A chaotic cutting process and determining optimal cutting parameter values using neural networks

A model of an orthogonal cutting system is described as an elastic structure deformable in two directions. In the system, a cutting force is generated by material flow against the tool. Nonlinear dependency of the cutting force on the cutting velocity can cause chaotic vibrations of the cutting tool which influence the quality of a manufactured surface. The intensity and the characteristics of vibrations are determined by the values of the cutting parameters. The influence of cutting depth on system dynamics is described by bifurcation diagrams. The properties of oscillations are illustrated by the time dependence of tool displacement, the corresponding frequency spectra and phase portraits. The corresponding strange attractors are characterized by correlation dimension. The vibrations are characterized by the maximum Lyapunov exponent. The manufactured surface at the first cut is taken as the incoming surface in the second cut, thus incorporating the influence of the rough surface in the model. Again, bifurcation diagrams, the correlation dimension and the maximum Lyapunov exponent are employed to describe the effects of parametrical excitation on the cutting dynamics. A cost function is defined which describes the dependence of the cutting performance on cutting depth. The cost function is empirically modeled using a self-organizing neural network. A conditional average estimator is applied to determine the optimal value of the cutting depth applicable as a control variable of the cutting process. Copyright (C) 1996.