Electrodynamic Bearings Modeling and Design

The number of high speed applications is sharply increasing in the last years so that the problem of the choice of the most suitable bearing must be handled. Considering the rotating machines, during the past ten years, high speed turbomolecular pumps have been mass produced showing that the high speed technology is mature. Since friction, wear, maintenance and lifetime represent the main issues of high speed applications, magnetic bearings, which are a contact free devices, could be considered as a possible solution. A magnetic bearing is a contact free bearing wherein the load is carried by magnetic forces. The magnetic field is generated in such a way that it provides necessary stiffness and damping to make the rotor hover safely during operation. Magnetic bearings are characterized by no wear, no maintenance and furthermore they don't require lubrication. The present work deals with a particular category of magnetic bearing: the electrodynamic bearings. The most interesting aspect of electrodynamic bearings is that levitation can be obtained by passive means, thus no electronic equipment, such as power electronics or sensors, are necessary. Therefore, electrodynamic suspensions are an advantageous alternative to active magnetic suspensions: they are less complex, less subject to failure, and possibly far lower in cost. On the other hand, the main drawback of electrodynamic bearings is that a stable levitation is provided only when the speed is above a threshold value, which opens stability issue at low speeds. Presently, the design of electrodynamic bearings is based on the force-to-angular speed characteristic obtained for a fixed eccentricity. Although this characteristic describes the behaviour of the bearing in quasi-static conditions, it is not suitable for dynamic conditions where the rotor is animated by a nonsynchronous whirl, or even a non periodic motion about the stator axis. A model that could take explicitly into account both the quasi-static and the dynamic conditions is still lacking. Therefore the first objective of the present work is to develop an analytical model of radial and axial electrodynamic bearings able to describe both quasi-static and dynamic behaviours. In this way not only the static characteristics such as achievable stiffness and force, but also the dynamic performance of a system involving electrodynamic bearings can be evaluated and used as design criteria. The developed models of radial and axial electrodynamic bearings have been experimentally validated. Two test rigs, the first based on a radial electrodynamic bearings, the second characterized by the presence of an axial electrodynamic bearing, have been designed and built to this end. Since the electrodynamic bearings are intrinsically unstable devices, the stability issue is examined in the dissertation. So far, the most common solution to achieve the stability is to add non-rotating damping between the rotor and the stator. It is natural to obtain the stability by adding non-rotating damping between the rotor and the stator. Nevertheless, this strategy is not as easy to apply as it seems, given that the stabilizing device must be contactless, consistently with the electrodynamic bearings issue. Although effective, this solution could imply the installation of a dedicated magnet on the rotor with a consequent increase of the rotor weight and complexity and the rising of some concerns about the mechanical resistance, and a conductor where eddy currents can arise on the statoric part of the system. In the dissertation a new stabilizing technique for electrodynamic bearings is proposed. Instead of introducing damping between the rotor and the non-rotating part of the bearing, the author propose to introduce an elastic and dissipative element between the statoric part of the bearing and the case of the machine. The innovative aspect of the proposed solution is that the stabilizing dissipation is introduced into the statoric part of the electrodynamic bearing, which does not rotate. The main advantages of this configuration are: reduced complexity from the constructive point of view since no rotating parts are involved; an easier tuning of the stabilizing system main parameters; an extremely effective contribution to the stability; conventional and low cost devices are suitable for the implementation of the proposed stabilizing system. The wide variety of practical solutions that can be adopted for the proposed stabilization techniques, such as rubber bushings or squeeze film dampers for example, is an indicative parameter of the true possibility of applying it in industrial applications. The impact of the proposed solution on the rotor stability is investigated, and it is demonstrated that a damping device between the rotor and the statoric part is no longer necessary. Although electrodynamic bearings are quite complex devices, they are still lacking a clear design procedure, therefore a procedure addressed to optimize the design of electrodynamic bearings for industrial applications could be useful. Since the developed models, able to describe the quasi-static and dynamic behaviours of electrodynamic bearings, have been experimentally validated, they can be assumed as useful tools oriented to the design of these devices. Therefore, at the end of the dissertation, a design procedure based on those models is presented. The developed models and the proposed stabilizing technique make the electrodynamic bearings ready for the industrial applications