Air-gap Magnetic Field Distribution Research Articles

Analytical calculation method of a liquid-cooling eddy current brake considering magnetic saturation and skin effect

In this article, a clear and concise analytical method for predicting the performance of a Liquid-cooling eddy current brake (LC-ECB) is proposed. The LC-ECB has a coolant channel in the rotor to allow direct cooling of the inner surface of the stator. The static air-gap magnetic field distribution is obtained by the dynamic magnetic equivalent circuit (MEC) method, and the magnetic flux leakage and global magnetic saturation effects are fully considered. The magnetic field intensity distribution function of the eddy current reaction magnetic field is derived for the first time based on Ampere circuital theorem. Considering the local magnetic saturation and skin effect, a novel double-iteration algorithm based on the conservation principle of magnetic pressure drop is applied to obtain the transient air-gap flux density distribution, and then the brake torque expression is obtained. The finite element method (FEM) and experimental results show that the proposed method is feasible and effective. The new model is easy to program and can be easily used in the initial design and optimization of LC-ECB.

A Planar Electromagnetic Actuator With Passive Adsorption for CubeSats Transport in a Weightless Environment

A planar electromagnetic actuator (PEA) with passive adsorption is proposed to transport multiple miniature satellites (CubeSats) in a weightless environment. It can realize reliable mover adsorption to the track and fast 2-Dof translational motion, even under the interference of external acceleration. Compared with the conventional layout of permanent magnets (PMs), the PEA with the structure of Halbach array can achieve higher force density. The magnetic equivalent circuits (MEC) method is applied to reveal the mechanism of electromagnetic performance improvement. An accurate electromagnetic force model is developed by combining the MEC and mirror magnetic charge methods to consider the positive effects of yokes on the PM operating point and airgap magnetic field distribution for PEAs with large airgaps. The influence of main structural parameters on adsorption and driving performances is analyzed. A kinetic model is derived to predict the mover velocity. A PEA prototype has been manufactured and tested to experimentally validate the improved models, electromagnetic performance, and motion characteristics.

High-integrated micro permanent magnet linear actuator positioning system

A tunnel magnetic resistance (TMR) sensor is a magnetic detection sensor with low power consumption and high sensitivity. The TMR sensor has promising applications in the position detection of micro permanent magnet linear actuators since the surrounding magnetic field of the micro actuator in this paper will be changed by its movement. Firstly, according to the air-gap magnetic field distribution characteristics of the micro permanent magnet linear actuator and the detection principle of the TMR sensor, the integrated installation parameters of TMR sensors were determined. Then, with the help of TMR technology, the backpropagation neural network (BPNN) algorithm and improved BPNN using particle swarm optimization (PSO) algorithm were used to study the position identification strategy of the slider, and the algorithm strategy with the minimum error was selected. Finally, the experimental results show that the slider position identification strategy based on the PSO-BPNN algorithm can achieve position tracking error within 0.1 mm under the given step position tracking and sinusoidal position tracking, and the movements can be repeated well.

Magnetic Field Analysis for the Permanent Magnet Spherical Motor With SMC Core

This paper presents a permanent magnet spherical motor (PMSM) with soft magnetic composite (SMC) core. The analytical model of the no-load air-gap magnetic field of the PMSM with SMC core is obtained based on the Laplace equation with the boundary conditions. When the SMC core is added to the stator teeth, a cogging effect occurs, which makes the three-dimensional magnetic circuit of the entire spherical surface uneven. When the spherical motor completes multi-degree-of-freedom motion, the air-gap magnetic field is severely distorted. In order to solve the above problems, this paper proposes for the first time the method of adding spherical shaped pole shoes to the stator teeth, which perfectly solves the problem of magnetic field distortion in this paper. The air-gap magnetic field distribution is improved by optimizing the structure of the stator tooth pole shoes. Finally, the static torque measurement platform was built to test the rotation energized output torque. The research results of this paper lay a theoretical foundation for the structural optimization design of the PMSM with SMC core.

