Steel Laminations Research Articles

Iron loss calculation considering temperature influence in non‐oriented steel laminations

In this study, the temperature influence on iron loss of non-oriented steel laminations is investigated. The iron loss variation under different flux densities, frequencies and temperatures is systematically measured and analysed by testing two typical non-oriented steel laminations, V300-35 A and V470-50 A. The iron loss variation with temperature is almost linear in the typical operating temperature range of electrical machines. Furthermore, the varying rate of iron loss with temperature varies with flux density and frequency. A coefficient which can fully consider the temperature influence is introduced to the existing iron loss model to improve the iron loss prediction accuracy. The predicted and measured results show that the temperature influence on the iron loss can be effectively considered by utilising the improved model, i.e. the prediction accuracy of the improved iron loss model remains constant, even when the temperature varies significantly. A potential simplification of this improved model is also discussed in this study.

Effects of different cutting methods for electrical steel sheets on performance of induction motors

In this study, by cutting electrical steel stator laminations, one of the most important components of electrical machines by different cutting methods, the effects of these cutting methods on motor efficiency are investigated. As cutting methods, wire electrical discharge machining, punching, laser and abrasive water jet methods are used. Burr formation at the cutting edge leads to short circuits during the steel packaging and causes magnetic losses in steel packages to increase. In addition, depending on the cutting methods, electrical steel lamination insulation layer is damaged as a result of residual and thermal stress formations. These negative conditions cause iron, friction and windage, stator, rotor and additional load losses occurred in the engine to decrease. In order to minimize these cases, electrical steel stator laminations are cut with the cutting parameters determined as a result of pre-cut tests and 5.5-kW induction motors are manufactured. These manufactured motors, according to IEC 60034-2-1-1B method, are subjected to no-load performance tests in addition to six different loading ratios of 25%–50%–75%–100%–115%–125% and constant 50 Hz frequency. As a result of the test measurements, losses occurred in electrical steels cut with abrasive water jet are found to be higher than the other cutting methods. In addition, in terms of the motor performance, the best results are obtained with wire electrical discharge machining cutting method.

Influence of Hole Size and Cutting Method on Localised Flux Density Distribution Around a Hole in Non-oriented Electrical Steels

In the manufacturing of electrical machine cores, there exist various cutting processes for electrical steel laminations such as mechanical, laser, and abrasive waterjet. The microstructure of the material changes near the edge affecting the magnetic domain structure and domain wall motion during the magnetization process. Variation of localised flux density distribution due to cutting method and hole size was investigated using the search coils located at 0∘, 25∘, 45∘, and 65∘ angles corresponding to the centre of holes with diameters 10 and 20 mm in non-oriented electrical steel sheet, which was namely N530. The localised flux density was measured over the peak flux density ranges 0.1–0.5 T at 50–400 Hz. The localised linear flux density concentrated on around both holes was obtained with increasing frequency. Also, cutting method was significant to deteriorate magnetic properties at the small cross sectional areas under the search coils located. The smaller hole has less to effect on the flux orientation around than the larger hole, due to their magnetostatic energy.

Scaling of Pseudo Direct Drives for Wind Turbine Application

An analytical model for the prediction of the magnetic field distribution in the air gaps and permanent magnet (PM) regions of a pseudo direct drive (PDD) is presented in scale-invariant form for magnetizations only dependent on the circumferential coordinate. The scale-invariance of the model is then employed to discuss the scaling laws of the PDD and investigate the effects of scaling on the efficiency and the mass of the various active components, i.e., copper, PM, and lamination materials for large wind turbines with powers between 5 and 20 MW. It is shown that, with the exception of the copper winding, the masses per megawatt of the steel laminations and the PMs are increased when the power rating of the wind turbine is increased.

Rotational Core Loss of Silicon Steel Laminations Based on Three-Dimensional Magnetic Properties Measurement

Magnetic properties of silicon steel laminations are important features in power transformer and electrical machine design and manufacture. Conventional testing methods such as Epstein Frame and Single Sheet Tester may only consider one direction or one sheet, which may deviate from the real application, particularly in core loss calculation. A 3-D magnetic properties' testing method is proposed in this paper. By using the designed special surface B-H sensing coils, the dynamic magnetic hysteresis properties of a laminated non-grain-oriented silicon steel sample are accurately measured. The relationship between B and H in alternating, 2-D rotational, and 3-D spherical rotational excitations, from 50 to 200 Hz, is studied and analyzed. In order to control the B waveform better, the harmonics of B x and B y signals are analyzed at 50 Hz. The alternating core losses in the rolling, transverse, and laminated directions and the rotational core losses in the xoy plane of this sample at 50, 100, and 200 Hz are calculated and analyzed. Moreover, the core losses in the three directions are well predicted by means of total core loss separation theory.

