Permeance Function Research Articles

Diagnostics of Interior PM Machine Rotor Faults Based on EMF Harmonics

This article presents a detailed study on the diagnosis of rotor faults in an Interior Permanent Magnet Machine based on a mathematical model. The authors provided a wide literature review, mentioning the fault diagnosis methods used for Permanent Magnet Machines. The research emphasizes the necessity of precise assumptions regarding winding construction to accurately analyze the additional harmonics appearing in rotor faults caused by electromotive force (EMF), i.e., rotor eccentricity and magnet damage. The article also discusses specific features appearing in the spectrum of air gap permeance functions and the impact of rotor eccentricity and magnet damage on PM flux density distribution and as a consequence on EMF stator windings. The novelty of the presented content is the analysis of induced EMFs for cases of the simultaneous occurrence of rotor eccentricity and PM damage. The findings of this study provide valuable insights for the diagnosis and understanding of internal asymmetries in Interior PM Machines.

Generalized Reluctance Network Framework for Fast Electromagnetic Analysis of Radial-Flux Machines

This article proposes a generalized reluctance network framework for analysis and non-parametric design optimization of rotating, radial-flux, electric machines, combining published state-of-the-art contributions and some original improvements. A novel element geometry and a novel airgap permeance function are proposed to support the automatic and systematic rotating radial-flux machine meshing without requiring the knowledge of geometrical parameters. An extensive and detailed validation of the proposed method was carried out on synchronous and asynchronous three-phase motor technologies, for a wide range of operating points, which constitutes an important contribution of this work. The numerical results obtained with the proposed method and with finite element analysis are compared for relevant design optimization quantities, such as input power, winding losses, core losses, power factor, permanent magnet Joule losses, and harmonic analysis. A satisfactory compromise between accuracy and computational speed was achieved, making the proposed method relevant not only for fast design/pre-design optimization purposes, enabling the evaluation of a large number of solutions in a relatively short time, but also for real-time, low-computational-intensity, reasonable-precision simulations.

Exact Analytical Magnetic Field Analysis, Optimization Design and Realization of an Eccentric Magnetic Harmonic Gear

The eccentric magnetic harmonic gear (EMHG) has a high efficiency and high gear ratio capability for large torque transmission. The air gap magnetic field can be calculated using an exact analytical model. The analytical approach is based on the theoretically accurate hyperbolic cotangent transformation method. The relative permeance function, which is derived from the impact of rotor eccentricity, can be used to find the eccentric air gap magnetic field solution. The proposed analytical approach is employed as the basis for a genetic algorithm that is used to develop and optimize the EMHG. The analytical results are in good agreement with the finite element method results, which verifies the correctness and validity of the proposed analytical model. The experimental measurements on the dual-stage EMHG confirm the validity of the analytical prediction.

Two-Dimensional Analytical Models for Cogging Torque Prediction in Interior Permanent Magnet Machine

Analytical prediction of cogging torque needs accurate flux density and relative permeance closed-form expressions. The accurate two-dimensional (2D) air gap flux density distribution function and the 2D permeance function are currently almost always applied to surface-mounted permanent magnet (SPM) machines, instead of interior permanent magnet (IPM) machines, due to complications from IPMs severe magnetic saturation and leakage flux. To address these issues, this paper proposes a set of new methods to derive the accurate closed-form 2D expressions of IPMs for both flux density and relative permeance. As for the flux density 2D model, a virtual equivalence model for IPM is introduced, so that Laplace’s equation and quasi-Poisson equation can be directly applied to IPM. As for permeance, the same virtual equivalence model also enables 2D models derivation for IPM. Subsequently, the resulting cogging torque analytical expression is obtained with the accurate relative permeance and air gap flux density models. The results from the proposed 2D analytical models showed similar accuracy to the finite element analysis (FEA). In addition, as demonstrated, the proposed 2D analytical models is a highly efficient tool set in the design process of cogging torque optimization, facilitating fast evaluation of different design factors.

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.

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.

