Spoke-type Permanent-magnet Machines Research Articles

Magnetic Field Prediction in Cubic Spoke-Type Permanent-Magnet Machine Considering Magnetic Saturation

In this article, a nonlinear semi-analytical model (SAM) is presented to predict the magnetic field distribution (MFD) and electromagnetic performances (EPs) in the cubic spoke-type permanent magnet (PM) machine. To model the rectangular PMs, the rectangular PM is simplified as a combination of fan-shaped regions with different arc angles. Then, the MFD and EPs of the cubic spoke-type machines can be obtained by the harmonic modeling (HM) technique. Particularly, the saturation of the magnetic bridges is considered by the nonlinear iterative algorithm. The proposed nonlinear SAM is studied on a 12-slot/8-pole cubic PM prototype, and the nonlinear finite element (FE) model and experiment verify its correctness. The main contribution of this article is to present a general analytical modeling method for cubic spoke-type PM machines and consider the magnetic saturation of magnetic bridges.

Design and Analysis of Axial-Flux Modular Spoke-Type Permanent Magnet Machines with Segmented Stators for Traction Applications

Design and Analysis of Axial-Flux Modular Spoke-Type Permanent Magnet Machines with Segmented Stators for Traction Applications

Investigation of Air-Gap Field Modulation Effect in Spoke-Type PM Machines

In this article, the air-gap field modulation effects (AFMEs) in spoke-type permanent magnet (STPM) machines with concentrated winding are investigated and revealed by quantifying the torque contributions of the various air-gap flux density harmonics. Due to the relatively stronger flux concentrated effect, the STPM structure exhibits greater resulting air-gap field harmonics for torque generation. In order to provide an in-depth understanding of their torque generation mechanism, the contributed torque components of the various air-gap field working harmonics are quantified by employing the Maxwell stress tensor (MST) approach. It identifies a fact that the abundant air-gap flux density harmonics have participated in torque production in the STPM machine. As a consequence, the field-modulated harmonics contributed a nonnegligible torque component, and hence, a pronounced AFME can be obtained in the STPM machine. Besides, the influences of the key dimension parameters, including split ratio, stator slot opening ratio, rotor PM thickness, and length, on AFEM for torque performance of the STPM machines are evaluated by the finite-element (FE) method. Finally, the reliability and effectiveness of theoretical analysis and FE simulation are verified by experiments on an STPM machine prototype.

Multi-objective optimization of high torque density spoke-type PM machine for special vehicle drive system

PurposeThis paper proposes a spoke-type fractional-slot concentrated windings (FSCW) permanent magnet (PM) machine for special vehicle driving systems to obtain higher torque and power density, high efficiency and wide field-weakening range. To enhance the efficiencies of multi-objective optimization processes, the respond surface (RS) method and black-hole (BH) algorithm are used.Design/methodology/approachThe spoke-type FSCW PM machine is optimized to meet the requirements of the special vehicle driving system. The combination of the RS and BH algorithm is used to obtain high torque, low torque ripple and high efficiency.FindingsThe optimal spoke-type PM machine is obtained, and it has higher torque density, lower torque ripple, cogging torque and wider magnetic field weakening range. Finally, a 15-kW prototype machine is fabricated and tested to verify the results of the optimization method and finite-element analysis.Originality/valueThis paper designs a high torque density and efficiency spoke-type FSCW PM machine, which is superior for special vehicle driving systems. Meanwhile, the RS model combined with BH algorithm is applied to the field of electrical machine multi-objective optimal design.

Comparative Study of High Torque Density Spoke-Type PM In-Wheel Motors for Special Vehicle Traction Applications

With the development of the transportation electrification, the demand for high-performance motor is growing rapidly. High torque density and wide constant power operating range are two key requirements of the electric vehicle (EV) traction applications. Considering the limited voltage and current, a successful EV traction machine should realize good linearity of torque–current characteristic and a proper characteristic current. In order to meet these strict demands, an optimized Fractional-Slot Concentrated-Winding(FSCW) permanent magnet (PM) machine with different rotor structures is proposed in this article based on the traditional spoke-type PM machine topology. The machine structures are introduced and optimized in the design procedure, and a magnetic equivalent circuit model is applied to illustrate its principle. The electromagnetic performances, including back electromotive force, output torque, and efficiency map, are compared between the original and optimized design to highlight the performance improvement of the optimized topology. Finally, a prototype machine has been built for the experimental validation. The experimental results, which agree well with the Finite Element (FE)-predicted results, confirm the validity of the analysis method used in predictions and the advantages of the optimized design.

