ELECTROMAGNETISM – PART – 08 – EDDY CURRENT LOSS

French physicist Léon Foucault discovered eddy currents in September 1855. Eddy current are those which are produced or induced in the masses of metals, whenever these metals are moved in the magnetic field, or the magnetic field moves through the metals. The direction of the eddy currents is always in the direction opposite to the cause (motion) producing them.

An eddy current (also called Foucault currents) is a swirl (like a whirlpool) of current that is induced in a solid conducting mass. The eddy currents are usually of small intensity but may be enormous. They always incur power loss i.e. I^2 R loss, which causes the output of the machine to decrease.

When AC current flows in a conductor, the resistance offered to the conductor is somewhat greater than the resistance that would be offered to dc current by the same conductor. The reasons for the increase in resistance, are due to the fact that when an AC current flows in a conductor, it causes voltages to be set up inside of the conductor. The voltage set up in the conductor cause small independent currents, called eddy currents. The eddy currents flowing through the resistance of the conductor consume power and therefore represent a power loss, or an increase in resistance, in the circuit.

TRANSFORMER

The transformer core is a conductor. The changing magnetic flux in the core of a transformer induces a voltage into any conductors which surround it and also in the core.

The voltage induced in the core causes the current to circulate in the core. This current is called eddy current. The eddy current flowing through the resistance of the core produce heat.

The amount of heat due to eddy current is dependent on

(a) Eddy current and (b) induced voltage.

1. Each lamination of the transformer core is insulated within a layer of oxide.

2. The oxide has much higher resistance than the rest of the silicon steel lamination.

3. The eddy current would have to flow through the oxide layers in order to circulate through the core.

4. The high resistance of the oxide on each lamination effectively reduces the flow of eddy current.

5. Thus laminating the core reduces the eddy current and its associated heat loss.

FORMULA FOR EDDY CURRENT LOSS

It is difficult to determine the magnitude of eddy current and actual resistance values directly.

Eddy current losses are caused by induced electric currents, called eddies since they tend to flow in closed paths within

the magnetic material itself.

The eddy current loss is sinusoidally excited material, neglecting saturation can be expressed by the relationship.

Eddy current loss = Pe = Ke Bm^2 t^2 f^2 V   watts

Ke – eddy current coefficient and its value depends upon the

nature of the material

Bm^2 – maximum flux density in T

t^2 – thickness of lamination in m

f^2 – frequency of flux in Hz

V – volume of material in m^3.

The eddy-current loss per unit volume of a magnetic core subjected to a time-varying flux is given by

Eddy current loss = Pe = [1.645/ρ] t^2 f^2 Bm^2 watts / m^3      

ρ = resistivity of the material.

METHODS OF MINIMIZING THE EDDY CURRENT  

Laminated core means the core is made of a number of thin sheets, called laminations. The sheets are painted (varnished) to provide insulation between them.

Eddy currents always tend to flow at right angles to the direction of the flux; if the resistance of the path is increased by laminating the cores etc., the power loss can be reduced because the eddy current loss varies as the square of the thickness of the laminations.

The lamination thickness varies from 0.5 to 5 mm in electrical machines and from 0.01 to 0.5 mm in devices used in electronics circuits operating at higher frequencies.

At radio frequencies, the eddy current loss is very high because the loss is proportional to the square of the frequency. Granulated or powdered-iron cores are used to make radio frequency transformers.

The main drawback of laminated core is that the total cross-sectional area of the magnetic material is reduced by the total thickness of the insulation.

This is generally taken into account by allowing about 10% reduction in the thickness of core when making the magnetic calculations.

STACKING FACTOR

It is defined as the ratio of the effective area to the overall area.
Ks = effective area / overall area

It is also defined as the ratio of the volume occupied by the magnetic material to the total volume of the core.

Ks = volume occupied by magnetic material / total volume of the core.

The stacking factor is important in calculating flux densities in magnetic parts. It is usually less than 1.0. It approaches 1.0 as the lamination thickness increases.

In powdered iron and ferrite magnetic parts, there is an equivalent staking factor that is approximately equal to the ratio of the volume of the magnetic particles to overall volume.

STACKING FACTOR FOR LAMINATED CORES

Laminated Thickness (mm)                    Staking Factor

0.0127                                                              0.50

0.0254                                                              0.75

0.0508                                                              0.85

0.1 – 0.25                                                          0.90

0.27 – 0.36                                                        0.95

APPLICATIONS OF EDDY CURRENTS

1. Eddy current heating is used for heating metals; for examples melting, hardening and other heat-treatment processes.

2. Eddy current damping is used in permanent magnet moving coil instruments.

3. Eddy current braking is used in induction energy meters.

ELECTROMAGNETISM – PART – 07 – HYSTERESIS LOSS

Magnetic domain - This means that the individual magnetic moments of the atoms are aligned with one another and they point in the same direction.

