Transmission error is the main excitation of gear vibration. It combines the influence of meshing time-varying stiffness and manufacturing error, and can determine the characteristics of gear vibration to a certain extent. For the convenience of description, the transmission error is defined on the meshing action line, i.e. linear transmission error (LTE). LTE will be used as the actual incentive in the model.

For the transmission error of the p-th planetary gear, there is L-order excitation, then the total excitation is:

Where, l ϕ is the phase of the first order transmission error, l = 1,…, L.

The signal of the p-th planetary gear needs to be windowed relative to the fixed measuring point:

When the p-th planetary gear passes through the fixed measuring point, the signal generated by engagement is:

The signal model in the whole period measured at a certain measuring point is as follows:

The frequency domain signal can be obtained by Fourier transform: