Air-gap Function Research Articles

Phase jumps in coupled magnonic waveguides

In this work we present an experimental study of the phase characteristics of magnetostatic quasi-surface waves (MQSW) in a tangentially magnetized yttrium iron garnet (YIG) thin film bilayer. The phase of MQSWs was measured as a function of air gap (g) between two magnonic waveguides. It is shown that the energy exchange between two YIG layers is accompanied by relatively sharp π-radian phase jumps of MQSWs, at specific values of g. The effect was studied at large wavelengths of the MQSWs, and at a propagation distance of 1 cm. The theory predicts that the slope of the phase shift (∂φ/∂g) at submicrometric values of g can be of the order of a few degrees per nm.

Accurate Modeling of a Flywheel Motor Considering Vehicle Start-Up Driving Conditions

The eccentricity type for flywheel motors under vehicle start-up driving conditions is very unique. It is difficult to characterize the air-gap function geometrically. Therefore, the existing methods cannot be used to solve the problem of accurate motor modeling in this case. To solve this problem, an accurate modeling method for flywheel motors considering vehicle start-up driving conditions is proposed in this study. First, the model is divided into two submodules corresponding to two different vehicle start-up driving conditions. Then, the change law for the flywheel motor air gap under vehicle start-up driving conditions is analyzed and summarized by using the curve fitting method. Subsequently, the predictive air-gap function is obtained, and an accurate flywheel motor model is established. Finally, accelerating and turning experiments are conducted, and good experimental results are obtained that show that a model adopting the proposed modeling method has high accuracy.

Analytical modelling of salient pole synchronous generators under eccentricity faults by including stator slotting effect

AbstractHere, a dynamic analytical model is provided for salient pole synchronous generators (SPSGs) under different eccentricity faults. A useful technique is developed first to describe the rotor position‐dependent non‐uniform air gap distribution by a proper function in the healthy state, which includes the stator slotting effect. Then, the exact air gap function is used along with the modified winding function theory to extract non‐integral equations for computing the SPSG various inductances that are playing critical role during analytical modelling and simulation of the machine. Afterword, the air gap function and the inductance equations are modified to include all types of the eccentricity fault. A 3 kW SPSG is simulated and then tested in laboratory under the healthy and the mixed eccentricity (ME) conditions. There are good accordance between the simulation and corresponding experimental results; they show that some harmonic components are introduced in the rotor and the stator currents due to the ME fault whose frequencies are integer multiples of the rotor speed frequency and whose amplitudes increase by increasing the fault severity. The load level change also affects the amplitudes of the harmonics.

Design and Analysis of Dual-Rotor Modular-Stator Hybrid-Excited Axial-Flux Permanent Magnet Vernier Machine

This paper proposes a new structure of the dual-rotor hybrid-excited axial-flux permanent magnet vernier machine (DR-HEAFPMVM) with the modular stator and the consequent-pole PM (CPM) rotor for low-speed, high torque density applications such as in-wheel electric vehicles. The tooth-wound non-overlapping armature windings and direct current (DC) excitation windings are, respectively, arranged in stator main-teeth and split-teeth to obtain the modulated and adjustable air-gap flux densities, resulting in high torque density and outstanding flux-weakening capability. First, the design considerations, operation principles, and air-gap flux density distributions of the proposed machine are elaborated based on the air-gap permeance function. Then, the influence of the pole ratios (PRs) and the DC excitation currents on the main electromagnetic performances of the DR-HEAFPMVM, such as the flux-weakening capability and back-electromotive force (back-EMF), on-load electromagnetic torque, loss distribution, and efficiencies, is investigated using the 3-D finite-element method (FEM). Results verify the feasibility of the flux adjustment of the DC excitation windings equipped in the split-tooth, and the design with a pole ratio of 8/1 tends to have higher torque density, higher machine efficiency, and considerable flux-weakening capability compared with the other two PRs.

