Design of Variable Magnetization Pattern Machines for Dynamic Changes in the Back EMF Waveform

I. IntroductionThere are many studies on axial flux permanent magnet machines (AFPMMs) due to their compactness [1]. The conventional AFPMMs comprise a stator and two rotors. In general, the stator with toroidal windings or overlapping windings is sandwiched between two rotors [2][3]. Toroidal windings have shorter ends than overlapping windings, which can reduce copper loss and ending effect. However, this structure also wastes the ends of windings, which means that the windings are not utilized sufficiently. To some extent, it reduces the torque density of the machine.This paper proposes a novel axial-radial flux permanent magnet machine (ARFPMM) to solve the problem. In the ARFPMM, the endings of windings are also used to produce torque with little increase of volume, which results in the improvement of torque density.II. Structure of ARFPMMThe proposed ARFPMM integrates both axial-flux and radial-flux machines in a compact space, which improves the torque density. As shown in Fig. 1(a), the ARFPMM is composed of one stator, two axial rotors and one radial rotor. Because the end of overlapping windings is useless, the machine adopts toroidal windings. Thus, the stator is equipped with opening slots on three faces. Permanent magnets are mounted on the surface of rotors. The radial rotor is fixed and aligned with two axial rotors, which can avoid the tilt of axial rotors and generation of harmonics in flux density per phase. The inner and outer diameters of permanent magnets on axial rotors are the same as those of stator. Similarly, the height of permanent magnets on radial rotor is equal to that of stator.In order to suppress air-gap flux density harmonics and get more sinusoidal waveform of air-gap flux [4], the permanent magnets are arranged as Halbach-array. It can also increase the flux density in the air gap. The magnetization direction of PMs is related to the number of segments per pole pair. As shown in Fig. 1(b), each pole pair is divided into six segments, so the magnetization direction of each segment varies 60° in turn.III. Design and AnalysisCompared with integer-slot concentrated windings, fractional-slot concentrated windings can enhance flux-weakening capability and reduce cogging torque [5]. Therefore, a 20 pole 24 slot fractional-slot concentrated-winding machine is chosen. In the case, the winding factor is 0.966. It is related to the no load back electromotive force (EMF) which can be calculated as equation (1). E0=4.44fkwNΦ10 (1)Where f is the electric frequency of the machine, kw is the winding factor, N is the number of coils per phase in series, Φ10 is the magnetic flux. In the ARFPMM, three rotors are used to increase the magnetic flux in air gap. The result of 3D FEA for back EMF is shown in Fig. 2(a). Fig. 2(b) is the fast Fourier transform of back EMF. It shows that the maximum harmonic is the third order harmonic, which can be neglected due to the star-connection of three phase windings.Because the magnetic flux in air gap is increased under the same operating state, the torque of ARFPMM is also increased. Fig. 2(c) shows the torque of the machine at rated conditions when the current is 7 A and rotor speed is 600 rpm. In the condition, the average torque is 41.63 Nm and the torque density is 28.58 Nm/L. The torque ripple is 3.4 Nm, 8.1% of the rated torque. As shown in Fig. 2(c), the peak-peak value of cogging torque is 3.26 Nm.IV. ConclusionThis paper proposes a novel ARFPMM with a unique structure of two axial rotors and one radial rotor, and implements its design and FEA. Due to the Halbach-array PMs, the main harmonics of back EMF is the third order harmonic, which is negligible when the windings are connected in star-connection. Compared with conventional AFPMM, the structure increases the torque through increasing the magnetic flux through windings per phase. Thus, the ARFPMM reaches an extremely high torque density of 28.58 Nm/L. On the other hand, fractional-slot concentrated winding configuration reduces the cogging torque, of which the peak-peak value is only 3.26 Nm.AcknowledgeThis work is supported in part by NSFC (52077186&51677159), in part by STIC of Shenzhen Municipality (JCYJ20180307123918658), and in part by ITF (ITP/027/19AP), HK. **

