Journal of Shandong University(Engineering Science) ›› 2026, Vol. 56 ›› Issue (5): 154-172.doi: 10.6040/j.issn.1672-3961.0.2025.325
• Mechanical, Energy and Power Engineering • Previous Articles
Ren Yongsheng, Yao Donghui, Zhang Jinfeng
CLC Number:
| [1] Wiercigroch M, Budak E. Sources of nonlinearities, chatter generation and suppression in metal cutting[J]. Philosophical Transactions of the Royal Society of London A, 2001, 359(1781): 663-693. [2] Munoa J, Beudaert X, Dombovari Z, et al. Chatter suppression techniques in metal cutting[J]. CIRP Annals Manufacturing Technology, 2016, 65(2): 785-808. [3] Taylor F W. On the art of cutting metals[J]. Transactions of the American Society of Mechanical Engineers, 1906, 28: 31-279. [4] Arnold R N. The mechanism of tool vibration in the cutting of steel[J]. ARCHIVE: Proceedings of the Institution of Mechanical Engineers, 1946, 154: 261-284. [5] Doi S, Kato S. Chatter vibration of lathe tools[J]. Transactions of the ASME, 1956, 78(5): 1127-1134. [6] Quintana G, Ciurana J. Chatter in machining processes: a review[J]. International Journal of Machine Tools and Manufacture, 2011, 51(5): 363-376. [7] Zhu L D, Liu C F. Recent progress of chatter prediction, detection and suppression in milling[J]. Mechanical Systems and Signal Processing, 2020, 143: 106840. [8] Wiercigroch M, Krivtsov A M. Frictional chatter in orthogonal metal cutting[J]. Philosophical Transactions of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 2001, 359: 713-738. [9] Davies M A, Burns T J. Thermomechanical oscillations in material flow during high-speed machining[J]. Philosophical Transactions of the Royal Society of London Series A, 2001, 359(1781): 821-846. [10] Hanna N H, Tobias S A. A theory of nonlinear regenerative chatter[J]. Journal of Engineering for Industry, 1974, 96(1): 247-255. [11] Shi H M, Tobias S A. Theory of finite amplitude machine tool instability[J]. International Journal of Machine Tool Design and Research, 1984, 24(1): 45-69. [12] Toblas S A. Machine-tool vibration[M]. Wiley, 1956. [13] Merritt H E. Theory of self-excited machine-tool chatter[J]. Journal of Engineering for Industry, 1965, 87(4): 447-454. [14] Hooke C J, Tobias S A. Finite amplitude instability: a new type of chatter[C] //Proceedings of the 4th International MTDR Conference. Marchester, UK: Pergamon, 1964: 97-109. [15] Pratt J R, Davies M A, Evans C J, et al. Dynamic interrogation of a basic cutting process[J]. CIRP Annals, 1999, 48(1): 39-42. [16] Nayfeh A H, Pratt J R. Chatter identification and control for a boring process[C] //IUTAM Symposium on New Applications of Nonlinear and Chaotic Dynamics in Mechanics. Ithaca, USA: Springer, 1999: 193-202. [17] Shaw S W, Balachandran B.A review of nonlinear dynamics of mechanical systems in year 2008[J].Journal of System Design and Dynamics, 2008, 2(3): 611-640. [18] Altintas Y. Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design[M]. 2nd Ed. Cambridge, UK: Cambridge University Press, 2012. [19] 师汉民. 金属切削理论及其应用新探[M]. 