Analysis of a Triple-Stator Axial-Flux Spoke-Type Permanent Magnet Vernier Machine

In this article, an axial-flux permanent-magnet (PM) Vernier machine with the triple-stator, spoke-type PM rotor, and toroidal winding wound on the innerstator is proposed. Benefited from the flux focusing spoke-type PM rotor and short end length toroidal winding, the proposed machine has a high torque density and the improved power factor. Based on the air-gap permeance function, the analytical expression of the proposed machine is derived to qualitatively analyze the machine's performance. The quasi-three-dimensional (3-D) finite element analysis (FEA) is adopted to optimize the design parameters, such as innerstator diameter, PM thickness, and slot opening width. The quasi-3-D FEA results match well with the 3-D FEA. The 3-D FEA results show the torque densities of the proposed machine reach 49.4 Nm/L and 11.4 Nm/kg, respectively, under the 232 A/cm average electrical loading. The performances, such as overload capacity, PM demagnetization, and PM and core losses, are also analyzed by 3-D FEA. The comparison with the other axial-flux PM Vernier machine is conducted, and the results reveal that the proposed machine has the great advantages of the torque density and power factor. Since the prototype is not built, in this article, the assembly scheme and thermal behavior of the proposed machine are discussed.

Investigation of Analytical Models for Surface-Mounted Permanent Magnet Motor Using Voltage Source Inverter

This article analyzed and compared the complex permeance model (CPM) and nonlinear analytical model (NAM) for surface-mounted permanent magnet (SPM) motor using a voltage source inverter (VSI). For linear CPM, the slotting effect is represented using the improved complex permeance function that describes the real slot shape rather than infinitely deep slot. NAM is extended from CPM and it replaces the magnetic potential drop of stator iron by the equivalent virtual current in the slot-opening and tooth-tip to account for the nonlinearity effect. The nonlinear inductance of SPM motor including the main phase inductance, slot leakage inductance, tooth-tip leakage inductance, and end winding leakage inductance is calculated using the frozen permeability method, which is the key to solve the electric circuit with VSI. The instantaneous back electromotive force (EMF) is calculated from the nonlinear back EMF coefficient and the back EMF neglecting iron nonlinearity. The electromagnetic torque obtained from motor model is used in the mechanical model and then the rotational speed and rotor position are obtained for the electric circuit model. Hence, the iterative solving process for the motor system is established to calculate the transient performance of SPM motor using VSI. Compared with CPM, NAM can greatly improve the calculation accuracy, which is also validated by both finite-element model and experiment. Besides, the proposed NAM is computationally efficient, which is useful for both motor design and motor control.

Improved Open-Circuit Airgap Field Model for FSCW-STPM Machines Considering PM-MMF Fluctuation

In this article, we propose an improved analytical model for the fractional-slot concentrated-winding spoke-type permanent-magnet (PM) machines, where the impact of slotting on magnetomotive force (MMF) is elaborately considered. First, the deficiency of the existing MMF-permeance model using Carter's coefficient is discussed. It is found that adopting Carter's coefficient will cause considerable prediction errors in flux density, especially for machines with a small equivalent airgap and considerable PM-MMF fluctuation. Second, an improved analytical model is proposed based on the relative permeance function and a simplified magnetic circuit model. The proposed model enables to predict common electromagnetic performance, such as PM flux density and back electromotive force with higher accuracy. Moreover, the radial forces exerted on the stator teeth can be predicted precisely as well, which is conducive to further vibration analysis. Both the experimental and finite-element analysis results indicate that the proposed model can enhance the characterization capability of the slotting effect and improve the performance prediction accuracy.

