Showing papers on "Magnetic circuit published in 2016"

High-Performance Low-Cost Electric Motor for Electric Vehicles Using Ferrite Magnets

Abstract: Permanent-magnet motors with rare-earth magnets are among the best candidates for high-performance applications such as automotive applications. However, due to their cost and risks relating to the security of supply, alternative solutions such as ferrite magnets have recently become popular. In this paper, the two major design challenges of using ferrite magnets for a high-torque-density and high-speed application, i.e., their low remanent flux density and low coercivity, are addressed. It is shown that a spoke-type design utilizing a distributed winding may overcome the torque density challenge due to a simultaneous flux concentration and a reluctance torque possibility. Furthermore, the demagnetization challenge can be overcome through the careful optimization of the rotor structure, with the inclusion of nonmagnetic voids on the top and bottom of the magnets. To meet the challenges of a high-speed operation, an extensive rotor structural analysis has been undertaken, during which electromagnetics and manufacturing tolerances are taken into account. Electromagnetic studies are validated through the testing of a prototype, which is custom built for static torque and demagnetization evaluation. The disclosed motor design surpasses the state-of-the-art performance and cost, merging the theories into a multidisciplinary product.

A New Perspective on the Operating Principle of Flux-Switching Permanent-Magnet Machines

Abstract: The flux-switching permanent-magnet (FSPM) machine attracts increasing attention recently due to its high power density, robust mechanical structure, good flux-weakening capability, and essential sinusoidal back-electromotive-force waveforms. In previous studies, the approach for analyzing FSPM machines is either by using the lumped parameter magnetic circuit models or from the “generator-oriented” perspective. In this paper, the operating principle of FSPM machines is reiterated from a new perspective, viz., the “motor-oriented” perspective. Some interesting findings and essential principles can be unveiled, which include how the stable electromagnetic torque can be developed, how the pole-pair number (PPN) of armature windings, the PPN of PMs, and the synchronous speed of the armature field should be defined, and how to determine the connection of coils for the sake of developing stable electromagnetic torques. This new perspective is more consistent with the classical theory on electric machines. There is no need to consider the polarity of coils when determining the connection of windings. Three typical FSPM machines with different combinations of stator and rotor poles, viz., 12/11-pole, 12/13-pole, and 12/26-pole, are investigated to verify the validity of the proposed analysis approach. Experimental verification concerning the latter two sample machines is also conducted.

Modeling and Analysis of a Novel Transverse-Flux Flux-Reversal Linear Motor for Long-Stroke Application

Abstract: In this paper, a transverse-flux flux-reversal linear motor (TF-FRLM) is proposed. With magnets on the primary side, the proposed motor is suitable for long-stroke application, benefiting from easy manufacturing and low-cost secondary cores. First, the basic structure and operating principle of the proposed motor are presented. Then, the expressions of back electromotive force (EMF) and electromagnetic thrust are obtained by an equivalent magnetic circuit model. Third, for saving computation time, a simplified half-phase model with a symmetry boundary is employed in the 3-D finite-element analysis (FEA) to investigate the TF-FRLM, and the field distribution, the back EMF, the detent force, as well as the thrust force are emphasized. Finally, a prototype is constructed, and experiments show good agreement with the FEA results.

Multiobjective Optimization of a Combined Radial-Axial Magnetic Bearing for Magnetically Suspended Compressor

Abstract: The combined radial-axial magnetic bearing (CRAMB) with permanent magnet (PM) providing bias magnetic flux is designed for magnetically suspended high-speed electromotor in the compressor for its compact construction. In this paper, the design principle and the initial model of CRAMB are introduced. To improve the performances of CRAMB and better meet the engineering requirements, the optimization is conducted on the bearing. Considering the incompatible objectives of the optimization model, the method of multiobjective optimization (MOO) on the bearing is proposed, which can balance these objectives compared with single-objective optimization (SOO). The objectives and constraints are provided in the form of analytical expressions by means of equivalent magnetic circuit whose rationality is demonstrated by finite-element method (FEM). To optimize the bearing efficiently, the integrated optimum methodology is adopted. After MOO process, the synthetical performances are improved, which are verified by FEM and experiment.

