Investigation of Thermal Effects in Rotors Levitated by Magnetic Bearings via Coupled Multiphysical Models – Theory and Experiment

Rotating machines are integral to modern society, particularly in the energy sector, where turbomachinery is essential in power generation. Climate goals, combined with advances in material science and computational power, are driving the need for more efficient machines. One way of doing so is by designing machines capable of spinning faster. In such conditions, conventional bearings such as roller bearings and oil bearings are pushed to their limit due to friction. Magnetic bearings offer a contactless solution by levitating the rotor with magnetic forces. These bearings can be classified into two groups: Passive magnetic bearings (PMBs) and active magnetic bearings (AMBs). In the first group, the magnetic force is generated using permanent magnets, while the second group relies on electromagnets controlled by a feedback system. The fact that in AMBs the magnetic force is controlled allows the adjustment of bearing characteristics, i.e., stiffness and damping, in real time, making them very attractive for industrial applications. Due to the contactless nature of the AMB and the lack of lubricants, greases, or auxiliary components related to these fluids, the necessity of maintenance of these bearings is considerably smaller. AMBs have been employed in several applications. For example: Gas
turbines, compressors for both above sea/onshore and subsea compression, highspeed spindles, expanders, turbo-blowers, and turbomolecular pumps. Some have been specifically focused on reducing energy consumption, a key design parameter, especially in Flywheel Energy Storage Systems (FESS).

In some of the machines cited above, where components are exposed to high-temperature gases or operating in a vacuum, the temperature of components, especially the rotor and the AMBs, can reach values where the thermal effects may affect the performance of the system, leading to sub-optimal operating conditions, and even to vibration instabilities.

In this context, this thesis aims to contribute to this field by presenting multiphysical mathematical models capable of investigating thermal effects in magnetic bearings with the novelty of combining i) rotordynamics, ii) electromagnetism, iii) control theory, and iv) temperature in one single model where all the equations are simultaneously solved. It means that rotor lateral and axial displacements, electrical currents of the AMBs, and temperatures at some important rotor and bearing locations, are treated as states variables of the global system. Usually, these domains – especially the thermal – are decoupled from the mechanical and electromagnetic due to the different time constant scales and due to the complexity of finite element models used to achieve good accuracy when modelling the temperature field in systems with complex geometries.

This thesis is based on two scientific articles that present the multiphysical models for two examples. In the first publication, which is a theoretical contribution, a multiphysical model is developed for a laboratory-scale test rig representing a flywheel, containing a vertical rotor with an axial passive magnetic bearing and supported radially by two active magnetic bearings. The losses in the system lead to an increase in temperature, which affects the dynamics due to components’ thermal expansion, change in permanent magnets’ magnetization, and increase in AMB coils’ resistance. The theoretical outcomes of the first article are compared with experimental data, with satisfactory correlation.

The multiphysical model of the second article is applied to a test rig designed especially for visualizing thermal effects. The test rig is a non-spinning vertical rotor supported axially by one AMB and radially by two PMBs. High-temperature environment is created around the AMB’s stator by blowing hot air with heat guns. During the experiments, the AMB with the original controller is not capable of maintaining the rotor levitated after the AMB stator reaches a certain temperature, indicating a loss of load capacity. The model can represent this effect with good accuracy, as it predicts the instant the rotor’s vertical vibration instabilities starts, the rotor drops, and the temperature increase in the AMB. These two examples show the relevance of thermal effects in rotor levitated by magnetic bearings and illustrate the usefulness of multiphysical models in such systems, especially in the design phase of these machines, and can also be used when synthesizing controllers for the AMBs.