[1] Tlusty J, Spacek L. Self-Excited Vibration in Machine Tools[M]. Prague, 1954.
[2] Sisson T R, Kegg R L. An Explanation of Low-Speed Chatter Effects[J]. Journal of Engineering for Industry. 1969, 91(4): 951.
[3] 刘习军,陈予恕. 机床速度型切削颤振的非线性研究[J]. 振动与冲击. 1999(02): 7-11.
LIU Xi-jun, CHEN Yu-shu. Nonlinear analysis of speed type cutting chatter of machine tools[J]. Journal of vibration and shock. 1999(02): 7-11
[4] 刘习军,王立刚,贾启芬. 一种由干摩擦引起的车床切削颤振[J]. 工程力学. 2005(01): 107-112.
LIU Xi-jun, WANG Li-gang, JIA Qi-fen. Cutting chatter of machine tools induced by dry friction[J]. Engineering Mechanics. 2005(01): 107-112.
[5] Tlusty J, Ismail F. Basic Non-Linearity in Machining Chatter[J]. CIRP Annals-Manufacturing Technology. 1981, 30(1): 299-304.
[6] Gasparetto A. Eigenvalue Analysis of Modecoupling Chatter for Machine-Tool Stabilization[J]. Journal of Vibration and Control. 2001(7): 181-197.
[7] Iturrospe A, Atxa V, Abete J M. State-Space Analysis of Mode-Coupling in Orthogonal Metal Cuttingunder Wave Regeneration[J]. International Journal of Adaptive Control and Signal Processing. 2007(47): 1583-1590.
[8] Huang C Y, Wang J. Mode Coupling Behavior in End Milling[M]. NEW YORK:AMER SOC MECHANICAL ENGINEERS, 2010, 875-884.
[9] Moradi H, Movahhedy M R, Vossoughi G, et al. Investigation of the Internal Resonance and Regenerative Chatter Dynamics in Nonlinear Milling Process[J]. Proceedings of the Asme International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2011, Vol 1, Pts a and B: 23Rd Biennial Conference On Mechanical Vibration and Noise. 2012: 141-150.
[10] 林洁琼,周晓勤,孔繁森,等. 刚度主轴方位对模态耦合再生切削系统动态响应谐参数的影响[J]. 振动与冲击. 2009(05): 63-68.
LIN Jie-qiong, ZHOU Xiao-qin, KONG Fan-sen, et al. Influence of orientations of principal stiffness axes on harmonic parameters of dynamic response in mode-coupled regenerative machining system[J]. Journal of vibration and shock. 2009(05):63-68.
[11] 吴雅. 机床切削系统的颤振及其控制[M]. 北京: 科学出版社, 1993.
[12] Stépán G, Kalmár-Nagy T. Nonlinear Regenerative Machine Tool Vibrations[C]. 1997.
[13] Balachandran B. Nonlinear Dynamics of Milling Processes[J]. Philosophical Transactions of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences. 2001, 359(1781): 793-819.
[14] Zhao M X, Balachandran B. Dynamics and Stability of Milling Process[J]. International Journal of Solids and Structures. 2001, 38(10): 2233-2248.
[15] Balachandran B, Zhao M X. A Mechanics Based Model for Study of Dynamics of Milling Operations[J]. Meccanica. 2000, 35(2): 89-109.
[16] 师汉民. 关于机床自激振动的一个非线性理论模型(第一部分)[J]. 应用力学学报. 1984(01): 1-14.
SHI Han-min. Nonlinear chatter theory of machine tools (part 1: the stablity of machine tool chatter amplitude) [J]. Journal of Applied Mechanics. 1984(01): 1-14.
[17] 师汉民. 关于机床自激振动的一个非线性理论模型(第二部份)[J]. 应用力学学报. 1984(02): 75-88.
SHI Han-min. Nonlinear chatter theory of machine tools (part 2: finite amplitude machine tool instability) [J]. Journal of Applied Mechanics. 1984(02): 75-88.
[18] Long X H, Balachandran B. Stability Analysis for Milling Process[J]. Nonlinear Dynamics. 2007, 49(3): 349-359.
[19] Long X H, Balachandran B, Mann B P. Dynamics of Milling Processes with Variable Time Delays[J]. Nonlinear Dynamics. 2007, 47(1-3): 49-63.