Magnetic moment - The property of a magnet that interacts with an applied field to give a mechanical moment.

Molecular magnet – A molecule having a non-vanishing magnetic dipole moment, whether it is permanent or produced by an external field.

Magnetic dipole moment – The magnetic moment of a magnet is a quantity that determines the torque it will experience in an external magnetic field. Magnetic moment normally refers to a system's magnetic dipole moment, which produces the first term in the multipole expansion of a general magnetic field.

Molecular friction – The opposition offered by the magnetic domains to the turning effect of the magnetizing force is sometimes referred to as the molecular friction. 

In order to set up the magnetic field certain, amount of energy has to be supplied which is stored in the field. If the field is in a magnetic field, not all energy supplied can be returned; part of it having been converted into heat due to the hysteresis effect.

HYSTERESIS LOSS

# When a magnetic material is magnetized, its domains are aligned in the same direction. If the material is magnetized in reverse direction, there is a cyclic variation of the applied field, the domains rotate to and fro, which creates the loss of power called hysteresis loss. [OR]

# If the material is magnetized in one direction and then in other an energy loss takes place due to the molecular friction in the material. The material resists being turned first in one direction and then in other. Energy is thus expanded in the material to overcoming this opposition. In this process, there is a loss. This loss appears in the form of heat and raises the temperature of the magnetic material.

Area of the hysteresis loop is proportional to the hysteresis loss.  

Hysteresis loss cannot be avoided but can be minimized by selecting proper materials.

The following table gives the hysteresis constants.

METALS                                   CONSTANT

Silicon Steel                             0.001

Thin sheet iron                        0.003

Wrought iron                            0.004

Soft annealed cast steel           0.008

Soft machine steel                   0.009

Cast steel                                 0.012

Cast iron                                  0.016

Lesser the hysteresis constant, better the metal for A.C. electromagnet. So usually the silicon steel is used for a.c machines.

The B-H curve is nonlinear and multivalued and no simple mathematical expression can describe the loop.

Charles Steinmetz, an electrical engineer of USA, carried out the investigation into hysteresis loss of a number of specimens of different materials and found that hysteresis loss can be expressed as Hysteresis loss = K_h v f (B_max)^1.6 watts.

Where k_h is a constant for a given specimen, v is the volume of the core in m^3, f is the frequency and B_max is the maximum flux density in Tesla.

The index 1.6 is an empirical value and does not have any theoretical basis. The index value can vary in the range 1.5 to 2.5.

ELECTROMAGNETISM – PART – 06 - IMPORTANCE AND FACTORS AFFECTING HYSTERESIS LOOP

FERRITE

Magnetic materials are classified as

(i) Ferromagnetic material and (ii) Ferrimagnetic material.

Ferromagnetic material – Iron and its various alloys

Hard ferromagnetic material – permanent magnetic materials such as alnicos, chrome steels, certain copper-nickel alloys

Ferrimagnetic materials – mixed oxides of iron and other metals.

The oxide mixture is sintered i.e. heated to a steady temperature of 1300 degree centigrade which is maintained for several hours. The material is known as ‘ferrite’ is chemically homogenous and extremely hard.

Ferrite has typically maximum flux density of 0.3 to 05 T, as compared to 2.18 T for pure iron.

HYSTERESIS

The word hysteresis means lagging behind. The curve gets its name from the fact that the flux density (B) lags behind the magnetic flux intensity (H). B is the cause -  H is the effect.

The lagging flux density (B) behind the magnetizing force (H) in a magnetic material subjected to cycles of magnetization is known as magnetic hysteresis. 

HYSTERESIS LOOP

When a magnetic material is subjected to one cycle of magnetization, B always lags behind H so that the resultant B-H curve forms a closed loop, called hysteresis loop.

B-H CURVE

1. The dotted curve passing through tips of the hysteresis loops is the normal magnetization curve or B-H curve of the material.

2. In a B-H curve, the value flux density (B) at H is equal to zero is known as the residual flux density (B_r). [OR] When a field strength is reduced to zero the core is not completely demagnetized. There still remains a certain flux, called remanent flux density or residual flux density.

3. This remaining flux density in the core when H fell from the saturation value H to zero is called remanence of the core material.

4. The value of H to reduce flux density B_r to zero is called coercive force H_C.

5. The maximum possible value of residual flux (B_r) corresponding to deep saturation is known as RETENTIVITY and the maximum value of Ho is the COERCIVITY.  

FACTORS AFFECTING THE SIZE AND SHAPE OF THE HYSTERESIS LOOP

1. If the material is easily magnetized, the loop will be narrow.

2. If the material does not get magnetized easily, the loop will be wide.

3. Different materials will saturate at different values ‘B’ thus affecting the height of the loop.

4. The size and shape of the hysterias loop depend upon the nature of the material.

5. The size and shape of the loop also depend upon the initial state of the specimen.

IMPORTANCE OF HYSTERESIS LOOP  

1. Silicon steel has less hysteresis loop area. Due to less area, the hysteresis loss is less. Hence, it is widely used for making transformer cores and rotating machines.

