Study On The Dynamic Properties During The Wear Process Of Cylinder Liner-piston Ring Based On Chaos And Fractal Theories

In this paper, cylinder linear-piston ring was adopted as research object, based on theresearch of actual friction signal and surface topography during wear process via fractaland chaos analysis and characterization, the variation of nonlinear behavior during thewear process of cylinder linear-piston ring was investigated, which provides theoreticalbasis for identification and prediction of wear stage. The results contribute on bothabundance of theoretical study of tribology and tribological design of the internalcombustion engine.The selection of scaling region is essential for calculation of chaotic characteristicquantities. In this paper, a novel non-scale region identification methodology was proposedand validated based on the correlation dimensions of four well known chaotic attractorsincluding Lorenz and five curves generated by the W-M function. The results show that theproposed new methodology can identify the scaling region objectively, accurately,automatically and quickly, which guaranteed the accuracy of numerical calculation.Sampling length, sampling interval and noise have great impact on the correlationdimension calculation results. In this paper, the correlation dimensions of theoretical timeseries and a measured nonlinear time series with different sampling length and samplinginterval as well as chaotic signals with mixed noise of different signal to noise ratio wereinvestigated. The calculation results show that the dimension increases as the samplinglength increases, and when the data points reach a certain number, the dimension basicallystabilized; the dimension increases with the increasing of the sampling interval andmaintain relatively stable within a certain interval; the lower the signal to noise ratio, thelarger the value of dimension. As a result, saturation dimension method and methodologybased on establishment of delay time and the sampling interval curve were proposed fordetermination of sampling length and sampling interval respectively. Wavelet analysis wasrecommended to eliminate the noise in actual signal.The chaotic characteristics of the friction signal must be verified before chaos analysis.The friction signal of cylinder linear-piston ring was proved possess significant chaoscharacteristics based on the integrated study of friction signal using power spectrummethod, main component method, maximum Lyapunov exponent, surrogate data methodand the Kolmogorov entropy method. The results show that the friction signal havesignificant chaotic characteristics, such as continuous power spectrum, a positivemaximum Lyapunov exponent and Kolmogorov entropy. Thus, chaos theory is qualified for the study of the actual friction signal.The wear tests of piston ring-cylinder liner under different conditions were carried outto investigate the nonlinear dynamical behaviors during the wear process based on thephase space reconstruction technology. Studies show that there exists "Running-inattractor" in cylinder linear-piston ring wear process, the wear state of the friction systemcan be qualitatively observed effectively by the evolution of the Running-in attractor'sphase trajectory. Correlation dimension was used to characterize the chaotic characteristicsof the running-in attractor and the results indicate that: speed has great impact on thecorrelation dimension values, followed by load and temperature. As the speed increases,the correlation dimension increases slowly within a certain range and then rapidlyincreased; with the increase of load, the correlation dimension first decreases linearlyfollowed by a rapid increase; as the temperature increases, the correlation show a rapidincrease trend after the first slowly decreasing. The correlation dimension of the running-inattractor decreases gradually and then maintain relatively stable in a certain range as thechanges of the product of load and speed. The value of the correlation dimension increasessharply when the product of load and speed reaches a certain value. The above conclusionscontribute applicable significance of identification and prediction of wear process.Fractal and chaotic characteristics parameters were used to characterize the frictionsignal of cylinder linear-piston ring wear process and quantitatively identify the wear stage.The research indicate that both chaotic and fractal characteristic parameters are able toeffectively characterize the complexity and irregularity degree of friction signal in differentwear stages, which verifies the feasibility of chaos and fractal characteristics parameters toquantitatively identify the wear state. In the three stages of running-in wear, normal wearand rapid wear, the correlation dimension, Kolmogorov entropy, multi-fractal spectrumwidth and the spectrum difference show the variation of "bathtub curve", while thevariation of the maximum Lyapunov exponent presents "inverted bathtub curve". Theinfluence of working conditions on the wear process time was investigated by calculationof the correlation dimension and research of multi-fractal spectrum width. The resultsindicate that, the temperature have the greatest impact on the running-in time, followed byspeed and load, with the increasing of load, speed and the product of load and speed, therunning-in time as well as the total time of the wear process decline, which changeinconspicuous within a certain range of the product of load and speed. Therefore,appropriate working parameters should be chosen before the wear tests.In this paper, the generation and characterization methods of rough surfaces withfractal characteristics were investigated, single-fractal and multi-fractal theory were used to characterize the surface topography of the cylinder linear in different wear stages. Theanalysis shows that: with the process of running-in, the fractal dimension of the cylinderlinear increases, the shape of the multi-fractal spectrum transit gradually from "invertedbell" to left hook and the spectrum width parameter decreases progressively, which meansthe distribution of the surface tend to be uniform with the conduct of running-in process.Besides, multi-fractal spectrum is able to characterize the variation of surface topographymore comprehensively.In addition, we carried out a preliminary study of surface contact model and thermalconductivity model for further research on the variation of contact and hear transfer duringthe wear process of cylinder linear-piston ring. A fractal contact model of rough surfaceswas established based on the three-dimensional W-M function and three kinds of asperitydeformation patterns, including elastic, elastic-plastic and plastic, further established afractal prediction model of thermal conductivity of the interface on the basis of thepresented contact model. At last, a single fractal asperity contact model was revised basedon the integration of fractal and traditional theory and numerical results indicate thevalidity of the model above, which provides theoretical foundation for further studies onfriction and wear, thermal resistance and conductivity between friction surfaces.