Abstract: A discrete-continuum dynamic model for spur planetary gear trains (SPGTs) is developed by using the sub-structure synthesis method. By combining the equation of motion of an elastic continuum ring subjected to internal and external constraints with lumped parameter equations of motion of rigid bodies, the system governing equations are obtained. A modal analysis is conducted to reveal the modal properties of spur planetary gear trains. The free vibration characteristics of the system are classified into four distinct modes: rotational, translational, planet and ring. For each vibration mode, the properties and reduced-order formulae are derived. The effect of ring elasticity on system natural characteristics is then discussed. The simulation results show that the elastic ring gear decreases the lower order natural frequencies and introduces a new vibration mode i.e. the ring mode. And the natural frequencies of the ring mode locate at the middle and low region of the overall system frequencies. The simulation indicates that the elasticity of ring gear must be considered during the dynamic design of planetary gear trains. A back-to-back test rig is constructed and some vibration tests are conducted. The experimental results agreed well with the theoretical and numerical analysis.

Key words: planetary gear trains;dynamic modeling;natural frequency;discrete-continuum model