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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.

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.

Various simulations demonstrate the feasibility, efficiency and versatility of the new MSFEM.

The novel MSFEM solves true three-dimensional eddy current problems in laminated iron cores taking into account of the edge effect.

This paper aims to consider a multiscale electromagnetic wave problem for a housing with a ventilation grill. Using the standard finite element method to discretise the apertures leads to an unduly large number of unknowns. An efficient approach to simulate the multiple scales is introduced. The aim is to significantly reduce the computational costs.

A domain decomposition technique with upscaling is applied to cope with the different scales. The idea is to split the domain of computation into an exterior domain and multiple non-overlapping sub-domains. Each sub-domain represents a single aperture and uses the same finite element mesh. The identical mesh of the sub-domains is efficiently exploited by the hybrid discontinuous Galerkin method and a Schur complement which facilitates the transition from fine meshes in the sub-domains to a coarse mesh in the exterior domain. A coarse skeleton grid is used on the interface between the exterior domain and the individual sub-domains to avoid large dense blocks in the finite element discretisation matrix.

Applying a Schur complement to the identical discretisation of the sub-domains leads to a method that scales very well with respect to the number of apertures.

The error compared to the standard finite element method is negligible and the computational costs are significantly reduced.

This work introduces an efficient and accurate technique to solve the eddy current problem in laminated iron cores considering vector hysteresis.

The mixed multiscale finite element method based on the based on the T,Φ-Φ formulation, with the current vector potential T and the magnetic scalar potential Φ allows the laminated core to be modelled as a single homogeneous block. This means that the individual sheets do not have to be resolved, which saves a lot of computing time and reduces the demands on the computer system enormously.

As a representative numerical example, a single-phase transformer with 4, 20 and 184 sheets is simulated with great success. The eddy current losses of the simulation using the standard finite element method and the simulation using the mixed multiscale finite element method agree very well and the required simulation time is tremendously reduced.

The vector Preisach model is used to account for vector hysteresis and is integrated into the mixed multiscale finite element method for the first time.

Prior investigations concerning misalignment resulting from journal deformation typically relied on predefined misaligned angles. Nevertheless, scant attention has been devoted to the determination of these misaligned angles. Furthermore, existing studies commonly treat the journal as rigid under such circumstances. Therefore, the present study aims to introduce a framework for determining misaligned angles and to compare outcomes between rigid and flexible journal configurations.

The bearing forces are considered as an external load leading to journal deformation. This deformation is calculated using the finite element method. The pressure distribution producing the bearing force is solved using the finite difference method. The mesh grids in the finite element and finite difference methods are matched for coupling calculation. By iteration, the pressure distribution of the lubricant film at the equilibrium position is determined.

Results show that the deformation-induced misalignment has a significant influence on the performance of the bearing when the journal flexibility is taken into account. The parametric study reveals that the misalignment relies on system parameters such as bearing length-diameter ratio and static load.

The investigation of this work provides a quantification method of misalignment of hydrodynamic bearings considering the elastic deformation of the journal, which assists in the design of bearing in a rotor-bearing system.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-10-2023-0337/

This study aims to reduce the redundant weight of the anti-roll torsion bar brought by the traditional empirical design and improving its strength and stiffness.

Based on the finite element approach coupled with the improved beluga whale optimization (IBWO) algorithm, a collaborative optimization method is suggested to optimize the design of the anti-roll torsion bar structure and weight. The dimensions and material properties of the torsion bar were defined as random variables, and the torsion bar's mass and strength were investigated using finite elements. Then, chaotic mapping and differential evolution (DE) operators are introduced to improve the beluga whale optimization (BWO) algorithm and run case studies.

The findings demonstrate that the IBWO has superior solution set distribution uniformity, convergence speed, solution correctness and stability than the BWO. The IBWO algorithm is used to optimize the anti-roll torsion bar design. The error between the optimization and finite element simulation results was less than 1%. The weight of the optimized anti-roll torsion bar was lessened by 4%, the maximum stress was reduced by 35% and the stiffness was increased by 1.9%.

The study provides a methodological reference for the simulation optimization process of the lateral anti-roll torsion bar.

The purpose of this paper is to present the freely available finite element simulation software Pyrit.

In a first step, the design principles and the objective of the software project are defined. Then, the software’s structure is established: The software is organized in packages for which an overview is given. The structure is based on the typical steps of a simulation workflow, i.e., problem definition, problem-solving and post-processing. State-of-the-art software engineering principles are applied to ensure a high code quality at all times. Finally, the modeling and simulation workflow of Pyrit is demonstrated by three examples.