[20] Hanna N H, Tobias S A. A Theory of Nonlinear Regenerative Chatter[J]. ASME Journal of Engineering for Industry. 1974, 96: 247-255.
[21] Banihasan M, Bakhtiari-Nejad F. Chaotic Vibrations in High-Speed Milling[J]. Nonlinear Dynamics. 2011, 66(4): 557-574.
[22] Altıntaş Y, Budak E, Engin S. Analytical Stability Prediction and Design of Variable Pitch Cutters[J]. Journal of Manufacturing Science and Engineering. 1999, 121(2): 173-178.
[23] Budak E. An Analytical Design Method for Milling Cutters with Nonconstant Pitch to Increase Stability, Part 1: Theory[J]. Journal of Manufacturing Science and Engineering-Transactions of the Asme. 2003, 125(1): 29-34.
[24] Budak E. An Analytical Design Method for Milling Cutters with Nonconstant Pitch to Increase Stability, Part 2: Application[J]. Journal of Manufacturing Science and Engineering-Transactions of the Asme. 2003, 125(1): 35-38.
[25] Turner S, Merdol D, Altintas Y, et al. Modelling of the Stability of Variable Helix End Mills[J]. International Journal of Machine Tools and Manufacture. 2007, 47(9): 1410-1416.
[26] Sellmeier V, Denkena B. Stable Islands in the Stability Chart of Milling Processes Due to Unequal Tooth Pitch[J]. International Journal of Machine Tools & Manufacture. 2011, 51(2): 152-164.
[27] Otto A, Radons G. Frequency Domain Stability Analysis of Milling Processes with Variable Helix Tools[C]. 2012.
[28] Dombovari Z, Stepan G. The Effect of Helix Angle Variation On Milling Stability[J]. Journal of Manufacturing Science and Engineering-Transactions of the Asme. 2012, 134(0510155).
[29] Eksioglu C, Kilic Z M, Altintas Y. Discrete-Time Prediction of Chatter Stability, Cutting Forces, and Surface Location Errors in Flexible Milling Systems[J]. Journal of Manufacturing Science and Engineering. 2012, 134(6): 61006.
[30] Dombovari Z, Altintas Y, Stepan G. The Effect of Serration On Mechanics and Stability of Milling Cutters[J]. International Journal of Machine Tools and Manufacture. 2010, 50(6): 511-520.
[31] Catania G, Mancinelli N. A Coupled Theoretical-Experimental Dynamical Model for Chatter Prediction in Milling Processes[J]. Proceedings of the Asme International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Vol 1, Pts a and B. 2010: 175-184.
[32] 李勤良,汪博,赵斌,等. 考虑非线性迟滞力的机床颤振系统稳定性研究[J]. 机械工程学报. 2013(11): 43-49.
LI Qin-liang, Wang Bo, ZHAO Bin, et al. Research on the chatter stability of machine system taking the nonlinear hysteretic force into consideration[J]. Journal of Mechanical Engineering. 2013(11): 43-49.
[33] Gao S H, Meng G, Long X H. Study of Milling Stability with Hertz Contact Stiffness of Ball Bearings[J]. Archive of Applied Mechanics. 2011, 81(8): 1141-1151.
[34] Movahhedy M R, Mosaddegh P. Prediction of Chatter in High Speed Milling Including Gyroscopic Effects[J]. International Journal of Machine Tools and Manufacture. 2006, 46(9): 996-1001.
[35] Xiong G L, Yi J M, Zeng C, 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(1): 379-384.
[36] Tian J, Hutton S G. Chatter Instability in Milling Systems with Flexible Rotating Spindles—a New Theoretical Approach[J]. Journal of Manufacturing Science and Engineering. 2001, 123(1): 1-9.
[37] Ertürk A, Budak E, özgüven H N. Selection of Design and Operational Parameters in Spindle–Holder–Tool Assemblies for Maximum Chatter Stability by Using a New Analytical Model[J]. International Journal of Machine Tools and Manufacture. 2007, 47(9): 1401-1409.