武汉: 华中科技大学出版社, 2003: 235-376. [20] Kalmár-Nagy T, Pratt J R, Davies M A, et al. Experimental and analytical investigation of the subcritical instability in metal cutting[C] // ASME 1999 Design Engineering Technical Conferences. Las Vegas, USA: ASME, 2021: 1721-1729. [21] Kienzle O. Spezifische schnittkräfte bei der metallbearbeitung[J]. Werkstattstechnik und Maschinenbau, 1957, 47: 224-225. [22] Tlusty J. Manufacturing processes and equipment[M]. New Jersey: Prentice Hall, 2000: 416-426. [23] Stépán G. Modelling nonlinear regenerative effects in metal cutting[J]. Philosophical Transactions of the Royal Society of London A, 2001, 359(1781): 739-757. [24] Dombovari Z, Wilson R E, Stepan G. Estimates of the bistable region in metal cutting[J]. Proceedings of the Royal Society A, 2008, 464(2100): 3255-3271. [25] Stepan G, Dombovari Z, Muñoa J. Identification of cutting force characteristics based on chatter experiments[J]. CIRP Annals-Manufacturing Technology, 2011, 60(1): 113-116. [26] Insperger T, Barton D A W, Stépán G. Criticality of Hopf bifurcation in state-dependent delay model of turning processes[J]. International Journal of Non-Linear Mechanics, 2008, 43(2): 140-149. [27] Molnar T G, Insperger T, Stepan G. Closed-form estimations of the bistable region in metal cutting via the method of averaging[J]. International Journal of Non-Linear Mechanics, 2019, 112: 49-56. [28] Yan Y, Xu J, Wiercigroch M, et al. Statistical basin of attraction in time-delayed cutting dynamics: modelling and computation[J]. Physica D: Nonlinear Phenomena, 2021, 416: 132779. [29] Jung J, Ngo C, Son D, et al. Nonlinear modeling and dynamic simulation using bifurcation and stability analyses of regenerative chatter of ball-end milling process[J]. Mathematical Problems in Engineering, 2016, 2016(1): 4368680. [30] Werner G. Influence of work material on grinding forces[J]. CIRP Annals-Manufacturing Technology, 1978, 27(1): 243-248. [31] Liu Z H, Payre G. Stability analysis of doubly regenerative cylindrical grinding process[J].Journal of Sound and Vibration, 2007, 301(2): 950-962. [32] Chung K W, Liu Z H. Nonlinear analysis of chatter vibration in a cylindrical transverse grinding process with two time delays using nonlinear time transformation method[J]. Nonlinear Dynamics, 2011, 66(4): 441-456. [33] Kim P, Jung J, Lee S, et al. Stability and bifurcation analyses of chatter vibrations in a nonlinear cylindrical traverse grinding process[J]. Journal of Sound and Vibration, 2013, 332(15): 3879-3896. [34] Yan Y, Xu J, Wang W Y. Nonlinear chatter with large amplitude in a cylindrical plunge grinding process[J]. Nonlinear Dynamics, 2012, 69(4): 1781-1793. [35] Moon F C, Kalmár-Nagy T. Nonlinear models for complex dynamics in cutting materials[J]. Philosophical Transactions of the Royal Society of London A, 2001, 359(1781): 695-711. [36] Molnár T G, Insperger T, Hogan S J, et al. Estimation of the bistable zone for machining operations for the case of a distributed cutting-force model[J]. Journal of Computational and Nonlinear Dynamics, 2016, 11(5): 051008. [37] Grabec I. Chaotic dynamics of the cutting process[J]. International Journal of Machine Tools and Manufacture, 1988, 28(1): 19-31. [38] Hastings W F, Mathew P, Oxley P L B. A machining theory for predicting chip geometry, cutting forces etc. from work material properties and cutting conditions[J]. Proceedings of the Royal Society of London Series A, Mathematical and Physical Sciences, 1980, 371(1747): 569-587. [39] Wiercigroch M. Chaotic vibration of a simple model of the machine tool-cutting process system[J]. Journal of Vibration and Acoustics, 1997, 119(3): 468-475. [40] Rusinek R, Wiercigroch M, Wahi P. Modelling of frictional chatter in metal cutting[J]. International Journal of Mechanical Sciences, 2014, 89: 167-176. [41] Rusinek R, Wiercigroch M, Wahi P. Orthogonal cutting process modelling considering tool-workpiece frictional effect[J]. Procedia CIRP, 2015, 31: 429-434. [42] Balachandran B. Nonlinear dynamics of milling process[J]. Philosophical Transactions of the Royal Society of London A, 2001, 359(1781): 793-819. [43] Grabec I. Chaos generated by the cutting process[J]. Physics Letters A, 1986, 117(8): 384-386. [44] Kalmar-Nagy T, Wahi P. Towards practical stability limits in turning[C] // Proceedings of the 6th EUROMECH Nonlinear Oscillations Conference. St. Petersburg, Russia: [s.n.] , 2008: 1-13. [45] 梁睿君, 叶文华, 黄翔. 