Design and Optimization of a Low-Cost Hybrid-Pole Rotor for Spoke-Type Permanent Magnet Machine

In this article, a novel spoke-type permanent magnet (PM) machine with two types of PM materials is proposed to reduce the cost. In order to improve torque density and reduce torque ripple, the multi-objective optimization combined finite element method (FEM) and genetic algorithm (GA) are used. In addition, the electromagnetic performances of the novel spoke-type PM machine, including no-load air-gap flux density, electromagnetic torque, torque ripple, efficiency, and cost are compared with the conventional spoke-type PM machine. It is demonstrated that the novel spoke-type PM machine obtains a 1.5% lower torque ripple and 36% lower cost, and the torque density is 4.3% lower than the conventional spoke-type PM machine. Meanwhile, the novel spoke-type PM machine has lower core loss and higher efficiency. Finally, a 40 kW spoke-type PM machine is manufactured to verify the analyzing method. Experimental results demonstrate that the proposed machine exhibits high torque density and low cost in the application of electric vehicles (EVs).

Analytical Calculation for Magnetic Field in Spoke-Type Permanent Magnet Machines Based on a Rotor Magnetic Potential Model

In this article, the rotor magnetic potential (RMP) model of spoke-type machines is proposed, which can accurately describe rotor surface magnetic potential distribution. No-load and load magnetic fields are calculated by using the proposed RMP model. In order to accurately establish and solve the RMP model, the magnetic field in the machine is divided into the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> -axis magnetic field and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> -axis magnetic field. Then, corresponding <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> - and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> -axis RMP models are proposed, which can consider the saturation of the bridge region and the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> -axis cross-coupling. The unknown parameters in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> - and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> -axis RMP models are then obtained using simple lumped magnetic circuit (LMC) models. Furthermore, the total RMP model can be obtained by superimposing the above <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> - and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> -axis RMP models. The modeling process proposed in this article is intuitive and straightforward, and it has fewer variables to be solved. Moreover, the proposed method does not need to consider the change of the relative position between the stator and rotor caused by rotor rotation. Finally, the FEA is used to validate the validity of the proposed method.

Vibration Investigation of Spoke-Type PM Machine With Asymmetric Rotor Considering Modulation Effect of Stator Teeth

In this article, we analyze the vibration of the spoke-type permanent-magnet (PM) machine with an asymmetric rotor considering the modulation effect of the stator teeth. First, the semianalytical expression of the radial pressure is derived to quickly estimate the radial pressure characteristic. The equivalent spatial order of the radial pressure is determined by considering the modulation effect. Second, a structural finite-element (FE) model is set up. The modal test validates the accurateness of the structural FE model and modal analysis. Third, the vibration is predicted by an FE method and verified by the experimental results. The results show that the radial pressure harmonics become richer, and the fundamental frequency and lowest nonzero order of the radial pressure are both reduced due to the asymmetric magnetic barrier. Furthermore, the zero-order radial pressure is no longer the dominant vibration source in this integer-slot PM machine with an asymmetric rotor. Some high-order radial pressures that can be modulated as equivalent low-order harmonics excite the low-order and large vibration. In terms of vibration and noise, the equivalent lowest nonzero-order harmonic should be fully considered in the performance optimization for the asymmetric rotor design.

