理进行了深入的分析,推导了铣削加工三维颤振稳定性模型,建立了动态分析有限元模型,进行了大量有限元模拟运算并与试验结果进行了对比,最后进行了稳定性仿真分析,得出了系列重要结论。本文具体研究内容如下:
1.建立了薄壁件铣削加工动态力学模型。分别针对薄壁侧壁和腹板建立了动态力学模型,重点建立了螺旋立铣刀(包括平刀和R刀)和牛鼻铣刀铣削加工薄壁腹板的动态力学模型,并进行了试验验证。在铣削力动态模型的基础上,建立了考虑机床-刀具-工件系统动态特性的薄壁件铣削加工系统动力学模型,为更精确地预测铣削力及分析加工振动及其稳定性奠定了基础。
2.对薄壁件铣削加工动态特性进行了深入研究。在前面建立的薄壁件铣削加工系统动力学模型的基础上建立了薄壁件切削加工动态特性有限元分析模型,提出了一种简化加载的薄壁件动态特性分析模型,以简化模型为基础进行了不同切削条件下切削过程中节点振动位移时域模拟,对模拟结果进行了评价,为制定正确的薄壁件切削加工工艺、开展更为复杂的动态分析奠定了基础。
3.对薄壁多框结构件进行了模态分析。按照加工顺序分别对不同的加工阶段进行了模态分析,得到了工件在不同加工阶段的模态参数,为后面稳定性分析提供了依据。
4.对切削加工颤振理论进行了研究。分析了颤振产生的原理以及颤振的基本特征,并在此基础上给出了稳定性的定义和高速铣削稳定性判据。
5.对高速铣削薄壁件的稳定性理论进行了研究。基于已建立的考虑再生颤振的牛鼻铣刀铣削力模型,系统地研究了高速铣削的切削稳定性问题,给出了高速铣削稳定性判据和轴向极限切深的解析解和时域解法,由稳定性极值解析解绘出稳定性图,并基于稳定性图分析了工件动态特性以及机床动态特性对切削稳定性的影响规律。
本文的研究工作对实现薄壁框体结构件无颤振高效铣削具有重要指导意义。
With characteristics of light mass, high intensity and perfect dynamic performance, the monolithic construction components are used more and more widely in aero, electronic and mold industries. As there are many complex characteristics such as thin-wall, varying thickness, complex curved face and big metal allowance in the monolithic construction components, chatter is an unavoidable phenomenon in all machining processes, causing a reduction in productivity and low quality of finished workpieces. Study on the maching vibration and cutting stability of the monolithic construction components is very important. This paper has theoretically analyzed the chatter and stability cutting of the monolithic construction components firstly. A three-dimensional chatter stability model is presented analytically in this article. Then built the FEM dynamic mechanistic analysis model of milling process. Finally conducted a simulation analysis of milling process. By large quantity of simulations and tests, some important conclusions have been gained. The main work in this paper is concluded as follows.
1. Built the dynamic force model of milling thin-walled structure components in detail. In this paper, several dynamic force models are built for milling of aeronautical parts that include thin walls and thin floors. This paper sets up dynamic force models for spiral end mills and bull-nose end mills during milling the thin floors. The model is verified with milling experiment. Based on the model, a dynamic model of the milling system of thin-walled parts is established by considering the machine subsystem, the tool subsystem and the workpiece subsystem. This will be helpful to estimate the cutting forces more accurately and to predict the chatter vibration.
2. Studied the milling dynamic characteristics of the thin-walled structure components. Based on the dynamic model of the milling system of thin-walled parts established in the previous paper, the FEM dynamic mechanistic analysis model of milling process is built theoretically. Then a kind of simplified model has been proposed in this paper, and large quantity simulations have been carried out based on the simplified model. The simulation results have been concluded.
3. Studied the modal analysis of the thin-walled structure component. The modal analyses are carried out in every machining location. Based on it, modal parameters have been gained which will be helpful to the stability anslysis.
4. Studied the chatter in the machining processes. The properties and mechanism of machining vibration have been studied. Then the definition of stability and the prediction method of stability criterion are presented based on it.
