When asymmetrically supplied, the dual three-phase motors produce electromagnetic (EM) forces on the rotor through the unbalance of the magnetic fields in the air gap. This article presents the design and prototyping of a novel setup for simultaneously measuring the EM torque and forces acting on the rotor of a dual three-phase induction machine (IM) under asymmetric operating conditions. A 3-D FEM model is developed to assess the operational stability of the prototype machine across a wide range of speeds. The design of the proposed setup along with its working principle as well as the results of measurements for the torque and forces and their comparison with the simulation results are presented. The study shows that the setup can simultaneously measure the forces and torque as predicted by the simulations. The proposed setup will be used for the development and validation of different control strategies in view of rotor dynamics stabilization.

This paper investigates the design methodology and optimisation of double-layer windings of dual three-phase induction motors that can generate torque and electromagnetic forces simultaneously. In high-power variable speed drives, the possibility of controlling the electromagnetic forces on the rotor enables these machines to operate at critical speed. Four winding topologies are developed to maximise both the torque and force through a systematic shift of return path of the winding coils and optimisation of the winding factors of both torque and force producing harmonics. The performance of the optimised winding configurations is also analysed for certain slot-pole combinations and the optimum scheme is presented. In addition to winding factors, the evaluation criteria consider key parameters such as mean torque, mean force, respective ripples and overall efficiency of machine. An experimental setup has been developed to validate the results and compare them with those from finite element analysis. The research shows that depending on the chosen topology, there is an optimal slot-pole combination that delivers enhanced torque and force performance or vice versa, for a given slot-pole combination, there is an optimal winding topology. These results are relevant for industry applications where an existing machine needs to be redesigned for better stability.

The multi-domain particle model (MDPM) is a physical magnetization model that can describe the magneto-mechanical interaction by considering the magnetoelastic energy. Using the MDPM, the stress dependence of hysteresis loss of non-oriented silicon steel sheet is simulated under biaxial stress conditions. The effect of biaxial or shear stress on the hysteresis loss is successfully predicted by the MDPM without parameter fitting to experimental data measured under mechanical stress.

This study investigates the impact of punching on the magnetic losses of non-oriented electrical steel by combining dedicated experiments with a viscoelastic simulation framework based on fractional-derivative operators. A set of specimens with increasing numbers of cut edges was characterized under alternating magnetization. The viscoelastic model, previously validated for various ferromagnetic materials, was applied to capture frequency-dependent losses. Results show that the fractional order $n$ increases almost monotonically with the number of punched edges, demonstrating the method's ability to quantify cutting-induced degradation.

This paper presents a physics-informed neural network approach for dynamic modeling of saturable synchronous machines, including cases with spatial harmonics. We introduce an architecture that incorporates gradient networks directly into the fundamental machine equations, enabling accurate modeling of the nonlinear and coupled electromagnetic constitutive relationship. By learning the gradient of the magnetic field energy, the model inherently satisfies energy balance (reciprocity conditions). The proposed architecture can universally approximate any physically feasible magnetic behavior and offers several advantages over lookup tables and standard machine learning models: it requires less training data, ensures monotonicity and reliable extrapolation, and produces smooth outputs. These properties further enable robust model inversion and optimal trajectory generation, often needed in control applications. We validate the proposed approach using measured and finite-element method (FEM) datasets from a 5.6-kW permanent-magnet (PM) synchronous reluctance machine. Results demonstrate accurate and physically consistent models, even with limited training data.

This study examines the effect of punching on magnetic losses in non-oriented electrical steel using a viscoelastic model based on fractional-derivative operators. Specimens with identical material volume and increasing edge-affected area were characterized under alternating magnetization with controlled sinusoidal flux density. The frequency dependence of losses is described by a fractional order n and a coefficient ρ, related to viscoelastic mechanisms and material properties, respectively. The results show an almost monotonic increase of n with edge-affected area, providing a compact indicator of cutting-induced degradation, while ρ remains close to analytically predicted values. A scaling analysis links the experimental configurations to 1 kW transformers and motors. Loss predictions at elevated frequencies highlight the significant contribution of punching-induced degradation under practical operating conditions.

This work focuses on the vectorization of the magnetic anisotropy model for grain-oriented steel sheets by exploiting coenergy computation and interpolation methods. The proposed approach is based on a modified representation of coenergy isocontours in elliptical form. A novel method for measuring the 2D anhysteretic properties with a rotational single sheet tester is proposed. The model precision is analyzed together with a reduced number of directions.

