Analysis of milling stability based on cutting force signal processing

國立臺灣科技大學 機械工程系 碩士學位論文 學號：M10403802 以切削力訊號分析銑削加工穩定性 Analysis of Milling Stability Based on Cutting Force Signal Processing (Draft) 研究生：Tran Minh Quang 指導教授：Chun-Hui Chung, Meng-Kun Liu 中華民國 一零六 年 六月 三十日 摘要 銑削加工是一種非常常見的成型加工方法，而在銑削加工的過程中，不 適當的加工參數會使刀具產生顫震，其顫震原因來自於刀刃與工件之間呈現週 期性的不連續切削行為，造成切屑厚度週期性的變化，使得刀具產生自激性的 震動以及不穩定的切削行為，而顫震會使銑削加工的不穩定性以及降低切削效 率，造成尺寸精度、刀具壽命以及表面完整性的下降，因此本研究主要目標為 建立完整之刀具壽命下，開發端銑刀的動態切削力模組，對於銑削加工潛在的 顫震進行探討。以模組的方式模擬出之切削立，與實際切削所獲得之切削力進 行時間及頻率域比較，我們發現時域、頻率域、短時距傅立葉變換、連率小波 轉換以及希爾伯特-黃轉換進行顫震訊號分析，相較於使用傅立葉變換光譜法 所獲得之結果是徹底地不同，傅立葉變換光譜法在應用於大量的非線性訊號效 率極低，進行動態切削力模組模擬之訊號與實驗所獲得之切削力訊號比較，發 現顫震頻率主要由兩個現象之頻率所構成，為刀刃通過工件時之頻率以及顫震 造成的不穩定高頻，此外，以 standard deviation 以及本質模態函數方式所獲 得之能量比，可有效率的辦別出刀具顫震，最後通過工件表面形貌、表面粗糙 度和穩定性波瓣圖驗證其分析結果。 關鍵字：銑削加工、刀具顫震、時頻分析、小波分析、希爾伯特-黃轉換 i Abstract The milling operation is the most common form of machining Because the action of each cutting edge and workpiece is intermittent and periodical, the chip thickness varies periodically This could lead to self-excited vibrations and unstable cutting which is called chatter vibration Chatter causes machining instability and reduces productivity in the metal cutting process It has negative effects on the surface finish, dimensional accuracy, tool life and machine life Chatter identification is therefore necessary to control, prevent, or eliminate chatter and to identify the stable machining condition A dynamic cutting force model of the end-milling process with tool runout error was established in this research to understand the underlying mechanism of chatter The accuracy of the cutting force model in both time and frequency domains was evaluated by comparing to experimental force signals Timefrequency analysis approaches, specifically short time Fourier transform, continuous wavelet transform and Hilbert-Huang transform, were utilized to give an utterly different perspective of chatter from the conventional Fourier spectrum which is insufficient in analyzing the signals of rich nonlinear characteristics By comparing the simulation with experimental result, chatter frequency was found to consist of two major components, frequency modulation alongside tooth passing frequency caused by the increased tool runout error and the non-stationary high frequency from the regenerative vibration Moreover, dimensionless chatter indicators, defined by the standard deviation and energy ratio of the specific intrinsic mode function, could identify the occurrence of chatter effectively The analysis result was then validated by the workpiece surface topography, surface roughness and the stability lobe diagram Keywords: Milling process, Chatter detection, Time-frequency analysis, Wavelet transform, Hilbert Huang transform ii Acknowledgement I would like to thank all the people who helped me to finish this thesis First of all, I would like to express my deep gratitude to my academic advisors: Professor Chun-Hui Chung and Professor Meng-Kun Liu for their valuable guidance, encouragement, and support throughout my work towards this thesis Without their help and guidance, this work would not be possible I also would like to thank Mr Yi-Wen Qui who provided his experimental data which was used to verify my methodology in this thesis I would like to thank all of my labmates who have supported me a lot with laboratory facilities so that I could conduct my experiments I thank my friends who always give me encouragements and supports during my research Finally, I would like to thank my parents who always give me love, encouragement, and support throughout my life I would specially thank my wife and my son for their patience and support during my study I am very grateful for their love iii Nomenclature radial and tangential edge db discretized axial depth of cut (mm) Kne , Kte dFn differential radial cutting force (N) Nt number of flutes r edge radius (mm) dFt dFx dFy differential tangential cutting force (N) differential cutting force in x-direction x, y (N) coefficients (N/mm) displacement in x and y directions (mm) differential cutting force in y direction (N) z absolute value of the distance from