Analytical Modeling of Magnetic Air-Gap Field Distribution Due to Armature Reaction

The following paper presents an analytical study of the air-gap magnetic field distribution produced by the armature reaction of a linear machine. Based on the method of images, the magnetic field generated by a current carrying conductor inside the air-gap between two smooth infinitely permeable iron surfaces is modeled as a complex 2D function. The conductor model then becomes a current sheet model and horizontally oriented current sheets are used to model the magnetic field produced by the armature reaction for smooth ferromagnetic surfaces. Focus will be given to the study of the slot opening function in front of energized slots in comparison to the not energized ones of the classical theory pointing out some remarkable differences. Later, the model is extended to slotted geometries using a complex slotting function adapted for energized slots. At last, the Maxwell tensor expressed in complex formulation will be integrated to obtain the force components acting on the machine tooth tips, quantities that will be compared with FEM simulations in order to validate the proposed analytical model.

Soft-Starting Brushless Doubly Fed Machine Winding Design and Magnetic Field Analysis

With the development and maturity of control technology, brushless doubly-fed motor (BDFM) is widely used in the field of variable frequency speed regulation. In order to improve motor starting performance, a soft starting method is proposed to reduce impulse current. The core of the method is to reconstruct the stator power winding and rotor winding. The BDFM with wound rotor is flexible in structure, and the air-gap magnetic field distribution can be changed by adjusting the pitch, turns and connection mode of stator and rotor windings, so as to improve the motor starting performance. In this paper, the design process, connection mode and working principle of the stator and rotor of a BDFM with a 2/4 pole pairs are introduced in detail. In addition, a multi-loop chain equivalent circuit is used to calculate the starting torque in this connection mode. Finally, the starting performance of the motor is analyzed by finite element method, and an experimental prototype is made, which proves the effectiveness of the scheme.

Analytical Calculation of Air-Gap Magnetic Field Distribution in IPMSMs with Mixed Eccentricity Accounting for Bridge Saturation

This paper presents an analytical model for calculating the detailed air-gap magnetic field distribution in interior permanent magnet synchronous motors (IPMSMs) with mixed eccentricity. In order to improve the efficiency of model solving, a modeling strategy combining the equivalent magnetic circuit network method and the subdomain method was adopted. Specifically, the magnetic field distribution of the rotor was modeled by using the magnetic circuit analysis method, and the magnetic field distributions of the air-gap, slot opening and stator slot along the radial direction were modeled in different regions according to their structure ruler. Then, the influence of bridge saturation was considered. Moreover, based on the analysis of the air-gap geometric structure with mixed eccentricity, a detailed spatiotemporal analytical model of the air-gap magnetic field was established, which provides a more accurate description of the mixed eccentricity composed of static and dynamic rotor eccentricities of different severity. The analytical models were compared with the corresponding models established by the finite element method, which proved the accuracy and validity of the models established in this paper. Finally, some key features related to radial and tangential air-gap flux density were extracted, which can significantly reflect the characteristics of eccentricities. The main findings reported in this paper will be of benefit for developing methods for early identification and diagnosis of eccentricity faults in IPMSMs.

Analysis of End-Effect Torque and Multi-Objective Optimization for Multi-Port Spatial Permanent Magnet Synchronous Motor

Multi-port spatial permanent magnet synchronous motor (MSPMSM) combines the advantages of disk motor and permanent magnet (PM) planetary gear drive, which solves the problem of single output port on traditional PM synchronous motor (PMSM) and realizes multi-port outputs and direct drive. Due to the special structure of disk stator, the planetary gear rotors are affected by end-effect torque in rotation process. The end-effect torque will not only cause torque ripple but also cause vibration and noise. Aiming at the problem of end-effect torque, the generation mechanism of end-effect torque is analyzed. In order to analyze air-gap magnetic field distribution accurately, the arc slotless subdomain (SD) model of planetary gear rotor and disk stator is established in polar coordinate system. The end-effect torque is derived by the Maxwell stress tensor method. Based on Box–Behnken design (BBD) method, a response surface model (RSM) is constructed to reduce end-effect torque amplitude and increase electromagnetic torque. The influences of structural parameters on end-effect torque amplitude are analyzed, and a set of optimal structural parameters are obtained. The end-effect torque and electromagnetic torque of the optimized MSPMSM are analyzed by finite-element analysis method (FEM), and the effectiveness of multi-objective optimization design method is verified. These research results have a good effect on improving the output performance of MSPMSM.