Calibration of the Tangential Coil Sensor for the Measurement of Core Losses in Electrical Machine Laminations

The measurement of core losses in electrical steel laminations is considered an essential step in the machine design process. Accordingly, the calibration of the tangential field sensor for measurements of magnetic field strength H is of importance in core loss measurements for estimation of electrical machine efficiency. Due to the stray field between the lamination surface and the tangential coil, a concern is raised regarding the certainty of the measured field. This paper presents a reliable technical approach to calibrate the tangential field sensor used in the investigation of core losses in electrical machine laminations, which compensates for the drop in the actual field value. The proposed approach is based on developing a magnetizing circuit, which consists of two test laminations. An array of Hall Effect sensors is used in this study as a reference for the tangential field. The calibration results show that the magnetic field strength measured at the specimen surface by the tangential coil is scaled down by 4.57% of the actual field. The results are verified experimentally and validated by finite-element simulations. Based on the obtained results, a correction factor is applied on pulsating and rotational core losses to attain more accurate data.

Effect of Shear Cutting on Microstructure and Magnetic Properties of Non-Oriented Electrical Steel

In manufacturing electrical machine cores, the electrical steel laminations are often mechanically cut, leading to residual stress and a deterioration in magnetic properties. Several cutting techniques are used in the industry, such as shear cutting, punching, and laser cutting. The influence of shear cutting on the steel microstructure and magnetic properties was investigated in this paper. A single sheet tester was used for the measurements of two different grades of non-oriented electrical steel at different induction levels (0.1–1.5 T) and a wide range frequency (3 Hz–1 kHz). A scanning electron microscope was used for the characterization of the microstructure (grain size) at the cutting edges. The mechanical properties near the edge of the lamination were measured using nanoindentation. An increase in magnetic loss due to cutting was observed to be $\sim 20$ % for B35AV1900 and $\sim 9$ % for 35WW300, corresponding to a damaged area extending up to a distance of $\sim 170$ and $\sim 140~\mu \text{m}$ , from the cut edge, respectively.

Power Loss Models in Punched Non-Oriented Electrical Steel Rings

The stresses and strains generated during punching of electrical steel laminations degenerate the magnetic properties in the region near the cut edge. The existing work has tended to focus on strips, with estimates of the damaged width ranging from less than 1 up to 10 mm. In this paper, ring samples, which are more representative of motor laminations, are considered. Increasing the diameter of the samples and, therefore, increasing the proportion damaged by the punching allowed the creation of mathematical models to describe and analyze the power loss and estimate the extent of the damaged region. Five samples each measuring five laminates high with a constant outer diameter of 200 mm and various inner diameters (150, 160, 170, 180, and 190 mm) were stamped from coils of M250–35A and M330–35A of a non-oriented electrical steel. A simple model was initially proposed, where power loss is proportional to the ratio of the undamaged to the total width and the square of the flux density passing through that region. An average width for the damaged region was calculated at 0.31 mm for the two materials.

A new approach to the critical induction in transformer cores

The most critical areas in power transformers are their corner joints where the magnetic flux distribution presents a very high heterogeneity. This heterogeneity results from several parameters such as the geometry of the magnetic core, the anisotropy level of the electrical steel laminations and a critical induction. This paper is focused on the magnetic steel grades influence on the critical induction, adding a new parameter to those classically considered, such as the number of steps in a multiple step lap stack. Due to the difficulty to perform local measurements inside a real transformer corner, the study is performed both experimentally and by Finite Element analyses on a simplified magnetic core structure. The paper highlights that, in a corner of a core, it exists a critical induction level which depends on the magnetic steel grades and that, in a lamination, the magnetic flux density value along the Transverse Direction can be of the same order that it has along the Rolling Direction.

Iron Loss Separation in High Frequency Using Numerical Techniques

This paper proposes a tractable and robust numerical method to predict iron losses in electrical steel laminations that are subjected to high-frequency excitations. To achieve this goal, Preisach modeling and the finite-difference method are first employed to simulate the hysteresis loss and eddy current loss, respectively. With this proposed algorithm, a better approximation of the excess loss and its optimal parameter identification is obtained. The proposed algorithm, when compared with conventional engineering models, reduces the errors between the estimated values and the measured values with tolerable computational burden.

