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10. Flux-current relation

Lecture's plan

Introduction

  1. The importance of the magnetic circuit notion
  2. An example of magnetic circuit
  3. Defining the integration contour for the application of Ampère's theorem
  4. The application of Ampère's theorem - emphasizing the magnetic circuit
  5. Hopkinson's law
  6. Analogy between magnetic circuits/electrical circuits
  7. Application for modelling an electromechanical converter
  8. Defining the equivalent magnetic circuit
  9. The reduction of the equivalent magnetic circuit
  10. Flux-current relation
  11. The calculus of the magnetic co-energy and attraction force

Knowing the medium lenght and the perpendicular S section of the different elements of the magnetic circuit as well as the permeability of the material they are made of, the nine reluctances of this circuit can be calculated by using the general relation

If r is the relative permeability of the ferromagnetic material from which () core is made of, permeability supposing to be constant whatever the value of the current (unsaturated circuit), we can calculate:

The flux which flows through each of the two circuit branches (circuit equal to half of the total flux) can be, then, written as follows:

(7)

It is rather noteable that if the total lenght of the magnetic circuit is negligible in proportion to the product of mr and the total lenght of the air-gap portions, in order to obtain flux-current relation, it can be approximated, without making significant errors, that the total reluctance of the magnetic circuit is equal to that of the air-gap portions 3. For a relative mr permeability higher than 1000 and for values of the air-gap lower than 1mm, this approximation stays valid as long as the total lenght of the circuit remains lower than 2m.

3 In fact, this kind of simplification is generally adopted in modelling the electromechanical converters , assuming that the permeability of the ferromagnetic materials they are made of, is infinite.

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Last update: 2005, September, 30 | Translation: Sergiu Ivanov | Realization: Florin Ravigan, Cristian Vladu