Cadiang, Kathrine Kate F.

2011-10143

1. What is Eddy Current?

Eddy currents (also called Foucault currents) are circular electric currents induced within conductors by a changing magnetic field in the conductor, due to Faraday's law of induction. Eddy currents flow in closed loops within conductors, in planes perpendicular to the magnetic field. They can be induced within nearby stationary conductors by a time-varying magnetic field created by an AC electromagnet or transformer, for example, or by relative motion between a magnet and a nearby conductor. The magnitude of the current in a given loop is proportional to the strength of the magnetic field, the area of the loop, and the rate of change of flux, and inversely proportional to the resistivity of the material.

By Lenz's law, an eddy current creates a magnetic field that opposes the magnetic field that created it, and thus eddy currents react back on the source of the magnetic field. For example, a nearby conductive surface will exert a drag force on a moving magnet that opposes its motion, due to eddy currents induced in the surface by the moving magnetic field. This effect is employed in eddy current brakes which are used to stop rotating power tools quickly when they are turned off. The current flowing through the resistance of the conductor also dissipates energy as heat in the material. Thus eddy currents are a source of energy loss in alternating current (AC)inductors, transformers, electric motors and generators, and other AC machinery, requiring special construction such as laminated magnetic cores to minimize them. Eddy currents are also used to heat objects in induction heating furnaces and equipment, and to detect cracks and flaws in metal parts using eddy-current testing instruments.

Explanation[edit]

Eddy currents (I, red) induced in a conductive metal plate (C) as it moves to right under a magnet (N). The magnetic

field (B, green) is directed down through the plate. The increasing field at the leading edge of the magnet (left)induces

a counterclockwise current, which by Lenz's lawcreates its own magnetic field (left blue arrow) directed up, which

opposes the magnet's field, producing a retarding force. Similarly, at the trailing edge of the magnet (right), a

clockwise current and downward counterfield is created(right blue arrow) also producing a retarding force.

Eddy current brake.

Eddy currents in conductors of non-zero resistivity generate heat as well as electromagnetic forces. The heat can be used for induction heating. The electromagnetic forces can be used for levitation, creating movement, or to give a strongbraking effect. Eddy currents can also have undesirable effects, for instance power loss in transformers. In this application, they are minimized with thin plates, by lamination of conductors or other details of conductor shape.

Self-induced eddy currents are responsible for the skin effect in conductors.[3] The latter can be used for non-destructive testing of materials for geometry features, like micro-cracks. [4] A similar effect is the proximity effect, which is caused by externally induced eddy currents.[5]

When a conductor moves through an inhomogeneous field generated by a source, electromotive forces (EMFs) can be generated around loops within the conductor. These EMFs acting on the resistivity of the material generate a current around the loop, in accordance with Faraday's law of

induction. These currents dissipate energy, and create a magnetic field that tends to oppose changes in the current- they have inductance.

Eddy currents are created when a conductor experiences changes in the magnetic field. If either the conductor is moving through a steady magnetic field, or the magnetic field is changing around a stationary conductor, eddy currents will occur in the conductor. Both effects are present when a conductor moves through a varying magnetic field, as is the case at the top and bottom edges of the magnetized region shown in the diagram. Eddy currents will be generated wherever a conducting object experiences a change in the intensity or direction of the magnetic field at any point within it, and not just at the boundaries.

The swirling current set up in the conductor is due to electrons experiencing a Lorentz force that is perpendicular to their motion. Hence, they veer to their right, or left, depending on the direction of the applied field and whether the strength of the field is increasing or declining. The resistivity of the conductor acts to damp the amplitude of the eddy currents, as well as straighten their paths. Lenz's law states that the current swirls in such a way as to create an induced magnetic field that opposes the phenomenon that created it. In the case of a varying applied field, the induced field will always be in the opposite direction to that applied. The same will be true when a varying external field is increasing in strength. However, when a varying field is falling in strength, the induced field will be in the same direction as that originally applied, in order to oppose the decline.

