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The purpose of this paper is to obtain a fully analytical model of an eddy current coupler and to use it in a multi‐objective optimisation algorithm.

Analytical expressions of device performances are adopted in the objective function and are obtained from a closed solution of the field problem. The optimisation has been carried out by considering both the torque and the momentum of inertia of the object. Two different structures have been considered.

A fully analytical expression of the torque has been obtained for two different geometrical configurations. The optimisation procedure has been used to compare these structures and it is possible to observe that the DSPM performances are better than the SSPM ones.

To obtain a closed form of the torque function, the non‐linearities of the iron have been neglected. Nevertheless, in the optimisation procedure has been limited the magnetic flux density in the iron core to a feasible value in the linear part of the ferromagnetic characteristic. The thermal effects have been neglected.

In the industry, eddy current couplers can be used as transmission, dampers and brakes. The use of objective functions (OFs) in a closed formulation allows to perform a light optimisation from the point of view of the time computation and to drastically increase the development efficiency.

In this paper, a model for computing the electromagnetic behaviour of eddy current couplers is presented. The optimisation of both the torque and the inertia momentum allows to obtain good static and dynamic performances.

The main aim of this paper is to explain how numerical magnetic field analysis can be adopted for the simulation of the effects generated when a rope fault occurs. In particular, some important aspects are examined regarding the magnetic flaw generated by internal and external rope faults and the capability of 2D and 3D magnetic field solutions to detect the magnetic flaws.

After a first explanation of the non‐destructive approach from the point of view of the many different methods that can be used to perform a test, an introduction about magnetic systems is provided. Then a 3D magnetic simulation, based on finite integrate technique, of the system is performed and the results compared with those obtained by a simpler 2D magnetic finite element analysis. In the 3D simulation real local damage to the rope is considered and the leakage fluxes around it plotted. A parametric simulation was performed by considering variations of the main geometrical parameters that in a real test can affect the results, such as the airgap between the rope and the measuring point (the position of the field sensors) and the radial position of the sensor itself. Finally, experimental results on the real prototype on many different commercial ropes are provided. In this last section an original method to evaluate the signal to noise ratio of the device is presented.

At first, a really good correspondence between 2D and 3D numerical results was observed. Then it was shown that the difference among the sensing capabilities of field probes placed around the rope is reduced when the position of the damage is higher than 90° in respect of the sensor itself. Moreover, when the angular distance between a sensor and a surface damage is higher than 90°, the damage signal provided by the sensor does not practically change.

Although the development method is always the same, the presented results are valid only for the configuration considered here. The experimental results of the signal to noise ratio are reported only for a reduced number of ropes.

The design procedure can be adopted to develop real devices and to identify the best position of the field sensing system. In particular, the paper shows the difference between radial and axial components of the leakage fluxes around the damage and their variation when the defect moves along the device.

The paper shows a methodology based on 2D and 3D numerical magnetic field analysis for the design of a non‐destructive device for metallic ropes with particular attention being given to the influence of field sensor and damage positions.

This paper aims to develop a new 3D analytical model in cylindrical coordinates to study radial flux eddy current couplers (RFECC) while considering the magnetic edge and 3D curvature effects, and the field reaction due to the induced currents.

The analytical model is developed by combining two formulations. A magnetic scalar potential formulation in the air and the magnets regions and a current density formulation in the conductive region. The magnetic field and eddy currents expressions are obtained by solving the 3D Maxwell equations in 3D cylindrical coordinates with the variable separation method. The torque expression is derived from the field solution using the Maxwell stress tensor. In addition to 3D magnetic edge effects, the proposed model takes into account the reaction field effect due to the induced currents in the conducting part. To show the accuracy of the developed 3D analytical model, its results are compared to those from the 3D finite element simulation.

The obtained results prove the accuracy of the new developed 3D analytical model. The comparison of the 3D analytical model with the 2D simulation proves the strong magnetic edge effects impact (in the axial direction) in these devices which must be considered in the modelling. The new analytical model allows the magnetic edge effects consideration without any correction factor and also presents a good compromise between precision and computation time.

The proposed 3D analytical model presents a considerably reduced computation time compared to 3D finite element simulation which makes it efficient as an accurate design and optimization tool for radial flux eddy current devices.

A new analytical model in 3D cylindrical coordinates has been developed to find the electromagnetic torque in radial flux eddy current couplers. This model considers the magnetic edge effects, the 3D curvature effects and the field reaction (without correction factors) while improving the computation time.

This paper aims to derive a simple and effective but still a reasonably accurate model for electromagnetic problems with hysteretic magnetic properties and/or induced currents in heterogeneous regions in 2D, meant particularly for non‐destructive testing (NDT) of steel cables by eddy‐currents.

