Analytical Solution of Air-Gap Field in Permanent-Magnet Motors Taking Into Account the Effect of Pole Transition Over Slots

We present an analytical method to study magnetic fields in permanent-magnet brushless motors, taking into consideration the effect of stator slotting. Our attention concentrates particularly on the instantaneous field distribution in the slot regions where the magnet pole transition passes over the slot opening. The accuracy in the flux density vector distribution in such regions plays a critical role in the prediction of the magnetic forces, i.e., the cogging torque and unbalanced magnetic pull. However, the currently available analytical solutions for calculating air-gap fields in permanent magnet motors can estimate only the distribution of the flux density component in the radial direction. Magnetic field and forces computed by the new analytical method agree well with those obtained by the finite-element method. The analytical method provides a useful tool for design and optimization of permanent-magnet motors.     

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.     

Analysis of magnetic field and levitation force characteristics for 3-DOF deflection type PM motors

The mechanism and characteristics of the electromagnetic radial force are important for motors with complicated structures. The three-dimensional analytical model of the air gap between the rotor and stator is established under rotor eccentricity conditions. Then, aiming at solving the unbalanced radial force problem with rotor static eccentricity, the air-gap flux density, radial electromagnetic force, and the comparisons of harmonic contents are calculated and presented based on FEA (Finite Element Analysis) and MATLAB simulation. Finally, the magnetic field model has been validated by experiments utilizing a prototype system. The results provide a theoretical guide for configuration design, optimization, and levitation control research on three degree of freedom deflection type motors.     

Influence of an aperture on the performance of a two-degree-of-freedom iron-cored spherical permanent-magnet actuator

This paper describes a computational and experimental study of a two-degree-of-freedom spherical permanent-magnet actuator equipped with an iron stator. In particular, it considers the effect of introducing an aperture in the stator core to facilitate access to the armature. The resultant magnetic field distribution in the region occupied by the stator windings, the net unbalanced radial force, and the resulting reluctance torque are determined by three-dimensional magnetostatic finite-element analysis. The predicted reluctance torque is validated experimentally, and its implications on actuator performance are described.     

Effect of Magnetic Saturation on Static and Mixed Eccentricity Fault Diagnosis in Induction Motor

We have investigated the effect of magnetic saturation of core materials on the diagnosis of static and mixed-eccentricity faults in induction motors. We modeled the faults by using a modified winding function (MWF) and time-stepping finite-element (TSFE) methods to compute the stator currents of both healthy and faulty motors for processing. We then analyzed the stator signal spectra of the motors by the MWF and TSFE methods and estimated the amplitudes of sideband components attributable to the faults. The results obtained by TSFE agreed well with experimental measurements. However, there was considerable discrepancy between the MWF results and the experimental measurements. We investigated the reason for the discrepancy by analyzing the air gap magnetic field distribution in both healthy and faulty induction motors in order to determine their linear and actual magnetization characteristics. We found that, in a faulty motor, for fixed permeability, the analytic method yields a much larger magnetic flux amplitude than is actually the case. At the same time, the distribution of magnetic flux in the air gap is more asymmetric than the actual case. Here, we present our experimental results and those obtained with the MWF method, using the finite-element analysis package Opera2d 10.5, for two three-phase, four-pole, 60-Hz, 3-hp motors having 36 stator slots and 44 and 28 rotor slots, respectively.      

Optimal Slot Numbers for Magnetic Noise Reduction in Variable-Speed Induction Motors

Although many empirical rules have been established for correctly choosing the number of stator and rotor slots so as to limit the audible magnetic noise level radiated by induction machines, these rules never take into account the stator natural frequencies or the fact that the motor is run at variable speed. In this paper, we present a fast simulation tool for the variable-speed magnetic noise emitted by induction machines, based on fully analytical models. On the basis of these models, we derive and experimentally validate an analytical expression for magnetic vibrations due to slotting reluctance harmonics, confirming the prime importance of slot combination in magnetic noise radiation. We ran simulations on a 700-W squirrel-cage motor in order to quantify the noise emitted by all possible combinations of slot numbers in two- and three-pole pairs, including odd slot numbers. We thus obtained a database that efficiently replaces the old empirical rules for slot combination numbers and helps in designing quiet induction motors. Similar databases can be built for other power ranges.      