An object or part of an object experiences steady field intensity and direction where there is still relative motion of the field and the object (for example in the center of the field in the diagram), or unsteady fields where the currents cannot circulate due to the geometry of the conductor. In these situations charges collect on or within the object and these charges then produce static electric potentials that oppose any further current. Currents may be initially associated with the creation of static potentials, but these may be transitory and small.

(left) Eddy currents (I, red) within a solid iron transformer core. (right) Making the core of laminations parallel to the

field (B, green) with insulation between them reduces the eddy currents. Although the field and currents are shown in

one direction, they actually reverse direction with the alternating current in the transformer winding.

Eddy currents generate resistive losses that transform some forms of energy, such as kinetic energy, into heat. This Joule heating reduces efficiency of iron-core transformers and electric motors and other devices that use changing magnetic fields. Eddy currents are minimized in these

devices by selecting magnetic core materials that have low electrical conductivity (e.g., ferrites) or by using thin sheets of magnetic material, known as laminations. Electrons cannot cross the insulating gap between the laminations and so are unable to circulate on wide arcs. Charges gather at the lamination boundaries, in a process analogous to the Hall effect, producing electric fields that oppose any further accumulation of charge and hence suppressing the eddy currents. The shorter the distance between adjacent laminations (i.e., the greater the number of laminations per unit area, perpendicular to the applied field), the greater the suppression of eddy currents.

The conversion of input energy to heat is not always undesirable, however, as there are some practical applications. One is in the brakes of some trains known as eddy current brakes. During braking, the metal wheels are exposed to a magnetic field from an electromagnet, generating eddy currents in the wheels. The eddy currents meet resistance as charges flow through the metal, thus dissipating energy as heat, and this acts to slow the wheels down. The faster the wheels are spinning, the stronger the effect, meaning that as the train slows the braking force is reduced, producing a smooth stopping motion.Induction heating makes use of eddy currents to provide heating of metal objects.

Power dissipation of eddy currents[edit]

Under certain assumptions (uniform material, uniform magnetic field, no skin effect, etc.) the power lost due to eddy currents per unit mass for a thin sheet or wire can be calculated from the following equation:[6]

where

P is the power lost per unit mass (W/kg),

Bp is the peak magnetic field (T),

d is the thickness of the sheet or diameter of the wire (m),

f is the frequency (Hz),

k is a constant equal to 1 for a thin sheet and 2 for a thin wire,

ρ is the resistivity of the material (Ω m), and

D is the density of the material (kg/m3).

This equation is valid only under the so-called quasi-static conditions, where the frequency of magnetisation does not result in the skin effect; that is, the electromagnetic wave fully penetrates the material.

Skin effect[edit]Main article: Skin effect

In very fast-changing fields, the magnetic field does not penetrate completely into the interior of the material. This skin effect renders the above equation invalid. However, in any case increased frequency of the same value of field will always increase eddy currents, even with non-uniform field penetration.[citation needed]

The penetration depth for a good conductor can be calculated from the following equation:[7]

where δ is the penetration depth (m), f is the frequency (Hz), μ is the magnetic permeability of the material (H/m), and σ is the electrical conductivity of the material (S/m).

Diffusion equation[edit]

The derivation of a useful equation for modelling the effect of eddy currents in a material starts with the differential, magnetostatic form of Ampère's Law ,[8] providing an expression for the magnetizing field H surrounding a current density J:

Taking the curl on both sides of this equation and then using a common vector calculus identity for the curl of the curl results in

From Gauss's law for magnetism, ∇ · H = 0, so

Using Ohm's law, J = σE, which relates current density J to electric field E in terms of a material's conductivity σ, and assuming isotropic homogeneous conductivity, the equation can be written as

Using the differential form of Faraday's law, ∇ × E = −∂B/∂t, this gives

By definition, B = μ0(H + M), where M is the magnetization of the material and μ0 is the vacuum permeability. The diffusion equation therefore is

Applications[edit]

