Numerical modelling of magnetic materials for computer aided design of electromagnetic devices
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In design and simulation of electromagnetic devices, it is essential to model the properties of magnetic materials, such as the relation between magnetic flux density B and magnetic field H or B-H curve and electromagnetic power losses or core losses with various kinds of magnetic field excitations, in order to assess the performance correctly. The major part of the work is concerned with the modelling of hysteresis loops with alternating magnetic field, and core losses with alternating and/or rotating magnetic fields. Various novel models are developed. A critical comparison between various available models of magnetic hysteresis shows that the Preisach theory appears to be suitable for practical engineering applications. A new normal Preisach model is obtained with the help of a graphical representation of the theory. The new model features simple formulation and easy parameter identification. The input data is the limiting hysteresis loop. It can provide correct results for a medium or large magnetic field, but fails when the hysteresis loop to be predicted is close to the origin of the B-H plane owing to some intrinsic defects of the model. These defects are eliminated in a new generalised model, which contains a reversible magnetisation component and a magnetisation feed back. The input data required by the generalised model are the limiting hysteresis loop and the normal magnetisation curve. These can be obtained from either manufacturers' data sheets or from simple measurements. Better accuracy is achieved by the generalised model. New dynamic discrete circuit models with hysteresis, eddy current, and anomalous losses included are developed to simulate the performance of magnetic cores in devices with nonsinusoidal alternating flux. At low frequencies, a simple equivalent circuit model consisting of a constant equivalent resistor for eddy current loss, a nonlinear equivalent resistor for anomalous loss, and a non-ideal inductor for modelling the hysteresis loop and hysteresis loss is used. This model is generalised into a ladder network model for simulation at high frequency by subdividing the cross section of the core into a few assumed eddy current paths. All parameters of these models can be identified from data sheets provided by manufacturers. For rotational core loss measurement, a single sheet square specimen tester is developed. The precision of two dimensional field strength measurement at the surface of the specimen is improved by a novel sandwich H sensing coil arrangement. The relationship between the core loss due to the rotational component of magnetic field and the total core loss is clarified using a new equation and the arguments are supported by the experimental results. Rotational core losses in grain oriented and non-oriented silicon steel sheets were measured using the testers at the University of Technology, Sydney and the Physikalisch-Technische Bundesanstalt, Braunschweig, Germany. These measurements provided much useful information for both understanding of the loss mechanisms and modelling of the losses. Similar to the case of alternating core losses, rotational core loss can also be separated into rotational hysteresis, eddy current, and anomalous losses. The rotational hysteresis loss is fitted by a novel model based on a strong analogy between the retarding torque due to the rotational hysteresis loss and the electromagnetic torque in a single phase induction machine. With a circular flux density, the rotational eddy current loss is twice as much as the alternating eddy current loss. The rotational anomalous loss can be modelled using the same formula as for alternating anomalous loss, but the coefficient of rotational anomalous loss is generally a function of flux density, and eventually reduces to zero when the material is saturated and all domain walls disappear. Total core losses with an elliptical flux density are predicted from the pure rotational and alternating core losses by a new formulation derived from the total core loss formula used in rotational core loss measurement. The new model is applicable to hysteresis as well as total core losses. Comparisons with experimental data show that this new model is more accurate than a linear interpolation between alternating and pure rotational core losses. Core losses in an AC permanent magnet motor are modelled. The magnetic flux density distribution is calculated by a finite element code. Fourier series analysis is used for an arbitrary two dimensional rotating flux density. The total core loss is finally calculated by summing up all the contributions from different elliptically rotating harmonics of flux density in each finite element. The discrepancy between calculated and measured results is about 13%.
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