Nonlinear dynamics of regenerative cutting processes: comparison of two models

Understanding the nonlinear dynamics of cutting processes is very important for improving the quality of machining technology. We study machine cutting processes by two different models, one is recently introduced by Litak (2002), the other is the classic delay differential equation model. Well known routes to chaos, such as period-doubling or quasi-periodic motion to chaos are not observed in either model. Chaotic solutions from both models are carefully analyzed, and it is found that the chaotic motion from the Litak's model resembles more like a periodic motion, has a smaller correlation dimension and a smaller value for the largest positive Lyapunov exponent. Implications to the control of chaos in cutting processes are discussed.