The spoke type permanent magnet synchronous motor (PMSM), which is a general ferrite magnetic flux concentrated motor, has a low portion of reluctance torque at the total torque magnitude. Therefore, as a way to increase the reluctance torque, there is a double-layer spoke type PMSM that can maximize the difference in inductance between the d-axis and the q-axis. However, in the double-layer spoke type PMSM, cogging torque, torque ripple, and total harmonic distortion (THD) increase as reluctance torque is maximized, which is the main cause of vibration and noise. In this paper, a method is proposed that provides the same effect as skew without dividing stages of the permanent magnet by dividing the core of the rotor into two types so that it is easy to manufacture according to the number of stages unlike extant skew methods. Based on the method, the reduction of cogging torque and THD was verified by Finite Element Analysis (FEA).1. IntroductionThe general interior permanent magnet synchronous motor (IPMSM) uses NdFeB magnets to take advantage of the high airgap magnetic flux density. However, it had an adverse impact on cost of the motor because there are fluctuation of the cost from limited sources of heavy rare earth. Therefore, for stable supply of permanent magnets, a lot of development of a spoke type permanent magnet synchronous motor (PMSM), which is a structure capable of concentrating magnetic flux by using a ferrite magnet having a low magnetic flux density, has been conducting. The spoke type PMSM concentrates the magnetic flux density and can replace the NdFeB magnet used in the extant PMSM with a ferrite magnet.However, in general spoke type PMSM, the portion of reluctance torque is low because the difference in inductance between the d-axis and the q-axis is not large. In order to further utilize this reluctance torque, a double-layer spoke type shape that can maximize the difference in inductance between the d-axis and the q-axis can be used to bigger reluctance torque to improve motor performance.However, increasing the reluctance torque increases cogging torque, torque ripple, and total harmonic distortion (THD), which in turn leads to vibration and noise problems. Therefore, the double-layer spoke type PMSM needs a design that can reduce cogging torque and THD. As a representative method, it can be solved by applying skew to the rotor, but the conventional method of applying skew is not a good method in terms of productivity because it is difficult to manufacture because it divides the stages of the permanent magnet. For ameliorate of the limitation, the shape of the rotor core is divided and cross-stacked into stack1 and stack2 so that the permanent magnet can be inserted in one shape as the conventional shape.Therefore, the shape of the rotor core is divided into stack1 and stack2 so that the permanent magnet can be inserted in one shape as before and cross-stacked. The stack1 cuts the left part fixing the permanent magnet, and the stack2 cuts the right part fixing the permanent magnet to apply the same effect as skew. In this paper, this is expressed as a core skew, and through this core skew, the design to reduce cogging torque, torque ripple, and THD is conducted while considering productivity.2. Concept of Core SkewThe core skew represents the stacking of only cores of opposite shapes when stacking the rotor cores of the motor. The contents of the basic theory are as follows.Fig. 1 shows stack No. 1 and stack No. 2, respectively. Due to the shape of the rotor core, the phases of the airgap magnetic flux density of stack No.1 and stack No.2 are shifted, and when the two stacks are synthesized due to the phase of the shifted airgap magnetic flux density. As shown in Fig. 2, the cogging torque decreases.Also Fig. 1 shows the shape of applying core skew to the conventional model by intersecting and stacking stack No. 1 and stack No. 2 .Through this core skew structure, research to reduce cogging torque, torque ripple, and THD is conducted. Most of the original skew research is conducted in 3D FEA, but since 3D FEA requires a lot of time, first calculate the optimal model using 2D FEA and then proceed with 3D FEA according to the number of steps considering 3D effect. The final result will be revealed on full paper.AcknowledgmentThis work was supported by the Technology Innovation Program (No. 20011495) funded By the Ministry of Trade, Industry & Energy(MOTIE, Korea), in part by the National Research Foundation of Korea (NRF) Grant funded by the Korean government. (No. 2020R1A2C1013724). **