Evaluation of experimental permanent-magnet brushless motor utilizing new magnetic material for stator core teeth

We prepared motors with experimental cores using a soft magnetic composite and an amorphous metal and evaluated their performance. We measured the magnetic and motor characteristics, such as iron loss, when the new materials were used in the stator core teeth. The amorphous metal was found to have very high permeability and low iron loss, whereas the soft magnetic composite had low permeability and had a comparable iron loss as low-grade magnetic steel. The soft magnetic composite had the added benefits of being able to form a three-dimensional shape and having relatively low core loss in high frequency conditions. The magnetic properties we measured were able to predict the motor characteristics with high accuracy based on numerical and finite-element-method analysis.     

Improved analytical model for predicting the magnetic fielddistribution in brushless permanent-magnet machines

A general analytical technique predicts the magnetic field distribution in brushless permanent magnet machines equipped with surface-mounted magnets. It accounts for the effects of both the magnets and the stator windings. The technique is based on two-dimensional models in polar coordinates and solves the governing Laplacian/quasi-Poissonian field equations in the airgap/magnet regions without any assumption regarding the relative recoil permeability of the magnets. The analysis works for both internal and external rotor motor topologies, and either radial or parallel magnetized magnets, as well as for overlapping and nonoverlapping stator windings. The paper validates results of the analytical models by finite-element analyses, for both slotless and slotted motors     

Modeling switched-reluctance Machines by decomposition of double magnetic saliencies

This paper presents a novel analytical model for a switched-reluctance machine (SRM) based on decomposition of its inherent double joint magnetic saliencies due to rotor and stator salient poles and saturation of magnetic field at high stator currents. With this method, the magnetic characteristics of the motor, such as flux linkage and incremental inductance, are decomposed to vector functions of rotor position and phase current. Dynamic state and torque equations for the SRM are derived on the basis of this representation. The proposed model is appropriate for online identification and for sensorless position control algorithms. It is easy to implement and computationally efficient. Comparison of the predicted motor magnetic characteristics to machine data from finite-element analysis verifies the accuracy of the model.     

Characterization and Reduction of Magnetic Noise Due to Saturation in Induction Machines

This paper derives the analytical characterization of Maxwell radial vibrations due to saturation effects in induction machines, and especially in traction motors. The number of nodes and the velocity of these particular force waves are experimentally validated by visualizing some operational deflection shapes of the stator. It is shown that according to the stator and rotor slot numbers, and stator natural frequencies, these forces can be responsible for high magnetic noise levels during starting and braking. A simple rule to avoid saturation magnetic noise is then proposed, and applied to an industrial motor. Simulation results show that the new proposed motor improves magnetic noise level up to 20 dB, whereas experiments give a 15 dB improvement.      

Eddy-current loss in the rotor magnets of permanent-magnet brushless machines having a fractional number of slots per pole

We develop an analytical model for predicting the eddy-current loss in the rotor magnets of permanent-magnet brushless machines that have a fractional number of slots per pole, when either all the teeth or only alternate teeth are wound, and in which the unwound teeth may be narrower than the wound teeth. The model enables the magnetic field distribution in the air gap and magnet regions to be determined, by neglecting the eddy-current redistribution effect and assuming that the eddy currents are resistance limited. It can account for space-harmonic magnetomotive forces (MMFs) resulting from the winding distribution and time-harmonic MMFs due to nonsinusoidal phase currents, as well as for the effect of curvature and circumferential segmentation of the magnets. We have validated the model by finite-element analysis, and used it to investigate the eddy-current loss in the magnets of three surface-mounted magnet brushless motors that have similar slot and pole numbers, and employ identical rotors but different stators, when they are operated in brushless ac (BLAC) and dc (BLDC) modes. We show that the stator winding configuration, as well as the operational mode, significantly influence the resultant eddy-current loss.     

