Continuous Modeling of a Multi-Link Flexible Transmission

Abstract

The problem of dynamic, infinite dimension, modeling of a transmission is considered. An accurate Laplace transfer function matrix of the system that consists of flexible shafts connected by gears that are either rigid or flexible is found. 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 combining these individual transfer functions into an overall model of the transmission, by means of the link reaction approach that makes use of the geometric relationships and reaction moments between neighboring links. The outcome is a generalized dynamic model with the moments in the gear pairs as the generalized state vector. The explicit and highly structured form of the transfer functions allows physical insight into the system, exact calculation of natural frequencies and the construction of exact simulation schemes built from standard blocks that are available in multi-purpose simulation software.