Air Gap Flux Density Waveform Research Articles

Incorporating the coupled effects of slot opening, armature reaction and saturation in the model of the airgap flux density distribution of permanent magnet synchronous machines

AbstractA new analytic model for calculating of the air‐gap flux density (AGFD) of surface‐mounted permanent magnet synchronous machines (SMPMSMs) is presented. This proposed model is capable to taking into account the effects of magnetic saturation, armature reaction and stator slots opening. Furthermore, the real form of air‐gap distribution and spatial distribution of flux density of the PM poles are considered. The armature reaction effect is modeled using phasor diagram analysis of the motor as a function of the load torque, the armature current amplitude, power factor and the inverse air gap length. Also, saturation phenomenon predicted using the new non‐linear proposed function in connection with the armature reaction effects and the properties of the lamination material. It is shown that the proposed model capable to predicting acceptably the air gap flux density waveform of the SMPMSMs at lagging and leading power factors and with the load torque variation. The presented analytical approach is verified by the two‐dimensional finite‐element analysis (FEA) results.

Design of Rotor Magnetic Barrier Structure of Built-in Permanent Magnet Motor Based on Taguchi Method

In this paper, a 20kW vehicle built-in permanent magnet synchronous motor is taken as an example, and a magnetic barrier structure is added to the rotor of the motor to solve the uneven saturation problem of the rotor side magnetic bridge. This structure improves the air-gap flux density waveform of the motor by influencing the internal magnetic flux path of the motor rotor, thus improving the sine of the no-load back EMF waveform of the motor and reducing the torque ripple of the motor. At the same time, Taguchi method is used to optimize the structural parameters of the added magnetic barrier. In order to facilitate the analysis of its uneven saturation phenomenon and improve the optimization effect, a simple equivalent magnetic network (EMN) model considering the uneven saturation of rotor magnetic bridge is established in this paper, and the initial values of optimization factors are selected based on this model. Finally, the no-load back EMF waveform distortion rate, torque ripple and output torque of the optimized motor are compared and analyzed, and the influence of magnetic barrier structure parameters on the electromagnetic performance of the motor is also analyzed. The results show that the optimized motor can not change the output torque of the motor as much as possible on the basis of reducing the waveform distortion rate of no-load back EMF and torque ripple.

Model Order Reduction of Cage Induction Motor With Skewed Rotor Slots Using Multiport Cauer Ladder Network Method

A method for efficiently deriving a reduced-order model of a cage induction motor (IM) with skewed rotor slots is proposed based on the multiport Cauer ladder network (CLN) method. This paper presents several formulations of the multiport CLN method for the skewed rotor, in which the continuity of the bar currents and the space harmonics included in the air-gap flux density waveform are treated differently. The effectiveness of the developed methods was verified from the viewpoints of computational accuracy and cost through application to a practical cage IM with skewed rotor slots.

The Loss and Efficiency Analysis and Research of Interior Permanent Magnet Synchronous Motors for Traction Applications

An IPMSM with I2V type rotor topology structure is proposed, its loss, efficiency and torque are analyzed and compared with V and IV type. Firstly, the optimized rotor topology structures are used to analyze the no-load air-gap flux density waveform and harmonic contents of the IPMSM. The results show that the THD of the no-load air-gap flux density with the I2V type is the smallest and the sinusoidal degree of the waveform is the highest. Secondly, the loss of the IPMSM with optimized rotor topology structures are analyzed and compared. Compared with the other two rotors, the results show that the iron loss of the IPMSM with the I2V type is the smallest. The iron loss of the IPMSM with I2V type is significantly less than that of the other two rotors especially under the deep flux weakening conditions. The output torque of the IPMSM under different current angles, current densities and speed are analyzed and compared. The results show that the torque performance of the IPMSM with I2V type is better than the other two rotors. this paper proposes a simple and effective method to optimize the position and diameter of the magnetic isolation holes by establishing a parameterized model. The results show that the torque ripple and cogging torque with the further optimized I2V type rotor topology structure are greatly reduced, the iron loss and magnet loss are also effectively reduced. Finally, the von Mises stress and the total displacement of the rotor deformation of the IPMSM with the further optimized I2V type under different working conditions are verified by finite element analysis. The results show that the rotor will not rupture, the displacement is small enough to avoid the touch between stator and rotor.

