Then, the chaoticity of the system were investigated using time series, phase portraits, Lyapunov exponents and bifurcation diagrams and the initial shear force intervals that the system exhibits chaos behavior were determined.
📌 3 Key Takeaways
🎯
Objective & Hypothesis:Vibrations that occur between the workpiece and the cutting tool during machining processes that are frequently used in the manufacturing sector, may pose serious problems in applications.
📊
Key Findings & Data:These vibrations have a negative impact on the process in terms of quality, cost and efficiency.
💡
Conclusion & Impact:Then, the chaoticity of the system were investigated using time series, phase portraits, Lyapunov exponents and bifurcation diagrams and the initial shear force intervals that the system exhibits chaos behavior were determined.
Vibrations that occur between the workpiece and the cutting tool during machining processes that are frequently used in the manufacturing sector, may pose serious problems in applications. These vibrations have a negative impact on the process in terms of quality, cost and efficiency. In this study, firstly the differential equations of these vibrations cited from the literature and are called as self-excited oscillations, have been reduced to the first order equations. Then, the chaoticity of the system were investigated using time series, phase portraits, Lyapunov exponents and bifurcation diagrams and the initial shear force intervals that the system exhibits chaos behavior were determined.
NASER, Y. H. E., KARAYEL, D., KUTLU, M. Ç. (2020). Investigation of Chaoticity of Vibrations in Machining. Journal of Smart Systems Research, Cilt: 1 - Sayı: 1, 18–24. https://ajindex.com/articles/854062
Warminski J,Litak G, Cartmell MP, Khanin R, Wiercigroch M. Approximate analytical solutions for primary chatter in the non-linear metal cutting model. J Sound Vib2003
259(4):917–933. [2]Wiercigroch M, Cheng AHD. Chaotic and stochastic dynamics of orthogonal metalcutting. Chaos Soliton Fract 1997
8(4):715–726. [3]Kuljanic E, Totis G, Sortino M. Vibrations and chatter in machining: state of art and new approaches. AMST’08 Advanced Manufacturing Systems and Technology 2008
CISM-Udine. [4]Karayel D, Özkan SS, Aksoy S. Manyetik yatak kullanılarak freze tezgahlarında aktif titreşim kontrolü. 4. Uluslararası Mekatronik Tasarım ve Modelleme Çalışma Toplantısı 1999
ODTÜ-Ankara. [5]Karayel D, Özkan SS, Kandilli İ. The active vibration control of the high speed machine tool spindle using the electromagnetic damper. 1. International Conference on Information Technology in Mechatronics 2001
Boğaziçi University-İstanbul. [6]Faassen RPH, Van de Wouw N, Oosterling JAJ, Nijmeijer H. Prediction of regenerative chatter by modelling and analysis of high-speed milling. Int J Mach Tools Manuf 2003
43(14):1437–1446. [7]Litak G, Syta A, Wiercigroch M. Identification of chaos in a cutting process by the 0-1 test. Chaos Soliton Fract2009
40(5):2095–2101. [8]Gradišek J, Govekar E, Grabec I. Chatter onset in non-regenerative cutting: A numerical study. J Sound Vib2001
242(5):829–838. [9]Litak G. Chaotic vibrations in a regenerative cutting process, Chaos Soliton Fract2002
13(7):1531–1535. [10]Litak G, Sen AK, Syta A. Intermittent and chaotic vibrations in a regenerative cutting process. Chaos Soliton Fract 2009
41(4):2115–2122. [11]Gradišek J, Govekar E, Grabec I. A chaotic cutting process and determining optimal cutting parameter values using neural networks. Int J Mach Tools Manuf 1996
36(10):1161–1172. [12]Wiercigroch M. Chaotic Vibration of a Simple Model of the Machine Tool-Cutting Process System. J Vib Acous 1997
119(3):468-475. [13]Wiercigroch M, Krivtsov AM. Frictional chatter in orthogonal metal cutting. Philos Trans R Soc A Math Phys Eng Sci2001
359(1781):713–738. [14]Cordes M, Hintze W, Altıntaş Y. Chatter stability in robotic milling. Robot Cim-Int Manuf 2019
Rusinek R, Wiercigroch M, Wahi P. Modelling of frictional chatter in metal cutting. Int J Mech Sci 2014
Njitacke Z, Fozin T, Kengne L K, Leutcho G, Kengne E M, Kengne J. Multistability and its Annihilation in the Chua’s Oscillator with Piecewise-Linear Nonlineari