5. Studied the stability limits of high-speed milling considering the flexibility of the workpiece and the machine. Aimed to bull-nose mill, the dynamic milling force model taking account of regenerative chatter are deduced, and high speed cutting stability is investigated according to dynamic milling force model, then the stability criterion and the ultimate axial depth of cut are studied. Finally, the stability lobes are drawn, and simulated the effect of different modal parameters on stability based on stability lobes.
The studies of this paper will be a guide for no chatter milling of the monolithic construction components.
1.建立了薄壁件铣削加工动态力学模型。分别针对薄壁侧壁和腹板建立了动态力学模型,重点建立了螺旋立铣刀(包括平刀和R刀)和牛鼻铣刀铣削加工薄壁腹板的动态力学模型,并进行了试验验证。在铣削力动态模型的基础上,建立了考虑机床-刀具-工件系统动态特性的薄壁件铣削加工系统动力学模型,为更精确地预测铣削力及分析加工振动及其稳定性奠定了基础。
2.对薄壁件铣削加工动态特性进行了深入研究。在前面建立的薄壁件铣削加工系统动力学模型的基础上建立了薄壁件切削加工动态特性有限元分析模型,提出了一种简化加载的薄壁件动态特性分析模型,以简化模型为基础进行了不同切削条件下切削过程中节点振动位移时域模拟,对模拟结果进行了评价,为制定正确的薄壁件切削加工工艺、开展更为复杂的动态分析奠定了基础。
3.对薄壁多框结构件进行了模态分析。按照加工顺序分别对不同的加工阶段进行了模态分析,得到了工件在不同加工阶段的模态参数,为后面稳定性分析提供了依据。
4.对切削加工颤振理论进行了研究。分析了颤振产生的原理以及颤振的基本特征,并在此基础上给出了稳定性的定义和高速铣削稳定性判据。
5.对高速铣削薄壁件的稳定性理论进行了研究。基于已建立的考虑再生颤振的牛鼻铣刀铣削力模型,系统地研究了高速铣削的切削稳定性问题,给出了高速铣削稳定性判据和轴向极限切深的解析解和时域解法,由稳定性极值解析解绘出稳定性图,并基于稳定性图分析了工件动态特性以及机床动态特性对切削稳定性的影响规律。
本文的研究工作对实现薄壁框体结构件无颤振高效铣削具有重要指导意义。
With characteristics of light mass, high intensity and perfect dynamic performance, the monolithic construction components are used more and more widely in aero, electronic and mold industries. As there are many complex characteristics such as thin-wall, varying thickness, complex curved face and big metal allowance in the monolithic construction components, chatter is an unavoidable phenomenon in all machining processes, causing a reduction in productivity and low quality of finished workpieces. Study on the maching vibration and cutting stability of the monolithic construction components is very important. This paper has theoretically analyzed the chatter and stability cutting of the monolithic construction components firstly. A three-dimensional chatter stability model is presented analytically in this article. Then built the FEM dynamic mechanistic analysis model of milling process. Finally conducted a simulation analysis of milling process. By large quantity of simulations and tests, some important conclusions have been gained. The main work in this paper is concluded as follows.
1. Built the dynamic force model of milling thin-walled structure components in detail. In this paper, several dynamic force models are built for milling of aeronautical parts that include thin walls and thin floors. This paper sets up dynamic force models for spiral end mills and bull-nose end mills during milling the thin floors. The model is verified with milling experiment. Based on the model, a dynamic model of the milling system of thin-walled parts is established by considering the machine subsystem, the tool subsystem and the workpiece subsystem. This will be helpful to estimate the cutting forces more accurately and to predict the chatter vibration.
2. Studied the milling dynamic characteristics of the thin-walled structure components. Based on the dynamic model of the milling system of thin-walled parts established in the previous paper, the FEM dynamic mechanistic analysis model of milling process is built theoretically. Then a kind of simplified model has been proposed in this paper, and large quantity simulations have been carried out based on the simplified model. The simulation results have been concluded.
3. Studied the modal analysis of the thin-walled structure component. The modal analyses are carried out in every machining location. Based on it, modal parameters have been gained which will be helpful to the stability anslysis.
4. Studied the chatter in the machining processes. The properties and mechanism of machining vibration have been studied. Then the definition of stability and the prediction method of stability criterion are presented based on it.
