Magnetomotive Force Research Articles

Torque Analytical Calculation of Formed Winding Permanent Magnet Motor

The development of electrification has put forward higher requirements for the efficiency and power density of permanent magnet motors. The combination of formed flat wire windings and open slots with rectangular cross-sections has been applied in permanent magnet motors, which makes the motor torque fluctuate significantly, and the vibration and noise caused by it seriously influence the stability of operation. Therefore, it is essential to study the torque characteristics for permanent magnet motors with formed windings. The open slot brings rich tooth harmonics to the air-gap magnetomotive force. In this study, an analytical model of the motor magnetic field was established based on magnetic potential and relative permeance theory. According to the Lorentz force law, an analytical model of the instantaneous torque of the permanent magnet motor with a formed winding is derived. The model points out that under the modulation of the relative permeance function, the constant torque and torque fluctuation are generated after the interaction of the stator magnetomotive force and rotor magnetic potential that meet the corresponding harmonic order relationship, and the order of the torque fluctuation is a multiple of 6. According to the analytical model, different torque components of the permanent magnet motor with formed windings are calculated and verified by the finite element method.

A Practical Analytical Expression and Estimation for Average Torque of High Saturation Permanent Magnet Synchronous Motor for Special Vehicles

Torque is a significant parameter in the design and control of permanent magnet synchronous motor (PMSM). Torque measurement systems are usually expensive, which correspondingly require extra room and add weight. Alternatively, torque can be estimated by the product of the measured current and the estimated magnetic flux. In general, the conventional torque estimation method for PMSM is established based on ignoring core saturation. However, in special vehicles, due to the high power density and narrow installation space of the motors, the saturation degree of the core is high, and the nonlinear characteristic between torque and current is more prominent, which would bring significant errors to the conventional torque estimation method. In order to solve the aforementioned problem, this paper studies on the torque from the perspective of magnetomotive force (MMF). A saturation coefficient is proposed to modify the conventional torque model by considering the core reluctance. Then, a practical analytical expression of average torque and an improved torque estimation method are proposed. Compared with the conventional method, the proposed method significantly improves the accuracy of the estimation. At last, comprehensive simulation and experimental results based on a prototyped 300 kW interior PMSM have fully demonstrated that the proposed method can get accurate torque under different load conditions.

Performance Comparison of Large-Scale Design-Optimized Non-Overlap and Overlap Winding Wound Rotor Synchronous Generators

The use of non-overlap windings rather than overlap windings is a topic for debate. Non-overlap windings are generally cheaper and easier to manufacture but result in a high amount of magnetomotive force sub- and higher-order harmonics. A strategy to reduce these harmonics has been previously published and this study aims to provide a performance comparison of a large-scale wound rotor synchronous generator with a modified non-overlap winding and a classical overlap winding. Hence, design optimisations of a 16/18 and 16/72 pole/slot grid-connected 3 MW wound rotor synchronous generator for medium-speed wind generation are conducted. The optimisations are performed using the modified method of feasible direction gradient-based optimisation because of its simplicity and fast results. Optimal solutions for the 16/18 and 16/72 3 MW models are obtained and the performance of the solutions compared. The results show that the 3 MW 16/18 model performs favourably against the 3 MW 16/72 model, especially regarding the lower active mass.

Development of new pole-changing winding for lifting and transport mechanisms

In many industries, lifting and transport machines are used, particularly cranes, conveyors, and hoists. Taking into account their wide prevalence and large installed capacity, as well as the complexity of the operating mode, special attention is paid to the creation of new energy- and resource-saving electric drives that facilitate the start-up process and ensure accurate stopping of highly inertial lifting and transport mechanisms. In this direction, one of the priority tasks is the development of two-speed pole-changing motors that meet the requirements of the electric drive of lifting and transport mechanisms. Based on the method of "Discretely-given spatial functions", a pole-changing winding was obtained for a ratio of 1/5 poles at 30 slots of the stator. Analysis of the electromagnetic properties of the developed pole-changing winding showed that, compared with a close analog, the differential scattering coefficient on the p=1 side of the pole decreases from 1.7% to 1.3%, and on the p=5 side of the pole decreases from 15.9% to 9.7%, and also in the picture of the magnetomotive force, the presence of higher harmonic ones on the side of the first velocity decreases up to 6%, and from the second speed up to 20%.

