Permanent Magnet Shape Research Articles

Robust design for reducing cogging torque in surface‐mounted permanent magnet synchronous motor considering tolerances of sub‐components

This study deals with a robust design for cogging torque reduction considering the production tolerances of motor sub-components, which is related to the dimensions of the permanent magnet and stator core shape. A 14-pole and 12-slot fractional slot concentrated winding motor is employed as the design model. Prior to a robust design, an initial model was implemented to satisfy the torque demand within some constraints. In the robust design, the main design variables were first selected for the design of experiment (DOE). The interaction effects were investigated using the full factorial design, which is one of the DOE techniques. Next, the direction of design variables to minimise the cogging torque and improve the signal-to-noise ratio were confirmed using the Taguchi method. Then, the response surface methodology was implemented based on the result from the Taguchi method to yield an optimum value of the design variables and approximate equivalent polynomial equation. Finally, the normal distribution curve of the cogging torque was simply determined by the equivalent polynomial equation using the Monte-Carlo method taking production tolerances based on the process capability of the sub-components into consideration.

Performance verification of DR-PMSM for traction system according to permanent magnet shape

Unlike the conventional railway traction motor, the concept of the dual-rotor in a dual-rotor permanent magnet synchronous motor (DR-PMSM) is that two rotors are mounted on the same rotation axis, and the outer rotor and the inner rotor rotate at different speeds. The DR-PMSM can transmit the power to the wheels in a structure that can cope with various problems of the reducer systems using mechanical gear mechanisms. In this research, the design study of the inner rotor including the permanent magnet is carried out in the application of the DR-PMSM. In designing the DR-PMSM models, surface permanent magnet (SPM) type and interior permanent magnet (IPM) type are considered according to the permanent magnet type of rotor, and IPM type is designed by dividing into bar type and V type. A comparative analysis of the three 1kW-class DR-PMSM models, in terms of electromagnetic properties, is performed to assess their general performance. The overall electromagnetic properties of the three designed models are similarly derived. But, the cogging torque and the rated torque characteristics of the IPM (V) type model are the best in comparison with the other models. In addition, the 1kW-class DR-PMSM prototype with V type magnet is fabricated to verify the validity of the analytical model and performance verification is performed.

Multiphysics Analysis of an Axial-Flux In-Wheel Motor With an Amorphous Alloy Stator

This paper presents a novel yokeless and segmented armature (YASA) axial-flux in-wheel motor with amorphous magnetic material (AMM) stator cores for a solar-powered electric vehicle. Although this new axial-flux in-wheel motor has many advantages such as high efficiency, shorter axial length, and high power density, its working condition is complicated. In-wheel motors are usually operated in electromagnetic, thermal, and other multiphysics environments. Increasing the performance requirements of in-wheel motors, such as power density, efficiency, and reliability, requires a multiphysics design approach. The focus of this paper is on the analysis of electromagnetic characteristics, losses, temperature distribution, mechanical behavior and other characteristics of the axial-flux in-wheel motor. The back electromotive force (EMF) and electromagnetic torque of the motor with harmonic current are obtained by the 3-D finite element method (FEM). The permanent magnet (PM) eddy-current losses when using different PM shapes are studied. The equivalent thermal model of the tape-wound AMM stator segments and the windings are established, and the temperature distribution of the motor is obtained. The mechanical behavior of the stator segments and the rotor disks when the motor is eccentric and axially offset is analyzed, and the structural strength of the motor is evaluated. Finally, a prototype of the motor is fabricated, and the electromagnetic performance and temperature of the motor are tested to verify the accuracy of the multiphysics design approach.