Physical modeling of progressive damage and failure of wood-frame coastal residential structures due to surge and wave forces

A physical model study was performed to examine the forces and response of 1:6 scale wood-frame coastal residential structures subjected to storm surge and waves. An on-grade and an elevated specimen were tested and exposed to regular waves with varying water depths and wave heights to simulate typical wave/surge conditions resulting from landfall hurricanes on low-lying barrier islands such as Hurricane Sandy that impacted the US East Coast in 2012 and Hurricane Ike that affected the US Gulf Coast in 2008. Results show that through careful design, wood-frame model specimens can be constructed to have similar strength and stiffness compared to full-scale structures. The two specimens were subjected to increasing surge and wave conditions, and the progressive damage was monitored using LiDAR. The on-grade specimen failed at a lower water level than the elevated specimen as expected. Both specimens showed failure modes consistent with the observed damage of residential structures in Ortley Beach, NJ, after Hurricane Sandy and on the Bolivar Peninsula, TX, after Hurricane Ike. The pressure distribution on the underside of the elevated structure and the resulting vertical forces on the on-grade structure were also examined in this study. The pressure distribution and the resulting vertical forces were significantly affected by water depth, wave height, and air gap. The results indicate that maximum vertical forces are positively correlated to wave height and water depth and negatively correlated to the air gap. The breaking type also affects vertical forces. Nonbreaking waves correlated to relatively small vertical forces, and waves breaking directly on the specimen correlated to peak vertical forces. Accelerometer data showed that the specimen decreased in stiffness during the tests due to progressive damage. An uplift pressure distribution equation was developed for an elevated residential structure as a function of wave height and air gap. The equation is generally conservative when compared to other data sets. The results and data presented in this study increase the current knowledge of the interaction between waves and residential structures, which may be useful to increase the resiliency of coastal communities.

2-D Analytical No-Load Electromagnetic Model for Slotted Interior Permanent Magnet Synchronous Machines

This paper presents a fast analytical model for estimating the components of the PM flux density distribution in the air-gap for a number of interior permanent magnet synchronous machines (IPMSMs). Deriving the two-dimensional (2-D) analytical model for IPMSMs is more challenging compared to that of surface-mounted permanent magnet synchronous machines (SPMSMs) due to the inconsistent geometry of the rotor in polar coordinates. IPMSMs are usually modeled by using 0-D or 1-D methods such as the magnetic equivalent circuit (MEC); however, the MEC method is unable to take into account the tangential component of the magnetic flux density vector. In this paper, a 2-D analytical no-load electromagnetic model for five rotor topologies of IPMSMs is proposed. The effects of the stator slots on the radial component of the PM flux density distribution in the air-gap are then included by defining an air-gap function. The effects of the stator slots on the tangential components of the PM flux density distribution in the air-gap are also considered by injecting virtual surface currents (VSCs) or virtual permanent magnets (VPMs). For verification purposes, the analytical results are compared with those of the finite element method (FEM) and the experimental results of one of the cases.

An Improved Winding Function Theory for Accurate Modeling of Small and Large Air-Gap Electric Machines

An improved winding function theory (IWFT) is presented in this article, which can be also used to calculate the self-inductance and mutual inductance of large air-gap electric machines, while accurately considering the air-gap length function and the magnetic saturation in iron parts, simultaneously. In IWFT, the radial length of flux path in different points inside air gap is calculated using the conformal mappings (CMs). The total air-gap length is the resultant of air-gap length at differential elements in the radial direction. A modified inverse air-gap function is then presented for a typical cage-rotor induction motor (CRIM) and a typical surface permanent magnet synchronous motor (SPMSM), which considers the real paths of flux lines in the slotted air gap. The high accuracy of these modified inverse air-gap functions is verified by comparing with the corresponding results obtained through the finite element method (FEM). To consider the magnetic saturation, a virtual winding function as a 2-D function is introduced in this article, which can consider the magneto-motive force (MMF) drops in iron parts of stator and rotor obtained through the magnetic equivalent circuit (MEC) model. By using IWFT, dependent on the structure of the relevant motor, a 2-D or 3-D lookup table is pre-calculated and stored for self/mutual inductances and their derivatives, and they are then used to model the running condition of CRIM and SPMSM under different loading conditions. Finally, the accuracy of IWFT results is verified by comparing them with the corresponding results obtained through FEM.

A Nonlinear Model for the Rapid Prediction of the Magnetic Field in Eccentric Synchronous Reluctance Machines

This article introduces a novel numerical model for the fast characterization of concentric and eccentric synchronous reluctance motors (SynRMs) used in electric vehicles (EVs) applications. Regarding the high impact of the air gap and permeance function on the modeling accuracy, a step variation function is used to consider the flux barriers' effect on the air gap. Then, different types of eccentricity, including static, dynamic, and mixed eccentricity, are modeled. Besides, this model considers the magnetic saturation and the stator slots effect. Numerical computation for the motor inductances is applied to avoid any approximation in the permeance function. The air-gap flux density, electromagnetic torque, and radial force on the rotor are then calculated. This model can be used for the preliminary design of SynRMs to analyze the motor performance in different conditions and accelerate the design procedure. The model is simply adjustable to different configurations. For instance, a four-pole single-layer distributed winding machine with 36-slot and three-flux barriers per pole is investigated. In order to verify the proposed model, the obtained results are compared with finite-element analysis (FEA) and experimental tests. The accuracy of the proposed model for eccentricities up to 30% is 98%, and for higher degrees, it is about 95%.

