Surface-mounted Permanent Magnet Machines Research Articles

Analytical Modeling of Steel Shielding Cylinder in Surface-Mounted Permanent Magnet Machines

Two-dimensional (2-D) analytical modeling of permanent magnet machines with shielding cylinder is a challenging task due to the saturation effect of the cylinder. This paper presents a 2-D hybrid analytical solution to model surface-mounted permanent magnet machines with a shielding cylinder attached to the exterior of the rotor body. The presented model provides an accurate representation of the motor response by accounting for the saturation effect of the shielding cylinder, as well as the stator slotting effect. For this purpose, the steel shielding cylinder is modeled by a vacuum cylinder (with the exact same size/dimension) and two inner and outer virtual surface currents. The values of the surface currents are determined by using the respective magnetic circuit model. Meanwhile, the slotting effect on the tangential flux component is modeled by injecting a virtual surface current onto a slotless stator surface. Next, the radial and tangential flux density are obtained by solving Poisson's equation via separation of variables theorem and applying relevant boundary conditions. The accuracy of the proposed model is verified by the finite element and experimental tests on the machine prototype.

Analysis and reduction of electromagnetic vibration in integral-slot PM machine by functional magnet structure

It is significant to balances torque and vibration performance for the surface-mounted permanent magnet (PM) machines. This paper proposes a functional magnet structure to suppress the vibration response of integral-slot surface-mounted PM machines. At the same time, the torque ripple is also greatly reduced without sacrificing the average torque. Firstly, taking the 48-slot/8-pole PM machine as an example, the main sources of the air-gap radial force are analyzed based on the Maxwell stress equation. Thereby, the main PM flux density harmonic components that contribute to the radial force are pointed out. Secondly, the design method of different functional magnet structure is investigated. Then, the effects of different magnet shapes on the torque and vibration performances are compared. The result shows that the proposed sinusoidal+3rd-order harmonic injection functional magnet structure can effectively improve the vibration performance without sacrificing the average torque. Finally, the prototype of the 48-slot/8-pole PM with functional magnet structure is manufactured, and the experiments are carried out for validation.

Multi-objective design optimization of five-phase fractional-slot concentrated-winding surface-mounted permanent-magnet machine

Multi-objective design optimization of five-phase fractional-slot concentrated-winding surface-mounted permanent-magnet machine

Design Modeling and Prototyping of a 55 Watts Surface Mounted PM Machine With High Torque and Low Torque Ripple for Cooling Fan Application

Design Modeling and Prototyping of a 55 Watts Surface Mounted PM Machine With High Torque and Low Torque Ripple for Cooling Fan Application

A Nonlinear 3-D Hybrid Model for Surface-Mounted Permanent Magnet Machines Considering End Effect

A Nonlinear 3-D Hybrid Model for Surface-Mounted Permanent Magnet Machines Considering End Effect

Simple and Accurate Computation of Rotor Eddy-Current Losses in Surface-Mounted Permanent Magnet Machines Accounting for Magnet Circumferential Segmentation

Simple and Accurate Computation of Rotor Eddy-Current Losses in Surface-Mounted Permanent Magnet Machines Accounting for Magnet Circumferential Segmentation

Inductance Calculation and Analysis of Axial-Flux Slotless Surface-mounted Permanent Magnet Machine with Equidirectional Toroidal Winding

Inductance Calculation and Analysis of Axial-Flux Slotless Surface-mounted Permanent Magnet Machine with Equidirectional Toroidal Winding

Development of a Novel Radial-Flux Machine With Enhanced Torque Profile Employing Quasi-Cylindrical PM Pattern

This article presents a novel radial-flux surface-mounted PM (SPM) machine with quasi-cylindrical pole pattern (QCPP). With the proposed configuration, the cogging torque and torque ripple of surface-mounted machines could be greatly decreased due to the adoption of large eccentric distance and the reduction of high-order airgap flux density harmonics. Moreover, the increase of fundamental flux component helps to improve torque generation well. Additionally, the magnet poles are semi-embedded into the rotor, and thus the sleeve in conventional SPM machines is no longer necessary, which helps to reduce the airgap size and improve the torque output further. Besides, the quasi-cylindrical magnet could offer lower rotor eddy loss and higher anti-demagnetization capability than conventional radial and eccentric pole patterns. Studies have been conducted on the novel structure to validate its advantages. Firstly, the topological structure and working principle of the QCPP machine are presented. Then, the influence of the QCPP structural parameters on the torque performance is investigated. Next, an electrical machine with quasi-cylindrical pole pattern is designed. Subsequently, the electromagnetic characteristics, such as flux density distribution, back EMF, average torque, cogging torque, torque ripple, eddy loss in sleeve, rotor stress and anti-demagnetization capability, of the proposed machine are analyzed and compared with those of conventional SPM machine with eccentric magnetic poles and skewing slots. Finally, one research prototype is developed, and experiments are carried out to evaluate the design concept and performance of the proposed QCPP machine.