Electrical parameter evaluation of a 1 MW HTS motor via analysis and experiments

A 1 MW class HTS (high-temperature superconducting) synchronous motor has been developed. Design concerns of the developed motor are focused on smaller machine size and higher efficiency than conventional motors or generators with the same rating simultaneously reducing expensive Bi-2223 HTS wire which is used for superconducting field coil carrying the operating current around 30 K (−243 °C). Influence of an important parameter, synchronous reactance, has been analyzed on the machine performances such as voltage variation and output power during motor and generator operation. The developed motor was also analyzed by three-dimensional electromagnetic FEM (finite element method) to get magnetic field distribution, inductance, electromagnetic stress and so forth.This motor is aimed to be utilized for industrial application such as large motors operating in large plants. The HTS field coil of the developed motor is cooled by way of Neon thermosiphon mechanism and the stator (armature) coil is cooled by water through hollow copper conductor. This paper also describes evaluation of some electrical parameters from performance test results which were obtained at steady state in generator and motor mode of our HTS machine.     

Analytical Modeling of a Permanent-Magnet Synchronous Machine in a Flywheel

We develop an analytical model for a radial-flux external-rotor permanent-magnet synchronous machine (PMSM) without slots in the stator iron and with a shielding cylinder. The machine is part of an energy storage flywheel, to be used as the peak-power unit in a hybrid electric passenger bus. To reduce the induced no-load losses due to the high rotational speed of the flywheel, the slots in the stator are made not of iron but of a nonmagnetic plastic material. This results in an air gap winding with a stator yoke consisting of stacked circular laminations. The analytical model includes the effect of the winding distribution on the field, the fact that it is in the air gap, and the effect of the eddy-current reaction field of the shielding cylinder. The two-dimensional magnetic field is solved in six defined machine layers and useful machine quantities are derived directly from it, leading to the machine voltage equation. We built a prototype flywheel machine. The locked-rotor machine resistance and inductance predicted by the analytical model was compared with the experimentally determined values. The values showed good agreement, thereby validating the analytical model of the machine.      

Design and performance of permanent-magnet DC linear motors

Energy-efficient direct linear electric drives are gaining increased attention as a result of continuous developments in high-energy permanent magnets and advances in power electronics and microcontrollers. This paper presents a step-by-step approach to the design of permanent-magnet dc linear motors (PMDCLMs). The problems of armature reaction and saturation of the permeable members of the motor lead to a nonlinear and asymmetric air-gap magnetic flux density as a function of position and, consequently, the static thrust versus position characteristics of PMDCLMs. The paper describes a prototype PMDCLM that reveals these phenomena and presents design concepts aimed at alleviating these problems.     

Magnetic Field Analysis of an Ironless Brushless DC Machine

This paper presents an analytical solution for the magnetic field inside an unconventional ironless brushless (ILBL) dc motor design. We discuss the unique characteristics of the design, which adopts an “inside-out” construction with an internal ironless stator. With the intention of obtaining an analytical solution for the magnetic field, we propose a model based on a magnetic pole concept for representing the magnetic circuit. The magnetic field inside the motor, which has no iron for guiding magnetic flux paths, is obtained by solving Laplace's equation for magnetic scalar potential. We present both analytical and numerical solutions for the magnetic field and compare them with measured results of a 20-pole prototype IL design to show the validity of the model. The IL design is simple, easy to manufacture and, as indicated by the results, has an optimum number of magnets, for which its performance becomes maximum.     