the end (mm) ft feed per tooth (mm/flute)  helix angle (deg) Fs sampling rate frequency (Hz)  immersion angle (deg) Fsi simulated cutting force (N) e exit angle (deg) Fex experimental cutting force (N) s start angle (deg) b axial depth of cut (mm) c chatter frequency (rad/s) h instantaneous chip thickness (mm)  spindle speed (rpm) Ks specific cutting force coefficient (N)  position angle (deg)  cutting force angle (deg)  runout of cutting edge (mm)  time for one rotation (sec) K n , Kt radial and tangential cutting coefficients (N/mm2) iv Contents 摘要 i Abstract ii Acknowledgement iii Nomenclature iv Contents v Chapter Introduction 1.1 Background 1.2 Objective and Scope 1.3 Outlines and Contribution of the Chapters Chapter Literature Review 2.1 Chatter Vibrations in Milling 2.2 Signal Analysis Approaches Chapter 10 Dynamic Cutting Force Model 10 3.1 Regenerative Chatter Model 10 3.2 Dynamic Cutting Force Model 15 Chapter 17 Experimental Setup and Model Verification 17 4.1 Overview and Aim 17 4.2 Experimental Setup 17 v 4.2.1 Machine, Cutter and Workpiece 17 4.2.2 Cutting Force Measurement Equipment 19 4.2.3 Surface Topography Measurement Equipment 20 4.2.4 Surface Roughness Measurement Equipment 20 4.3 Cutting Force Coefficients 21 4 Experimental Design Parameters 25 4.5 Tool Tip Dynamics 27 4.5.1 Impact Testing 27 4.5.2 Modal Analysis 27 4.5.3 Stability Lobe Diagram 31 4.6 Simulation and Experimental Results 33 Chapter 36 Chatter Detection Methodology 36 5.1 Short-Time Fourier Transform Analysis 36 5.2 Continuous Wavelet Transform Analysis 38 5.3 Time-Frequency Analysis Based on HHT 41 5.3.1 Chatter Detection Methodology 41 5.3.2 Results and Discussions 44 5.3.3 Dimensionless Indexes for Chatter Identification 50 5.3.4 Method Verification 51 5.4 Chatter Identification in Small Size of End Mill 54 5.4.1 Overview and Aim 54 5.4.2 Experimental Setup 54 5.4.3 Chatter Identification by Time-Frequency Analysis 57 vi Chapter 60 Conclusions and Future Works 60 6.1 Conclusions 60 6.2 Future Works 60 Bibliography 61 vii List of Figures Figure 2.1 Milling regenerative chatter Figure 2.2 Stability lobe diagram Figure 2.3 Time-frequency resolution of STFT [9] Figure 3.1 The model of helical end mill geometry 10 Figure 3.2 Dynamic cutting force model 11 Figure 3.3 Flow chart of dynamic cutting force 16 Figure 4.1 The three- axis CNC milling machine at NTUST 18 Figure 4.2 A carbide end mill 18 Figure 4.3 Kistler Dynamometer 19 Figure 4.4 Experimental setup 19 Figure 4.5 Olympus BX51 at NUTST 20 Figure 4.6 A Mitutoyo portable surface roughness tester 21 Figure 4.7 The modeling of slot milling 21 Figure 4.8 Measured cutting forced signal at feed rate of 0.03 mm/tooth in (a) x direction and (b) y direction 23 Figure 4.9 Relationship between feet per tooth and mean force 25 Figure 4.10 Setup of the impact testing 27 Figure 4.11 Relative frequency response in x direction 28 Figure 4.12 Relative frequency response in y direction 29 Figure 4.13 Direct FRF in x direction 31 Figure 4.14 Direct FRF in y direction 32 Figure 4.15 Stability lobe diagram and experimental design parameters 33 viii 5.3.3 Dimensionless Indexes for Chatter Identification Although chatter could be observed from the analysis tools such as Fourier transform, continuous wavelet transform, and instantaneous frequency, it is still necessary to identify chatter quantitatively for practical applications The standard deviation and energy ratio of the specific IMF are suggested as dimensionless chatter indicators that can be calculated by using Eqs (5-9) and (5-10) respectively In the unstable cutting condition, chatter causes a rapid increase in standard deviation and energy ratio values in IMF2 These values could therefore be used as the dimensionless indicators to identify chatter The presence of chatter could be clearly indicated in Table 5-2 and Table 5-3 when the spindle speeds are at 3000, 3750, 4500, and 5250rpm with the DOC of 1.4 and 1.6mm Unstable cutting conditions were also found at spindle speed of 5250rpm with the DOC of 1.0 and 1.2mm The thresholds of standard deviation and energy ratio of IMF2 were and 0.05, respectively The