Comparison of Flux-Switching PM Motors With Different Winding Configurations Using Magnetic Gearing Principle

Abstract: In this paper, the magnetic gearing principle is extended to the flux-switching permanent magnet (FSPM) motor for its armature winding configuration design. First, the no-load flux density in motor air gap is qualitatively analytically calculated using the equivalent magnetic circuit method, so that the predominant space harmonic components (PSHCs) can be separated. Then, the slot vector graph can be drawn according to the pole-pair numbers and rotation directions of these PSHCs. Consequently, the armature winding configuration of a 12/10-pole FSPM motor is designed based on the slot vector graph using the conventional motor design method. In addition, two new 12/7-pole FSPM motors with the conventional non-overlapping concentrated and distributed winding are proposed, and the electromagnetic performances of the three motors are analyzed and compared. Finally, the analytical results are verified by the finite-element analysis and experimentation.

Development of a novel rotary magnetic refrigerator.

Abstract: A novel rotary magnetic refrigerator was designed and built at the Federal University of Santa Catarina (UFSC). The optimized magnetic circuit is a two-pole system in a rotor-stator configuration with high flux density regions of approximately 1 T. Eight pairs of stationary regenerator beds filled with approximately 1.7 kg of gadolinium spheres (425–600 µm diameter) were placed in the magnetic gap. Two low-friction rotary valves were developed to synchronize the hydraulic and magnetic cycles. The valves were positioned at the hot end to avoid heat generation in the cold end. In this work, experimental results are presented as a function of the operating frequency, fluid flow rate, hot reservoir temperature and thermal load. The performance of the device was evaluated in terms of the coefficient of performance (COP) and overall second-law efficiency ( η 2 nd ). The maximum no-load temperature span was 12 K at 1.5 Hz and 150 L h−1, and the maximum zero-span cooling power was 150 W at 0.8 Hz and 200 L h−1. For a thermal load of 80.4 W, at 0.8 Hz and 200 L h−1, the device generated a temperature span of 7.1 K, with a COP of 0.54 and η 2 nd of 1.16%.

2-D Analytical Magnetic Field Prediction for Consequent-Pole Permanent Magnet Synchronous Machines

Abstract: Consequent-pole permanent magnet (PM) synchronous machines (PMSMs) provide especial features by the use of alternate PM and ferromagnetic poles. The design of these types of electric machines requires an accurate model due to the asymmetrical flux distribution in the air gap under adjacent poles. The equivalent magnetic circuit technique can hardly offer an accurate model for consequent-pole PMSMs. To this end, a 2-D analytical model is presented for consequent-pole slotted stator PMSMs to accurately compute the magnetic field distribution due to PMs and armature reaction. The slotting effects and the tooth-tip effects are taken into consideration by using the subdomain technique. The proposed model is used to calculate the magnetic flux density distributions of three consequent-pole PMSMs: an 8-pole, 9-slot machine with a non-overlapping winding; a 4-pole, 15-slot machine with an overlapping winding; and a 10-pole, 12-slot machine with a non-overlapping winding, each with three different magnetization patterns, i.e., radial, parallel, and Halbach. Based on the magnetic flux distribution, the electromagnetic torque, the self- and mutual-inductances, and the unbalanced magnetic forces have been analytically calculated. The analytical results are compared with those obtained from the finite-element method to show the accuracy and efficacy of the proposed 2-D analytical model.

Dual-Axial Motion Control of a Magnetic Levitation System Using Hall-Effect Sensors

Abstract: This paper presents a new methodology to determine the position of a magnetically guided robot (MGR) in horizontal planes using magnetic flux sensors. This position determination methodology can be used independently as well as in collaboration with optical sensors in the case of the optical blockage. A combination of linear Hall-effect sensors (two sensors for each axis of motion) was employed to measure the magnetic flux in the MGR's working space. A configuration of several electromagnets was used as a source of magnetic field, and an analytical model of the system is developed. The MGR's position was determined based on the polynomial relation between the Hall-effect sensors' output and the location of the minimum magnetic potential energy point in horizontal planes. Using the cross-validation method, it was found that a fourth-order polynomial model could accurately predict the MGR's position. Experiments were conducted on a horizontal plane to validate the performance of position estimation using the magnetic flux sensing method. The accuracy of the position determination method was 0.4-mm root-mean-square errors in both the x - and y -direction over 8 × 8 mm2 working area. This paper also experimentally validates a combined optical-magnetic position determination technique for the motion control of a magnetically guided robot in optical blockage conditions as unknown environment that can be used as a promising replacement of X-ray and ultrasound techniques.