5. Studied the stability limits of high-speed milling considering the flexibility of the workpiece and the machine. Aimed to bull-nose mill, the dynamic milling force model taking account of regenerative chatter are deduced, and high speed cutting stability is investigated according to dynamic milling force model, then the stability criterion and the ultimate axial depth of cut are studied. Finally, the stability lobes are drawn, and simulated the effect of different modal parameters on stability based on stability lobes.
The studies of this paper will be a guide for no chatter milling of the monolithic construction components.
引文
[1]航空制造工程手册总编委会.航空制造工程手册—飞机机械加工[M].航空工业出版社,1995.1
[2]航空制造工程手册总编委会.航空制造工程手册—框架壳体工艺[M].航空工业出版社,1997.12
[3]Kline W.A,Devor R.E,and Lindberg R.The Prediction of Cutting Forces in End Milling with Application to Cornering Cut[J].International Journal of Machine Tool Design and Research,1982,22(1):7-22
[4]Kline W.A,Devor R.E.The Effect of Cutting Geometry and Forces in Milling[J].International Journal of Machine Tool Design and Research,1983,2(1):123-140
[5]Sutherland J.W.,DeVor R.E.An Improved Method for Cutting Force and Surface Error Predication in Flexible End Milling Systems[J].Journal of Engineering for Industry,1986,108(4):269-279
[6]Armarego E.J.A,Deshpande N.P.Computerized End-Milling Force Predications With Cutting Models Allowing for Eccentricity and Cutter Deflections[J].Annals of the CIRP,1991,40(1):25-29
[7]Won-Soo Yun.Accurate 3-D cutting force prediction using cutting condition independ -ent coefficients in end milling[J].International Journal of Machine Tools &Manufacture,2001,41:463-478
[8]Engin S.,Altintas Y.Mechanics and dynamics of general milling cutters—Part Ⅰ:helical end mills[J].International Journal of Machine Tools&Manufacture,2001,41(15):2195-2212
[9]Huaizhong Li,Wenbin Zhang,Xiaoping Li.A Predictive Model for Helical End Milling Forces[C].2000 ASME International Mechanical Engineering Congress and Exposition.November 5-10,2000,Orlando,Florida:231-236
[10]Oxley,P.L.B.Mechanics of machining[C].Ellie Horwood Limited Chichester,1989
[11]Ozturk B.,Lazoglu I.Machining of flee-form surfaces—Part Ⅰ:Analytical chip load[J].International Journal of Machine Tools&Manufacture,2006,46(7):728-735
[12]冯志勇.一种新的铣削力模型[J].天津大学学报,1998,31(3):314-320
[13]武凯,何宁等.立铣空间力学模型分析研究[J].南京航空航天大学学报,2002,34(6):553-556
[14]武凯,何宁等.基于薄壁件变形分析的铣削加工瞬态力学模型研究[J].应用科学学 报,2005,23(6):631-634
[15]Elbestawi M.A.,Ismail E,Du R.et al.Modeling Machining Dynamics Including Damping in the Tool-Workpiece Interface[J].Journal of Engineering for Industry,1994,116(4):435-439
[16]Smith,S,Alitintas.Update on High Speed Milling Dynamics[J].ASME journal of Engineering Industry,1990,112:142-149
[17]Waters A.J.Modeling and Simulation of Cutting Forces during Face Milling Operation[D].USA:Purdue University,1995:1-200
[18]Jensen S.A.Vibration and Stability Analysis of Face Milling Operations[D].USA:Purdue University,1997:1-150
[19]Altintas Y.,Budak E.Analytical Predication of Stability Lobes in Milling[C].Annals of the CIRP,1995,44(1):357-362
[20]Altintas Y.,Lee P.Combined Mechanics and Dynamics of Ball End Milling[C].ASME Winter Annual Meeting,1995,MED 2(1):657-677
