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At least 55 records · Page 3

Enhanced Eddy Activity in the Beaufort Gyre in Response to Sea Ice Loss

The Beaufort Gyre freshwater content has increased since the 1990s, potentially stabilizing in recent years. The mechanisms proposed to explain the stabilization involve either mesoscale eddy activity that opposes Ekman pumping or the reduction of Ekman pumping due to reduced sea ice?ocean surface stress. However, the relative importance of these mechanisms is unclear. Here, we present observational estimates of the Beaufort Gyre mechanical energy budget and show that energy dissipation and freshwater content stabilization by eddies increased in the late-2000s. The loss of sea ice and acceleration of ocean currents after 2007 resulted in enhanced mechanical energy input but without corresponding increases in potential energy storage. To balance the energy surplus, eddy dissipation and its role in gyre stabilization must have increased after 2007. Our results imply that declining Arctic sea ice will lead to an increasingly energetic Beaufort Gyre with eddies playing a greater role in its stabilization.

Armitage, Thomas W.K.↗

Experimental Comparison of Piezoelectric and Magnetostrictive Shunt Dampers

A novel mechanism called the vibration ring is being developed to enable energy conversion elements to be incorporated into the driveline of a helicopter or other rotating machines. Unwanted vibration is transduced into electrical energy, which provides a damping effect on the driveline. The generated electrical energy may also be used to power other devices (e.g., health monitoring sensors). PZT (piezoceramic) and PMN-30PT (single crystal) stacks, as well as a Tb_0.3 Dy_0.7 Fe_1.92 (Terfenol-D) rod with a bias magnet array and a pickup coil, were tested as alternative energy conversion elements to use within the vibration ring. They were tuned for broadband damping using shunt resistors, and dynamic compression testing was conducted in a high-speed load frame. Energy conversion was experimentally optimized at 750Hz by tuning the applied bias stress and resistance values. Dynamic testing was conducted up to 1000Hz to determine the effective compressive modulus, shunt loss factor, internal loss factor, and total loss factor. Some of the trends of modulus and internal loss factor versus frequency were unexplained. The single crystal device exhibited the greatest shunt loss factor whereas the Terfenol-D device had the highest internal and total loss factors. Simulations revealed that internal losses in the Terfenol-D device were elevated by eddy current effects, and an improved magnetic circuit could enhance its shunt damping capabilities. Alternatively, the Terfenol-D device may be simplified to utilize only the eddy current dissipation mechanism (no pickup coil or shunt) to create broadband damping.

energy conversion↗

Experimental Comparison of Piezoelectric and Magnetostrictive Shunt Dampers

A novel mechanism called the vibration ring is being developed to enable energy conversion elements to be incorporated into the driveline of a helicopter or other rotating machines. Unwanted vibration is transduced into electrical energy, which provides a damping effect on the driveline. The generated electrical energy may also be used to power other devices (e.g., health monitoring sensors). PZT (piezoceramic) and PMN-30%PT (single crystal) stacks, as well as a Tb_0.3 Dy_0.7 Fe_1.92 (Terfenol-D) rod with a bias magnet array and a pickup coil, were tested as alternative energy conversion elements to use within the vibration ring. They were tuned for broadband damping using shunt resistors, and dynamic compression testing was conducted in a high-speed load frame. Energy conversion was experimentally optimized at 750Hz by tuning the applied bias stress and resistance values. Dynamic testing was conducted up to 1000Hz to determine the effective compressive modulus, shunt loss factor, internal loss factor, and total loss factor. Some of the trends of modulus and internal loss factor versus frequency were unexplained. The single crystal device exhibited the greatest shunt loss factor whereas the Terfenol-D device had the highest internal and total loss factors. Simulations revealed that internal losses in the Terfenol-D device were elevated by eddy current effects, and an improved magnetic circuit could enhance its shunt damping capabilities. Alternatively, the Terfenol-D device may be simplified to utilize only the eddy current dissipation mechanism (no pickup coil or shunt) to create broadband damping.

piezoelectric↗

Qualifying the Sunpower M87N Cryocooler for Operation in the AMS-02 Magnetic Field