Design and analysis of consequent pole permanent magnet synchronous motor with low torque ripple

AbstractPermanent magnet (PM) motor with consequent pole (CP) rotor can improve the PM utilisation ratio. However, one group of PMs with the same polarity is replaced by iron core, which deteriorates the electromagnetic performances of the motor, including asymmetric air‐gap magnetic field and larger torque ripple. To solve this problem, this study analyses the relationship between the torque ripple and the stator‐rotor magnetomotive force (MMF) harmonics, determines the harmonic orders causing the torque ripple of the CP PM (CPPM) motor, and proposes an unequal‐turn four‐layer winding structure which can eliminate the determining harmonics in the stator MMF. Furthermore, the electromagnetic performances of the CPPM motors with the proposed winding structure and traditional CPPM motors are investigated by the finite‐element analysis. It is verified that the CPPM motor with the proposed structure has better motor performances.

Optimal Pole Ratio of Spoke-type Permanent Magnet Vernier Machines for Direct-drive Applications

Due to magnetic gearing effects, spoke-type permanent magnet vernier machines (ST-PMVMs) have the merit of high torque density, where an extra torque amplification coefficient, i.e., pole ratio (the pole-pair ratio of PMs to armature windings) is introduced. However, different from surface-mounted PMVM, the variation of torque against pole ratio in ST-PMVMs is non-linear, which is increased at first and then decreased. This article is devoted to identify the optimal pole ratio of ST-PMVMs by equivalent magnetic circuit model. It is found that except the P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</inf> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> air-gap magnetomotive force (MMF) harmonic having the same pole-pair of PM, the Pa <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> air-gap MMF harmonic having the same pole-pair of armature winding is also induced due to the modulation of doubly salient air-gap structure. The P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</inf> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> MMF harmonic produces positive torque, while Pa <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> MMF harmonic produces negative torque. With the increase of pole ratio, the proportion of Pa <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> MMF harmonic as well as negative torque is increased, which reduces the advantages of high pole ratio coefficient. Further, the influence of dimension parameters on the performance of ST-PMVMs under different pole ratio are investigated. Results show that ST-PMVMs with pole ratio 2.6 have high torque density, low cogging torque and high power factor simultaneously. Finally, a prototype is manufactured to validate the analysis.

A Low Coupling Fault Tolerant PMA-SynRM With Mixed-Pitch Segregated Windings

Mutual coupling effect between different winding modules causes undesirable effects for the fault tolerant machine drives, such as current distortion, torque ripple, and increased fault current. In this article, a mixed-pitch segregated winding configuration is presented for a triple modular fault tolerant permanent magnet (PM)-assisted synchronous reluctance machine (PMA-SynRM). It exhibits less mutual coupling effect between the different winding sets, which leads to improved fault tolerance compared to the existing full-pitched segregated windings. The mutual coupling effect is described by deriving the magnetomotive force (MMF) profile, and the fault tolerant performance improvement is proven by detailed finite-element (FE) analysis and prototyping tests in healthy and various fault conditions. The results confirm that the presented winding machine has the same healthy performance as the conventional full-pitched windings, and it operates in a more balanced manner with less current distortion and lower turn fault current. It will become a more competing candidate for the safety critical applications.