Nonphysical Reverse Currents in Transient Finite-Element Magnetics Simulation

We are concerned with the simulation of low-frequency transient magnetic fields and currents in conductors as modeled by the vector diffusion equation. In particular, the key topic of this paper is the diffusion of fields and currents into a conductor due to a rapidly varying magnetic field in the surrounding air. As an example, an explosive magnetic flux compression generator may be designed to produce an exponentially increasing magnetic field in the in the air gap between armature and stator. As a second example, in a standard railgun the motion of the armature causes a rapidly increasing magnetic field in the air ahead of the armature, inducing currents in the rails ahead of the armature. It has been observed that for these types of transient magnetics problems finite-element simulations can produce nonphysical “reverse currents” in conductors, currents that are flowing in the wrong direction. In this paper the root cause of these nonphysical reverse currents is explained, and several mitigation strategies are discussed.      

Variable-airgap, cylindrical, linear variable reluctance actuators for high-force, medium-stroke applications

This study describes a design feature for variable-airgap, cylindrical, linear variable reluctance actuators, which enhances their force capability at large airgaps. These features enable the actuators? force?displacement characteristics to be tailored to the requirements of a particular application. The method presented is based on incorporating a series of circular grooves into the stator pole faces and corresponding projections into the armature. The utility of these features is demonstrated by means of a design study on an actuator with a rated force of 1 kN over a stroke of 3 mm. The findings from the design study are validated by experimental measurements.     

An indirect test method for the characterization of variablereluctance motors

The determination of the characteristics of the variable reluctance motors (both in static and dynamic conditions) represents a quite critical point, due to the heavy nonlinearity of the motor magnetic paths, to the high distortion of the supply voltage from the converter, and to the high level of saturation of the magnetic paths in normal working conditions. This creates a great difficulty in the accurate measurement of the motor magnetic characteristics (saturation curves or flux linkage versus current curves) and consequently in the determination of the mechanical characteristics (static torque versus current and static torque versus rotor position) which are directly related to the saturation curves. The paper proposes an original digital method that, starting from the measurement of the flux linkage in the motor magnetic paths, determines the saturation curves, evaluates the coenergy versus current curves and then the motor torque characteristics in static conditions. It is then shown how the availability of a fast and accurate method for the measurement of the flux linkage allows the determination of the electromagnetic torque in dynamic conditions, too     

Novel modeling technique for the stator of traveling wave ultrasonic motors

Traveling wave ultrasonic motors (TWUM) are a promising type of piezoelectric transducers, which are based on the friction transmission of mechanical propagating waves. These waves are excited on the stator by using high Q piezoelectric ceramics. This article presents a modeling strategy, which allows for a quick and precise modal and forced analysis of the stator of TWUM. First-order shear deformation laminated plate theory is applied to annular subdomains (super-elements) of the stator. In addition to shear deformations, the model takes into account the effect of rotary inertia, the stiffness contribution of the teeth, and the linear varying thickness of the stator. Moreover, the formulation considers a more realistic function for the electric field inside the piezoelectric ceramic, i.e., a linear function, instead of the generally assumed constant electric field. The Ritz method is used to find an approximated solution for the dynamic equations. Finally, the modal response is obtained and compared against the results from classical simplified models and the finite element method. Thus, the high accuracy and short computation times of the novel strategy were demonstrated.     

A Quantitative Comparative Analysis of a Novel Flux-Modulated Permanent-Magnet Motor for Low-Speed Drive

A novel low-speed flux-modulated (FM) permanent-magnet (PM) motor that breaks the traditional design rule, which stipulates that the number of stator pole pairs and the number of rotor pole pairs must be the same, is proposed. The FM motor has a special physical structure with iron segments in the air gap to modulate the magnetic field. In the design, the free space between adjacent stationary iron segments also acts as ventilating ducts to help improving the heat dissipation and ventilation of the motor. Its cogging torque is very small. In this paper, a rule for comparing the power density of electric motors is proposed. The performance of the FM motor is compared with those of a magnetic-geared PM motor, a traditional PM motor, and a fractional-slot PM motor by using magnetic field finite-element analysis.