An Analytical Method for Determining Flux Density in Surface-Mounted Permanent Magnet Machines with Unequal Magnetic Poles

An analytical method was proposed for obtaining the magnetic field distribution for surface-mounted permanent magnet machines with the structure of unequal magnetic poles. Firstly, the Laplace equation and Poisson equation were solved using the method of the separation of variables, and then the mathematical model of the motor structure with unequal magnetic poles was obtained. Secondly, according to the design parameters of the two types of prototypes motors, the flux density in the air gap region of the two types of prototypes motors was calculated, respectively. Thirdly, by comparing the results calculated using the analytical method with the results obtained using the finite element method, the analytical method proposed in this paper was proven to be effective. Moreover, the armature reaction field and the effect of the stator slotting were considered in the mathematical model as well. Overall, the analytical method presented in this paper provides a theoretical basis for the analytical calculation of motors with the structure of unequal magnetic poles.

Design and Analysis of a Novel Dual-PM Flux Reversal Machine for Electric Vehicle Propulsion

Flux reversal machine with evenly distributed permanent magnet (EDFRM) is proved to have high torque density and low torque ripple. To further improve the torque density, a novel dual permanent magnet flux reversal machine (DPM-FRM) with PM on both stator and rotor is proposed and designed in this paper. The machine topology and operation principles are first introduced in detail. Then, with the goal of maximum torque and with the restriction of fixed copper loss, the proposed DPM-FRM is optimized based on finite element (FE) method. To verify the superiority of the proposed machine, its electromagnetic performance is compared with existing EDFRM and regular surface mounted PM machine (SPM), including flux linkage, back-electromagnetic force (back-EMF), cogging torque, rated torque, power factor, overload capability and so on. It is shown that the proposed DPM-FRM can deliver 78% and 26% higher torque compared with EDFRM and SPM. Finally, a prototype is manufactured and tested. The experimental results have verified the FE predictions.

Modelling and Analysis of Inter-Turn Short-Circuit Fault of PM Machines With Parallel-Connected Coils

This paper presents a general analytical fault model in a compact matrix form for surface-mounted permanent magnet (SPM) machines with parallel-connected coils, which is useful to study the machine performance under the inter-turn short circuit (ITSC) fault. To simplify the fault model, the multiphase Clarke transformation has been proposed. In the model, the branch currents rather than the phase currents are employed as state variables to describe machine behaviours under fault. Additionally, self- and mutual-inductances are obtained by winding function approach (WFA) plus slot permeance method. The proposed analytical fault model is applied to a 3 kW 96-slot 32-pole SPM machine and validated by time-stepping FE simulations. A small scale 12-slot 4-pole SPM machine prototype has also been built to further validate the accuracy of the proposed fault model.

In‐depth investigation of inter‐turn short‐circuit faults of surface‐mounted permanent magnet machines with series‐parallel coil connections

AbstractA general analytical model is developed in a concise block matrix form for surface‐mounted permanent magnet (SPM) machines with series‐parallel coil connections under inter‐turn short circuit (ITSC) fault. In the model, branch currents are used as state variables and inductances of different series‐parallel coil connections are calculated using an analytical method, namely winding function approach (WFA) together with slot permeance method. Based on the characteristics of the calculated inductances and the developed fault model, the multiphase Clarke transformation has been proposed to simplify the fault model. In the process of model simplification, the healthy machine model using branch currents as state variables have been proven to be equivalent to that using 3‐phase currents as state variables. The proposed fault models of a 3kW 96‐slot 32‐pole SPM machine with different series‐parallel coil connections have been built in Matlab/Simulink and validated by time‐stepping 2D FE simulations. Simulation results show that different series‐parallel coil connections have little influence on the amplitude of the ITSC current. Finally, a small scale 24‐slot 8‐pole SPM machine prototype has been built to further validate the accuracy of the proposed fault model.

