Publications

This paper presents an approach for blade loss simulation including thermal growth effects for a dual-rotor gas turbine engine supported on bearing and squeeze film damper. A nonlinear ball bearing model using the Hertzian formula predicts ball contact load and stress, while a simple thermal model estimates the thermal growths of bearing components during the blade loss event. The modal truncation augmentation method combined with a proposed staggered integration scheme is verified through simulation results as an efficient tool for analyzing a flexible dual-rotor gas turbine engine dynamics with the localized nonlinearities of the bearing and damper, with the thermal growths and with a flexible casing model. The new integration scheme with enhanced modeling capability reduces the computation time by a factor of 12, while providing a variety of solutions with acceptable accuracy for durations extending over several thermal time constants.

 

Long duration blade loss simulations including thermal growths for dual-rotor gas turbine engine

Conventional use of magnetic bearings relies on a zero reference to keep the rotor centered in the radial and axial axes. This paper compares different control methods developed for the alternate control task of tracking an axial dynamic target. Controllers based on fuzzy logic, sliding mode, and direct linearization were designed to meet this task. Performance criteria, such as maximum axial displacement, minimum phase lag and I^2 R power losses were compared for each controller. The large motion, tracking problem for a rotor has utility in applications where dynamic seal clearances are required. This has a variety of potential applications in turbo-machinery, such as active stall control.

 

Large motion tracking control for thrust magnetic bearings with fuzzy logic, sliding mode, and direct linearization

An energy-storage flywheel consists of a large inertia wheel sharing a common shaft with a motor generator (MG) set and with magnetic bearings to support the entire rotating assembly. Flywheels mounted on a special slug car are charged from the local utility grid and from regenerative-braking events. Usage of these power sources reduces fuel consumption and the related NOx emission by the locomotive-mounted Diesel generator sets (DGS). The flywheel-supplied power can replace the DGS-supplied power in one or more of the eight fixed power settings (notches), plus idle and reverse, which are common to most locomotives either for line-haul or switchyard service. The slug cars have separate traction motors to be driven by the flywheel systems so that the flywheel power and DGS power are electrically and physically decoupled. A system model is presented that includes the train dynamics coupled with the electromechanical models for the flywheels and traction motors. The modified Davis equation is employed in the train model to account for windage and other losses. A novel, feedback-based flux-weakening control of the flywheel’s motor generator current-torque and speed-back electromotive force (emf) gain is employed to increase the charge capacity, depth of discharge, and regenerative-braking efficiency for the flywheels. The simulation results show significant cost- and emissions-reduction potential for the proposed hybrid DGS–flywheel locomotive power system in line-haul and switcher service.

 

Hybrid Train Power with Diesel Locomotive and Slug Car-Based Flywheels for NOx and Fuel Reduction

An objective in the design of high performance machinery is to minimize weight so magnetic bearings are often designed to operate slightly lower than their magnetic material saturation. Further weight reduction in the bearings requires operation in the nonlinear portion of the B-H curve. This necessitates a more sophisticated analysis at the bearing and rotordynamic system levels during the design stage. This paper addresses this problem in a unique manner by developing a fully nonlinear homopolar magnetic bearing model. The nonlinear dynamics of a permanent magnet-biased homopolar magnetic bearing (PMB HoMB) system with a flexible rotor is analyzed. Nonlinear effects due to power amplifier voltage and current saturation and position dependent reluctances are also included in the
model. A new curve fit model of the B-H curve is shown to have significantly better agreement with the measured counterpart than conventional piecewise linear. The modified Langmuir method, with a novel correction terms for the weak flux region, is used to form an analytical model of the experimental magnetization curve of Hiperco 50. High static and dynamic loads applied to the rotor force the magnetic bearing to operate in a flux saturated state. The response of the heavily loaded 4-DOF rotor-bearing system shows that limit cycle stability can be achieved due to the magnetic flux saturation or current saturation in the amplifier. The stable limit cycle prevents the linear model instability, creating what is experimentally observed as a “virtual catcher bearing.” To the authors’ knowledge this is
the first explanation of this commonly observed phenomenon

 

Homopolar Magnetic Bearing Saturation Effects on Rotating Machinery Vibration

This paper summarizes the development of a magnetic bearing designed to operate at 1,000F. A novel feature of this high temperature magnetic bearing is its homopolar construction which incorporates state of the art high temperature, 1,000F, permanent magnets. A second feature is its fault tolerance capability which provides the desired control forces with over one-half of the coils failed. The construction and design methodology of the bearing is outlined and test results are shown. The agreement between a 3D finite element, magnetic field based prediction for force is shown to be in good agreement with predictions at room and high temperature. A 5 axis test rig will be complete soon to provide a means to test the magnetic bearings at high temperature and speed.