Pyrit is a field simulation software based on the finite element method written in Python to solve coupled systems of partial differential equations. It is designed as a modular software that is easily modifiable and extendable. The framework can, therefore, be adapted to various activities, i.e., research, education and industry collaboration.

The focus of Pyrit are static and quasistatic electromagnetic problems as well as (coupled) heat conduction problems. It allows for both time domain and frequency domain simulations.

In research, problem-specific modifications and direct access to the source code of simulation tools are essential. With Pyrit, the authors present a computationally efficient and platform-independent simulation software for various electromagnetic and thermal field problems.

This paper aims to analyze the stress and strain distribution on the track wheel web surface and study the optimal strain gauge location for force measurement system of the track wheel.

Finite element method was employed to analyze the stress and strain distribution on the track wheel web surface under varying wheel-rail forces. Locations with minimal coupling interference between vertical and lateral forces were identified as suitable for strain gauge installation.

The results show that due to the track wheel web’s unique curved shape and wheel-rail force loading mechanism, both tensile and compressive states exit on the surface of the web. When vertical force is applied, Mises stress and strain are relatively high near the inner radius of 710 mm and the outer radius of 1110 mm of the web. Under lateral force, high Mises stress and strain are observed near the radius of 670 mm on the inner and outer sides of the web. As the wheel-rail force application point shifts laterally toward the outer side, the Mises stress and strain near the inner radius of 710 mm of the web gradually decrease under vertical force while gradually increasing near the outer radius of 1110 mm of the web. Under lateral force, the Mises stress and strain on the surface of the web remain relatively unchanged regardless of the wheel-rail force application point. Based on the analysis of stress and strain on the surface of the web under different wheel-rail forces, the inner radius of 870 mm is recommended as the optimal mounting location of strain gauges for measuring vertical force, while the inner radius of 1143 mm is suitable for measuring lateral force.

The research findings provide valuable insights for determining optimal strain gauge locations and designing an effective track wheel force measurement system.

This paper focuses on the unconditionally optimal error estimates of a linearized second-order scheme for a nonlocal nonlinear parabolic problem. The first step of the scheme is based on Crank–Nicholson method while the second step is the second-order BDF method.

A rigorous error analysis is done, and optimal L² error estimates are derived using the error splitting technique. Some numerical simulations are presented to confirm the study’s theoretical analysis.

Optimal L² error estimates and energy norm.

The goal of this research article is to present and establish the unconditionally optimal error estimates of a linearized second-order BDF finite element scheme for the reaction-diffusion problem. An optimal error estimate for the proposed methods is derived by using the temporal-spatial error splitting techniques, which split the error between the exact solution and the numerical solution into two parts, that is, the temporal error and the spatial error. Since the spatial error is not dependent on the time step, the boundedness of the numerical solution in L∞-norm follows an inverse inequality immediately without any restriction on the grid mesh.

This paper aims to model a three-dimensional twisted geometry of a twisted pair studied in an electrostatic approximation using only two-dimensional (2D) finite elements.

The proposed method is based on the reformulation of the weak formulation of the electrostatics problem to deal with twisted geometries only in 2D.

The method is based on a change of coordinates and enables a faster computational time as well as a high accuracy.

The effectiveness of the adopted approach is demonstrated by studying different configurations related to the IEC 60851-5 standard defined for the measurement of the electrical properties of the insulation of the winding wires used in electrical machines.

Detection of hidden defects of aluminum alloy plate with damping coating is a challenging problem. At present, only a few non-destructive testing methods exist to address this engineering problem. Without the restriction of skin effect, remote field eddy current (RFEC) overcomes the interference caused by the damping coating. The RFEC, which has potential advantages for detecting the hidden defects of aluminum plate with damping coating, can penetrate the metal plate to detect buried depth defects. This study aims to test how thick the RFEC sensor can penetrate the metal plate to detect the buried defects.

The magnetic field distribution characteristics are analyzed, the magnetic field intensity distribution is calculated, and the structure and parameters of the coil, magnetic circuit and shielding damping are determined through the two- and three-dimensional finite element simulation methods. Optimal excitation frequency is obtained, and the distance between the excitation coil and detection coil is determined by analyzing the relationship between excitation frequency and remote field points.

Simulation and experimental results verify the feasibility of applying the RFEC detection technology in detecting the hidden defects of aluminum alloy plate with damping coating.

In this paper, the RFEC testing model of hidden defects in aluminum plate sample with damping coating is established by using the finite element method.