基于混沌与分形理论的缸套—活塞环磨损过程动力学行为研究
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摘要
本文以实际缸套-活塞环摩擦副为研究对象，以实际采集得到的摩擦信号和表面形貌为载体，综合运用混沌与分形理论对磨损过程中的摩擦信号与磨损表面形貌进行分析与表征计算，以此揭示缸套-活塞环磨损过程中存在的非线性行为规律并为缸套-活塞环的磨损状态的识别和预测提供理论依据。研究结果对丰富摩擦学理论和对相关技术人员进行内燃机的摩擦学设计具有参考意义。
在混沌特征量计算时，无标度区间的选取极为重要。为此，本文首先提出研究无标度区间识别的新方法。通过对Lorenz等理论混沌吸引子信号及W-M分形函数产生的信号进行关联维数计算来验证所提出方法的有效性。计算结果均表明新方法能够客观准确并自动快速地识别无标度区间。这为混沌特征参数计算结果的准确性提供了保证。
时间序列信号的采样长度、采样间隔和噪声等因素对混沌特征量关联维数的计算结果具有重要影响，本文分别对不同采样长度和采样间隔的理论混沌时间序列和实测时间序列，以及含有不同信噪比的混沌时间序列的关联维数进行了计算。结果表明关联维数的计算值随着采样长度的增加而增加，但当数据长度达到一定值后，维数值趋于稳定；维数值随着采样间隔的增大而增大，仅在一定的间隔范围内保持相对稳定；维数值随着信噪比的减小而增大。对此，本文提出了合理确定采样长度的维数饱和方法和通过建立延迟坐标时间差与采样间隔关系曲线来确定采样间隔的方法，并采用小波分析技术来消除实际采集信号中的噪声成分以提高信噪比。
在对实际系统中的信号运用混沌理论进行研究分析之前必须验证信号是否具有混沌特性。本文综合运用功率谱法、主分量法、最大Lyapunov指数法、替代数据法及Kolmogorov熵法对缸套-活塞环系统的摩擦信号进行检验。结果表明摩擦信号具有显著的混沌特性，如连续宽带的功率谱、正的最大Lyapunov指数和Kolmogorov熵等，因此可以运用混沌理论对实际摩擦信号进行研究。
进行了多种工况条件下的缸套-活塞环摩擦磨损试验并获取摩擦信号时间序列，运用相空间重构理论研究磨损过程的动力学行为。结果表明：缸套-活塞环的摩擦磨损过程存在混沌行为的“磨合吸引子”，通过磨合吸引子的相轨迹演变可以定性地观察摩擦系统的磨损状态。对不同工况条件下磨合吸引子的关联维数进行了计算，结果表明：速度对吸引子关联维数值的影响最大，其次为载荷与温度。随着速度的增加，吸引子的关联维数先在一定范围内变化不大随后迅速增大；随着载荷的增加，吸引子的关联维数先是线性减小随后迅速增大；随着温度的增加，关联维数呈现出先缓慢减小后快速增加的趋势。磨合吸引子关联维数随着载荷与速度的乘积先逐渐减小后在一定的范围内保持相对稳定，当载荷与速度乘积达到一定值后，吸引子的关联维数值急剧增大。该结论对磨合状态识别和磨损过程预测具有应用意义。
综合运用混沌和分形理论对缸套-活塞环摩擦磨损过程中的摩擦信号进行研究来识别磨损状态。结果表明混沌和分形特征参数均能有效地表征不同磨损阶段摩擦信号的复杂性与不规则程度。因而可以用混沌与分形特征参数来定量识别磨损状态。在磨合磨损、正常磨损和急剧磨损三个阶段，关联维数、Kolmogorov熵、多重分形谱宽和谱值差呈“正浴盆曲线”的变化规律，而最大Lyapunov指数的变化规律呈“倒浴盆曲线”的变化规律。通过计算关联维数与多重分形谱宽研究工况条件对磨损过程时间影响的结果表明，温度对磨损过程时间的影响最大，其次分别为速度与载荷；磨合时间与磨损过程总时间均随着速度、载荷及载荷与速度的乘积的增大而呈总体下降的趋势，当速度与载荷乘积在一定范围内，磨合时间与总磨损时间变化不大。因此，应恰当地选取缸套-活塞环工况参数的大小。
研究了分形粗糙表面的生成与表征方法，并运用单重分形和多重分形参数分别对磨合过程不同时刻的缸套磨损表面形貌进行了表征计算。结果表明：随着磨合过程的进行，缸套表面的分形维数逐渐增大，多重分形谱的谱宽参数逐渐减小，并且谱线的形状逐渐由“倒钟状”过渡到向左的钩状。这表明在磨合过程中缸套表面形貌变得越来越均匀。并且运用多重分形谱能够更加全面地表征表面形貌的变化规律。
此外，为了进一步研究缸套-活塞环磨损过程中表面间的接触、传热等行为规律，本文对表面接触模型和接触热导模型进行了初步研究。采用三维W-M分形函数模拟粗糙表面，综合考虑接触微凸体的弹性、弹塑性和塑性三种变形形式，建立了一个表面接触分形模型；在该模型的基础上，进一步建立了预测接触界面热导的分形模型；最后还对单个微凸体的接触模型进行了修正，使得基于分形理论和基于传统理论建立的微凸体接触模型相统一。计算结果表明了上述所建模型的有效性。这为进一步研究缸套-活塞环摩擦副表面间的接触、磨损和热学等行为奠定了理论基础。
该论文有图115幅，表23个，参考文献213篇。
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.