On the Analysis and Torque Enhancement of Flux-Switching Permanent Magnet Machines in Electric Power Steering Systems

Modern road vehicles are more and more often being equipped with electric actuators. These are intended to play critical roles in passengers comfort and safety. Among the electrified components onboard road vehicles, one can distinguish electric power steering (EPS) systems, which have been the subject of intensive investigations covering both design and control aspects. The abilities of several AC motor topologies to fulfil the EPS systems’ requirements have been assessed by a large scientific community in both academia and industry. The present work was aimed at the prediction of the electromagnetic features of the flux-switching permanent magnet machines (FSPMMs), with an emphasis on the air gap flux density. The latter was firstly formulated while neglecting the slotting effect at both sides of the air gap. Then, stator and rotor permeance functions, taking into account the slotting effect and the PM flux concentrating arrangement, were incorporated into the derived flux density spatial repartition. Moreover, the accuracy of the latter was improved through two dedicated correction functions that take into account the rotor position and the magnetic saturation. The last part of the paper presents a simple approach to enhance the developed torque of FSPMMs in an attempt to meet the EPS requirements.

Multiobjective Design and Performance Analysis of the Ultra-Low Speed Axial Flux Disc Motor for Maglev Wind Yaw System

A novel maglev wind yaw system (MWYS) based on the maglev technique and direct-drive structure was proposed to reduce the yaw power and failure rate. We first introduced the attraction force fluctuation and dynamic response time into the optimized design of axial flux motor, and constraints considering suspension startup, dc input voltage of suspension converter, and safe pitch limitation are given. Using multiobjective sequential quadratic programming technique, an optimization process is performed for minimizing the suspension losses, attraction force fluctuation, and the fastest attraction force dynamic response, considering the practical constraints. Ultra-low speed requirement makes the yaw motion easily vibrate with torque pulsation; we adopt the stator fractional slot structure and build stator slot permeance function and some constraints to perform the optimization of the stator construct parameters for minimizing cogging torque by the Lagrange function method. Finally, the design example is given and a prototype is manufactured. The experimental results show that the presented design method, structure, and the MWYS are feasible.

Analytical Modeling of Open-Circuit Magnetic Field in Permanent Magnet Assisted Synchronous Reluctance Motors Considering Iron Bridge Saturation Effects

<div class="section abstract"><div class="htmlview paragraph">Calculating accurately iron bridge saturation effects of the magnetic field, for Permanent Magnet Assisted Synchronous Reluctance Motors (PMASynRMs), remains to be a knotty problem. This paper presents an analytical modeling method to predict open-circuit magnetic field distributions and electromagnetic performances of PMASynRMs, considering iron bridge saturation effects. This analytical modeling method combines the magnetic equivalent circuit method, superposition principle, the solution of the governing Maxwell’s field equations and a complex relative permeance function. A quadruple-layer PMASynRM are remodeled into four surface-inserted permanent magnet synchronous motors (SPMSMs) which have different surface-inserted permanent magnets. Each layer of the interior permanent magnets of the PMASynRM is transformed into a new equivalent surface-inserted permanent magnet whose equivalent thickness needs to be defined by the magnetic equivalent circuit method due to iron bridge saturation effects. Based on superposition principle and the solution of the Laplace’s or Poisson’s field equation, the distribution characteristics of the radial and tangential magnetic flux density are obtained for PMASynRMs. The slotting effect is considered by a complex relative permeance function. To confirm the accuracy of the proposed analytical modeling method, the analytical solutions of magnetic flux density and cogging torque have been compared with Finite Element Method (FEM) simulation results. The root mean square errors of radial and tangential magnetic flux density between analytical and FEM results are 0.000553 and 0.0000916 respectively. The results indicate that the proposed analytical modeling method can consider iron bridge saturation effects effectively, which is suitable for performance predictions and parametric studies of PMASynRMs.</div></div>

Torque and Radial Force Optimization of Arc Flux Switching Permanent Magnet Linear Motor Used for Large Scanning Equipment

This paper deals with the analysis and comprehensive optimization of the torque and radial force ripples in the arc flux switching permanent magnet linear motor, which is equipped in the large scanning equipment. The torque ripple is caused by the no-load torque including cogging torque and end force. Specially, a worth noting problem of unbalanced radial forces is caused by the discontinuity of the arc stator, which is easily behaved as the rotor and load vibrations. In this paper, an analytical model based on the magnetic permeance function is established to analyze the principle of the no-load torque and radial force. Based on it, the optimization goal of force harmonics can be determined, and the feasible optimization approach can be predicted. It demonstrates the harmonic distribution of the torque is completely opposite to that of the radial force. Pure structural parameter optimization can not achieve the satisfactory results. To effectively suppress the no-load torque and radial force at the same time, a novel structure with two sets of specially arranged three-phase stator is proposed. An obvious optimization effect is verified according to the detailed FEM and experiment analysis.

