1. مکاترونیک مدرس : دکتر پدرام پیوندی

2. Magnetism & Electromagnetism 2

3. Learning Outcomes At the end of the chapter, students should be able to: magnetic and electromagnetic. understand the theory of magnetic and electromagnetic. electromagnetic induction understand the law of electromagnetic induction. 3

4. Introduction to Magnetism Basic Magnetism Effects of magnetism known as early as 800 BC by the Greeks. Certain stones called "magnetite or iron oxide (Fe2O3)" attracted, pieces of iron. 4

5. Magnetism magnets do not come in separate charges Any magnetic/magnetized object has a North and South pole If you break a magnet in half, each piece will have a North and a South end 5 Introduction to Magnetism

6. Magnetic field Magnetic field lines – 3D lines which tiny bar magnets lie along. Magnetic field lines run from N to S. A compass can be used to map out the magnetic field. Field forms closed “flux lines” around the magnet (lines of magnetic flux never intersect) 6 Introduction to Magnetism

7. Magnetic field The strength of the magnetic field is greater where the lines are closer together and weaker where they are farther apart. Field is strongest in regions of dense field lines. Field is weakest in regions of sparse field lines. Strong Field Weak Field The density of field lines indicates the strength of the field 7 Introduction to Magnetism

8. Magnetism Magnetism is a basic force of attraction and repulsion in nature that is created, by moving charges. A magnet is an object, which has a magnetic field that causes a push or pulling action. Similar to electric charges, unlike poles attract, while like poles repel 8 Introduction to Magnetism

9. Magnetism Magnetism is a basic force of attraction and repulsion in nature that is created, by moving charges. A magnet is an object, which has a magnetic field that causes a push or pulling action. Similar to electric charges, unlike poles attract, while like poles repel 9 Introduction to Magnetism

10. Magnetic flux Magnetic flux is measurement of the quantity of magnetism, the description of how certain materials relate to magnetic fields. Specifically, it describes the strength and extent of the object's interaction with the field. Magnetic lines of force (flux) are assumed to be continuous loops. Magnetic flux measured in Webers (Wb) Symbol 10 Introduction to Magnetism

11. Magnetism Magnetism can be transferred or induced into other materials, this is known as Magnetic Induction The induction of magnetism into a material can be permanent or temporary 11 Introduction to Magnetism

12. Magnetism Magnetic materials (ferromagnetic): iron, steel, cobalt, nickel and some of their alloys. Non magnetic materials: water, wood, air, quartz. In an un-magnetised state, the molecular magnets lie in random manner, hence there is no resultant external magnetism exhibited by the iron bar. wood Non-magnetic molecules Iron bar Magnetic molecules 12

13. Introduction to Magnetism Magnetism When the iron bar is placed in a magnetic field or under the influence of a magnetising force, then these molecular magnets start turning their axes and orientate themselves more or less along a straight lines. Iron bar Magnetic molecules S N SN 13

14. Introduction to Magnetism Magnetism When the iron bar is placed in a very strong magnetic field, all these molecular magnets orientate themselves along a straight lines (saturated). Iron bar Magnetic molecules S N N S 14

15. Introduction to Electromagnetism A simple electromagnet can be made by coiling some wire around a steel nail, and connecting a battery to it. A magnetic field is produced when an electric current flows through a coil of wire. We can make an electromagnet stronger by doing these things: wrapping the coil around an iron core adding more turns to the coil increasing the current flowing through the coil. 15

16. Introduction to Electromagnetism Using Electromagnets Many objects around you contain electromagnets They are found in electric motors and loudspeakers Very large and powerful electromagnets are used as lifting magnets in scrap yards to pick up, then drop, old cars and other scrap iron and steel They are better than magnets because the magnetism can be turned off and on 16

17. Introduction to Electromagnetism A moving electric field creates a magnetic field that rotates around it A moving magnetic field creates an electric field that rotates around it The Right Hand Rule helps describe this 17

