Free torsional vibration characteristics of compound planetary gear sets

A family of torsional dynamic models of compound gear sets is developed to predict the free vibration characteristics under different kinematic configurations resulting in different speed ratios. The compound gear sets considered consist of two planes of single- or double-planet gear sets connected by a straight long planet. All of the planets are mounted on a single carrier. The system matrices are derived for each power flow configuration separately and natural frequencies and the mode shapes are solved using the corresponding eigenvalue problem. Based on the predictions, the natural modes are classified into three groups: a rigid body mode, asymmetric planet modes and axi-symmetric overall modes. Smaller sub-system models are also proposed to predict each group of modes separately.