Design and Analysis of Dual-Rotor Modular-Stator Hybrid-Excited Axial-Flux Permanent Magnet Vernier Machine

This paper proposes a new structure of the dual-rotor hybrid-excited axial-flux permanent magnet vernier machine (DR-HEAFPMVM) with the modular stator and the consequent-pole PM (CPM) rotor for low-speed, high torque density applications such as in-wheel electric vehicles. The tooth-wound non-overlapping armature windings and direct current (DC) excitation windings are, respectively, arranged in stator main-teeth and split-teeth to obtain the modulated and adjustable air-gap flux densities, resulting in high torque density and outstanding flux-weakening capability. First, the design considerations, operation principles, and air-gap flux density distributions of the proposed machine are elaborated based on the air-gap permeance function. Then, the influence of the pole ratios (PRs) and the DC excitation currents on the main electromagnetic performances of the DR-HEAFPMVM, such as the flux-weakening capability and back-electromotive force (back-EMF), on-load electromagnetic torque, loss distribution, and efficiencies, is investigated using the 3-D finite-element method (FEM). Results verify the feasibility of the flux adjustment of the DC excitation windings equipped in the split-tooth, and the design with a pole ratio of 8/1 tends to have higher torque density, higher machine efficiency, and considerable flux-weakening capability compared with the other two PRs.

Development and experimental validation of a fast and accurate field calculation tool for axial flux permanent magnet machines

A fast calculation method of magnetic flux density in axial flux permanent magnet (AFPM) machine is presented. This method is based on an original combination of magnetic charges concept, image theory, and relative permeance functions. Using this combined approach, significant 3D effects, which are present in axial flux machines such as curvature and edge effects as well as slotting effects due to stator slots, are considered. The main electromagnetic specifications of the AFPM machine such as cogging torque, Back Electromotive Force (EMF), and local air-gap flux density are calculated accurately in very short times. To validate this approach, an original prototype of double stator ironless rotor AFPM machine with adjustable air-gap is used. Experimental protocol including measurements of global characteristics (EMF, Torque) and measurements of local field density is presented. The obtained results are in good agreement with the experimental measurements which allows validating the proposed computation method.

Investigation of the Effects of the Pole Shoe Geometry on the IPM T-LSM Features: Application to Free Piston Engines

The paper is aimed at an analytical approach dedicated to the investigation of the effects of the pole shoe geometry on the no-load flux features of inner permanent magnet tubular-linear synchronous machines (IPM T-LSMs). It considers the most common geometries: (i) rectangular pole shoes, and (ii) trapezoidal pole shoes. The proposed approach combines two analytical models which are the magnetic equivalent circuit (MEC) and the permeance function. First, a basic MEC of an elementary part of the machine is considered to predict a preliminary air gap flux density trapezoidal waveform. Then, the accuracy of the proposed approach is enhanced by the incorporation of a mover permeance function that accounts for the PM spoke-type arrangement. The proposed approach is applied to the investigation of the impact of the mover pole shoe shape on the air gap flux density. The developed pole shoe sizing procedure makes it possible the selection of an IPM T-LSM with an appropriate mover geometry for which an investigation of the no- and on-load features is carried out by finite element analysis. The prototyping of the selected topology enables the experimental validation of the back-EMF and the load characteristic.