[21]Altintas Y.,Lee P.A General Mechanics and Dynamics Model for Helical end Mills[C].Annals of the CIRP,1996,45(1):59-64
[22]M.A.Elbestawi,R.Sagherian.Dynamic modeling for the prediction of surface errors in the milling of thin-walled sections[J].Journal of Materials Processing Technology,1991(25):215-228
[23]E.Budak,Y.Altintas.Analytical Prediction of Chatter Stability in Milling—Part Ⅱ:Application of the General Formulation to Common Milling Systems[J].Journal of Dynamic Systems,Measurement,and Control,1998,120:31-36
[24]M.A.Davies.Impact dynamics in milling of thin-walled structures[J].Nonlinear Dynamics,2000,22:375-392
[25]李忠群.复杂切削条件高速铣削加工动力学建模、仿真与切削参数优化研究[D].北京:北京航空航天大学博士学位论文,2008
[26]张智海.铣削工艺系统瞬态力学模型和非线性动力学特性的研究[D].北京:清华大学博士学位论文,2001
[27]Xu A.P.,Qu Y.X.,Zhang D.W.,et al.Simulation and experimental investigation of the end milling process considering the cutter flexibility[J].International Journal of Machine Tools&Manufacture,2003,43(3):283-292
[28]Jer-shyong Tsai,Chung-Li Liao.Dynamic finite element modeling of surface errors in peripheral milling of thin-walled workpieees[J].Journal of the Chinese society of mechanical engineers,2000,21(3):265-282
[29]Jochem C.Roukema Yusuf Altintas.Generalized modeling of drilling vibrations—Part Ⅱ:Chatter stability in frequency domain[J].International Journal of Machine Tools &Manufacture,doi:10.1016/j.ijmachtools.2006.10.006
[30]S.Ema,E.Marui.Theoretical analysis on chatter vibration in drilling and its suppression[J].Journal of Materials Processing Technology,2003,138:572-578
[31]M.Xiao S.Karube,T.Soutome K.Sato.Analysis of chatter suppression in vibration cutting[J].International Journal of Machine Tools & Manufacture,2002,42:1677-1685
[32]Evita Edhi,Tetsutaro Hoshi.Stability of high frequency machining vibration by extended chatter model[J].Journal of the International Societies for Precision Engineering and Nanotechnology,2002,26:204-213
[33]Y.S.Tarnga,J.Y.Kaob,E.C.Leea.Chatter suppression in turning operations with a tuned vibration absorber[J].Journal of Materials Processing Technology,2000,105:55-60
[34]Neil D.Sims.Vibration absorbers for chatter suppression:A new analytical tuning methodology[J].Journal of Sound and Vibration,2007,301:592-607
[35]S.Turner et al.Modelling of the stability of variable helix end mills[J].International Journal of Machine Tools &Manufacture,doi:10.1016/j.ijmachtools.2006.08.028
[36]Evita Edhi,Tetsutaro Hoshi.Stability of high frequency machining vibration by extended chatter model[J].Journal of the International Societies for Precision Engineering and Nanotechnology,2002,26:204-213
[37]U.Bravo,O.Altuzarra,L.N.Lopez de Lacalle.Stability limits of milling considering the flexibility of the workpiece and the machine[J].International Journal of Machine Tools & Manufacture,2005,45:1669-1680
[38]E.Budak,Y.Altintas.Analytical Prediction of Chatter Stability in Milling—Part Ⅰ:General Formulation[J].Journal of Dynamic Systems,Measurement,and Control,1998,120:22-30
[39]宋清华,艾兴,万熠,唐委校.考虑刀具偏心的变径向切深铣削稳定性研究[J].振动、测试与诊断,2008,28(3):701-705
[40]汤爱君,刘战强.铣削加工系统三维稳定性理论研究与进展[J].工具技术,2008,42(5):3-5
[41]宋清华,艾兴万熠,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
[42]李亮.薄壁零件的加工振动分析与加工工艺研究[D].南京:南京航空航天大学硕 士学位论文,2005
[43]师汉民.影响机床颤振的几个非线性因素及其数学模型[J].华中工学院学报,1984,12(6):102-112
