1 Zhu L M, Ding H, Xiong Y L. Third-order point contact approach for five-axis sculptured surface machining using non-ball-end tools (I): Third-order approximation of tool envelope surface. Sci China Technol Sci, 2010, 53: 1904-1912？？
[2]
2 Zhu L M, Ding H, Xiong Y L. Third-order point contact approach for five-axis sculptured surface machining using non-ball-end tools (Ⅱ): Tool positioning strategy. Sci China Technol Sci, 2010, 53: 2190-2197？？
[3]
3 Ye T, Xiong C H, Xiong Y L, et al. Kinematics constrained five-axis tool path planning for high material removal rate. Sci China Technol Sci, 2011, 54: 3155-3165？？
[4]
5 Bi Q Z, Wang Y H, Zhu L M, et al. Wholly smoothing cutter orientations for five-axis NC machining based on cutter contact point mesh. Sci China Technol Sci, 2010, 53: 1294-1303？？
[5]
8 Wiercigroch M, Krivtsov A M. Frictional chatter in orthogonal metal cutting. Phil Trans R Soc A, 2001, 359: 713-738？？
[6]
9 Davies M A, Burns T J. Thermomechanical oscillations in material flow during high-speed machining. Phil Trans R Soc A, 2001, 359: 821-846 ？？
[7]
17 Schmitz T L. Predicting high-speed machining dynamics by substructure analysis. CIRP Ann-Manuf Techn, 2000, 49: 303-308？？
[8]
18 Schmitz T L, Davies M A, Kennedy M D. Tool point frequency response prediction for high-speed machining by RCSA. J Manuf Sci E-T ASME, 2001, 123: 700-707？？
[9]
19 Zhu R X, Kapoor S G, Devor R E. Mechanistic modeling of the ball end milling process for multi-axis machining of free-form surfaces. J Manuf Sci E-T ASME, 2001, 123: 369-379？？
[10]
20 Budak E, Altintas Y, Armarego E J A. Prediction of milling force coefficients from orthogonal cutting data. J Manuf Sci E-T ASME, 1996, 118: 216-224？？
[11]
26 Sridhar R, Hohn R E, Long G W. A stability algorithm for the general milling process. J Eng Ind-T ASME, 1968, 90: 330-334？？
[12]
27 Tlusty J, Ismail F. Basic non-linearity in machining chatter. CIRP Ann-Manuf Techn, 1981, 30: 299-304？？
[13]
29 Smith S, Tlusty J. Efficient simulation programs for chatter in milling. CIRP Ann-Manuf Techn, 1993, 42: 463-466？？
[14]
31 Davies M A, Pratt J R, Dutterer B, et al. Stability prediction for low radial immersion milling. J Manuf Sci E-T ASME, 2002, 124: 217-225？？
[15]
32 Campomanes M L, Altintas Y. An improved time domain simulation for dynamic milling at small radial immersions. J Manuf Sci E-T ASME, 2003, 125: 416-422？？
[16]
33 Li Z Q, Liu Q. Solution and analysis of chatter stability for end milling in the time-domain. Chin J Aeronaut, 2008, 21: 169-178？？
[17]
34 Minis I, Yanushevsky R. A new theoretical approach for the prediction of machine tool chatter in milling. J Eng Ind-T ASME, 1993, 115: 1-8？？
[18]
35 Altintas Y, Budak E. Analytical prediction of stability lobes in milling. CIRP Ann-Manuf Techn, 1995, 44: 357-362？？
[19]
36 Budak E, Altintas Y. Analytical prediction of chatter stability in milling—Part I: General formulation. J Dyn Syst-T ASME, 1998, 120: 22-30？？
[20]
39 Mann B P, Patel B R. Stability of delay equations written as state space models. J Vib Control, 2010, 16: 1067-1085？？
[21]
40 Garg N K, Mann B P, Kim N H, et al. Stability of a time-delayed system with parametric excitation. J Dyn Syst-T ASME, 2007, 129: 125-135？？
[22]
41 Insperger T, Stépán G. Semi-discretization method for delayed systems. Int J Number Meth Eng, 2002, 55: 503-518？？
51 Olgac N, Sipahi R. Dynamics and stability of variable-pitch milling. J Vib Control, 2007, 13: 1031-1043？？
[25]
53 Yi S, Nelson P W, Ulsoy A G. Delay differential equations via the matrix Lambert W function and bifurcation analysis: Application to machine tool chatter. Math Biosci Eng, 2007, 4: 355-368？？
