Publications

Catcher bearings (CBs) or auxiliary bearings provide mechanical backup protection in the events of magnetic bearing failure. This paper presents numerical analysis for a rotor drop on CBs and following thermal growths due to their mechanical rub using detailed CB and damper models. The detailed CB model is determined based on its material, geometry, speed and preload using the nonlinear Hertzian load–deflection formula, and the thermal growths of bearing components during the rotor drop are estimated using a 1D thermal model. A finite-element squeeze film damper provides the pressure profile of an annular oil film and the resulting viscous damping force. Numerical simulations of an energy storage flywheel with magnetic suspensions failed reveal that an optimal CB design using the detailed simulation models stabilizes the rotor drop dynamics and lowers the thermal growths while preventing the high-speed backward whirl. Furthermore, CB design guides based on the simulation results are presented.

 

Rotor Drop and Following Thermal Growth Simulations Using Detailed Auxiliary Bearing and Damper Models

An approach is presented for the analysis and design of magnetic suspension systems with large flexible rotordynamics models including dynamics, control, and simulation. The objective is to formulate and synthesize a large-order, flexible shaft rotordynamics model for a flywheel supported with magnetic bearings. A finite element model of the rotor system is assembled and then employed to develop a magnetic suspension compensator to provide good reliability and disturbance rejection. Stable operation over the complete speed range and optimization of the closed-loop rotordynamic properties are obtained via synthesis of eigenvalue analysis, Campbell plots, waterfall plots, and mode shapes. The large order of the rotor model and high spin speed of the rotor present a challenge for magnetic suspension control. A flywheel system is studied as an example for realizing a physical controller that provides stable rotor suspension and good disturbance rejection in all operating states. The baseline flywheel system control is determined from extensive rotordynamics synthesis and analysis for rotor critical speeds, mode shapes, frequency responses, and time responses.

 

Control of flexible rotor systems with active magnetic bearings

Jet engines may experience severe vibration due to the sudden imbalance caused by blade failure. The current research investigates employment of piezoelectric actuators to suppress this using active vibration control. This requires identification of the source of the vibrations via an expert system, determination of the required phase angles and amplitudes for the correction forces, and application of the desired control signals to the piezoelectric actuators. Correction forces may exceed the physical limitations of the actuators; hence results of ‘‘constrained force’’ quadratic programming, least squares and multi-point correction algorithms will be compared. It is demonstrated that simply scaling down the least squares predicted correction forces to satisfy the actuator saturation constraints does not necessarily yield optimal reductions in vibration. In this paper test results are shown for sudden imbalance, and the computational time requirements and balancing effectiveness for the various approaches are compared.

 

CONSTRAINED QUADRATIC PROGRAMMING, ACTIVE CONTROL OF ROTATING MASS IMBALANCE

A pressure-based computational fluid dynamics (CFD) code is employed to calculate the flow field and rotordynamic forces in a whirling, grooved liquid annular seal. To validate the capabilities of the CFD code for this class of problems, comparisons of basic fluid dynamic parameters are made to three-dimensional laser Doppler anemometer (LDA) measurements for a spinning, centered grooved seal. Predictions are made using both a standard and low Reynolds number K-B turbulence model. Comparisons show good overall agreement of the axial and radial velocities in the through flow jet, shear layer, and recirculation zone. The tangential swirl velocity is slightly under-predicted as the flow passes through the seal. By generating an eccentric three-dimensional, body fitted mesh of the geometry, a quasi-steady solution may be obtained in the whirling reference frame allowing the net reaction force to be calculated for different whirl frequency ratios, yielding the rotordynamic force coefficients. Comparisons are made to the rotordynamic force measurements for a grooved liquid annular seal. The CFD predictions show improved stiffness prediction over traditional multi-control volume, bulk flow methods over a wide range of operating conditions. In cases where the flow conditions at the seal inlet are unknown, a twodimensional, axisymmetric CFD analysis may be employed to efficiently calculate these boundary conditions by including the upstream region leading to the seal. This approach is also demonstrated in this study.

 

CFD Comparison to 3D Laser Anemometer and Rotordynamic Force Measurements for Grooved Liquid Annular Seals

A code for designing magnetic bearings is described. The code generates curves from magnetic circuit equations relating important bearing performance parameters, Bearing parameters selected from the curves by a designer to meet the requirements of a particular application are input directly by the code into a three dimensional finite element analysis preprocessor. This means that a three dimensional computer model of the bearing being developed is immediately available for viewing. The finite element model solution can be used to show areas of magnetic saturation and make more accurate predictions of the bearing load capacity, current stiffness, position stiffness, and inductance than the magnetic circuit equations did at the start of the design process. In summary the code combines one dimensional and three dimensional modeling methods for designing magnetic bearings.