[38] Radulescu R, Kapoor S G, Devor R E. An Investigation of Variable Spindle Speed Face Milling for Tool-Work Structures with Complex Dynamics, Part 1: Simulation Results[J]. Journal of Manufacturing Science and Engineering. 1997, 119(3): 266-272.
[39] Radulescu R, Kapoor S G, Devor R E. An Investigation of Variable Spindle Speed Face Milling for Tool-Work Structures with Complex Dynamics, Part 2: Physical Explanation[J]. Journal of Manufacturing Science and Engineering. 1997, 119(3): 273-280.
[40] Takemura T, Kitamura T, Hoshi T, et al. Active Suppression of Chatter by Programmed Variation of Spindle Speed[J]. Annals of the CIRP. 1974, 23(1): 121-122.
[41] Sastry S, Kapoor S G, Devor R E. Floquet Theory Based Approach for Stability Analysis of the Variable Speed Face-Milling Process[J]. Journal of Manufacturing Science and Engineering-Transactions of the Asme. 2002, 124(1): 10-17.
[42] Zatarain M, Bediaga I, Munoa J, et al. Stability of Milling Processes with Continuous Spindle Speed Variation: Analysis in the Frequency and Time Domains, and Experimental Correlation[J]. Cirp Annals-Manufacturing Technology. 2008, 57(1): 379-384.
[43] Xinhua L, Balachandran B. Stability of Up-Milling and Down-Milling Operations with Variable Spindle Speed[J]. Journal of Vibration and Control. 2010, 16(7-8): 1151-1168.
[44] Seguy S, Insperger T, Arnaud L, et al. Suppression of Period Doubling Chatter in High-Speed Milling by Spindle Speed Variation[J]. Machining Science and Technology. 2011, 15(PII 9380210952): 153-171.
[45] Budak E, Altintas Y. Analytical Prediction of Chatter Stability in Milling. I. General Formulation[J]. Transactions of the ASME. Journal of Dynamic Systems, Measurement and Control. 1998, 120(1): 22-30.
[46] Altintaş Y, Budak E. Analytical Prediction of Stability Lobes in Milling[J]. CIRP Annals - Manufacturing Technology. 1995, 44(1): 357-362.
[47] Merdol S D, Altintas Y. Multi Frequency Solution of Chatter Stability for Low Immersion Milling[J]. Transactions of the ASME. Journal of Manufacturing Science and Engineering. 2004, 126(3): 459-466.
[48] Bachrathy D, Stepan G. Improved Prediction of Stability Lobes with Extended Multi Frequency Solution[J]. Cirp Annals-Manufacturing Technology. 2013, 62(1): 411-414.
[49] Insperger T, Stepan G. Semi-Discretization Method for Delayed Systems[J]. International Journal for Numerical Methods in Engineering. 2002, 55(5): 503-518.
[50] Insperger T, Stepan G. Updated Semi-Discretization Method for Periodic Delay-Differential Equations with Discrete Delay[J]. International Journal for Numerical Methods in Engineering. 2004, 61(1): 117-141.
[51] Insperger T, Stepan G, Turi J. On the Higher-Order Semi-Discretizations for Periodic Delayed Systems[J]. Journal of Sound and Vibration. 2008, 313(1-2): 334-341.
[52] Altintas Y, Stepan G, Merdol D, et al. Chatter Stability of Milling in Frequency and Discrete Time Domain[J]. CIRP Journal of Manufacturing Science and Technology. 2008, 1(1): 35-44.
[53] 李中伟,龙新华,孟光. 基于Magnus-Gaussian截断的铣削系统稳定性的半离散分析法[J]. 振动与冲击. 2009(05): 69-73.
LI Zhong-wei, LONG Xin-hua, MENG Guang. Stability analysis of milling process by semi discretization method based on Magnus-Guassian truncation[J]. Journal of vibration and shock. 2009(05): 69-73.
[54] Niu J, Ding Y, Zhu L, et al. Runge-Kutta Methods for a Semi-Analytical Prediction of Milling Stability[J]. Nonlinear Dynamics. 2014, 76(1): 289-304.
[55] Ding Y, Zhu L, Zhang X, et al. A Full-Discretization Method for Prediction of Milling Stability[J]. International Journal of Machine Tools and Manufacture. 2010, 50(5): 502-509.
