Overview

Rotors are defined by the ISO as bodies rotating about a fixed axis, constrained to do so by bearings, acting as cylindrical hinges. Bearings may be more or less compliant, but even in this case, their deformations are considered to be small if compared with the dimensions of the system. The dynamic study of rotors is thus usually performed under the assumptions of small displacements and rotations. These assumptions allow a number of linearizations of both the inertial and the elastic terms in the equations of motion. The assumptions of small displacements and rotations are retained even when studying the behavior of nonlinear rotors, the nonlinearities being usually ascribed to bearings (of the fluid, rolling elements or even magnetic type), dampers, or other causes, as the presence of cracks.

Moreover, the angular velocity is assumed to be constant, or at least a known function of time, because the presence of a driving system that controls the spin speed is postulated.

However, there are rotating systems that are not constrained by bearings, like spinning spacecraft or celestial bodies. They can after all be considered as rotors and are often defined as free rotors, as opposed to the more conventional fixed rotors, supported in bearings.

Although the absence of the bearings does not change the nature of the problem, the displacements can be far greater in the case of free rotors and this makes the small displacements and, above all, small rotations assumptions more problematic. Moreover, although in the...