Shape optimization of PM devices using constrained gradient based inverse problem methodology

Consequent pole (CP) permanent magnet (PM) machines offer scope for reducing the quantity of PM material and hence cost compared to more conventional PM machine topologies of the same rating. In this type of machine, the rotor pole arc is usually optimized to realize the largest output torque with pole shaping methods used to reduce torque ripple. However, such approaches tend to be limited by constraints imposed on the pole shapes. It is a common practice to adopt similar PM and iron pole shapes, an approach that does not fully account for the different characteristics of PM and iron poles in CPPM machines, often leading to large even order harmonics in the airgap flux density. This article proposes a shaping method with a variable rotor profile and pole arc span being established by means of optimization by Genetic Algorithm. It is demonstrated that for a fixed quantity of PM material, different PM and iron pole shapes in combination with optimal PM and iron pole arc spans are essential for ensuring both maximum output torque and lower torque ripple when the due account is taken of flux leakage. It also demonstrates that since the flux density in the region under a PM pole is governed by the magnetic potential produced by magnets while it is governed by magnetic reluctance under iron pole, different PM pole and iron pole shapes are necessary to reduce the even-order harmonics in a CPPM machine and consequently to reduce torque ripple. The performances of optimized and more conventional CP machines are compared by finite-element method on 12-slot/8-pole prototype motors.

This paper proposes an alternative interior permanent magnet machine (IPMM) design in which the rotor consists of stacks varied in the axial direction. The proposed design aims to reduce the amount of permanent magnet (PM) materials in conventional IPMMs. The PM width and the PM pole arc on the rotor surface for each rotor stack are both optimized to provide a resultant PM flux distribution in the air gap that contains fewer harmonics. Not only is the pulsating torque reduced significantly, the PM materials are also minimized since the PM portion making up the spatial PM flux harmonics is effectively removed. The results of the proposed design concept indicate a significant torque pulsation reduction in comparison with the base-line model 2007 Camry motor. Moreover, a trade-off is discovered between the average torque production and the PM utilization in an IPMM. The improvement made in the proposed designs proves that the PM materials can be used efficiently and the torque pulsation can be further minimized in IPMM designs.

The price fluctuation and the unstable supply chain of rare-earth permanent magnet (PM) have posed potential risks for further application of rare-earth PM motors. To alleviate the consumption of rare-earth PM material, a less-rare-earth PM brushless motor with two types of PM materials is proposed in this paper. The key of this motor is that the rare-earth PM is purposely combined with a non-rare-earth ferrite PM, forming the hybrid PM excitation. To design the proposed motor efficiently, a multi-objective stratified optimization strategy is proposed, where the selected five optimization objectives of output torque, PM cost, cogging torque, torque ripple, and efficiency are divided into two levels. Then, different optimization methods are skillfully combined to meet the specific design requirements. The corresponding electromagnetic performances are analyzed and compared with the baseline rare-earth PM brushless motor. Finally, several experiments of the two motors are carried out for evaluation. Both theoretical analysis and experimental results verify the feasibility and validity of the proposed motor and the optimization method.

The motivation of this article is to minimize the cogging torque and the torque ripple in a 6-pole 27-slot variable flux interior permanent magnet synchronous machine (VF IPMSM) by skewing the permanent magnets (PMs) in several steps. AlNiCo9 is used as the PM material in the rotor as the magnetization level of the AlNiCo9 PM can be changed and controlled by proper current control. The optimum skewing angles to minimize the cogging torque are found analytically and verified by using the finite-element analysis (FEA). The effect of these skewing angles on the back electromotive force and the torque ripple is also studied at different magnetization levels of the AlNiCo9 magnets. An FEA shows that a step skewed PM pole significantly minimizes the cogging torque and the torque ripple in the VF IPMSM. A current pulse in the d -axis is applied to magnetize or demagnetize each step in the step skewed PM pole. The minimum optimum skewing angle is chosen such that each step of the step skewed PM pole is magnetized or demagnetized with minimum nonuniformity.

