Modeling, Design and Control of Power-Electronic-Actuated Electromagnetic Bearings

Abstract

Many practical electrical machines, turbines, and compressors operate in speeds ranging from tens of thousands of rpm to hundreds of thousands of rpm, also handling a significant amount of power. While high-speed operation reduces the machine dimensions for a given power rating, its challenges include high bearing loss, reduced bearing life, and high viscous drag. Contactless bearings, such as gas, oil, or electromagnetic bearings (EMB), offer longer life than conventional bearings in high-speed applications. In addition to being contactless, an electromagnetic bearing (EMB) is lubrication-free; hence this is suited for both clean conditions (e.g., food and pharmaceutical industry) and hazardous applications (e.g., petroleum and chemical industry).

This thesis presents the modelling, analysis, design and control of power-electronic-actuated EMBs. The scope of thesis includes both radial EMB and axial (or thrust) EMB, which handle the radial and axial forces, respectively, acting on the rotor assembly. The specific contributions include (i) selection of angular contact bearing for a high-speed machine, (ii) improved electromagnetic design procedures for radial and axial EMB, (iii) modified geometry of axial EMB to reduce thrust disc diameter, (iv) prototyping and static characterization of radial and axial EMBs, (v) position controller design and its validation, (vi) development of SiC-MOSFET based fault-tolerant power amplifiers for excitation of EMBs, and (vii) development of a novel test rig for characterization of EMB.

The thesis presents a selection procedure for angular contact ball bearings, considering a 5 kW, 10,000 rpm switched reluctance machine (SRM) as an example. This procedure includes identifying requirements, determining the bearing arrangement, establishing pre-loading specifications, and validating bearing selection through lifetime calculations. The selected bearings are then assembled and tested on the SRM, fed from asymmetric H-bridge converters, at various speeds up to 10,500 rpm. The phase currents, rotor position, and vibration on bearing housings are measured at different speeds. The vibration amplitudes are found to be quite low at the bearing fundamental defect frequencies. The vibration plots confirm satisfactory operation of the bearings selected.

The radial EMB supports the rotor against the radial forces acting on it. The dynamic load capacity and force slew rate of the EMB are related to the maximum allowable rotor displacement through mathematical analysis. This analysis is helpful in deciding the specifications of the radial EMB. A preliminary design, based on magnetic circuit analysis, is seen to fall short in terms of load capacity. Iterative changes to the EMB dimensions achieve the required load capacity, but the characteristics are still nonlinear. Finite-element analysis bring out the effects of magnetic saturation on load capacity, force-current relationship, and force slew rate. An improved electromagnetic design procedure is proposed for radial EMB, which requires no iterations. In addition to ensuring the desired load capacity and force slew rate, this procedure guarantees linearity between magnetic force and control current up to the load capacity of the bearing in differential-mode operation. The improved procedure maximizes the force per unit pole area per unit MMF. The proposed design leads to improved dynamic response and stability. A radial EMB with a load capacity of 180 N is designed and validated using finite element analysis tools. The designed EMB is fabricated, and its force-current characteristics are measured using a specially designed test rig to validate the design.

An electromagnetic axial bearing (EAB) exerts a magnetic force on a thrust disc, which is attached to the rotating shaft, countering the axial forces on the rotor. Firstly, the improved design procedure for the radial EMB is adapted for the conventional geometry EAB, which maximizes force density per unit MMF. The conventional EAB requires a large thrust disc diameter to produce large axial forces, which can adversely affect the mechanical stresses, rotordynamics, and maximum operating speed. This work arrives at a modified EAB geometry, along with a systematic design procedure, to reduce the thrust disc diameter significantly for a given load capacity. Laboratory prototypes of both conventional and modified geometries are fabricated and are compared theoretically as well as experimentally. The modified geometry is shown to achieve a load capacity comparable to that of the conventional geometry, along with 30\% reduction in thrust-disc diameter and 50\% reduction in peak material stress.

Position control of EMB, which is used to support the shaft of a high-speed rotating machine, involves stabilization of an unstable system and high-bandwidth position control of the rotor being supported. PID controller is most widely used in industries due to its simple structure and easy implementation. A systematic design procedure for the PID controller is proposed. This involves identifying the feasible stability margins of the controller in terms of gain margin (GM), phase margin (PM), and the gain roll-off slope at the gain crossover frequency, as a first step. Closed-form expressions are then derived to relate the controller specifications to the controller parameters. The plant model considered includes the bandwidth limitation of the actuator (i.e. power amplifier and EMB). The proposed controller procedure ensures sensitivity and maximum displacement, as specified by relevant ISO standards. The stability margins are ensured over the complete range of variation in plant parameters. The controller is shown to reject disturbance forces due to inevitable rotor mass unbalance. The proposed procedure is applied to design a position controller for a radial EMB with a load capacity of 180 N, and is verified through simulations. Furthermore, the controller design procedure is validated through both simulations and experiments in the context of one-degree-of-freedom position control for a shaft with a mass of 2.285 kg.

Position control of the EMB, which is an unstable system, requires high-bandwidth control of the EMB coil currents. This, in turn, requires high-switching-frequency power amplifiers to feed the coils. An SiC device-based asymmetric H-bridge converter of 300V, 10 A, with a switching frequency of 50 kHz, is designed and tested. Protection of power devices against short circuits is critical for the reliability of power electronic converters. SiC MOSFETs, known for their fast switching, have a shorter short-circuit-withstanding-time (SCWT) than the IGBTs. Device voltage sensing-based Desat protection, commonly used for IGBTs, can also be employed to protect SiC MOSFETs. An evaluation of a gate driver and its ability to protect SiC MOSFETs against various fault conditions is presented. The evaluation includes testing over a wide range of DC bus voltages, fault inductance values, different gate resistors, and load currents. Additionally, hard switching fault (HSF) and fault under load (FUL) tests are performed on the power amplifier to assess the converter's fault-tolerant capabilities. The power amplifier, equipped with an advanced gate driver, successfully detects and clears faults of HSF type within 200 ns and of FUL type well within 100 ns.

A novel test rig is developed for the comprehensive characterization of electromagnetic bearings (EMBs). Design of different components and sub-assemblies of the test rig are detailed, highlighting its versatility and capabilities. The assembly of the test rig for static characterization of radial EMB and that of axial EMB are discussed. The current-controlled power amplifier is an integral part of the test rig, which provides the dynamic current required to drive the EMB coils under various testing conditions. The coil currents that need to be injected under different dynamic conditions are obtained through system-level simulations of the EMB. The capability of the current-controlled power amplifier to inject such currents or to track such current references is demonstrated experimentally.