Parametrization of in-air spot size as a function of energy and air gap for the ProteusPLUS pencil beam scanning proton therapy system.

The purpose of this study was to parametrize the in-air one sigma spot size for various energies and air gaps in pencil beam scanning (PBS) proton therapy. The current study included range shifters with a water equivalent thickness (WET) of 40mm (RS40) and 75mm (RS75). For RS40, the spot sizes were measured for energies ranging from 80 to 225MeV in increments of 2.5MeV, whereas the air gap was varied from 5 to 25cm in increments of 2.5cm. For RS75, the spot sizes were measured for energies ranging from 120 to 225MeV in increments of 2.5MeV, whereas the air gap was varied from 5 to 35cm in increments of 2.5cm. For both RS40 and RS75, all measurements (n = 1090) were acquired at the isocenter using a Lynx 2D scintillation detector. For RS40, the spot sizes increased from 3.1mm to 10.4mm, whereas the variation in spot sizes for RS75 ranged from 3.3mm to 13.1mm. For each range shifter, an analytical equation demonstrating the relationship of the spot size with the proton energy and air gap was obtained. The best parametrization results were obtained with the 3rd degree polynomial fits of the energy and air gap parameters. The average difference between the modeled and measured spot sizes was 0.0 ± 0.1mm (range, -0.24-0.21mm) for RS40, and 0.0 ± 0.1mm (range, -0.23-0.15mm) for RS75. In conclusion, the analytical model agrees within ± 0.25mm of the measured spot sizes on a ProteusPLUS PBS proton system with a PBS dedicated nozzle.

Calculation of PM Vernier Motors Using an Improved Air-Gap Permeance Function

This paper proposes a more convenient and more accurate air-gap permeance function for the calculation of the air-gap flux density of flux modulation machines with permanent magnets (PMs). First, we review the previous air-gap permeance obtained from the approximated linear model and explain the problem that the accuracy of calculation becomes worse as the magnet thickness becomes larger. To solve this problem, we introduce an equivalent model that reflects the actual cylindrical structure of the machine with slots and, then, derives the air-gap function that is easy to be converted into the Fourier series, and finally propose the new air-gap permeance function. Using the proposed permeance function, the working harmonic components in the air-gap flux density of the surface magnet vernier motor are easily predicted, and then additional characteristics as well as flux density are compared with the finite-element simulation results to check the validity of the proposed method.

Analytical Energy-Based Approaches for Cogging Torque Calculation in Surface-Mounted PM Motors

This paper deals with the cogging torque calculation in permanent-magnet (PM) surface-mounted machines based on energy approach. Three different analytical co-energy methods are assessed, and innovative computation techniques for calculating co-energy are applied to reduce the computations time and burden. Also, an air-gap function due to the slot is presented for the simple method. Then, the results achieved by the analytical methods are validated by the finite-element method (FEM). The cogging torque using such methods has a good agreement with FEM. Three case studies consisting of brushless PM (BLPM) motors with slotted stator structure are considered to show the efficiency of the proposed methods. Finally, different methods are compared in terms of their computational complexity and accuracy.

Performance Analysis of Squirrel-Cage Induction Motors Under Broken Rotor Bar and Stator Inter-Turn Fault Conditions Using Analytical Modeling

Stator winding inter-turn (SWI) short-circuit fault and broken rotor bar (BRB) fault are two common faulty modes of the squirrel cage induction motors (SCIMs). These faults have various impacts on the motor performance and may be rooted in each other; therefore, they may be presented at the same time in an SCIM. This paper proposes an exact analytical model for the SCIMs, which is able to include the SWI and BRB faults presenting simultaneously or individually with variable severities. Multiple coupled circuit modeling is applied to achieve such analytical model. The magnetic saturation effect is included in the model by applying appropriate air gap function and the rotor bars skew effect is taken into account by using 2-D winding function theory. Simulation results as well as the corresponding experimental results approve the presence of the same harmonics in the stator line currents due to the proposed faults. However, more detailed study gives solution for discrimination of the faults. The attained analytical model can be applied to examine the performance of the related fault diagnosis methods and to design novel fault diagnosis techniques including the model-based ones.

