Characteristic parameter extraction of running-in attractors based on phase trajectory and grey relation analysis

Abstract

The coefficient of friction signals were extracted throughout the friction process, and the morphology of phase trajectory reconstructed from the obtained scalar time series was analysed. Experimental results show that the morphology of the phase trajectory follows the evolution rule of “convergence–stabilization–divergence”. To characterize the convergence degree of the phase trajectory, a brand new parameter named “grey phase density $$d_{\mathrm{G}}$$ ” was defined using the grey relation analysis. It was found that $$d_{\mathrm{G}}$$ shows significant advantages with regard to the robustness against noise and the friction state identification, suggesting that the convergence degree of the phase trajectory can describe the change in friction states. Hence, the results indicate that grey phase density $$ d_{\mathrm{G}}$$ is amenable for characterizing the friction process.