某型滚动轴承故障与分形维数的确立

Fault Diagnosis of a Bearing Based on Chaos and Fractal Theory

针对轴承传动本身具有非线性而在传统故障诊断中又被忽略掉的问题,运用最大李雅普诺夫指数进行齿轮箱轴承运行混沌状态的辨识,然后采用关联维数对轴承故障进行准确定位。通过实验获取齿轮箱轴承的外圈故障、内圈故障、滚动体故障和正常状态的振动信号,并进行小波包去噪,对去噪信号分别计算各种状态下的最大李雅普诺夫指数和关联维数,得出各故障状态下对应的混沌状态和分形维数,可将此分形维数作为特征向量进行轴承故障诊断。在进行系统状态辨识和关联维数计算的同时讨论了嵌入维数、延迟时间和无标度区的确定方法。

Aiming at the non-linearity which exists in the bearing transmission but is ignored in the traditional fault diagnosis methods, the max-Lyapunov exponent was calculated in order to judge the system state of chaos firstly, then the correlation dimensions was calculated for the sake of judging the fault type. Some experimentation were carded out on a gear case, and the vibrating signals under normal working conditions and fault working conditions including outside-rolling fault, inside-rolling fault and roll fault were acquired. The system state of chaos and fractal dimensions were obtained according to the calculation results after getting rid of the noise in the original signals. The experimentation shows that fractal dimensions can be used as the fault character parameter for fault diagnosis. In addition, the embedding dimension, delaying time are also studied in this paper.