Analytical Modeling for Optimal Rotor Shape to Design Highly Efficient Line-Start Permanent Magnet Synchronous Motor

In this study, an analytical technique for the rotor geometry optimization based on lumped magnetic parametric approach is used to design a two-pole, three-phase, 7.5-kW line-start permanent magnet (LSPM) synchronous motor. The permanent magnet shape substantially affects the air-gap flux density distribution, back electromotive force (EMF) as well as the copper loss, which have a great impact on the performance characteristics of the permanent magnet synchronous motors. Principal advantages involve in adjusting the rotor shape are to achieve the effective air-gap flux density and optimize the fundamental component of the back EMF with low harmonic content for minimum ripple torque. Therefore, to enhance the efficiency (η) and power factor, an optimized slot shape considering various design parameters is selected for the permanent magnet of the rotor in the prototype LSPM machine. A linear saturated lumped magnetic parametric model is developed to exhibit magnetic characteristics, and analytical equations are acquired under the open-circuit condition without considering the slotting effect for design simplicity. The influence of design variables on the air-gap flux density distribution and the flux leakage is investigated precisely using an analytical circuit model. A parametric study of the prototype model demonstrates that the steady-state performance of the LSPM motor are significantly influenced by the design variables. The inductance saliency ratio and electromagnetic torque components are carefully analyzed in terms of their effects on the load characteristics of the LSPM motor in order to determine the optimal shape of the PM slots and the magnetic flux barriers. The validity of the proposed method has been checked by evaluating the numerical solution of the analytical model using a two-dimensional finite element method.

Permanent Magnet Shape Optimization of Driving Motor for In-wheel Considering Eddy Current Loss

Permanent Magnet Shape Optimization of Driving Motor for In-wheel Considering Eddy Current Loss

Analysis of Torque Ripple and Cogging Torque Reduction and Vibration Characteristics by Changing Permanent Magnet Shape of 5 kW SPM Type Generator

In this paper, the characteristics of the electromagnetic field using FEM are analyzed for the PMSG basic model, and the optimized design is performed to improve the performance of the generator. In the case of the SPM type 5 kW generator used in this paper, the torque ripple level was analyzed to be relatively high compared with the load torque generated during operation. Therefore, shape design was performed to reduce it, and permanent magnet shape was selected as design variables. Particularly, the characteristics of permanent magnet attached to the rotor surface by segment type and magnet tapering were compared. As a result, reduction in torque ripple and cogging torque was confirmed through the design of the shape of the permanent magnet. Also, the influence of the change of torque ripple and cogging torque on the vibration characteristics was studied. The vibration characteristics of the basic model and the improvement model were compared and analyzed based on the electromagnetic characteristics data. Simulation data shows that the amplitude of vibration is reduced in the improved model.

The Effect of Cone Additional Permanent Magnet Thickness on Magnetic Field Distribution and the Levitation Force of Single Domain GdBCO Bulk Superconductor

It has been investigated that the interaction force between truncated cone permanent magnet (PM) and a GdBCO bulk (HTSC) superconducting permanent magnet (SCPM) magnetized by a truncated cone permanent magnet in their configurations at 77K. The influence of two configurations in different thickness of truncated cone permanent magnets of single domain GdBCO bulk capture field and superconducting magnetic levitation force results. The maximum superconducting magnetic levitation force first increases as H increase, and then decreases with H when it reaches a certain value, from 5.7N to 16.6N at first, and then it decreases to 3.8N. The vertical component of the magnetic field intensity on the top surface (h=2mm) of truncated cone permanent magnet first increases, and then decreases also, from 0.20T to 0.54T, and then decrease to 0.25T. These results indicate that the levitation force of high temperature superconductor bulk can be effectively improved by scientific choosing of shape and size of permanent magnet, and reasonable designing of the system configurations, which is very important during the practical design and applications of superconducting magnetic levitation system.

Electromagnetic Characteristics of Permanent Magnet Linear Generator (PMLG) Applied to Free-Piston Engine (FPE)

