Several pairs of algorithms were used to determine the phase space reconstruction parameters to analyze the dynamic characteristics of chaotic time series. The reconstructed phase trajectories were compared with the original phase trajectories of the Lorenz attractor, Rössler attractor, and Chen's attractor to obtain the optimum method for determining the phase space reconstruction parameters with high precision and efficiency. The research results show that the false nearest neighbor method and the complex autocorrelation method provided the best results. The saturated embedding dimension method based on the saturated correlation dimension method is proposed to calculate the time delay. Different time delays are obtained by changing the embedding dimension parameters of the complex autocorrelation method. The optimum time delay occurs at the point where the time delay is stable. The validity of the method is verified by combing the application of the correlation dimension, showing that the proposed method is suitable for the effective determination of the phase space reconstruction parameters.

To investigate the influence of surface roughnesses on the dynamic characteristics of AISI 5120 steel in sliding friction process, a suite of running-in experiments are performed on a pin-on-disk tribometer. The running-in attractor is used to analyze the high-dimensional features of a friction system under different surface roughnesses. The experimental results show that the roughnesses of different original surfaces evolve to the same value in stable wear stage. The pin-on-disk friction system has a chaotic nature and exists a running-in attractor. The original surface of a disk of Ra = 0.953 μm is the most conducive to shorten the running-in duration, reduce the friction coefficient value, and improve the stability of the friction system. This roughness value is termed as the optimum surface roughness. It is an ideal working surface for the friction pair in the running-in design.

In this study, the coefficient of friction (COF) signals throughout the running-in process were examined by sliding a ring against a static disc. By reconstructing the scalar time-series into multi-dimensional phase spaces, friction-induced attractors were obtained and quantified by recursive characteristics analysis, which can effectively realize the running-in status identification. Moreover, a recursive characteristics analysis-based evaluation model was established to investigate the stationarity of the friction-induced attractors based on the recurrence quantification analysis (RQA) measures. The analyses of the numerically simulated signals and experimental results indicate that the extracted model is an intuitive and effective method. Furthermore, to improve the stationary of the friction-induced attractors, the normal pressure should be low, whereas the relative sliding velocities should be increased appropriately. These results would contribute to the revelation of the recursive characteristics of the tribosystem and the improvement of the stationarity of friction-induced attractors.