Electromagnetic braking[edit]Main article: Eddy current brake

Braking forces resulting from eddy

currents in a metal plate moving through

an external magnetic field

Eddy currents are used for braking; since there is no contact with a brake shoe or drum, there is no mechanical wear. However, an eddy current brake cannot provide a "holding" torque and so may be used in combination with mechanical brakes, for example, on overhead cranes. Another application is on some roller coasters, where heavy copper plates extending from the car are moved between pairs of very strong permanent magnets. Electrical resistance within the plates causes a dragging effect

analogous to friction, which dissipates the kinetic energy of the car. The same technique is used in electromagnetic brakes in railroad cars and to quickly stop the blades in power tools such as circular saws. Using electromagnets, the strength of the magnetic field can be adjusted and so the magnitude of braking effect changed.

Repulsive effects and levitation[edit]Main article: electrodynamic suspension

A cross section through a linear motor

placed above a thick aluminium slab. As

the linear induction motor's field pattern

sweeps to the left, eddy currents are left

behind in the metal and this causes the

field lines to lean.

In a varying magnetic field the induced currents exhibit diamagnetic-like repulsion effects. A conductive object will experience a repulsion force. This can lift objects against gravity, though with continual power input to replace the energy dissipated by the eddy currents. An example application is separation of aluminum cans from other metals in an eddy current

separator. Ferrous metals cling to the magnet, and aluminum (and other non-ferrous conductors) are forced away from the magnet; this can separate a waste stream into ferrous and non-ferrous scrap metal.

With a very strong handheld magnet, such as those made from neodymium, one can easily observe a very similar effect by rapidly sweeping the magnet over a coin with only a small separation. Depending on the strength of the magnet, identity of the coin, and separation between the magnet and coin, one may induce the coin to be pushed slightly ahead of the magnet – even if the coin contains no magnetic elements, such as the US penny. Another example involves dropping a strong magnet down a tube of copper[9] – the magnet falls at a dramatically slow pace.

In a perfect conductor with no resistance (a superconductor), surface eddy currents exactly cancel the field inside the conductor, so no magnetic field penetrates the conductor. Since no energy is lost in resistance, eddy currents created when a magnet is brought near the conductor persist even after the magnet is stationary, and can exactly balance the force of gravity, allowing magnetic levitation. Superconductors also exhibit a separate inherently quantum mechanical phenomenon called

the Meissner effect  in which any magnetic field lines present in the material when it becomes superconducting are expelled, thus the magnetic field in a superconductor is always zero.

Using electromagnets with electronic switching comparable to electronic speed control it is possible to generate electromagnetic fields moving in an arbitrary direction. As described in the section above about eddy current brakes, a non-ferromagnetic conductor surface tends to rest within this moving field. When however this field is moving, a vehicle can be levitated and propulsed. This is comparable to a maglev but is not bound to a rail.[10]

Attractive effects[edit]

In some geometries the overall force of eddy currents can be attractive, for example, where the flux lines are past 90 degrees to a surface, the induced currents in a nearby conductor cause a force that pushes a conductor towards an electromagnet.[11]

Identification of metals[edit]

In coin operated vending machines, eddy currents are used to detect counterfeit coins, or slugs. The coin rolls past a stationary magnet, and eddy currents slow its speed. The strength of the eddy currents, and thus the retardation, depends on the

conductivity of the coin's metal. Slugs are slowed to a different degree than genuine coins, and this is used to send them into the rejection slot.

Vibration and position sensing[edit]

Eddy currents are used in certain types of proximity sensors to observe the vibration and position of rotating shafts within their bearings. This technology was originally pioneered in the 1930s by researchers at General Electric using vacuum tube circuitry. In the late 1950s, solid-state versions were developed by Donald E. Bently at Bently Nevada Corporation. These sensors are extremely sensitive to very small displacements making them well suited to observe the minute vibrations (on the order of several thousandths of an inch) in modern turbomachinery. A typical proximity sensor used for vibration monitoring has a scale factor of 200 mV/mil. Widespread use of such sensors in turbomachinery has led to development of industry standards that prescribe their use and application. Examples of such standards are American Petroleum Institute (API) Standard 670 and ISO7919.