Through-Wall Excitation of a Magnet Coil by an External-Rotor HTS Flux Pump

Abstract: High-temperature superconducting (HTS) magnet systems conventionally require normal-conducting current leads, which connect between the HTS circuit and an external power supply located at room temperature. These current leads form a thermal bridge across the cryostat wall, and they represent the dominant heat load for many magnet applications. The use of a superconducting flux pump device is an alternative approach to exciting a magnet coil, which can eradicate this parasitic heat load, as such devices do not require direct physical connection to the HTS circuit. However, earlier proposed flux pump designs have required power-dissipating active components to be located within the cryogenic envelope, thus imposing their own parasitic heat load. Here, we report the successful demonstration of a mechanically rotating HTS flux pump, which operates entirely outside of the cryogenic envelope. This prototype device projects flux across a cryostat wall, leading to the injection of a direct current into a thermally isolated closed HTS circuit. This is achieved through the implementation of a flux-concentrating magnetic circuit employing ferromagnetic yoke pieces, which enables flux penetration of the HTS circuit at large flux gaps. We have demonstrated the injection of direct currents of > 30 A into a closed HTS circuit while operating this device across a cryostat wall.

Downsizing Effects of Integrated Magnetic Components in High Power Density DC–DC Converters for EV and HEV Applications

Abstract: Interleaved dc–dc converters with integrated magnetic components capable to achieve high power density have recently gained attention in automotive applications for eco-friendly transportation. These circuits may contribute to the downsizing of powertrains for electric vehicles (EVs) and hybrid electric vehicles (HEVs) using close-coupled inductors (CCIs) and loosely coupled inductors (LCIs). In this study, a novel core model for size and loss calculation of the interleaved converter with integrated winding coupled inductors (IWCIs) is proposed to assess the size of magnetic components. This assessment was carried out using the parameters of a 1-kW circuit. As a result, interleaved converters with IWCIs proved to be more effective than the converters with LCIs and CCIs for downsizing the magnetic components. In contrast, it was also found that the interleaved converter with LCIs achieved downsizing of the magnetic component at a duty ratio close to 50%. Finally, the effectiveness of the calculation model was validated through experimental tests.

Performance evaluation of an active magnetic regenerator for cooling applications – part I: Experimental analysis and thermodynamic performance

Abstract: In this first part of a two-part paper, a new active magnetic regenerator (AMR) laboratory apparatus is presented and evaluated. The setup is composed of a nested Halbach cylinder magnetic circuit (maximum magnetic flux density of 1.69 T) assembled in phase with a double effect displacer that provides the cold and hot blows to the regenerator. A single packed-bed regenerator with 195.5 g of gadolinium spheres is used in a discontinuous (i.e., reciprocating) cycle. The system performance is evaluated in terms of characteristic curves (i.e., cooling capacity as a function of temperature span), coefficient of performance and second-law efficiency as a function of the utilization factor and operating frequency. Maximum values of COP have been identified for a given temperature span. The maximum values of second-law efficiency were obtained at system temperature spans between 15 and 20 K.

Design and Optimization Method of Magnetic Bearing for High-Speed Motor Considering Eddy Current Effects

Abstract: With the development of the magnetic bearing (MB) and its application in industry, the demands of high-speed MB are developing, which bring up new problems and requirement for the design. The motor with a high-speed rigid rotor requires that the axial length of MB is minimized to increase the critical speed, and the diameter of thrust disk is minimized to reduce the air friction loss. Also because of the high speed, the eddy currents induced in the iron cores have a significant influence on the dynamic characteristics of the MB. To design a high-performance MB for a high-speed motor, first an MB structure that has the feature of short axial length and small thrust disk is recommended for the high-speed motor. Next, the dynamic model, which takes into consideration eddy current effects, and leakage effects is developed. Then, an optimal design method with multiobjective of minimum length and air friction loss is presented. Design constraints are imposed, which includes the simultaneous consideration of material properties, load capacity, and power amplifier. Finally, a design example is given and a prototype is manufactured. The experimental results demonstrate that the proposed MB structure and the optimization method are feasible and valid in the application of a high-speed motor.

