Microwave absorbing properties of ferrites and their composites: A review

High-speed permanent-magnet synchronous machines (HS PMSMs) are a popular topology among modern electrical machines. Suitable applications for such machines are low-power vacuum pumps, compressors, and chillers. This paper describes a systematic design methodology for an HS PMSM using two case studies. The design process for such high-speed (HS) machines is multidisciplinary and highly iterative due to the complex interaction of the many design variables involved. Consequently, no single optimum solution exists, and multiple possible solutions can meet the customer requirements. Practical solutions should be within acceptable thermal limits, should be energy-efficient, and should be rigid enough to withstand the forces exerted during operation. The proposed design flow is divided into steps that are presented in this paper in the form of a flowchart with emphasis on mechanical aspects. Each step represents a task for a thermal, mechanical, or electrical engineer. The features of each step and the prerequisites for moving to the next step are discussed. The described methodology was implemented in the design of two HS PMSMs. The output performance results of the design flow are compared with measured results of the prototypes. The design process described in this paper provides a straightforward procedure for the multidisciplinary design of HS permanent magnet electrical machines.

Multidisciplinary Design Process of a 6-Slot 2-Pole High-Speed Permanent-Magnet Synchronous Machine

Analytical models play an important role in the design of electromagnetic devices by providing computationally efficient solutions. In this paper, by combining magnetic equivalent circuit approaches and Faraday's and Ampere's laws, a model for radial-flux eddy-current couplers is developed, which can easily handle complex geometries as well as account for iron saturation, all material properties, and three-dimensional (3-D) parameters. The characteristics and the design considerations of a surface-mounted permanent-magnet structure are presented. Also, a procedure aimed at an optimal design of the yoke thicknesses is utilized. Moreover, 2-D and 3-D finite-element methods are employed in the analyses and evaluation of the model. Finally, sensitivity analysis is performed to explore the impacts of the machine parameters on the device performance.

Nonlinear Modeling of Eddy-Current Couplers

In this paper, the design optimization of a nonsalient high-speed permanent magnet synchronous machine (PMSM) for electric vehicle applications is presented. It will be shown how, with a new approach, it is possible to find a deterministic solution to solve the sizing of the machine from a given driving cycle. The optimal geometry and the optimal control strategy over the cycle minimizing both the energy losses and the volume of the machine will be calculated. At first, the one-dimensional analytical model used is presented and validated for the most significant point of the driving cycle using a finite element method. Then, the design methodology and the results through a specific application are detailed. Particularly, it will be shown how the flux weakening, directly given by the design process via the optimization of the control strategy, allows reducing both the energy losses and the constraints on the power converter. At last, in order to validate the solution considering the whole cycle while keeping a reduced computation time, a reluctance network model of the PMSM is used. This model validate the energy losses and the flux densities in the steel parts over the cycle. The study will be done considering the urban dynamometer driving schedule.

Design Optimization with Flux Weakening of High-Speed PMSM for Electrical Vehicle Considering the Driving Cycle

A directly coupled magneto-mechanical model is proposed for simulating the effect of the magnetostriction and electromagnetic stress in iron. The model is based on the general balance laws of electromagnetism, mechanics, and continuum thermodynamics. It is implemented in 2-D by using a conforming finite element method for the magnetic vector potential and the displacement field. The method is applied to two different types of induction machines.

FEM for directly coupled magneto-mechanical phenomena in electrical machinesKatarzyna

This paper presents an anisotropic and mechanical strain-dependent model of magnetostriction in electrical steel sheets and its application in finite-element computations. The presented model is bidirectional and the data needed for its derivation is extracted solely from unidirectional measurements under mechanical loading. The model has six parameters that describe the magnetic and strain behavior and two parameters that describe the anisotropy. The validation of the model is carried out through measurements and computations on a single-phase transformer-like device. The comparison between computation and measurement results seems to be reasonable regardless of the fact that the magnetic behavior is modeled as single valued, isotropic, and anhysteretic. Original magnetostriction measurements are also presented and the importance of magnetostriction anisotropy in a priori isotropic electrical steel sheets is demonstrated. The model is easy to implement in existing codes and the anisotropic behavior is straightforward to modify according to a specific material.

Anisotropic and Strain-Dependent Model of Magnetostriction in Electrical Steel Sheets

A coupled magnetomechanical model for hysteresis in an electrical steel sheet is presented. The foundation of the model developed is the classical Sablik–Jiles–Atherton (SJA) model. A comprehensive model for the stress-dependent magnetostriction is also proposed and implemented in the SJA model. Improvements in the SJA model as well are proposed and validated with simultaneous measurements of magnetostriction, magnetic field, and flux density. The measurements were performed on a single electrical steel sheet under various levels of stress (−35 to 100 MPa). The proposed model was found to adequately model the permeability change and the local bowing of the $B$ – $H$ -loop due to stress.

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Magnetomechanical Model for Hysteresis in Electrical Steel Sheet

Even non-oriented steel sheets present a magnetic anisotropic behavior. From rotational flux density measurements at 5 Hz, the model of magnetic anisotropy is derived from two surface basis-cubic splines with the boundary conditions matching with ferromagnetic theory. Furthermore, the investigation of the magnetic anisotropy shows that the $H(B)$ characteristic is not strictly monotonous due to the angle difference between the field and the flux density. Hence, the standard non-linear solvers would either diverge or converge toward the closest local minimum. Thus, we propose two different specific solvers: 1) a combined particle swarm optimization with a relaxed Newton-Raphson and 2) a modified Newton method.

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Model of Magnetic Anisotropy of Non-Oriented Steel Sheets for Finite-Element Method

Cutting the electrical steel sheets to form the shape of the stator and the rotor affects the magnetic properties of the sheets. The increase of the magnetic losses as well as the drop of the magnetic permeability can impact on the design of electrical devices. This paper investigates this deterioration effect on the optimal design of the stator of a high-speed permanent magnet synchronous motor. The deterioration due to punching is phenomenologically analyzed based on measurement of strips of steel sheets with various widths on an enlarged Epstein frame. The losses are computed with a Bertotti model whose coefficients depend on the width of the sheets. The optimization of a synchronous machine is then carried out with this magnetic losses model.

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Effect of Punching the Electrical Sheets on Optimal Design of a Permanent Magnet Synchronous Motor

The abilities of a simplified multiscale and a Helmholtz energy HE models models from the literature to predict the multiaxial stress dependent magnetic hysteresis behavior of electrical steel sheets are analyzed. The identification of the models is performed using only uniaxial magneto-mechanical measurements. Reasonable accuracy between the measurements and the modeled results is obtained. With this paper, the applicability of the HE-based model for predicting the multiaxial magneto-mechanical behavior of electrical steel sheets is verified for the first time. The differences between the studied models and possible modifications to increase the accuracy of them are discussed. Some brief guidelines for the applications are given.

/pdf/modeling-the-effect-of-multiaxial-stress-on-magnetic-1zujk93awz.pdf

Floran Martin

Papers

Anisotropic and Strain-Dependent Model of Magnetostriction in Electrical Steel Sheets

Magnetomechanical Model for Hysteresis in Electrical Steel Sheet

Model of Magnetic Anisotropy of Non-Oriented Steel Sheets for Finite-Element Method

Effect of Punching the Electrical Sheets on Optimal Design of a Permanent Magnet Synchronous Motor

Modeling the Effect of Multiaxial Stress on Magnetic Hysteresis of Electrical Steel Sheets: A Comparison