An improved model for performances calculation in spoke-type permanent-magnet machines considering magnetization orientation and finite soft-magnetic material permeability

PurposeIn semi-analytical modeling of spoke-type permanent-magnet (PM) machines (STPMM), the saturation effect is usually neglected (i.e. iron parts are considered to be infinitely permeable) and the PM magnetization is assumed tangential (i.e. magnetization pattern is considered to be tangential-parallel). This paper aims to present an improved two-dimensional (2D) subdomain technique for STPMM with the PM magnetization orientation in quasi-Cartesian coordinates by using hyperbolic functions considering non-homogeneous Neumann boundary conditions (BCs) in non-periodic regions and by applying the interfaces conditions (ICs) in both directions (i.e. t- and θ edges ICs).Design/methodology/approachThe polar coordinate system is transformed into a quasi-Cartesian coordinate system. The rotor and stator regions are divided into primary subdomains, and a partial differential equation (PDE) is assigned to each subdomain. In the PM region, the magnetization orientation is considered in the equations. By applying BCs, the general solution of the equations is determined, and by applying the ICs, the corresponding coefficients are determined.FindingsUsing the proposed coordinate system, the general solution of PDEs and their coefficients can mathematically be simplified. The magnetic field and non-intrinsic unbalanced magnetic forces (UMF) calculations have been performed for three different values of iron core relative permeability (200, 800 and ∞), as well as different magnetization orientation values (135 and 80 degrees). The semi-analytical model based on the subdomain technique is compared with those obtained by the 2D finite-element analysis (FEA). Results disclose that the PM magnetization angle can affect directly the performance characteristics of the STPMM.Originality/valueA new model for prediction of electromagnetic performances in the STPMM takes into account magnetization direction, and soft magnetic material relative permeability in a pseudo-Cartesian coordinate system by using subdomain technique is presented.

Analytical Method for Calculating the Magnetic Field of Spoke-Type Permanent Magnet Machines Accounting for Eccentric Magnetic Pole

This article proposes an analytical method to calculate the magnetic field, back electromotive force (BEMF), inductance, and torque of spoke-type permanent magnet machine (PMM) accounting for eccentric magnetic pole. The magnetic field in the slotted spoke-type PMM is predicted according to conformal mapping, flux continuity theorem, double reaction theory, superposing principle, and complex relative air-gap permeance. Then, BEMF, inductance, and torque are obtained according to the results of magnetic field. A spoke-type PMM with eccentric magnetic pole is used to verify the analytical model. The harmonics of BEMF and torque ripple of spoke-type PMM with eccentric magnetic pole are very slight. Results of magnetic field, BEMF, inductance, and torque by the analytical model are verified by finite element. The validation to calculate BEMF and electromagnetic torque with analytical model is confirmed by experimental result. The analytical method proposed in this article can be applied to the spoke-type PMM with all kinds of magnetic-pole shape.

Comparative analysis of spoke‐type, consequent‐pole and hybrid‐pole permanent magnet machines

In recent years, consequent-pole permanent magnet (CPM) machines draw much attention due to their high utilisation ratio of permanent magnet (PM) material. However, they have some disadvantages, such as the even-order harmonics of airgap flux density, which may cause asymmetric phase back-EMF and the increase of torque ripple. In this study, a novel hybrid-pole PM (HPM) machine is proposed, in which the rotor combines consequent-pole and spoke-type PM rotors. The working principle of the proposed HPM machine is analysed based on the equivalent magnetic circuit, and validated by the finite-element method. Then, the electromagnetic performance of the HPM machine is compared with those of the existing CPM and spoke-type PM machines. It is shown that the HPM machine obtains similar average torque, PM utilisation ratio, torque ripple and efficiency to the spoke-type PM machine, whilst it has a higher PM utilisation ratio and much lower torque ripple than the conventional CPM machines. Finally, these analyses are validated by the tested results of a 9-slot/6-pole HPM machine.

Analytical approach for spoke-type permanent magnet machine including finite permeability of iron core

Purpose The purpose of this study is the introduction of finite permeability of ferromagnetic core in analytical approach for slotted spoke-type permanent magnet machine. Design/methodology/approach A two-dimensional analytical approach of magnetic field distribution is established for spoke-type permanent magnet machine to calculate the flux density distribution in the middle of airgap. The paper presents an analytical subdomain model accounting for stator slotting effect. The governing equations are obtained from Maxwell’s equations by using vector potential in all regions of the machine, i.e. magnet, airgap, stator slots and rotor/stator yoke. The finite element analysis is used to validate the analytical results. Findings It is found that the developed subdomain model including finite permeability of ferromagnetic core is accurate and is applicable for spoke-type permanent magnet machine for no-load and on-load condition. The analytical results are in accurate agreement with the numerical simulation. Originality/value Some assumptions and conditions are presented to improve and simplify the analytical method for analyzing the global saturation for spoke-type permanent magnet machine.

