Investigation of Chaoticity of Vibrations in Machining

Yıl 2020, Cilt: 1 Sayı: 1, 18 - 24, 31.12.2020

Yusuf Hamida El Naser Durmuş Karayel Mustafa Çağrı Kutlu

Öz

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.

Anahtar Kelimeler

Metal cutting, chaos, self-excited oscillations, bifurcation, stability analysis

Kaynakça

• [1]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; 15-36: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;11-23: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;453-458: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;55:11-18.
• [15]Rusinek R, Wiercigroch M, Wahi P. Modelling of frictional chatter in metal cutting. Int J Mech Sci 2014;89:167-176.
• [16]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 Nonlinearity.Chaos Theory and Applications,2(2), 77-89.
• [17]Guanrong C. Chaos theory and applications: a new trend.Chaos Theory and Applications,3(1), 1-2.
• [18]Pehlivan İ, Kurt E, Lai Q, Basaran A, Kutlu M C (2019). A multiscroll chaotic attractor and its electronic circuit implementation.Chaos Theory and Applications,1(1), 29-37.
• [19]Cimen M E, Garip Z B, Pala M A, Boz A F, Akgul A. (2019). Modelling of a Chaotic System Motion in Video with Artiıficial Neural Networks.Chaos Theory and Applications,1(1), 38-50.