Time-stepping Finite Element Method Research Articles

Waveform relaxation–Newton method to determine steady state of an electromagnetic structure

PurposeThe purpose of this study is to determine the steady state of an electromagnetic structure using the finite element method (FEM) without calculation of the transient state. The proposed method permits to reduce the computation time if the transient state is important.Design/methodology/approachIn the case of coupling magnetic and electric circuit equations to obtain the steady state with periodic conditions, an approach can be to discretise the time with periodic conditions and to solve the equation system. Unfortunately, the computation time can be prohibitive. In this paper, the authors proposed to use the waveform relaxation method associated with the Newton method to accelerate the convergence.FindingsThe obtained results show that the proposed approach is efficient if the transient state is important. On the contrary, if the transient state is very low, it is preferable to use the classical approach, namely, the time-stepping FEM.Research limitations/implicationsThe main limitation of the proposed approach is the necessity to evaluate or to know the time constant and consequently the duration of the transient state. Moreover the method requires some important memory resources.Practical/implicationsIn the context of the use of the time-stepping FEM, one of the problems is the computation time which can be important to obtain the steady state. The proposed method permits avoidance of this difficulty and directly gives the steady state.Social/implicationsThe proposed approach will permit to model and study the electromagnetic systems in the steady state, and particularly the transformers. Because of the gain in computing time, the use of optimisation techniques will be facilitated.Originality/valueThe novelty of this study is the proposal of the waveform relaxation–Newton method to directly obtain the steady state when applied to the three-phase transformer.

Analysis of two decoupled time-stepping finite-element methods for incompressible fluids with microstructure

ABSTRACTIn this article, two full discrete schemes of the micropolar Navier–Stokes equations (MNSE) are proposed and analysed, namely a fully decoupled scheme and a decoupled penalty-projection scheme. The fully decoupled scheme decouples the MNSE system into two sub-problems, one is the velocity–pressure system, the other is the angular velocity system, but still keeps unconditional stability with respect to the time step size. The stability and the optimal rate of convergence of the scheme are proved. Moreover, the decoupled penalty-projection method is derived based on the Chorin/Temam projection methods for the velocity–pressure system equipped with grad-div stabilization with parameter γ, we also prove that this scheme is unconditionally stable. In particular, we show that the solution of the decoupled penalty-projection method converges to the associated full decoupled method solution as . These time-stepping discretization schemes can be implemented efficiently in practice. Numerical experiments are given to validate the convergence rate predictions and demonstrate the efficiency of the new methods.

Design and Simulation of a Moving-magnet-type Linear Synchronous Motor for Electromagnetic Launch System

The Electromagnetic Aircraft Launch System (EMALS) offers significant benefits to the aircraft, ship, personnel, and operational capabilities. EMALS has such advantages as high thrust, good controllability, reusable, etc., as a launching motor, a double-side plate Permanent Magnet Linear Synchronous Motor (PMLSM) can provide high instantaneous thrust. This paper presents the design and analysis of the moving-magnet-type permanent magnet linear synchronous motor (PMLSM). A detailed analytical modeling based on Maxwell’s equations is presented for analysis and design of PMLSM with Halbach array. In order to improve the thrust characteristics of PMLSM, the structural characteristics and magnetic field are analyzed. The results show an enhancement in the motor performance. Finally, we have used 2-D nonlinear time-stepping transient finite element method to demonstrate validity of the analytical analysis and parametric search is used for multi-objective optimization of PMLSM. Using Finite Element Analysis (FEA), the effects of the parameters on the thrust and thrust ripple waveforms are analyzed.

Design, Analysis, and Prototyping of a New Wound-Rotor Axial Flux Brushless Resolver

Resolvers are electromagnetic position sensors that are widely used in industrial applications. In this study, a new axial flux brushless resolver (AFBR) with a wound rotor is introduced. In the proposed resolver, the core of the rotary transformer (RT) is omitted, and an innovative design is used to supply the excitation winding of the resolver. The proposed resolver can be built with smaller dimensions, and its thermal stability and mechanical strength are increased compared with conventional AFBRs. The performance of the proposed structure is simulated and optimized by using a three-dimensional time-stepping finite element method. The effect of the leakage flux of the RT on the excitation and signal windings is also discussed for both the proposed and conventional structures. A prototype based on the optimized topology is constructed and tested. Good agreement is obtained between the simulation and experimental results, validating the success of the proposed resolver.

