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1 – 10 of 14The simulation of eddy currents in laminated iron cores by the finite element method (FEM) is of great interest in the design of electrical devices. Modeling each laminate by…
Abstract
Purpose
The simulation of eddy currents in laminated iron cores by the finite element method (FEM) is of great interest in the design of electrical devices. Modeling each laminate by finite elements leads to extremely large nonlinear systems of equations impossible to solve with present computer resources reasonably. The purpose of this study is to show that the multiscale finite element method (MSFEM) overcomes this difficulty.
Design/methodology/approach
A new MSFEM approach for eddy currents of laminated nonlinear iron cores in three dimensions based on the magnetic vector potential is presented. How to construct the MSFEM approach in principal is shown. The MSFEM with the Biot–Savart field in the frequency domain, a higher-order approach, the time stepping method and with the harmonic balance method are introduced and studied.
Findings
Various simulations demonstrate the feasibility, efficiency and versatility of the new MSFEM.
Originality/value
The novel MSFEM solves true three-dimensional eddy current problems in laminated iron cores taking into account of the edge effect.
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Piergiorgio Alotto, Paolo Di Barba, Alessandro Formisano, Gabriele Maria Lozito, Raffaele Martone, Maria Evelina Mognaschi, Maurizio Repetto, Alessandro Salvini and Antonio Savini
Inverse problems in electromagnetism, namely, the recovery of sources (currents or charges) or system data from measured effects, are usually ill-posed or, in the numerical…
Abstract
Purpose
Inverse problems in electromagnetism, namely, the recovery of sources (currents or charges) or system data from measured effects, are usually ill-posed or, in the numerical formulation, ill-conditioned and require suitable regularization to provide meaningful results. To test new regularization methods, there is the need of benchmark problems, which numerical properties and solutions should be well known. Hence, this study aims to define a benchmark problem, suitable to test new regularization approaches and solves with different methods.
Design/methodology/approach
To assess reliability and performance of different solving strategies for inverse source problems, a benchmark problem of current synthesis is defined and solved by means of several regularization methods in a comparative way; subsequently, an approach in terms of an artificial neural network (ANN) is considered as a viable alternative to classical regularization schemes. The solution of the underlying forward problem is based on a finite element analysis.
Findings
The paper provides a very detailed analysis of the proposed inverse problem in terms of numerical properties of the lead field matrix. The solutions found by different regularization approaches and an ANN method are provided, showing the performance of the applied methods and the numerical issues of the benchmark problem.
Originality/value
The value of the paper is to provide the numerical characteristics and issues of the proposed benchmark problem in a comprehensive way, by means of a wide variety of regularization methods and an ANN approach.
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Yahya Alnashri and Hasan Alzubaidi
The main purpose of this paper is to introduce the gradient discretisation method (GDM) to a system of reaction diffusion equations subject to non-homogeneous Dirichlet boundary…
Abstract
Purpose
The main purpose of this paper is to introduce the gradient discretisation method (GDM) to a system of reaction diffusion equations subject to non-homogeneous Dirichlet boundary conditions. Then, the authors show that the GDM provides a comprehensive convergence analysis of several numerical methods for the considered model. The convergence is established without non-physical regularity assumptions on the solutions.
Design/methodology/approach
In this paper, the authors use the GDM to discretise a system of reaction diffusion equations with non-homogeneous Dirichlet boundary conditions.
Findings
The authors provide a generic convergence analysis of a system of reaction diffusion equations. The authors introduce a specific example of numerical scheme that fits in the gradient discretisation method. The authors conduct a numerical test to measure the efficiency of the proposed method.
Originality/value
This work provides a unified convergence analysis of several numerical methods for a system of reaction diffusion equations. The generic convergence is proved under the classical assumptions on the solutions.
Details
Keywords
- A gradient discretisation method (GDM)
- Gradient schemes
- Convergence analysis
- Existence of weak solutions
- Two-dimensional reaction–diffusion Brusselator system
- Dirichlet boundary conditions
- Non-conforming finite element methods
- Finite volume schemes
- Hybrid mixed mimetic (HMM) method
- 35K57
- 65N12
- 65M08
Klaus Roppert, Florian Toth and Manfred Kaltenbacher
The purpose of this paper is to examine a solution strategy for coupled nonlinear magnetic-thermal problems and apply it to the heating process of a thin moving steel sheet…
Abstract
Purpose
The purpose of this paper is to examine a solution strategy for coupled nonlinear magnetic-thermal problems and apply it to the heating process of a thin moving steel sheet. Performing efficient numerical simulations of induction heating processes becomes ever more important because of faster production development cycles, where the quasi steady-state solution of the problem plays a pivotal role.
Design/methodology/approach
To avoid time-consuming transient simulations, the eddy current problem is transformed into frequency domain and a harmonic balancing scheme is used to take into account the nonlinear BH-curve. The thermal problem is solved in steady-state domain, which is carried out by including a convective term to model the stationary heat transport due to the sheet velocity.
