Although the effect observed in this system is due to the saturation in the magn

Question

Although the effect observed in this system is due to the saturation in the magnetization (the permeability is not constant) and the equations raised are only valid if the magnetic system is linear, the use of finite element tools to find the relationship between the applied current and the magnetic flux obtained is not to linearize the system. Explain then, what these tools are used for (Matlab).

Consider the nonlinear magnetic circuit. Ampere's law states that the line integral of B-around the closed path is proportional to the net current through the enclosed area. However, the value of permeability of the ferromagnetic material depends on the external field, and ? is not constant. This effect is observed due to the saturation magnetization and, in general, one should use the nonlinear magnetization curves. That is, the equation LaN ?=? const is valid only if the magnetic system is linear. As an illustrative example, consider a set of data for the flux linkage current relation for an electric motor. In particular, we use i-100.20.40.60.811.21.41.61.82] and ? [00.0220.0440.0650.0850. 10. 1 1 30. 1 230. 1 3 10. I 360. I 38] Using MATLAB, the curve fitting, interpolation, and approximation can be performed; see the script. MATLAB Script NUMERICAL ANALYSIS OF THE CUREVE-FLUX DATA The current-tíux data points t-linapace (0,2,11) [0 0.022 0.044 0.065 0.084 0.1 0-113 0.123 0.131 0.136 0.138 subplot (3.2.1 plotI.Pxis(to 2 0 0.141 xlabelt Current).ylabel'Flux titlel The plot of the Current-Flux data') pausei % Differentiation of the current-flux data dl#A1:length (I)-1); subplot (3,2,2 label Current-ylabel rluxdOurrent titl ('Derivativo dFlux /dcurrent as a funetion, et current', pauses Linterval linspace (0.2.1001)

Explanation / Answer

In above example MATLAB as a tool is used to get an approximate realtion between current and flux density with variable permiability.

when a magnetic circuit gets saturated that means a high density of current is needed to change the flux density hence the system becomes non linear, but in this condition if a relation is desired between current and flux density we have to make some approximations and use some tool like MATLAB which have finite elements

System is non linear means with small change in current the magnotomotive force is not changing . hence thats why it is said permiability is not constant

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