Numerical computation and nonlinear dynamic analysis of ultrasonic cutting system

摘要

The dynamic behavior of an ultrasonic cutting system is analyzed using a two-degree-of freedom Duffing oscillator model. The governing equations of the system are derived using a Lagrangian formulation and are solved in dimensionless time using the differential transformation method (DTM). The analyses focus specifically on the effects of the nonlinear cubic stiffness coefficient ratio of the Duffing model on the dynamics of the system given known values of the excitation frequency,and driving force. The dynamic behavior of the system is evaluated by means of system phase portraits, power spectra, Poincare maps, bifurcation diagrams, and the maximum Lyapunov exponent. It is shown that the system exhibits a complex dynamic behavior consisting of quasi-periodic, periodic and chaotic motions under different operating conditions. In general, the results provide a useful basis for the further analysis and design of ultrasonic cutting systems. (C) 2015 Elsevier Ltd. All rights reserved.