The Alpha Magnetic Spectrometer-02 (AMs-02) experiment uses a superfluid helium dewar to cool a large superconducting magnet. The outer vapor-cooled shields of the dewar are to be held at 80 K by four Sunpower M87N cryocoolers. These cryocoolers have magnetic components that might interact with the external applied field generated by the superconducting magnet, thereby degrading the cryocoolers' performance. Engineering models of the Sunpower M87 have been qualified for operation in a magnetic environment similar to the AMs-02 magnetic environment. Although there was no noticeable performance degradation at field levels that were comparable to AMs-02 field levels, there appears to be a small performance degradation at higher field levels. It was theorized that there were three possible issues related to these performance losses at high magnetic fields: i) induced piston rubbing on the cylinder wall due to forces and torques on the linear motor due to the applied magnetic fields; ii) Magnetic hysteretic and/or eddy current damping of the balancer due to its motion in the applied magnetic fields; iii) Inductance losses in motor due to the applied magnetic field. The experiments conducted at the Massachusetts Institute of Technology (MIT) cyclotron facility in June 2002 were designed to test these. Tests were performed over a range of field levels that were lower, comparable, and higher than the field levels that the cryocoolers will experience in the AMs-02 operating environment. This paper describes the experiments and the inferences derived from them.

Mustafi, Shuvo↗

In-situ measurements of alloy oxidation/corrosion/erosion using a video camera and proximity sensor with microcomputer control

Two noncontacting and nondestructive, remotely controlled methods of measuring the progress of oxidation/corrosion/erosion of metal alloys, exposed to flame test conditions, are described. The external diameter of a sample under test in a flame was measured by a video camera width measurement system. An eddy current proximity probe system, for measurements outside of the flame, was also developed and tested. The two techniques were applied to the measurement of the oxidation of 304 stainless steel at 910 C using a Mach 0.3 flame. The eddy current probe system yielded a recession rate of 0.41 mils diameter loss per hour and the video system gave 0.27.

Deadmore, D. L.↗

Flux focusing eddy current probe

A flux-focusing electromagnetic sensor which uses a ferromagnetic flux-focusing lens simplifies inspections and increases detectability of fatigue cracks and material loss in high conductivity material. The unique feature of the device is the ferrous shield isolating a high-turn pick-up coil from an excitation coil. The use of the magnetic shield is shown to produce a null voltage output across the receiving coil in the presence of an unflawed sample. A redistribution of the current flow in the sample caused by the presence of flaws, however, eliminates the shielding condition and a large output voltage is produced, yielding a clear unambiguous flaw signal. The maximum sensor output is obtained when positioned symmetrically above the crack. Hence, by obtaining the position of the maximum sensor output, it is possible to track the fault and locate the area surrounding its tip. The accuracy of tip location is enhanced by two unique features of the sensor; a very high signal-to-noise ratio of the probe's output which results in an extremely smooth signal peak across the fault, and a rapidly decaying sensor output outside a small area surrounding the crack tip which enables the region for searching to be clearly defined. Under low frequency operation, material thinning due to corrosion damage causes an incomplete shielding of the pick-up coil. The low frequency output voltage of the probe is therefore a direct indicator of the thickness of the test sample.

Simpson, John W.↗

Parametric study of power absorption from electromagnetic waves by small ferrite spheres

Algebraic expressions in terms of elementary mathematical functions are derived for power absorption and dissipation by eddy currents and magnetic hysteresis in ferrite spheres. Skin depth is determined by using a variable inner radius in descriptive integral equations. Numerical results are presented for sphere diameters less than one wavelength. A generalized power absorption parameter for both eddy currents and hysteresis is expressed in terms of the independent parameters involving wave frequency, sphere radius, resistivity, and complex permeability. In general, the hysteresis phenomenon has a greater sensitivity to these independent parameters than do eddy currents over the ranges of independent parameters studied herein. Working curves are presented for obtaining power losses from input to the independent parameters.

