An efficient reformulation of a multiscale method for the eddy current problem

2017 ◽  
Vol 36 (5) ◽  
pp. 1421-1429
Author(s):  
Markus Schöbinger ◽  
Karl Hollaus ◽  
Joachim Schöberl
Keyword(s):  
Eddy Current ◽  
Design Methodology ◽  
Degrees Of Freedom ◽  
Current Problem ◽  
Multiscale Method ◽  
Content Type ◽  
Eddy Current Problem ◽  
Laminate Thickness ◽  
The Cost ◽  
Laminated Material

Purpose This paper aims to improve the efficiency of a numerical method to treat the eddy current problem on a laminated material, where using a mesh that resolves each individual laminate would be too computationally expensive. Design/methodology/approach The domain is modeled using a coarse mesh that treats the laminated material as a bulk with averaged properties. The fine-structured behavior is recovered by introducing micro-shape functions in the ansatz space. One such method is analyzed to find further model restrictions. Findings By using a special reformulation, it is possible to eliminate the additional degrees of freedom introduced by the multiscale ansatz at the cost of an additional modeling error that decreases with the laminate thickness. Originality/value The paper gives a computationally more efficient approximate variant to a known multiscale method.

scholarly journals A mixed multiscale FEM for the eddy current problem with T,Φ-Φ and vector hysteresis

2022 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Valentin Hanser ◽  
Markus Schöbinger ◽  
Karl Hollaus
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Eddy Current ◽  
Current Problem ◽  
Great Success ◽  
Content Type ◽  
Multiscale Finite Element Method ◽  
Multiscale Finite Element ◽  
Eddy Current Problem ◽  
Element Method

Purpose This work introduces an efficient and accurate technique to solve the eddy current problem in laminated iron cores considering vector hysteresis. Design/methodology/approach 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. Findings 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. Originality/value 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.

scholarly journals Simulating induction heating processes using harmonic balance FEM

2019 ◽  
Vol 38 (5) ◽  
pp. 1562-1574
Author(s):  
Klaus Roppert ◽  
Florian Toth ◽  
Manfred Kaltenbacher
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Induction Heating ◽  
Eddy Current ◽  
Current Problem ◽  
Heating Process ◽  
Solution Strategy ◽  
Content Type ◽  
Good Convergence ◽  
Eddy Current Problem

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.

Locating complex eigenvalues for analytical eddy-current models used to detect flaws

2019 ◽  
Vol 38 (6) ◽  
pp. 1800-1809
Author(s):  
Grzegorz Tytko ◽  
Łukasz Dawidowski
Keyword(s):  
Eddy Current ◽  
Design Methodology ◽  
Complex Function ◽  
Precise Determination ◽  
Argument Principle ◽  
Content Type ◽  
Conductive Material ◽  
Complex Roots ◽  
Complex Eigenvalues

Purpose Discrete eigenvalues occur in eddy current problems in which the solution domain was truncated on its edge. In case of conductive material with a hole, the eigenvalues are complex numbers. Their computation consists of finding complex roots of a complex function that satisfies the electromagnetic interface conditions. The purpose of this paper is to present a method of computing complex eigenvalues that are roots of such a function. Design/methodology/approach The proposed approach involves precise determination of regions in which the roots are found and applying sets of initial points, as well as the Cauchy argument principle to calculate them. Findings The elaborated algorithm was implemented in Matlab and the obtained results were verified using Newton’s method and the fsolve procedure. Both in the case of magnetic and nonmagnetic materials, such a solution was the only one that did not skip any of the eigenvalues, obtaining the results in the shortest time. Originality/value The paper presents a new effective method of locating complex eigenvalues for analytical solutions of eddy current problems containing a conductive material with a hole.

Autopilot design for an aircraft by using Luenberger observer design

2018 ◽  
Vol 90 (5) ◽  
pp. 858-868 ◽  
Author(s):  
Muhammad Taimoor ◽  
Li Aijun ◽  
Rooh ul Amin ◽  
Hongshi Lu
Keyword(s):  
Design Methodology ◽  
Research Work ◽  
Linear Quadratic Regulator ◽  
Observer Design ◽  
Linear Quadratic ◽  
Content Type ◽  
Luenberger Observer ◽  
Level Flight ◽  
Aerial Vehicle ◽  
The Cost