AbstractIn this paper, two co‐simulations are introduced to study the behaviour of a 2‐D finite‐element model and a magnetic equivalent model of an induction machine, both coupled with a mechanical radial ball bearing model. This comprehensive approach allows for the generation of synthetic vibration and current signals of a ball bearing mounted on a shaft, taking into account the entire machinery. The study investigates the misalignment effect caused by an inner ring defect in a ball bearing, analysing its impact on the current of the IM models. Likewise, the effects of eccentricity in the induction machine models on rotor vibration are studied through their coupling with the mechanical ball bearing model. This multiphysics co‐simulation provides a novel numerical application to generate data relative to mechanical defects in induction machines. By using this coupled method, an inner ring defect of 1 mm depth and 3 mm length in the bearing model is accurately identified in the frequency spectrum of the stator current, whereas eccentricity faults for levels ranging between 5% and 40% are detected in the vibration spectrum of the ball bearing. The findings are accurately supported by related theory, and further validated through experimental verification for the case of the inner ring fault.

This study delves into the strategic layer alternation along the axial direction to mitigate electromagnetic torque ripple and minimize eddy current losses within synchronous reluctance electric machine with 3D-printed axially laminated rotor. A meticulous comparative analysis is conducted, scrutinizing the printing depth in the radial direction alongside variations in the number of alternating layers to discern the optimal ratio. Emphasis is placed on implementing two distinct 3D sliced models: one incorporating current continuity between slices and the other without. The article meticulously delineates the nuances of these models and draws a comprehensive comparison with a full 3D FEM model, elucidating their respective merits and drawbacks.

Grain oriented material presents highly anisotropic properties involving both the magnetocrystalline anisotropy and shape anisotropy. Whereas the former is generally well known for iron silicon alloys, the later involves a complex domain decomposition. In this paper, we propose to model the anhysteretic vector properties of grain-oriented steel sheet with a multiscale model. The complexity of the domain decomposition is simplified by a simple shape anisotropy term. The general trend of the measured anhysteretic flux density components can be reproduced by the model.

This study investigates the magnetic Barkhausen noise (MBN) in non-oriented electrical steel under rotational magnetization conditions, focusing on its application to improve the understanding of magnetic losses and the behavior of ferromagnetic domains. MBN serves as a powerful tool for characterizing domain wall dynamics, and its use under rotational magnetization offers new insights into energy losses in electromagnetic devices. We developed an experimental setup to measure MBN under different levels of flux density and to compare the results with conventional alternating magnetization. For the first time, MBNenergy ( H ) hysteresis loops were plotted under rotational magnetization, offering unique perspectives on domain wall activity and domain structure kinetics. Our findings indicate a significant reduction in domain wall motion beyond a threshold magnetic flux density under rotational conditions. The differences observed between classical hysteresis loops and MBNenergy ( H ) loops under both unidirectional and rotational magnetization clarify the specific contributions of rotational magnetization, as well as the distinct roles of 180 degrees and 90 degrees domain wall motions.

Abstract This paper introduces a novel application of the inverse modelling method, which is designed to estimate core losses in both the stator and rotor regions of an electrical machine. The technique focuses on the use of short‐term transient temperature measurements obtained from the stator core of a slotless induction machine, with a focus on validating the measured temperature rise through a forward model. The measurement setup involves two primary approaches: (i) the use of thermal sensors embedded in a printed circuit board inside the stator core and (ii) surface sensors embedded on the stator yoke. Through the use of this innovative approach, the results indicate that the inverse modelling technique is highly effective in predicting core losses based on short‐time transient temperature rise measurements.

A novel thermodynamically consistent macroscopic magnetic hysteresis model is presented. Magnetization is calculated from the reversible part of the magnetic field, while the evolution law of the irreversible part involves physically meaningful material constants: the coercive field and the initial susceptibilities of the hysteretic and anhysteretic curves. It is possible to invert the model through an iterative procedure, allowing either the magnetic field or the flux density as an input to the model. The model is tested on both soft and hard magnetic materials for major and minor loops.