The electromagnetic characteristics of the permanent magnet linear generator (PMLG), which is the key components of the free-piston engine (FPE), are studied in this paper. First of all, the velocity, displacement, and output voltage of the flat-type linear generator used in the experimental platform in the half-motion cycle are simulated by the model of 3D electromagnetic field and verified by experiment, and the relation curves of the output voltage to running velocity are found. Then, the PMLG is re-designed as a tubular type with two different structures of the permanent magnet on the steel backing of the mover: rectangular and the I-shaped. Third, the new PMLGs are modeled, and the models are used to do a simulation to investigate the influence of the structure of permanent magnet on the electromagnetic characteristics under no-load and load conditions. It is found that the fundamental wave amplitude of the flux density in the air gap of I-shaped PMLG is 0.93 T, greater than the rectangular one (0.87 T), and the proportion of the fundamental wave is higher. The waveform of the no-load induced electromotive force of the I-shaped PMLG is much better than that of the rectangular one, and the voltage total harmonic distortion (VTHD) is only 3.05%. The detent force analysis shows that the permanent magnet shape has a great influence on the detent force, and the peak value of detent force between I-shaped and rectangular PMLGs is significantly decreased from 25.4 to 7.75N. Moreover, the relation of the generator output power-velocity and efficiency-velocity under different loads is found. When the load is constant, with the velocity increases, the difference of output power between the I-shaped and rectangular structures becomes bigger. The optimum range of running velocity of the generator with the higher efficiency under different loads is presented. In conclusion, the I-shaped structure of the permanent magnet is a better choice for FPE.

Analytical Model of Torque-Prediction for a Novel Hybrid Rotor Permanent Magnet Machines

This paper presents an analytical method for predicting the electromagnetic performance in permanent magnet (PM) machine with the spoke-type rotor (STR) and a proposed hybrid rotor structure (HRS), respectively. The key of this method is to combine magnetic field analysis model (MFAM) with the magnetic equivalent circuit model. The influence of the irregular PM shape is considered by the segmentation calculation. To obtain the boundary condition in the MFAM, respectively, two equivalent methods on the rotor side are proposed. In the STR, the average flux density of the rotor core outer-surface is calculated to solve the Laplace's equation with considering for the rotor core outer-surface eccentric. In the HRS, based on the Thevenin's theorem, the equivalent parameters of PM remanence BreB and thickness hpme are obtained as a given condition, which can be utilized to compute the air-gap flux density by conventional classic magnetic field analysis model of surface-mounted PMs with air-gap region. Finally, the proposed analytical models are verified by the finite element analysis (FEA) with comparisons of the air-gap flux density, flux linkage, back-EMF and electromagnetic torque, respectively. Furthermore, the performance that the machine with the proposed hybrid structure rotor can improve the torque density as explained.

Influence of Shape and Arrangement of Permanent Magnets on Characteristics of Outer-Rotor IPM Motor

Influence of Shape and Arrangement of Permanent Magnets on Characteristics of Outer-Rotor IPM Motor

Structural Expression Code Method and its Application in Optimal Design of Permanent Magnet

In the process of designing electromagnetic equipment how to obtain the satisfied distribution of magnetically dense precisely though the variation of permanent magnet structure is a big challenge. The existing methods only do optimization for parameters under a fixed or several fixed structures. However, no optimization is done concern both structure and parameters simultaneously. To address this, a structural expression code (SEC) method is proposed. It can encode the structure and parameters simultaneously, realizing the optimization of the real structural scheme and parameters at the same time. The SEC method can solve a large proportion of the optimal design of electromagnetic equipment with flexible structure. Of course, it can also be used in other mechanical structural optimal design. The SEC method is proved by optimizing the structure and parameters of a permanent magnet for permanent magnet synchronous motor (PMSM) combined with genetic operator and evolutionary framework. The simulation result obtained by finite element method shows the optimal designed permanent magnet shape produces an air gap flux density waveform whose sinusoidal distribution is 99.78%.

Permanent magnet shaping for cogging torque and torque ripple reduction of PMSM

PurposeThis paper aims to the improvement of permanent magnet shape in the popular permanent magnet synchronous machine (PMSM) is proposed in this paper in view to mitigate cogging torque magnitude and torque ripple.Design/methodology/approachA two-dimensional exact analytical approach of magnetic field distribution is established for the PMSM considering magnet shape and slot opening. The optimal magnet shape is constituted of small number of layers stacked radially. The thickness of each magnet layer is considered equal to about one mm or more; however, a parametric study was performed to determine pole pitch ratio value. The finite element method is used to validate the analytical results.FindingsCogging torque peaks and torque ripples can be mitigated significantly more than 90 per cent compared to results issued from machine having classical magnet shape. Raising the number of magnet layers can give better results. The results of this paper are compared also with those issued from the machine having sinusoidal magnet shape and give a good solution.Originality/valueA new technique for cogging torque and torque ripple mitigation is proposed in this paper by changing permanent magnet shape. The proposed final magnet shape is constituted of a set of stacked and well-dimensioned layers relative to the opening angle.