Multiobjective Deterministic and Robust Optimization Design of a New Spoke-Type Permanent Magnet Machine for the Improvement of Torque Performance

This article proposes a comprehensive multiobjective optimization design method for a new spoke-type permanent magnet machine with auxiliary salient poles for the improvement of torque performance. The key of this method is to consider the deterministic and robust performances simultaneously. First, the sensitivity analysis is adopted to classify design parameters into different levels and the corresponding optimization techniques are skillfully employed to realize the tradeoff design based on the appropriate model constructed by the response surface methodology. However, inevitable perturbations especially during the mass production will result in big fluctuations of torque performances and affect the reliability and quality of the machine, which are often neglected in deterministic design. Therefore, a robust design method, i.e., the design for six sigma, is presented to address the parametric uncertainties. Afterward, the Monte Carlo analysis is used to obtain the statistic samples and the barebones multiobjective particle swarm optimization algorithm is employed to find the robust optimal solution. The corresponding electromagnetic performances and reliability of the products are compared and analyzed. Finally, a prototype is manufactured and tested to verify the validity of the proposed optimization design method.

A novel analytical calculation of magnetic field in the slotted air gap of spoke-type permanent-magnet machines using conformal mapping

This paper presented a novel analytical method for calculating magnetic field in the slotted air gap of spoke-type permanent-magnet machines using conformal mapping. Firstly, flux density without slots and complex relative air-gap permeance of slotted air gap are derived from conformal transformation separately. Secondly, they are combined in order to obtain normalized flux density taking account into the slots effect. The finite element (FE) results confirmed the validity of the analytical method for predicting magnetic field and back electromotive force (BEMF) in the slotted air gap of spoke-type permanent-magnet machines. In comparison with FE result, the analytical solution yields higher peak value of cogging torque.

Comparative Study on Two Modular Spoke-Type PM Machines for In-Wheel Traction Applications

This paper focuses on the comparative analysis of modular spoke-type permanent magnet machines with two magnetization modes, which are referred to as M-I and M-II types. The analytical models of the proposed machines are built based on the simple magneto-motive-force-permeance method. With the help of finite element analysis and the analytical models, magnetic fields in machines with different magnetization modes are compared. Then, taking as a base an existing commercial in-wheel machine used in an electric motorcycle, two proposed machines with different magnetization modes are designed as in-wheel traction machines and compared with respect to electromagnetic torque, flux-weakening performance, over-load capability, etc. The machines are prototyped and experimentally tested to verify the prediction that the M-II machines exhibit a higher torque output whereas the M-I machines have a wider speed range.

A Novel Spoke-Type PM Machine Employing Asymmetric Modular Consequent-Pole Rotor

This paper proposes a novel spoke-type permanent magnet (PM) machine, which adopts asymmetric modular consequent-pole (AMCP) rotor to enhance the effective PM flux due to the increased flux-focusing effect and reduced leakage flux and to improve the flux-weakening capability due to the increased d -axis inductance. Moreover, the pole-shaping method based on three sectional arcs is proposed to suppress the harmonics of airgap flux density. Since the rotor structure is relatively complex, the finite-element analysis together with multiobjective genetic algorithm is adopted to optimize this design. Furthermore, the electromagnetic performance of the spoke-type PM machine with the proposed AMCP rotor (Spoke-AMCP), including the open-circuit airgap flux density, phase back electromotive force, torque, PM utilization ratio, efficiency, and flux-weakening capability, are compared with two conventional spoke-type PM machines with evenly distributed and alternate flux barriers (Spoke1 and Spoke2) and consequent-pole spoke-type PM machine (Spoke-CP). It is demonstrated that the Spoke-AMCP machine obtains the largest output torque and PM utilization ratio, lowest torque ripple and similar efficiency compared to Spoke1, Spoke2 and Spoke-CP machines. Moreover, although the Spoke-AMCP machine has the largest PM flux linkage, it has slightly better flux-weakening capability than the Spoke1 and Spoke2 machines. Finally, a 12-slot/10-pole Spoke-AMCP machine is built and tested to verify the analyses.