[44]吴雅.机床切学系统的颤振及其控制[M].科学出版社,1993
[45]何庆编译.高速加工的切削动力学[J].VMEM,2006,6:90-91
[46]李小雷,童水光.高速切削刀具系统固有特性和动态响应分析[J].工程设计学报,2004,11(5):268-272
[47]石莉,贾春德,孙玉龙.应用小波研究动态铣削力及预报铣削颤振[J].哈尔滨工业大学学报,2006,38(10):1978-1980
[48]F.Abrari,M.A.Elbestawi,A.D.Spence.On the Dynamics of Ball End Milling:Modeling of Cutting Forces and Stability Analysis[J].In.J.Mach.Tools Manufact,1998,38(3):215-237
[49]M.S.Fofana.Effect of regenerative process on the sample stability of a multiple delay differential equation[J].Chaos,Solitons and Fractals,2002,14:301-309
[50]T.Insperger,B.P.Mann,P.V.Bayly.Stability of up-milling and down-milling,part Ⅰ:alternative analytical methods[J].International Journal of Machine Tools &Manufacture,2003,43:25-34
[51]Y.Altintas,E.Shamto,P.Lee,E.Budka.Analytical Prediction of stability lobes in ball end milling[J].Trans.ASME,JManu.f Science and Eng.,1999,121:586-592
[52]S.Engin,Y.Altintas.Mechanics and dynamics of general milling cutters—Part Ⅰ:inserthed cutters,Part Ⅱ:helical end mills[J].Journal of Machine Tools and Manufacture,2001,41:2292-2231
[53]E.Budak.Analytical models for high performance milling—part Ⅱ:process dynamics and stability[J].International Journal of Machine Tools & Manufacture,2006,46:1489-1499
[54]B.Balachandran,M.X.Zhao.A Mechanics Based Model for Study of Dynamics of Milling Operations,Kluwer Academic Publishers[J].Printed in the Netherlands Meccanica,2000,35:89-109
[55]JanezGradisek,Martin Kalveram.On stability prediction for milling[J].International Journal of Machine Tools & Manufacture,2005,45:769-781
[56]Neil D.Sims,PhilliP V.Bayly,Keith A.Young.Piezoelec sensors and actuators for milling tool stability lobes[J].Journal of Sound and Vibration.2005(281):734-762.
[57]E.Solis,C.R.Peers,J.E.Jime,etal..A new analytical-experimental method for the identification of stability lobes in high-speed milling[J].International Journal of Machine Tools & Manufacture,2004(44):1591-1597
[58]F.J.Campa,L.N.L(?)pez de Lacalle,A.Lamikiz,J.A.Sanchez.Selection of cutting conditions for a stable milling of flexible parts with bull-nose end mills[J].Journal of Materials Process-ing Technology,2007,191:279-282
[59]I.Mane,V.Gagnol,B.C.Bouzgarrou,P.Ray.Stability-based spindle speed control during flexible workpiece high-speed milling[J].International Journal of Machine Tools & Manufacture,2008,48:184-194
[60]赵宏伟,王晓军,于骏一.机床再生型切削颤振系统稳定性极限预测[J].西南交通大学学报,2003,38(5):547-552
[61]孔繁森,于骏一,潘志刚.切削过程再生颤振的模糊稳定性分析[J].振动工程学报,1998,11(1):106-109
[62]张军,唐文彦,强锡富.再生型切削颤振稳定性极限的图解法[J].中国机械工程,2000,11(5):496-498
[63]唐委校,艾兴.高速切削稳定性数据库的研究[J].工艺与检测,2005,6:76-78
[64]李志刚,刘桓龙,王国志.铣削加工过程的动态稳定性极限分析[J].机械,2007,34(1):45-47
[65]武凯.航空薄壁件加工变形分析与控制研究[D].南京:南京航空航天大学博士学位论文,2002
[66]武凯.基于复杂结构件加工变形控制的高效数控加工技术基础研究[R].南京:南京航空航天大学博士后工作报告,2004
[67]Y.Altintas,S.Engin,E.Budak.Analytical Prediction of Chatter Stability and Design for Variable Pitch Cutters[J].Journal of Manufacturing Science and Engineering,Transactions of the ASME.1999,121:173-178
[68]Sam Turner,Doruk Merdol,Yusuf Altintas,Keith Ridgway.Modeling of the stability of variable helix end mills[J].International Journal of Machine Tools & Manufacture,2007,47:1410-1416