18. The Right Hand Rule First define positive electric current as flowing from the positive (+) end of a battery, through an electric circuit, and back into the negative (-) end. Next define a magnetic field as always pointing away from a North pole and towards a South pole. Curl your fingers in the direction of the rotating field. Current Field Lines 18

19. The Right Hand Rule Extend your thumb. It now points in the direction of the other field. If your fingers are curling along with a rotating electric field, your thumb will point in the direction of the magnetic field and vice versa. 19

20. The Right Hand Rule Wire carrying current out of page Wire carrying current into page Representing Currents X 20

21. Wire carrying current out of page Wire carrying current into page The magnetic field of two wires X 21 The Right Hand Rule

22. Wire carrying current out of page Wire carrying current into page The magnetic field of two wires X 22 The Right Hand Rule

23. Both of the wire carrying current out of page The magnetic field of two wires 23

24. The Right Hand Rule The overall field around a coil is the sum of the fields around each individual wire The magnetic field of a coil 24

25. The Right Hand Rule The magnetic field around a solenoid resembles that of a bar magnet. uniform field Inside the solenoid the field lines are parallel to one another. We say it is a uniform field. The magnetic field of a solenoid 25

26. The Electromagnetism By the Right Hand Rule, a coil of wire with current flowing in it will create a magnetic field The strength of the magnetic field depends on current The amount of current in a wire – More current means stronger magnetic field turns The number of turns in the coil – More turns means stronger magnetic field material The material in the coil – Magnetic materials like iron and steel make the magnetic field stronger In other word, the magnetic field only exists when electric current is flowing 26

27. The Electromagnetism The lines of flux, formed by current flow through the conductor, combine to produce a larger and stronger magnetic field. The center of the coil is known as the core. In this simple electromagnet the core is air. 27

28. The Electromagnetism Iron is a better conductor of flux than air. The air core of an electromagnet can be replaced by a piece of soft iron. When a piece of iron is placed in the center of the coil more lines of flux can flow and the magnetic field is strengthened. 28

29. The Electromagnetism Notice that a carrying-current coil of wire will produce a perpendicular field Magnetic field - wire coil 29

30. The Electromagnetism Magnetic field - wire coil 30

31. Magnetic Field Flux Flux Ф can be increased by increasing the current I, I Ф I 31

32. Magnetic Field Flux Flux Ф can be increased by increasing the number of turns N, I Ф N N 32

33. Magnetic Field Flux Flux Ф can be increased by increasing the cross-section area of coil A, I Ф A N A 33

34. Magnetic Field Flux Flux Ф can be increased by increasing the cross-section area of coil A, I Ф A N A 34

35. Magnetic Field Flux Flux Ф is decreased by increasing the length of coil l, I Ф N A 1 l l 35

36. Magnetic Field Flux Therefore we can write an equation for flux Ф as, I Ф N A NIA l l hence Ф = μ 0 NIA l 36

37. Where μ 0 is vacuum or non-magnetic material permeability μ 0 = 4π x 10 -7 H/m Magnetic Field Flux Ф = μ 0 NIA l 37

38. Magnetic Field: Coil ferrous Placing a ferrous material inside the coil increases the magnetic field Acts to concentrate the field also notice field lines are parallel inside ferrous element ‘flux density’ has increased 38

39. Magnetic Field Flux By placing a magnetic material inside the coil, I N A l Ф = μ NIA l Where μ is the permeability of the magnetic material (core). 39

40. Magnetic Field Flux By placing a magnetic material inside the coil, I N A l Ф = μ NIA l Where μ is the permeability of the magnetic material (core). 40

41. Flux Density 41 Flux Density – The amount of magnetic field flux concentrated in a given area.

42. Permeability Permeability μ is a measure of the ease by which a magnetic flux can pass through a material (Wb/Am) Permeability of free space μ o = 4π x 10 -7 (Wb/Am) Relative permeability: 42

43. Reluctance Reluctance: “resistance” to flow of magnetic flux Reluctance – The opposition to magnetic field flux through a given volume of space or material. Analogous to electrical resistance Associated with “magnetic circuit” – flux equivalent to current 43 ie: Ampere-turns per Weber

