Study on the Fractal and Chaotic Prediction Model and Dynamics Characteristics of Friction Force During Running-in

Abstract In order to establish the prediction model and reveal the dynamic characteristics of friction force in friction systems, the fractal and chaotic prediction model using Monte Carlo simulation method were established and the chaotic parameters are introduced. First, considering the interactions of various wear mechanism, the vectors of the coulomb friction force, microconvex deformation friction force, adhesive friction force, and plowing force were superposed to obtain the friction force and the state equation of the fractal dimension was introduced. The running-in tests and Monte Carlo simulation method were used to obtain the friction force prediction model with fractal and chaotic characteristic. The results showed that the friction signals obtained from the proposed prediction model and the experiment had similar amplitudes and trend, demonstrating the model's reliability. The phase trajectories and chaotic characteristics were the same for the predicted and the experimental signals, they exhibited divergence, convergence, and stability, reflecting the chaotic characteristics of the system. The proposed fractal and chaotic prediction models using the Monte Carlo methods of the friction force not can provide new theoretical methods for predicting the running-in process of other friction pairs with the system parameters identification, but can reflect the chaos dynamic characteristics.