小径向切深铣削稳定性分析与验证[J]. 中国机械工程, 2010, 21(2): 218-221. Liang Ruijun, Ye Wenhua, Huang Xiang. Analyses and validation of stability in low radial immersion milling[J].China Mechanical Engineering, 2010, 21(2): 218-221. [46] Stépán G, Szalai R, Insperger T. Nonlinear dynamics of high-speed milling subjected to regenerative effect[M] // Radons G, Neugebauer R. Non-linear dynamics of production systems. Weinheim: Wiley-VCH, 2004: 111-127. [47] Wahi P, Chatterjee A. Regenerative tool chatter near a codimension 2 Hopf point using multiple scales[J]. Nonlinear Dynamics, 2005, 40(4): 323-338. [48] Wahi P, Chatterjee A. Self-interrupted regenerative metal cutting in turning[J]. International Journal of Non-Linear Mechanics, 2008, 43(2): 111-123. [49] Batzer S A, Gouskov A M, Voronov S A. Modeling vibratory drilling dynamics[J]. Transaction of ASME Journal of Vibration and Acoustics, 2001, 123(4): 435-43. [50] Kondo Y, Kawano O, Sato H. Behavior of chatter due to multiple regenerative effect[J]. Journal of Manufacturing Science and Engineering, 1981, 103(3): 324-9. [51] Szalai R, Stépán G. Lobes and lenses in the stability chart of interrupted turning[J]. Journal of Computational and Nonlinear Dynamics, 2006, 1(3): 205-211. [52] Balachandran B, Zhao M X. A mechanics based model for study of dynamics of milling operations[J]. Meccanica, 2000, 35(2): 89-109. [53] Nie W Y, Zheng M L, Zhang W, et al. Analytical prediction of chatter stability with the effect of multiple delays for variable pitch end mills and optimization of pitch parameters[J]. The International Journal of Advanced Manufacturing Technology, 2022, 124(7-8): 2645-2658. [54] Banihasan M, Bakhtiari-Nejad F. Chaotic vibrations in high-speed milling[J]. Nonlinear Dynamics, 2011, 66(4): 557-574. [55] Tlusty J, Ismail F. Basic non-linearity in machining chatter[J]. CIRP Annals, 1982, 30(1): 299-304. [56] Long X H, Balachandran B. Stability analysis for milling process[J]. Nonlinear Dynamics, 2007, 49(3): 349-359. [57] Long X H, Balachandran B, Mann B P. Dynamics of milling processes with variable time delays[J]. Nonlinear Dynamics, 2007, 47(1): 49-63. [58] Hanna N H, Tobias S A. The non-linear dynamic behavior of a machine tool structure[J]. International Journal of Machine Tool Design and Research, 1969, 9(3): 293-307. [59] Sato R, Noguchi S, Hokazono T, et al. Time domain coupled simulation of machine tool dynamics and cutting forces considering the influences of nonlinear friction characteristics and process damping[J]. Precision Engineering, 2020, 61: 103-109. [60] Semm T, Spescha D, Ceresa N, et al. Efficient dynamic machine tool simulation with included damping and linearized friction effects[J]. Procedia CIRP, 2020, 93: 1442-1447. [61] Tanaka T, Ikeda K, Otsuka J, et al. Influence of rolling friction in linear ball guideway on positioning accuracy[J]. International Journal of Precision Engineering and Manufacturing, 2007, 8(2): 85-90. [62] Miao H H, Li C Y, Wang C Y, et al. The vibration analysis of the CNC vertical milling machine spindle system considering nonlinear and nonsmooth bearing restoring force[J]. Mechanical Systems and Signal Processing, 2021, 161: 107970. [63] Wang W, Zhou Y X, Wang