在金屬加工過程中，切削通常伴隨著刀具和工件之間的劇烈相對運動，一旦刀具開始產生振動，在切割過程中會成週期性擺動並在工件表面留下再生波狀起伏。因此不僅系統的瞬時振動會影響切割過程，而且前一切割所留下的波動量也會起作用，這導致更複雜的現象稱為再生顫振，再生顫振除了會導致加工表面不佳之外，還會造成刀具破損、縮短機台壽命、噪音等。若能建立一套加工顫振分析與抑制之策略，即可改善加工表面，延長機台壽命進而提升加工效率。本研究首先透過文獻探討了解導致顫振的成因，以運動方程式推導解析工具機刀具與加工件之動態行為模式，利用聲訊感測器量測因切削條件造成之再生顫振現象，並使用Daubechies小波進行訊號分析，利用所分析出的小波訊號算出能量Shannon比，依據能量Shannon比找出再生顫振指標。針對因切削條件所產生之再生顫振，本研究使用正弦主軸轉速變化法修改加工時主軸轉速，避開導致再生性顫振之加工參數，從而改善切削表面品質。本研究並以實際切削五軸加工單葉片工件驗證，證實本研究所提出之改善方式可有效抑制再生顫振現象。

The cutting processes usually cause vibration from the tool and the workpiece. Once the tool begins to vibrate, it will left wavy cuts on the surface of the workpiece. Therefore, not only the instantaneous vibration of the system but also the amount of fluctuation left by the previous cutting affects the cutting process. It calls regenerative chatter. If there is a strategy for regenerative chatter suppression, the workpiece topography and the processing efficiency can be improved.
This study explores the causes of regenerative chatter through literature, and uses the equations of motion to derive the dynamic behavior patterns of tool and workpieces. In order to know when the regenerative chatter occur, we use audio sensor to get the sound of the cutting processes and uses Daubechies wavelet to analyze the signal. The energy-to-Shannon Entropy ratio is calculated by using the wavelet signal, and we can use it to get the chattering index. To suppress regenerative chatter, this study uses the sinusoidal spindle speed variation to change the spindle speed during the cutting processes. This can avoid the processing parameters that cause regenerative chatter, and let surface finish has better quality.

1. S.A. Tobias, “Vibration of machine tools.”, Production Engineer, Vol. 43, pp. 599-608 (1964)
2. S.A. Tobias, W. Fishwick, “The chatter of lathe tools under orthogonal cutting conditions.”, Transactions of ASME, Vol. 80, pp. 1079-1088 (1958)
3. F.W. Taylor, “On the art of cutting metals.”, Transactions of ASME, Vol. 28, pp. 31-248 (1907)
4. P.S. Paul, A.S. Varadarajan, X.A. Vasanth, “Effect of magnetic field on damping ability of magnetorheological damper during hard turning.”, Archives of Civil and Mechanical Engineering, Vol. 14, pp. 433-443 (2014)
5. M. Siddhpura, A. Siddhpura, R. Paurobally, “Chatter stability prediction for a flexible tool-workpiece system in a turning process.” , The International Journal of Advanced Manufacturing Technology, Vol. 92, pp. 1–16 ( 2017)
6. Y. Li, S. Zhou, J. Lin, X. Wang, “Regenerative chatter identification in grinding using instantaneous nonlinearity indicator of servomotor current signal.”, The International Journal of Advanced Manufacturing Technology, Vol. 89, pp. 779–790 (2017)
7. R.P.H. Faassen, “Chatter prediction and control for high-speed milling: modelling and experiments.”, Technische Universiteit Eindhoven, Thesis (2007)
8. H.M. Chen, K.C. Fan, T.H. Kuo, C.H. Wang, “Development of a low cost in-process chatter suppression system in milling process.”, Journal of the Chinese Society of Mechanical Engineers, Vol. 33, pp. 419-426 (2012)
9. C. Lauro, L. Brandão, D. Baldo, R. Reis, J. Davim, “Monitoring and processing signal applied in machining processes - a review.”, Measurement, Vol. 58, pp. 73-86 (2014)
10. D. Pérez-Canales, L. Vela-Martínez, J. Carlos Jáuregui-Correa, J. Alvarez-Ramirez,“Analysis of the entropy randomness index for machining chatter detection.”, International Journal of Machine Tools and Manufacture, Vol. 62, pp. 39-45 (2012)
11. H.R. Cao, Y.G. Lei, Z.G. He, “Chatter identification in end milling process using wavelet packets and Hilbert-Huang transform.”, International Journal of Machine Tools and Manufacture, Vol. 69, pp. 11-19 (2013)