It is assumed that the diffusion of electromagnetic fields in a heterogeneous cable, which consists of many strands, can be described by the Maxwell equations with periodically oscillating coefficients. A computationally efficient model can then be derived. The idea behind this is to replace the heterogeneous material in the cross‐section by a fictitious homogeneous one, whose behaviour at the macroscopic level is a good approximation of the one of the composite material. Such a homogenized model is obtained by employing the two‐scale convergence.

The model is validated based on experimental electromagnetic data from a steel cable (measured magnetic hysteresis loops) to show that the model is applicable for NDT of cables. The model is useful for studying NDT of cables, both for excitation at low frequency (where changes in magnetic properties are investigated) and at higher frequency (eddy current testing). It is valid for a wide range of amplitudes and frequencies.

From the mathematical point of view the model incorporated a non‐local boundary condition that has to be included in the analysis. From the engineering point of view, by solving an inverse problem based on this model and on measured hysteresis loops at several frequencies, a broader range of defects in the cable can be detected.

The purpose of this paper is to develop an effective, yet simple analytical framework for optimization of permanent-magnet synchronous machines. Also, single/multi-objective optimizations are performed for a case-study machine with surface-mounted permanent magnets.

First, an accurate magnetic equivalent circuit is developed which takes all the material such as iron saturation and PM parameters into account. Then, through a Fourier analysis, it is combined with the d-q model of PM synchronous machines to achieve an optimization framework including the developed torque, back-EMF and a number of design considerations. Finally, a genetic algorithm (GA) is employed in the single/multi-objective design optimizations, which offers several design characteristics upon different desired outcomes.

An analytical design framework for the optimization of permanent-magnet synchronous machines is developed in this paper that can effectively account for all material properties such as iron saturation and PM characteristics, and take into account the design considerations, all of which are shown as superiorities of the proposed approach over the existing method. In addition, the proposed framework is relatively simpler in terms of implementing. The model is verified by employing finite element method. Moreover, sensitivity analysis is carried out to investigate the influence of the design parameters on the machine performance, which provides valuable information for the designer of such devices. Finally, a GA is utilized to perform single/multi-objective optimization schemes whose objectives are minimizing the torque ripples, back-EMF total harmonic distortion and PM volume.

The proposed framework is new approach that could be employed in the design optimization of PM synchronous machines. Contrary to existing method, it is simpler and more effective in taking the material properties such as iron saturation and PM characteristics into account.

The purpose of this paper is to develop a new and fast three-dimensional (3D) analytical model to study a synchronous axial magnetic coupling with rectangular shaped magnets. This model takes into account edge and curvature 3D effects.

This paper firstly introduces a 3D analytical model for an axial coupler with sector shaped permanent magnet (PM) based on magnetic scalar potential formulation in cylindrical coordinates. The magnetic field in PM, air gap and iron disks is computed by solving Laplace’s and Poisson’s partial differential equation. This solution is then used to compute the field in rectangular shaped magnets. To do so, the adopted approach consists to divide the rectangular magnet into sector radial slices each of which the 3D model allows the determination of the magnetic field distribution. The results obtained by the proposed 3D analytical model are validated through 3D finite element computations. Furthermore, a prototype axial magnetic coupler has been constructed so air gap flux density and static torque measurements are compared to the analytical predictions.

The results obtained by the analytical model show the effectiveness of the proposed geometry transformation approach. The developed model takes into account all the 3D effects without needing any correction factor.

The developed method provides an efficient and rapid tool for evaluating the influence of geometric and physical parameters of a synchronous magnetic coupling as part of a design optimization process.

The developed method provides an efficient and rapid tool for evaluating the influence of geometric and physical parameters of a synchronous magnetic coupling as part of a design optimization process.

A new and fast 3D analytical model, to improve the computation of the electromagnetic torque developed by a synchronous magnetic coupler with rectangular shaped magnets, has been developed. The proposed approach is really effective as it leads to consistent results when compared to 3D finite element method ones without any need for correction factor.

The purpose of this paper was to create conditions for the correct decision concerning an exchange of the used rope for a new one. A cognitive goal was to indicate the causes of its wear and determining its mechanism reliability and durability.

The magnetic, organoleptic and strength standard tests of lifting triangle-strand ropes of a mining hoist were carried out. This way the current state of the tested rope was defined.

On the basis of an analysis of the results of the performed tests: magnetic, organoleptic and fatigue tests, it can be said that the magnetic one is accurate enough only to indicate the place of the rope’s biggest weakening, though the degree of weakening is not defined precisely – with significant excess. The accurate rope’s destruction degree is indicated by the strength tests.

The results of described investigations can improve safety of the mining rope mechanisms operation, even for an increased resource.

The elementary wear processes, which are the basic reason for the destruction of the rope, are indicated. Rope destruction is caused mainly by tribological factors: abrasion, corrosion and fatigue wear. Magnetic tests are accurate enough only to indicate the place of the rope’s biggest weakening (qualitative index). Most precisely, the rope’s destruction degree (quantitative index) can be found by the strength tests.