Steady state response of gear system based on harmonic balance method

The transmission ratio of the reducer variable speed integrated gear is as follows:

Where ε is the eccentricity.

The expressions of KM and E are obtained by neglecting the high-order harmonic terms in meshing stiffness and error


KR — stiffness and error fluctuation amplitude;

Er — stiffness and error fluctuation amplitude;

φ m – phase angle of stiffness;

φ e — phase angle of error.

Considering the influence of stiffness and phase difference of error excitation on vibration, and taking φ M = π / 2 and φ e = 0 respectively, then on the right side of the formula:

The rigid angular acceleration in the formula is expanded by Fourier series. Taking the first two terms, the load of gear is constant