A Ferraris acceleration sensor, also called a Ferraris sensor, is a contactless sensor that uses eddy currents to measure relative acceleration.[12][13][14]

Structural testing[edit]

Eddy current techniques are commonly used for the nondestructive examination (NDE) and condition monitoring of a large variety of metallic structures, including heat exchangertubes, aircraft fuselage, and aircraft structural components..

Side effects[edit]

Eddy currents are the root cause of the skin effect in conductors carrying AC current.

Lamination of magnetic cores in

transformers greatly improves the

efficiency by minimising eddy currents

Similarly, in magnetic materials of finite conductivity eddy currents cause the confinement of the majority of the magnetic fields to only a couple skin depths of the surface of the material. This effect limits the flux linkage in inductors and transformers having magnetic cores.

Other applications[edit]

Metal detectors

Conductivity meters for non-magnetic metals[15][16]

Eddy current adjustable-speed drives

Eddy-current testing

Electric meters (Electromechanical Induction Meters)

Induction heating

Proximity sensor  (Displacement sensors)

Vending machines  (detection of coins)

Coating Thickness Measurements [17]

Sheet Resistance Measurement [18]

Eddy current separator  for metal separation [19]

Mechanical speedometers

Safety Hazard and defect detection applications

An eddy current is the current is induced in little swirls ("eddies") on a large conductor (picture a sheet of copper).If a large conductive metal plate is moved through a magnetic field which intersects perpendicularly to the sheet, the magnetic field will induce small "rings" of current which will actually create internal magnetic fields opposing the change. This is why a large sheet of metal swung through a strong magnetic field will stop as it starts to move through the field. All of its kinetic energy will cause a major change in the magnetic field as it enters it which will induce rings of current which will oppose the surrounding magnetic field and slow the object down. In effect, the kinetic energy will go into driving small currents inside the metal which will give off that energy as heat as they push through the metal.

If this isn't a satisfying answer, consider a simple wire loop being moved through a magnetic field. If you've learned anything about motors and/or generators, you will have probably learned that a current will be induced in this loop in a similar fashion. Likewise, a wire loop being pushed into a magnetic field will induce a current which will make it difficult to continue pushing. Likewise, it will resist being pulled out as well. An eddy current does the

same thing, but instead of being forced in the path of the loop, it is allowed to travel in the "eddy" pattern that nature provides.

To get rid of eddy currents, slits can be cut in metals so that large eddies cannot occur. This is why the metal cores of transformers are often assembled in small laminations with an insulator in between. This prevents AC energy from being lost to eddies generated within the magnetic core (which typically is also conductive because it is a metal like iron).

Now, sometimes eddy currents are a good thing. Mentioned above, eddy currents help turn kinetic energy quickly into other forms of energy. Because of this, braking systems have been created which take advantage of it. Adding a magnetic field around a spinning piece of metal will cause eddy currents in that metal to create magnetic fields which will slow the object spinning down quickly as long as the magnetic is strong enough.

Now, this can be taken one step farther and a circuit can be built which shuffles kinetic energy turned into electrical energy back into a battery. This is what many Hybrid cars do (and Dean Kamen's "Segway" not only when it is stopping but when it is going downhill). 

Uses of eddy currents

Just like in our transformer experiment, these induced eddy currents generate their own magnetic field. After all, this is an actual electrical current and any current flowing in a conductor produces a magnetic field, right? The detection and measurements of the strength of the magnetic fields produced by the eddy currents makes it possible for us to learn things about conductive materials without even contacting them. For example, the electrical conductivity of a material can be determined by the strength of the eddy currents that form. Also since cracks and other breaks in the surface of a material will prevent eddy currents from forming in that region of the surface, eddy currents can be used to detect cracks in materials. This is referred to as eddy current testing in the field of nondestructive testing (NDT). NDT technicians and engineers use eddy current testing to find cracks and other flaws in part of airplanes and other systems where bad things can happen if the part breaks. 

