Nonlinear dynamics of milling processes

Abstract

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Balachandran B. 2001Nonlinear dynamics of milling processesPhil. Trans. R. Soc. A.359793–819http://doi.org/10.1098/rsta.2000.0755SectionRestricted accessNonlinear dynamics of milling processes B. Balachandran B. Balachandran Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USA Google Scholar Find this author on PubMed Search for more papers by this author B. Balachandran B. Balachandran Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USA Google Scholar Find this author on PubMed Search for more papers by this author Published:15 April 2001https://doi.org/10.1098/rsta.2000.0755AbstractIn this article, dynamics and stability of milling operations with cylindrical end mills are investigated. A unified–mechanics–based model, which allows for both regenerative effects and loss–of–contact effects, is presented for study of partial–immersion, high–immersion and slotting operations. Reduced–order models that can be used for certain milling operations such as full–immersion operations and finishing cuts are also presented. On the basis of these models, the loss of stability of periodic motions of the workpiece–tool system is assessed by using Poincare sections and the numerical predictions of stable and unstable motions are found to correlate well with the corresponding experimental observations. Bifurcations experienced by periodic motions of the workpiece–tool system with respect to quasi–static variation of parameters such as axial depth of cut are examined and discussed. For partial–immersion operations, consideration of both time–delay effects and loss–of–contact effects is shown to have a significant influence on the structure of the stability boundaries in the space of spindle speed and axial depth of cut. The sensitivity of system dynamics to multiple–regenerative effects, mode–coupling effects and feed rate is also discussed. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Dou C, Fan J and Gao M (2021) On discontinuous dynamics of a 2-DOF system with bilateral rigid constraints and nonlinear friction, Nonlinear Dynamics, 10.1007/s11071-021-06349-8, 104:2, (1175-1204), Online publication date: 1-Apr-2021. Okolewski A and Blazejczyk-Okolewska B (2021) Hard vs soft impacts in oscillatory systems' modeling revisited, Chaos: An Interdisciplinary Journal of Nonlinear Science, 10.1063/5.0057029, 31:8, (083110), Online publication date: 1-Aug-2021. 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Dai Y, Li H, Yang G and Peng D (2021) A novel method with Newton polynomial-Chebyshev nodes for milling stability prediction, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-020-06090-3, 112:5-6, (1373-1387), Online publication date: 1-Jan-2021. Niu J, Jia J, Wang R, Xu J, Sun Y and Guo D (2021) State dependent regenerative stability and surface location error in peripheral milling of thin-walled parts, International Journal of Mechanical Sciences, 10.1016/j.ijmecsci.2021.106294, 196, (106294), Online publication date: 1-Apr-2021. Dong X, Tu G, Wang X and Chen S (2021) Real-time chatter detection via iterative Vold-Kalman filter and energy entropy, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-021-07509-1, 116:5-6, (2003-2019), Online publication date: 1-Sep-2021. Wang A, Jin W and Lin Q (2020) Effect of the Regenerative and Frictional Force on Chatter in Turning Process Nonlinear Dynamics of Structures, Systems and Devices, 10.1007/978-3-030-34713-0_51, (513-521), . Ikkache K, Chellil A, Lecheb S and Sichaib M (2020) Study of Dynamic Behavior Milling for an Aluminum Alloy Part of Type 6061-T6 Proceedings of the 4th International Symposium on Materials and Sustainable Development, 10.1007/978-3-030-43268-3_8, (86-99), . Zhu W, Zhuang J, Guo B, Teng W and Wu F (2020) An optimized convolutional neural network for chatter detection in the milling of thin-walled parts, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-019-04899-1, 106:9-10, (3881-3895), Online publication date: 1-Feb-2020. Yan Z, Zhang C, Jiang X and Ma B (2020) Comparison of the full-discretization methods for milling stability analysis by using different high-order polynomials to interpolate both state term and delayed term, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-020-05328-4, 108:1-2, (571-588), Online publication date: 1-May-2020. Wu Y, You Y, Liu