Mathematical modeling and computations for electromagnetic problems

Three-dimensional eddy current problems are widely used in the iron loss computations and the magnetic flux simulation of large power transformers. GO silicon steel laminations in large transformers have multiple scales and the ratio of the largest scale to the smallest scale can be up to 10 6 . Direct solution of threedimensional nonlinear Maxwells equations is very challenging and unrealistic for large electromagnetic devices. Based on the magnetic vector potential and the magnetic field respectively, we propose two macro-scale models for the quasi-static Maxwells equations. We establish the wellposedness of the homogenized model, and prove that the micro-scale solutions converge to the solutions of the macro-scale models weakly in H ( curl ; Ω) and strongly in L 2 (Ω) as the thickness of lamination tends to zero. We also propose a new eddy current model for the nonlinear Maxwells equations with laminated conductors. The new model omits coating films and thus reduces the scale ratio by 3 orders of magnitude. We establish the well-posedness of the new model and prove the convergence of the solution of the original problem to the solution of the new model as the thickness of coating films tends to zero. Both the macro-scale model and the new model are validated by finite element computations of an engineering benchmark problem—TEAM Workshop Problem 21 c -M1.

In-situ visualization of stress-dependent bulk magnetic domain formation by neutron grating interferometry

The performance and degree of efficiency of industrial transformers are directly influenced by the magnetic properties of high-permeability steel laminations (HPSLs). Industrial transformer cores are built of stacks of single HPSLs. While the insulating coating on each HPSL reduces eddy-current losses in the transformer core, the coating also induces favorable inter-granular tensile stresses that significantly influence the underlying magnetic domain structure. Here, we show that the neutron dark-field image can be used to analyze the influence of the coating on the volume and supplementary surface magnetic domain structures. To visualize the stress effect of the coating on the bulk domain formation, we used an uncoated HPSL and stepwise increased the applied external tensile stress up to 20 MPa. We imaged the domain configuration of the intermediate stress states and were able to reproduce the original domain structure of the coated state. Furthermore, we were able to visualize how the applied stresses lead to a refinement of the volume domain structure and the suppression and reoccurrence of supplementary domains.

Rotor Eddy Current Losses Reduction in an Axial Flux Permanent Magnet Machine

A novel rotor structure for a tooth-coil-winding (concentrated winding) open-slot axial-flux permanent-magnet (PM) machine that reduces the eddy currents and increases the main flux linkage is proposed in this paper. A composite-body-based rotor assembly and a steel-laminated layer inserted on top of the magnets are used to reduce eddy-current losses in the PMs. A prototype of an axial flux generator for a heavy-duty vehicle following this structure is optimized, analyzed and measured. The tooth coil windings produce high-amplitude harmonics in the air gap and the large slot openings reduce the rotor flux. Consequently, a rotor structure that decreases the amount of harmonics travelling through the magnets is required. Steel laminations covering the magnets have positive effects on both phenomena. Two-dimensional and three-dimensional finite-element analysis is used to verify and optimize the geometry of the laminations. Computations are verified by experimental measurements of a 100 kW test machine prototype.

Modeling and Analysis of Leakage Flux and Iron Loss Inside Silicon Steel Laminations

This paper investigates the leakage flux and the iron loss generated in the laminated silicon sheets of the core or the magnetic shields of large power transformers. A verification model is well established, and proposed parabolic model (non-saturated region) and hybrid model (saturation region) to simulate the magnetic properties of the silicon steel with different angles to the rolling direction. An efficient analysis method is implemented and validated. The calculated and measured results with respect to the test models are in good agreement.

Modeling of Temperature Effects on Magnetic Property of Nonoriented Silicon Steel Lamination

This paper proposed a temperature-dependent iron loss model and corresponding dynamic hysteresis model, where temperature coefficient ${k}$ is introduced to consider the thermal effect on eddy-current loss. The iron loss model is validated by massive experimental measurement of test samples, 1174 combinations of various temperatures, magnetic inductions, and frequencies for nonoriented silicon steel specimen. The relative error of the model is $\sim 11$ % in a wide range of 50–400 Hz, 26 °C–200 °C, and 0–2 T. The proposed method can be applicable to other types of magnetic materials as long as whose resistivity rate exhibits approximately linear thermal dependence within a temperature range of 26 °C–200 °C.