The aviation industry is undergoing electrification due to the increased global focus on reducing emissions in air traffic. Regarding the volatility of raw material prices, one main objective is the increase in the specific power of the motor. This matches the ambitious targets of the CoE project (Center of Excellence) in Finland on high-speed electric motors. The targeted specific power is 20 kW/kg. In this work, motors are designed and optimized for a fully electric regional aircraft. motors with different slot/pole configurations and rotational speed values are studied to determine the advantage of increasing speed in terms of weight reduction. As increasing speed requires the use of a gearbox, the overall weight of the motor and the gearbox is evaluated in post-processing, which allows for determining the impact of high speed on the overall weight. An optimization tool coupled with an electromagnetic and mechanical analysis is used to optimize 1 MW surface mounted permanent magnet synchronous motors (S-PMSMs) for given specifications of regional electric aircraft. Optimization results indicate that there is considerable gain in terms of overall weight only when increasing the speed to the range of 10,000–15,000 rpm.

The magnetic anisotropic of steel sheets tends to increase the core losses and the magnetizing current of electric machines. Their accurate evaluation can adjust the machine design to improve the machine performances. Whereas various non-linear magnetic anisotropic models can represent the material behavior properly, their implementation into finite element requires the magnetic model to be derived from a thermodynamic potential. In this article, we implement the anisotropic model based on the effective field into a finite element model.

Hysteresis model of soft magnetic material enables an accurate estimation of the losses in electrical application. In rotating machine, the flux distribution can magnetized many directions of the iron core. The combination of the rotational and the alternating flux density appears between the slot and the yoke region. Even if the alternating flux density appears in the middle of each tooth, the magnetic properties varies with the magnetized direction with respect to the rolling direction. Whereas the losses strictly increases with the amplitude of an alternating flux density, the hysteresis loss presents a maximum under rotational flux density condition. Although this phenomenon is properly described by the coherent rotation of the domains at the microscopic scale, the macroscopic representation of the material should represent this specific feature. In this paper, a general vectorization technique is applied to the Jiles-Atherton model of hysteresis. The anisotropic anhysteresis behavior is derived from the analysis of a cubic crystal. This anhysteresis model drives the coherent rotation of the hysteresis model. Even if the model parameters are identified with alternating flux condition, the rotational flux density can be predicted properly.

In this abstract, the multiscale model incorporates an energy based hysteresis model for ferromagnetic material. The coherent rotational phenomena are considered by letting the magnetic domains rotates with the applied field. Finally, the model of steel sheets is simulated in a finite element model of a transformer.

This article presents a novel data augmentation method that generates feature values for unmeasured loading levels based on limited measured and simulated loading level data.The incorporation of offline simulated data in the augmentation framework and the mapping of the error distribution over the loading levels greatly reduce the dependency on including a large number of loading levels in the curve fitting process.Furthermore, the proposed method shows high potential to minimize the deviation between measured and simulated data at the feature level.The method is applied to the induction machine to generate feature values at 25% and 50% loading levels for healthy, one, two, and three broken rotor bars conditions.An excellent agreement is observed between the augmented and actual feature values calculated from the measured data at 25% and 50% loading levels.The inclusion of this augmented data in the training phase aids in resolving the generalization issue and enhancing the average classification accuracy of the XGBoost algorithm by 9.4% and 4.4% at 25% and 50% loading levels, respectively.

Abstract The authors present two fast and accurate methodologies for the computation of eddy current losses in the axially laminated rotor of a synchronous reluctance machine. The methodologies are based on different combinations of the finite element method in time and frequency domains with 2D and 3D formulations. First, a comparative study of the 2D and 3D formulations for loss calculation is presented, considering various load angles of the machine to illustrate the problem of eddy‐current losses in this type of machines and its dependence on the load angle. The influence of the iron saturation on the loss calculation is also evaluated in these computations. A novel correction factor based on the computations at two load angles is proposed to convert the losses computed from a 2D model to match those computed from a 3D model. For the sake of generality, investigations are also conducted for various thicknesses of the lamination layers and different machine lengths, and an analytical method to describe the dependency of eddy‐current losses on the load angle of the machine is introduced. Moreover, a simplified method is proposed for modelling eddy currents in the frequency domain and calculating losses in an axially laminated structure based solely on the results of a magnetostatic solution. The results obtained by the simplified model demonstrate excellent agreement with the full 3D magneto‐dynamic simulation. Overall, the findings contribute to understanding and accurately characterising the eddy current losses in axially laminated rotors, offering potential insights for designing and optimising axially laminated synchronous reluctance electric machines.