H, et al. Vibration analysis of a coupled feed system with nonlinear kinematic joints[J]. Mechanism and Machine Theory, 2019, 134: 562-581. [64] Xu M T, Li C Y, Zhang H Z, et al. A comprehensive nonlinear dynamic model for ball screw feed system with rolling joint characteristics[J]. Nonlinear Dynamics, 2021, 106(1): 169-210. [65] Fukada S, Fang B, Shigeno A. Experimental analysis and simulation of nonlinear microscopic behavior of ball screw mechanism for ultra-precision positioning[J]. Precision Engineering, 2011, 35(4): 650-668. [66] Zhang G P, Huang Y M, Shi W H, et al. Predicting dynamic behaviours of a whole machine tool structure based on computer-aided engineering[J]. International Journal of Machine Tools and Manufacture, 2003, 43(7): 699-706. [67] Li B, Luo B, Mao X Y, et al. A new approach to identifying the dynamic behavior of CNC machine tools with respect to different worktable feed speeds[J]. International Journal of Machine Tools and Manufacture, 2013, 72: 73-84. [68] Hung J P, Lai Y L, Lin C Y, et al. Modeling the machining stability of a vertical milling machine under the influence of the preloaded linear guide[J]. International Journal of Machine Tools and Manufacture, 2011, 51(9): 731-739. [69] Zhang J, Zhang H J, Du C, et al. Research on the dynamics of ball screw feed system with high acceleration[J]. International Journal of Machine Tools and Manufacture, 2016, 111: 9-16. [70] Wang W, Li C Y, Zhou Y X, et al. Nonlinear dynamic analysis for machine tool table system mounted on linear guides[J]. Nonlinear Dynamics, 2018, 94(3): 2033-2045. [71] Miao H H, Wang C Y, Hao J, et al. Dynamic analysis of the column-spindle system considering the nonlinear characteristics of kinematic joints[J]. Mechanism and Machine Theory, 2022, 174: 104922. [72] Yang T Z, Hou S, Qin Z H, et al. A dynamic reconfigurable nonlinear energy sink[J]. Journal of Sound Vibration, 2021, 494: 115629. [73] Shinagawa M. Prediction of chatter stability of machine tool with consideration of friction damping in guide(development of basic model and investigation on effects of friction and stiffness)[J]. TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series C, 2012, 78(787): 1013-1025. [74] Tlusty J, Livingston R, Teng Y B. Nonlinearities in spindle bearings and their effects[J]. CIRP Annals Manufacturing Technology, 1986, 35(1): 269-273. [75] Watanabe K, Sato H. Development of nonlinear building block approach[J]. Transactions ASME, Journal Vibration Acoustics Stress Reliability Design, 1988, 110: 37-41. [76] Altintas Y, Cao Y. Virtual design and optimization of machine tool spindles[J]. CIRP Annals, 2005, 54(1): 379-382. [77] Sakai Y, Tanaka T, Yoshioka H, et al. Influence of nonlinear spring behavior of friction on dynamic characteristics of a rolling guideway[J]. Journal of Advanced Mechanical Design, Systems, and Manu-facturing, 2015, 9(1): JAMDSM0004. [78] Zaeh M F, Rebelein C, Semm T. Predictive simulation of damping effects in machine tools[J]. CIRP Annals, 2019, 68(1): 393-396. [79] Woydt M, Wäsche R. The history of the Stribeck curve and ball bearing steels: the role of Adolf Martens[J]. Wear, 2010, 268: 1542-1546. [80] Kaneko S, Sato R, Tsutsumi M. Mathematical model of linear motor stage with non-linear friction characteristics[J]. Journal of Advanced Mechanical Design, Systems and Manufacturing, 2008, 2(4): 675-684. [81] Canudas de Wit C, Olsson H, Astrom K J, et al. A new model for control of systems with friction[J]. IEEE Transactions on Automatic Control, 1995, 40(3): 419-425. [82] Sato