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Determination of the thickness of copper coatings on steel by measuring the impedance of a thin elliptic coil
Linköping University, Department of Physics, Chemistry and Biology. Linköping University, The Institute of Technology.
2002 (English)In: Measurement science and technology, ISSN 0957-0233, E-ISSN 1361-6501, Vol. 13, no 4, 510-519 p.Article in journal (Refereed) Published
Abstract [en]

When a thin elliptically shaped coil is placed above a flat plate with a coat of metal, the magnetic fields in the vicinity of the coil is altered by eddy currents in the plate and the coat. The thickness of the coat influences the magnetic field and can be determined by measuring the coil impedance. An electromagnetic model utilizing an elliptic cylinder coordinate system accounting for the coil impedance with different values on the numerical eccentricity and the coating thickness is described. The model is based on a potential formulation of the problem from which the magnetic vector potential and hence the impedance is evaluated. The derivation utilizes a proper choice of the transversal field, giving a scalar Helmholtz equation in which the solution to the boundary value problem is separated. The resulting integral equation is expressed in closed form in terms of Mathieu functions. Numerical calculations and experimental measurements show how the model can be used to model a steel surface with a coat of copper to find expected impedance as function of the coating thickness.

Place, publisher, year, edition, pages
2002. Vol. 13, no 4, 510-519 p.
Keyword [en]
elliptic coil, thickness measuring, eddy current testing, coil impedance
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-48917DOI: 10.1088/0957-0233/13/4/313OAI: oai:DiVA.org:liu-48917DiVA: diva2:269813
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-12
In thesis
1. A measurement approach to determination of coating thickness with eddy currents and to a capacitive person detector for robot safety
Open this publication in new window or tab >>A measurement approach to determination of coating thickness with eddy currents and to a capacitive person detector for robot safety
2004 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The research presented in this thesis is about coating thickness measurements using eddy currents, and a capacitive detector for detecting humans, for safety in industry.

A method for determination of coating thickness of a copper-plated steel wire by measurement of the internal wire impedance, when this is forced by a constant, sinusoidal current, is presented. An electromagnetic model describes how the internal impedance depends on the thickness of the coat, taking into account non-linear effects in the steel. Numerical calculations based on the model are compared with results from measurements.

Determination of coating thickness on plane samples using an elliptically shaped coil is the objective of two investigations. The first is about determination of thickness of silver coatings on a flat brass substrate by measuring the impedance of a thin elliptic test coil. An electromagnetic model based on a dyadic Green function formulation of the problem is described. A Green function expansion in elliptic vector wave functions is derived, from which the electric field and hence the impedance is evaluated by scattering superposition. The model uses an elliptical co-ordinate system and gives an expression of the coil impedance in closed form. Results from calculations using this model and experimental measurements are presented for different values of the eccentricity of the coil and the thickness of the coating for some chosen frequencies. The second investigation also deals with determination of coating thickness with a thin elliptic coil, but is applied for a flat steel substrate, where the coating was made of copper. Thedescribed model, which allows the sample also to be permeable, is in this case based on a second-order potential formulation from which the magnetic vector potential and hence the coil impedance is evaluated. The derivation utilizes a proper choice of transversal field, giving a scalar Helmholtz equation from which the solution to the boundary value problem is separated. The resulting integral equation is expressed in closed form. Performed calculations and experimentsshow how the model can be used to model a steel surface with a coating of copper to find the impedance as a function of the coating thickness and the eccentricity.

Finally capacitive detection of humans for safeguarding in industry has been studied. The work describes how the electric and magnetic fields change when a human body, approximated by a dielectric prolate spheroid, is placed in an originally uniform homogeneous electric field. The evaluation of the fields utilizes a potential solution, arising from the Laplace equation, giving the fields in terms of the Legendre polynomials, from which the reactive power impinging into the detector volume is calculated. Numerical calculations and experiments have beenperformed both in a full-scale prototype for detection of humans and in a small-scale model with paraffin and aluminium bodies.

Place, publisher, year, edition, pages
Linköping: Linköpings universitet, 2004. 32 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 843
National Category
Natural Sciences
Identifiers
urn:nbn:se:liu:diva-40207 (URN)52610 (Local ID)91-7373-734-8 (ISBN)52610 (Archive number)52610 (OAI)
Public defence
2004-01-16, Sal Planck, Fysikhuset, Linköpings Universitet, Linköping, 10:15 (Swedish)
Opponent
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2013-01-11

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Båvall, Lennart

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