Combined ON/OFF and conformal mapping method for magnet shape optimisation of SPMSM

In this study, a combined ON/OFF and conformal mapping method is applied to the permanent magnet shape optimisation of the surface-mounted permanent magnet synchronous motor (SPMSM). The magnet shape has a profound impact on the cogging torque and torque profile of the SPMSM. The proposed method is based on the combination of the conformal mapping and ON/OFF methods, which can reduce computation time significantly as compared with methods that are based on the finite-element method (FEM). For the optimisation process, genetic algorithms are used and applied to three cases. Finally, the FEM is used to verify the magnetic model and characteristics of the optimised machine.

Back‐electromotive force analysis of permanent magnet micromotor using applicational 3D analytical model

Permanent magnet (PM) axial flux machines are well adopted in microelectromechanical systems application, which needs a short axial length. PM micromotors have special characteristics such as transition zone which made their analysis different from macro ones. Due to the three-dimensional (3D) nature of PM micromotors, analysis and design of these micromotors require a fast and adopted 3D analytical model. This study presents a new 3D analytical model for a PM micromotor. In the presented analytical model, the micromotor is divided into several radial slices to take into account a part of 3D effects. In each slice, magneto-quasi-static Maxwell's equations are solved and back-electromotive force voltage is calculated as the most important parameter of micromotors. The accuracy of the model is verified by experimental and a 3D finite-element method model. The universality of the presented analytical model is challenged by using micromotors with different PM shapes including circular and trapezoidal. The presented analytical model is much faster than the 3D finite element model, but has the same accuracy, which makes it suitable for sensitive analysis and optimisation procedures.

Multi-Material Topology Optimization of Magnetic Actuator With Segmented Permanent Magnets

This paper proposes the multi-material topology optimization for the simultaneous design of segmented permanent magnet (PM) arrays, coil, and iron materials in magnetic actuators. Specifically, the proposed approach can find the optimal layout and shape of PM, coil, and iron materials, as well as the optimal border and magnetization direction of segmented PM arrays. For designing the layout and shape of actuator components, the discrete material optimization-type material interpolation scheme is employed in this paper. To attain the design of segmented PM arrays, an orientation design variable in Cartesian coordinate is utilized with the penalization scheme for the discrete PM magnetization directions. To validate the effectiveness of the proposed actuator design approach, two numerical examples are presented. In the examples, the actuator components (i.e., segmented PM arrays, coil winding, and back iron) are designed aiming for maximizing the magnetic force magnitude acting on the actuator plunger.

Methods for Increasing the Saturation Current and Charging Speed of a Rotary HTS Flux-Pump to Charge the Field Coil of a Synchronous Motor

The rotary flux-pump using HTS tape has been studied for superconducting rotating machinery application. The charging speed and saturation current of the rotary HTS flux-pump is closely related to magnetic flux linkage passing through the HTS tape. To analyze charging parameters that effect pumping rate and saturation current of the flux-pump, methods of changing the rotating speed, shape of permanent magnet, width of HTS tape, and magnetic flux intensity have been investigated in previous studies [1] – [3] . In this paper, we have tried to test three cases to investigate the pumping rate and saturation current: 1) two different background materials, iron and Bakelite, were used to compare the magnetic flux linkage reinforcement; 2) two HTS tapes were overlapped to extend the magnetic flux linkage area, and each HTS tape was connected to an HTS coil; and 3) the parallel joint was conducted between the flux-pump and the HTS coil to compose a closed loop for persistent current mode. In order to measure the charging speed and pumping rate, a Hall sensor was installed at the center of the HTS coil.

