Reinhard Schmidt

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.

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.

Lorentz force evaluation with an extended area approach

A goal function scan based on an extended area approach is applied to determine size and depth of a defect in Lorentz force evaluation (LFE). Four datasets of a laminated aluminium specimen with a cylindrical defect at depths of 2, 4, 8 and 14 mm are simulated with the finite element method. LFE yields the correct defect sizes and depths for all four defects with a root mean square error of 0.95, 1.21, 1.57 and 4.41 %, respectively.