Principle and Modeling of a Novel Moving Coil Linear-Rotary Electromagnetic Actuator

Abstract: This paper presents a novel electromagnetic actuator that adopts an air-core coil mover to deliver decoupled linear and rotary motions. It uses light-weight moving coil to achieve high speed and dynamic response, and single-phase Lorentz-force driving scheme to realize direct and noncommutation actuation. To overcome the low thrust force of such driving scheme, unique magnetic circuits are used to enhance the thrust force and torque of the proposed actuator. Closed-form analytical solutions for modeling the magnetic field within the coil operating regions of these unique magnetic circuits are presented together with the complete thermal analyses. A prototype was developed and it delivers 10 mm stroke and 90 $^{\circ }$ angular displacement. Using commercially available drivers, it achieved a high throughput of 8000 units/h with 20 $\mu$ m, and 0.66 $^{\circ }$ tracking accuracy.

High Step-Up Trans-Inverse (Tx −1 ) DC–DC Converter for the Distributed Generation System

Abstract: This paper introduces a new magnetically coupled single-switch nonisolated dc–dc converter with a high-voltage gain. The topology utilizes magnetic coupling for boosting its output voltage, but unlike other converters with coupled magnetics, its voltage gain is increased by reducing its magnetic turns ratio. The name “Trans-inverse (Tx−1)” is thus used for representing this inverse operating principle of the converter. The converter draws a continuous current from the source and is, hence, suitable for many types of renewable sources. Its leakage energy from the coupled magnetics has further been recycled and transferred to the load by an integrated regenerative snubber circuit. Its inclusion of dc-current-blocking capacitors has also helped to prevent core saturation, which, together with other performance features, has been verified experimentally.

A Novel Partitioned Stator Flux Reversal Permanent Magnet Linear Machine

Abstract: A new flux reversal permanent magnet (FRPM) linear machine known as the partitioned stator FRPM (PS-FRPM) linear machine is proposed. The structure and the operation principle of the machine are described, and the major design parameters are optimized for maximum thrust force. A periodic model is also used in the analysis in order to highlight the significant effect of the longitudinal end effect on the machine performance, particularly in terms of unbalanced magnetic circuit and cogging force. Furthermore, the proposed machine is compared with the conventional FRPM linear machine. It is concluded that higher thrust force, less cogging force, and consequently less thrust force ripple can be obtained by the proposed machine.

A New Model of Electromechanical Relays for Predicting the Motion and Electromagnetic Dynamics

Abstract: In this paper, a novel multiphysics and nonlinear model for electromechanical relays is presented. The electromagnetic dynamics is analyzed by calculating the total reluctance of the magnetic equivalent circuit (MEC), which is composed of a fixed length iron core and an angular air gap. Magnetic saturation and angular dependency of the reluctance are considered in the analysis. Then, an energy balance over the electromagnetic components of the system is used to obtain the torque which drives the movable armature. A planar mechanism of four rigid bodies, including spring-damping torques that restrict the motion and model the contact bounces that occur in the switchings, is proposed to explain the dynamics of the movable components. Experimental tests show the accuracy of the model in both the electromagnetic and the mechanical parts.

Computer simulations of Hall thrusters without wall losses designed using two permanent magnetic rings

Abstract: A type of Hall thruster without wall losses is designed by adding two permanent magnet rings in the magnetic circuit. The maximum strength of the magnetic field is set outside the channel. Discharge without wall losses is achieved by pushing down the magnetic field and adjusting the channel accordingly. The feasibility of the Hall thrusters without wall losses is verified via a numerical simulation. The simulation results show that the ionization region is located in the discharge channel and the acceleration region is outside the channel, which decreases the energy and flux of ions and electrons spattering on the wall. The power deposition on the channel walls can be reduced by approximately 30 times.

Impact of S tator Wire Width on Output of a Dynamo-Type HTS Flux Pump

Abstract: Superconducting flux pumps enable dc supercurrents to be injected into a superconducting coil without direct connection to an external current supply. Here, we report experimental data from a dynamo-type flux pump employing a high-T c superconducting stator. This device employs a mechanical rotor that rotates outside the cryogenic envelope, and excites the superconducting circuit through the cryostat wall via a magnetic circuit formed between the rotor and stator. We show that the width of the stator wire employed in this device has a significant effect on its output performance. At low frequencies, both the short circuit current, I sc , and the open-circuit voltage, V oc increase with stator width, and we obtain a maximum value of I sc > 340 A using a stator wire width of 46 mm. However at higher operating frequencies, we observe that I sc reaches a maximum value before dropping with any further increase in stator width. We attribute this to thermally dissipative effects due to circulating eddy currents in these wide superconducting stators. At frequencies above ~400 Hz, we observe a sharp rise in the internal resistance of the stator wire that we attribute to a local quench due to the eddy currents driven by the local electromotive force (EMF) beneath the rotor magnet. This paper emphasizes the importance of frequency dependence when defining optimum operating parameters of a high-T c superconductor (HTS) flux pump. Our results also offer the promise that very high current flux pumps may be developed through maximizing the ratio of the stator wire width to the peak width of the rotor field profile.