As symbolized in many logos, mechanical gears have significant impact on daily life and industrial modern society. By fully utilizing the mechanical gears and gearboxes, torque and speed can be properly varied for various applications. However, they inevitably suffer from the demerits of annoying noise, contact friction and regular maintenance. Magnetic gears are considered as one of the most promising candidate for the traditional mechanical gears because they offer the advantages of physical isolation, maintenance free, silent operation and inherent overload protection. However, a direct replacement of mechanical gears by magnetic gears cannot solve the problems aroused by the mechanical gearboxes. Namely, the gear ratio of magnetic gears cannot be adjusted whereas the gear ratio of mechanical gears can be flexibly varied via the gearboxes for different load requirements.
\n
\nIt is well known that the renaissance of magnetic gears mainly attributes to the invention of rare-earth permanent magnet (PM) materials which take the definite advantages of high energy and flux density. Although the rare-earth PM materials such as neodymium-iron-born (NdFeB) and samarium-cobalt (SmCo) are widely adopted for magnetic gears, there is an increasing concern on the price and supply of the rare-earth elements. Particularly, the use of non-rare-earth aluminum- nickel-cobalt (Alnico) PM material takes the merit of high Curie temperature which is very acceptable for industrial application. Also, by purposely employing the low coercivity of the Alnico PM material, the memory machines perform controllable magnetization to flexibly vary the air-gap flux density, hence achieving the wide constant-power speed range.
\n
\nThe purpose of this thesis is to design a new type of magnetic variable gear by combining the concept of magnetic gear and the concept of memory machine. Firstly, the background information and the development of flux-controllable PMs are introduced. Secondly, the previous research worked on magnetic gears is presented. Next, the cost-effectiveness comparison between rare-earth PMs and non-rare-earth PMs is sufficiently conducted. After that, a new magnetic gear with multiple controllable gear ratios is proposed, with emphasis on mathematical deduction of the design principle and operation principle. By using finite element analysis, the electromagnetic performances of proposed magnetic variable gear at different gear ratios are investigated. Then design optimization of coaxial magnetic variable gear is conducted and analyzed. Two kinds of methods aiming to increase the torque capability and reduce the torque ripple are discussed. Furthermore, the concept of coaxial magnetic variable gear is extended to the axial-field counterpart. The electromagnetic performances of proposed axial-field MVG is investigated by finite element method. Furthermore, two kinds of industrial applications of coaxial magnetic gears, including wind power system and hybrid propulsion system, are investigated. Finally, a prototype is built up for the verification of the gear ratio changing concept. Hence the corresponding validities are further verified by experimental results.

This paper deals with the modeling of a novel permanent magnet (PM) pole shape for a surface-mounted permanent magnet (SPM) motor so as to generate sinusoidal back EMF and linear electromagnetic torque. Conventional SPM motors have a square-shaped PM pole structure; therefore, square back EMF is generated along with the torque pulsations. This novel SPM motor has sinusoidal PM pole shape in the axial direction; therefore, sinusoidal back EMF is generated due to the sinusoidal magnetic flux distribution. Sinusoidal back EMF eliminates most of the cogging torque; thus, a linear electromagnetic torque is generated. Square and sinusoidal current excitation is provided as to analyze the electromagnetic torque characteristics of SPM motor models. As compared to square current excitation, sinusoidal current excitation shows better linearity as well as average electromagnetic torque for the novel SPM motor model. 3-D finite element analysis (FEA) is utilized to analyze and compare the back EMF, cogging torque, and electromagnetic torque of conventional and proposed novel PM pole shaped SPM motor models for both square and sinusoidal current excitation.

Design of a New Consequent-Pole Segmented Dual-Stator Permanent Magnet Machine

This study proposes a new configuration for line start permanent magnet (PM) motors with low consumption of PM material, providing improved performance. The configuration is developed by analysing PM flux density distribution in the machine airgap and focusing on the d ‐axis armature reaction flux path and also different magnetisation types in the PM poles. It features double flux barriers for each rotor pole to facilitate near sinusoidal flux density distribution. Main characteristics of a motor with the proposed configuration are analysed by finite element method (FEM) and compared with the characteristics of a motor with the conventional configuration. Finally, the motor is built and tested. The FEM and experimental results verify the advantages of the proposed configuration. The results show that the required PM material reduces by one‐third, while desirable performance is provided. The machine is capable of working with delta connection causing negligible circulating current and low torque ripples.