cutting would be unstable if the indicator value is larger than the threshold On the other hand, the stable cutting is still maintained Table 5-2 The energy ratio values of IMF2s  Depth of cut (mm) (rpm) 0.4 0.6 0.8 1.0 1200 9.9 x10-5 8.5 x10-5 7.2 x10-5 3.4 x10-5 6.9 x10-5 7.2 x10-5 2.8 x10-5 1500 2.8x10-4 8.2x10-5 3.6x10-4 1.5x10-4 3.2x10-4 2.1x10-4 2.8x10-4 2250 2.3x10-4 9.1x10-4 3.2x10-4 1.1x10-4 1.3x10-4 1.2x10-4 7.0x10-4 3000 3.6x10-4 7.8x10-4 5.8x10-4 7.3x10-4 1.8x10-4 0.051 0.13 3750 5.2x10-4 1.8x10-4 3.7x10-4 8.6x10-5 4.2x10-4 0.054 0.19 4500 3.9x10-4 6.1x10-4 1.4x10-3 9.5x10-4 5.5x10-4 0.2 0.3 5250 3.15x10-5 3.78x10-5 2.82x10-5 0.17 0.09 0.13 0.21 Bold: unstable cutting 50 1.2 1.4 1.6 Table 5-3 The standard deviation values of IMF2s  (rpm) Depth of cut (mm) 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1200 0.14 0.19 0.23 0.19 0.33 0.36 0.31 1500 0.2 0.15 0.41 0.35 0.45 0.51 0.8 2250 0.17 0.42 0.32 0.2 0.3 0.28 0.91 3000 0.16 0.31 0.34 0.46 0.27 4.52 5.15 3750 0.2 0.14 0.23 0.43 0.36 6.5 7.23 4500 0.15 0.23 0.4 0.41 0.37 11.22 12.7 5250 0.12 0.10 0.11 4.28 3.07 4.15 6.35 Bold: unstable cutting 5.3.4 Method Verification The decisions made by chatter indicators showed good agreement with the stability lobe diagram in most experiments except the cases at the stability margin, as indicated in Fig 5.14 The difference was possibly because of the linearization procedure conducted when deriving the stability lobe diagram which would inevitably misinterpret the stability of the cutting process The proposed indicators hence provided a reliable alternative to determine chatter The surface topography images of the machined surface in Fig 5.15 were utilized to validate the result from the indicators as well The irregular wavy surfaces are manifested in Fig 5.15 (d), (e) and (f), which represent the occurrence of chatter On the contrary, the surface topography images in Fig 5.15 (a), (b) and (c) illustrate very consistent cutting marks which indicate the stable cutting conditions All these results are in good accord with that obtained from the signal processing Evidently, the proposed approach could detect chatter accurately and effectively 51 Figure 5.14 Stability lobe diagram and the stability determined by proposed method Figure 5.15 Microscopic of the surface machined with different spindle speed and constant depth of cut of 1.4 m 52 Table 5-4 Surface roughness measured along the feed direction at different cutting conditions DOC (mm) Spindle speed (rpm) Average surface roughness (μm) 1.4 1200 1500 2250 3000 3750 4500 1.698 1.216 0.307 0.591 0.649 0.638 The surface roughness under different milling conditions was measured along the feed direction and provided in Table 5-4 to show the evidence of chatter along with surface topography images It can be seen that the surface roughness (Ra) decreases with the increase of the spindle speed from 1200 to 2250 rpm under stable cutting conditions On the other hand, at the spindle speed of 3000, 3700 and 4500 rpm, the surface roughness does not decrease continuously but suddenly increase The increase of surface roughness values in those cases is resulted by the irregular wavy surfaces manifested in Fig 5.15 (d, e, f) in which the clear evidence of chatter was showed 53 5.4 Chatter Identification in Small Size of End Mill 5.4.1 Overview and Aim In this section, the method for chatter detection proposed in the previous section is applied to detect chatter in slender end mill Because of small tool diameter, the stiffness of tool is reduced This makes the cutter weak and causes deflection and instability easily during cutting process When the diameter of cutter is down to or mm, it is become difficult to conduct impact testing which is demanded to create the stability lobe diagram A method for chatter detection based on cutting force signal plays an important role in determining the rage of stable cutting conditions This chapter introduces the machines and equipment used to conduct the experiments when mm diameter of end mill was utilized The cutting force signals obtained from different cutting conditions are processing by using proposed method 5.4.2 