scholarly journals Teaching Magnetic Circuits With Minimum Vector Algebra

2020 ◽  
Author(s):  
Bruno Osorno
2020 ◽  
pp. 54-58
Author(s):  
S. M. Plotnikov

The division of the total core losses in the electrical steel of the magnetic circuit into two components – losses dueto hysteresis and eddy currents – is a serious technical problem, the solution of which will effectively design and construct electrical machines with magnetic circuits having low magnetic losses. In this regard, an important parameter is the exponent α, with which the frequency of magnetization reversal is included in the total losses in steel. Theoretically, this indicator can take values from 1 to 2. Most authors take α equal to 1.3, which corresponds to the special case when the eddy current losses are three times higher than the hysteresis losses. In fact, for modern electrical steels, the opposite is true. To refine the index α, an attempt was made to separate the total core losses on the basis that the hysteresis component is proportional to the first degree of the magnetization reversal frequency, and the eddy current component is proportional to the second degree. In the article, the calculation formulas of these components are obtained, containing the values of the total losses measured in idling experiments at two different frequencies, and the ratio of these frequencies. It is shown that the rational frequency ratio is within 1.2. Presented the graphs and expressions to determine the exponent α depending on the measured no-load losses and the frequency of magnetization reversal.


2018 ◽  
pp. 14-18
Author(s):  
V. V. Artyushenko ◽  
A. V. Nikulin

To simulate echoes from the earth’s surface in the low flight mode, it is necessary to reproduce reliably the delayed reflected sounding signal of the radar in real time. For this, it is necessary to be able to calculate accurately and quickly the dependence of the distance to the object being measured from the angular position of the line of sight of the radar station. Obviously, the simplest expressions for calculating the range can be obtained for a segment or a plane. In the text of the article, analytical expressions for the calculation of range for two-dimensional and three-dimensional cases are obtained. Methods of statistical physics, vector algebra, and the theory of the radar of extended objects were used. Since the calculation of the dependence of the range of the object to the target from the angular position of the line of sight is carried out on the analytical expressions found in the paper, the result obtained is accurate, and due to the relative simplicity of the expressions obtained, the calculation does not require much time.


Author(s):  
Gerhard Oertel

Students of geology who may have only a modest background in mathematics need to become familiar with the theories of stress, strain, and other tensor quantities, so that they can follow, and apply to their own research, developments in modern, quantitative geology. This book, based on a course taught by the author at UCLA, can provide the proper introduction. Included throughout the eight chapters are 136 complex problems, advancing from vector algebra in standard and subscript notations, to the mathematical description of finite strain and its compounding and decomposition. Fully worked solutions to the problems make up the largest part of the book. With their help, students can monitor their progress, and geologists will be able to utilize subscript and matrix notations and formulate and solve tensor problems on their own. The book can be successfully used by anyone with some training in calculus and the rudiments of differential equations.


Energies ◽  
2021 ◽  
Vol 14 (15) ◽  
pp. 4400
Author(s):  
Luca Ferraris ◽  
Fausto Franchini ◽  
Emir Pošković ◽  
Marco Actis Grande ◽  
Róbert Bidulský

In recent years, innovative magnetic materials have been introduced in the field of electrical machines. In the ambit of soft magnetic materials, laminated steels guarantee good robustness and high magnetic performance but, in some high-frequency applications, can be replaced by Soft Magnetic Composite (SMC) materials. SMC materials allow us to reduce the eddy currents and to design innovative 3D magnetic circuits. In general, SMCs are characterized at room temperature, but as electrical machines operate at high temperature (around 100 °C), an investigation analysis of the temperature effect has been carried out on these materials; in particular, three SMC samples with different binder percentages and process parameters have been considered for magnetic and energetic characterization.


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