R. Generation mechanism of quadrant glitches and compensation for it in feed drive systems of NC machine tools[J]. International Journal of Automation Tech-nology, 2012, 6(2): 154-162. [83] Tiwari M, Gupta K, Prakash O. Dynamic response of an unbalanced rotor supported on ball bearings[J].Journal of Sound and Vibration, 2000, 238(5): 757-779. [84] Harsha S P, Sandeep K, Prakash R. The effect of speed of balanced rotor on nonlinear vibrations associated with ball bearings[J]. International Journal of Mechanical Sciences, 2003, 45(4): 725-740. [85] Bai C Q, Xu Q Y. Dynamic model of ball bearings with internal clearance and waviness[J]. Journal of Sound and Vibration, 2006, 294: 23-48. [86] Zhang Z Y, Chen Y S, Cao Q J. Bifurcations and hysteresis of varying compliance vibrations in the primary parametric resonance for a ball bearing[J]. Journal of Sound and Vibration, 2015, 350: 171-184. [87] Wu D Y, Han Q K, Wang H, et al. Nonlinear dynamic analysis of rotor-bearing-pedestal systems with multiple fit clearances[J]. IEEE Access, 2020, 8: 26715-26725. [88] Ruderman M, Hoffmann F, Bertram T. Modeling and identification of elastic robot joints with hysteresis and backlash[J]. IEEE Transactions on Industrial Electronics, 2009, 56(10): 3840-3847. [89] Cordes M, Hintze W. Offline simulation of path deviation due to joint compliance and hysteresis for robot machining[J]. The International Journal of Advanced Manufacturing Technology, 2017, 90(1): 1075-1083. [90] Mohammadi Y, Ahmadi K. Structural nonlinearity of robotic machining systems[C] //ASME 2020 15th International Manufacturing Science and Engineering Conference, American Society of Mechanical Engineers Digital Collection. [S.l.] : ASME, 2020: V002T09A009. [91] Mohammadi Y, Ahmadi K. Single degree-of-freedom modeling of the nonlinear vibration response of a machining robot[J]. Journal of Manufacturing Science and Engineering, 2021, 143(5): 051003. [92] Zhao Z S, Niu J C, Shen Y J, et al. Forced vibration of two-degrees-of-freedom machine tool feed system with clearance and friction[J]. Applied Mathematical Modelling, 2021, 92: 281-296. [93] Nayfeh A H, Chin C M, Pratt J. Perturbation methods in nonlinear dynamics: applications to machining dynamics[J]. Journal of Manufacturing Science and Engineering, 1997, 119(4A): 485-493. [94] Pratt J R, Nayfeh A H. Design and modeling for chatter control[J]. Nonlinear Dynamics, 1999, 19(1): 49-69. [95] Pratt J R, Nayfeh A H. Chatter control and stability analysis of a cantilever boring bar under regenerative cutting conditions[J]. Philosophical Transactions: Mathematical, Physical and Engineering Sciences, 2001, 359(1781): 759-792. [96] Irino N, Imabeppu Y, Higuchi Y, et al. Vibration analysis and cutting simulation of structural nonlinearity for machine tool[J]. CIRP Annals, 2021, 70(1): 317-320. [97] Mohammadi Y, Ahmadi K. Chatter in milling with robots with structural nonlinearity[J]. Mechanical Systems and Signal Processing, 2022, 167: 108523. [98] Wang Z Y, Li C Y, Xu M T, et al. Dynamic analysis and stability prediction of nonlinear feed system coupled with flexible workpiece[J]. Journal of Sound and Vibration, 2022, 520: 116597. [99] Moradi H, Movahhedy M R, Vossoughi G. Dynamics of regenerative chatter and internal resonance in milling process with structural and cutting force nonlinearities[J]. Journal of Sound and Vibration, 2012, 331(16): 3844-3865. [100] Kármán T V. Festigkeitsprobleme im maschinenbau [M] // Mechanik. Wiesbaden: Vieweg+Teubner Verlag, 1907: 311-385. [101] Crespo da Silva M