Experimental Setup Machining experiments were performed in a five-axis CNC milling machine shown in Fig 5.16 The machine features are provided in Table 5-5 The workpiece was a block of Al6061-T6 with size of 30x40x30mm Figure 5.17 represents an uncoated carbide end mill cutter used in following experiments Its diameter is mm, with helix angle of 30° and two flutes The cutting tool parameters in detail are shown in Table 5-6 As the same to previous part, the cutting force signals were also measured directly by using a Kistler dynamometer (type 9129AA) The dynamometer was mounted between the workpiece and workbench Figures 5.18 shows the whole experimental setup 54 Figure 5.16 Five-axis CNC milling machine Table 5-5 Machine’s features Mini 5–Axis-CNC Machine size 75x70x172 cm Max Speed 24000 RPM Max Power 750 W Table diameter φ130 mm Axis travel X 200 mm Y 150 mm Z 180 mm B (+)110 ~ (-)30° C 360° 55 Figure 5.17 A carbide end mill Table 5-6 Parameters of Tool Tool company Tool diameter Flutes (mm) YCHI Cutting edge length (mm) 2 Figure 5.18 Experimental setup 56 In order to examine the dynamic cutting force model and to investigate the proposed methodology for chatter identification, a series of end milling experiments were conducted The cutting force signals in the feed direction were measured from the cutting experiments conducted with different sets of cutting parameters shown in Table 5-7, in which the feed rate was a constant value of 250 mm/min The DOCs ranged from 0.1 to 0.8 mm, while the spindle speeds ranged from 15000 to 22500 rpm The topographical images of the machined surface from cutting experiments were obtained by using the optical microscope (Olympus BX51) with CCD sensor Table 5-7 Experimental design parameters Spindle peed (rpm) Feed rate of 250 mm/min Depth of cut (mm) 0.1 0.3 0.5 0.8 15000 A1 A2 A3 A4 18000 B1 B2 B3 B4 22500 C1 C2 C3 C4 5.4.3 Chatter Identification by Time-Frequency Analysis The cutting forces in x direction which were obtained from experiments are extracted into a set of IMFs by using EEMD The Hilbert Transform was then applied on each IMF to determine the instantaneous frequency that represents both of time and frequency domain The standard deviation and energy ratio values that proposed in the previous section are utilized to identify the chatter during the milling processes Table 5-8 and 5-9 show all the values of standard deviation and energy ratio corresponding to the cutting condition shown in Table 5-7 It can be seen that all of the standard deviation and energy ratio values are larger than the thresholds that proposed in the previous section except the cutting condition at a spindle speed of 15000 rpm, 0.1 mm depth of cut Therefore, those cutting conditions lead to chatter during machining 57 Table 5-8 The standard deviation values of IMF2s Depth of cut (mm) Feed rate of 250 mm/min Spindle speed (rpm) 0.1 0.3 0.5 0.8 15000 0.486 1.066 2.0241 1.3872 18000 1.1817 1.4034 1.9941 1.5650 22500 1.9699 2.6514 2.6074 3.9132 Table 5-9 The energy ratio values of IMF2s Depth of cut (mm) Feed rate of 250 mm/min Spindle speed (rpm) 0.1 0.3 0.5 0.8 15000 0.2399 0.1823 0.0726 0.0545 18000 0.4624 0.2130 0.1199 0.0490 22500 0.3850 0.2905 0.1259 0.1315 The surface topography images of the machined surface in Fig 5.19 were utilized to validate the result from the indicators in Table 5-8 and 5-9 as well The irregular wavy surfaces are manifested in all experiments except the cutting condition (A1) reveal the occurrence of chatter at those cutting conditions With the condition of spindle speed of 15000 rpm and 0.1 mm depth of cut, on the other hand, the marks left by cutter present quite consistent which indicate the stable cutting conditions All these results are in good accord with the signal processing results Evidently, even though in the small size of end mill, the proposed approach could identify chatter accurately and effectively 58 Spindle speed (rpm) 15000 18000 0.1 Depth of cut (mm) 0.3 0.5 0.8 Figure 5.19 Machined surface topography 59 22500 Chapter Conclusions and Future Works 6.1 Conclusions Chatter detection plays an important role in improving