Effect of Laser Cut on the Performance of Permanent Magnet Assisted Synchronous Reluctance Machines

It is well established that various electrical machine manufacturing steps induce stresses which affect the magnetic properties of electrical steel laminations. Some of these stresses, such as those associated with cutting of the laminations, result in irreversible changes. In fact, punching and laser cutting, are frequently identified as the most severe cause of magnetic degradation [1]. Recent studies show that punching and laser cutting exhibit different deterioration mechanisms due to the nature of internal stresses they induce [2]. Namely, punching causes plastic deformation near the cut edge, whereas laser induces thermal stresses during cutting. In [2-3], the experimental characterization of the spatial distribution (i.e., edge-to-edge) of the magnetic degradation from the two cutting processes revealed that for punching a significant drop in permeability occurs near the cut edge. Whereas, in the case of laser cutting the damage seems to extend further from the edge due to the temperature gradient during processing, resulting in a substantial permeability reduction over the total sample width. The intensity of degradation was strongly influenced by the geometry of the sample, i.e., the strip width and thickness. Therefore, it is important to understand and model such complex phenomena in order to predict their influence on the performance of electrical machines. Discrepancies between predictions and measurements are frequently observed and reported in the literature. For instance, for the case of iron loss these are reported as “built-factors”. Such an approach neglects to reflect the link between the machine design geometrical details and the degree of electrical steel degradation [1]. The quantification of the effects of the magnetic degradation of electrical steel laminations on the machine's flux or back-EMF has received little attention in the literature (to date).

Application of an advanced eddy‐current loss modelling to magnetic properties of electrical steel laminations in a wide range of measurements

This study investigates the influence of a wide range of magnetising frequencies and peak flux densities on the magnetic properties of the electrical steels. In the relevant studies some important factors and operational properties, for example, skin effect, non-uniform flux density distribution, complex relative permeability and magnetisation characteristic of the material, which are often neglected in the literature, are highlighted. Analytical modelling and experimental works were performed for 3% grain oriented silicon steel. In order to show the impact of peak flux density on the magnetic properties, two peak flux densities 1.3 T as a high permeability point and 1.7 T as a low permeability point were considered. The results highlighted that magnetising frequency and peak flux density are two determinant factors with significant effect on the magnetic properties of electrical steels.

Effects of interfaces on heat transfer in laser welding of electrical steel laminations

Laser welding is one of the most potential methods for joining of electrical steel laminations, which is commonly used in motor, transformer and compressor. Because of the existence of multiple interfaces in the welding path, the heat transfer in laser welding of the electrical steel laminations is significantly different from that in the normal welding. In this study, a finite element model (FEM) considering the effects of interfaces has been developed in ANSYS to analyze the heat transfer in laser welding of electrical steel laminations. The contact elements with birth and death options were used to describe both the existed and the vanished statuses of the interfaces during welding. The simulation results showed that the temperature distribution in the zone beside the interfaces was discontinuous at first and then changed to be continuous after the interface vanished. The highest temperature fluctuated periodically during the welding process because of the effects of multiple interfaces. The joint area decreased with the increase of sheet thickness but was robust with respect to the normal pressure applied on the sheets and the contact statuses of the interfaces to some extent. The estimated joint areas at various welding velocities were validated by experimental results. This work provides a better understanding of the heat transfer in laser welding of the electrical steel laminations.

Subspace Correction Method for Computing Magnetic Shields in Large Power Transformers

In a large power transformer, magnetic shields of the oil tank are made of grain-oriented silicon steel laminations. The thickness of a lamination is 0.3 mm and the thickness of its coating film is only 4 μm. Accurate solution of non-linear eddy current problem in such a multi-scale structure is very challenging. This paper proposes a subspace correction method (SCM) to solve the nonlinear eddy current problem in the lamination system. The method can compute 3-D eddy currents in the steel laminations and is very efficient for large-scale simulations. Numerical experiments on the TEAM benchmark model P21 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sup> -M1 show good agreements between the calculated and measured data and demonstrate the competitive behavior of the SCM.

Pragmatic two‐step homogenisation technique for ferromagnetic laminated cores

Electromagnetic fields and eddy currents in thin electrical steel laminations are governed by the laws of magnetodynamics with hysteresis. If the lateral dimension of the laminations is large with respect to their width, the fields and currents generated under arbitrary excitation inside a lamination can be resolved accurately by solving a one-dimensional finite element magnetodynamic problem across half the lamination thickness. This mesoscopic model is able to produce, by averaging the necessary information, a homogenised laminated core model, to be used in the macroscopic modelling of electrical devices involving ferromagnetic lamination stacks. As each evaluation of the homogenised model at the macroscale implies a finite element simulation at the mesoscale, a monolithic implementation of the homogenisation method would be extremely time-consuming. Hence the idea of this study to use system identification techniques to construct an algebraic approximation of the homogenised model, to be used as a conventional constitutive relationship in two- or three-dimensional macroscale simulations. This pragmatic two-step homogenisation approach turns out to be quite accurate and efficient in practice, and it entails no implementation in the FE code, provided the latter offers enough flexibility in the description of the material laws.