 

An integrated magnetic circuit model and finite element model approach to magnetic bearing design

Advanced energy storage systems for electric guns and other pulsed weapons on combat vehicles present significant challenges for rotor bearing design. Active magnetic bearings (AMB’s) present one emerging bearing option with major advantages in terms of lifetime and rotational speed, and also favorably integrate into high-speed flywheel systems. The Department of Defense Combat Hybrid Power Systems (CHPS) program serves as an excellent case study for magnetic bearing applications on combat vehicles. Under the sponsorship of the CHPS program, The University of Texas at Austin Center for Electromechanics (UT-CEM) has designed active magnetic bearing actuators for use in a 5 MW flywheel alternator with a 318 kg (700 lb), 20 000 rpm rotor. The flywheel alternator serves as a power supply for multiple systems on a military vehicle, including mobility load leveling and weapons systems. Because of continuous duty requirements, magnetic bearings were chosen for this high-speed application to minimize losses and to enable the flywheel to meet a planned vehicle life of 15 to 25 years. To minimize CHPS flywheel size and mass, a topology was chosen in which the rotating portion of the flywheel is located outside the stationary components. Accordingly, magnetic bearing actuators are required which share this “inside–out” configuration. Because of inherent low loss and nearly linear force characteristics, UT-CEM has designed and analyzed permanent magnet bias bearing actuators for this application. To verify actuator performance, a nonrotating bearing test fixture was designed and built which permits measurement of static and dynamic force. An active magnetic bearing (AMB) control system was designed to provide robust, efficient magnetic levitation of the CHPS rotor over a wide range of operating speeds and disturbance inputs, while minimizing the occurrence of backup bearing touchdowns. This paper discusses bearing system requirements, actuator and controller design, and predicted performance; it also compares theoretical vs. measured actuator characteristics.

 

Active magnetic bearings for energy storage systems for combat vehicles

The paper provides an overview of many areas of the flywheel magnetic suspension (MS) R&D being performed at the Texas A&M Vibration Control and Electromechanics Lab (TAMU-VCEL). This includes system response prediction, actuator optimization and redundancy, controller realizations and stages, sensor enhancements and backup bearing reliability

 

Flywheel magnetic suspension developments

Theoretical predictions were made for the dynamic performance of a tangential flux magnetic thrust bearing. A prototype bearing was built with the stators and rotors made from tape wound strip. The performance of this bearing was measured and compared to the theoretical predictions and also to the performance of a radial flux thrust bearing. Tangential flux bearings are intrinsically amenable to construction from tape wound cores. Tape wound cores come in high saturation alloys like supermenduer which can give the bearing a high force to size ratio. The thin tape laminates give the bearing a broad frequency bandwidth. By comparison it is shown that it is difficult to make a laminated rotor magnetically efficient for radial flux bearings. A test rig is described that was built to measure the performance of the tangential flux bearing. A power amplifier with current feedback provided dc and harmonic current to the coils. A load cell was built into the test rig to measure the axial thrust, an inductive/hall sensor was included to measure the coil current, and a hall probe to measure the gap flux.

 

Comparison of the dynamic response of radial and tangential magnetic flux thrust bearings

Catcher bearings (CB) are an essential component for rotating machine with active magnetic bearings (AMBs) suspensions. The CB’s role is to protect the magnetic bearing and other close clearance component in the event of an AMB failure. The contact load, the Hertzian stress, and the sub/surface shear stress between rotor, races, and balls are calculated, using a nonlinear ball bearing model with thermal growth, during the rotor drop event. Fatigue life of the CB in terms of the number of drop occurrences prior to failure is calculated by applying the Rainflow Counting Algorithm to the sub/surface shear stress-time history. Numerical simulations including high fidelity bearing models and a Timoshenko beam finite element rotor model show that CB life is dramatically reduced when high-speed backward whirl occurs. The life of the CB is seen to be extended by reducing the CB clearances, by applying static side-loads to the rotor during the drop occurrence, by reducing the drop speed, by reducing the support stiffness and increasing the support damping and by reducing the rotor (journal)—bearing contact friction.

 

Catcher Bearing Life Prediction Using a Rainflow Counting Approach

The purpose of this paper is to present a methodology to predict vibrations of drilllstrings for oil recovery service. The paper extends a previous model in the literature to include drill collar flexibility utilizing a modal coordinate condensed, finite element approach. The nonlinear effects of drillstring / borehole contact, friction and quadratic damping are included. Bifurcation diagrams are presented to illustrate the effects of speed, friction, stabilizer gap and drill collar length on chaotic vibration response. A study is conducted on factors for improving the accuracy of Lyapunov Exponents to predict the presence of chaos. This study considers the length of time to steady state, the number and duration of linearization sub-intervals, the presence of rigid body modes and the number of finite elements and modal coordinates. The results may be helpful for computing Lyapunov exponents of other types of nonlinear vibrating systems with many degrees of freedom.

 

A MODAL APPROACH FOR CHAOTIC VIBRATIONS OF A DRILLSTRING