A, Deng B and Liu W (2019) An implicit exponentially fitted method for chatter stability prediction of milling processes, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-019-04722-x, 106:5-6, (2189-2204), Online publication date: 1-Jan-2020. Wu Y, You Y and Jiang J (2020) New predictor-corrector methods based on piecewise polynomial interpolation for milling stability prediction, Machining Science and Technology, 10.1080/10910344.2020.1752235, 24:5, (688-718), Online publication date: 2-Sep-2020. Cao J, Fan J, Chen S, Dou C and Gao M (2020) On discontinuous dynamics of a SDOF nonlinear friction impact oscillator, International Journal of Non-Linear Mechanics, 10.1016/j.ijnonlinmec.2020.103457, 121, (103457), Online publication date: 1-May-2020. Zheng Z, Jin X, Sun Y, Zhang Z, Sun H and Li Q (2020) Prediction of chatter stability for enhanced productivity in parallel orthogonal turn-milling, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-020-06015-0, 110:9-10, (2377-2388), Online publication date: 1-Oct-2020. Yang W, Huang C, Cai X and You Y (2020) Effective and fast prediction of milling stability using a precise integration-based third-order full-discretization method, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-019-04790-z, 106:9-10, (4477-4498), Online publication date: 1-Feb-2020. Samukham S, Uchida T and Vyasarayani C (2020) Fast Generation of Stability Charts for Time-Delay Systems Using Continuation of Characteristic Roots, Journal of Computational and Nonlinear Dynamics, 10.1115/1.4048362, 15:11, Online publication date: 1-Nov-2020. Yan Z, Zhang C, Jiang X and Ma B (2020) Chatter stability analysis for milling with single-delay and multi-delay using combined high-order full-discretization method, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-020-06147-3, 111:5-6, (1401-1413), Online publication date: 1-Nov-2020. Dou C, Fan J, Li C, Cao J and Gao M (2020) On discontinuous dynamics of a class of friction-influenced oscillators with nonlinear damping under bilateral rigid constraints, Mechanism and Machine Theory, 10.1016/j.mechmachtheory.2019.103750, 147, (103750), Online publication date: 1-May-2020. Fan J, Cao J, Chen S, Dou C and Xue S (2020) Discontinuous dynamic analysis of a class of three degrees of freedom mechanical oscillatory systems with dry friction and one-sided rigid impact, Mechanism and Machine Theory, 10.1016/j.mechmachtheory.2020.103928, 151, (103928), Online publication date: 1-Sep-2020. Zhi H, Zhang T, Du J and Yan X (2020) An efficient full-discretization method for milling stability prediction, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-020-05290-1, 107:11-12, (4955-4967), Online publication date: 1-Apr-2020. Wang D, Löser M, Ihlenfeldt S, Wang X and Liu Z (2019) Milling stability analysis with considering process damping and mode shapes of in-process thin-walled workpiece, International Journal of Mechanical Sciences, 10.1016/j.ijmecsci.2019.06.005, 159, (382-397), Online publication date: 1-Aug-2019. Mei Y, Mo R, Sun H, He B and Wan N (2019) Stability prediction in milling based on linear multistep method, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-019-04379-6, 105:5-6, (2677-2688), Online publication date: 1-Dec-2019. Li C, Fan J, Yang Z and Xue S (2019) On discontinuous dynamical behaviors of a 2-DOF impact oscillator with friction and a periodically forced excitation, Mechanism and Machine Theory, 10.1016/j.mechmachtheory.2019.01.020, 135, (81-108), Online publication date: 1-May-2019. Li H, Dai Y and Fan Z (2018) Improved precise integration method for chatter stability prediction of two-DOF milling system, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-018-2981-y, 101:5-8, (1235-1246), Online publication date: 1-Apr-2019. Kandala S, Uchida T and Vyasarayani C (2019) Pole Placement for Time-Delayed Systems Using Galerkin Approximations, Journal of Dynamic Systems, Measurement, and Control, 10.1115/1.4042465, 141:5, Online publication date: 1-May-2019. Esmailzadeh E, Younesian D and Askari H (2019) Introduction Analytical Methods in Nonlinear Oscillations, 10.1007/978-94-024-1542-1_1, (1-27), . Wu Y, You Y and Jiang J (2019) A stability prediction method research for milling processes based on implicit multistep schemes, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-019-04487-3, 105:7-8, (3271-3288), Online publication date: 1-Dec-2019. Wang X, Han Z