Passive magnetic bearings are known due to the excellent characteristics in terms of friction and no requirement of additional energy sources to work. However, passive magnetic bearings do not provide damping, are not stable and, depending on their design, may also introduce magnetic eccentricity. Such magnetic eccentricities are generated by discrepancies in magnet fabrication. In this framework the main focus of the work is the theoretical as well as experimental investigation of the non-linear dynamics of a rotor-bearing system with strong emphasis on the magnetic eccentricities and non-linear stiffness.

In this investigation passive magnetic bearings using axially-aligned neodymium cylinder magnets are investigated. The cylinder magnets are axially magnetised for rotor as well as bearings. Compared to bearings with radial magnetisation, the magnetic stiffness of axially-aligned bearings is considerably lower, nevertheless they allow for asymmetric stiffness mounting, and it could be beneficial for rotor stabilization.

A theoretical model is proposed to describe the non-linear rotor-bearing dynamics. It takes into account non-linear behaviour of the magnetic forces and their interaction with a multi-body system composed of rigid rotor and flexible foundation. The magnetic eccentricities of the shaft magnets are modelled using the distances (amplitudes) and directions (phase angles) between the shaft axis and the centre of the magnetic fields generated. A perturbation method, i.e. harmonic balancing, is used in order to evaluate the frequency response of the non-linear system.

The experimental validation of the model is carried out using a dedicated rotor-bearing system set-up. The test set-up consists of a vertical rigid shaft and disc supported by two passive magnetic bearings using axially-aligned neodymium cylinder magnets. The magnetic bearing housings are flexibly supported, allowing horizontal motions. The housings are connected to each other by means of elastic beams. The shaft is free in one end and coupled to a DC motor on the other by means of a flexible coupling. On the free end a disc is attached where imbalances and gyroscopic effect can be generated.

Comparison between theory and experiment shows high level of resemblance, which validates the theoretical model and the explanations for the quasi-static and dynamic responses. The magnetic eccentricities and mass imbalance effects are clearly detected and distinguished.

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