[69]E.Budak,Y.Altintas,Armarego.E.J.A.,Prediction of Milling Force Coefficient from Orthogonal Cutting Data[J].Transactions of ASME,Journal of Manufacturing Science and Engineering.1996,118(2):216-224
[70]S.A Jensen,Y.C Shin.Stability analysis in face milling operations,Part Ⅰ:Theory of stability lobeprediction[J].1999,(121):600-614
[71]梁岩里.基于加工变形与振动控制的多框结构件高效铣削加工机理研究[D].南京:南京理工大学硕士学位论文,2008
[72]傅志方.振动模态分析与参数辨识[M].第4版.北京:机械工业出版社,2004
[2]航空制造工程手册总编委会.航空制造工程手册—框架壳体工艺[M].航空工业出版社,1997.12
[3]Kline W.A,Devor R.E,and Lindberg R.The Prediction of Cutting Forces in End Milling with Application to Cornering Cut[J].International Journal of Machine Tool Design and Research,1982,22(1):7-22
[4]Kline W.A,Devor R.E.The Effect of Cutting Geometry and Forces in Milling[J].International Journal of Machine Tool Design and Research,1983,2(1):123-140
[5]Sutherland J.W.,DeVor R.E.An Improved Method for Cutting Force and Surface Error Predication in Flexible End Milling Systems[J].Journal of Engineering for Industry,1986,108(4):269-279
[6]Armarego E.J.A,Deshpande N.P.Computerized End-Milling Force Predications With Cutting Models Allowing for Eccentricity and Cutter Deflections[J].Annals of the CIRP,1991,40(1):25-29
[7]Won-Soo Yun.Accurate 3-D cutting force prediction using cutting condition independ -ent coefficients in end milling[J].International Journal of Machine Tools &Manufacture,2001,41:463-478
[8]Engin S.,Altintas Y.Mechanics and dynamics of general milling cutters—Part Ⅰ:helical end mills[J].International Journal of Machine Tools&Manufacture,2001,41(15):2195-2212
[9]Huaizhong Li,Wenbin Zhang,Xiaoping Li.A Predictive Model for Helical End Milling Forces[C].2000 ASME International Mechanical Engineering Congress and Exposition.November 5-10,2000,Orlando,Florida:231-236
[10]Oxley,P.L.B.Mechanics of machining[C].Ellie Horwood Limited Chichester,1989
[11]Ozturk B.,Lazoglu I.Machining of flee-form surfaces—Part Ⅰ:Analytical chip load[J].International Journal of Machine Tools&Manufacture,2006,46(7):728-735
[12]冯志勇.一种新的铣削力模型[J].天津大学学报,1998,31(3):314-320
[13]武凯,何宁等.立铣空间力学模型分析研究[J].南京航空航天大学学报,2002,34(6):553-556
[14]武凯,何宁等.基于薄壁件变形分析的铣削加工瞬态力学模型研究[J].应用科学学 报,2005,23(6):631-634
[15]Elbestawi M.A.,Ismail E,Du R.et al.Modeling Machining Dynamics Including Damping in the Tool-Workpiece Interface[J].Journal of Engineering for Industry,1994,116(4):435-439
[16]Smith,S,Alitintas.Update on High Speed Milling Dynamics[J].ASME journal of Engineering Industry,1990,112:142-149
[17]Waters A.J.Modeling and Simulation of Cutting Forces during Face Milling Operation[D].USA:Purdue University,1995:1-200
[18]Jensen S.A.Vibration and Stability Analysis of Face Milling Operations[D].USA:Purdue University,1997:1-150
[19]Altintas Y.,Budak E.Analytical Predication of Stability Lobes in Milling[C].Annals of the CIRP,1995,44(1):357-362
[20]Altintas Y.,Lee P.Combined Mechanics and Dynamics of Ball End Milling[C].ASME Winter Annual Meeting,1995,MED 2(1):657-677
[21]Altintas Y.,Lee P.A General Mechanics and Dynamics Model for Helical end Mills[C].Annals of the CIRP,1996,45(1):59-64
[22]M.A.Elbestawi,R.Sagherian.Dynamic modeling for the prediction of surface errors in the milling of thin-walled sections[J].Journal of Materials Processing Technology,1991(25):215-228