Englert, Gerald W.↗

Modeling and Analysis of Stirling Power Convertors

Modeling and Analysis of Stirling Power Convertors Luis A. Rodriguez1 Steven M. Geng, Terry V. Reid, Scott D. Wilson NASA Glenn Research Center, Cleveland, OH, 44135, USA NASA Glenn’s Thermal Energy Conversion Branch is supporting the development of the next generation free-piston Stirling power convertors. American Superconductor (AMSC) and Sunpower Inc. are the two firms under contract to develop the Flexure Isotope Stirling Convertor (FISC) and the Sunpower Robust Stirling Convertor (SRSC), respectively. To comprehend and forecast convertor performance, Sage, ANSYS® Maxwell, and ANSYS® Fluent were used to model the Stirling thermodynamic cycle, alternator electromagnetics, and piston and displacer dynamics. I. Introduction Stirling convertors are being developed by NASA as a potential steady source of electrical power for NASA’s future scientific space missions. Currently, NASA Glenn Research Center has two corporations under contract, American Superconductor (AMSC) and Sunpower Inc., for the development of the next generation of free-piston Stirling convertors for dynamic radioisotope power systems. AMSC is developing the Flexure Isotope Stirling Convertor (FISC), which uses flexures to prevent side motion and rubbing of the piston. Similarly, Sunpower Inc, is developing the Sunpower Robust Stirling Convertor (SRSC). The SRSC uses gas bearings to prevent radial contact of the moving piston. As convertor development continues, it is increasingly important to understand and predict the interactions of components in the system, how they respond to one another, and how they perform as a response to changes in operating conditions. A suitable and enlightening way to demonstrate and foresee these interactions is with the use of accurate modeling software. Sage, ANSYS® Maxwell, and ANSYS® Fluent are the current modeling tools used by NASA to analytically determine convertor performance. Sage is a one-dimensional object-oriented commercial software package used for modeling and optimizing Stirling convertors for Dynamic Radioisotope Power Systems (DRPS) and it is one of the most accurate Stirling convertor codes in use by NASA. This code is the successor to GLIMPS (Globally-Implicit Stirling Cycle Simulation) and GLOP (GLIMPS Optimization) software created by Gedeon Associates [1]. Model input parameters are typically material/gas type, component physical dimensions, temperatures, frequency, charge pressure, and number of time/space nodes. Sage is used to model both the FISC’s and SRSC’s Stirling cycle thermodynamics and piston/displacer dynamics. Performance maps were created and analyzed for both power systems to better understand the relationship between the following conditions: cold-end temperature, hot-end temperature, piston/displacer amplitudes, pressure drop, and thermal input power. The synergy between these conditions will help determine parameter sensitivity. ANSYS® Maxwell was used to create a three-dimensional (3-D) axisymmetric model for both FISC and SRSC alternators. The significant physical components included in each model are the magnets, magnet carrier, outer/inner laminations, and the coil. Inputs to the model are piston amplitude, piston frequency, alternator load, coil resistance, tuning capacitance, and specific material properties. The alternator models calculate terminal voltage, current, piston/current phase, voltage/current phase, coil inductance, terminal power and efficiency. The RI2 losses, core (hysteresis and eddy) losses, and magnet/can eddy losses are also a part of the final results. ANSYS® Fluent is used to build 3-D computational fluid dynamic (CFD) models to examine the Stirling cycle thermodynamics for both the FISC and SRSC systems. Three-dimensional Computer Aided Design (CAD) models were used to create the physical components of each convertor. Steady-state simulations were conducted for hardware testing, prediction of environmental losses during testing, and generation of radiation look-up tables. The model inputs to the aforementioned analysis are the material properties and boundary thermal conditions. The steady-state model calculates temperature and heat flow distributions. Transient 3-D calculations were also part of the CFD analysis. In this study a physically reduced version of the FISC is used to obtain a prediction of available engine power. For the gas bearing SRSC, the transient effort is used to obtain a prediction of bearing pad performance and its sensitivity to micro-channel geometric variation. The model inputs to the transient simulations are the piston amplitude, displacer amplitude, frequency, displacer/piston phase angle, dynamic deforming CFD grid, temperature boundary conditions, and user defined files describing motion profile of piston/displacer. The results of the model are temperature distributions, heat distributions, and PV power produced at pre-determined conditions.