 

HIGH TEMPERATURE, PERMANENT MAGNET BIASED, FAULT TOLERANT, HOMOPOLAR MAGNETIC BEARING DEVELOPMENT

Open loop, experimental force and power measurements of a radial, redundant-axis, magnetic bearing at temperatures to 1000°F (538°C) and rotor speeds to 15,000 rpm along with theoretical temperature and force models are presented in this paper. The experimentally measured force produced by a single C-core circuit using 22A was 600 lb (2.67 kN) at room temperature and 380 lb (1.69 kN) at 538°C. These values were compared with force predictions based on a one-dimensional magnetic circuit analysis and a thermal analysis of gap growth as a function of temperature. The analysis showed that the reduction of force at high temperature is mostly due to an increase in radial gap due to test conditions, rather than to reduced core permeability. Tests under rotating conditions showed that rotor speed has a negligible effect on the bearing’s static force capacity. One C-core required approximately 340 W of power to generate 190 lb (845 N) of magnetic force at 538°C, however the magnetic air gap was much larger than at room temperature. The data presented are after bearing operation for eleven total hours at 538°C and six thermal cycles.

 

High Temperature Characterization of a Radial Magnetic Bearing for Turbomachinery

This paper presents a fuzzy logic based intelligent control system applied to magnetic bearings. The core in the expert system is fuzzy logic controllers with Mamdani architecture. The fuzzy logic controllers for rub detection and automatic gain scheduling were implemented. The expert system not only provides a means to capture the run time data of the magnetic bearings, to process and monitor the parameters, and to diagnose malfunctions, but also protects the magnetic bearings from rub anomaly and implements the control on a real time basis.

 

Fuzzy logic intelligent control system of magnetic bearings

This paper summarizes the development of a novel magnetic suspension that improves reliability via fault-tolerant operation. The suspension is suitable for flywheels used in satellites and space stations for attitude control and energy storage. Specifically, we show that flux coupling between poles of a homopolar magnetic bearing can deliver desired forces even after termination of coil currents to a subset of “failed poles.” Linear, coordinate-decoupled force voltage relations are also maintained before and after failure by bias linearization. We determined current distribution matrices that adjust the currents and fluxes following a pole set failure for many faulted pole combinations. We used one-dimensional magnetic circuit models with fringe and leakage factors derived from detailed, three-dimensional finite-element field models to obtain the current distribution matrices and the system response. Reliability is based on the success criterion that catcher bearing-shaft contact does not occur after pole failures. The magnetic bearing reliability is improved by increasing the number of the radial poles. An advantage of our method over other redundant approaches is a significantly reduced requirement for backup hardware such as additional actuators or power amplifiers.

 

Fault-tolerant homopolar magnetic bearings

An equivalent magnetic circuit of an eight-pole heteropolar magnetic bearing with path reluctances is developed with nondimensional forms of flux, flux density, and magnetic force equations. The results show that fluxes and magnetic forces are considerably reduced for the magnetic circuit with relatively large path reluctances. A Lagrange multiplier optimization method is used to determine current distribution matrices for the magnetic bearing with large path reluctances. A cost function is defined in a manner that represents load capacity in a specific direction. Optimizing this cost function yields distribution matrices calculated for certain combinations of five poles failed out of eight poles. Position stiffnesses and voltage stiffnesses are calculated for the fault-tolerant magnetic bearings. Fault-tolerant control of a horizontal rigid rotor supported on multiple-coil failed magnetic bearings including large path reluctances is simulated to investigate the effect of path reluctances on imbalance response.

 

Fault tolerance of magnetic bearings with material path reluctances and fringing factors

Electromechanical modeling of a hybrid piezohydraulic actuator system for active vibration control was developed. The transfer function of piezoelectric actuator was derived from the electromechanical potential energy law. This transfer function represents the dynamic relationship between input electric voltage and piezoelectric actuator displacement. The hydraulic actuator was characterized by impedance matching in which its transfer functions were experimentally determined. The transfer functions were transformed into a state-space representation, which is easily assembled into an active vibration control (AVC) closed-loop simulation. Good correlation of simulation and test was achieved for the hybrid system. A closed-loop dynamic simulation for imbalance response with/without AVC of a spinning rotor test rig at NASA Lewis was performed and showed excellent agreement with test results. The simulation couples the piezoelectric, hydraulic, and structural (rotor) components.

 

Electromechanical modeling of hybrid piezohydraulic actuator system for active vibration control