Non-stationary Operating Conditions of Rotating Machines: Assumptions and Their Consequences

Abstract

The growing use of rotating machines operating in non-stationary conditions gave rise to a greater need to a higher precision for describing their dynamic behavior. The latter has always been based on a certain number of simplifying assumptions. In particular, the spinning speed is considered either constant or following a given law of variation as a function of time, resulting in a dynamic model that is limited to specific operating conditions. The aim of this work is to present a more general dynamic model of rotating machines, which accurately reflects its behavior in real working conditions. No assumption is made on the speed of rotation; it is included as an unknown of the dynamic problem by introducing a degree of freedom combining both the free body rotation and the torsional deformation. The instantaneous angular speed (IAS) is then deduced not only from the induced torque, but also from the whole dynamic behavior of the structure taking into account the periodic geometry (e.g.: gears, bearings) as well as the operating conditions (e.g.: going through the critical speeds). Making no assumption on the angular speed leads to a new formulation of the gyroscopic effect strongly present at very high speeds. This new formulation shows a coupling between the different degrees of freedom as well as a nonlinear behavior of the structure. The results of both classic and new formulations are compared for an architecture of a rotating machine to highlight the utility of the innovative approach in non-stationary operating conditions.