Axial Magnetic Fields, Axial Force, and Losses in the Stator Core and Clamping Structure of a Synchronous Generator with Axially Displaced Stator

Axial displacement of the stator in a synchronous machine gives rise to axial magnetic field both at the ends and deep inside the stator. The axial magnetic field causes losses. This article contains results from two studies with an axially displaced stator. In the first study, axial magnetic leakage fields in the ends of a small synchronous generator at load and no load were measured and simulated. In the second study, axial force and iron losses at no load were calculated with non-linear materials and a three-dimensional, time-stepped finite element method. For some machines with vertical shafts, the sum of iron losses and thrust bearing losses can be reduced if the rotor is lowered or the stator raised, whichever is best.

Numerical calculation of primary slot leakage inductance of a Single-sided HTS linear induction motor used for linear metro

In the paper, the numerical method calculating asymmetric primary slot leakage inductances of Single-sided High-Temperature Superconducting (HTS) Linear Induction Motor (HTS LIM) is presented. The mathematical and geometric models of three-dimensional nonlinear transient electromagnetic field are established and the boundary conditions are also given. The established model is solved by time-stepping Finite Element Method (FEM). Then, the three-phase asymmetric primary slot leakage inductances under different operation conditions are calculated by using the obtained electromagnetic field distribution. The influences of the special effects such as longitudinal end effects, transversal edge effects, etc. on the primary slot leakage inductance are investigated. The presented numerical method is validated by experiments carried out on a 3.5kW prototype with copper wires which has the same structures with the HTS LIM.

A novel axial flux stator and rotor dual permanent magnet machine

A novel structure of axial flux stator and rotor dual PMs Vernier machine is presented as an effective option for high torque-density direct-driven applications. The key is to locate PMs on both sides of rotor and stator. With dual PMs, this proposed machine with a novel structure generates an improved torque per armature current at low speed. It is very suitable for direct drive applications with limited space such as the in-wheel electric vehicle (EV) motors. The theory of the structure with PMs on both sides is analyzed theoretically. The structure and operation principle of machine are introduced and the steady and steady performance of machine is analyzed and verified with time-stepping finite element method (TS-FEM).

A novel stator and rotor dual PM flux modulated machine

A novel structure of Veriner permanent magnet (VPM) machine is presented as an effective option for high torque density direct-driven applications. The key is to locate PMs on both sides of rotor and stator, and design the stator PMs as a cylinder shape, the rotation of which can be controlled by an external driven system. With this design, magnetic field in the airgap can be directly regulated by the rotation of stator PMs. The structure and operation principle are introduced and the performance is analyzed with time-stepping finite element method (FEM). Analysis results show that the novel structure has really high torque density and good field weakening performance.

A Novel Five-phase Double-Stator Tubular Fault-tolerant Flux-Modulation Permanent Magnet Motor

Tubular permanent magnet motors have been applied to many direct drive systems. This paper proposes a novel double-stator tubular fault-tolerant flux-modulation permanent magnet motor for an electromagnetic suspension system. The key of the proposed motor is the special double-stator and flux-modulation structure. The double-stator structure can make best use of the inner space of the motor. The flux-modulation structure is based on the magnetic gear effect, which can use effective harmonic components of magnetic field. Thus, the thrust force density is improved. Additionally, the idea of single-layer fractional-slot concentrated windings and fault-tolerant teeth is used to enhance fault-tolerant capability. The electromagnetic performance is analyzed by using the time-stepping finite-element method, verifying the effectiveness of the theoretical analysis.

Calculation of PM Eddy Current Loss in IPM Machine Under PWM VSI Supply With Combined 2-D FE and Analytical Method

A hybrid method combining 2-D finite-element (FE) method and analytical model is proposed for permanent magnet (PM) eddy current loss calculation in interior PM machines under pulsewidth modulation (PWM) voltage source inverter (VSI) supply, in which the PM eddy current reaction effect and PM axial segmentation are taken into consideration. First, the 2-D time-stepping (TS) FE analysis results considering and neglecting PM eddy current under PWM VSI supply are compared so that the cause of PM eddy current loss, the increase of high-order armature current components due to PM eddy current effect, and the decrease of the high-order components in average flux density due to leakage flux are revealed. Second, an analytical model for PM eddy current loss calculation using voltage input is deduced with the average flux density as input and a leakage flux factor is introduced in the model to meet the real case in PM machine. Moreover, the 3-D frequency FE analysis is used to verify the derived model. Third, the ratio between the average flux density and the imposed flux density is defined as a key parameter to reflect the PM eddy current reaction effect quantitatively, for both 2-D and 3-D cases. A functional relationship is established to describe the variation of the average flux density with and without considering the PM eddy current, where the parameter is obtained with nonlinear fitting of the 2-D FEA results. At last, the calculation procedure of the hybrid method is presented and a flux-concentrating field-modulated PM machine is taken as an example for calculation. The results are verified by an FE analysis. The proposed method is more efficient compared with the 3-D TS FE method while maintaining rather good accuracy.