[56] Insperger T. Full-Discretization and Semi-Discretization for Milling Stability Prediction: Some Comments[J]. International Journal of Machine Tools & Manufacture. 2010, 50(7): 658-662.
[57] Zhang X, Xiong C, Ding Y. Improved Full-Discretization Method for Milling Chatter Stability Prediction with Multiple Delays[M]. Intelligent robotics and applications, Springer, 2010, 541-552.
[58] Ding Y, Zhu L, Zhang X, et al. Second-Order Full-Discretization Method for Milling Stability Prediction[J]. International Journal of Machine Tools and Manufacture. 2010, 50(10): 926-932.
[59] Li M, Zhang G, Huang Y. Complete Discretization Scheme for Milling Stability Prediction[J]. Nonlinear Dynamics. 2013, 71(1-2): 187-199.
[60] Bayly P V, Halley J E, Mann B P, et al. Stability of Interrupted Cutting by Temporal Finite Element Analysis[J]. Journal of Manufacturing Science and EngineeringJournal of Manufacturing Science and Engineering. 2003, 125(2): 220.
[61] Garg N K, Mann B P, Kim N H, et al. Stability of a Time-Delayed System with Parametric Excitation[J]. Journal of Dynamic Systems Measurement and Control-Transactions of the Asme. 2007, 129(2): 125-135.
[62] Mann B P, Patel B R. Stability of Delay Equations Written as State Space Models[J]. Journal of Vibration and Control. 2010, 16(7-8SI): 1067-1085.
[63] Ding Y, Zhang X, Ding H, et al. Numerical Integration Method for Prediction of Milling Stability[J]. Journal of Manufacturing Science and Engineering. 2011, 133(3): 31005.
[64] Ding Y, Zhu L, Zhang X, et al. Milling Stability Analysis Using the Spectral Method[J]. Science China Technological Sciences. 2011, 54(12): 3130-3136.
[65] Zhang X, Xiong C, Ding Y, et al. Variable-Step Integration Method for Milling Chatter Stability Prediction with Multiple Delays[J]. Science China Technological Sciences. 2011, 54(12): 3137-3154.
[66] Yi S, Nelson P, Ulsoy A. Delay Differential Equations Via the Matrix Lambert W Function and Bifurcation Analysis: Application to Machine Tool Chatter[J]. Mathematical Biosciences and Engineering. 2007, 4(2): 355.
[67] Maghami Asl F, Ulsoy A G. Analysis of a System of Linear Delay Differential Equations[J]. Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME. 2003, 125(2): 215-223.
[68] Butcher E A, Bobrenkov O A, Bueler E, et al. Analysis of Milling Stability by the Chebyshev Collocation Method: Algorithm and Optimal Stable Immersion Levels[J]. Journal of Computational and Nonlinear Dynamics. 2009, 4(3): 1-12.
[69] Butcher E A, Ma H, Bueler E, et al. Stability of Linear Time-Periodic Delay-Differential Equations Via Chebyshev Polynomials[J]. International Journal for Numerical Methods in Engineering. 2004, 59(7): 895-922.
[70] Ding Y, Zhu L, Zhang X, et al. Stability Analysis of Milling Via the Differential Quadrature Method[J]. Journal of Manufacturing Science and Engineering. 2013, 135(4): 44502.
[71] Tlusty J, Ismail F. Special Aspects of Chatter in Milling[J]. Journal of Vibration, Acoustics Stress and Reliability in Design. 1983, 105(1): 24-32.
[72] Smith S, Tlusty J. Efficient Simulation Programs for Chatter in Milling[J]. CIRP Annals-Manufacturing Technology. 1993, 42(1): 463-466.
[73] Campomanes M L, Altintas Y. An Improved Time Domain Simulation for Dynamic Milling at Small Radial Immersions[J]. Journal of Manufacturing Science and Engineering. 2003, 125(3): 416-422.
[74] Li H Z, Li X P, Chen X Q. A Novel Chatter Stability Criterion for the Modelling and Simulation of the Dynamic Milling Process in the Time Domain[J]. The International Journal of Advanced Manufacturing Technology. 2003, 22(9-10): 619-625.