and Xu G (2019) Spectral analysis of Timoshenko beam with time delay in interior damping, Zeitschrift für angewandte Mathematik und Physik, 10.1007/s00033-019-1109-z, 70:2, Online publication date: 1-Apr-2019. Chen S, Fan J and Liu T (2019) On discontinuous dynamics of a 2-DOF friction-influenced oscillator with multiple elastic constraints, International Journal of Non-Linear Mechanics, 10.1016/j.ijnonlinmec.2018.12.004, 110, (131-150), Online publication date: 1-Apr-2019. Niu J, Ning G, Shen Y and Yang S (2019) Detection and identification of cutting chatter based on improved variational nonlinear chirp mode decomposition, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-019-04035-z, 104:5-8, (2567-2578), Online publication date: 1-Oct-2019. Shi F, Cao H, Zhang X and Chen X (2018) A chatter mitigation technique in milling based on H∞-ADDPMS and piezoelectric stack actuators, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-018-2913-x, 101:9-12, (2233-2248), Online publication date: 1-Apr-2019. Li Z, Jiang S and Sun Y (2017) Chatter stability and surface location error predictions in milling with mode coupling and process damping, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 10.1177/0954405417708225, 233:3, (686-698), Online publication date: 1-Feb-2019. Fan J, Liu T and Chen S (2019) Analysis of dynamical behaviors of a 2-DOF friction-induced oscillator with one-sided impact on a conveyor belt, Nonlinear Dynamics, 10.1007/s11071-019-05014-5, 97:1, (797-830), Online publication date: 1-Jul-2019. YUE C, GAO H, LIU X, LIANG S and WANG L (2019) A review of chatter vibration research in milling, Chinese Journal of Aeronautics, 10.1016/j.cja.2018.11.007, 32:2, (215-242), Online publication date: 1-Feb-2019. Zakovorotny V, Lapshin V, Gvindjiliya V, Ahn N, Mladenovic V, Petkovic M, Tung P and Tooraj A (2019) The energy efficiency of the process of metal cutting at the expense of the sustainability of the evolutionary trajectory of the cutting, E3S Web of Conferences, 10.1051/e3sconf/201910401017, 104, (01017), . Binder R, Ellermann K and Sehrschön H (2019) Chatter Stability Analysis of Milling Processes, PAMM, 10.1002/pamm.201900134, 19:1, Online publication date: 1-Nov-2019. Natsiavas S (2019) Analytical Modeling of Discrete Mechanical Systems Involving Contact, Impact, and Friction, Applied Mechanics Reviews, 10.1115/1.4044549, 71:5, Online publication date: 1-Sep-2019. Huynh H, Rivière-Lorphèvre E, Ducobu F, Ozcan A and Verlinden O (2018) Dystamill: a framework dedicated to the dynamic simulation of milling operations for stability assessment, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-018-2357-3, 98:5-8, (2109-2126), Online publication date: 1-Sep-2018. Xue S and Fan J (2018) Discontinuous dynamical behaviors in a vibro-impact system with multiple constraints, International Journal of Non-Linear Mechanics, 10.1016/j.ijnonlinmec.2017.10.009, 98, (75-101), Online publication date: 1-Jan-2018. Zhou K, Zhang J, Xu C, Feng P and Wu Z (2018) Effects of helix angle and multi-mode on the milling stability prediction using full-discretization method, Precision Engineering, 10.1016/j.precisioneng.2018.04.016, 54, (39-50), Online publication date: 1-Oct-2018. Dai Y, Li H and Hao B (2018) An improved full-discretization method for chatter stability prediction, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-018-1767-6, 96:9-12, (3503-3510), Online publication date: 1-Jun-2018. Tung P, Ahn N, Gross H, Khaled H, Abbasian Najafabadi T, Nguyen D, Kudish I, Sevostyanov I, Cen Y, Egiazarian K, Mladenovic V, Karapetyan G and Minkin M (2018) The effect of parametric excitation on a dynamic system of cutting process, MATEC Web of Conferences, 10.1051/matecconf/201822602018, 226, (02018), . Wang C, Zhang X, Cao H, Chen X and Xiang J (2017) Milling stability prediction and adaptive chatter suppression considering helix angle and bending, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-017-1389-4, 95:9-12, (3665-3677), Online publication date: 1-Apr-2018. Tung P, Gross H, Khaled H, Abbasian Najafabadi T, Nguyen D, Kudish I, Sevostyanov I, Cen Y, Egiazarian K, Mladenovic V, Karapetyan G and Minkin M (2018) Mathematical modeling and parametric identification of dynamic properties of mechanical subsystems tool and workpiece in turning process, MATEC Web of Conferences, 10.1051/matecconf/201822602017, 226, (02017), . Ye J, Feng P, Xu