In this paper, an outer rotor interior permanent magnet synchronous machine (IPMSM) with hybrid permanent magnet (PM) material is proposed. The key is to adopt the outer rotor structure with two-layer crescent barriers and hybrid PM material to maximize the output torque and reduce the usage of high-cost rare-earth PM. The ferrite PMs are filled in the middle of the crescent barriers with thicker thickness, while the rare-earth PMs are filled into the bilateral of the crescent barriers with thinner thickness. To verify the effectiveness of the proposed rotor structure, optimizations are first carried out among the conventional rotor structures with single kind of PM material and the proposed rotor structure with hybrid PMs. Then, detailed comparisons have been investigated. Results indicate that the proposed machine has higher torque density than the machine with only ferrite PM and can reduce almost half the usage of rare-earth PM in comparison to the machine with only rare-earth PM. Moreover, the proposed rotor structure is further optimized considering productivity.

Axial flux magnetic-geared double-rotor machines (AMGDRMs) are characterized as a potential core component of the power splitting system in hybrid electric vehicles (HEVs). Conventional AMGDRMs suffer from low mechanical strength due to high axial magnetic force. In this paper, an interior-modulating-rotor axial flux magnetic-geared double-rotor machine (IMR-AMGDRM) is proposed to solve this problem. An analytical model of the IMR-AMGDRM is proposed to predict the magnetic field distribution and electromagnetic performances. Since analytical model is based on 2-D geometry, a 2-D approximation of IMR-AMGDRM which has similar output performance to 3-D finite element analysis (FEA) is presented based on the permanent magnet (PM) magnetic energy equivalent principle. Utilizing subdomain method, the magnetic field distribution and electromagnetic performances are calculated. Finally, the accuracy of the proposed analytical model is validated by 3-D FEA.Index Terms—Analytical model, axial flux, magnetic-geared machine, double-rotor machine.I. IntroductionAxial flux magnetic-geared double-rotor machines (AMGDRMs), which enable high torque density, have been considered a promising candidate for power splitting in hybrid electric vehicles (HEVs) [1]. However, conventional AMGDRMs suffer from low mechanical strength due to high axial magnetic force. To enhance mechanical strength, an interior-modulating-rotor axial flux magnetic-geared double-rotor machine (IMR-AMGDRM) which can reduce axial magnetic force dramatically is proposed in this paper. Fig. 1 (a) and (b) illustrate the configuration of the proposed IMR-AMGDRM.As axial flux type machine, IMR-AMGDRMs have complex 3-D magnetic circuits. 3-D finite element analysis (FEA) can offer accurate results by taking into account the nonlinear factors such as magnetic saturation and flux leakage. But the major drawback of 3-D FEA is serious time cost. Analytical model which is much lower time-consuming provides an alternative for electromagnetic performance prediction in the initial design procedure.In this paper, an analytical model of the IMR-AMGDRM is proposed. The geometry of analytical model is derived based on PM magnetic energy equivalent principle to guarantee similar output performance to 3-D FEA. The solution to analytical model is calculated by subdomain method. To evaluate the accuracy of the proposed analytical model, the results computed by analytical model and that of 3-D FEA are compared.II. Configuration of IMR-AMGDRMIn conventional configuration, the inner and outer rotors are the permanent magnet (PM) rotor and the modulating rotor, respectively. Since the modulating rotor is closer to the PM rotor than stator, the modulating rotor suffers from high axial magnetic force. Furthermore, the modulating rotor is hollow and thus the low mechanical strength of modulating rotor becomes the major drawback of conventional configuration [1]. To solve this problem, the IMR-AMGDRM which switches positions of the PM rotor and the modulating rotor is proposed. In interior-modulating-rotor configuration, as shown in Fig. 1 (a) and (b), the PM rotor is between the modulating rotor and stator, i.e. the inner and outer rotors are the modulating rotor and the PM rotor, respectively. Owing to that the PM rotor suffers from reverse axial magnetic forces from both sides simultaneously, the total axial magnetic force is dramatically reduced. Hence, although the outer rotor is hollow in both configurations, the axial magnetic force of interior-modulating-rotor configuration is significantly decreased, leading to higher mechanical strength and reliability.III.Geometry of 2-D ApproximationGenerally, the unrolled section of axial flux machine at mean radius is used as 2-D approximation. However, few references are found to evaluate the electromagnetic performance equivalence of such approximation. To make the electromagnetic performance of 3-D model and 2-D approximation equal, the amount of magnetic energy of the PM should remain unchanged after approximation, i.e. PM magnetic energy equivalent principle [2]. A 2-D approximation of IMR-AMGDRM which has identical output performance is presented by using PM magnetic energy equivalent principle.IV. Analytical Calculation of IMR-AMGDRMThe proposed analytical model is illustrated in Fig. 1 (c). It can be seen that the model consists of four subdomains. Region i, I, II and III represent the ith slot of the modulating rotor, the inner air gap, the PM rotor and the outer air gap, respectively. Utilizing subdomain method, the magnetic field distributions in the inner and outer air gaps are obtained by the solution of Laplace’s and Poisson’s equations. Then, the electromagnetic performances such as no-load back EMF, torque and axial force can be derived from the calculated magnetic field distributions.Comparisons of computation accuracy between analytical model and 3-D FEA is shown in Fig. 2. As can be observed, the results of analytical model are well consistent with that of 3-D FEA, validating the proposed method. **