Accurate Analytical Model for Synchronous Reluctance Machine With Multiple Flux Barriers Considering the Slotting Effect

This article presents an accurate analytical model (AM) for synchronous reluctance machine (SynRM) that incorporates the effect of stator slots on the air gap flux density and torque waveforms. From the formulation of magnetic potential in the air gap for both the stator and rotor, the flux density is obtained, considering the first harmonic of the flux density and the electric loading, the average torque is calculated using the Lorentz’s force. The ripple torque is obtained from the energy stored in magnetic circuit. The method is developed for a rotor with one flux barrier per pole and then extended to a larger number of barriers. To validate the results obtained by the AM proposed finite element analysis have been carried out. Several comparisons have been derived considering different rotor positions as well as different harmonic orders, and the pros and cons of the method are highlighted. The model performs fast and can predict results with high accuracy, and can be adopted to speed up the preliminary design and optimizations of this type of motors, with respect to finite element. In addition, from the analytical expressions it is possible to obtain all the correlations between electrical, magnetic, and geometrical characteristics of the machine, with the advantage of enabling a faster machine design.

An Efficient Air-Gap Flux Density Analysis Method for the Design of Induction Machines

The magnetic field distribution in the air gap is of great importance in the design of rotary machines. In this article, an efficient analytical method is presented, which is capable of plotting the air-gap flux density waveform of induction machines (IMs) less time-consuming than the finite element method (FEM) does. The proposed method, based on the product of the current linkage waveform and the permeance waveform, utilizes the calculations of the steady-state equivalent circuit to ensure the accuracy and an equivalent air-gap reluctance model to take into account both the slot opening effect and the rotor movement. The method is tested on a general IM with different load cases and different design parameters, and the results are compared to the FEM calculations. It can be concluded that the proposed analytical method is an efficient option in the motor design to investigate the influence of the parameters on the flux density distribution.

Analysis of Characteristics of the Magnetic Field in Demagnetization Fault for Permanent Magnet Synchronous Motor

To demagnetization fault for permanent magnet synchronous motor, referring to the 96-slot 32-pole permanent magnet synchronous motor, set up motor model using finite element software, and the demagnetization fault of single magnetic steel and double magnetic steel in the motor were simulated and analyzed. The motor flux-density waveforms on different kinds of demagnetization fault were analyzed for the flux-density wave-form periodic trends and volatility in different numbers of magnets or different demagnetization rates. The motor flux-density component path diagram on different kinds of demagnetization fault were analyzed to get radial-tangential flux-density path diagram to analyze regular of path diagram distribution. The air gap flux-density waveform is analyzed by finite element software on different kinds of demagnetization fault, which fourier analysis is used to analyze each harmonic frequency and its weight, and the rule of change of harmonic between the normal condition and under the condition of demagnetization fault is compared. The simulation of tooth electromagnetic force density waveform curves and harmonics for different demagnetization faults is used to analyze its effect on the vibration. The results concerning permanent magnet motor of demagnetization fault lays the foundation of motor fault tolerance analysis and characteristic analysis.

Permanent magnet shape optimization method for PMSM air gap flux density harmonics reduction

This paper proposed a permanent magnet optimization method to suppress the air gap flux density harmonic of permanent magnet synchronous motor (PMSM). The method corrected the effective air gap length of the motor, calculated the magnetization length of the permanent in the case of parallel magnetization, and took the influence of the permanent magnet relative permeability into consideration. Based on these works, for a given sinusoidal air gap flux density waveform, the corresponding structural parameters can be calculated, so as to achieve the optimization of the permanent magnet. By using this method to optimize the shape of the magnet, the fundamental wave of the air gap flux density can be retained to the greatest extent, so as to eliminate harmonics and maintain the output capacity at the same time. The feasibility and accuracy of the method have been verified by finite element analysis (FEA) and prototype machine experiment. This method is simple and time-saving, and has a satisfactory accuracy, which provides a reference method for permanent magnet optimization of PMSM.