2. What do you mean by “plex” in armature winding?

(wala mahanap na sagot)

Armature Winding Of A DC Machine

Basically armature winding of a DC machine is wound by one of the two methods, lap winding or wave winding. The difference between these two is merely due to the end connections and commutator connections of the conductor.

Lap Winding And Wave WindingIn lap winding, the finishing end of the coil is connected to a commutator segment and starting end of the following coil.In wave winding, a conductor under one pole is connected at the back to a conductor which occupies an almost corresponding position under the next pole which is of opposite polarity.The diagram below will help you to differentiate between lap winding and wave winding.

Some definitions regarding armature winding

1. Pole pitch: It is the periphery of the armature divided by the number of poles of

the generator (ormotor). We can say that it is the number of armature conductors (or

armature slots) per pole. e.g if there are 36 conductors and 4 poles, the pole pitch is

36/4=9.

2. Coil span or coil pitch (Ys): It is the distance between two sides of a coil measured in

terms of armature conductors (or armature slots).

3. Front pitch (Yf): It is the distance in terms of  armature conductors, between  the

second conductor of one coil and the first conductor of the next coil which are

connected together at the front. 

4. Back pitch (Yb): The distance by which a coil advances on the back of the armature in

terms of armature conductor is known as back pitch of the coil.

5. Resultant pitch (Yr): It is the distance in terms of armature conductor, between the

beginning of one coil and the beginning of the next coil is called as resultant pitch of

the coil.

Winding can be done as single layer or double layer.  Winding may be simplex, duplex or multiplex, and this multiplicity affects number of parallel paths.

Link: http://www.electricaleasy.com/2012/12/armature-winding-of-dc-machine.html

Lap Winding Simplex and Duplex Lap Winding

Armature windings are mainly of two types – lap winding and wave winding. Here we are going to discuss about lap winding.Lap winding is the winding in which successive coils overlap each other. It is named "Lap" winding because it doubles or laps back with its succeeding coils.

In this winding the finishing end of one coil is connected to one commutator segment and the starting end of the next coil situated under the same pole and connected with same commutator segment. Here we can see in picture, the finishing end of coil - 1 and starting end of coil - 2 are both connected to the commutator segment - 2 and both coils are under the same magnetic pole that is N pole here.

Simplex Lap WindingA winding in which the number of parallel path between the brushes is equal to the number of poles is called simplex lap winding.

Duplex Lap WindingA winding in which the number of parallel path between the brushes is twice the number of poles is called duplex lap winding.

Some important points to remember while designing the Lap winding: If, Z = the number conductors P = number of poles YB = Back pitch YF = Front pitch YC = Commutator pitch YA = Average pole pitch YP = Pole pitch YR = Resultant pitch

Then, the back and front pitches are of opposite sign and they cannot be equal. YB = YF ± 2m m = multiplicity of the winding. m = 1 for Simplex Lap winding m = 2 for Duplex Lap winding When, YB > YF, it is called progressive winding. YB < YF , it is called retrogressive winding. Back pitch and front pitch must be odd. Resultant pitch (YR) = YB - YF = 2m YR is even because it is the difference between two odd numbers.

[math] Average\; pitch\; (Y_A) = \frac{Y_B + Y_F}{2}\; =\; polepitch\; (Y_P )\;=\;\frac{Z}{P}[/math] [math] Back\; pitch \;(Y_B)\;\approx \;\frac{Z}{P}[/math] Commutator pitch (YC) = ±m Number of parallel path in the Lap winding = mPLet us start from 1st conductor,

Back connections Front connections 1 to (1+YB)=(1+5)=6 6 to (6-YF)=(6-3)=3 3 to (3+5)=8 8 to (8-3)=5 5to (5+5)=10 10 to (10-3)=7 7 to (7+5)=12 12 t0 (12-3)=9 9 to (9+5)=14 14 to (14-3)=11 11 to (11+5))=16 16 to (16-3)=13 13 to (13+5)=18=(18-16)=2 2 to (18-3)=15 15 to (15+5)=20=(20-16)=4 4 to(20-3)=17=(17-16)=1

Advantages of Lap Winding1. This winding is necessarily required for large current application because it has more parallel paths. 2. It is suitable for low voltage and high current generators.

