随机稳定性理论在磨合过程研究中的应用

项目名称： 随机稳定性理论在磨合过程研究中的应用

项目编号： No.51305441

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 机械、仪表工业

项目作者： 杨建华

作者单位： 中国矿业大学

项目金额： 24万元

中文摘要： 本项目通过研究磨合过程中摩擦振动信号的随机稳定性问题，实现对磨合过程的定量描述。基于随机动力学理论体系分析采集到的多个实验样本，通过计算最大Lyapunov指数、矩Lyapunov指数、平稳概率密度函数等动力学指标，确定磨合过程的摩擦学行为。最大Lyapunov指数是系统概率1稳定性及发生D分岔的判别指标，利用它来界定磨合过程的不同磨损阶段。平稳概率密度函数用于定量描述摩擦学信息的统计分布，是判别系统发生P分岔的理论依据，利用P分岔研究磨合过程出现临界稳定性的原因。D分岔和P分岔的依次出现意味着随机Hopf分岔的发生，即在磨合过程中产生了自激振动。对处于同一磨损阶段的不同实验样本，引入矩Lyapunov指数定量研究磨合系统运行的动态平稳性能。稳定指标越大，动态平稳性能越好，磨损程度越轻。通过磨合过程随机稳定性的研究确定系统运行的最佳工况参数，实现最"友好"的摩擦环境。

中文关键词： 摩擦学系统；动力学稳定性；随机分岔；Lyapunov指数；

英文摘要： In order to give a quantitative understanding of the running-in problem, the stochastic stability of the frictional vibration signals from the running-in process will be studied. Based on the mechanism of stochastic dynamics, some indexes such as the maximal Lyapunov exponent, moment Lyapunov exponent and the stationary probability density function will be calculated from the collected signals to determine the tribology information of the running-in process. The maximal Lyapunov exponent is the target for the stochastic stability in probability 1 and the D bifurcation, and the change of its sign corresponding to different wear stages. The stationary probability density function describes the statistical distribution of the tribology information, and it is used to study the P bifurcation that is the causation for the critical stability phenomenon in the running-in process. When the D bifurcation and P bifurcation occurs in turn, the stochastic Hopf bifurcation that means the self-excited vibration occurs. For different test samples, the moment Lyapunov exponent is introduced to study the dynamical property in the same wear stage of the running-in process. For larger stability index, the dynamical property is better and the wear is slighter. By investigating the stochastic stability of the running-in process, the

英文关键词： Tribology system；Dynamical stability；Stochastic bifurcation；Lyapunov exponent；