Compared to permanent magnetic brushless DC machine with trapezoidal back EMF waveforms (BLDCM), permanent magnetic synchronous machine with sinusoidal back EMF waveforms (PMSM) has superior performance. To enhance performances of BLDCM, this paper adopts a new type oriented vector control strategy. Contrary to traditional rotor-flux oriented vector control in PMSM, the new control strategy takes back EMF as the oriented vector for improving the capability of maximum torque per ampere (MTPA) of BLDCM and reducing the torque ripple [1]. Also, a Space vector PWM modulation (SVPWM) based on “120° conduction mode” is utilized for three-phase bridge inverter [2]. Combined the oriented strategy aforementioned with proposed SVPWM method, a new control system is constructed. Simulation validates effectiveness of this new control scheme.

Purpose – The purpose of this paper is to reduce the torque ripple but not to decrease the average torque of synchronous reluctance machines by using one step or more than two axially laminated rotors with asymmetric flux-barrier. Design/methodology/approach – A 24-slot four-pole synchronous reluctance machine with overlapping windings and asymmetric flux-barrier in the rotor is, first, described and designed by finite element (FE) method for maximizing average torque. The dimensions of asymmetric flux-barrier including the pole span angle and flux-barrier angle will be optimized to minimize the torque ripple and its influence on the average torque is also investigated by FE analysis. The impact of current angle on the average torque and torque ripple are also analysed. The step laminations together with the asymmetric flux-barrier are employed for further torque ripple reduction which can consider the both rotation directions. Findings – The torque ripple of synchronous reluctance machine can be significantly reduced by employing asymmetric flux-barrier but the average torque is not reduced. Research limitations/implications – The purely sinusoidal currents are applied in this analysis and the effects of harmonics in the current on torque ripple are not considered in this application. The 24-slot/four-pole synchronous reluctance machine with single-layer flux-barrier has been employed in this analysis, but this work can be continued to investigate the synchronous reluctance machine with multilayer flux-barrier. This asymmetric flux-barrier can be easily applied to permanent magnet (PM)-assisted synchronous reluctance machine and the interior PM machine with flux-barrier in the rotor, since the space which is used for PM insertion is the same as the SynRM machines. Originality/value – This paper has analysed the torque ripple and average torque of synchronous reluctance machines with asymmetric flux-barrier and step laminations with asymmetric flux-barrier. The torque ripple can be reduced by this flux-barrier arrangement. The difference of this technique with the other techniques such as stator/rotor skew is that the average torque can be improved.

Consequent-pole permanent magnet (CPM) machines have considerable potential for low-cost applications because they can improve the permanent magnet (PM) utilization ratio. However, the phase back electromotive force (EMF) of CPM machines with Ns /( mt ) = odd ( t is the greatest common divisor of the stator slot number Ns and the rotor pole-pair number p , and m is the phase number) is asymmetric, i.e., the phase back EMF has even-order harmonics, which will increase torque ripples. This paper utilized the staggered rotor to eliminate the even-order harmonics and reduce the cogging torque of CPM machines, thereby potentially decreasing torque ripples considerably. The axial flux barrier in the middle of the rotor was used and optimized using three-dimensional finite element (FE) analysis to reduce the axial leakage flux of the CPM machine with the proposed staggered rotor. Furthermore, the axial magnetized PM was embedded in the flux barrier, which improved the flux density of the airgap above the iron-pole and, consequently, further increased the output torque. The electromagnetic performance of the proposed machine, including the open-circuit airgap flux density, back EMF, average torque, torque ripples, and PM utilization, was compared with that of the conventional CPM machine. Results showed that the proposed machine obtained a similar torque and PM utilization ratio but a much lower torque ripple compared with the conventional one.