R M, Glynn C C. Nonlinear flexural-flexural-torsional dynamics of inextensional beams. I. equations of motion[J]. Journal of Structural Mechanics, 1978, 6(4): 437-448. [102] Moradi H, Bakhtiari-Nejad F, Movahhedy M R, et al. Nonlinear behaviour of the regenerative chatter in turning process with a worn tool: forced oscillation and stability analysis[J]. Mechanism and Machine Theory, 2010, 45(8): 1050-1066. [103] Nayfeh A H, Nayfeh N A. Analysis of the cutting tool on a lathe [J]. Nonlinear Dynamics, 2011, 63(3): 395-416. [104] Moradi H, Vossoughi G, Movahhedy M R, et al. Forced vibration analysis of the milling process with structural nonlinearity, internal resonance, tool wear and process damping effects[J]. International Journal of Non-Linear Mechanics, 2013, 54: 22-34. [105] Mokhtari A, Jalili M M, Mazidi A, et al. Size dependent vibration analysis of micro-milling operations with process damping and structural nonlinearities[J]. European Journal of Mechanics-A, 2019, 76: 57-69. [106] 任勇生, 马伯乐, 马静敏. 考虑刀杆结构非线性的铣削过程颤振稳定性与主共振[J]. 振动与冲击, 2019, 38(23): 62-69. Ren Yongsheng, Ma Bole, Ma Jingmin. Flutter stability and main resonance of a milling system considering structural nonlinearity of cutter bar[J].Journal of Vibration and Shock, 2019, 38(23): 62-69. [107] Chanda A, Dwivedy S K. Nonlinear dynamic analysis of flexible workpiece and tool in turning operation with delay and internal resonance[J]. Journal of Sound and Vibration, 2018, 434: 358-378. [108] Chanda A, Dwivedy S K. A study of nonlinear behavior of flexible tool and workpiece in turning operation with regenerative effect under internal and primary resonance conditions[J]. Journal of Computational and Nonlinear Dynamics, 2020, 15(6): 061004. [109] Zhou R, Zhang W, Zu J W. Analysis on nonlinear dynamics of a thin-plate workpiece in milling process with cutting force nonlinearities[J]. Journal of Mechanical Science and Technology, 2014, 28(7): 2511-2526. [110] Wu S, Liu Z, Liu X L. Bifurcation and chaos analysis of nonlinear vibration in thin-walled components under thermal-mechanical coupling[J]. Archive of Applied Mechanics, 2022, 92(4): 1325-1338. [111] Zhang W, Zhou R, Zu J W. Nonlinear vibrations of a shell-shaped workpiece during high-speed milling process[J]. Nonlinear Dynamics, 2013, 72(4): 767-787. [112] Ren Y S, Yao D H. Forced vibration in cutting process considering the nonlinear curvature and inertia of a rotating composite cutter bar[J]. Mathematical Problems in Engineering, 2020, 2020: 2463136. [113] Wang A, Jin W Y, Chen W K, et al. Bifurcation and chaotic vibration of frictional chatter in turning process[J]. Advances in Mechanical Engineering, 2018, 10(4): 1687814018771262. [114] Rusinek R, Wiercigroch M, Wahi P. Influence of tool flank forces on complex dynamics of cutting process[J]. International Journal of Bifurcation and Chaos, 2014, 24(9): 1450115. [115] Zakovorotny V L, Lukyanov A D, Gubanova A A, et al. Bifurcation of stationary manifolds formed in the neighborhood of the equilibrium in a dynamic system of cutting[J]. Journal of Sound and Vibration, 2016, 368: 174-190. [116] Beri B, Stepan G. Essential chaotic dynamics of chatter in turning processes[J]. Chaos, 2020, 30(5): 053108. [117] Litak G. Chaotic vibrations in a regenerative cutting process[J]. Chaos, Solitons & Fractals, 2002, 13(7): 1531-1535. [118] Hale J K. Theory of functional differential equations[M]. New York, USA: Springer, 1977: 245-271. [119] Guckenheimer J, Holmes P. Global bifurcations[M] //Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. New