Luis A Rodriguez↗

Eddy Current Method for Fatigue Testing

Flux-focusing electromagnetic sensor using a ferromagnetic flux-focusing lens simplifies inspections and increases detectability of fatigue cracks and material loss in high conductivity material. A ferrous shield isolates a high-turn pick-up coil from an excitation coil. Use of the magnetic shield produces a null voltage output across the receiving coil in presence of an unflawed sample. Redistribution of the current flow in the sample caused by the presence of flaws. eliminates the shielding condition and a large output voltage is produced, yielding a clear unambiguous flaw signal. Maximum sensor output is obtained when positioned symmetrically above the crack. By obtaining position of maximum sensor output, it is possible to track the fault and locate the area surrounding its tip. Accuracy of tip location is enhanced by two unique features of the sensor; a very high signal-to-noise ratio of the probe's output resulting in an extremely smooth signal peak across the fault, and a rapidly decaying sensor output outside a small area surrounding the crack tip enabling the search region to be clearly defined. Under low frequency operation, material thinning due to corrosion causes incomplete shielding of the pick-up coil. Low frequency output voltage of the probe is therefore a direct indicator of thickness of the test sample. Fatigue testing a conductive material is accomplished by applying load to the material, applying current to the sensor, scanning the material with the sensor, monitoring the sensor output signal, adjusting material load based on the sensor output signal of the sensor, and adjusting position of the sensor based on its output signal.

Simpson, John W.↗

Nondestructive Determination of Heat/Fire Damage to Polymer- Matrix Composites Using Obliquely Insonified Ultrasonic Waves

Heat and fire damage to composite structures cause loss of strength that cannot be detected by current NDE methods unless physical damage occurs. Further, there is a lack of fundamental understanding of the mechanism of damage from thermal exposure of organic matrix composites to elevated temperatures. Information compiled from field reports and lab experiments increasingly suggests that there is material degradation and it is not necessarily involved with the introduction of physical defects. In recent years, various researchers examined the potential to identifying thermal degradation to organic matrix composites prior to delamination. The methods that were used include: ultrasonics, backscattered X-ray, eddy current, thermography, drift and LPF spectroscopies, acousto-ultrasonics and hardness testing. None of these methods were able to correlate NDE results with loss of mechanical properties.

polymer-matrix composite fire damage NDE nondestru↗

Flux-focusing eddy current probe and method for flaw detection

A flux-focusing electromagnetic sensor which uses a ferromagnetic flux-focusing lens simplifies inspections and increases detectability of fatigue cracks and material loss in high conductivity material is presented. The unique feature of the device is the ferrous shield isolating a high-turn pick-up coil from an excitation coil. The use of the magnetic shield is shown to produce a null voltage output across the receiving coil in the presence of an unflawed sample. A redistribution of the current flow in the sample caused by the presence of flaws, however, eliminates the shielding condition and a large output voltage is produced, yielding a clear unambiguous flaw signal. The maximum sensor output is obtained when positioned symmetrically above the crack. Hence, by obtaining the position of the maximum sensor output, it is possible to track the fault and locate the area surrounding its tip. The accuracy of tip location is enhanced by two unique features of the sensor; a very high signal-to-noise ratio of the probe's output which results in an extremely smooth signal peak across the fault, and a rapidly decaying sensor output outside a small area surrounding the crack tip which enables the region for searching to be clearly defined. Under low frequency operation, material thinning due to corrosion damage causes an incomplete shielding of the pick-up coil. The low frequency output voltage of the probe is therefore a direct indicator of the thickness of the test sample.

Simpson, John W.↗

Continued Development of Meandering Winding Magnetometer (MWM (Register Trademark)) Eddy Current Sensors for the Health Monitoring, Modeling and Damage Detection of Composite Overwrapped Pressure Vessels

Composite Overwrapped Pressure Vessels (COPVs) are used in essentially all NASA spacecraft, launch. vehicles and payloads to contain high-pressure fluids for propulsion, life support systems and science experiments. Failure of any COPV either in flight or during ground processing would result in catastrophic damage to the spacecraft or payload, and could lead to loss of life. Therefore, NASA continues to investigate new methods to non-destructively inspect (NDE) COPVs for structural anomalies and to provide a means for in-situ structural health monitoring (SHM) during operational service. Partnering with JENTEK Sensors, engineers at NASA, Kennedy Space Center have successfully conducted a proof-of-concept study to develop Meandering Winding Magnetometer (MWM) eddy current sensors designed to make direct measurements of the stresses of the internal layers of a carbon fiber composite wrapped COPV. During this study three different MWM sensors were tested at three orientations to demonstrate the ability of the technology to measure stresses at various fiber orientations and depths. These results showed good correlation with actual surface strain gage measurements. MWM-Array technology for scanning COPVs can reliably be used to image and detect mechanical damage. To validate this conclusion, several COPVs were scanned to obtain a baseline, and then each COPV was impacted at varying energy levels and then rescanned. The baseline subtracted images were used to demonstrate damage detection. These scans were performed with two different MWM-Arrays. with different geometries for near-surface and deeper penetration imaging at multiple frequencies and in multiple orientations of the linear MWM drive. This presentation will include a review of micromechanical models that relate measured sensor responses to composite material constituent properties, validated by the proof of concept study, as the basis for SHM and NDE data analysis as well as potential improvements including design changes to miniaturize and make the sensors durable in the vacuum of space

