It can be seen from the formula that the harmonic components of ω C and N ω e (n is a positive integer) must exist in the reducer variable speed integrated gear. In addition, it can be seen from the dynamic model that the elastic meshing force will produce the harmonic components of ω C, 2 ω C, n ω e, ω C ± n ω E and 2 ω C ± n ω e under the combined action of stiffness excitation and instantaneous center excitation. According to the previous research and analysis, in most cases, the main role is the fundamental frequency steady-state response in the system. In the actual production and engineering design work, the fundamental frequency steady-state response is also the most concerned influence factor. In order to be as close as possible to the actual working condition characteristics of the gear system, at the same time, the fundamental frequency steady-state response is also the most important influence factor Because the mesh stiffness and error excitation phase angle only affect the trigonometric transformation of sine and cosine functions, the expressions of stiffness excitation and error excitation are as follows:
KR is the change amplitude of gear meshing stiffness. The parameters K0 and Kr can be obtained by finite element calculation;
EI — change amplitude of gear static transmission error;
φ m — phase angle of meshing stiffness;
φ e — phase angle of error excitation.
The expression of F (γ) is obtained as follows
Where, β represents the amplitude ratio of pitch diameter of noncircular gear pitch curve, β = E / L.