Torque Improvement of Dual Three-Phase Permanent Magnet Machine Using Zero Sequence Components

This paper investigates the interaction of the zero sequence component into both permanent magnet (PM) shape and phase current to improve the output torque in dual three-phase surface-mounted PM (SPM) machines. The optimal zero sequence components are analytically derived and validated by finite element (FE) analyses. It is found that the optimal zero sequence components into both PM shape and current waveform are dependent on the fundamental and zero sequence harmonic winding factors. For the dual three-phase SPM machines having rotors without shaping, Sine shape, Sine shape with the zero sequence components, the electromagnetic performances including the back electromotive force (EMF) waveform, cogging torque, average torque, and torque ripple are compared. It is demonstrated that the average torque with the optimal zero sequence component in PM shaping and current waveform can be improved by >30% while the torque ripple remains similar to that of the one with Sine shaping. Finally, the experiments are given to verify both the analytical and FE analysis.

Additive Manufacturing of Bonded Nd–Fe–B—Effect of Process Parameters on Magnetic Properties

Isotropic-bonded magnets were fabricated by powder bed fusion additive manufacturing (AM) using a feedstock composed of polymeric binder polyamide 12 (PA-12) and a near stoichiometric Nd2Fe14B atomized nanocrystalline powder. The AM equipment constructed for that purpose uses a computer-controlled laser beam to melt the binder and build the parts layer by layer. Three process parameters were evaluated: layer thickness (LT), hatch spacing (HS), and laser power (LP). For the evaluation of magnetic properties, cylindrical samples with diameter and height of 10 mm were produced and measured in a hysteresisgraph. For a feedstock, based on a 34% volumetric fraction of PA-12, the highest density value achieved was 3.6 g/cm3, resulting in a remanence of 0.3 T. These relatively low values for remanence are due to the isotropic characteristic of the powder, the binder fraction, and the interparticle porosity not being completely eliminated. Results indicate that LT affects densification more significantly than LP and HS. Consequently, remanence follows the same trend. Coercivity has not been affected much by optimized process parameters, since the values of original atomized powder of around 700 kA/m remained practically the same. The overall conclusion shows encouraging results to explore this alternative AM technique to produce net shape permanent magnets.

Performance comparison of a spoke‐type PM motor with different permanent magnet shapes and the same magnet volume

This study investigates the characteristics of a spoke-type permanent magnet (PM) motor with one of three magnet shapes, rectangular magnet (RM), trapezoidal magnet (TM), or inverted TM (ITM) in order to compare motor performance for the same magnet volume. The three magnet shapes vary in terms of upper thickness, lower thickness, and width of the magnet. Two-dimensional (2D) finite element method is performed to analyse torque, inductance, core loss, efficiency, and demagnetisation reliability. Advantages and disadvantages of each magnet shape are presented based on the analysis results. The ITM motor shows higher efficiency at its rated load due to the reduced core loss resulting from the decreased armature reaction field coupled with the increased magnetic reluctance circuit of the rotor near the airgap. However, the ITM motor shows lower maximum torque due to the reduced reluctance torque and demagnetisation reliability with a heavy over-current. ITM is thus suitable for applications that require low core loss with small starting torque, e.g. fans, TM is helpful for increasing maximum torque, and RM is appropriate for low-cost applications that require high demagnetisation reliability. Therefore, magnet shape should be carefully considered based on the required specifications of the motor application.

Optimum Injected Harmonics Into Magnet Shape in Multiphase Surface-Mounted PM Machine for Maximum Output Torque

Harmonics can be injected into the permanent magnet (PM) shape to maximize the output torque in five-phase machines. The optimal harmonics of different orders for maximum torque is mathematically derived and validated by the finite element (FE) method in this paper. The output torque of the five-phase machine with sinusoidal shape can be improved by 12.5% by injecting the optimal third harmonic. Meanwhile, 3.2% further more torque improvement can be obtained with the optimal third and fifth harmonics injected. However, the output torque barely change with the seventh harmonic injection. The torque ripple of the machines with shaped PMs is much lower than the machines with conventional tile PM. The electromagnetic performance for all the machines including back electromotive force, average torque, torque ripple, etc., are compared. Finally, the five-phase machine with third and fifth harmonics injection into the rotors is prototyped to verify the analytical and FE analyses.