Influence of End Structure on Electromagnetic Forces on End Winding of a 1550 MW Nuclear Generator

A 3D electromagnetic model of the end region of a 1550 MW nuclear generator is set up. The electromagnetic forces on the involute and nose parts of the end winding under a rated operation are obtained through the 3D time-step finite element method. The electromagnetic forces on different coils in the same phase are analyzed. By changing the rotor’s relative length and stator coil’s linear length in the 3D electromagnetic model, the electromagnetic force distributions on the end winding are obtained. The influence of each structure change on the electromagnetic force in different directions is studied in detail. Conclusions that can be helpful in decreasing the electromagnetic forces on the end winding through optimizing the end region design are presented.

Performance comparison of axial-flux-modulated motor with two pole-slot combinations

Axial-flux-modulated motors (AFMMs) with two pole-slot combinations are presented and analyzed quantitatively. They all have new topology structures, and their design rules differ from those of the traditional machine. The concentrated stator windings are designed to reduce the end length and copper losses; therefore, the efficiency of the motors can be improved. Special iron segments in the air-gap are used to modulate the magnetic field. The two proposed AFMMs have 36 stator slots and 30 stator slots, respectively, and the pole-slot combinations are 6 poles for 36 slots and 4 poles for 30 slots. This paper focuses on the comparative performance analysis of the two proposed AFMMs by using the 3D time-stepping finite element method. The flux linkage, air-gap flux density, electromotive force waveforms, output torque, core losses, and efficiency of the two proposed AFMMs have been investigated.

Twelve‐slot two‐saliency variable reluctance resolver with non‐overlapping signal windings and axial flux excitation

In this study, a new 12-slot two-saliency variable reluctance (VR) resolver with simple non-overlapping windings is proposed. The excitation winding in the proposed resolver is replaced with one axial coil that is perpendicular to the signal windings. Both distributed and non-overlapping concentric windings with uniform coil turns are used. The rotor has two upper and lower saliencies located in front of each other. The shape and width of each saliency are determined based on the optimisation. Compared with conventional 12-slot VR resolvers, the proposed resolver has a simpler rotor structure and the advantages of two-saliency resolvers against eccentricity, absolute output position, and higher accuracy. The operation principle of the proposed resolver is analytically shown. Then, a three-dimensional time-stepping finite-element method (FEM) is used for the design, analysis, and optimisation of the proposed sensor. After optimisation, a prototype of the most accurate resolver is built. The good agreement obtained between the FEM and the practical results verifies the design and optimisation process.

Design oriented technique for mitigating position error due to shaft run‐out in sinusoidal‐rotor variable reluctance resolvers

Variable reluctance (VR) resolvers have some distinguish features over wounded rotor resolvers that make them suitable for industrial applications. Among different types of VR resolvers, sinusoidal-rotor resolvers are preferred due to simple structure and high performance under eccentricities. However, their accuracy is affected by inevitable run-out error. As they work based on sinusoidal variation of coupling area between stator and rotor and under run-out error the coupling area is impaired. Hence, in this study, a new disk shape configuration is proposed for sinusoidal-rotor resolver that is robust against run-out error. Geometrical dimensions are calculated based on optimisations to achieve more accuracy. Three-dimensional time-stepping finite-element method is used to show the preference of the proposed resolver. Finally, prototypes of both conventional and proposed sensors are built and tested. Experimental results verify the success of the proposed structure.

Electromagnetic Design Optimization of a Modular Linear Flux-reversal Motor

Although modular linear flux-reversal permanent magnet motors are widely attractive for high reliability urban rail transit because of their advantages such as high power density, high reliability, low permanent magnet flux leakage problem, and improved fault-tolerant capability, they suffer from high thrust ripples. In this article the authors use a layer model for defining different optimization problems to improve thrust density, efficiency, and thrust ripples, independently and simultaneously. Design variables are chosen based on the sensitivity analysis of different objective functions relative to motor different geometrical parameters and some constraints are taken into account to avoid undesirable results. Then the proposed analytical model and optimization process are verified by time-stepping finite-element method.

