Thermal Analysis of an Axial Flux Permanent-Magnet Synchronous Machine

The paper presents a thermal analysis of an axial flux synchronous permanent-magnet machine (AFSPM) with a core of soft magnetic composite (SMC) material. We obtained the temperature distribution by using a coupled thermal and fluid dynamic finite-element model. The study considers two 2-D approaches and compares their results to experimental tests.      

Analytical Modeling of Open-Circuit Air-Gap Field Distributions in Multisegment and Multilayer Interior Permanent-Magnet Machines

We present a simple lumped magnetic circuit model for interior permanent-magnet (IPM) machines with multisegment and multilayer permanent magnets. We derived analytically the open-circuit air-gap field distribution, average air-gap flux density, and leakage fluxes. To verify the developed models and analytical method, we adopted finite-element analysis (FEA). We show that for prototype machines, the errors between the FEA and analytically predicted results are $≪$1% for multisegment IPM machines and $≪$ 2% for multilayer IPM machines. By utilizing the developed lumped magnetic circuit models, the IPM machines can be optimized for maximum fundamental and minimum total harmonic distortion of the air-gap flux density distribution.      

Improved Analytical Model of a Permanent-Magnet Brushless DC Motor

In this paper, we develop a comprehensive model of a permanent-magnet brushless DC (BLDC) motor. An analytical model for determining instantaneous air-gap field density is developed. This instantaneous field distribution can be further used to determine the cogging torque, induced back electromotive force, and iron losses in the motor. The advantage of analytical models is that they can be readily used for optimization of BLDC motor because they are fast.      

Three-Dimensional Magnetic Effects in Permanent-Magnet Magnet Synchronous Machines

This paper presents the results of an investigation of the three-dimensional (3-D) magnetic effects in permanent-magnet synchronous machines (PMSMs). Using 3-D finite-element analysis, effects of geometry and also a high-frequency excitation on the magnetic parameters of the machine have been studied. According to our findings, high-frequency phenomena come into effect at excitation frequencies of the order of a few kilohertz, which is not uncommon when the machine is operated at super high speeds. Our results show that normalized torque productivity is a function of stack length and an increase in stack length results in an increased torque density. It is also observed that an increase in excitation frequency decreases the self inductance of the stator windings while the phase difference between the flux linkage and magnetomotive force increases. This is a significant finding, especially the shift in the phase of the air gap flux, as it has a direct impact on the accuracy of the controller that drives the PMSM under field-oriented control. Another significant observation was the reduction in the induced voltage (back electromotive force) in a search coil located in the stator slots at high frequencies. Such observations mandate the use of 3-D analysis of machine geometry to optimize performance throughout the machine's speed range.     

Demagnetization Testing for a Mixed-Grade Dovetail Permanent-Magnet Machine

A dovetail machine is a novel design developed to solve the strength problems of traditional buried magnet machines. A mixed-grade construction can be easily applied to a dovetail machine, because a dovetail machine has several magnets in a single pole in different positions. The basic idea of the mixed-grade construction is to use high intrinsic coercivity material in the positions of the high demagnetization risk and high remanence material in the positions of low demagnetization risk. We have developed a demagnetization model that takes into account the temperature dependence of the properties of the permanent-magnet materials to model a dovetail permanent-magnet motor with mixed-grade construction. We compared the model with a real motor. By comparing the testing and the calculations, we show that our demagnetization model can predict the demagnetization of the permanent magnets with reasonable accuracy. We discuss the benefits of the mixed-grade construction in a dovetail machine.      

Iron Loss Model for Permanent-Magnet Synchronous Motors

Iron losses in permanent-magnet synchronous machines form a larger portion of the total losses than in induction machines and, hence, more importance should be given to the iron losses. Previously, models have been presented for the calculations of these losses, but these models still rely on finite-element simulations to obtain correction factors, which are substantial, to apply to the theoretically derived formulas in order to obtain good agreement with the experimental data. This paper points out the source of this correction factor: the neglect of the excess eddy-current loss component. In many cases, this loss component dominates the total iron losses and needs to be incorporated in the theoretical considerations. The paper also provides a more complete model of iron loss, which greatly reduces the need for calculating the correction factors using the finite-element method (FEM). This more complete model reduces design time, especially when a number of candidate designs need to be analyzed. Otherwise, the calculation of the correction factors using FEM would be cumbersome, as the correction factors tend to be nonlinear.     

Performance Assessment of Air-Core Linear Permanent-Magnet Synchronous Motors

Performance assessment is crucial during the motor design process as a basis for comparison between different candidate designs. The objective of this paper is to determine how quickly an air-core linear permanent-magnet synchronous motor can perform a point-to-point positioning task while not exceeding a given limit on allowable average power dissipation. The magnetic field in the air gap is obtained by solving the Poisson equation, and an explicit representation for the Lorentz force is derived. Using this force model, performance limits are identified by solving a family of optimal control problems numerically.      