Modular Spoke-Type Permanent-Magnet Machine for In-Wheel Traction Applications

This paper proposes a novel modular spoke-type permanent-magnet machine for in-wheel traction applications. First, the topology and the operating principle are briefly introduced. Then, an analytical model of the proposed machine is deduced based on conformal mapping. A three-phase 48-slot 52-pole modular spoke-type permanent-magnet (PM) machine is designed based on the deduced mathematical model where the dimensions and power source are constrained the same as those of a commercial three-phase surface PM machine in electric motorcycles. Electromagnetic performance comparisons among the proposed machine, the commercial machine, and a conventional spoke-type PM machine are conducted based on finite-element analysis (FEA) with respect to magnetic field, back electromotive force (EMF), flux-weakening capability, torque capability, machine efficiency, etc. The results indicate that the proposed machine has an improved torque, a higher efficiency, and an extremely better flux-weakening capability than the conventional in-wheel machine. Finally, a prototype machine is manufactured and tested to verify both the analytically and FEA predicted results.

Analytical Calculation and Optimization of Magnetic Field in Spoke-Type Permanent-Magnet Machines Accounting for Eccentric Pole-Arc Shape

This paper presents an analytical method for calculating and optimizing magnetic field in spoke-type permanent-magnet machines accounting for eccentric pole-arc shape. Normalized flux density is derived from conformal transformation taking into account eccentric pole-arc shape, and final field solution is predicted according to the flux continuity theorem. The optimal results show the harmonic content of flux density can be reduced a lot by optimizing eccentric distance of eccentric pole arc while fundamental content will reduce a little. The proposed analytical solution on prototype machines is implemented. The finite element (FE) and experimental results confirm that the developed analytical method has high accuracy for predicting and optimizing magnetic field.

Analytical model and design of spoke-type permanent-magnet machines accounting for saturation and nonlinearity of magnetic bridges

Based on subdomain model, this paper presents an analytical method for predicting the no-load magnetic field distribution, back-EMF and torque in general spoke-type motors with magnetic bridges. Taking into account the saturation and nonlinearity of magnetic material, the magnetic bridges are equivalent to fan-shaped saturation regions. For getting standard boundary conditions, a lumped parameter magnetic circuit model and iterative method are employed to calculate the permeability. The final field domain is divided into five types of simple subdomains. Based on the method of separation of variables, the analytical expression of each subdomain is derived. The analytical results of the magnetic field distribution, Back-EMF and torque are verified by finite element method, which confirms the validity of the proposed model for facilitating the motor design and optimization.

Establishing the Relative Merits of Interior and Spoke-Type Permanent-Magnet Machines With Ferrite or &lt;roman&gt;NdFeB&lt;/roman&gt; Through Systematic Design Optimization

In this paper, a multiobjective design optimization method combining design-of-experiments techniques and differential-evolution algorithms is presented. The method was implemented and utilized in order to provide practical engineering insights for the optimal design of interior and spoke-type permanent-magnet machines. Two combinations with 12 slots and 8 poles and 12 slots and 10 poles, respectively, have been studied in conjunction with rare-earth neodymium-iron-boron (NdFeB) and ferrites. As part of the optimization process, a computationally efficient finite-element electromagnetic analysis was employed for estimating the performance of thousands of candidate designs. Three optimization objectives were concurrently considered for minimum total material cost, power losses, and torque ripple, respectively. Independent variables were considered for both the stator and rotor geometries. A discussion based on a systematic comparison is included, showing, among other things and despite common misconception, that comparable cost versus loss Paretos can be achieved with any of the rotor topologies studied.