Shape Design Optimization of Interior Permanent-Magnet Synchronous Motor with Machaon Flux Barriers for Reduction of Torque Pulsation

The main aim of this work is to present the results of the shape design optimization process of an interior permanent-magnet synchronous motor. The shape design optimization process is accomplished based on the variations of the rotor structure using the Taguchi method. The time-stepping finite-element method is used for analysis of the motor. It is found that the optimal two-layer Machaon design has the lowest torque pulsation compared with the other structures. Finally, the optimized Machaon and preliminary one-layer interior permanent-magnet synchronous motors, which are amended from industrial three-phase induction motors, are manufactured. The results of numerical, analytical, and practical tests are in good agreement.

Performance analysis of variable speed multiphase induction motor with pole phase modulation

Abstract The pole phase modulation (PPM) technique is an effective method to extend speed range and torque capabilities for an integrated starter and hybrid electric vehicles applications. In this paper, the five pole-phase combination types of a multiphase induction motor (IM) with 36 stator slots and 36 stator conductors are presented and compared quantitatively by using the time-stepping finite element method (TS-FEM). The 36 stator conductors of the proposed multiphase IM are fed by a 36 leg inverter and the current phase angle and amplitude of each stator conductor can be controlled independently. This paper focuses on the winding connection, the PPM technique and the performance comparative analysis of each pole-phase combination types of the proposed multiphase IM. The flux distribution, air-gap flux density, output torque, core losses and efficiency of five pole-phase combination types have been investigated.

Optimization Design and Performance Analysis of a PM Brushless Rotor Claw Pole Motor with FEM

A new type of permanent magnet (PM) brushless claw pole motor (CPM) with soft magnetic composite (SMC) core is designed and analyzed in this paper. The PMs are mounted on the claw pole surface, and the three-phase stator windings are fed by variable-frequency three-phase AC currents. The advantages of the proposed CPM are that the slip rings on the rotor are cast off and it can achieve the efficiency improvement and higher power density. The effects of the claw-pole structure parameters, the air-gap length, and the PM thinner parameter of the proposed CPM on the output torque are investigated by using three-dimensional time-stepping finite element method (3D TS-FEM). The optimal rotor structure of the proposed CPM is obtained by using the response surface methodology (RSM) and the particle swarm optimization (PSO) method and the comparison of full-load performances of the proposed CPM with different material cores (SMC and silicon steel) is analyzed.

High-Performance Fault Tolerant Halbach Permanent Magnet Vernier Machines for Safety-Critical Applications

This paper proposes new fault-tolerant permanent magnet vernier (FTPMV) machines with Halbach array. By utilizing a flux concentration of Halbach array, the performances of the proposed machines are significantly enhanced. In addition, influences of rotor yoke materials on performances of the proposed machines are investigated, revealing that both ferromagnetic and nonmagnetic rotor yokes can be applicable to the FTPMV machines. Significant torque and power factor enhancements can be achieved in the proposed FTPMV machines with a ferromagnetic rotor yoke and a nonmagnetic rotor yoke, respectively. In addition, the reduced magnetic gearing effect in the proposed nonmagnetic rotor yoke machine can be compensated by the flux concentration of Halbach array, thus enabling the machine to obtain comparable torque capability with the existing one. The electromagnetic performances of the existing and proposed machines are analyzed and compared by using the time-stepping finite-element method, verifying the effectiveness of the theoretical analysis.

Design of a New Magnetic Screw With Discretized PMs

This paper introduces a new type of high-performance linear actuator that is attractive for many potential applications. Structure simplification and processing technology are quite essential in promoting the development of the magnetic screw. The novelty of the proposed magnetic screw is the adoption of a discretized permanent magnet (PM), discretized ferromagnetic iron, and an ideal helix ferromagnetic iron ring. The discretized ferromagnetic iron is sandwiched between the two discretized PMs for forming a cell, and the ideal helix ferromagnetic iron was surfaced on the specified lead composed of PM cells. The configuration of the newly designed magnetic screws is presented, and its electromagnetic performances are analyzed by using the time-stepping finite-element method, verifying the advantages of the proposed structure.