44. Relationship between B-H The magnetic field intensity, H produces a magnetic flux density, B everywhere it exists. - Permeability of the medium - Permeability of free space, - Relative permeability of the medium For free space or electrical conductor (Al or Cu) or insulators, is unity 44 The H-field is defined as a modification of B due to magnetic fields produced by material media

45. The relationship between current and magnetic field intensity can be obtained by using Ampere’s Law. Ampere’s Law Ampere’s Law states that the line integral of the magnetic field intensity(or Magnetizing Force), H around a closed path is equal to the total current linked by the contour. H: the magnetic field intensity at a point on the contour dl: the incremental length at that point If θ : the angle between vectors H and dl then 45

46. Ampere’s Law 1 2 3 Consider a rectangular core with N winding Therefore 46 H - magnetic field intensity

47. Assumption: 1. All fluxes are confined to the core 2. The fluxes are uniformly distributed in the core Magnetic Equivalent Circuit The flux outside the toroid (called leakage flux), is so small (can be neglected) Use Ampere’s Law, 47 The amount of magnetic field force generated by a coiled wire is proportional to the current through the wire multiplied by the number of ”turns” or ”wraps” of wire in the coil. This field force is called magnetomotive force (mmf) = ∑ i By means of defn: ampere-turns in magnetic circuit is refered as mmf i can be Ni, where there are N conductors carrying current i, N can also means N turns of conductors

48. Magnetic Equivalent Circuit Where; N – no of turns of coil i – current in the coil H – magnetic field intensity l – mean length of the core 48 H- Magnetic Field Intensity: The amount of field force (mmf) distributed over the length of the electromagnet. Sometimes referred to as Magnetizing Force. B - Magnetic Flux Density – The amount of magnetic field flux concentrated in a given area

49. Magnetomotive Force, F Coil generates magnetic field in ferrous torroid Driving force F needed to overcome torroid reluctance Magnetic equivalent of ohms law Circuit Analogy 49

50. Magnetomotive Force The MMF is generated by the coil Strength related to number of turns and current, measured in Ampere turns (At) 50

51. Field Intensity longermagnetic path The longer the magnetic path the greater the MMF required to drive the flux magnetizing force” H Magnetomotive force per unit length is known as the “magnetizing force” H Magnetizing force and flux density related by: 51

52. Magnetomotive Force Electric circuit: Emf = V = I x R Magnetic circuit: mmf = F = Φ x = (B x A) x l μAμA l μ = B x= H x l 52

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55. = Φ x l μ A = 0.16 1.818 x 10 -3 x 2 x 10 -3 = = 44004.4 55

56. = Φ x = 4 x 10 -4 x 44004.4 = 17.6 I = F N = 17.6 400 = 44 mA 56

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59. Circuit Analogy 59

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63. Fleming’s Left Hand Rule 63

64. Force on a current-carrying conductor N S It is found that whenever a current-carrying conductor is placed in a magnetic field, it experiences a force which acts in a direction perpendicular both to the direction of the current and the field. 64

65. Force on a current-carrying conductor N S It is found that whenever a current-carrying conductor is placed in a magnetic field, it experiences a force which acts in a direction perpendicular both to the direction of the current and the field. 65

66. N S Force on a current-carrying conductor It is found that whenever a current-carrying conductor is placed in a magnetic field, it experiences a force which acts in a direction perpendicular both to the direction of the current and the field. 66

67. N S On the left hand side, the two fields in the same direction On the right hand side, the two fields in the opposition Force on a current-carrying conductor It is found that whenever a current-carrying conductor is placed in a magnetic field, it experiences a force which acts in a direction perpendicular both to the direction of the current and the field. 67

68. N S On the left hand side, the two fields in the same direction On the right hand side, the two fields in the opposition Force on a current-carrying conductor Hence, the combined effect is to strengthen the magnetic field on the left hand side and weaken it on the right hand side, 68