[26]
54 Butcher E A, Ma H, Bueler E, et al. Stability of linear time-periodic delay-differential equations via Chebyshev polynomials. Int J Number Meth Eng, 2004, 59: 895-922？？
[27]
55 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 Comput Nonlin Dyn, 2009, 4: 031003？？
[28]
56 Schmitz T L, Mann B P. Closed-form solutions for surface location error in milling. Int J Mach Tool Manu, 2006, 46: 1369-1377？？
[29]
60 Bayly P V, Mann B P, Schmitz T L, et al. Effects of radial immersion and cutting direction on chatter instability in end-milling. ASME, Manuf Eng Div, MED, 2002, 13: 351-363
[30]
62 Ding Y, Zhu L M, Zhang X J, et al. Numerical integration method for prediction of milling stability. J Manuf Sci E-T ASME, 2011, 133: 031005？？
[31]
63 Bayly P V, Halley J E, Mann B P, et al. Stability of interrupted cutting by temporal finite element analysis. J Manuf Sci E-T ASME, 2003, 125: 220-225？？
[32]
64 Ding Y, Zhu L M, Zhang X J, et al. Second-order full-discretization method for milling stability prediction. Int J Mach Tool Manu, 2010, 50: 926-932？？
[33]
65 Zhang X J, Xiong C H, Ding Y. Improved full-discretization method for milling chatter stability prediction with multiple delays. Lect Notes Comput Sc, 2010, 6425: 541-552？？
[34]
66 Delves L M, Mohamed J L. Computational Methods for Integral Equations. Cambridge: Cambridge University Press, 1985
[35]
69 Zhang X J, Xiong C H, Ding Y, et al. Variable-step integration method for milling chatter stability prediction with multiple delays. Sci China Technol Sci, 2011, 54: 3137-3154？？
[36]
71 Ding Y, Zhu L M, Zhang X J, et al. Response sensitivity analysis of the dynamic milling process based on the numerical integration method. Chin J Mech Eng, 2012, 25: 940-946？？
[37]
72 Kurdi M H, Haftka R T, Schmitz T L, et al. A robust semi-analytical method for calculating the response sensitivity of a time delay system. J Vib Acoust-T ASME, 2008, 130: 064504？？
[38]
4 Guo Q, Sun Y W, Guo D M. Analytical modeling of geometric errors induced by cutter runout and tool path optimization for five-axis flank machining. Sci China Technol Sci, 2011, 54: 3180-3190？？
[39]
6 Wiercigroch M, Budak E. Sources of nonlinearities, chatter generation and suppression in metal cutting. Phil Trans R Soc A, 2001, 359: 663-693？？
[40]
7 Ismail F, Vadari V R. Machining chatter of end mills with unequal modes. J Eng Ind-T ASME, 1990, 112: 229-235？？
[41]
10 Altintas Y, Weck M. Chatter stability of metal cutting and grinding. CIRP Ann-Manuf Techn, 2004, 53: 619-642？？
[42]
11 Altintas Y, Stépán G, Merdol D, et al. Chatter stability of milling in frequency and discrete time domain. CIRP J Manuf Sci Techn, 2008, 1: 35-44？？
[43]
12 Schmitz T, Ziegert J. Examination of surface location error due to phasing of cutter vibrations. Precis Eng, 1999, 23: 51-62？？
[44]
13 Bachrathy D, Insperger T, Stepan G. Surface properties of the machined workpiece for helical mills. Mach Sci Technol, 2009, 13: 227-245？？
[45]
14 Altintas Y. Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations, and CNC design. Cambridge: Cambridge University Press, 2000
[46]
15 Gradisek J, Kalveram M, Insperger T, et al. On stability prediction for milling. Int J Mach Tool Manu, 2005, 45: 769-781？？
[47]
16 Mann B P, Young K A, Schmitz T L, et al. Simultaneous stability and surface location error predictions in milling. J Manuf Sci E-T ASME, 2005, 127: 446-453？？
[48]
21 Budak E, Ozturk E, Tunc L T. Modeling and simulation of 5-axis milling processes. CIRP Ann-Manuf Techn, 2009, 58: 347-350？？