Static magnetic field analysis of hollow-cup motor model and bow-shaped permanent magnet design

The hollow-cup Permanent Magnet (PM) motors have the characteristics of low power consumption, and are widely used in the aerospace field. At present, the tile-shaped PMs used by hollow-cup PM motors have poor sinusoidal characteristics of the air gap magnetic flux density waveform, which will cause torque ripple. The existing method for improving the air gap magnetic flux density waveform is not very effective when applied to hollow cup, a special motor with no stator core and large air gap. A bow-shaped PMs structure is designed for the hollow-cup motor in this paper. First, the equivalent surface current method is used to calculate the analytical formula of the static magnetic field of the model. Then, the Finite Element (FE) method is used to calculate the static air gap flux density waveform of conventional tile-shaped PMs and bow-shaped PMs with different bow heights, and the corresponding harmonics and sine distortion are obtained by Fourier decomposition. The simulation results show that the bow-shaped PMs can effectively improve the sinusoidal characteristics of the static air gap flux density waveform. And the suitable bow height is determined. Finally, a prototype is made based on the suitable bow height for experiments, and compared with the analytical result and the FE result, and the accuracy and effectiveness of the bow-shaped PMs with the suitable bow height are verified.

Analytical analysis and performance characterization of brushless doubly fed induction machines based on general air-gap field modulation theory

Air-gap magnetic field modulation has been widely observed in electric machines. In this study, we present an analytical analysis and performance characterization of brushless doubly fed induction machines (BDFIMs) fed by two independent converters from the perspective of air-gap field modulation. The spiral-loop winding is studied in detail as an example to show the generalized workflow that can also be used to analyze other short-circuited rotor winding types, such as nested-loop and multiphase double-layer windings. Magnetic field conversion factors are introduced to characterize the modulation behavior of special rotor windings and facilitate their comparison in terms of cross-coupling capability, average torque, and harmonic content of the air-gap flux density waveforms. The stator magnetomotive force (MMF), rotor MMF, and resultant air-gap MMF are considered, based on which the closed-form inductance formulas are derived, and the torque equation is obtained along with the optimal current angle for maximum torque operation by using the virtual work principle. The design equations are then developed for the initial sizing and geometry scaling of the BDFIMs. Transient finite element analysis and experimental measurements are performed to validate the analysis.

Core-Loss Analysis of Linear Magnetic Gears Using the Analytical Method

In this study, analysis of core-loss occurring in the magnetic flux modulation core of a linear magnetic gear and the core of each mover is presented, using an analytical method. Losses in electric machines were generally calculated and analyzed using the finite element method (FEM). However, in the case of core-loss, the exact loss value could not be calculated using FEM data. Therefore, we considered the harmonic component of the air-gap magnetic flux density waveform with the modified Steinmetz equation, and performed a more accurate core-loss analysis with magnetic behavior analysis. Thus, we performed a calculated core-loss characteristic comparison with the FEM and the modified Steinmetz equation.

Harmonic Suppression and Torque Ripple Reduction of a High-Speed Permanent Magnet Spindle Motor

In this paper, the method of harmonic suppression and torque ripple reduction is studied for the structure characteristics and design requirements of a high-speed permanent magnet spindle motor. According to the magnetic circuit analysis and calculation theory of the permanent magnet synchronous motor (PMSM), magnetic reluctance slots are arranged at the two ends of the rotor yoke to change the external magnetic field distribution of the permanent magnet in order to optimize the air gap magnetic density waveform. To obtain air gap flux density waveforms that are close to a sinusoidal distribution and not destroy the permanent magnet under the pre-pressure, several reluctance slots with different widths and depths arranged at two ends of the rotor yoke are used to achieve the sinusoidal distribution. Based on the selection of the pole-slot proportion, skewed-slot and a decrease in the end effect, the effects of the harmonic suppression of the harmonic electromotive force (EMF) and the reduction in the torque ripple are discussed. It is concluded that the additional loss and torque ripple of the high-speed permanent magnet spindle motor can be reduced through a reasonable design.