69. N S On the left hand side, the two fields in the same direction On the right hand side, the two fields in the opposition Force on a current-carrying conductor Hence, the combined effect is to strengthen the magnetic field on the left hand side and weaken it on the right hand side, thus giving the distribution shown below. 69

70. N S On the left hand side, the two fields in the same direction On the right hand side, the two fields in the opposition F This distorted flux acts like stretched elastic cords bend out of the straight, the line of the flux try to return to the shortest paths, thereby exerting a force F urging the conductor out of the way. Force on a current-carrying conductor 70

71. Faraday’s Law First Law Whenever the magnetic flux linked with a coil changes, an emf (voltage) is always induced in it. Or Whenever a conductor cuts magnetic flux, an emf (voltage) is induced in that conductor. 71

72. Faraday’s Law Second Law The magnitude of the induced emf (voltage) is equal to the rate of change of flux-linkages. where  a b If a magnetic flux, , in a coil is changing in time (n turns), hence a voltage, e ab is induced e = induced voltage N = no of turns in coil d  = change of flux in coil dt = time interval 72

73. Voltage Induced from a time changing magnetic field 73

74. Lenz’s Law Lenz’s Law the polarity of the induced voltage produce a current that opposes the change in flux linkages Lenz’s law states that the polarity of the induced voltage is such that the voltage would produce a current that opposes the change in flux linkages responsible for inducing that emf. If the loop is closed, a connected to b, the current would flow in the direction to produce the flux inside the coil opposing the original flux change. The direction (polarity) of induced emf (voltage) can be determined by applying Lenz’s Law. Lenz’s law is equivalent to Newton’s law. 74

75. N S I Lenz’s Law Lenz’s Law 75

76. Self Inductance, L i e Φ From Faraday’s Law: By substituting Ф = μ NIA l v 76

77. Self Inductance, L i Φ Rearrange the equation, yield v e 77

78. Self Inductance, L i Φ or where v e 78

79. Magnetic saturation & hysteresis in ac magnetic field Iron becomes magnetically saturated Magnetism increase as magnetic field magnetized unmagnetized iron a b c d Applied field is reduced; the magnetism reduced thru diff. curve since iron tends to retains magnetized state - hence produced permanent magnet, Residual Flux,  res AC increased in negative direction, magnetic field reversed, the iron reversely magnetized until saturated again If continue apply ac current, curve continue to follow S-shaped curve (hysteresis curve) The area enclosed by hysteresis curve is energy loss per unit volume per cycle – heats the iron and is one reason why electric machines become hot. Therefore, it is required to select magnetic materials that have a narrow hysteresis loop. HmHm Magnetic field density BmBm 79

80. Eddy Current Loss Eddy current Along the closed path, apply Faraday's law where A is the closed area Changes in B → = BA changes → induce emf along the closed path → produce circulating circuit (eddy current) in the core Eddy current loss where R is the equivalent resistance along the closed path 80

81. Eddy Current Loss How to reduce Eddy current loss i) Use high resistivity core material e.g. silicon steel, ferrite core (semiconductor) ii) Use laminated core To decrease the area closed by closed path Lamination thickness 0.5~5mm for machines, transformers at line frequency 0.01~0.5mm for high frequency devices 81

82. Inside a Toy Motor (Similar to TekBot Motor)

83. Toy DC Motor, cont. End Views of Motor – Axle – Battery Leads Axle will turn if connect battery leads to a 9V battery Reverse battery leads and axle will turn the Opposite direction! The white nylon cap on the motor can be removed to reveal…

84. A View of the Brushes Inside the Nylon cap are the Brushes Brushes can be made of various types of metal. Their purpose is to transfer power to the commutator as it spins.

85. Inside the Motor, cont. The Axle is the rotating part of the motor that holds the armature and commutator. This armature is comprised of 3 electromagnets. (3-Pole DC Motor) Each electromagnet is a set of stacked metal plates with thin copper wire wound around each. The two ends of each coil wire is terminated and wired to a contact on the commutator. Thus, there are 3 commutator contacts in all.