High torque density and low torque ripple are crucial for traction applications, which allow electrified powertrains to perform properly during start-up, acceleration, and cruising. High-quality anisotropic magnetic materials such as cold-rolled grain-oriented electrical steels can be used for achieving higher efficiency, torque density, and compactness in synchronous reluctance motors equipped with transverse laminated rotors. However, the rotor cylindrical geometry makes utilization of these materials with pole numbers higher than two more difficult. From a reduced torque ripple viewpoint, particular attention to the rotor slot pitch angle design can lead to improvements. This paper presents an innovative rotor lamination design and assembly using cold-rolled grain-oriented electrical steel to achieve higher torque density along with an algorithm for rotor slot pitch angle design for reduced torque ripple. The design methods and prototyping process are discussed, finite-element analyses and experimental examinations are carried out, and the results are compared to verify and validate the proposed methods.

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.

Permanent magnet (PM) synchronous motors (PMSMs) have been used to drive a number of vehicles. They have high torque density, high efficiency, and a wide speed range. However, the high cost of PMs is disadvantageous. This paper presents a technique for increasing the torque density by modifying the shape of the PMs and minimizing the magnet volume. The PM characteristics such as flux density, demagnetizing force, PM energy product, and the air-gap flux density are represented by a lumped magnetic equivalent circuit when the thickness and width of the PM are increased for the same volume but with different shapes. The torque, torque ripple, core loss, magnet loss, and efficiency of three interior (IPMSM) models designed by the proposed method are compared by finite element analysis. In addition, the demagnetization of the PM due to high temperature, maximum torque load angle, and an adverse field is analyzed. Finally, the analysis result is compared with that of the experiment to verify the proposed model.

Permanent magnet machines with trapezoidal back EMF waveform have been the subject of several papers in the past. The simplicity in control and the absence of an absolute position sensor makes this type of motor very attractive. Idealized analysis of such a machine is simple and will result in trapezoidal or square wave back EMF waveforms depending on the assumptions made. In the case of an idealized quasi-square wave current excitation, a ripple-free torque will be obtained. The actual back EMF waveform of these machines depends on the flux density and the conductor distributions. This in turn is a function of the magnet magnetization and the stator tooth and slot structure. In applications where a fairly smooth torque is needed, these machines are made with either the stator slots or the rotor magnets skewed by one slot. This paper deals with the analysis of the back EMF waveform and of the torque ripple waveform of such a machine when the stator slots or rotor magnets are skewed by one slot. The analysis takes into consideration the actual stator conductor distribution and the effect of magnet magnetization on the back EMF waveform. An empirical formula is developed for the magnet flux density distribution which could be used for various magnetization conditions of the magnet. Experimental results are included to confirm the analytical results.

The paper is focused on the modeling and measurement of core losses in an AlNiCo-based variable flux permanent magnet machine. The application of AlNiCo as a low coercivity magnet provides the ability of the magnet flux control using short-time $d$ -axis current pulses. This allows a reduction in the machine core losses under high-speed conditions, thus improving the machine efficiency. In order to identify the machine efficiency gains, the core losses have to be accurately modeled at different magnetization levels. An advanced core loss model for the variable flux machine (VFM) is first presented. This model is based on the calculation of an equivalent sinusoidal waveform of nonsinusoidal magnetic flux density. The model is then utilized to calculate the core losses in a tangentially magnetized VFM using finite-element simulation. In order to validate the developed model experimentally, a measurement method is developed to segregate the mechanical losses and the no-load core losses at different speeds and magnetization levels for a 5-hp VFM. Finally, the proposed model accuracy is verified through a comparison with the experimentally measured core losses under a no-load condition.

An analytical method for performance prediction of surface mounted magnet based Variable flux permanent magnet machine is proposed. The mathematical equations and performance prediction algorithm is discussed. Upon applying the superposition of the main field flux component (permanent magnet (PM)) and flux component due to stator excitation (the effect of each phase is considered separately) the stator flux linkage is calculated and the performance of the machine is predicted. The results obtained in this method are compared with finite element simulation results.