Design and Performance Analysis of a Staggered Vernier Generator for Wave Power Generation

In this paper, a staggered vernier generator suitable for a counter-rotating self-adaptable WEC is proposed to meet the energy demand of the small-scale engineering equipment in the deep sea. According to the vernier effect of the magnetic gear, the generator modulates the low-order rotating magnetic field generated by the rotation of the low-speed permanent magnet rotor into a high-order magnetic field rotating at a high speed, thereby realizing the acceleration of the generator magnetic field. A staggered structure permanent magnet vernier generator with 18 teeth/28 poles is designed. The main magnetic flux path on the staggered structure in the staggered vernier generator is analyzed, and the air-gap magnetic field distribution of the generator is analyzed with the help of numerical simulation software. The influence of different design parameters on the vernier generator is discussed. The staggered vernier structure can improve the main magnetic flux of the generator, reduce the magnetic flux leakage, and improve the performance of the generator without adding additional structures and materials.

Effect of Stator Slots on Electromagnetic Performance of a High-Voltage Line-Start Permanent Magnet Synchronous Motor

It is well known that the use of slotted stators in motors produces undesirable effects, such as magnetic flux distortion, additional losses, ripple torque, and vibration. However, a large number of studies pay more attention to stator slots and magnetic slot wedges (MSW) in asynchronous motors and permanent magnet motors, ignoring the same problems in large capacity high voltage line start permanent magnet synchronous motors (HVLSPMSM). In order to disclose the effect of the stator slot on HVLSPMSMs, the no-load air gap magnetic field distribution and stator leakage reactance are studied. Meanwhile, the differences in the starting torque, pull-in torque and pull-out torque of four slot models are compared, and the starting performance is more affected by stator slot. In practical manufacturing, the application of MSWs is the main way to change the electromagnetic performance of stator slots, so the influence of MSWs under different permeabilities on the performance of HVLSPMSMs is investigated. Finally, the effect of a stator slot on the motor starting performance and the rated performance are verified by prototypes and experimental tests, which provide a reference for the application of MSWs in HVLSPMSMs.

Robust Controller Design for Maglev Suspension Systems Based on Improved Suspension Force Model

The electromagnetic suspension-type maglev train can reach ultrahigh-speed using long stator linear synchronous motors; however, slot effect makes the motors suffer from suspension force ripple, since it causes the nonsinusoidal airgap magnetic field distribution. It has been expounded that the suspension electromagnet system is highly nonlinear and unstable in open loops. Additionally, maglev trains experience disturbances and uncertainties in service. Therefore, the robust disturbance-rejection control for electromagnet suspension system is highly necessary to maintain a constant airgap position. In this article, it is intended to propose a novel robust controller for suspension systems which ensures superior system performances despite suspension force ripple, disturbances, and uncertainties while sustaining stable suspension despite system nonlinearity. First, field harmonics are investigated along with slot effects, and an improved nonlinear mathematical model of electromagnetic force is derived. Second, the controller based on the improved force model is formulated. Then, the performance of the designed controller is evaluated on a maglev suspension system with disturbances and uncertainties. Simulation and hardware-in-the-loop experimental results demonstrate that the improved suspension force model is more accurate than the conventional models, and the corresponding controller excels in attenuating larger disturbance without sacrificing tracking performances at different speeds.

Hybrid Analytical Modeling of Air-Gap Magnetic Field in Asymmetric-Stator-Pole Flux Reversal Permanent Magnet Machine Considering Slotting Effect

This article proposes an accurate and computationally efficient hybrid analytical (HA) model for the air-gap magnetic field computation of asymmetric-stator-pole flux reversal permanent magnet machine, which can provide a thorough insight into the working mechanism by taking the slotting effects into account. The proposed HA model combines the subdomain method and Schwarz–Christoffel (SC) transformation, which can account for the stator and rotor slotting effects, respectively. The subdomain method is first employed to predict the air-gap magnetic field considering the rotor slotting effect by converting the machine geometry to a slotless stator model. Afterward, a complex relative permeance function is obtained by the SC transformation, in which the stator slotting effect is taken into account. Finally, the complete air-gap magnetic field distribution of the machine can be efficiently predicted by the proposed HA analytical model. The effectiveness of the proposed HA model is verified by both finite-element analyses and experimental results.

A Novel 2-DOF Lorentz Force Actuator for the Modular Magnetic Suspension Platform.