Russell, Richard↗

Aerodynamic loss generation in a low-pressure turbine stage with high lift blading

The present work aims to investigate the loss generation mechanisms in a highly loaded low-pressure turbine (LPT) stage. The turbine employs high-lift airfoils to reduce the number of blades and therefore the overall engine weight. Large Eddy Simulation (LES) is applied to study the detailed flow fields at two representative Reynolds numbers (150,000 and 40,000). The calculated flow fields are compared with available measured data. LES calculates the measured aerodynamic performance of the current turbine stage well. Both the measurements and the CFD simulations indicate that most of the aerodynamic loss is generated by the development of secondary flows near the rotor hub. An area of low momentum and high aerodynamic loss forms at roughly 25 % span above the hub downstream of the rotor. Formation and migration of a vortex system near the hub is the primary source of the loss generation. The hub wall vortex system in this highly loaded turbine stage is quite different from the horse-shoe vortex system in a typical stationary turbine cascade. Calculated instantaneous and time-averaged flow fields at two Reynolds numbers are examined in detail to study Reynolds number effects on the turbine stage performance. Steady and unsteady flow separation on the rotor suction side is calculated at both high and low Reynolds numbers. At the lower Reynolds number of 40,000, thicker blade boundary layers increase the area of flow separation on the rotor suction side, resulting in a 1.9 % increase in aerodynamic loss compared to the higher Reynolds number case.

low pressure turbine↗

Dynamic Characterization of Galfenol (Fe81.6Ga18.4)

Galfenol has the potential to transform the smart materials industry by allowing for the development of multifunctional, load-bearing devices. One of the primary technical challenges faced by this development is the very limited experimental data on Galfenol's frequency-dependent response to dynamic stress, which is critically important for the design of such devices. This report details a novel and precise characterization of the constitutive behavior of polycrystalline Galfenol (Fe81.6Ga18.4) under quasi-static (1 Hz) and dynamic (4 to 1000 Hz) stress loadings. Mechanical loads are applied using a high-frequency load frame. Quasi-static minor and major hysteresis loop measurements of magnetic flux density and strain are presented for constant electromagnet currents (0 to 1.1 A) and constant magnetic fields 0 to 14 kA/m (0 to 180 Oe). The dynamic stress amplitude for minor and major loops is 2.88 and 31.4 MPa (418 and 4550 psi), respectively. Quasi-static material properties closely match published values for similar Galfenol materials. Quasi-static actuation responses are also measured and compared to quasi-static sensing responses; the high degree of reversibility seen in the comparison is consistent with published measurements and modeling results. Dynamic major and minor loops are measured for dynamic stresses up to 31 MPa (4496 psi) and 1 kHz, and the bias condition resulting in maximum, quasi-static sensitivity. Eddy current effects are quantified by considering solid and laminated Galfenol rods. Three key sources of error in the dynamic measurements are accounted for: (1) electromagnetic noise in strain signals due to Galfenol's magnetic response, (2) error in load signals due to the inertial force of fixturing, and (3) phase misalignment between signals due to conditioning electronics. For dynamic characterization, strain error is kept below 1.2 percent of full scale by wiring two collocated gauges in series (noise cancellation) and through leadwire weaving. Inertial force error is kept below 0.41 percent by measuring the dynamic force in the specimen using a nearly collocated piezoelectric load washer. The phase response of all conditioning electronics is explicitly measured and corrected for. In general, as frequency is increased, the sensing response becomes more linear because of an increase in eddy currents. As frequency increases above approximately 100 Hz, the elbow in the strain-versus-stress response disappears as the active (soft) regime stiffens toward the passive (hard) regime. Under constant-field conditions, the loss factors of the solid rod peak between 200 and 600 Hz, rather than exhibiting a monotonic increase. Compared to the solid rod, the laminated rod exhibits much slower increases in hysteresis with frequency, and its quasi-static behavior extends to higher frequencies. The elastic modulus of the laminated rod decreases between 100 and 300 Hz; this trend is currently unexplained.