York, USA: Springer New York, 1983: 289-352. [120] Campbell S A. Calculating centre manifolds for delay differential equations using mapleTM[M] //Delay Differential Equations. Boston, USA: Springer US, 2009: 1-24. [121] Gilsinn D E. Estimating critical Hopf bifurcation parameters for a second-order delay differential equation with application to machine tool chatter[J]. Nonlinear Dynamics, 2002, 30(2): 103-154. [122] Nayfeh A H. Order reduction of retarded nonlinear systems: the method of multiple scales versus center-manifold reduction[J]. Nonlinear Dynamics, 2008, 51(4): 483-500. [123] Xie Q Z, Zhang Q C, Han J X. Hopf bifurcation for delay differential equation with application to machine tool chatter[J]. Applied Mathematical Modelling, 2012, 36(8): 3803-3812. [124] Fofana M S. Delay dynamical systems and applications to nonlinear machine-tool chatter[J]. Chaos, Solitons & Fractals, 2003, 17(4): 731-747. [125] Stepan G, Szalai R, Mann B P, et al. Nonlinear dynamics of high-speed milling: analyses, numerics, and experiments[J]. Journal of Vibration and Acoustics, 2005, 127(2): 197-203. [126] Weremczuk A, Rusinek R. Influence of frictional mechanism on chatter vibrations in the cutting process-analytical approach[J]. The International Journal of Advanced Manufacturing Technology, 2017, 89(9): 2837-2844. [127] Warmiński J, Litak G, Cartmell M P, et al. Approximate analytical solutions for primary chatter in the non-linear metal cutting model[J]. Journal of Sound and Vibration, 2003, 259(4): 917-933. [128] Yao D H, Ren Y S, Zhang Y H, et al. Nonlinear dynamics of cutting process considering higher-order deformation of composite cutting tool[J]. Shock and Vibration, 2021, 2021(1): 8699218. [129] Páez Chávez J, Zhang Z, Liu Y. A numerical approach for the bifurcation analysis of nonsmooth delay equations[J]. Communications in Nonlinear Science and Numerical Simulation, 2020, 83: 105095. [130] Engelborghs K, Luzyanina T, Roose D. Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL[J]. Journal of Computational and Applied Mathematics, 2000, 125(1/2): 265-275. [131] Li L, Sun B B, Hua H T. Nonlinear system modeling and damping implementation of a boring bar[J]. The International Journal of Advanced Manufacturing Technology, 2019, 104(1): 921-930. [132] Jalili M M, Fazel R, Abootorabi M M. Simulation of chatter in plunge grinding process with structural and cutting force nonlinearities[J]. International Journal of Advanced Manufacturing Technology, 2017, 89(9): 2863-2881. [133] Szalai R. Nonlinear dynamics of high-speed milling[D]. Budapest: Budapest University of Technology and Economics, 2005. [134] Molnar T G, Dombovari Z, Insperger T, et al. On the analysis of the double Hopf bifurcation in machining processes via centre manifold reduction[J]. Proceedings Mathematical, Physical, and Engineering Sciences, 2017, 473(2207): 20170502. [135] Lelkes J, Kalmár-Nagy T. A nonlinear delay-differential equation with harmonic excitation[J]. IFAC-Papers OnLine, 2018, 51(14): 224-229. [136] Doedel E, Keller H B, Kernevez J P. Numerical analysis and control of bifurcation problems(i): bifurcation in finite dimensions[J]. International Journal of Bifurcation and Chaos, 1991, 1(3): 493-520. [137] Doedel E, Keller H B, Kernevez J P. Numerical analysis and control of bifurcation problems(ii): bifurcation in infinite dimensions[J]. International Journal of Bifurcation and Chaos, 1991, 1(4): 745-772. [138] Sieber J, Engelborghs K, Luzyanina T, et al. DDE-BIFTOOL Manual-bifurcation analysis of delay differential equations[PP/OL]. V4.