The modular magnetic suspension platform depends on multi degree of freedom of Lorentz force actuators for large bearing capacity, high precision positioning and structure miniaturization. To achieve the integration of vertical driving force and horizontal driving force, a novel 2- (two degrees-of-freedom) DOF Lorentz force actuator is developed by designing the pose of the windings and permanent magnets (PMs). The structure and the working principle are introduced. The electromagnetic force mathematical model is established by the equivalent magnetic circuit method to analyze the coupling of magnetic flux. The distribution characteristics of magnetic flux density are analyzed by the finite-element method (FEM). It is found that the coupling of the magnetic flux and the large magnetic field gradient severely reduce the uniformity of the air-gap magnetic field. The electromagnetic force characteristic is investigated by FEM and measurement experiments. The difference between FEM and experiment results is within 10%. The reasons of driving force fluctuation are explained based on the distribution of air-gap magnetic field. The actuator performance are compared under the sliding mode control algorithm and PID control algorithm and the positioning accuracy is 20 μm and 15 μm respectively. Compared with the similar configuration, the motion range and force coefficient of the Lorentz force actuator in this paper are larger. It has a certain guiding significance on the structure design of the multi degree of freed Lorentz force actuator.

Tilting Torque Analysis of an Iron-Cored Tiered-Type Permanent Magnet Spherical Motor

This article mainly studies the tilting torque characteristic of a novel iron-cored tiered-type permanent magnet spherical motor (T-PMSpM), which has the merit of large torque ability benefitted from the use of iron cores in both rotor and stator. However, the use of ferromagnetic materials also makes the iron-cored T-PMSpM much different from other air-cored spherical motors. Thus, the influence on the tilting torque characteristic is investigated theoretically and numerically. First of all, the active tilting torque is obtained based on a simplified model of air-gap magnetic field distribution. According to this model, the influence of the magnetic field distortion caused by the tilting motion is evaluated. Then, the characteristic of the restoring torque, which obviously exists in the iron-cored T-PMSpM and hinders the tilting motion, is analyzed under different working conditions. The three-dimensional finite-element analysis (FEA) is adopted to calculate the accurate output tilting torque. Finally, an experimental procedure is designed to measure the output tilting torque of the prototype motor for verification. The measured results are compared with the FEA results.

Improved EL Model of Long Stator Linear Synchronous Motor Via Analytical Magnetic Coenergy Reconstruction Method

Electromagnetic-suspension (EMS)-type maglev, based on long stator linear synchronous motor (LSLSM), suffers from the flux linkage and thrust ripple. This is due to the non-sinusoidal airgap magnetic field distribution caused by the slot effect and end effect. In this article, it is intended to address this issue by establishing a nonlinear mathematical model of LSLSM for real-time simulation and controller design, considering the spatial harmonics and core saturation. The Euler-Lagrange (EL) model is improved by means of coenergy and then applied to obtain the general equations of LSLSM. At first, the variation in coenergy in LSLSM regarding the mover position and stator current are analyzed, in the presence of spatial harmonics and core saturation. Afterward, an analytical model of coenergy is constructed by two Fourier basis vectors of mover position and torque angle, and a coefficient matrix polynomial of stator current magnitude. Then, a new model of LSLSM is derived based on the coenergy model and EL method. The parameters of the model can be obtained from the numerical data of coenergy in all operation ranges via finite-element analysis (FEA). Finally, the new model of LSLSM and its propulsion system are integrated in MATLAB/Simulink setup. The simulation results show that the improved EL model can achieve satisfactory accuracy compared with the FEA results well, whereas the computational efficiency is improved largely.

Modeling of airgap flux density for the study of stator core vibration in low speed synchronous machines