[75] Zhongqun L, Qiang L. Solution and Analysis of Chatter Stability for End Milling in the Time-Domain[J]. Chinese Journal of Aeronautics. 2008, 21(2): 169-178.
[76] Quintana G, Ciurana J, Ferrer I, et al. Sound Mapping for Identification of Stability Lobe Diagrams in Milling Processes[J]. International Journal of Machine Tools and Manufacture. 2009, 49(3): 203-211.
[77] Quintana G, Ciurana J, Teixidor D. A New Experimental Methodology for Identification of Stability Lobes Diagram in Milling Operations[J]. International Journal of Machine Tools and Manufacture. 2008, 48(15): 1637-1645.
[78] 迟玉伦, 李郝林. 铣削颤振稳定域叶瓣图确定方法研究[J]. 振动与冲击. 2014,33(4):90-93.
CHI Yu-lun,LI Hao-lin.Determination of chatter stability field lobe diagrams for a milling processing[J].Journal of Vibration and Shock,2014,33(4):90-93.
[79] Mascardelli B A, Park S S, Freiheit T. Substructure Coupling of Microend Mills to Aid in the Suppression of Chatter[J]. Journal of Manufacturing Science and Engineering. 2008, 130(1): 11010.
[80] Filiz S, Ozdoganlar O B. Microendmill Dynamics Including the Actual Fluted Geometry and Setup Errors—Part I: Model Development and Numerical Solution[J]. Journal of Manufacturing Science and Engineering. 2008, 130(3): 31119.
[81] Tajalli S A, Movahhedy M R, Akbari J. Chatter Instability Analysis of Spinning Micro-End Mill with Process Damping Effect Via Semi-Discretization Approach[J]. Acta Mechanica. 2014, 225(3): 715-734.
[82] Tajalli S A, Movahhedy M R, Akbari J. Size Dependent Vibrations of Micro-End Mill Incorporating Strain Gradient Elasticity Theory[J]. Journal of Sound and Vibration. 2013, 332(15): 3922-3944.
[83] Tajalli S A, Movahhedy M R, Akbari J. Investigation of the Effects of Process Damping on Chatter Instability in Micro End Milling[J]. Procedia CIRP. 2012: 156-161.
[84] Uhlmann E, Mahr F. A Time Domain Simulation Approach for Micro Milling Processes[J]. Procedia CIRP. 2012, 4(0): 22-28.
[85] Mustapha K B, Zhong Z W. A Hybrid Analytical Model for the Transverse Vibration Response of a Micro-End Mill[J]. Mechanical Systems and Signal Processing. 2013, 34(1–2): 321-339.
[86] Rahnama R, Sajjadi M, Park S S. Chatter Suppression in Micro End Milling with Process Damping[J]. Journal of Materials Processing Technology. 2009, 209(17): 5766-5776.
[87] Afazov S M, Ratchev S M, Segal J, et al. Chatter Modelling in Micro-Milling by Considering Process Nonlinearities[J]. International Journal of Machine Tools and Manufacture. 2012: 28-38.
[88] Afazov S M, Zdebski D, Ratchev S M, et al. Effects of Micro-Milling Conditions On the Cutting Forces and Process Stability[J]. Journal of Materials Processing Technology. 2013, 213(5): 671-684.
[89] Jin X, Altintas Y. Chatter Stability Model of Micro-Milling with Process Damping[J]. Journal of Manufacturing Science and Engineering. 2013, 135(3): 31011.
[90] Song Q, Liu Z, Shi Z. Chatter Stability for Micromilling Processes with Flat End Mill[J]. International Journal of Advanced Manufacturing Technology. 2014, 71(5-8): 1159-1174.
[91] Biermann D, Baschin A. Influence of Cutting Edge Geometry and Cutting Edge Radius On the Stability of Micromilling Processes[J]. Production Engineering. 2009, 3(4-5): 375-380.
[92] Baschin A, Kahnis P, Biermann D. Dynamic Analysis of the Micromilling Process – Influence of Tool Vibrations On the Quality of Microstructures[J]. Materialwissenschaft Und Werkstofftechnik. 2008, 39(9): 616-621.
[93] Park S S, Rahnama R. Robust Chatter Stability in Micro-Milling Operations[J]. CIRP Annals - Manufacturing Technology. 2010, 59(1): 391-394.