A Hybrid Field Analytical Method of Hybrid-Magnetic-Circuit Variable Flux Memory Machine Considering Magnet Hysteresis Nonlinearity

Variable flux memory machine (VFMM) is considered a promising solution for traction drives due to their distinctive merits of globally high efficiency over an extended operating range. However, the variable flux property of the low-coercive-force (LCF) permanent magnet (PM) together with an interior hybrid magnet rotor structure brings great challenges for the magnetic field modeling of VFMM. To address the above issues, this article proposes a new hybrid field analytical method for a recently developed hybrid-magnetic-circuit VFMM (HMC-VFMM), which combines the magnetic equivalent circuit (MEC) solution, the Schwarz–Christoffel (SC) transformation, and the subdomain model. First, the remanences of LCF PMs subject to different <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> -axis magnetizing currents are determined by the MEC model, in which the nonlinear magnetic reluctances are calculated by the finite element (FE) model. Subsequently, the air-gap flux density distributions of the slotless stator model under different magnetization states (MSs) are predicted by adopting the open-circuit MEC model. Afterward, the relative permeance function is obtained by using SC transformation considering the stator slotting effect. Then, the no-load flux density distributions of the machine under different MSs are predicted by the proposed method. Besides, a subdomain model taking into account the armature reaction is employed to further obtain the torque characteristic of the machine. Finally, the effectiveness of the proposed method is verified by both FE simulations and test results.

Analytical modeling and experimental validation of the six pole axial active magnetic bearing

The article presents a novel design of the axial active magnetic bearing with six poles. An analytical magnetic bearing model was developed to provide the axial magnetic induction distribution in 3D. The model utilizes magnetic vector potential formulation and Schwarz-Christoffel mapping. The paper covers in-depth deliberations on the end effect influence and the conjugate complex permeance function. Numerical model and simulations were provided in 3D mode with support of COMSOL Multiphysics software. The six pole axial active magnetic bearing was manufactured and investigated experimentally. Identification of the magnetic field distribution was carried out with a single axis magnetic induction sensor using custom automatic field scanner. High convergence of the modeling results and experimental research was demonstrated. The main advantage of the proposed analytical method is significantly shorter computation time compared to the numerical one that is useful from the modeling and controller study point of view. The configuration, modeling, simulation and experimental investigation results are well illustrated for the better overview.

Analysis and detection of turn‐to‐turn short circuit fault in a permanent magnet Vernier generator based on modified winding function

Operation of Vernier machines is based on flux modulation. They have some advantages including maintaining the rated torque in motor applications and the rated output power in generator applications at low speeds, high torque density and relatively low torque ripple due to their magnetic gear property and fault-tolerance. In recent years, the motor with various topologies has been developed for different applications. Therefore, analysing and monitoring different faults is essential in the design and implementation stages. This study has two main purposes. First, to introduce an accurate frequency index independent of load variations for detecting the turn-to-turn short circuit (TTSC) faults in the stator windings of a permanent magnet Vernier machine. Second, modelling the machine in a healthy condition and in the presence of TTSC faults to investigate its effect on machine performance and output characteristics. An analytical model is presented using the modified winding function theory under the TTSC fault by taking into account the effect of stator slots which enhances the accuracy of the air-gap permeance function estimation. In the process of calculating the fault index, frequency components of the output characteristics of the machine are obtained from the mathematical equations of the magnetic field. It is shown that the proposed indicators are robust against load variations.

Winding MMF and PM MMF Analysis of Axial-Flux Machine with Multi-Phase and Multi-Layer Winding

According to star graph and winding distribution, winding MMFs of three kinds of 12-slot/10-pole multi-phase and multi-layer winding layout are analyzed by the improved winding function method. Analysis results show that multi-phase and multi-layer winding can suppress even order and (12n ± 1) order harmonics, thereby reducing the eddy-current loss in PMs. Based on the unfolded LPMSM model, rotor MMF, air gap flux density, and no-load back-EMF are analyzed by the analytical permeance function method, which is validated by Teslameter and no-load experiment. Winding MMF is validated by FEM. An axial-flux integrated starting/generator (ISG) with double-three-phase four-layer (DTP-FL) winding, segmented armature and PM, and centrifugal fan is designed and manufactured. The no-load and load test with two groups of resistance established has validated the reasonability of the mentioned method. Experiments show that the axial-flux ISG prototype can run at a relative temperature rise.