Summary form only given. The 120A° voltage source inverter (VSI) driven brushless dc (BLDC) motors are very common in many applications. This paper extends the previous work and presents an improved dynamic average-value model (AVM) for such BLDC motor-drive systems. The new model is explicit and uses a proper qd model of the permanent magnet synchronous machine with non-sinusoidal rotor flux. The model utilizes multiple reference frame theory to properly include the back EMF harmonics as well as commutation and conduction intervals into the averaged voltage and torque relationships. The commutation angle is readily obtained from the detailed simulation. The proposed model is demonstrated on a typical industrial BLDC motor with trapezoidal back EMF waveforms. The results of studies are compared with experimental measurements as well as previously established models, whereas the new model is shown to provide appreciable improvement.

This paper presents a method that has been developed to reduce the torque ripples under healthy and open-circuit fault-tolerant (OCFT) conditions for a multiphase permanent magnet (PM) machine. For smooth torque, both the phase current and the back electromotive force (back-EMF) should be purely sinusoidal. To improve the torque in a multiphase machine, higher-order current harmonics are injected, which are related to the harmonics in the back-EMF. For this reason, generally, multiphase machines are designed with higher-order back-EMF harmonics. However, these harmonics produce ripples in the torque. In light of this, a torque ripple cancellation method has been developed that first determines an additional current component from the harmonic content of the back-EMF and then injects these additional components to cancel the torque ripple. It has been found that this new torque ripple cancellation method works for both faultless and faulty conditions in a five-phase PM machine. The method has been validated using Finite Element Analysis, and the results are presented in this paper.

Permanent magnet synchronous motors (PMSMs) have been extensively adopted in a range of industrial applications, particularly in the electric vehicle industry, due to their high power and torque density, high efficiency, reliability, and excellent dynamic performance. Between the types of PMSMs, a surface-mounted PMSM (SPMSM) is characterized by identical <i>d</i>- and <i>q</i>-inductances, due to which it only generates magnetic torque. However, SPMSMs also exhibit higher flux density, since the air gap in these motors is smaller and the permanent magnets are located very close to the stator teeth. In contrast, an interior PMSM (IPMSMs) features different <i>d</i>-axis and <i>q</i>-axis inductance components, due to which it can create not only magnetic torque but also reluctance torque. In this paper, two processes are conducted to examine these motors. First, an analytical technique is proposed to design the required parameters for an SPMSM and an IPMSM, where the dimensions of the latter are defined using the fractional-slot concentrated winding configuration, and those of the former are designed based on the approach of keeping the rotor volume, permanent magnet volume, pole–slot combination, and power supply unchanged. Subsequently, a finite element method is presented for computing, simulating, and comparing the electromagnetic parameters of both proposed motors, including their back electromotive force, torque ripple, efficiency, and power factor. Finally, the proposed methods are validated using a 7.5 kW practical motor.

This paper investigates the torque production and the torque ripple reduction of a six-stator/seven-rotor-pole (6/7) variable flux reluctance machine (VFRM). As a main advantage, the 6/7 VFRM produces higher torque density, but less torque ripple compared with the 6/4 VFRM. The instantaneous torque equation of the 6/7 VFRM is derived by considering the spectra of the winding inductance and current. Based on the derived equation, the average torque is found to be mainly produced by the mutual inductance between the field and armature windings. The even-order harmonics of self-inductance and odd-order harmonics in mutual inductance between the field and armature windings are eliminated due to the opposite polarity connection of the armature coils in each phase. This results in the elimination of the third harmonic torque ripple, while a multiple of the sixth harmonic torque ripple exists. In order to mitigate the sixth harmonic torque ripple, the harmonic current injection method is implemented into the field winding. The field harmonic current is calculated from the analytical torque ripple equation. The performance of the proposed methods is verified by both finite element analysis (FEA) and experiment.