Disadvantages of Lap Winding1. It gives less emf compared to wave winding. This winding is required more

no. of conductors for giving the same emf, it results high winding cost. 2. It has less efficient utilization of space in the armature slots.

Link: http://www.electrical4u.com/lap-winding-simplex-and-duplex-lap-winding/

Wave Winding

Under Electrical GeneratorWave winding is one type of armature winding. In this winding the end of one coil is connected to the starting of another coil of the same polarity as that of the first coil.

In this type of winding the coil side(A-B) progressforward around the armature to another coil side and goes on successively passing through N and S pole till it returns to a conductor (A1-B1) lying under the starting pole. This winding forms a wave with its coil, that’s why it is named as wave winding. It is also called series winding because its coils are connected in series.

Progressive wave winding

If after one round of the armature the coil falls in a slot right to its starting slot the winging is called Progressive wave winding.

Retrogressive wave windingIf after one round of the armature the coil falls in a slot left to its starting slot the winging is called Retrogressive wave winding.

Here in the picture above we can see that 2nd conductor CD is in the left of the 1st conductor.

Important points about Wave winding

In simplex wave winding Back pitch(YB) and front pitch (YF) are both odd and are of same sign. Back pitch and front pitch are nearly equals to the pole pitch and may be equal or differ by ±2. + for progressive winding, - for retrogressive winding.

here, Z is the no of conductors in the winding. P is the no of poles. average pitch (YA) must be an integer no. because it may close itself. ±2 is taken because after one round of the armature the winding falls sort of two conductors. If average pitch is taken Z/P then after one round the winding will close itself without including all coil sides. Since average pitch must be an integer, this winding is not possible with any no. of conductors. Let us take 8 conductors in a 4 pole machine.

Being fractional no the wave winding is no possible but if there was 6 conductors then the winding can be done. Since,

For this problem the DUMMY COILS are introduced.

Dummy CoilThe wave winding is possible only with particular number of conductors and slots combinations. It is not always possible to have the standard stampings in the winding shop consist of the number of slots according to the design requirements. In such cases dummy coils are employed. This coils are placed in the slots to give the machine the mechanical balance but they are not electrically connected to the rest of the winding.

In multiplex wave winding … m is the multiplicity of the winding. m = 1 for simplex winding m = 2 for duplex

winding.

Construction of Wave windingLet us develop a simplex and progressive wave winding diagram of a machine having 34 conductor in 17 slots and 4 poles. Average pitch:

Now we have to construct a table for the connection diagram:

Winding Diagram

Characteristics and advantage of simplex wave winding1. In this winding only two brushes are required but more parallel brushes can be

added to make it equal to the no. of poles. If one or more brushes set poor contacts with the commutator, satisfactory operation is still possible.

2. This winding gives sparkles commutation. The reason behind that it has two parallel paths irrespective of no of poles of the machine. The conductors in each of the two parallel path distributed around the armature in the entire circumference.

3. No. of conductors in each path = Z/2 , Z is the total no. of conductors.4. Generated emf = average emf induced in each path X Z/25. For a given no of poles and armature conductors it gives more emf than that of

lap winding. Hence wave winding is used in high voltage and low current machines. This winding is suitable for small generators circuit with voltage rating 500-600V.

6. Current flowing through each conductor Ia is the armature current. Current per path for this kind of winding must not be exceeded 250A.

7. Resultant emf around the entire circuit is zero.

Disadvantage of simplex wave winding

1. Wave winding cannot be used in the machines having higher current rating because it has only two parallel paths.

Link: http://www.electrical4u.com/wave-winding/

3. Nasa PDF’s!!!

4.WALA SAGOT!