在混沌特征量计算时，无标度区间的选取极为重要。为此，本文首先提出研究无标度区间识别的新方法。通过对Lorenz等理论混沌吸引子信号及W-M分形函数产生的信号进行关联维数计算来验证所提出方法的有效性。计算结果均表明新方法能够客观准确并自动快速地识别无标度区间。这为混沌特征参数计算结果的准确性提供了保证。
时间序列信号的采样长度、采样间隔和噪声等因素对混沌特征量关联维数的计算结果具有重要影响，本文分别对不同采样长度和采样间隔的理论混沌时间序列和实测时间序列，以及含有不同信噪比的混沌时间序列的关联维数进行了计算。结果表明关联维数的计算值随着采样长度的增加而增加，但当数据长度达到一定值后，维数值趋于稳定；维数值随着采样间隔的增大而增大，仅在一定的间隔范围内保持相对稳定；维数值随着信噪比的减小而增大。对此，本文提出了合理确定采样长度的维数饱和方法和通过建立延迟坐标时间差与采样间隔关系曲线来确定采样间隔的方法，并采用小波分析技术来消除实际采集信号中的噪声成分以提高信噪比。
在对实际系统中的信号运用混沌理论进行研究分析之前必须验证信号是否具有混沌特性。本文综合运用功率谱法、主分量法、最大Lyapunov指数法、替代数据法及Kolmogorov熵法对缸套-活塞环系统的摩擦信号进行检验。结果表明摩擦信号具有显著的混沌特性，如连续宽带的功率谱、正的最大Lyapunov指数和Kolmogorov熵等，因此可以运用混沌理论对实际摩擦信号进行研究。
进行了多种工况条件下的缸套-活塞环摩擦磨损试验并获取摩擦信号时间序列，运用相空间重构理论研究磨损过程的动力学行为。结果表明：缸套-活塞环的摩擦磨损过程存在混沌行为的“磨合吸引子”，通过磨合吸引子的相轨迹演变可以定性地观察摩擦系统的磨损状态。对不同工况条件下磨合吸引子的关联维数进行了计算，结果表明：速度对吸引子关联维数值的影响最大，其次为载荷与温度。随着速度的增加，吸引子的关联维数先在一定范围内变化不大随后迅速增大；随着载荷的增加，吸引子的关联维数先是线性减小随后迅速增大；随着温度的增加，关联维数呈现出先缓慢减小后快速增加的趋势。磨合吸引子关联维数随着载荷与速度的乘积先逐渐减小后在一定的范围内保持相对稳定，当载荷与速度乘积达到一定值后，吸引子的关联维数值急剧增大。该结论对磨合状态识别和磨损过程预测具有应用意义。
综合运用混沌和分形理论对缸套-活塞环摩擦磨损过程中的摩擦信号进行研究来识别磨损状态。结果表明混沌和分形特征参数均能有效地表征不同磨损阶段摩擦信号的复杂性与不规则程度。因而可以用混沌与分形特征参数来定量识别磨损状态。在磨合磨损、正常磨损和急剧磨损三个阶段，关联维数、Kolmogorov熵、多重分形谱宽和谱值差呈“正浴盆曲线”的变化规律，而最大Lyapunov指数的变化规律呈“倒浴盆曲线”的变化规律。通过计算关联维数与多重分形谱宽研究工况条件对磨损过程时间影响的结果表明，温度对磨损过程时间的影响最大，其次分别为速度与载荷；磨合时间与磨损过程总时间均随着速度、载荷及载荷与速度的乘积的增大而呈总体下降的趋势，当速度与载荷乘积在一定范围内，磨合时间与总磨损时间变化不大。因此，应恰当地选取缸套-活塞环工况参数的大小。
研究了分形粗糙表面的生成与表征方法，并运用单重分形和多重分形参数分别对磨合过程不同时刻的缸套磨损表面形貌进行了表征计算。结果表明：随着磨合过程的进行，缸套表面的分形维数逐渐增大，多重分形谱的谱宽参数逐渐减小，并且谱线的形状逐渐由“倒钟状”过渡到向左的钩状。这表明在磨合过程中缸套表面形貌变得越来越均匀。并且运用多重分形谱能够更加全面地表征表面形貌的变化规律。
此外，为了进一步研究缸套-活塞环磨损过程中表面间的接触、传热等行为规律，本文对表面接触模型和接触热导模型进行了初步研究。采用三维W-M分形函数模拟粗糙表面，综合考虑接触微凸体的弹性、弹塑性和塑性三种变形形式，建立了一个表面接触分形模型；在该模型的基础上，进一步建立了预测接触界面热导的分形模型；最后还对单个微凸体的接触模型进行了修正，使得基于分形理论和基于传统理论建立的微凸体接触模型相统一。计算结果表明了上述所建模型的有效性。这为进一步研究缸套-活塞环摩擦副表面间的接触、磨损和热学等行为奠定了理论基础。
该论文有图115幅，表23个，参考文献213篇。
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.
引文
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