基于混沌与分形理论的磨损过程动力学行为研究

Quantitative researches will be carried on to study the dynamic behavior of friction and wear process in this project based on chaos and fractal theories, firstly, in order to improve the accuracy of the calculation of the chaotic characteristic quantities and to guarantee the accurate reflection of the dynamic characteristics of the friction system, researches will be conducted on the non-scale region identification methodology of the chaotic characteristic quantities and the sampling method of friction signal; secondly, based on the variation of parameters of chaos and fractal, consistency research will be conducted on the chaos and fractal behavior of friction signal (frictional force, friction-induced vibration and noise, and frictional temperature), worn surface topographies, wear debris, the relationship between these behaviors and the initial condition containing contact surface, operating conditions, material characteristics, lubricating conditions will be studied as well, in order to reveal the intrinsic property of friction system and its chaotic characteristic of sensitive dependence on the initial condition, and lay the foundation to establish a friction and wear laws comprehensively; moreover, the evolution of the chaotic attractor of the friction system will be investigated both qualitatively and quantitatively, and the calculations will also be done on chaotic characteristic quantities, a dynamic model of the wear process which consistented with three wear stages will be presented to provide a new method for the quantitative recognition of the wear process.

本项目运用混沌与分形理论开展摩擦磨损过程动力学行为的定量研究，首先开展混沌系统特征量计算中无标度区间的识别方法和摩擦信号的采样方法研究，为提高混沌特征量的计算精度和准确反映摩擦系统的动力学特性提供保证；然后以混沌和分形特征量的变化规律为依据，开展磨损过程中的摩擦信号（摩擦力、摩擦振动、摩擦噪声、摩擦温度）、摩擦表面和磨损磨粒的混沌及分形行为的一致性研究，以及这些行为与接触表面、摩擦工况、材料特性、润滑条件等摩擦初始条件的相关性研究，以揭示摩擦系统行为的内禀特性和对初始条件敏感依赖的混沌特性，为建立统一的摩擦磨损定律奠定基础；进而进行摩擦系统混沌吸引子演变规律的定性和定量研究以及对多个混沌特征量的计算研究，提出与磨损过程3个阶段相一致的摩擦磨损过程的动力学原理模型，为磨损过程的量化识别提供新的方法。

摩擦系统是一个非线性耗散动力系统，发生在这一系统中的各种摩擦、磨损行为具有混沌和分形特性。为了揭示磨损过程的动力学行为规律，分别进行了如下研究：（1）对无标度区间识别问题进行了研究，提出了点斜率误差算法，并将其结合K-means算法，设计了一种识别无标度区间的新方法。运用该方法能够客观准确地识别出无标度区间，从而使得关联维数的计算更加精确，这对非线性时间序列的混沌特征分析具有重要的意义。（2）研究了采样长度、采样间隔和噪声这三个因素对关联维数计算的影响，提出了确定采样长度和采样间隔的方法，发现EMD方法对于混沌特性信号中含有的周期性噪声和白噪声具有良好的滤波效果。（3）研究了磨损过程中混沌及分形行为规律的一致性，发现摩擦力信号和磨粒群的分形维数具有一致的演化规律；摩擦温度、摩擦力和摩擦振动信号在相空间中的混沌特性具有高度的一致性和相关性。（4）研究了摩擦磨损过程中混沌及分形行为与摩擦初始条件的相关性，得到了磨合表面分形维数和磨合时间与系统参数的关系。（5）研究了磨损过程的动力学突变行为和动力学模型。研究了磨损过程中的动力学突变行为，发现在磨损过程中依次出现动力学渐变区、动力学稳定区和动力学突变区，这三个区域分别对应于磨合吸引子的形成、维持和消失阶段，建立了粗糙表面分形接触模型。项目研究成果对摩擦学复杂问题的量化研究和丰富摩擦学理论具有科学意义，而且对磨合状态识别和磨损故障诊断具有工程价值。