12. C. Tyler, T. Schmitz, “Analytical process damping stability prediction.”, Journal of Manufacturing Processes, Vol. 15, pp. 69-76 (2013)
13. P. Huang, J. Li, J. Sun, J. Zhou, “Vibration analysis in milling titanium alloy based on signal processing of cutting force.”, The International Journal of Advanced Manufacturing Technology, Vol. 64, pp. 613-621 (2013)
14. S. Tangjitsitcharoen, T. Saksri, S. Ratanakuakangwan, “Advance in chatter detection in ball end milling process by utilizing wavelet transform.”, Journal of Intelligent Manufacturing, Vol. 26, pp. 485-499 (2015)
15. M. Lamraoui, M. Thomas, M. El Badaoui, F. Girardin, “Indicators for monitoring chatter in milling based on instantaneous angular speeds.”, J Mechanical Systems and Signal Processing, Vol. 44, pp. 72-85 (2014)
16. K.M. Hynynen, J. Ratava, T. Lindh, M. Rikkonen, V. Ryynänen, M. Lohtander, J. Varis, “Chatter detection in turning processes using coherence of acceleration and audio signals.”, Journal of Manufacturing Science and Engineering, Vol. 136, pp. 1-4 (2014)
17. U. Nair, B.M. Krishna, V. Namboothiri, V. Nampoori, “Permutation entropy based real-time chatter detection using audio signal in turning process.”, The International Journal of Advanced Manufacturing Technology, Vol. 46, pp. 61-68 (2010)
18. T. Thaler, P. Potočnik, I. Bric, E. Govekar, “Chatter detection in band sawing based on discriminant analysis of sound features.”, Applied Acoustics, Vol. 77, pp. 114-121 (2014)
19. Y. Shao, X. Deng, Y. Yuan, C.K. Mechefske, Z. Chen, “Characteristic recognition of chatter mark vibration in a rolling mill based on the non-dimensional parameters of the vibration signal.”, Journal of Mechanical Science and Technology, Vol. 28, pp. 2075–2080 (2014)
20. E. Kondo, H. Ota, T. Kawai, “A new method to detect regenerative chatter using spectral analysis. part 1. basic study on criteria for detection of chatter.”, Journal of Manufacturing Science and Engineering, Vol. 119, pp. 461-466 (1997)
21. J. Barros, R.I. Diego, M. Apráiz, “Applications of wavelets in electric power quality: voltage events.”, Electric Power Systems Research, Vol. 88, pp. 130-136 (2012)
22. J. Upendar, C. P.Gupta, G.K. Singh, “Statistical decision-tree based fault classification scheme for protection of power transmission lines.”, International Journal of Electrical Power & Energy Systems, Vol. 36, pp. 1-12 (2012)
23. P. Pillay, A. Bhattacharjee, “Application of wavelets to model short-term power system disturbances.”, IEEE Transactions on Power Systems, Vol. 11, pp. 2031-2037 (1996)
24. S.G. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation.”, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol.11, pp. 674 - 693 (1989)
25. O. González-Brambilaa, E. Rubioa, J.C. Jáureguia, G. Herrera-Ruiz, “Chattering detection in cylindrical grinding processes using the wavelet transform.”, International Journal of Machine Tools and Manufacture, Vol. 46, pp. 1934-1938 (2006)
26. K. Dragomiretskiy, D. Zosso, “Variational mode decomposition.”, IEEE Transactions on Signal Processing, Vol. 62, pp. 531 - 544 (2014)
27. J.P. Amezquita-Sanchez, H. Adeli i, “Signal processing techniques for vibration-based health monitoring of smart structures.”, Archives of Computational Methods in Engineering, Vol. 23, pp. 1-15 (2016)
28. H. Cao, K. Zhou, X. Chen, “Chatter identification in end milling process based on EEMD and nonlinear dimensionless indicators.”, International Journal of Machine Tools and Manufacture, Vol. 92, pp. 52-59 (2015)
29. L. Vela-Martinez, J. Carlos Jauregui-Correa, E. Rodriguez, J. Alvarez-Ramirez, “Using detrended fluctuation analysis to monitor chattering in cutter tool machines.”, International Journal of Machine Tools and Manufacture, Vol. 50, pp. 651-657 (2010)