[23]E.Budak,Y.Altintas.Analytical Prediction of Chatter Stability in Milling—Part Ⅱ:Application of the General Formulation to Common Milling Systems[J].Journal of Dynamic Systems,Measurement,and Control,1998,120:31-36
[24]M.A.Davies.Impact dynamics in milling of thin-walled structures[J].Nonlinear Dynamics,2000,22:375-392
[25]李忠群.复杂切削条件高速铣削加工动力学建模、仿真与切削参数优化研究[D].北京:北京航空航天大学博士学位论文,2008
[26]张智海.铣削工艺系统瞬态力学模型和非线性动力学特性的研究[D].北京:清华大学博士学位论文,2001
[27]Xu A.P.,Qu Y.X.,Zhang D.W.,et al.Simulation and experimental investigation of the end milling process considering the cutter flexibility[J].International Journal of Machine Tools&Manufacture,2003,43(3):283-292
[28]Jer-shyong Tsai,Chung-Li Liao.Dynamic finite element modeling of surface errors in peripheral milling of thin-walled workpieees[J].Journal of the Chinese society of mechanical engineers,2000,21(3):265-282
[29]Jochem C.Roukema Yusuf Altintas.Generalized modeling of drilling vibrations—Part Ⅱ:Chatter stability in frequency domain[J].International Journal of Machine Tools &Manufacture,doi:10.1016/j.ijmachtools.2006.10.006
[30]S.Ema,E.Marui.Theoretical analysis on chatter vibration in drilling and its suppression[J].Journal of Materials Processing Technology,2003,138:572-578
[31]M.Xiao S.Karube,T.Soutome K.Sato.Analysis of chatter suppression in vibration cutting[J].International Journal of Machine Tools & Manufacture,2002,42:1677-1685
[32]Evita Edhi,Tetsutaro Hoshi.Stability of high frequency machining vibration by extended chatter model[J].Journal of the International Societies for Precision Engineering and Nanotechnology,2002,26:204-213
[33]Y.S.Tarnga,J.Y.Kaob,E.C.Leea.Chatter suppression in turning operations with a tuned vibration absorber[J].Journal of Materials Processing Technology,2000,105:55-60
[34]Neil D.Sims.Vibration absorbers for chatter suppression:A new analytical tuning methodology[J].Journal of Sound and Vibration,2007,301:592-607
[35]S.Turner et al.Modelling of the stability of variable helix end mills[J].International Journal of Machine Tools &Manufacture,doi:10.1016/j.ijmachtools.2006.08.028
[36]Evita Edhi,Tetsutaro Hoshi.Stability of high frequency machining vibration by extended chatter model[J].Journal of the International Societies for Precision Engineering and Nanotechnology,2002,26:204-213
[37]U.Bravo,O.Altuzarra,L.N.Lopez de Lacalle.Stability limits of milling considering the flexibility of the workpiece and the machine[J].International Journal of Machine Tools & Manufacture,2005,45:1669-1680
[38]E.Budak,Y.Altintas.Analytical Prediction of Chatter Stability in Milling—Part Ⅰ:General Formulation[J].Journal of Dynamic Systems,Measurement,and Control,1998,120:22-30
[39]宋清华,艾兴,万熠,唐委校.考虑刀具偏心的变径向切深铣削稳定性研究[J].振动、测试与诊断,2008,28(3):701-705
[40]汤爱君,刘战强.铣削加工系统三维稳定性理论研究与进展[J].工具技术,2008,42(5):3-5
[41]宋清华,艾兴万熠,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
[42]李亮.薄壁零件的加工振动分析与加工工艺研究[D].南京:南京航空航天大学硕 士学位论文,2005
[43]师汉民.影响机床颤振的几个非线性因素及其数学模型[J].华中工学院学报,1984,12(6):102-112
[44]吴雅.机床切学系统的颤振及其控制[M].科学出版社,1993
[45]何庆编译.高速加工的切削动力学[J].VMEM,2006,6:90-91
[46]李小雷,童水光.高速切削刀具系统固有特性和动态响应分析[J].工程设计学报,2004,11(5):268-272
[47]石莉,贾春德,孙玉龙.应用小波研究动态铣削力及预报铣削颤振[J].哈尔滨工业大学学报,2006,38(10):1978-1980
[48]F.Abrari,M.A.Elbestawi,A.D.Spence.On the Dynamics of Ball End Milling:Modeling of Cutting Forces and Stability Analysis[J].In.J.Mach.Tools Manufact,1998,38(3):215-237
