基于奇异值分解的摩擦振动吸引子特征参数提取方法

Feature parameter extraction of a friction vibration attractor based on singular value decomposition

为定量研究摩擦副磨损过程中摩擦振动吸引子的变化,根据相空间重构理论,应用C-C法重构摩擦振动吸引子相空间矩阵,对相空间矩阵进行奇异值分解,通过奇异值构建矩阵奇异值特征向量,定义其特征参数为摩擦振动吸引子特征参数K,并分析特征参数K在摩擦副磨合磨损过程中的变化规律。结果表明:磨合开始,摩擦振动能量较低,吸引子体积较小,K值亦较小,为9.36;随磨合进行,摩擦振动能量逐渐增加,吸引子体积逐渐增大,K值亦逐渐增大;43min后,摩擦振动能量保持平稳,吸引子体积趋于稳定,K值在24.72附近平稳波动。因此,摩擦振动吸引子参数K可用于定量分析磨合过程中摩擦振动能量的变化;K与摩擦因数对磨损阶段的判断一致,进而可用于磨损状态的识别。

An attractor feature parameter K was defined to quantitatively study a friction vibration attractor, and its variation was investigated in the running-in wear process. K was the feature parameter of the eigenvectors built with the attractor phase-space-matrix singular values obtained using the C-C method and the phase-space reconstruction theory. Results showed that friction vibration energy is lower in the beginning stage, the attractor volume is smaller and ^ is 9. 36; when the running-in continues, the friction vibration energy increases, the attractor volume gets larger and K also increases gradually; friction vibration energy is stable after 43 min, attractor volumes are also stable and K fluctuates near 24. 72 ; therefore, K can be used to quantitatively analyze the variation of friction vibration energy in the running-in process; the identification of wear state with K is consistent with that using friction coefficient, and K can be used to monitor the wear state of tribological pairs.