The change in the correlation dimension can reflect the degree of fault of the gear and identify the characteristics of the gear fault. When calculating the correlation dimension, the influencing factors should be selected appropriately. Although in theory, if there is a sufficiently long and sufficiently accurate time series, the delay can be chosen arbitrarily. However, the time series used in practice is limited and there are noises and errors. Therefore, in the case where the number of sampling points and the embedding dimension are sufficiently large, a reasonable delay time should be selected to reconstruct the attractor in the phase space to reflect the dynamic characteristics of the system in a higher dimensional phase space.
The correlation dimension of the vibration signal of the gear under different fault degrees is analyzed, and the influence of the signal sampling frequency and the vibration measuring point is analyzed. The results show that the correlation dimension can effectively reflect the shock signal component of the fault excitation in the gear vibration signal, and properly describe the development state of the gear fault. Therefore, using the correlation dimension in the fractal theory to analyze the vibration signal, the inherent law in the operation process of the equipment can be obtained. However, the embedding dimension and delay time should be chosen reasonably when calculating the correlation dimension. When the embedding dimension reaches a certain level, the magnetic powder clutch must find a delay time suitable for describing the system to construct the phase space. In the past, in the GP algorithm, the number of delay points was directly selected to be 1 to form the pattern space, which is unreliable. In this paper, the autocorrelation function method is used to determine the delay time, thus avoiding the arbitrariness and randomness of the correlation dimension calculation.
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