Decomposition of a tribological system by chaos theory on rough surfaces

The purpose of this paper is to analyze the turning machinability of a martensitic steel, according to the cutting speed, and through signal analyses of the morphology of the machined surface. We initially carried out the classification of a large number of parameters of roughness, on the basis of their relevance with regard to cutting speed. The originality of the proposed method lies in the combination of the classical technique of analysis of variance with the statistical technique of resampling of data, called Bootstrap. Another characteristic of the study consists in the addition to the traditional categories of roughness parameters (Amplitude, Frequency, Morphological and Hybrid parameters) to analyze multiscale aspect of surface topography through fractal analysis. According to the analysis carried out, the fractal dimension and the slope of the signal (dz/dx) of the topographical signal of the studied surface appear much more relevant than all the other Euclidian parameters. The fractal dimension and the slope of profile allow us to estimate a critical transition speed between the cutting states by generalized strain hardening and those by localized strain hardening. This parameter is also more relevant than the others, because it allows a good analysis of the influence of cutting speed, within each of the two machining modes. The obtained result is relevant because it provides a practical and inexpensive method for the quality control of the machined surface, to manufacturers and engineering companies, without removing some mechanical part, but only through a direct analysis of the slopes of the profile, with, in particular, the help of a portable instrument. We establish later that the transition between disorder and order of the aspect of the observed profiles is essentially due to an instability, which we analyze by the chaos theory. For that purpose, we propose an original construction of an attractor that presents a fixed point for low cutting speeds. This attractor characterizes, beyond the critical cutting speed, an instability described by a phenomenon of successions of states on the attractor between work hardening by localized shear plastic deformation and softening due to the rise in temperature