Principle and Performance of a New Brushless Doubly Fed Reluctance Machine With Asymmetrical Composite Modulator

For the brushless doubly fed reluctance machine (BDFRM), a composite rotor featuring salient pole reluctance and short-circuited coils (SCC) is applied to efficiently improve the cross-coupling capability and magnetic field modulation effects, where the SCCs induce symmetrical multiphase current and then establish the corresponding additional magnetizing magnetomotive force to modulate the source one. This article investigates the modulation behavior and evaluates the modulation capability of the composite modulator from the perspective of the magnetic field conversion mechanism. The modulated airgap harmonic phase-shift phenomenon in space caused by the SCC modulator is first observed, resulting in the reduction on the effective magnetic field conversion factors in the BDFRM with conventional symmetrical composite rotor. The phase-shift mechanism is revealed for the first time, then an asymmetrical composite modulator configuration is proposed to eliminate the phase shift so as to enhance the rotor cross-coupling capability and improve torque performance. A BDFRM prototype with the asymmetrical composite modulator is designed and manufactured for experimentation. Theoretical predictions are verified by two-dimensional finite-element analysis together with experiments.

Iron Loss Calculation for FSPM Machine With the PWM Inverter Supply Based on General Airgap Field Modulation Theory

In this article, an iron loss for the flux switching permanent magnet machine with the pulsewidth modulation (PWM) inverter supply is calculated based on the general airgap field modulation theory (GAFMT). First, the amplitudes and rotation speeds of the main space harmonics of the airgap magnetic flux density with the supply of PWM harmonics are calculated based on the GAFMT. When calculating the source magnetizing magnetomotive force based on the GAFMT, the equivalent magnetic circuit is applied to calculate the working point of the permanent magnet. Second, each spatial harmonic in the airgap magnetic field is synthesized by an equivalent current layer in the airgap and then is substituted into the 2-D finite element analysis models to calculate the iron losses. Finally, the iron losses calculated by the proposed method with different speeds, loads, and control strategies are compared with the experimental results.

Characteristic Analysis of Coreless-Type Linear Synchronous Motor With the Racetrack Coils as Secondary for EDS Maglev Train

The characteristics of coreless-type linear synchronous motor, which is applied in the propulsion system of electrodynamic suspension maglev train are calculated and analyzed by the more accurate analytical model. First, the magnetomotive force distribution model of the vehicle coils is proposed according to their racetrack shape. Then, on the basis of the space harmonic method, the characteristic analysis formula of coreless-type linear synchronous motor with single-layer and double-layer armature winding are presented. Second, the air-gap flux density, back electrodynamic force, and thrust of the coreless-type linear synchronous motor are analyzed by the three-dimensional finite element simulation method and the analytical methods. Then, the relationship of efficiency, power factor, and power angle with the number of feeder units is obtained. Finally, the accuracy of the analytical model and numerical result are experimentally validated by comparing with the transient operation data on Yamanashi and Miyazaki test line.

Characteristics Evaluation of a Segmental Rotor Type Switched Reluctance Motor with Concentrated Winding for Torque Density and Efficiency Improvement

With the rapid development of power electronic techniques and the increasing cost of permanent magnets (PMs) materials, switched reluctance motors (SRMs) have recently gained more attention. However, traditional SRMs have a relatively low torque density. For the sake of increasing the motor torque density, this paper proposes a novel segmental rotor type SRM. The proposed motor adopts hybrid stator poles and concentrated windings in the stator side and a segmental rotor structure in the rotor side, which is completely different from the structures of the traditional SRM. The special structure of the motor shortens the magnetic flux paths of the motor, separates the parts of the magnetic flux paths from one another, and eradicates the magnetic flux reversal in the motor stator in order to improve the electric utilization and output torque density of the motor. Meanwhile, the requirement of the magneto-motive force and the core loss of the motor is also decreased, thereby improving the efficiency of the motor. For the purpose of proving the proposed structure, the characteristics of the motor are analyzed using the finite element method and are compared to those of the traditional 12/8 SRM, which is designed for the same application. Moreover, the prototypes of the traditional 12/8 and proposed SRMs are manufactured, and experiments based on the prototypes are performed. Finally, the effectiveness of the structure of the proposed motor is further proven by the experimental results.