[49]
22 Zhang X J, Xiong C H, Ding Y. A new solution for stability prediction in flexible part milling. Lect Notes Comput Sci, 2011, 7102: 452-464？？
[50]
23 Zhang X J, Xiong C H, Ding Y, et al. Milling stability analysis with simultaneously considering the structural mode coupling effect and regenerative effect. Int J Mach Tool Manu, 2011, 53: 127-140
[51]
24 Mao X Y, Liu H Q, Li B. Time-frequency analysis and detecting method research on milling force token signal in spindle current signal. Sci China Ser E-Technol Sci, 2009, 52: 2810-2813？？
[52]
25 Liu H Q, Chen Q H, Li B, et al. On-line chatter detection using servo motor current signal in turning. Sci China Technol Sci, 2011, 54: 3119-3129？？
[53]
28 Tlusty J, Ismail F. Special aspects of chatter in milling. J Vib Acoust Stress Reliab Des-T ASME, 1983, 105: 24-32
[54]
30 Davies M A, Pratt J R, Dutterer B S, et al. Stability of low radial immersion milling. CIRP Ann-Manuf Techn, 2000, 49: 37-40？？
[55]
37 Merdol S D, Altintas Y. Multi frequency solution of chatter stability for low immersion milling. J Manuf Sci E-T ASME, 2004, 126: 459-466？？
[56]
38 Bayly P V, Halley J E, Mann B P, et al. Stability of interrupted cutting by temporal finite element analysis. Pro ASME Des Eng Tech Conf, 2001, 6C: 2361-2370
[57]
42 Insperger T, Stépán G. Updated semi-discretization method for periodic delay-differential equations with discrete delay. Int J Number Meth Eng, 2004, 61: 117-141？？
[58]
43 Insperger T, Stépán G, Turi J. On the higher-order semi-discretizations for periodic delayed systems. J Sound Vib, 2008, 313: 334-341？？
[59]
44 Long X H, Balachandran B, Mann B P. Dynamics of milling processes with variable time delays. Nonlinear Dynam, 2007, 47: 49-63
[60]
45 Long X H, Balachandran B. Stability of up-milling and down-milling operations with variable spindle speed. J Vib Control, 2010, 16: 1151-1168？？
49 Wan M, Zhang W H, Dang J W, et al. A unified stability prediction method for milling process with multiple delays. Int J Mach Tool Manu, 2010, 50: 29-41？？
[64]
50 Olgac N, Hosek M. A new perspective and analysis for regenerative machine tool chatter. Int J Mach Tool Manu, 1998, 38: 783-798？？
[65]
52 Maghami Asl F, Ulsoy A G. Analysis of a system of linear delay differential equations. J Dyn Syst-T ASME, 2003, 125: 215-223？？
[66]
57 Mann B P, Bartow M J, Young K A, et al. Machining accuracy due to tool or workpiece vibrations. ASME, Manuf Eng Div, MED, 2003, 14: 55-62
[67]
58 Mann B P, Edes B T, Easley S J, et al. Chatter vibration and surface location error prediction for helical end mills. Int J Mach Tool Manu, 2008, 48: 350-361？？
[68]
59 Insperger T, Gradisek J, Kalveram M, et al. Machine tool chatter and surface location error in milling processes. J Manuf Sci E-T ASME, 2006, 128: 913-920？？
[69]
61 Ding Y, Zhu L M, Zhang X J, et al. A full-discretization method for prediction of milling stability. Int J Mach Tool Manu, 2010, 50: 502-509？？
[70]
67 Yang W Y, Cao W, Chung T-S, et al. Applied Numerical Methods Using Matlab. Hoboken N. J.: Wiley-Interscience, 2005
[71]
68 Ding Y, Zhu L M, Zhang X J, et al. Milling stability analysis using the spectral method. Sci China Technol Sci, 2011, 54: 3130-3136？？
[72]
70 Ding Y, Zhu L M, Zhang X J, et al. On a numerical method for simultaneous prediction of stability and surface location error in low radial immersion milling. J Dyn Syst-T ASME, 2011, 133: 024503？？
[73]
73 Lax P D. Linear Algebra and Its Applications. New York: Wiley-Interscience, 2007