C, Ma Y and Huang S (2018) A novel approach for chatter online monitoring using coefficient of variation in machining process, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-017-1544-y, 96:1-4, (287-297), Online publication date: 1-Apr-2018. Ji Y, Wang X, Liu Z, Wang H, Jiao L, Zhang L and Huang T (2018) Milling stability prediction with simultaneously considering the multiple factors coupling effects—regenerative effect, mode coupling, and process damping, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-018-2017-7, 97:5-8, (2509-2527), Online publication date: 1-Jul-2018. Simpson D and Kuske R (2016) The influence of localized randomness on regular grazing bifurcations with applications to impacting dynamics, Journal of Vibration and Control, 10.1177/1077546316642054, 24:2, (407-426), Online publication date: 1-Jan-2018. Yu G, Wang L and Wu J (2018) Prediction of chatter considering the effect of axial cutting depth on cutting force coefficients in end milling, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-018-1745-z, 96:9-12, (3345-3354), Online publication date: 1-Jun-2018. Fan J, Liu T and Liu P (2018) Analysis of discontinuous dynamical behavior of a class of friction oscillators with impact, International Journal of Non-Linear Mechanics, 10.1016/j.ijnonlinmec.2018.08.021, 106, (38-54), Online publication date: 1-Nov-2018. Zhang Y and Luo G (2017) Detecting unstable periodic orbits and unstable quasiperiodic orbits in vibro-impact systems, International Journal of Non-Linear Mechanics, 10.1016/j.ijnonlinmec.2017.07.011, 96, (12-21), Online publication date: 1-Nov-2017. Reith M and Stepan G (2017) Effect of non-proportional damping on the dynamics and stability of multi-cutter turning systems, International Journal of Machine Tools and Manufacture, 10.1016/j.ijmachtools.2017.02.006, 117, (23-30), Online publication date: 1-Jun-2017. Gusev V, Fomin A and Sadrtdinov A (2017) Dynamics of Stock Removal in Profile Milling Process by Shaped Tool, Procedia Engineering, 10.1016/j.proeng.2017.10.474, 206, (279-285), . Jalili M, Fazel R and Abootorabi M (2016) Simulation of chatter in plunge grinding process with structural and cutting force nonlinearities, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-016-9561-9, 89:9-12, (2863-2881), Online publication date: 1-Apr-2017. Yan Z, Wang X, Liu Z, Wang D, Jiao L and Ji Y (2017) Third-order updated full-discretization method for milling stability prediction, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-017-0243-z, 92:5-8, (2299-2309), Online publication date: 1-Sep-2017. Zhou K, Feng P, Xu C, Zhang J and Wu Z (2017) High-order full-discretization methods for milling stability prediction by interpolating the delay term of time-delayed differential equations, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-017-0692-4, 93:5-8, (2201-2214), Online publication date: 1-Nov-2017. Guo Q, Sun Y, Jiang Y, Yan Y and Ming P (2016) Determination of the stability lobes with multi-delays considering cutter’s helix angle effect for machining process, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 10.1177/0954405415623480, 231:12, (2059-2071), Online publication date: 1-Oct-2017. Reith M, Bachrathy D and Stepan G (2016) Optimal Detuning of a Parallel Turning System—Theory and Experiments, Journal of Dynamic Systems, Measurement, and Control, 10.1115/1.4034497, 139:1, Online publication date: 1-Jan-2017. (2016) Machining Dynamics Metal Cutting Theory and Practice, Third Edition, 10.1201/b19559-13, (665-750), Online publication date: 24-Mar-2016. Ding Y, Niu J, Zhu L and Ding H (2015) Numerical Integration Method for Stability Analysis of Milling With Variable Spindle Speeds, Journal of Vibration and Acoustics, 10.1115/1.4031617, 138:1, Online publication date: 1-Feb-2016. Niu J, Ding Y, Zhu L and Ding H (2016) Stability Analysis of Milling Processes With Periodic Spindle Speed Variation Via the Variable-Step Numerical Integration Method, Journal of Manufacturing Science and Engineering, 10.1115/1.4033043, 138:11, Online publication date: 1-Nov-2016. Guo Q, Jiang Y, Zhao B and Ming P (2016) Chatter modeling and stability lobes predicting for non-uniform helix tools, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-016-8458-y, 87:1-4, (251-266), Online publication date: 1-Oct-2016. Reith M, Bachrathy D and Stepan G (2016) Improving the stability of multi-cutter turning with