2. Hard steel is large hysteresis loop area hence which has high retentivity and coercivity. Due to the large area of the loop, there is greater hysteresis loss. Hence, it is suitable for making permanent magnets.

3. Wrought iron has fairly good residual magnetism and coercivity. Hence, it is suitable for making cores of electromagnets.

4. Ferrite material is known as magnetic ceramic has square hysteresis loop. Hence it is suitable for switching circuits, as storage elements in computers, and in a special type of transformers in electronic circuits.

5. The magnetization curves for different ferromagnetic materials are shown in the figure. For economic reasons, magnetic circuits are designed with magnetic materials in a slightly saturated state. 

ELECTROMAGNETISM – PART – 05 – COMPARSION BETWEEN ELECTRIC AND MAGNETIC CIRCUITS

SOLENOID

Solenoid is a Greek work meaning ‘tube like’. A long coil of wire consisting of closely packed loops is called solenoid.

The length of the solenoid is very large as compared to its diameter.

FUNCTION OF AIRGAP

1. To prevent magnetic saturation of the magnetic circuit.

2. To allow an object to move in the magnetic field.

KIRCHHOFF’S LAWS

The sum of the fluxes entering a junction in a magnetic circuit is equal to the sum of the fluxes leaving the junction (KCL).

In a closed path of a magnetic circuit, the algebraic sum of MMFs required to force the flux through the elements must be equal to the net ampere turns of excitation (KVL).

SERIES MAGNETIC CIRCUIT

In a series magnetic circuit, the same flux flows through each part of the circuit.

PARALLEL CIRCUIT

A magnetic circuit which has more than one path for flux is called a parallel magnetic circuit. 

ELECTRIC WELDING PART – 10 – CARBON ARC WELDING

Carbon Arc Welding (CAW) is a process which produces coalescence of metals by heating them with an arc between a non-consumable carbon (graphite) electrode and the work-piece. 

Carbon arc welding is one of the oldest welding techniques that are still in use today. DC power supply is used in this welding process. It is essential that the welding circuit is set-up for straight polarity. If a reversed-polarity setting is used, the arc will not be stable and a carbon residue will be left to become entrapped in the weld.

PRINCIPLE

In carbon arc welding, the intense of the heat of an electric arc developed between a carbon electrode and work-piece metal is used for welding.

The carbon electrode is connected to the negative terminal and work-piece is connected to the positive terminal, because the positive terminal is hotter (4000°c) than the negative terminal (3000°c) when an arc is produced. 

The process of carbon arc welding uses low voltage, high amp electricity to heat the metal once an arc is formed between a carbon electrode and the piece being welded; if an arc is formed between two carbon electrodes that technique is known as a twin-carbon arc.

PROCESS

1. In this method, an electric arc is produced between the carbon electrode and the ‘work’. A rod of carbon is used as negative (-) pole and the ‘work’ being welded as positive (+) pole.

2. The carbon electrode does not melt itself. It is a non-consumable electrode.

3. The electrodes that are used in carbon arc welding consisted of baked carbon or pure graphite which was placed inside a copper jacket. 

4. During the welding process, the electrode is not consumed as the weld progresses; overtime, however, the electrodes will need to be replaced due to erosion. 

5. A filler rod is used separately at the welding joint.  The arc is established between the work-piece and a carbon electrode held in the electrode holder.

6. A long carbon arc is often desirable in order to prevent contamination of the weld metal with the carbon monoxide given, off by the carbon electrode under the energy of the arc.

7. In the carbon arc welding of light-gauge plates, the use of filler rod may not be necessary. But in welding of heavy plates of filler rod consisting of the same material as the base metal is generally used.

8. The filler rod is then inserted in the pool, the arc being directed against it just above the surface of the molten metal.

9. The end of the rod is thus melted off and deposited in the pool. The arc is played to and fro in the pool, thoroughly melting and mixing with the metal. No filler rod is necessary to make a lap weld on light-gauge metal with a carbon electrode.

10. The amount of fusion will depend upon the speed with which the arc is moved over the surface. For less fusion, the current should be increased and the electrode advanced at a faster rate. 

ADVANTAGES

1. Low cost of equipment and welding operation

2. Skilled operator is not required;

3. The process can be easily automated

4. Low distortion of the work-piece.

DISADVANTAGES

1. Unstable quality of the weld produces porosity

2. Carbon of electrode contaminates weld material with carbides.

3. This welding process develops extremely bright light.  This bright light can be dangerous for the welder if they are not wearing the proper eye protection and clothing.

APPLICATIONS

This process is used for welding both ferrous and non-ferrous metals like steel sheet, Brass, Bronze, Gunmetal, M/S-sheet, carbon-steel etc.