Employing neutral-voltage spectrum for internal turn-to-turn fault detection in the induction machine drives

This paper introduces a diagnostic method for a Stator Internal Turn-to-Turn Fault (ITTF) in induction machine drives. Conventional Winding Function (WF) and Finite Element Method (FEM) are employed for modelling induction machines with the ITTF. The effects of machine slots, winding distributed types and different air-gap functions on machine inductance spectra are investigated. In the end, based on the theoretical and experimental analysis, the spectrum of the neutral-voltage is shown to be a proper approach for a hidden ITTF signature in Pulse Width Modulation (PWM) drives.

Generalized optimization procedure for rotational magnetized direction permanent magnet thrust bearing configuration

Optimization of rotational magnetized direction permanent magnet thrust bearing configuration is carried out using generalized three-dimensional mathematical model. The bearing features namely axial force and stiffness are maximized using in-house developed mathematical expressions solved using MATLAB. The design variables selected for the optimization are axial offset, number of ring pairs, air gap and inner radius of inner and outer rings. The maximized axial force values of the optimized configuration are validated with the finite element analysis results. To overcome the high computational cost associated with three-dimensional equations, generalized method of optimization is sucessfully demonstrated using plots representing variation of optimal design variables as a function of air gap with respect to bearing’s outer diameter. Simple and useful method of using the generalized plots for the process of optimization is presented by dimension optimization of representative bearing configuration with a particular aspect ratio. The proposed optimization using mathematical model and generalized approach assists designer in selecting optimized geometrical parameters of rotational magnetized direction thrust bearing configurations easily for variety of high-speed applications.

Analytic Model for Induction Motors Under Localized Bearing Faults

The bearing faults are the major root cause for the induction motor failures; however, almost all the related fault diagnosis methods have been based on the laboratory tests, which are costly and inflexible. Localized defects in various components of roller bearings cause radial vibration of the rotor, little variation of the load torque, and various harmonics in the stator current. Ignoring the load torque variation, this paper applies the multiple coupled circuit modeling to simulate three-phase squirrel-cage induction motors under the localized bearing faults by introducing appropriate air gap function. Fast Fourier transform is used for exact analysis of the harmonic content of the inverse of the air gap function. The analysis is completed by including the saturation effect and the inherent eccentricity of the motor. Then, a broad list of harmonics presentable in the stator current spectrum under the bearing faults is determined. The list may include the characteristic vibration frequencies related to the bearing components faults. Also, it is clear that the inner raceway fault can produce the same harmonics in the stator current as produced by the mixed eccentricity. Experimental results approve the simulation results and the mentioned facts.

Characterization and Modeling of a Virtual Air Gap by Means of a Reluctance Network

This paper deals with an analytical model of the virtual air gap (VAG) function in order to define design rules when this technique is used inside complex devices. The establishment of those design rules constitutes the main originality of the developments presented in this paper, which are about a single-phase magnetic core. It is based on the definition of a nonlinear reluctance network that takes simultaneously into account the effects of dc and ac magnetic flux components in the disturbed area that contains the VAG. The results are validated using a finite-element analysis and experimentally.

Analytical Modeling of Armature Reaction Air-Gap Flux Density Considering the Non-Homogeneously Saturated Rotor in a Fractional-Slot Concentrated-Wound IPM Machine

The flux of the embedded magnets in the rotor of an interior permanent magnet (IPM) synchronous machine causes a nonhomogeneously saturated rotor iron. This alters the reluctance of the stator flux path due to the nonlinear B-H curve of the rotor iron and should be considered in the analytical field calculations; however, it is often neglected in the prior-art methods leading to inaccurate results. Moreover, the effect of a fractional-slot concentrated-wound (FSCW) stator on the analytical field calculations is not addressed in the existing literature. The magnetic field characteristics of IPM synchronous machines are commonly formulated using an equivalent air-gap function. In order to account for the aforementioned shortcomings in the existing methods for the analytical field calculations, an equivalent air-gap function is proposed in this paper that considers the particular properties of an IPM rotor and an FSCW stator. To this aim, based on the rotor geometry and the nonlinear B-H curve of the iron core, a method is first proposed to model the saturation level and the relative permeability at different regions of the rotor iron. This model is then used in the proposed equivalent air-gap function to compute the armature reaction air-gap flux density. The proposed theory is validated through finite element analysis and experimental results on a prototype FSCW IPM machine in the laboratory.