Findings
The presented solution strategy is compared to a classical nonlinear transient reference solution of the eddy current problem and shows good convergence, even for a small number of considered harmonics.
Originality/value
Numerical simulations of induction heating processes are necessary to fully understand certain phenomena, e.g. local overheating of areas in thin structures. With the presented approach it is possible to perform large 3D simulations without excessive computational resources by exploiting certain properties of the multiharmonic solution of the eddy current problem. Together with the use of nonconforming interfaces, the overall computational complexity of the problem can be decreased significantly.
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Yangyiwei Yang, Patrick Kühn, Mozhdeh Fathidoost and Bai-Xiang Xu
Confronting the unveiled sophisticated structural and physical characteristics of permanent magnets, notably the samarium–cobalt (Sm-Co) alloy, This work aims to introduce a…
Abstract
Purpose
Confronting the unveiled sophisticated structural and physical characteristics of permanent magnets, notably the samarium–cobalt (Sm-Co) alloy, This work aims to introduce a simulation scheme that can link physics-based micromagnetics on the nanostructures and magnetostatic homogenization on the mesoscale polycrystalline structures.
Design/methodology/approach
The simulation scheme is arranged in a multiscale fashion. The magnetization behaviors on the nanostructures examined with various orientations are surrogated as the micromagnetic-informed hysterons. The hysteresis behavior of the mesoscale polycrystalline structures with micromagnetic-informed hysterons is then evaluated by computational magnetostatic homogenization.
Findings
The micromagnetic-informed hysterons can emulate the magnetization reversal of the parameterized Sm-Co nanostructures as the local hysteresis behavior on the mesostructures. The simulation results of the mesoscale polycrystal demonstrate that the demagnetization process starts from the grain with the largest orientation angle (a) and then propagates to the surrounding grains.
Research limitations/implications
The presented scheme depicts the demand for integrating data-driven methods, as the parameters of the surrogate hysteron intrinsically depend on the nanostructure and its orientation. Further hysteron parameters that help the surrogate hysteron emulate the micromagnetic-simulated magnetization reversal should be examined.
Originality/value
This work provides a novel multiscale scheme for simulating the polycrystalline permanent magnets’ hysteresis while recapitulating the nanoscale mechanisms, such as the nucleation of domains, and domain wall migration and pinning. This scheme can be further extended to simulate the part-level hysteresis considering the mesoscale features.
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In this paper we study a class of complexity measures, induced by a new data structure for representing k-valued functions (operations), called minor decision diagram. When…
Abstract
In this paper we study a class of complexity measures, induced by a new data structure for representing k-valued functions (operations), called minor decision diagram. When assigning values to some variables in a function the resulting functions are called subfunctions, and when identifying some variables the resulting functions are called minors. The sets of essential variables in subfunctions of
We examine the maximal separable subsets of variables and their conjugates, introduced in the paper, proving that each such set has at least one conjugate. The essential arity gap
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Abstract
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Xingwen Wu, Zhenxian Zhang, Wubin Cai, Ningrui Yang, Xuesong Jin, Ping Wang, Zefeng Wen, Maoru Chi, Shuling Liang and Yunhua Huang
This review aims to give a critical view of the wheel/rail high frequency vibration-induced vibration fatigue in railway bogie.
Abstract
Purpose
This review aims to give a critical view of the wheel/rail high frequency vibration-induced vibration fatigue in railway bogie.
Design/methodology/approach
Vibration fatigue of railway bogie arising from the wheel/rail high frequency vibration has become the main concern of railway operators. Previous reviews usually focused on the formation mechanism of wheel/rail high frequency vibration. This paper thus gives a critical review of the vibration fatigue of railway bogie owing to the short-pitch irregularities-induced high frequency vibration, including a brief introduction of short-pitch irregularities, associated high frequency vibration in railway bogie, typical vibration fatigue failure cases of railway bogie and methodologies used for the assessment of vibration fatigue and research gaps.
Findings
The results showed that the resulting excitation frequencies of short-pitch irregularity vary substantially due to different track types and formation mechanisms. The axle box-mounted components are much more vulnerable to vibration fatigue compared with other components. The wheel polygonal wear and rail corrugation-induced high frequency vibration is the main driving force of fatigue failure, and the fatigue crack usually initiates from the defect of the weld seam. Vibration spectrum for attachments of railway bogie defined in the standard underestimates the vibration level arising from the short-pitch irregularities. The current investigations on vibration fatigue mainly focus on the methods to improve the accuracy of fatigue damage assessment, and a systematical design method for vibration fatigue remains a huge gap to improve the survival probability when the rail vehicle is subjected to vibration fatigue.
Originality/value
The research can facilitate the development of a new methodology to improve the fatigue life of railway vehicles when subjected to wheel/rail high frequency vibration.
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