A Systematic Approach to Modeling Complex Magnetic Devices Using SPICE: Application to Variable Inductors

Abstract: In this paper, a methodology to develop SPICE-based models of complex magnetic devices is presented. The proposed methodology is based on a reluctance equivalent circuit, which allows the user to study both the magnetic and electric behavior of the structure under any operating conditions. The different elements required to implement the reluctance model, namely, constant reluctances, variable reluctances, and windings, are implemented using SPICE behavioral modeling. These elements can thus be used to build a complete model for any magnetic device. The modeling process is illustrated with a particular example for a variable inductor. Simulations and experimental results are presented and compared to evaluate the accuracy and usefulness of the proposed modeling procedure.

A Novel Flux-Weakening Control Strategy for Permanent-Magnet Actuator of Vacuum Circuit Breaker

Abstract: Traditional vacuum circuit breaker (CB) equipped with a bistable permanent-magnet (PM) actuator suffers from the disadvantages of having long start-up time and large current peak, and these shortcomings are limiting its applications on synchronization operation and high-voltage switchgear. In this paper, a new drive circuit which can significantly weaken the flux of the holding force with the usage of an auxiliary capacitor is proposed. In the proposed circuit, a negative current is circulated in the respective coil when the PM actuator is ready to switch on or off . Cosimulation which integrates the PM actuator and the circuit is carried out with the Maxwell and Simplorer software. The prototype is tested on the platform in conjunction with a 10-kV PM vacuum CB (VCB) to showcase the success of the proposed flux-weakening control strategy.

A flux pumping method applied to the magnetization of YBCO superconducting coils: frequency, amplitude and waveform characteristics

Abstract: This letter presents a flux pumping method and the results gained when it was used to magnetize a range of different YBCO coils. The pumping device consists of an iron magnetic circuit with eight copper coils which apply a traveling magnetic field to the superconductor. The copper poles are arranged vertically with an air gap length of 1 mm and the iron cores are made of laminated electric steel plates to minimize eddy-current losses. We have used this arrangement to investigate the best possible pumping result when parameters such as frequency, amplitude and waveform are varied. We have successfully pumped current into the superconducting coil up to a value of 90% of I c and achieved a resultant magnetic field of 1.5 T.

A New Partitioned-Rotor Flux-Switching Permanent Magnet Motor With High Torque Density and Improved Magnet Utilization

Abstract: In this paper, by incorporating the new concept of “partitioned structure,” a type of new partitioned-rotor flux-switching permanent magnet (PR-FSPM) motors is proposed, where the parallel and serial magnetic circuit topologies are involved, respectively. The topologies and the operation principle of the two motors are introduced first. Then, by using the finite-element method, the basic electromagnetic performances are analyzed. Moreover, the two proposed motors and the conventional 12/10-pole FSPM motor are quantitatively compared, in terms of their output torque, torque capability in per unit PM volume, as well as torque–speed and power–speed characteristics, in detail. Both the theoretical analysis and simulation results indicate that the proposed motors not only can retain the high torque density and efficiency but also can avoid the stator flux leakage and improve the PM utilization significantly.

Saturated Core Fault Current Limiters in a Live Grid

Abstract: With two recent successful installations in a U.K. live grid, the saturated core fault current limiter (SCFCL) has become one of the leading candidates for commercial fault current limiting devices. In this work, we review the concept developed at Bar-Ilan University, which was later adapted by GridON, for a novel compact SCFCL. This SCFCL utilizes a superposition of a closed dc magnetic circuit and an open ac magnetic circuit to overcome the intrinsic problem of transformer coupling found in traditional SCFCL designs. It also allows the use of a single magnetic core for a full ac current cycle limiting. In addition, the relatively short path for the dc magnetic circuit supports copper coils as an alternative to superconducting bias coils, allowing easier market penetration. The performances of the SFCL devices installed in live grids are described.