Analysis of DC Winding Induced Voltage in Wound-Rotor Synchronous Machines by Using the Air-Gap Field Modulation Principle

In order to analyze the DC winding induced voltage in the wound-rotor synchronous machine, this paper uses the air-gap field modulation principle to investigate its operation mechanism and harmonic order. By establishing the analytical magneto-motive force (MMF)-permeance model, the DC winding induced voltage per electrical cycle under open-circuit condition, armature reaction condition and on-load condition are deduced. Analytical analysis shows that the MMF function, stator and rotor permeance function are critical factors that influence the harmonic order of the DC winding induced voltage. The analysis results are compared with those predicted by the finite element analysis (FEA). Both non-linear steel and linear steel conditions are accounted in the FEA analysis, and the results show that the analytical deduction result agrees well with the FEA analysis result.

Temperature drift mechanism of deflector jet servo valve under temperature shock

To study the mechanism of the deflector jet servo valve under temperature shock, a complete temperature theoretical model is proposed in this article. The temperature change affects the performance change of the torque motor by affecting the drift of the air gaps’ thickness, the permanent magnets’ reluctance, and the magnetomotive polarization force. Moreover, the temperature variation will act on the flow coefficient of the pilot stage, the size of the deflector, and jet pan, which influences the performance of the pilot stage hydraulic amplifier. Furthermore, the armature components, including the stiffness of the spring tube, the stiffness of the feedback rod, and the armature’s arm of force, are also related to the temperature variation. Comprehensively, considering the interaction influence of these factors, by analyzing the electromagnetic characteristics of the torque motor, the fluid mechanics’ characteristics of the pilot stage hydraulic amplifier, and the temperature performance of the armature assembly, the temperature drift model of deflector jet servo valve is constructed, which is represented as a ninth-order nonlinear equation. Based on the equation, the influence of temperature on the control precision of the servo valve is analyzed. The calculation results show that in the range of 20°C–250°C, the impact of temperature on the control accuracy will exceed 30%, the flow coefficient is the most significant affecting on the control accuracy, followed by the structural deformation of the pilot stage is the second factor affecting the temperature drift, and other factors have little effect. Comparison with the experimental results, the temperature drift model of the deflector jet servo valve can predict the control accuracy caused by temperature and provide a theoretical foundation for the optimization of the deflector jet servo valve.

Controlling Torque Ripple Vibration in a Single-Phase PFC Using the Neutral Point of an IPMSM

This paper proposes a method to reduce the torque ripple vibration of an integrated power factor correction (PFC) converter by using the zero-phase inductance of an interior permanent magnet synchronous motor (IPMSM) when the motor is not running. When an integrated PFC converter is applied to electric vehicle (EV) chargers, it is necessary to reduce the torque oscillation of the motor caused by the charging current. In an integrated PFC converter using an IPMSM, the zero-phase current and magnetomotive force harmonics of the permanent magnet cause torque vibration. In the proposed control method, the generated torque is estimated using the back EMF table, and the phase current is controlled to cancel it. The proposed method can be used to suppress torque vibration irrespective of the mechanical angle of the rotor. The effectiveness of the proposed method is experimentally verified. Using the proposed method, the torque vibration can be suppressed by up to 91.3% as compared to that in the case of the conventional control method. Furthermore, a power factor of 99.9% is achieved under a load condition of 1kW.

Triple three-phase permanent magnet synchronous motor with shaped magnets for low vibration applications

This paper presents a triple three-phase permanent magnet synchronous motor (PMSM) with shaped magnets for low vibration applications. Firstly, the features of the designed PMSM are investigated from three aspects, including triple three-phase windings, shaped magnets, and multi-layered housing. Then, the armature reaction, magnetomotive force, torque performance, and fault tolerance ability of the designed PMSM are investigated. Subsequently, the radial force of the designed PMSM with shaped magnets is studied, in which the radial force modulation effect is considered. In addition, the radial force and vibration reduction principle is elaborated in detail. The modal simulation and experiment are carried out, and the vibration reduction effect of the designed PMSM is verified by the multiphysics vibration predicted model. The result shows that the vibration can be effectively reduced by the shaped magnets and multi-layered housing design, and the output torque of the designed PMSM has been reduced insignificantly thanks to the triple three-phase windings.