(2016-09-06)[2024-12-09]. https://doi.org/10.48550/arXiv.1406.7144 [139] Dombovari Z, Barton D A W, Wilson R E, et al. On the global dynamics of chatter in the orthogonal cuttingmodel[J]. International Journal of Non-Linear Mechanics, 2011, 46(1): 330-338. [140] Hwang C C, Fung R F, Lin J S. Strong non-linear dynamics of cutting processes[J]. Journal of Sound and Vibration, 1997, 203(3): 363-372. [141] Vela-Martínez L, Jáuregui-Correa J C, González-Brambila O M, et al. Instability conditions due to structural nonlinearities in regenerative chatter[J]. Nonlinear Dynamics, 2009, 56: 415-427. [142] Moradi H, Vossoughi G, Movahhedy M R. Bifurcation analysis of nonlinear milling process with tool wear and process damping: Sub-harmonic resonance under regenerative chatter[J]. International Journal of Mechanical Sciences, 2014, 85: 1-19. [143] Ma B L, Ren Y S. Nonlinear dynamic analysis of the cutting process of a nonextensible composite boring bar [J]. Shock and Vibration, 2020, 2020(1): 5971540. [144] Altinta?瘙塂 Y, Budak E. Analytical prediction of stability lobes in milling[J]. CIRP Annals-Manufacturing Technology, 1995, 44(1): 357-362. [145] Merdol S D, Altintas Y. Multi frequency solution of chatter stability for low immersion milling[J]. Journal of Manufacturing Science and Engineering, 2004, 126(3): 459-466. [146] Insperger T, Stépán G. Semi-discretization method for delayed systems[J]. International Journal for Numerical Methods in Engineering, 2002, 55(5): 503-518. [147] Insperger T, Stépán 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. [148] Ding Y, Zhu L M, Zhang X J, et al. A full-discretization method for prediction of milling stability[J]. International Journal of Machine Tools and Manufacture, 2010, 50(5): 502-509. [149] Insperger T, Stépán G, Bayly P V, et al. Multiple chatter frequencies in milling processes[J]. Journal of Sound and Vibration, 2003, 262(2): 333-345. [150] Yuvaraju B A G, Srinivas J, Nanda B K. Nonlinear dynamics of friction-induced regenerative chatter in internal turning with process damping forces[J]. Journal of Sound and Vibration, 2023, 544: 117386. [151] Moon F, Johnson M. Nonlinear dynamics and chaos in manufacturing processes[M] // Moon F C. Dynamics and chaos in manufacturing processes. Weinheim: Wiley, 1998: 3-32. [152] Johnson M A, Moon F C. Experimental characterization of quasiperiodicity and chaos in a mechanical system with delay[J]. International Journal of Bifurcation and Chaos, 1999, 9(1): 49-65. [153] Johnson M A, Moon F C. Nonlinear techniques to characterize prechatter and chatter vibrations in the machining of metals[J]. International Journal of Bifurcation and Chaos, 2001, 11(2): 449-467. [154] Mann B P, Insperger T, Bayly P V, et al. Stability of up-milling and down-milling, part 2: experimental verification[J]. International Journal of Machine Tools and Manufacture, 2003, 43(1): 35-40. [155] 傅卫平, 蒋耀林. 机床动力学中含时滞颤振系统的分岔问题的研究[J]. 非线性动力学学报, 1994, 1(4): 319-325. Fu Weiping, Jiang Yaolin. Study on bifurcation of chatter system with time delay in machine tool dynamics [J]. Journal of Nonlinear Dynamics in Science and Technology, 1994, 1(4): 319-325. [156] Lelkes J, Kalmár-Nagy T. Bifurcation analysis of a forced delay equation for machine tool vibrations[J]. Nonlinear Dynamics, 2019, 98(4): 2961-2974. [157] Barton D A W. Stability calculations for piecewise-smooth delay equations[J]. International Journal of Bifurcation and Chaos, 2009, 19(2): 639-650. |
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