Purpose The purpose of this paper is to design linear quadratic regulator (LQR) based Luenberger observer for the estimation of unknown states of aircraft. Design/methodology/approach In this paper, the LQR-based Luenberger observer is deliberated for autonomous level flight of unmanned aerial vehicle (UAV) which has been attained productively. Various modes like phugoid and roll modes are exploited for controlling the rates of UAV. The Luenberger observer is exploited for estimation of the mysterious states of the system. The rates of roll, yaw and pitch are used as an input to the observer, while the remaining states such as velocities and angles have been anticipated. The main advantage of using Luenberger observer was to reduce the cost of the system which has been achieved lucratively. The Luenberger observer proposes sturdiness at the rate of completion to conquest over the turmoil and insecurities to overcome the privileged recital. The FlightGear simulator is exploited for the endorsement of the recital of the Luenberger observer-based autopilot. The level flight has been subjugated lucratively and has been legitimated by exploiting the FlightGear simulator. The authenticated and the validated results are offered in this paper. Microsoft Visual Studio has been engaged as a medium between the MATLAB and FlightGear Simulator. Findings The suggested observer based on LQR ensures the lucrative approximation of the unknown states of the system as well as the successful level flight of the system. The Luenberger observer is used for approximation of states while LQR is used as controller. Originality/value In this research work, not only the estimation of unknown states of both longitudinal and lateral model is made but also the level flight is achieved by using those estimated states and the autopilot is validated by using the FlightGear, while in most of the research work only the estimation is made of only longitudinal or lateral model.

Factors explaining a cost-based pricing essence

2019 ◽  
Vol 34 (8) ◽  
pp. 1850-1865
Author(s):  
Juliana Ventura Amaral ◽  
Reinaldo Guerreiro
Keyword(s):  
Design Methodology ◽  
Empirical Studies ◽  
Pricing Strategy ◽  
Company Size ◽  
Price Setting ◽  
Marketing Theory ◽  
Content Type ◽  
Industrial Companies ◽  
Five Factors ◽  
The Cost

Purpose Empirical studies have found that cost-based pricing remains dominant in pricing practice and suggest that practice conflicts with marketing theory, which recommends value-based prices. However, empirical studies have yet to examine whether cost-plus formulas represent the pricing approach or essence. Design/methodology/approach This study aims to address the factors that explain price setting whereby the cost-plus formula is not just the pricing approach but also the pricing essence. This examination is grounded in a survey conducted on 380 Brazilian industrial companies. Findings The results show that, for price-makers, the cost-based pricing essence is positively associated with four factors (two obstacles to deploying value-based pricing, company size and differentiation), but it is negatively related to one factor (premium pricing strategy). For price-takers, the cost-based pricing essence is positively associated with four factors (two obstacles to deploying value-based pricing, coercive isomorphism and use of full costs), but it is negatively related to five factors (one obstacle to deploying value-based pricing, company size, competitors’ ability to copy, normative isomorphism and experience). Originality/value The key contribution of this paper is demonstrating that cost-plus formulas do not go against the incorporation of competitors and value information. This study reveals that it is possible to set prices based on either value or competitors’ prices while simultaneously preserving the simplicity of the cost-plus formulas. Via the margin, firms may connect costs to information about competition and value. The authors also demonstrate the drawbacks of not segregating companies into price-makers and price-takers and an excessive focus on the pricing approach at the expense of pricing essence.

Stigmatized products: how conflicting laws can influence decisions to proceed

2020 ◽  
Vol 42 (1) ◽  
pp. 41-49
Author(s):  
Stephanie Geiger-Oneto ◽  
Betsy D. Gelb ◽  
Travis Simkins
Keyword(s):  
Design Methodology ◽  
State Legislatures ◽  
Strategic Decisions ◽  
Content Type ◽  
State Laws ◽  
Product Categories ◽  
Plastic Bags ◽  
Single Use ◽  
The Cost ◽  
Different Levels

Purpose The purpose of this paper is to offers the authors’ perspective on a problem rarely considered by those making strategic decisions: conflicting laws at different levels of jurisdiction, specifically those related to stigmatized products. Design/methodology/approach The authors use as examples of product categories from marijuana to single-use plastic bags, describing the conflicting laws that add to costs for marketers and consumers. Findings The authors find that conflicting laws add to the uncertainty, legal expenses, and therefore, the cost of marketing a stigmatized product, whether stigmatized because of its impact on the environment, on health or on moral grounds. Research limitations/implications The examples are not exhaustive, but their implications are significant: that as state legislatures are preempting local bans, Congress may preempt state laws. Originality/value This paper adds one more complexity to decision-making in the area of products to offer and/or merger/acquisition decisions that may bring company products that face conflicting laws.

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