Dynamic sensing↗

Advanced analysis technique for the evaluation of linear alternators and linear motors

A method for the mathematical analysis of linear alternator and linear motor devices and designs is described, and an example of its use is included. The technique seeks to surpass other methods of analysis by including more rigorous treatment of phenomena normally omitted or coarsely approximated such as eddy braking, non-linear material properties, and power losses generated within structures surrounding the device. The technique is broadly applicable to linear alternators and linear motors involving iron yoke structures and moving permanent magnets. The technique involves the application of Amperian current equivalents to the modeling of the moving permanent magnet components within a finite element formulation. The resulting steady state and transient mode field solutions can simultaneously account for the moving and static field sources within and around the device.

Holliday, Jeffrey C.↗

Transpiration and film cooling boundary layer computer program. Volume 1: Numerical solutions of the turbulent boundary layer equations with equilibrium chemistry

A finite difference turbulent boundary layer computer program has been developed. The program is primarily oriented towards the calculation of boundary layer performance losses in rocket engines; however, the solution is general, and has much broader applicability. The effects of transpiration and film cooling as well as the effect of equilibrium chemical reactions (currently restricted to the H2-O2 system) can be calculated. The turbulent transport terms are evaluated using the phenomenological mixing length - eddy viscosity concept. The equations of motion are solved using the Crank-Nicolson implicit finite difference technique. The analysis and computer program have been checked out by solving a series of both laminar and turbulent test cases and comparing the results to data or other solutions. These comparisons have shown that the program is capable of producing very satisfactory results for a wide range of flows. Further refinements to the analysis and program, especially as applied to film cooling solutions, would be aided by the acquisition of a firm data base.

Levine, J. N.↗

Effects of Unsteady Flow Interactions on the Performance of a Highly-Loaded Transonic Compressor Stage

The primary focus of this paper is to investigate the loss sources in an advanced GE transonic compressor design with high reaction and high stage loading. This advanced compressor has been investigated both experimentally and analytically in the past. The measured compressor efficiency is significantly lower than the efficiency calculated with various existing tools based on RANS and URANS. The general understanding is that some important flow physics in this modern compressor design are not represented in the current tools. To pinpoint the source of the efficiency miss, an advanced test with detailed flow traverse was performed for the front one and a half stage at the NASA Glenn Research Center. In the present paper, a Large Eddy Simulation (LES) is employed to determine whether a higher-fidelity simulation can pick up any additional flow physics that can explain past efficiency miss with RANS and URANS. The results from the Large Eddy Simulation were compared with the NASA test results and the GE interpretation of the test data. LES calculates lower total pressure and higher total temperature on the pressure side of the stator, resulting in large loss generation on the pressure side of the stator. On the other hand, existing tools based on the RANS and URANS do not calculate this high total temperature and low total pressure on the pressure side of the stator. The calculated loss through the stator from LES seems to match the measured data and the GE data interpretation. Detailed examination of the unsteady flow field from LES indicates that the accumulation of high loss near the pressure side of the stator is due to the interaction of the rotor wake with the stator blade. The strong rotor wake interacts quite differently with the pressure side of the stator than with the suction side of the stator blade. The concave curvature on the pressure side of the stator blade increases the mixing of the rotor wake with the pressure side boundary layer significantly. On the other hand, the convex curvature on the suction side of the stator blade decreases the mixing and the suction side blade boundary layer remains thin. The jet velocity in the rotor wake in the stator frame seems to magnify the curvature effect in addition to inviscid redistribution of wake fluid toward the pressure side of the blade.

LES↗

Linear and Nonlinear Analysis of Magnetic Bearing Bandwidth Due to Eddy Current Limitations

Finite element analysis was used to study the bandwidth of alloy hyperco50a and silicon iron laminated rotors and stators in magnetic bearings. A three dimensional model was made of a heteropolar bearing in which all the flux circulated in the plane of the rotor and stator laminate. A three dimensional model of a plate similar to the region of a pole near the gap was also studied with a very fine mesh. Nonlinear time transient solutions for the net flux carried by the plate were compared to steady state time harmonic solutions. Both linear and quasi-nonlinear steady state time harmonic solutions were calculated and compared. The finite element solutions for power loss and flux bandwidth were compared to those determined from classical analytical solutions to Maxwell's equations.

Kenny, Andrew↗