Coupled Electromagnetic–Thermal Modelling of Dynamic Performance for Modular SPM Machines

This paper presents coupled electromagnetic (EM)–thermal modelling of the steady-state dynamic performances, such as torque speed curve and the efficiency map, for surface-mounted permanent magnet machines. One important feature of such a model is that it considers the demagnetization caused by magnet temperature rise at different rotor speeds. EM-only simulations, which often assume that the machines operate under constant temperature, have been widely used in the literature. However, the interaction between EM and thermal performances could lead to very different dynamic performance prediction. This is because the material properties, e.g., magnet remanence, coercivity, and copper resistivity are temperature-dependent. The temperature rise within electrical machines reduces torque/power density, PM eddy current losses, and iron losses but increases copper loss. Therefore, the coupled EM–thermal modelling is essential to determine accurate temperature variation and to obtain accurate EM performances of electrical machines. In this paper, the coupled EM–thermal modelling is implemented for both modular and non-modular machines to reveal the advantages of the modular machine under different operating conditions. The results show that the modular machine generally has better dynamic performance than the non-modular machine because the introduced flux gaps in alternate stator teeth can boost both EM and thermal performance.

Investigation of Six-Phase Surface Permanent Magnet Machine With Typical Slot/Pole Combinations for Integrated Onboard Chargers Through Methodical Design Optimization

This article presents an analytical magnetic equivalent circuit (MEC) modeling approach for a six-phase surface-mounted permanent magnet (SPM) machine equipped with fractional slot concentrated winding (FSCW) for integrated onboard chargers. For the sake of comparison, the selected asymmetrical six-phase slot/pole combinations with the same design specifications and constraints are first designed based on the parametric MEC model and then optimized using a multiobjective genetic algorithm (MOGA). The commercial BMW i3 design specifications are adopted in this article. The main focus of this study is to achieve optimal design of the SPM machine considering both the propulsion and charging performances. Thus, a comparative study of the optimization cost functions, including the peak-to-peak torque ripple and core losses under both motoring and charging modes and electromagnetic forces (EMFs) under charging, is conducted. In addition, the demagnetization capability in the charging mode and the overall cost of the employed machines are optimized. Since the average propulsion torque is crucial in electric vehicle (EV) applications, it is maintained through the design optimization process. Furthermore, finite element (FE) simulations have been carried out to verify the results obtained from the analytical MEC model. Eventually, the effectiveness of the proposed design optimization process is corroborated by experimental tests on a 2-kW prototype system.

Two-Dimensional Analytical Models for Cogging Torque Prediction in Interior Permanent Magnet Machine

Analytical prediction of cogging torque needs accurate flux density and relative permeance closed-form expressions. The accurate two-dimensional (2D) air gap flux density distribution function and the 2D permeance function are currently almost always applied to surface-mounted permanent magnet (SPM) machines, instead of interior permanent magnet (IPM) machines, due to complications from IPMs severe magnetic saturation and leakage flux. To address these issues, this paper proposes a set of new methods to derive the accurate closed-form 2D expressions of IPMs for both flux density and relative permeance. As for the flux density 2D model, a virtual equivalence model for IPM is introduced, so that Laplace’s equation and quasi-Poisson equation can be directly applied to IPM. As for permeance, the same virtual equivalence model also enables 2D models derivation for IPM. Subsequently, the resulting cogging torque analytical expression is obtained with the accurate relative permeance and air gap flux density models. The results from the proposed 2D analytical models showed similar accuracy to the finite element analysis (FEA). In addition, as demonstrated, the proposed 2D analytical models is a highly efficient tool set in the design process of cogging torque optimization, facilitating fast evaluation of different design factors.

A Hybrid Analytical Model for the Electromagnetic Analysis of Surface-Mounted Permanent-Magnet Machines Considering Stator Saturation

This article presents the process of building a hybrid analytical model (HAM) for surface-mounted permanent-magnet machines. The HAM couples a reluctance network (RN) model in the stator region with a magnetic scalar potential analytical model in the air gap and magnets regions. This hybrid model can deal with the slotting effect with straight teeth, and takes magnetic saturation into account in the stator iron material using the RN model. It is calculated under open-circuit and loaded conditions. The magnetic flux density, flux linkage, back electromotive force (EMF), and torque of the machines are also calculated. This hybrid model is compared with the subdomain method. It is also compared with the finite element method (FEM) both in terms of the size of the matrix that needs to be calculated and in terms of the torque error. We analyzed this method for two surface-mounted permanent-magnet machines, one with a symmetry factor of four and another with a symmetry factor of three. In both cases, HAM reduced the size of the matrix that needed to be solved compared to FEM. In the machine with a symmetry factor of three, when the matrix size of both FEM and HAM was around 1700 × 1700, the torque error of FEM was 2.62% compared to the high-mesh-density FEM simulation, while the torque error of HAM was only 0.17% compared to the same simulation. HAM also had significant advantages over the subdomain method, as it reduced the torque error from 16.8% to 0.08% in the case of high magnetic saturation. The HAM can, hence, play a significant role in the design and optimization of surface-mounted permanent-magnet machines, especially in cases where magnetic saturation is present.

