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Electrical Machines (EELE 4350)

Electrical Machines (EELE 4350). Assad Abu-Jasser, PhD Electric Power Engineering site.iugaza.edu.ps /ajasser ajasser@iugaza.edu.ps. Chapter Two Review of Basic Laws of Electromagnetism. Induced Electromotive Force. Example 2.1.

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Electrical Machines (EELE 4350)

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  1. Electrical Machines(EELE 4350)

  2. Assad Abu-Jasser, PhD Electric Power Engineering site.iugaza.edu.ps/ajasser ajasser@iugaza.edu.ps

  3. Chapter Two Review of Basic Laws of Electromagnetism

  4. Induced Electromotive Force

  5. Example 2.1 A 1000-turn coil is placed in a magnetic field that varies uniformly from 100 mWb to 20 mWb in 5 seconds. Determine the induced emf in the coil

  6. Example 2.2 A square loop with each side 10 cm in length is immersed in a magnetic filed intensity of 100 A/m (peak) varying sinusoidally at a frequency of 50 megahertz. The plane of the loop is perpendicular to the direction of the magnetic field. A voltmeter is connected in series with the loop. What is the reading of the voltmeter?

  7. Example 2.3 A square loop with each side equal to 2a meters is rotating with an angular velocity of ωradians/second in a magnetic field that varies as B=Bmsinωt Tesla. The axis of the loop is at right angle to the magnetic field. Determine the induced emf in the loop.

  8. Ampere’s Law A very long cylindrical conductor of radius b carries a uniformly distributed current I. Determine the magnetic field intensity (a) within the conductor (b) outside the conductor.

  9. Ampere’s Force Law

  10. Example 2.5 A straight conductor carrying current I is placed in a uniform magnetic field as shown. Determine the force acting on the conductor.

  11. Torque on a Current Loop

  12. Magnetic MaterialsFerromagnetic Materials Iron, cobalt, and nickel are good examples of ferromagnetic materials. Random orientation of magnetic dipoles

  13. Magnetizing CharacteristicFerromagnetic Materials

  14. Hysteresis Loop Hard Magnetic Materialshave high residual & Large coercive force While Soft Materials have very low residual & coercive

  15. Magnetic CircuitsToroid The magnetic flux flows in the magnetic material Fringing at the air-gap is neglected The magnetic flux density is uniform

  16. Analogous Equivalent CircuitOhm’s law for magnetic circuit

  17. Series-Parallel Magnetic Circuit

  18. Example 2.6 An electromagnet of square cross-section has a tightly wound coil with 1500 turns. The inner and outer radii of the magnetic core are 10 cm and 12 cm, respectively. The length of the air-gap is 1 cm. if the current in the coil is 4 A and the relative permeability of the magnetic material is 1200, determine the flux density in the magnetic circuit.

  19. Example 2.7 A series-parallel magnetic circuit with its pertinent dimensions in centimeters. If the flux density in the air-gap is 0.05 Tesla and the relative permeability of the magnetic region is 500, calculate the current in the 1000-turn coil using the fields approach.

  20. Example 2.8 A magnetic circuit with its pertinent dimensions in millimeters. The magnetization characteristic of the magnetic material is also given. If the magnetic circuit has a uniform thickness of 20 mm and the flux density in the air-gap is 1.0 T, find the current in the 500-turn coil.

  21. Example 2.9 A magnetic circuit with its mean lengths and cross-sectional areas are given. If a 600-turn coil carries a current of 10 A, what is the flux in the series magnetic circuit? Use the magnetization curve of example 2.8 First Iteration 50% A-G mmf Second Iteration 80% A-G mmf Third Iteration 4600 A.t A-G mmf

  22. Self Inductance Φ= the magnetic flux (Weber) L= self inductance (Henry)

  23. Self InductanceToroid

  24. Mutual Inductance

  25. Example 2.10 Two identical 500-turn coils are wound on the same magnetic core. A current changing at a rate of 2000 A/s in coil-1 induces a voltage of 20 V in coil-2. what is the mutual inductance of this arrangement? If the self inductance of coil-1 is 25 mH, what percentage of the flux set up by coil-1 links coil-2?

  26. Magnetically Coupled CoilsSeries Connection Series Aiding Series opposing

  27. Example 2.11 The effective inductances when two coils are connected in series aiding and series opposing are 2.38 H and 1.02 H, respectively. If the inductance of one coil is 16 times the inductance of the other, determine (a) the inductance of each coil, (b) the mutual inductance, and (c) the coefficient of coupling.

  28. Magnetically Coupled CoilsParallel Connection Parallel Aiding Parallel Opposing

  29. Example 2.12 Two magnetically coupled coils with self inductances of 1.6 H and 0.1 H are connected in parallel. The mutual inductance is 0.34 H. calculate the effective inductance when (a) the coils connected in parallel aiding and (b) parallel opposing.

  30. Magnetic LossesEddy-Current Losses

  31. Magnetic LossesHysteresis Losses Energy loss per unit volume per cycle

  32. Total Magnetic Losses

  33. Example 2.13 The following data were obtained on a thin sheet of silicon steel. Compute the hysteresis loss and the eddy-current loss.

  34. Permanent Magnet

  35. Example 2.14 The physical dimensions of the magnet circuit shown arelg=1 cm, Ag=As=Am=10 cm2, ls=50 cm and µr=500 for steel. What is the minimum length of the magnet required to maintain the maximum energy in the air-gap?

  36. Example 2.15 Calculate the induced emf in a 10-turn coil rotating at 100 rad/s in a permanent magnet system with axial length of 50 mm as shown. The rotor and the yoke are made of an alloy with a relative permeability of 3000. The demagnetization curve of the magnet is also shown.

  37. End ofChapter Two

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