Improved V‐shaped interior permanent magnet rotor topology with inward‐extended bridges for reduced torque ripple

Interior permanent magnet synchronous machines (IPMSMs) with V-shaped permanent magnet (PM) rotors are widely used as traction motors in electric vehicles because of their high torque density and high efficiency. However, the V-shape IPMSMs have the disadvantages of inevitable torque ripple due to the non-sinusoidal air-gap flux density distribution and the utilisation of the reluctance torque. In this study, with the aim of improving the torque ripple characteristics, a modified V-shaped IPMSM rotor configuration with bridges extended inwards towards the pole centre is proposed to generate a more sinusoidal air-gap flux density waveform. The proposed topology, referred to as ‘Type C’ within this study, is compared with baseline rotor configuration references, namely ‘Type A’ which is a conventional V-shaped PM rotor, as well as ‘Type B’ which is a related configuration with a mechanically non-uniform air gap. The analysis results show that the rotor ‘Type C’ exhibits significant advantages in terms of reducing cogging torque, torque ripple and radial force, without incurring additional air-gap friction losses. Finally, a prototype of the IPMSM with the proposed rotor configuration is manufactured and tested, verifying the predicted benefits experimentally.

Design and Analysis of Normal Saliency IPM Spoke Motor

This article deals with the design of a normal saliency interior permanent magnet (PM) motor, also referred as flux-intensifying PM motor. A multibarrier rotor geometry is adopted and studied through an analytical model to obtain an almost sinusoidal airgap flux density waveform, so as to improve the performance and reduce the torque ripple. The developed analytical model is generic and applicable for any number of rotor flux barriers and for any number of poles. The motor performance improvement has been evaluated by finite-element analysis. Experimental validation has been carried out on a motor prototype.

Chaotic Search Optimal Design and Modeling of Permanent Magnet Synchronous Linear Motor

This paper presents an electromagnetic finite element model of permanent magnet synchronous linear motor and distortion rate of the air gap flux density waveform is analyzed in detail. By designing the sample space of the parameters, nonlinear regression modeling of the orthogonal experimental design is introduced. We put forward possible air gap flux density waveform sine electromagnetic scheme. Parameters optimization of the permanent magnet synchronous linear motor is also introduced, which is based on chaotic search and adaptation function. Simulation results prove that the pole shifting does not affect the motor back electromotive symmetry based on the structural parameters, which provides a novel way for the optimum design of permanent magnet synchronous linear motor and other engineering.

Study on permanent magnet thickness of high-speed permanent magnet generator

The permanent magnet thickness (PMT) is an important parameter in the design of the permanent magnet machine, and it directly affects the air-gap magnetic field and performance of generator. In this paper, a 117-kW, 60,000-rpm, high-speed permanent magnet generator (HSPMG) is taken as an example, and a two-dimensional finite element model (FEM) is established. By comparing calculation result and test data, the accuracy of the model is verified. The air-gap flux density waveform is obtained by the FEM, and the waveform is decomposed by the Fourier transform principle. The nonlinear variation law of harmonic content with the increase in PMT is obtained, and the nonlinear variation mechanism of air-gap flux density is revealed. On this basis, the variation law of voltage and voltage regulation with the increase in PMT is given, and the PMT is optimized. In addition, the nonlinear variation law of the loss is determined. The research shows that the purpose of optimizing performance of HSPMG can be achieved by adjusting the PMT. The PMT is finally determined when the generator performance is optimal. The conclusions provide some reference for the research of HSPMG.

Use of fractional‐conductor windings and semi‐magnetic slot wedges in synchronous machines

This paper discusses two methods of altering the harmonic content of the spatial air-gap flux density waveform in synchronous machines (generators and motors). First, fractional-conductor windings are analysed for adoption as a replacement for a conventional distributed winding arrangement, their advantages and disadvantages briefly discussed and an example design scenario presented. Second, analysis and discussion regarding the use of semi-magnetic slot wedges as a replacement for glass-fibre type wedges is presented to complement the choice of winding in synchronous machines. Both methods are shown to benefit machine performance under certain circumstances.