Electromagnetic and Electromechanical Compatibility Improvement of a Multi-Winding Switch Control-Based Induction Motor—Theoretical Description and Mathematical Modeling

The main advantages of multi-winding (multiphase) induction machines include reducing torque ripple, decreasing rotor harmonics losses, reducing the current per phase without increasing the voltage per phase, reducing the current harmonics of the DC voltage source, and high fault tolerance. The authors propose a theoretical description for the harmonic content of the DC-link current, magnetomotive force, and electromagnetic torque of a multi-winding induction machine (IM), and an account of the interaction of the time harmonics for the power supply and the spatial harmonics for winding functions is presented. The proposed theoretical analysis has made it possible to substantiate supply-winding schemes for the compensation of higher harmonics (6th and 12th in the DC-link current and the IM’s electromagnetic torque) and the improvement of the electromagnetic and electromechanical compatibility of the multi-winding machine, which are justified according to the proposed theoretical description. Further, a schematic solution for the multi-winding induction motor with electronic changing of the pole number is proposed to provide a reduction in speed ripples at low rotation speeds. This decrease is ensured by increasing the number of pole pairs and increasing the frequency of the supply voltage. Mathematical models of multi-winding switch control-based induction machines are developed using the method of average voltages in the integration step for an investigation of electromagnetic and electromechanical processes. It is shown that the developed models are distinguished by high speed of response and accuracy. This is confirmed by the comparative analysis using known methods and models in the Matlab environment, as well as a comparison of the simulation results with the known results of physical experiments. The results of mathematical modeling show that the use of a multi-winding IM with appropriate supply-winding schemes stands to significantly reduce the ripples of the IM’s electromagnetic torque and DC-link current in the case of using six-step voltage source inverters. This makes this type of inverter suitable for use in a frequency-controlled electric drive as an alternative to using a PWM inverter, which has a negative influence on the IM’s state.

Theoretical and Experimental Study on Claw-Pole Magnetic Levitation Torque Motor for 2D Valve Using Cogging Torque

In this paper, a claw-pole magnetic levitation torque motor (CPMLTM) utilizing cogging torque is proposed as an electromechanical converter (EMC) for two-dimensional valves (2D valve). Compared to the existing torque motor, CPMLTM utilizes the cogging torque between the stator and the rotor, and has the ability of automatic neutral adjustment, which greatly reduces the difficulty of neutral adjustment of two-dimensional valves and improves the accuracy of neutral adjustment. First, the structure and working principle of CPMLTM are introduced, followed by an analysis of the cogging torque of CPMLTM based on the energy method and Fourier expansion. The effects of the claw pole tooth (CPT) shape and slot opening coefficient on the cogging torque of CPMLTM are investigated. To analyze the sensitivity of the electromagnetic torque to each design parameter, a qualitative expression for the electromagnetic torque containing various design parameters was derived based on the equivalent magnetic circuit method, and a set of orthogonal tests were designed to calculate the electromagnetic torque using the finite element method (FEM). To demonstrate the feasibility of the proposed CPMLTM principle and to verify the correctness of the cogging torque analysis model and FEM, a prototype was fabricated and a test rig was constructed for experimental study. The experiments show that CPMLTM can indeed utilize cogging torque to achieve automatic neutral adjustment, and that the neutral adjustment is more accurate. Moreover, the CPMLTM has good static and dynamic characteristics: a neutral electromagnetic torque of 0.1 Nm at a coil magnetomotive force (MMF) of 100 A, step response time up to 4.575 ms, and amplitude frequency bandwidth and phase frequency bandwidth of 173.7 Hz and 86.5 Hz, respectively.

