Simulation of planetary gear trains, modelling and numerical validation

This article introduces a novel set of multi-bond graph diagrams (MBGDs), which are intended for modelling an arbitrary planetary gear train (PGT). In this regard, three standard MBGDs are proposed: (a)one was developed for representing a single moving body, (b)another was designed for describing a revolute joint, and (c)the last one was created for representing a gear pair. Thus, by taking advantage of the module handling facility offered by the multibond graph technique (MBGT)and by adopting a multi-body-based approach, such models can be systematically coupled, through an assembling procedure, thereby forming the complete model for the whole PGT. Moreover, the obtained model incorporates both kinematics and kinetics equations of the PGT under study and allows us to perform a comprehensive power-flow analysis. The proposed approach also offers the capability of computing the dynamic loads of bearings and gear teeth for an adequate design of the PGT at hand. Furthermore, the resulting MBGD of the PGT has assigned an integral causality, which is a salient feature to be pursued in the resulting set of state equations, and mathematically means that an explicit set of first-order, differential equations can be obtained. Finally, the proposed diagrams are numerically validated by means of the imulation of a typical PGT and by its corresponding comparison with the Lagrange's equations and also with the Euler's laws.