Diagnosis of Short Circuit Faults Within Turbogenerator Excitation Winding Based on the Expected Electromotive Force Method

Abstract: Short circuit faults in an excitation winding pose a potential threat to the safe and stable operation of turbine generators. Some turbine generators are forced to shut down for an overhaul whenever a fault occurs, and the economic losses can be serious. In this paper, a 2-D simulation model has been established using the basic electromagnetic and structural parameters of a generator. Here, the generator's excitation current at normal working conditions is calculated, and two binary function is used for the calculation of no-load electromotive force (EMF) expectations on the excitation current and active power is derived. Based on the fundamental characteristics associated with the reduction of effective turns in the excitation winding after a short circuit, the excitation winding short circuit fault can be determined using the deviation between the actual value and the desired value of generator no-load EMF. Fault examples showed that this method can achieve higher diagnosis accuracy, and that it can be used for the real-time monitoring and diagnosis of an overall excitation winding health inside a turbine generator.

Modeling and Identification of a Solid-Core Active Magnetic Bearing Including Eddy Currents

Abstract: Eddy currents are evident in solid-core active magnetic bearings (AMBs), but they are omitted in the commonly-used models, leading to a significant error between the analytical model and the real system. Based on the magnetic circuit method, this paper presents an analytical model including the eddy-current effects of a solid-core AMB under both current drive and voltage drive, after setting up the relationship between the magnetic force and the effective reluctance. A half-order term is induced in the effective reluctance due to eddy currents, turning the analytical model to fractional-order. The effective reluctance only appears in the coefficient of the s 2 -term, and affects the system dynamics under current and voltage drives distinctively. The half-order term changes the order of the model from 2 to 2.5 under current drive, whereas the order of the model is not changed and is still kept 3 under voltage drive. System identification of a solid-core AMB verifies the proposed models, which indicates that the voltage drive can effectively reduce the eddy-current effects compared with the current drive. In addition, although the solid-core AMB shows fractional-order characteristics, it can be described well with an integer order model under voltage drive. As a result, the voltage drive is a more reasonable choice to a solid-core AMB, since it avoids the complex fractional-order modeling and control.

Actively Shielded High-Field Air-Core Superconducting Machines

Abstract: This paper describes an approach for obtaining very high power density in an electrical machine by significantly increasing the air-gap magnetic flux density and eliminating the ferromagnetic steel traditionally employed to carry and shield magnetic flux. A novel concept is used to address a key challenge with this topology, that of containing the magnetic fields within the machine. An arrangement of main coils and a set of compensating coils, inspired by actively shielded magnetic resonance imaging magnet designs, are employed to cancel out the field outside the machine without the use of iron while maintaining air-gap field levels that are three to five times greater than conventional machines. For an example 10-MW motor study, the outer diameter is reduced by 35%, with corresponding weight reduction, using only 17% more superconductors.

Magnetic equivalent circuit modelling of doubly-fed induction generator with assessment of rotor inter-turn short-circuit fault indices

Abstract: In this study, a wound rotor induction machine, as the core of a doubly-fed induction generator (DFIG) system, is modelled using the magnetic equivalent circuit approach. The entire DFIG system is implemented in Matlab/Simulink environment, including the machine model, power converters, control system and the grid. The model, which includes the ability to simulate rotor inter-turn short-circuits (RITSCs), is subsequently used for the investigation and comparison of the impact of this fault in several DFIG quantities, namely in the stator current and in some control variables. This research also deals in detail with the differences found when comparing RITSC and unbalanced rotor resistance (URR) faults. It is observed that on the contrary to the URR, the stator current spectrum is more appropriate than the control signals for the detection of RITSC. Simulation and experimental results obtained with a DFIG system operating at sub-synchronous and super-synchronous speeds, for different values of the active and reactive powers injected into the grid, corroborate the findings reported in this study.

2-D Analytical Model for External Rotor Brushless PM Machines

Abstract: This paper presents a 2-dimensional analytical model for external rotor brushless machines with surface mounted magnets. The subdomain technique is used to divide the problem into magnets, airgap, slot-openings, and slots regions. The magnetic flux density distributions are initially calculated, and then the important quantities of the machine such as back electromotive force, cogging torque, electromagnetic torque, self- and mutual-inductances, and unbalanced magnetic forces are computed. The finite-element method and experimental results are used to confirm the validity of the proposed model.