86. Inside the Motor, cont. The final piece is the stator, a permanent field magnet. It is formed by the motor enclosure and two curved permanent magnets (2 Pole: 1 North, 1 South) shown.

87. How Does a Permanent Magnet DC Motor Work? "DC Motors" use magnets to produce motion – Permanent magnets NORTHSOUTH

88. "DC Motors" use magnets to produce motion – Permanent magnets – An electromagnet armature How Does a Permanent Magnet DC Motor Work? NORTHSOUTH

89. NORTHSOUTH Electromagnet armature is mounted on axle so that it can rotate Permanent Magnet DC Motor Rotating Armature

90. NORTHSOUTH Electromagnet armature is mounted on axle so that it can rotate A commutator makes an electrical contact with the motor's brushes Permanent Magnet DC Motor Commutator and Brushes

91. Permanent Magnet DC Motor Commutator Structure Commutator is comprised of two "near- halves" of a ring

92. Mounted on the armature's axle to rotate with the rotor Armature Permanent Magnet DC Motor Commutator Structure

93. Armature's windings are connected to the commutator

94. Permanent Magnet DC Motor Commutator and Brushes Armature's windings are connected to the commutator Brushes connect the commutator to the battery

95. NORTHSOUTH Current flows through the armature's windings, which polarizes the electromagnet + - Permanent Magnet DC Motor Electromagnet Polarization

96. NORTHSOUTH The like magnets (NORTH-NORTH and SOUTH-SOUTH) repel As the like magnets repel, the armature rotates, creating mechanical motion + - Permanent Magnet DC Motor Rotation

97. NORTHSOUTH What direction will the armature spin? Clockwise? Counterclockwise? Clockwise ? Counterclockwise ? Permanent Magnet DC Motor Rotation Direction? + -

98. To determine the direction of the motor's rotation, we need to use the "Left Hand Rule" Permanent Magnet DC Motor Rotation Direction? Magnetic Field Current Force

99. Left Hand Rule Start with two opposite ends of a magnet NORTH SOUTH

100. Left Hand Rule: Magnetic Field NORTH SOUTH The magnetic field (B) is from the NORTH pole to the opposite SOUTH pole The pointing finger follows B into screen B

101. Left Hand Rule: Current Flow NORTH SOUTH Current flows in a wire through the magnetic field from left to right The middle finger follows I 1 right, or I 2 left I1I1 I2I2

102. Left Hand Rule: Force NORTH SOUTH The force, F, acting on each wire is in the direction of the thumb The wire with I 1 is pushed up, I 2 down I1I1 I2I2 F1F1 F2F2

103. Left Hand Rule: Force NORTH SOUTH The magnitude of F is give by: | F | = | I | * * | B | where is the length of the wire in B I1I1 I2I2 F1F1 F2F2

104. Left Hand Rule: Current Loop NORTH SOUTH If the current flows in a loop, the force(s) will cause the loop to rotate I F F

105. NORTHSOUTH Magnetic field is from right to left Imagine current flows out of the screen in this cross section + - Permanent Magnet DC Motor Rotation

106. NORTHSOUTH Magnetic field is from right to left Imagine current flows out of the screen in this cross section The force causes the armature to rotate clockwise + - Permanent Magnet DC Motor Rotation

107. NORTHSOUTH + - Permanent Magnet DC Motor Rotation At some point, the commutator halves will rotate away from the brushes Momentum keeps the electromagnet and the commutator ring rotating

108. NORTHSOUTH + - Permanent Magnet DC Motor Rotation When the commutator halves reconnect with the other brush, the current in the windings is reversed

109. NORTHSOUTH + - Permanent Magnet DC Motor Rotation When the commutator halves reconnect with the other brush, the current in the windings is reversed The polarity is reversed and the armature continues to rotate + -

110. NORTHSOUTH Magnetic field is from right to left Imagine current flows out of the screen in this cross section The force causes the armature to rotate clockwise + - Permanent Magnet DC Motor Rotation