Dynamic response of planetary trains to mesh parametric excitations

An extended three-dimensional model is used for calculating dynamic tooth loads an a planetary gear set Time dependent mesh stiffnesses are determined and an original Ritz method aimed at solving large parametrically excited differential systems is proposed. Results from the Ritz method compare favorably with those given by direct integrations for highly reduced computation times. The difference between local critical speeds (for one individual mesh) and global critical speeds (for sun or ring gear-planet meshes) on a sequential spur gear train is pointed out. Finally, it is shown that, for linear behaviors, mesh stiffnesses are largely controlling dynamic tooth loads while the influence of a floating sun or ring gear is less important.