A Hybrid Calculation Method of Electromagnetic Vibration for Electrical Machines Considering High-Frequency Current Harmonics

This article proposes a hybrid evaluation method of electromagnetic force and vibration for electrical machines considering high-frequency current harmonics caused by the inverter. First, the permeance and armature magnetomotive force (MMF) is calculated based on the virtual MMF and the slot matrix. Then, the air-gap flux density and electromagnetic force construction process under arbitrary current is thoroughly studied. The vibration transfer function is obtained by utilizing the modal analysis and the modal test. Finally, the vibration can be calculated according to the modal superposition method. By applying this method to an interior permanent magnet machine, it can significantly reduce the computation efforts compared with the multiphysics procedure due to the extensive use of the finite-element method. In addition, the accuracy of this method is validated by conducting an experimental study.

Active Electric Dipole Energy Sources: Transduction via Electric Scalar and Vector Potentials.

The creation of electromagnetic energy may be realised by engineering a device with a method of transduction, which allows an external energy source, such as mechanical, chemical, nuclear, etc., to be impressed into the electromagnetic system through a mechanism that enables the separation of opposite polarity charges. For example, a voltage generator, such as a triboelectric nanogenerator, enables the separation of charges through the transduction of mechanical energy, creating an active physical dipole in the static case, or an active Hertzian dipole in the time-dependent case. The net result is the creation of a static or time-dependent permanent polarisation, respectively, without an applied electric field and with a non-zero vector curl. This system is the dual of a magnetic solenoid or permanent magnet excited by a circulating electrical current or fictitious bound current, respectively, which supplies a magnetomotive force described by a magnetic vector potential and a magnetic geometric phase proportional to the enclosed magnetic flux. Thus, the active electric dipole voltage generator has been described macroscopically by a circulating fictitious magnetic current boundary source and exhibits an electric vector potential with an electric geometric phase proportional to the enclosed electric flux density. This macroscopic description of an active dipole is a semi-classical average description of some underlying microscopic physics, which exhibits emergent nonconservative behaviour not found in classical closed-system laws of electrodynamics. We show that the electromotive force produced by an active dipole in general has both electric scalar and vector potential components to account for the magnitude of the electromotive force it produces. Independent of the electromagnetic gauge, we show that Faraday’s and Ampere’s law may be derived from the time rate of change of the magnetic and dual electric geometric phases. Finally, we analyse an active cylindrical dipole in terms of scalar and vector potential and confirm that the electromotive force produced, and hence potential difference across the terminals is a combination of vector and scalar potential difference depending on the aspect ratio (AR) of the dipole. For long thin active dipoles (AR approaches 0), the electric field is suppressed inside, and the voltage is determined mainly by the electric vector potential. For large flat active dipoles (AR approaches infinity), the electric flux density is suppressed inside, and the voltage is mainly determined by the scalar potential.

Verifying the calculation approach for radial suspension force based on the airgap flux density for SPM, consequent‐pole, and bearingless AC homopolar motors

AbstractIn this paper, a calculation method is proposed for the radial suspension force of a bearingless motor with a surface‐mounted permanent magnet (SPM) rotor, a consequent‐pole permanent magnet (CPM) rotor, and a homopolar permanent rotor (HPM). The radial suspension forces are calculated mathematically and analytically using the airgap flux density. It was confirmed that the proposed radial force equations are practical to calculate the suspension force based on the airgap flux density. The CPM bearingless motor and bearingless AC HPM have salient pole rotors that interact with the 2‐pole Magnetomotive force (MMF) to generate 6‐ and 10‐pole components. As a result, the radial suspension force of the CPM bearingless motor is generated by 8‐ and 6‐pole, and 8‐ and 10‐pole magnetic flux, whereas the bearingless AC HPM produces the radial suspension force by DC and 2‐pole components. The shaft torque, the suspension force, and efficiency were also compared for SPM, CPM bearingless motors, and bearingless AC HPM. Consequently, the torque value of the CPM bearingless motor is quite close to SPM bearingless motor. Moreover, the suspension force of the CPM bearingless motor is quite close to bearingless AC HPM.