Analytical Prediction of Cogging Torque in Surface-Mounted Permanent-Magnet Motors

We present a new approach to computing cogging torque based on only one analytical field solution in surface-mounted permanent-magnet (PM) motors. We use conformal transformation to compute the magnetic field created by the permanent magnets in the air gap with a single slot. Then, we derive the cogging torque due to the single-slot effect at different rotor positions directly from the 2-D analytical field solution. The total cogging torque is synthesized from the contribution of each slot. We have applied our approach to predicting the cogging torque of two surface-mounted PM motors, one with 4 poles, 24 slots and the other with 42 poles, 36 slots. The predicted cogging torques for both applications agree well with those obtained from 2-D finite-element analysis.      

Analytical Methods for Minimizing Cogging Torque in Permanent-Magnet Machines

Cogging torque in permanent-magnet machines causes torque and speed ripples, as well as acoustic noise and vibration, especially in low speed and direct drive applications. In this paper, a general analytical expression for cogging torque is derived by the energy method and the Fourier series analysis, based on the air gap permeance and the flux density distribution in an equivalent slotless machine. The optimal design parameters, such as slot number and pole number combination, skewing, pole-arc to pole-pitch ratio, and slot opening, are derived analytically to minimize the cogging torque. Finally, the finite-element analysis is adopted to verify the correctness of analytical methods.      

Modeling Ironless Permanent-Magnet Planar Actuator Structures

This paper describes an analytical model that includes end effects for ironless synchronous permanent-magnet planar actuators. Because of its flexibility, the model can be used to predict the performance of various permanent-magnet array and coil array topologies and commutation schemes. Moreover, since control currents have to be nonsinusoidal, it allows analysis of the motor performance without specifying a commutation scheme by directly dealing with the motor-coupling matrix that links the coil currents to the forces or accelerations acting on the translator.     

Detection of Demagnetization Faults in Permanent-Magnet Synchronous Motors Under Nonstationary Conditions

This paper presents the results of our study of the permanent-magnet synchronous motor (PMSM) running under demagnetization. We examined the effect of demagnetization on the current spectrum of PMSMs with the aim of developing an effective condition-monitoring scheme. Harmonics of the stator currents induced by the fault conditions are examined. Simulation by means of a two-dimensional finite-element analysis (FEA) software package and experimental results are presented to substantiate the successful application of the proposed method over a wide range of motor operation conditions. Methods based on continuous wavelet transform (CWT) and discrete wavelet transform (DWT) have been successfully applied to detect and to discriminate demagnetization faults in PMSM motors under nonstationary conditions. Additionally, a reduced set of easy-to-compute discriminating features for both CWT and DWT methods has been defined. We have shown the effectiveness of the proposed method by means of experimental results.      

Flux Distribution in Linear Permanent-Magnet Synchronous Machines Including Longitudinal End Effects

We investigated the longitudinal ends' influence on the flux distribution in a permanent-magnet linear synchronous machine with an analytic model and with numeric finite-element methods. We derived a general analytic expression, on closed form, from a linear reluctance model. The model reveals that the flux in a linear machine differs from that in a rotating machine in several aspects. The longitudinal ends introduce a pairwise coupled flux pattern, which will behave differently in circuits with odd or even numbers of magnets. In linear machines with an even number of magnets the pairwise coupled flux will spread throughout the whole machine, whereas in linear machines with an odd number of magnets it will be transformed into an equally distributed flux in the middle. The latter case will give rise to a nonsymmetric air gap flux distribution, where every second pole has larger flux. We confirmed the pairwise coupled flux and the nonsymmetric air gap distribution predicted by the analytic model by finite-element simulations. We noted additional effects when nonlinear behavior of the steel is taken into account. We conclude that saturation counteracts the pairwise coupled flux pattern at the longitudinal ends. Again, a nonsymmetric air gap flux distribution occurs as the pairwise coupled flux is transformed into an equally coupled flux. The pairwise coupling of the flux and the nonsymmetric air gap flux distribution give rise to a number of secondary effects, which we discuss.     

Comparison of Demagnetization Models for Finite-Element Analysis of Permanent-Magnet Synchronous Machines

We have studied a few simple demagnetization models, which are quick and easy to implement in finite-element calculations, and compared them with measured recoil behavior of Nd-Fe-B magnet material, also using a hysteresis model for comparison. The models are used to estimate post-demagnetization performance of an overloaded surface magnet synchronous machine. Two of the simple models, the sloped linear model and the exponent function model, give the most accurate results without significantly increasing the computation time.     

Analytical Calculation of the Magnetic Field Created by Permanent-Magnet Rings

We present analytical formulations, based on a coulombian approach, of the magnetic field created by permanent-magnet rings. For axially magnetized magnets, we establish the expressions for the three components. We also give the analytical 3-D formulation of the created magnetic field for radially magnetized rings. We compare the results determined by a 2-D analytical approximation to those for the 3-D analytical formulation, in order to determine the range of validity of the 2-D approximation.      