Influence of slot/pole number combinations and pole shaping on electromagnetic performance of permanent magnet machines with unbalanced north and south poles

AbstractThe influences of slot/pole number combinations on electromagnetic performances, including flux linkage, inductance, and torque ripple harmonic components etc., resulting from unbalanced characteristics between north and south poles in concentrated winding permanent magnet (PM) machines with symmetrical and asymmetric rotor pole shaping methods are theoretically analysed and experimentally validated in this paper. It shows that for the PM machines with odd number of coils per phase per submachine, including consequent pole (CP) and surface‐mounted PM (SPM) machines, the influences of unbalanced pole characteristics can lead to additional torque ripple harmonics due to additive effects in windings, but can be cancelled in other machines. Compared with symmetrical pole shaping method, asymmetric pole shaping method can result in lower torque ripple for CPPM machines with odd number of coils per phase per submachine, while symmetrical and asymmetric pole shapes have similar effects on torque ripple reduction for other CPPM machines and all the SPM machines. The findings have been validated by finite element analyses on 12‐slot/8‐pole, 12‐slot/10‐pole, 9‐slot/6‐pole, and 12‐slot/14‐pole machines, and by experiments with 12‐slot/8‐pole and 12‐slot/10‐pole CPPM prototypes.

Scaling Effect On Inter-Turn Short-Circuit Fault of PM Machines for Wind Power Application

This paper proposes a general analytical model of surface-mounted permanent magnet (SPM) machines with series-connected coils under inter-turn short circuit (ITSC) fault. One prominent feature of this fault model is that the air-gap and slot-leakage components of inductances under fault are calculated separately, and the influences of pole number and spatial distribution of coils have been considered in the calculations. In the model, the winding function approach (WFA) is used to calculate the air-gap inductance components by considering all space harmonics whilst slot-leakage inductance components are obtained by using slot permeance method. The proposed fault model built in Matlab/Simulink is validated by time stepping FE simulations for a 3 kW 96-slot 32-pole SPM machine. The fault model has acceptable accuracy and is suitable for the fast evaluation of fault performance of SPM machines and its accuracy considering core saturation can be improved using FE-based results. Other power ratings (0.5 MW and 3 MW) have also been investigated to study the scaling effect on machine fault-tolerant capability. A 12-slot 4-pole small scale prototype has been built to validate the developed fault models.

A Multi-Objective Finite-Element Method Optimization That Reduces Computation Resources Through Subdomain Model Assistance, for Surface-Mounted Permanent-Magnet Machines Used in Motion Systems

Surface-mounted permanent-magnet (PM) motors are widely used in motion control systems because of their high peak torque-to-inertia ratio. These motors exhibit high magnetic saturation to produce high peak torque. A precise finite-element model (FEM) is needed to optimize these motors. It requires high computation power, especially for multi-objective optimizations. On the contrary, subdomain models require low computing power but are inaccurate when magnetic saturation occurs. To solve this problem, we use a subdomain-assisted FEM optimization method (SAFEMOM) that combines subdomain models for preoptimization and FEM for refined optimization. We provide the quantitative measurement methods to compare SAFEMOM with FEM-only optimization. If the constraints in the magnetic fluxes in the subdomain part of SAFEMOM are based on the actual saturation value of the materials, then the advantage of SAFEMOM is not significant. The machines in this study use non-linear material with a knee point at 1.3 T and hence show heavy magnetic saturation above 1.5 T. In that case, contrary to what could be intuitively thought, we need to increase the magnetic flux density limit to 2.6 T - 3.0 T in SAFEMOM to have a significant advantage. SAFEMOM reduces about 80% of computing time to obtain a slightly better convergence than the one using FEM only. Also, if limited computing resource is allowed, SAFEMOM gives an error reduced by a factor of nearly eight compared to the optimization error using FEM only. Those results are validated on a family of surface-mounted permanent-magnet machines with a wide range of design parameters.

Vibration Reduction Design of Consequent Pole PM Machine by Symmetrizing Local and Global Magnetic Field

The consequent pole permanent magnet (CPM) machine is well known for its high magnet utilization ratio and poor vibration performance. This article focuses on electromagnetic vibration and its reduction design in CPM machines, and the conventional surface-mounted permanent magnet (SPM) machine is used as a benchmark. First, the asymmetrical magnetic field and unbalanced radial force of the CPM machine are investigated with emphasis. The slot-pole combination and force modulation effect are the two reasons for the unbalanced radial force generation. Afterward, two new designs to reduce the vibration caused by the unbalanced radial force are proposed, and the reduction principles are described in detail. Finally, the prototypes of the 12-slot/10-pole SPM and proposed CPM machines are manufactured. The tests are conducted to validate the theoretical analysis and proposed vibration reduction design.