detuned dynamics, Machining Science and Technology, 10.1080/10910344.2016.1191029, 20:3, (440-459), Online publication date: 2-Jul-2016. Blum J and Anderegg R (2016) Modelling of an Innovative Technology for Pavement Milling, IFAC-PapersOnLine, 10.1016/j.ifacol.2016.10.665, 49:21, (591-597), . Dombovari Z and Stepan G (2015) On the bistable zone of milling processes, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 373:2051, Online publication date: 28-Sep-2015. Weremczuk A, Rusinek R and Warminski J (2015) The Concept of Active Elimination of Vibrations in Milling Process, Procedia CIRP, 10.1016/j.procir.2015.03.036, 31, (82-87), . Ahsan Z, Sadath A, Uchida T and Vyasarayani C (2015) Galerkin–Arnoldi algorithm for stability analysis of time-periodic delay differential equations, Nonlinear Dynamics, 10.1007/s11071-015-2285-9, 82:4, (1893-1904), Online publication date: 1-Dec-2015. Ahsan Z, Uchida T and Vyasarayani C (2015) Galerkin approximations with embedded boundary conditions for retarded delay differential equations, Mathematical and Computer Modelling of Dynamical Systems, 10.1080/13873954.2015.1043741, 21:6, (560-572), Online publication date: 2-Nov-2015. Koohestani A, Mo J and Yang S (2014) Application of linear regression model on chatter threshold delineation, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 10.1177/0954405414535770, 229:8, (1337-1347), Online publication date: 1-Aug-2015. Long X, Meng D and Chai Y (2015) Effects of spindle speed-dependent dynamic characteristics of ball bearing and multi-modes on the stability of milling processes, Meccanica, 10.1007/s11012-015-0183-3, 50:12, (3119-3132), Online publication date: 1-Dec-2015. Zhou R, Zhang W and Zu J (2014) Analysis on nonlinear dynamics of a thin-plate workpiece in milling process with cutting force nonlinearities, Journal of Mechanical Science and Technology, 10.1007/s12206-014-0608-2, 28:7, (2511-2526), Online publication date: 1-Jul-2014. Vyasarayani C, Subhash S and Kalmár-Nagy T (2014) Spectral approximations for characteristic roots of delay differential equations, International Journal of Dynamics and Control, 10.1007/s40435-014-0060-2, 2:2, (126-132), Online publication date: 1-Jun-2014. Rusinek R, Wiercigroch M and Wahi P (2014) Modelling of frictional chatter in metal cutting, International Journal of Mechanical Sciences, 10.1016/j.ijmecsci.2014.08.020, 89, (167-176), Online publication date: 1-Dec-2014. Urbikain G, López de Lacalle L and Fernández A (2014) Regenerative vibration avoidance due to tool tangential dynamics in interrupted turning operations, Journal of Sound and Vibration, 10.1016/j.jsv.2014.03.028, 333:17, (3996-4006), Online publication date: 1-Aug-2014. Liu X, Lei M, Long X, Li H and Meng G (2014) High-Dimensional Chaotic Dynamics in Cutting Systems with Time-Delay Effects Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty, Modeling, and Analysis (ISUMA), 10.1061/9780784413609.189, 9780784413609, (1888-1897), Online publication date: 27-Jun-2014. Liu X, Vlajic N, Long X, Meng G and Balachandran B (2014) Coupled axial-torsional dynamics in rotary drilling with state-dependent delay: stability and control, Nonlinear Dynamics, 10.1007/s11071-014-1567-y, 78:3, (1891-1906), Online publication date: 1-Nov-2014. Liu X, Vlajic N, Long X, Meng G and Balachandran B (2014) Multiple regenerative effects in cutting process and nonlinear oscillations, International Journal of Dynamics and Control, 10.1007/s40435-014-0078-5, 2:1, (86-101), Online publication date: 1-Mar-2014. Niu J, Ding Y, Zhu L and Ding H (2013) Runge–Kutta methods for a semi-analytical prediction of milling stability, Nonlinear Dynamics, 10.1007/s11071-013-1127-x, 76:1, (289-304), Online publication date: 1-Apr-2014. Rusinek R, Wiercigroch M and Wahi P (2014) Influence of Tool Flank Forces on Complex Dynamics of Cutting Process, International Journal of Bifurcation and Chaos, 10.1142/S0218127414501156, 24:09, (1450115), Online publication date: 1-Sep-2014. Ji C, Liu Z and Ai X (2014) Effect of cutter geometric configuration on aerodynamic noise generation in face milling cutters, Applied Acoustics, 10.1016/j.apacoust.2013.07.004, 75, (43-51), Online publication date: 1-Jan-2014. Koohestani A, Mo J and Yang S (2014) STABILITY PREDICTION OF TITANIUM MILLING WITH DATA DRIVEN RECONSTRUCTION OF PHASE-SPACE, Machining Science and Technology, 10.1080/10910344.2014.863638, 