A Three-Dimensional Semi-Analytical Study of the Magnetic Field Excitation in a Radial Surface Permanent-Magnet Synchronous Motor

This paper presents a three-dimensional analytic study of some radial surface permanent-magnet machines, these machines being slotless and without polar pieces. The permanent magnets are represented by Coulomb's model. The sources are developed into a Fourier series. The method of separation of variables in Laplace's equations is used to calculate the magnetic scalar potentials, which lead directly to the flux density. The study yielded a new three-dimensional analytical formulation of such synchronous machines. The results are constituted by analytical expressions of magnetic scalar potentials, the flux densities, and some of their graphs     

A Modular Permanent-Magnet Flux-Switching Linear Machine With Fault-Tolerant Capability

We propose a new topology for a permanent-magnet flux-switching (PMFS) linear machine. We describe its unique structure and compare it with the conventional PMFS linear machine. Finite-element analysis (FEA) shows that the proposed machine not only inherits advantages from the conventional PMFS machines, but also possesses many new merits such as more efficient usage of magnets, high fault tolerance, and easy assembly. These positive features make the proposed machine suitable for many applications. We prototyped both the conventional and proposed machines for verification and found good agreement between FEA and the experimental results.      

Design, Prototyping, and Analysis of a Novel Tubular Permanent-Magnet Linear Machine

In this paper, we present a new tubular permanent-magnet linear machine with square-shaped cross section and derive its corresponding analytical model by solving Maxwell equations and applying the superposition theorem. The analytical field solution is necessary for obtaining an analytic form of the machine parameters and variables such as the self- and mutual inductances of the windings, the thrust force, and the windings electromotive force (EMF). These provide a valuable tool for tubular machine analysis, design, and optimization. In order to achieve maximum force density, we optimized the design parameters of the proposed machine using the analytical model. We used finite-element analysis and experimental results to demonstrate the validity of the developed analytical model. Again using the Fourier series of the cogging force and its harmonic analysis, in this paper, we introduce two techniques for cogging force reduction in the new tubular linear permanent-magnet machine. The first technique reduces the cogging force due to interaction between the permanent magnets and the stator teeth, and the other reduces the cogging force due to finite length of the armature. These techniques are straightforward, and their implementations in the tubular linear permanent magnet machine with square cross section are easy. We investigated the effectiveness of the proposed techniques in cogging force reduction by 3-D finite-element analysis and experimental measurements.      

Analytical Solution for Electromagnetic Torque in Surface Permanent-Magnet Motors Using Conformal Mapping

We present an analytical method for the calculation of electromagnetic torque in surface permanent-magnet (PM) motors. Our method uses conformal mapping to calculate the electromagnetic torque by integrating the Maxwell stress tensor inside the air gap. It uses the radial and tangential components of the flux density in the slotted air-gap produced by the currents flowing in the three-phase armature winding. We demonstrate our analytical solution on a 7-kW four-pole surface PM motor and compare the results with finite-element solutions. We present the results for various angular spans of permanent magnets and various sizes of the slot opening to confirm the validity of the analytical approach.      

An Improved Magnetic Equivalent Circuit Model for Iron-Core Linear Permanent-Magnet Synchronous Motors

The aim of this work is to establish an accurate yet simple method for predicting flux density distribution and iron losses in linear permanent-magnet synchronous motors (LPMSMs) for iterative design procedures. For this purpose, an improved magnetic equivalent circuit for calculation of the teeth and yoke flux densities in the LPMSMs is presented. The magnetic saturation of iron core is considered by nonlinear elements and an iterative procedure is used to update these elements. The armature reaction is also taken into account in the modeling by flux sources located on the teeth of motors. These sources are time dependent and can model every winding configuration. The relative motion between the motor primary and secondary is considered by wisely designing air gap elements simplifying the permeance network construction and preventing permeance matrix distortion during primary motion. Flux densities in different load conditions are calculated by means of the proposed model. The effects of saturation and armature reaction on the flux density distribution are shown in detail. Using these flux densities, iron losses in the motor are examined and its variations versus motor parameters are then studied. All results obtained by proposed model are verified by finite-element method based on an extensive analysis.     

Analytical Calculation of No-Load Voltage Waveforms in Machines Based on Permanent-Magnet Volume Integration

We develop an analytical expression for predicting electromotive force (EMF) waveforms resulting from permanent magnets (PMs) in electrical machines. The expressions for the flux linkage are based on a volume integral over the magnet volume, rather than the usual surface integral over the coil. The proposed method consists of applying a virtual current in the coil of the machine and calculating the magnetic field generated inside the PM volume. The EMF waveform is obtained by taking the derivative of the flux linkage with respect to time. We present analytical expressions of the EMF for various PM shapes and Halbach magnetization patterns. We tested a total of four configurations of PMs, and the experimental waveforms confirmed the validity of the expressions obtained theoretically.