30. L. Angrisani, P. Daponte, M. D'Apuzzo, A. Testa, “A measurement method based on the wavelet transform for power quality analysis”, IEEE Transactions on Power Delivery, Vol. 13, pp. 990 - 998 (1998)
31. Y.H. Peng, X.G. Xu ,H.X. Zhao, “Application of wavelet packet analysis in turbine fault diagnosis.”, 2006 International Conference on Machine Learning and Cybernetics, pp. 13-16 (2006)
32. H. Cao, Y. Lei, Z. He ,” Chatter identification in end milling process using wavelet packets and Hilbert–Huang transform.”, International Journal of Machine Tools and Manufacture, Vol. 69, pp. 11-19 (2013)
33. C. Peng, L Wang, T.W. Liao ,” 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, Vol. 354, pp. 118-131 (2015)
34. R. Yan, R.X.Gao, X. Chen ,” Wavelets for fault diagnosis of rotary machines: A review with applications.”, Signal Processing, Vol. 96, pp. 1-15 (2014)
35. T. Takemura, T. Kitamura, T. Hoshi, “Active suppression of chatter by programmed variation of spindle speed.”, Annals of CIRP, Vol. 23, pp. 121-122 (1974)
36. E. Al-Regib, J. Ni, S. Lee, “Programming spindle speed variation for machine tool chatter suppression.”, International Journal of Machine Tools and Manufacture, Vol. 43, pp. 1229-1240 (2003)
37. S. Seguy, T. Insperger, L. Arnaud, G. Dessein, G. Peigné, “Suppression of period doubling chatter in high-speed milling by spindle speed variation.”, Machining Science and Technology, Vol. 15, pp. 153-171 (2011)
38. J. Niu, Y. Ding, L.M. Zhu, H. Ding, “Stability analysis of milling processes with periodic spindle speed variation via the variable-step numerical integration method.”, Journal of Manufacturing Science and Engineering, Vol. 138, pp. 107-118 (2016)
39. H. Meng, Y. Kang, Z. Chen, Y. Zhao, G. Liu, “Stability analysis and stabilization of a class of cutting systems with chatter suppression.”, IEEE/ASME Trans. Mechatronics, Vol. 20, pp. 991-996 (2015)
40. G. Urbikain, D. Olvera, L.N.L. de Lacalle, A. Elías-Zúńiga, “Spindle speed variation technique in turning operations: modeling and real implementation.”, Journal of Sound and Vibration, Vol. 383, pp. 384-396 (2016)
41. Y. Ding, J. Niu, L. Zhu, H. Ding, “Numerical integration method for stability analysis of milling with variable spindle speeds.”, Journal of Vibration and Acoustics, Vol. 138, pp. 1-11 (2015)
42. Y. Altintas, M.Weck, “Chatter stability of metal cutting and grinding.”, CIRP Annals Vol. 53, pp. 619 – 642 (2004)
43. T. H. Le and L. Caracoglia, “Wavelet-galerkin analysis to study the coupled dynamic response of a tall building against transient wind loads.”, Engineering Structures, Vol. 100, pp.763-778, (2015)
44. Y. Fu, Y. Zhang, H. Zhou, D. Li, H. Liu, H. Qiao, X. Wang, “Timely online chatter detection in end milling process.”, Mechanical Systems and Signal Processing, Vol. 75, pp.668-688 (2016)
45. Q. Yang, J. Wang, “Multi-level wavelet shannon entropy-based method for single-sensor fault location.”, Entropy, Vol. 17, pp. 01-17 (2015)
46. H. Heidari Bafroui, A. Ohadi, “Application of wavelet energy and Shannon entropy for feature extraction in gearbox fault detection under varying speed conditions.”, Neurocomputing, Vol. 133, pp. 437-445 (2014)
47. R. Yan, R.X. Gao, X. Chen, “Wavelets for fault diagnosis of rotary machines: a review with applications.”, Signal Process, Vol. 96, pp. 1-15 (2014)
48. X. Zhang, N. Feng, Y. Wang, Y. Shen, “Acoustic emission detection of rail defect based on wavelet transform and Shannon entropy.”, Journal of Sound and Vibration, Vol. 17 pp. 419-432 (2015)
49. U. Yigit, E. Cigeroglu, E. Budak, “Chatter reduction in boring process by using piezoelectric shunt damping with experimental verification.”, Mechanical Systems and Signal Processing, Vol. 94, pp. 312-321 (2017)