Vibration analysis of a planetary gear system based on the transfer matrix method

This study models a 3-dimensional planetary gear system using the transfer matrix method. The local transfer matrices between each component of the planetary gear set were derived with consideration of the tooth width, and the transfer matrix of a planetary gear system corresponding to the inertial transfer matrix was determined. The eigenvalue analysis of the transfer matrix suggested an analysis method in the form of a lambda matrix, instead of the direct search method through a characteristic polynomial. The boundary conditions at the first and the last stations of the entire transfer matrix were partitioned into known and unknown values to generate a concentrated transfer matrix and a latent equation, and the eigenvalue problem in the lambda matrix was solved. The characteristics of the responses according to the phase state of the harmonic component of the transmission error were reviewed through the steady-state response and mode shape type.