A Novel Dual-Stator Radial-Flux Machine With Diametrically Magnetized Cylindrical Permanent Magnets

This paper presents a dual-stator permanent magnet synchronous machine (DS-PMSM) with diametrically magnetized cylindrical PMs (DMCPMs) . The advantages of the proposed DS-PMSM are its small cogging torque and torque ripple, sinusoidal (low harmonic) air-gap flux density waveforms, and a high pole-pair number structure, which can be used to increase the torque density. To confirm the advantages of the proposed DS-PMSMs, first, the cogging torques produced with conventional arc PMs and cylindrical PMs are compared. Next, a DS-PMSM with DMCPMs is designed, and its cogging torque is calculated. Then, all the relevant machine characteristics, including the cogging torque, air-gap flux density, back electromotive force, and torque–angle characteristics, are predicted by the two- and three-dimensional finite-element method. Finally, the machine is prototyped, and the validity of its advantages is investigated with the experimental tests.

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%.

Influence of Soft Magnetic Material Type in Fixture Components on the Magnetization of Bonded Neo Magnet and Motor Performance

The advantages like higher magnetic properties than ferrite, near net shape magnet production, and no use of heavy rare earth elements makes the bonded neo magnet very attractive in motors used for automotive accessory, home appliance and office automation. The isotropic nature of bonded neo magnets offers a feasibility to obtain wide range of magnetization profiles. The magnetization of the magnet influences the air-gap flux distribution and hence the motor performance 1. Magnetizing fixture comprising of copper coils embedded in soft magnetic material is used to magnetize the magnet. When radial magnetization profile is desired, a back iron made up of soft magnetic material is also used to reduce the amount of magnetizing energy needed to saturate the magnet. Laminated steel is the preferred material for the magnetizing fixture as well as back iron. We have observed that at times solid steel is used in place of laminated steel. This paper presents the effects of using solid steel in place of laminated steel on the magnetization and motor performance. A magnetizing fixture is designed using the 2-D finite element analysis (FEA). The designed fixture is fabricated with fixture core and back iron made of laminated steel (LCLB). The magnetization performance of the designed fixture is evaluated using 2-D FEA and validated by performing magnetization of the magnets. To evaluate the influence of solid steel as a soft magnetic material two more combinations; (i) fixture core is of laminated steel but the back iron is of solid steel (LCSB) and (iii) both fixture core and back iron made of solid steel (SCSB) are simulated and evaluated. To ensure the full saturation in a bonded neo magnet a magnetizing field of 3T is desired through the thickness of the magnet 2. From the simulation it is observed that to achieve 3T magnetizing field for LCLB combination the magnetizing energy required is 5.44 kJ. The required energy increases to 34.02 kJ and 68.28 kJ for LCSB and SCSB combinations respectively. The increase in energy is due to the generation of eddy currents in solid steel components which counteract the applied field, reducing the available field for magnetization. The energy needed to achieve full magnet saturation in LCSB and SCSB combination exceeds the capability of most of the commercially available magnetizers also the increase in magnetization energy requirement will lead to higher thermal stress and reduced fixture reliability. Based on the capability of the available magnetizer we applied up to 6 kJ for LCSB and SCSB combinations. We have also measured the corresponding applied field at the back of the magnet as 1.6 T and 1.4 T respectively. The less than desired applied field led to the partial saturation of the magnet. Figure 1 shows the measured mid airgap closed circuit flux density waveforms for magnets magnetized using various combinations. From this figure it is observed that the use of solid steel component makes the airgap flux density waveform less radial. The flux integral is reduced by 11% and 6.6% for LCSB and SCSB combinations compared to LCLB combination. The magnets magnetized using various combinations are assembled in a motor for performance measurement, the results of which are summarized in Table I. The presence of solid steel component during magnetization leads to partial magnetization of the magnet, resulting in higher no-load speed and lower stall torque. It is also observed that the motor with the magnets magnetized using LCSB and SCSB combinations has 64% and 60% lower cogging torque compared to LCLB combination. This is due to partial magnetization and hence lower flux offered by the magnets from these combinations.