Purpose This paper aims to develop models and simulations focused on the prediction of electromagnetic forces acting on the stator core of a synchronous machine. It contributes to the study of stator core vibrations. Design/methodology/approach An analytical model based on the rotating fields’ theory including the damper winding contribution was developed. Such model allows the comprehension of airgap magnetic field distribution and the consequent pressure distribution. Focus was given to the pressure sub-harmonics due to the usual fractional winding configuration of low speed machines. A comparative numerical model was also developed and applied to an example laboratory machine. Partial validation measurements were performed. Findings The paper provides the predicted electromagnetic forces and the relative influences of damper winding and teeth tangential forces on each pressure harmonic. It is shown by how much such effects can influence the amplitude of pressure sub-harmonics from a fractional stator winding. Research limitations/implications The performed validation measurements were based on the airgap field distribution, but the resulting core vibration at load was not measured. Therefore, researchers are encouraged to perform additional tests for improved validation. Practical implications The obtained models and results are of great importance for the design phase of new generators and for the diagnosis process of existing machines with core vibration problems. Originality/value As a contribution of this paper, the magnitude of indirect effect of tangential forces and the effect of damper winding are comparatively quantified for each pressure harmonic. The given approach contributes to the relative evaluation of these effects especially on the sub-harmonics from the fractional stator winding.

Analytical Modeling of Misalignment in Axial Flux Permanent Magnet Machine

This paper proposes an analytical model for the prediction of air gap magnetic field distribution for axial flux permanent magnet (AFPM) machine with various types of misalignments. The AFPM machine geometry is first transformed to a polar representation. Consequently, the subdomain model based on current sheet technique is developed. Then the stator coordinate system is chosen as reference coordinate to consider both static/dynamic angular and axis misalignments. The back electromagnetic forces and cogging torque are obtained accordingly based on Maxwell's equations. The results show that the proposed approach agrees with the finite-element method. The model is further validated by experiments under healthy, dynamic angular and axis misalignment conditions, which can validate the proposed approach. It turns out that the proposed approach can predict the performance of AFPM machines with types of misalignment quickly and effectively, which is greatly significant for further fault detection.

Analysis of air‐gap permeance functions in flux‐modulation double‐stator electrical excitation synchronous machine

The air-gap magnetic field analysis of the field-modulation double-stator electrical excitation synchronous machine (FM-DSEESM) is complicated due to its double stator and modulation-ring rotor configuration. Aimed to investigate the influence of the each part of the machine on the magnetic fields in the air-gaps, this study focuses on the permeance function analysis of FM-DSEESM to reveal its air-gap magnetic field distribution. Due to the limited physical space, the non-ferromagnetic segments of modulation-ring rotor in FM-DSEESM cannot be regarded as infinitely deep slots. Therefore, by adding a new flux line in the non-ferromagnetic segments, a new permeance function is proposed based on the calculation of the equivalent air-gaps. Then, analytical results of flux densities in the air-gaps are calculated and verified by finite element analysis. Finally, a FM-DSEESM prototype is fabricated to prove the feasibility of the permeance functions.

Magnetic Force Enhancement Using Air-Gap Magnetic Field Manipulation by Optimized Coil Currents

This paper presents an air-gap magnetic field manipulation by optimized coil currents for a magnetic force enhancement in electromechanical devices. The external coil is designed near the device air-gap for manipulating the magnetic field distribution. The distribution of external coil currents is then optimized for maximizing the magnetic force in the tangential direction to the air-gap line. For the optimization, the design domain near air-gap is divided into small areas, and design variables are assigned at each small design area. The design variables determines not only the strength of coil current density (i.e., number of coil turns) but also whether the material state is coil or iron. In a benchmark actuator example, it is shown that 11.12% force enhancement is available by manipulating the air-gap magnetic field distribution using the optimized coil current. By investigating the magnetic field distribution, it is confirmed that the optimized coil current manipulated the magnetic field, forwarding a focused and inclined distribution that is an ideal distribution for maximizing the magnetic force.

Effect of Slot Opening Width on the Air-Gap Magnetic Field of a Direct Drive Permanent Magnet Motor

The direct drive permanent magnet motor (DDPMM) is a promising candidate for applications because of its high efficiency, high power density, and low maintenance costs. This study focused on the effect of slot opening width on the air-gap magnetic field of a DDPMM. An exact analytical model based on Fourier analysis was established to calculate the air-gap magnetic field. The analytical general solution of the air-gap magnetic field shows that the slot opening greatly affects the air-gap magnetic field distribution when the amount of the permanent magnet is constant. Then, the air-gap magnetic fields of the DDPMM with closed and open slots were compared at different positions. Furthermore, several finite-element models of motors composed of different numbers of unit motor were established based on the different slot opening widths to study the effect of slot opening width on the air-gap magnetic field. The results obtained using the finite element method verify that the slot opening width greatly affects the air-gap magnetic field.