Matthias Carlstedt

Lorentz force eddy current testing: a novel NDE-technique

Purpose – The purpose of this paper is to present a novel electromagnetic non-destructive evaluation technique, so called Lorentz force eddy current testing (LET). This method can be applied for the detection and reconstruction of defects lying deep inside a non-magnetic conducting material. Design/methodology/approach – In this paper the technique is described in general as well as its experimental realization. Besides that, numerical simulations are performed and compared to experimental data. Using the output data of measurements and simulations, an inverse calculation is performed in order to reconstruct the geometry of a defect by means of sophisticated optimization algorithms. Findings – The results show that measurement data and numerical simulations are in a good agreement. The applied inverse calculation methods allow to reconstruct the dimensions of the defect in a suitable accuracy. Originality/value – LET overcomes the frequency dependent skin-depth of traditional eddy current testing due to t...

Optimal Magnet Design for Lorentz Force Eddy-Current Testing

We propose a procedure to determine optimal magnet systems in the framework of the nondestructive evaluation technique Lorentz force eddy-current testing (LET). The underlying optimization problem is clearly defined considering the problem specificity of nondestructive testing scenarios. The quantities involved are classified as design variables, and system and scaling parameters to provide a high level of generality. The objective function is defined as the absolute defect response signal (ADS) of the Lorentz force resulting from an inclusion inside the object under test. Associated constraints are defined according to the applied force sensor technology. A numerical procedure based on the finite-element method is proposed to evaluate the nonlinear objective and constraint functions, and the method of sequential quadratic programming is applied to determine unconstrained and constrained optimal magnet designs. Consequently, we propose a new magnet design based on the Halbach principle in combination with high saturation magnetization iron-cobalt alloys. The proposed magnet system outperforms currently available cylindrical magnets in terms of weight and performance. The corresponding defect response signal is increased up to 180% in the case of small defects located close to the surface of the specimen. The combination of active and passive magnetic materials provides an increase of the ADS by 15% compared with the magnet designs that are built solely from permanent magnet material. The proposed procedure provides a highly adaptive optimization strategy in the framework of LET and proposes new magnet systems with inherently improved characteristics.

Application of Lorentz force eddy current testing and eddy current testing on moving nonmagnetic conductors

Lorentz force eddy current testing is a novel nondestructive testing technique which can be applied preferably to the identification of internal defects in non-ferromagnetic moving conductors. This paper describes the comparison of this new technique with well-known eddy current testing. Measurements and numerical simulations have been done for both techniques for artificial subsurface defects in a test specimen made of Aluminum alloy moving with constant velocity.

Permanent Magnet Modeling for Lorentz Force Evaluation

Lorentz force evaluation (LFE) is a technique to reconstruct defects in electrically conductive materials. The accuracy of the forward and inverse solution highly depends on the applied model of the permanent magnet. The resolution of the technique relies upon the shape and size of the permanent magnet. Furthermore, the application of an existing forward solution requires an analytic integral of the magnetic flux density. Motivated by these aspects, we propose a magnetic dipoles model (MDM), in which the permanent magnet is substituted with an assembly of magnetic dipoles. This approach allows modeling of magnets of arbitrary shape by appropriate positioning of the dipoles, and the integral can be expressed by elementary mathematical functions. We apply the MDM to cuboidal-shaped and cylindrical-shaped magnets and evaluate the obtained magnetic flux density by comparing it to reference solutions. We consider distances of 2-6 mm to the permanent magnet. The representation of a cuboidal magnet with 832 dipoles yields a maximum error of 0.02% between the computed magnetic field of the MDM and the reference solution. Comparable accuracy for the cylindrical magnet is achieved with 1890 dipoles. In addition, we embed the MDM of the cuboidal magnet into an existing forward solution for LFE and find that the errors of the magnetic flux density are partly compensated by the forward calculations. We conclude that our modeling approach can be used to determine the most efficient MDMs for LFE.

Uncertainty Analysis in Lorentz Force Eddy Current Testing

The paper addresses the analysis of uncertainties in the framework of the nondestructive evaluation technique Lorentz force eddy current testing. A non-intrusive generalized polynomial chaos expansion is used in order to quantify the impact of multiple unknown input parameters. In this context, the statistics of the velocity and the conductivity of the specimen as well as the magnetic remanence and the lift-off distance of the permanent magnet are determined experimentally and modeled as β-distributed and uniform distributed random variables. The results are compared with Monte Carlo simulations and showed errors <;0.2%. Furthermore, the numerically predicted force profiles are validated with experiments. A sensitivity analysis by means of the Sobol decomposition revealed that the magnetic remanence and the lift-off distance contribute to more than 90% of the total variance of the resulting Lorentz force profile and should be considered first to improve reproducibility.

