Attractor reconstruction of self-excited mechanical systems

This paper deals with a method of delay coordinates applied for signals obtained from nonlinear mechanical systems with self-excitation. Both experimentally and numerically received signals are analysed. Experimental time series of cutting force come from a turning process which is performed for several different rotational speeds. Since, in a cutting process chaotic behaviour is also possible therefore Lyapunov exponents are calculated by application of two algorithms. Numerical signals are obtained from a nonlinear system with dry friction. Poincaré maps and phase spaces are reconstructed by means of the method of delay coordinates. It is shown that efficiency of the method depends on kind of vibrations which are reconstructed.