Transfer Function Modeling of a Flexible Gear Train

The problem of dynamic, infinite dimension, modeling of a gear train is considered. It includes derivation of the accurate, Laplace transfer function matrix of the system that consists of flexible shafts, individually governed by the wave equation, connected by gears that are either rigid or flexible. The first step is deriving a set of single input, infinite dimension, transfer functions for a single uniform link. The building blocks of those transfer functions are time delays, representing the wave motion, and low order rational expressions, representing the boundary phenomena. The next step is constructing a model for the multi-link gear train system, by using the natural feedback within the system to arrive at a generalized dynamic model. This explicit and highly structured form of transfer functions, allows physical insight into the system, which is lacking in finite dimension approximations. It was used for the analysis of the dynamical behavior of the gear train and may also be used for the design of dedicated control laws.