Determination of the inductances of synchronous machines with unsymmetrical stator winding based on the voltage equation of a single coil in the stator winding

An improved model for calculating the current distribution of synchronous machines with cylindrical rotor (SMCR) and internal faults or missing coils in the stator winding is established using the multi-loop method. For this purpose, a good knowledge of the time-depending inductances is necessary. In this paper, a calculation method is presented to determine the mutual and self-inductances of the stator coils as well as the mutual inductances between the stator coils and the field winding of a SMCR. The damper winding is not considered in this step. The method presented here considers the analytical calculation of the magnetic flux density based on the magnetomotive force (M.M.F.) and the time-depending air-gap permeance function of the SMCR.

WE‐DE‐201‐05: Evaluation of a Windowless Extrapolation Chamber Design and Monte Carlo Based Corrections for the Calibration of Ophthalmic Applicators

Purpose:To test the validity of a windowless extrapolation chamber used to measure surface dose rate from planar ophthalmic applicators and to compare different Monte Carlo based codes for deriving correction factors.Methods:Dose rate measurements were performed using a windowless, planar extrapolation chamber with a 90Sr/90Y Tracerlab RA‐1 ophthalmic applicator previously calibrated at the National Institute of Standards and Technology (NIST). Capacitance measurements were performed to estimate the initial air gap width between the source face and collecting electrode. Current was measured as a function of air gap, and Bragg‐Gray cavity theory was used to calculate the absorbed dose rate to water. To determine correction factors for backscatter, divergence, and attenuation from the Mylar entrance window found in the NIST extrapolation chamber, both EGSnrc Monte Carlo user code and Monte Carlo N‐Particle Transport Code (MCNP) were utilized. Simulation results were compared with experimental current readings from the windowless extrapolation chamber as a function of air gap. Additionally, measured dose rate values were compared with the expected result from the NIST source calibration to test the validity of the windowless chamber design.Results:Better agreement was seen between EGSnrc simulated dose results and experimental current readings at very small air gaps (<100 µm) for the windowless extrapolation chamber, while MCNP results demonstrated divergence at these small gap widths. Three separate dose rate measurements were performed with the RA‐1 applicator. The average observed difference from the expected result based on the NIST calibration was −1.88% with a statistical standard deviation of 0.39% (k=1).Conclusion:EGSnrc user code will be used during future work to derive correction factors for extrapolation chamber measurements. Additionally, experiment results suggest that an entrance window is not needed in order for an extrapolation chamber to provide accurate dose rate measurements for a planar ophthalmic applicator.

SU‐F‐T‐194: Analyzing the Effect of Range Shifter Air Gap On TPS Dose Modeling Accuracy in Superficial PBS Proton Therapy

Purpose:Treatment planning systems (TPS) may not accurately model superficial dose distributions of range shifted proton pencil beam scanning (PBS) treatments. Numerous patient‐specific QA tests performed on superficially treated PBS plans have shown a consistent overestimate of dose by the TPS. This study quantifies variations between TPS planned dose and measured dose as a function of range shifter air gap and treatment depths up to 5 cm.Methods:PBS treatment plans were created in the TPS to uniformly irradiate a volume of solid water. One plan was created for each range shifter position analyzed, and all plans utilized identical dose optimization parameters. Each optimized plan was analyzed in the TPS to determine the planned dose at varying depths. A PBS proton therapy system with a 3.5 cm lucite range shifter delivered the treatment plans, and a parallel plate chamber embedded in RW3 solid water measured dose at shallow depths for each air gap. Differences between measured and planned doses were plotted and analyzed.Results:The data show that the TPS more accurately models superficial dose as the air gap between the range shifter and patient surface decreases. Air gaps less than 10 cm have an average dose difference of only 1.6%, whereas air gaps between 10 and 20 cm differ by 3.0% and gaps greater than 20 cm differ by 4.4%.Conclusion:This study has shown that the TPS is unable to accurately model superficial dose with a large range shifter air gap. Dose differences greater than 3% will likely cause QA failure, as many institutions analyze patient QA with a 3%/3mm gamma analysis. For superficial PBS therapy, range shifter positions should be chosen to keep the air gap less then 10 cm when patient setup and gantry geometry allow.