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The vibration signal correlation dimension is the largest under normal conditions. When the individual gear teeth fail, the correlation dimension of the vibration signal is significantly reduced. However, as the number of fault teeth increases, the correlation dimension decreases gradually, and the fault expands to In most tooth flanks, the correlation dimension value even rises slightly, but it is still smaller than the fractal dimension under normal conditions; this variation law is not affected by the gearbox load condition, vibration measurement point and acquisition parameters; in the appropriate embedding dimension Under the conditions of number and time delay, the correlation dimension calculated by the motor type test is very close.
In the non-faulty working state, the vibration 1 generated by the gear meshing can be regarded as a stationary random vibration, and its fractal dimension is close to the embedding dimension of the reconstructed phase space. When the local tooth surface of the gear fails, the meshing process occurs. The obvious periodic impact, thus including the local shock signal component in the vibration signal, tends to a certain finite-dimensional attractor and singularity in the phase space, and the correlation dimension in this state is significantly smaller than the correlation dimension in the normal state. number.
When the fault spreads to all the teeth, the impact components in the vibration signal are distributed throughout the signal time history, so the correlation dimension has an upward trend. However, at this time, the correlation dimension should still be small compared with the normal state. Therefore, the associated shape dimension can reflect the state of motion of the system.
