Study on the boundedness, stability and dynamic characteristics of friction system based on fractal and chaotic theory

Friction signals under different working conditions are obtained, the phase trajectories and the recurrence plots are constructed to identify the wear states in the Friction System (FS). The phase trajectory moves in limited space without exceeding the critical range, the recurrence plots represent different wear states, the boundedness, stability and dynamics are studied using the chaotic parameters of correlation dimension D, recurrence degree RR and the proposed saturation radius rs. The rs has the evolution law of "decrease-stability- increase" variation while D and RR have the opposite law. Therefore, it is significant to describe the complex friction behavior through chaotic representation methods, constantly explore the boundedness, stability and dynamic characteristics to realize the state identification, the wear prediction and quantitative design control.