Characterization And Prediction Modeling Of Running-In Attractors

Owing to strong system dependence and time-varying characteristics of the tribological system,the study of friction and wear is different from other studies in terms of difficulty and complexity.Additionally,it has been proved that the established running-in prediction models based on classical friction laws and/or contact theories associated with the various wear mechanisms cannot objectively reflect the real situation of complex running-in friction process.It is of great scientific significance and application prospect to carry out the research on the running-in process prediction and further running-in design starting from the principle of nonlinear system theory.Running-in attractor,a spontaneous ordered spatial-temporal structure formed during the running-in process,has been proved to be an effective tool to characterize the nonlinear nature of tribological behaviors.The running-in friction process was considered as a black box system,and a prediction model has been established based on the relationship between the characteristic parameters of running-in attractors and the control running-in parameters.The research results can be used to quantitatively characterize the friction and wear process,and it is expected to provide theoretical guidance for the design of running-in parameters.The major conclusions and innovations of this project are summarized as follow:When using the running-in attractors to characterize the tribological behaviors,the commonly employed procedure is to reconstruct the measured discrete time-series into an appropriate high-dimensional phase space using the time delay technique.The determination of embedding parameters?embedding dimension and time delay?plays a significant role in the characterization of running-in attractors.The common methods of embedding parameters selection have been compared using both theoretical chaotic attractors and measured friction signals based on phase space reconstruction.The results showed that the methods of mutual information?MI?and false nearest neighbors?FNN?show significant advantages in the determination of the time delay and embedding dimension.Further results indicate that the system characteristics of the reconstructed high-dimensional phase space changes little when the embedding parameters fluctuate within a small range.Additionally,to investigate the evolution laws of the tribological behaviors throughout the whole friction process,the discrete time-series was usually divided into a several non-overlapping segments using sliding window method.Therefore,this project proposed a brand new embedding parameters selection method based on statistical method,namely using the method of MI and FNN to determine the embedding parameters for each calculating window,then select the parameters with the most frequency to reconstruct the high-dimensional phase space.Ring-on-disc specimens were used as the tribopairs in the friction experiments,and four friction experiments were carried out under different normal loads and speeding velocities.The coefficient of friction?COF?signal was then calculated via the collected friction torque signal,and the EMD method was adapted to realize the denoising of the COF signal.The methods of phase trajectory,Recurrence Plots?RPs?and Multivariate Graphic Analysis were adapted to investigate the nonlinear dynamics of the reonstructed running-in attractors,whilst the characteristic parameters were computed to the realize the quantitative description.The evolution laws of running-in attractors obtained by different methods are basically consistent.During the running-in process,the phase trajectory converges gradually from the non-equilibrium state toward a balanced state with stable shape and volume,and the running-in attractor is formed when the running-in process ends.The macroscopic patterns RPs of the system depict an evolution of“disrupted-drifted-homogenous”patterns,and the multivariate graphic centrobaric trajectory?MGCT?also show a tendency of converge to a small attractor.In the steady process,both phase trajectory and the MGCT of the running-in attractors maintain relatively stable volume and/or shape,while the homogenous-patterned RPs can be found in this period.In the rapid friction process,the phase trajectory and the MGCT show the tendency of divergence and RPs appears as disrupted pattern.The RQA measures,the feature parameter K_V based on the boundedness,and the grey phase density follow the same evolution laws of“initial decrease-midterm stabilization-final increase”,which is consistent with the“bathtub curve”.The chaotic parameters evolve consistently when characterize the same COF signal.The evolution of phase trajectory,macroscopic patterns of RPs and the MGCT,along with the evolution laws of the characteristic parameters,indicate that the running-in attractors can be used for friction state identification.In particular,the feature parameter K_V and the grey phase density d_G were proposed innovator in this project.The feature parameter K_V was used to describe the boundedness and the volume of the attractors,while the parameter d_G characterize the degree of the convergence of the attractors.The nonlinear multifractal behavior of the COF signal was studied using the method of Multifractal Detrended Fluctuation Analysis,and the distinguishing of the multifractality was explored based on the corresponding randomly shuffled time-series.It indicated that both multifractal spectrum and eigenvalues can be used as effective indicators for the friction state identification.The evolution of multifractal spectrum width is consistent with the“bathtub curve”.The generalized Hurst exponent of the shuffled series is smaller than the origin series but not equals to 0.5,indicating that the multifractality can be ascribed to both different long-range correlations of fluctuation and the fat-tailed probability distribution of the values.Since the large number of chaotic parameters of running-in attractors,and the obvious correlation and redundancy can be found among the parameters,it is necessary to determine a proper chaotic parameter sets before establishing the prediction model of running-in process.Based on the minimum redundancy-maximum relevance feature selection,a new method for the determination of extracting chaotic parameter sets of running-in attractors was proposed.The parameter sets consists of three kinds of chaotic parameters:Determinism DET,Trapping time TT and the feature parameter K_V.These chaotic parameters in this set are the most relevant to the multifractal eigenvalue and have the least redundancy with other chaotic parameters.The determination of chaotic parameter sets can effectively reduce the redundancy of the measures and also provides a variable basis for the subsequent establishing of the prediction model.The effects of various running-in parameters?normal loads,sliding speed,lubrication and the initial surface roughness?on the running-in process were analyzed,and the input parameters were selected based on the influence and the tribometer.The running-in friction experiments were performed by using a sliding ring against a disc to investigate the relationship between the running-in parameters and the running-in control parameters.Finally,the GMDH model of the running-in attractors was established using the Self-organization Data Mining method.Moreover,the evolution method of the running-in quality based on running-in attractors was put forward by studying the correlation of the chaotic parameter of running-in attractors and the stability of the COF signals.A recursive matrix was established by combining the vertical structured based vertical structures measures(LAM,V_max and TT)to quantitatively describe the stability of the time-series,the evolution object was then obtained using the method of PCA.The evolution index of time-series stability was computed by the establishment of the grey correlation relationship of the evolution object of the measured time-series and the stationary Gaussian white noise.The method of running-in design based on the running-in attractors was proposed by combing the prediction model and the running-in attractor based evolution method of running-in quality.The great TT,small DET and K_V were considered as the goals of running-in parameters optimal design.The Pareto optimal solutions and corresponding parameters were obtained using the method of Multi-Objective Particle Swarm Optimization.According to the calculation results,the running-in quality increases with the normal loads and decreases with the sliding speed.In terms of the lubrication oil,too large or too small viscosity of lubricating oil will cause the decrease of running-in quality.For the surfaces of the tribopair,the initial surface roughness of harder material should be machined to a smaller amplitude,while the initial surface roughness of softer material can be chosen in a wider range.