18:1, (78-98), Online publication date: 2-Jan-2014. Aggarwal S and Xirouchakis P (2012) Selection of optimal cutting conditions for pocket milling using genetic algorithm, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-012-4472-x, 66:9-12, (1943-1958), Online publication date: 1-Jun-2013. Zhang W, Zhou R and Zu J (2013) Nonlinear vibrations of a shell-shaped workpiece during high-speed milling process, Nonlinear Dynamics, 10.1007/s11071-013-0752-8, 72:4, (767-787), Online publication date: 1-Jun-2013. (2013) Time-Frequency Control of Milling Instability and Chatter at High Speed Control of Cutting Vibration and Machining Instability, 10.1002/9781118402795.ch8, (165-176) Liu X, Vlajic N, Long X, Meng G and Balachandran B (2012) Nonlinear motions of a flexible rotor with a drill bit: stick-slip and delay effects, Nonlinear Dynamics, 10.1007/s11071-012-0690-x, 72:1-2, (61-77), Online publication date: 1-Apr-2013. Rubio L, De la Sen M, Longstaff A and Fletcher S (2013) Model-based expert system to automatically adapt milling forces in Pareto optimal multi-objective working points, Expert Systems with Applications, 10.1016/j.eswa.2012.10.034, 40:6, (2312-2322), Online publication date: 1-May-2013. Liang X, Yao Z, Luo L and Hu J (2013) An improved numerical integration method for predicting milling stability with varying time delay, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-013-4813-4, 68:9-12, (1967-1976), Online publication date: 1-Oct-2013. Petrie A and Zhao X (2012) Estimating eigenvalues of dynamical systems from time series with applications to predicting cardiac alternans, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 468:2147, (3649-3666), Online publication date: 8-Nov-2012. Vyasarayani C (2012) Galerkin Approximations for Higher Order Delay Differential Equations, Journal of Computational and Nonlinear Dynamics, 10.1115/1.4005931, 7:3, Online publication date: 1-Jul-2012. Zhang X, Xiong C, Ding Y, Feng M and Lun Xiong Y (2012) Milling stability analysis with simultaneously considering the structural mode coupling effect and regenerative effect, International Journal of Machine Tools and Manufacture, 10.1016/j.ijmachtools.2011.10.004, 53:1, (127-140), Online publication date: 1-Feb-2012. Kurmann L, Anderegg R, Wiedmer S and Ruschkamp H (2012) Control of weak and strong nonlinear dynamics in a novel milling cutting process 2012 IEEE International Conference on Mechatronics and Automation (ICMA), 10.1109/ICMA.2012.6282861, 978-1-4673-1278-3, (316-320) Khasawneh F, Bobrenkov O, Mann B and Butcher E (2012) Investigation of Period-Doubling Islands in Milling With Simultaneously Engaged Helical Flutes, Journal of Vibration and Acoustics, 10.1115/1.4005022, 134:2, Online publication date: 1-Apr-2012. Deshmukh V (2011) Solutions of Delayed Partial Differential Equations With Space-Time Varying Coefficients, Journal of Computational and Nonlinear Dynamics, 10.1115/1.4005081, 7:2, Online publication date: 1-Apr-2012. Turner D (2011) Process Damping Parameters, IOP Conference Series: Materials Science and Engineering, 10.1088/1757-899X/26/1/012008, 26, (012008), Online publication date: 8-Dec-2011. Banihasan M and Bakhtiari-Nejad F (2011) Chaotic vibrations in high-speed milling, Nonlinear Dynamics, 10.1007/s11071-010-9935-8, 66:4, (557-574), Online publication date: 1-Dec-2011. Ding Y, Zhu L, Zhang X and Ding H (2011) Numerical Integration Method for Prediction of Milling Stability, Journal of Manufacturing Science and Engineering, 10.1115/1.4004136, 133:3, Online publication date: 1-Jun-2011. Bachrathy D, Stépán G and Turi J (2011) State Dependent Regenerative Effect in Milling Processes, Journal of Computational and Nonlinear Dynamics, 10.1115/1.4003624, 6:4, Online publication date: 1-Oct-2011. Deshmukh V (2011) Parametric Estimation for Delayed Nonlinear Time-Varying Dynamical Systems, Journal of Computational and Nonlinear Dynamics, 10.1115/1.4003626, 6:4, Online publication date: 1-Oct-2011. Song Q, Ai X and Tang W (2011) Prediction of simultaneous dynamic stability limit of time–variable parameters system in thin-walled workpiece high-speed milling processes, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-010-3139-8, 55:9-12, (883-889), Online publication date: 1-Aug-2011. Ding Y, Zhu L, Zhang X and Ding H (2011) On a Numerical Method for Simultaneous Prediction of Stability and Surface Location Error in Low Radial Immersion