[49]M.S.Fofana.Effect of regenerative process on the sample stability of a multiple delay differential equation[J].Chaos,Solitons and Fractals,2002,14:301-309
[50]T.Insperger,B.P.Mann,P.V.Bayly.Stability of up-milling and down-milling,part Ⅰ:alternative analytical methods[J].International Journal of Machine Tools &Manufacture,2003,43:25-34
[51]Y.Altintas,E.Shamto,P.Lee,E.Budka.Analytical Prediction of stability lobes in ball end milling[J].Trans.ASME,JManu.f Science and Eng.,1999,121:586-592
[52]S.Engin,Y.Altintas.Mechanics and dynamics of general milling cutters—Part Ⅰ:inserthed cutters,Part Ⅱ:helical end mills[J].Journal of Machine Tools and Manufacture,2001,41:2292-2231
[53]E.Budak.Analytical models for high performance milling—part Ⅱ:process dynamics and stability[J].International Journal of Machine Tools & Manufacture,2006,46:1489-1499
[54]B.Balachandran,M.X.Zhao.A Mechanics Based Model for Study of Dynamics of Milling Operations,Kluwer Academic Publishers[J].Printed in the Netherlands Meccanica,2000,35:89-109
[55]JanezGradisek,Martin Kalveram.On stability prediction for milling[J].International Journal of Machine Tools & Manufacture,2005,45:769-781
[56]Neil D.Sims,PhilliP V.Bayly,Keith A.Young.Piezoelec sensors and actuators for milling tool stability lobes[J].Journal of Sound and Vibration.2005(281):734-762.
[57]E.Solis,C.R.Peers,J.E.Jime,etal..A new analytical-experimental method for the identification of stability lobes in high-speed milling[J].International Journal of Machine Tools & Manufacture,2004(44):1591-1597
[58]F.J.Campa,L.N.L(?)pez de Lacalle,A.Lamikiz,J.A.Sanchez.Selection of cutting conditions for a stable milling of flexible parts with bull-nose end mills[J].Journal of Materials Process-ing Technology,2007,191:279-282
[59]I.Mane,V.Gagnol,B.C.Bouzgarrou,P.Ray.Stability-based spindle speed control during flexible workpiece high-speed milling[J].International Journal of Machine Tools & Manufacture,2008,48:184-194
[60]赵宏伟,王晓军,于骏一.机床再生型切削颤振系统稳定性极限预测[J].西南交通大学学报,2003,38(5):547-552
[61]孔繁森,于骏一,潘志刚.切削过程再生颤振的模糊稳定性分析[J].振动工程学报,1998,11(1):106-109
[62]张军,唐文彦,强锡富.再生型切削颤振稳定性极限的图解法[J].中国机械工程,2000,11(5):496-498
[63]唐委校,艾兴.高速切削稳定性数据库的研究[J].工艺与检测,2005,6:76-78
[64]李志刚,刘桓龙,王国志.铣削加工过程的动态稳定性极限分析[J].机械,2007,34(1):45-47
[65]武凯.航空薄壁件加工变形分析与控制研究[D].南京:南京航空航天大学博士学位论文,2002
[66]武凯.基于复杂结构件加工变形控制的高效数控加工技术基础研究[R].南京:南京航空航天大学博士后工作报告,2004
[67]Y.Altintas,S.Engin,E.Budak.Analytical Prediction of Chatter Stability and Design for Variable Pitch Cutters[J].Journal of Manufacturing Science and Engineering,Transactions of the ASME.1999,121:173-178
[68]Sam Turner,Doruk Merdol,Yusuf Altintas,Keith Ridgway.Modeling of the stability of variable helix end mills[J].International Journal of Machine Tools & Manufacture,2007,47:1410-1416
[69]E.Budak,Y.Altintas,Armarego.E.J.A.,Prediction of Milling Force Coefficient from Orthogonal Cutting Data[J].Transactions of ASME,Journal of Manufacturing Science and Engineering.1996,118(2):216-224
[70]S.A Jensen,Y.C Shin.Stability analysis in face milling operations,Part Ⅰ:Theory of stability lobeprediction[J].1999,(121):600-614
[71]梁岩里.基于加工变形与振动控制的多框结构件高效铣削加工机理研究[D].南京:南京理工大学硕士学位论文,2008
[72]傅志方.振动模态分析与参数辨识[M].第4版.北京:机械工业出版社,2004