Equivalent energized coil model for magnetic field of permanent-magnet spherical actuators

In order to increase the electromagnetic torque density of micromotor with axial magnetic field, numerical analysis of permanent magnetic field and electromagnetic torque were deduced and the key factors of increasing torque density of micromotor was obtained. The numerical analysis of three-dimensional magnetic field in air gap produced by spliced sector permanent magnetic poles is done, and the way of improving flux density and permanent magnet use efficiency are given through investigating the influence of magnet thickness, height of air gap and pole interval rate and other parameters to air gap flux density and leakage flux. Based on the test of axial magnetic field and torque characteristic of micromotor, the analysis of micromotor magnetic field and calculation of torque are verified, meanwhile using the plane stator with 0.7mm thickness assemble micromotor having minimum air gap height of 1mm and its torque constant up to 3.8mNm/A.

In this paper, a variable-mode concept is proposed for the speed range extension of a stator-consequent-pole memory machine (SCPMM). An integrated permanent magnet (PM) and electrically excited control scheme is utilized to simplify the flux-weakening control instead of relatively complicated continuous PM magnetization control. Due to the nature of memory machine, the magnetization state of low coercive force (LCF) magnets can be easily changed by applying either a positive or negative current pulse. Therefore, the number of PM poles may be changed to satisfy the specific performance requirement under different speed ranges, i.e. the machine with all PM poles can offer high torque output while that with half PM poles provides wide constant power range. In addition, the SCPMM with non-magnetized PMs can be considered as a dual-three phase electrically excited reluctance machine, which can be fed by an open-winding based dual inverters that provide direct current (DC) bias excitation to further extend the speed range. The effectiveness of the proposed variable-mode operation for extending its operating region and improving the system reliability is verified by both finite element analysis (FEA) and experiments.

A novel method for post-assembly magnetization of surface-mounted permanent-magnet motors is proposed. The magnetizing windings are directly wound on the outer surface of the permanent magnet (PM), and then assembled on surface of the rotor. The PM poles can be magnetized and demagnetized after assembly by the integrated magnetizing windings. Once the PM poles experience demagnetization fault, the magnetizing windings can magnetize the PM poles again without disassemble of the motor. In this paper, a 32-pole 20 kW surface-mounted PM motor is selected as the prototype, the integrated magnetizing windings are designed and the magnetizing test of a single pole is carried out.

This paper deals with synchronous machines with different permanent magnet (PM) materials. Three PMSM are presented in this paper. At first, the PMSM with NdFeB PM, which is really constructed. Second, the NdFeB has been replaced by ferrites PM. Third, the new design of synchronous motor with ferrites is presented. The volume of PM and the whole size is increased to keep the same power output as that of the initial motor. Parameters, EMF, V-curves, efficiency and thermal behavior of all three machines are investigated and compared.