productivity by providing a range of stable cutting conditions A dynamic cutting force model of the end-milling process has been presented in this paper to understand the underlying mechanism of chatter The stability of the milling process was investigated based on time-frequency analysis approaches, and STFT, WT and HHT were utilized in this study The results indicated that both of WT and HHT approaches are more suitable to identify chatter Chatter was then interpreted from a distinct perspective which defines chatter frequency as the combination of two major components, frequency modulation alongside tooth passing frequency caused by the increased tool runout error and the non-stationary high frequency from the regenerative vibration In addition, the standard deviation and energy ratio of the specific IMF of cutting force signals were proposed as chatter indicators which increase observably as chatter occurs, while their values were close to zero in stable cutting conditions The proposed method was validated by comparing its results to the stability lobe diagram and the machined surface topography along with surface roughness As a result, the approach presented in this study showed the potential to identify chatter effectively 6.2 Future Works For future works, the elastic deformation of the workpiece and cutter in the cutting zone can consider developing the cutting force model The tool wear effected by machining instability will be investigated as well Time-frequency analysis can be utilized for tool condition monitoring such as tool wear monitoring 60 Bibliography [1] D A Stephenson, J S Agapiou, 2006 Metal cutting Theory and Practice, CRC Press Taylor & Francis Group [2] Schmitz, L., Smith, S., 2008 Machining Dynamics: Frequency Response to Improved Productivity Springer Science & Business Media [3] Altintas, Yusuf, 2012 Manufacturing automation: Metal cutting mechanics, machine tool vibrations, and CNC design Cambridge university press [4] Lacerda, H., Lima, V., 2004 “Evaluation of Cutting Forces and Prediction of Chatter Vibrations in Milling”, Journal of the Brazilian Society of Mechanical Sciences and Engineering 26 (1), pp 74-81 [5] Abele, E., Fiedler, U., 2004 “Creating Stability Lobe Diagrams during Milling”, CIRP Annals - Manufacturing Technology 53, pp 309-312 [6] Wei, C., Liu, K., Huang, H., 2016 “Chatter Identification of Face Milling Operation via Time-Frequency and Fourier Analysis”, International Journal of Automation and Smart Technology (1), pp 25-36 [7] Feng, J., Sun, Z., Jiang, Z., Yang, L., 2015 “Identification of chatter in milling of Ti-6Al4V titanium alloy thin-walled workpieces based on cutting force signals and surface topography”, International Journal of Advanced Manufacturing Technology 82, pp 19091920 [8] Kundan Singh, Ramesh Singh, Kartik, V., 2015 “Comparative Study of Chatter Detection Methods for High-Speed Micromilling of Ti6Al4V”, Procedia Manufacturing 1, pp 593–606 [9] Zhu, K., Wong, S., Hong S., 2009 “Wavelet analysis of sensor signals for tool condition monitoring: A review and some new results”, International Journal of Machine Tools & Manufacture 49, pp 537–553 [10] Huang, N., et al., 1998 “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis”, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, Vol 454, pp 903-995 61 [11] Martellotti M E., 1941 “An Analysis of the Milling Process”, Transactions of the ASME 63, pp 677-700 [12] Kline, A., Devor, E., Lindberg R., 1982 “The Prediction of Cutting Forces in End Milling with Application to Cornering Cuts”, International Journal of Machine Tool Design and Research, 22 (1), pp 7-22 [13] Tsai, C., 2007 “Analysis and prediction of cutting forces in end milling by means of a geometrical model”, International Journal of Advanced Manufacturing Technology 31, pp 888–896 [14] Altintas, Y., Engin, S., 2001 “Generalized Modeling of Mechanics and Dynamics of Milling Cutters”, CIRP Annals - Manufacturing Technology 50 (1), pp 25-30 [15] Kline, W., Devor, R., 1983 “The effect of runout on cutting geometry and forces in end milling”, International Journal of Machine Tool Design and Research 23 (2/3) pp 123-140 [16] Cifuentesa, E., Garcíab, H., Villasora, M., Idoipec, A., 2010 “Dynamic analysis of runout correction in milling”, International Journal of Machine Tools and Manufacture 50 (8) pp 709–717 [17] Tobias, A., Fishwick, W., 1958 “Theory of regenerative machine tool chatter”, The Engineer 205 (7), pp 199-203 [18] Altintas, Y., Budak, E., 1995 “Analytical prediction of stability lobes in milling”, CIRP Annals - Manufacturing Technology 44 (1) pp 357-362 [19] Tlusty, J., Polacek, M., 1963 “The stability of machine tools against self-excited vibrations in machining”, Proceedings of the International Research in Production Engineering Conference, Pittsburgh, PA, ASME, New York, pp 454-465 [20] Dimla, D., Lister, P., 2000 “On-line metal cutting tool condition monitoring: force and vibration analyses”, International Journal of Machine Tools & Manufacture 40, pp 739–768 [21] Oppenheim, V., Willsky, S., Nawab, N., Nawab, H., 1996 Signals and Systems 2nd edn Prentice-Hall, Englewood Cliffs, NJ [22] Elbestawi, A., Papazafiriou, A., Du, X., 1991 “In-process monitoring of tool wear in milling using cutting force signature”, International Journal of Machine Tools and Manufacture 31, pp 55-73 62 [23] Huang, P., Li, J., Sun, J., Zhou, J., 2013 “Vibration analysis in milling titanium alloy based on signal processing of cutting force”, International Journal of Advanced Manufacturing Technology 64, pp 613-621 [25] Berger, S., Harlay, J., Rokni, M., Papadopoulos, M., 1988 “Wavelet based cutting state identification”, Journal of Sound and Vibration 213(5), pp 813–827 [26] Kunpeng, Z., San, Y., Soon, G., 2009 “Wavelet analysis of sensor signals for tool condition monitoring: A review and some new results”, International Journal of Machine Tools and Manufacture 49, pp 537-553 [27] Khraisheh, K., Pezeshki, C., Bayoumi, E., 1995 “Time series based analysis for primary chatter in metal cutting”, Journal of Sound and Vibration 180(1), pp 67-87 [28] Tangjitsitcharoen, S., Saksri, T., Ratanakuakangwan, S., 2015 “Advance in chatter detection in ball end milling process by utilizing wavelet transform”, Journal of Intelligent Manufacturing 26, pp 485-499 [29] Peng, C., Wang, L., Liao, W., 2015 “A new method for the prediction of chatter stability lobes based on dynamic cutting force simulation model and support vector machine”, Journal of Sound and Vibration 354, pp 118-131 [30] Yoon, C., Chin, H., 2005 “Cutting force monitoring in the end milling operation for chatter detection”, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, Vol 219 (6), pp 455-465 [31] Yan, R., Gao, X., 2006 “Hilbert–Huang Transform-Based Vibration Signal Analysis for Machine Health Monitoring”, IEEE Transactions on Instrumentation and Measurement, 55 (6), pp 2320-2329 [32] Huang, N., Samuel, S., 2005 Hilbert-Huang transform and its applications, Vol World Scientific, Hackensack, NJ [33] Peng, W., Hu, Z., Yuan, L., Zhu, P., 2013 “Chatter identification using HHT for boring process”, Proceedings of SPIE - The International Society for Optical Engineering [34] Cao, H., Lei, Y., He, Z., 2013 “Chatter identification in end milling process using wavelet packets and Hilbert–Huang transform”, International Journal of Machine Tools and Manufacture 69, pp 11-19 63 [35] Cao, H., Zhou, K., Chen, X., 2015 “Chatter identification in end milling process based on EEMD and nonlinear dimensionless indicators”, International Journal of Machine Tools and Manufacture 92, pp 52-59 [36] Michel Misiti Yves Misiti Georges Oppenheim Jean-Michel Poggi, 2002 Wavelet Toolbox 64 ... time-frequency analysis of nonlinear and non-stationary signals due to performing a time adaptive decomposition operation on signals and no uncertainty principle limitation on time or frequency resolution... because of the variation of chip thickness [2] There are two kinds of vibration: (1) forced vibrations caused by the periodic cutting forces acting on the machine structure and (2) chatter vibration... machining vibration This method is a powerful tool for time-frequency analysis of nonlinear and non-stationary signals due to a time adaptive decomposition operation on the signals It is moreover