Milling, Journal of Dynamic Systems, Measurement, and Control, 10.1115/1.4003374, 133:2, Online publication date: 1-Mar-2011. Peng Z, Jackson M, Guo L, Parkin R and Meng G (2010) Effects of bearing clearance on the chatter stability of milling process, Nonlinear Analysis: Real World Applications, 10.1016/j.nonrwa.2010.01.005, 11:5, (3577-3589), Online publication date: 1-Oct-2010. Xinhua Long and Balachandran B (2017) Stability of Up-milling and Down-milling Operations with Variable Spindle Speed, Journal of Vibration and Control, 10.1177/1077546309341131, 16:7-8, (1151-1168), Online publication date: 1-Jun-2010. Zhang X, Xiong C and Ding Y (2010) Improved Full-Discretization Method for Milling Chatter Stability Prediction with Multiple Delays Intelligent Robotics and Applications, 10.1007/978-3-642-16587-0_50, (541-552), . Gilsinn D (2009) Bifurcations, Center Manifolds, and Periodic Solutions Delay Differential Equations, 10.1007/978-0-387-85595-0_6, (1-48), . Sims N Dynamics Diagnostics: Methods, Equipment and Analysis Tools Machining Dynamics, 10.1007/978-1-84628-368-0_4, (85-115) Butcher E and Mann B (2009) Stability Analysis and Control of Linear Periodic Delayed Systems Using Chebyshev and Temporal Finite Element Methods Delay Differential Equations, 10.1007/978-0-387-85595-0_4, (93-129), . Yuan L and Järvenpää V (2009) Nonlinear vibrations in a covered roll system with viscoelastic contact, Communications in Nonlinear Science and Numerical Simulation, 10.1016/j.cnsns.2008.10.028, 14:7, (3170-3178), Online publication date: 1-Jul-2009. Gilsinn D (2009) On algorithms for estimating computable error bounds for approximate periodic solutions of an autonomous delay differential equation, Communications in Nonlinear Science and Numerical Simulation, 10.1016/j.cnsns.2008.02.006, 14:4, (1526-1550), Online publication date: 1-Apr-2009. Svoboda A, Tatar K, Norman P and Bäckström M (2008) Integrated approach for prediction of stability limits for machining with large volumes of material removal, International Journal of Production Research, 10.1080/00207540601100924, 46:12, (3207-3222), Online publication date: 15-Jun-2008. SHAW S and BALACHANDRAN B (2008) A Review of Nonlinear Dynamics of Mechanical Systems in Year 2008, Journal of System Design and Dynamics, 10.1299/jsdd.2.611, 2:3, (611-640), . Patel B, Mann B and Young K (2008) Uncharted islands of chatter instability in milling, International Journal of Machine Tools and Manufacture, 10.1016/j.ijmachtools.2007.06.009, 48:1, (124-134), Online publication date: 1-Jan-2008. Long X, Lin G and Balachandran B (2008) Grazing bifurcations in an elastic structure excited by harmonic impactor motions, Physica D: Nonlinear Phenomena, 10.1016/j.physd.2007.12.001, 237:8, (1129-1138), Online publication date: 1-Jun-2008. Wahi P and Chatterjee A (2008) Self-interrupted regenerative metal cutting in turning, International Journal of Non-Linear Mechanics, 10.1016/j.ijnonlinmec.2007.10.010, 43:2, (111-123), Online publication date: 1-Mar-2008. Long X and Balachandran B (2007) Stability analysis for milling process, Nonlinear Dynamics, 10.1007/s11071-006-9127-8, 49:3, (349-359), Online publication date: 22-Jun-2007. Faassen R, van de Wouw N, Nijmeijer H and Oosterling J (2006) An Improved Tool Path Model Including Periodic Delay for Chatter Prediction in Milling, Journal of Computational and Nonlinear Dynamics, 10.1115/1.2447465, 2:2, (167-179), Online publication date: 1-Apr-2007. Geng Z, Ridgway K and Turner S (2007) Linear improvement of the machining stability lobes and application in milling process prediction, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 10.1243/09544054JEM529, 221:3, (369-378), Online publication date: 1-Mar-2007. Olgac N and Sipahi R (2016) Dynamics and Stability of Variable-pitch Milling, Journal of Vibration and Control, 10.1177/1077546307078754, 13:7, (1031-1043), Online publication date: 1-Jul-2007. Mann B and Young K (2006) An empirical approach for delayed oscillator stability and parametric identification, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 462:2071, (2145-2160), Online publication date: 8-Jul-2006. Szalai R and Stépán G (2003) Lobes and Lenses in the Stability Chart of Interrupted Turning, Journal of Computational and Nonlinear Dynamics, 10.1115/1.2198216, 1:3, (205-211), Online publication date: 1-Jul-2006. Long X, Balachandran B and Mann B (2006) Dynamics of milling processes with variable time delays, Nonlinear Dynamics, 10.1007/s11071-006-9058-4, 47:1-3, (49-63), Online publication date: 29-Dec-2006. Gilsinn D and Potra F Integral Operators and Delay Differential Equations, Journal of Integral Equations and Applications, 10.1216/jiea/1181075393, 18:3 Balachandran B and Gilsinn D (2005) Non-linear oscillations of milling, Mathematical and Computer Modelling of Dynamical Systems, 10.1080/13873950500076479, 11:3, (273-290), Online publication date: 1-Sep-2005. Stepan G, Szalai R, Mann B, Bayly P, Insperger T, Gradisek J and Govekar E (2004) Nonlinear Dynamics of High-Speed Milling—Analyses, Numerics, and Experiments, Journal of Vibration and Acoustics, 10.1115/1.1891818, 127:2, (197-203), Online publication date: 1-Apr-2005. Mann B, Garg N, Young K and Helvey A (2005) Milling Bifurcations from Structural Asymmetry and Nonlinear Regeneration, Nonlinear Dynamics, 10.1007/s11071-005-5719-y, 42:4, (319-337), Online publication date: 1-Dec-2005. STÉPÁN G, INSPERGER T and SZALAI R (2011) DELAY, PARAMETRIC EXCITATION, AND THE NONLINEAR DYNAMICS OF CUTTING PROCESSES, International Journal of Bifurcation and Chaos, 10.1142/S0218127405013642, 15:09, (2783-2798), Online publication date: 1-Sep-2005. Mann B, Young K, Schmitz T and Dilley D (2004) Simultaneous Stability and Surface Location Error Predictions in Milling, Journal of Manufacturing Science and Engineering, 10.1115/1.1948394, 127:3, (446-453), Online publication date: 1-Aug-2005. Szalai R, Stépán G and Hogan S (2004) Global dynamics of low immersion high-speed milling, Chaos: An Interdisciplinary Journal of Nonlinear Science, 10.1063/1.1807395, 14:4, (1069-1077), Online publication date: 1-Dec-2004. Schmitz T, Burns T, Ziegert J, Dutterer B and Winfough W (2006) Tool Length-Dependent Stability Surfaces, Machining Science and Technology, 10.1081/MST-200038989, 8:3, (377-397), Online publication date: 30-Dec-2005. Insperger T, Stépán G, Bayly P and Mann B (2003) Multiple chatter frequencies in milling processes, Journal of Sound and Vibration, 10.1016/S0022-460X(02)01131-8, 262:2, (333-345), Online publication date: 1-Apr-2003. Insperger T, Mann B, Stépán G and Bayly P (2003) Stability of up-milling and down-milling, part 1: alternative analytical methods, International Journal of Machine Tools and Manufacture, 10.1016/S0890-6955(02)00159-1, 43:1, (25-34), Online publication date: 1-Jan-2003. Insperger T and Stépán G (2002) Stability chart for the delayed Mathieu equation, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 458:2024, (1989-1998), Online publication date: 8-Aug-2002. Insperger T and Stépán G (2002) Semi-discretization method for delayed systems, International Journal for Numerical Methods in Engineering, 10.1002/nme.505, 55:5, (503-518), Online publication date: 20-Oct-2002. Zakovorotny V, Gubanova A and Khristoforova V (2015) Bifurcations of stationary manifolds formed in the neighborhood of equilibrium in the dynamic cutting system, Вестник Донского государственного технического университета, 10.12737/10369, 15:1, (11-22) Xia Y, Wan Y, Luo X, Liu Z and Song Q (2021) An improved numerical integration method to predict the milling stability based on the Lagrange interpolation scheme, The International Journal of Advanced Manufacturing Technology, 10.1007/s00170-021-07311-z Fomin A (2017) Determining Undeformed Chip Thickness Models in Milling and its Verification during Wood Processing, Solid State Phenomena, 10.4028/www.scientific.net/SSP.265.598, 265, (598-605) Fomin A, Gusev V and Sattarova Z (2018) Geometrical Errors of Surfaces Milled with Convex and Concave Profile Tools, Solid State Phenomena, 10.4028/www.scientific.net/SSP.284.281, 284, (281-288) Lapshin V and Turkin I (2021) Vibration dynamics and cutting process temperature at various stages of forming the wear of the cutting wedge, IOP Conference Series: Materials Science and Engineering, 10.1088/1757-899X/1029/1/012031, 1029, (012031) This Issue15 April 2001Volume 359Issue 1781Theme Issue ‘Nonlinear dynamics in metal cutting’ compiled by M. Wiercigroch Article InformationDOI:https://doi.org/10.1098/rsta.2000.0755Published by:Royal SocietyPrint ISSN:1364-503XOnline ISSN:1471-2962History: Published online15/04/2001Published in print15/04/2001 License: Citations and impact KeywordsRegenerative EffectMilling ProcessStabilityBifurcationsLoss–Of–Contact EffectChatter