Lorentz Force Evaluation With Differential Evolution

In the framework of nondestructive testing and evaluation, Lorentz force evaluation (LFE) is a method for reconstructing defects in electrically conducting laminated composites. In this paper, we propose a new inverse calculation strategy for LFE based on a stochastic optimization, the differential evolution (DE) algorithm. We determined the optimal control parameters for the DE and assessed its performance based on simulated and measured data. The results show that the depth of the defect was estimated correctly for all of the data sets that we evaluated. The geometry was reconstructed with errors of less than 4% relative to the size of the defect. The proposed scheme was robust against noise and distortions in the data measurements. We conclude that the proposed reconstruction scheme is a promising method for solving the inverse problem in LFE.

Reverse engineering of ECT probes for nondestructive evaluation of moving conductors

Numerical modeling of commercial ECT equipment requires preparatory work in reverse engineering. The reconstruction of given ECT probes was performed in terms of (i) geometry, (ii) material properties and source parameters, (iii) impedance computation. High-resolution X-ray images were taken in order to build appropriate CAD models of given ECT probes. An optimization strategy was applied in order to estimate the permeability of the magnetic shield as well as the supply current by means of measurement data of the magnetic flux density. Subsequently, normalized impedance calculations were performed and compared to measurements in generic benchmark models containing artificial defects.

Current Density Reconstructions for Lorentz Force Evaluation

ABSTRACT The detection and reconstruction of fatigue fractures is of great interest in quality assurance. In the framework of nondestructive testing, Lorentz force evaluation (LFE) is an evaluation technique to estimate flaws in electrically conductive materials based on measured Lorentz forces. In the forward solution for LFE, a defect can be interpreted as a distributed current source. This has motivated the authors to propose current density reconstructions (CDRs) calculated with minimum norm estimates to estimate defect geometries. The L1 and L2 norms tend to produce a solution which is either very focused or very smeared. To balance these constraints, the general Lp norm with 1 ≤ p ≤ 2 was used and the inverse solutions compared. This approach was applied to measured data obtained from a laminated composite and simulated data from a monolithic material. The results show that the L1.5 norm provides the most accurate inverse solutions. The location and extent of the defect are determined with an error of 15 % relative to the size of the defect. The depth estimation has a deviation of 50 %. It can be concluded that CDRs are a powerful method to reconstruct and characterize defects in LFE.

Estimation of Lorentz Force From Dimensional Analysis: Similarity Solutions and Scaling Laws

In this paper, we consider the use of dimensional analysis for modeling electromagnetic levitation and braking problems, which are described by the Lorentz force law. Based on Maxwells equations, to illustrate the underlying field problem, we formulate a complete mathematical model of a simple academic example, where a permanent magnet is moving over an infinite plate at constant velocity. The step-by-step procedure employed for dimensional analysis is described in detail for the given problem. A dimensionless model with a reduced number of parameters is obtained, which highlights the dominant dependences, and it is invariant to the dimensional system employed. Using the dimensionless model, a concise parametric study is conducted to illustrate the advantages of the dimensionless representation for displaying complex data in an efficient manner. We provide an exhaustive study of the dependences of the Lorentz force on the dimensionless parameters to complete the analysis, and we give results for a generalized representation of the problem. Finally, scaling laws are derived and illustrated based on practical examples.

Oscillatory Motion of Permanent Magnets Above a Conducting Slab

This paper provides the 3-D time-dependent analytical solution of the electromagnetic fields and forces emerging if a coil or a permanent magnet moves with a sinusoidal velocity profile relative to a conducting slab of finite thickness. The results can be readily used in application scenarios related to electromagnetic damping, eddy current braking, energy harvesting, or nondestructive testing in order to efficiently analyze diffusion and advection processes in case of harmonic motion. This paper is performed for rectangular and circular coils as well as for cuboidal and cylindrical permanent magnets. The back reaction of the conductor and therewith associated inductive effects are considered. The solutions of the governing equations and the integral expressions for the time-dependent drag and lift force are provided. The analytical results are verified by a comparison with numerical simulations obtained by the finite-element method. The relative difference between the analytically and numerically evaluated force profiles was <;0.1%. Exemplary calculations show that the waveforms of both force components strongly depend on the level of constant nominal velocity