Hysteresis and Eddy Current Loss

1. Hysteresis Loss

 • According to the molecular theory of magnetism groups of molecules acts like elementary magnets, which are magnetized to saturation. This magnetism is developed because of the magnetic effect of electron spins, which are known as 'domains'.

• When the material is unmagnetized, the axis of the different domains are in various direction. Thus the resultant magnetic effect is zero.

 • When the external magnetomotive force is applied the axes of the various domains are oriented. The axes coincide with the direction of the magnetomotive force. Hence the resultant of individual magnetic effects is a strong magnetic field.

• When a magnetic material is subjected to repeated cycles of magnetization and demagnetization, it results into disturbance in the alignment of the various domain. Now energy gets stored when magnetic field is established and energy is returned when field collapses. But due to hysteresis, all the energy is never returned though field completely collapses. This loss of energy appears as heat in the magnetic material. This is called as hysteresis loss. So disturbance in the alignment of the various domains causes hysteresis loss to take place. This hysteresis loss is undesirable and may cause undesirable high temperature rise due to heat produced. Due to such loss overall efficiency also reduces.

 Such hysteresis loss depends on the following factors :

1. The hysteresis loss is directly proportional to the area under the hysteresis curve i.e. area of the hysteresis loop.

2. It is directly proportional to frequency i.e. number of cycles of magnetization per second.

3. It is directly proportional to volume of the material. It can be shown that quantitatively the hysteresis loss in joules per unit volume of the material in one cycle is equal to the area of the hysteresis loop.

a. Hysteresis Loss Per Unit Volume

 • Consider a ring shaped test piece of magnetic material having length of 'l' metres, cross-sectional area of 'a' m2, wound with uniform 'N' turns of a coil.

• The hysteresis loop for the piece is obtained as in the Fig. 1.18.1.

• Consider an instant when material is magnetized to a point P. The corresponding current be I1.

H₁ = (NI₁ / 1)AT/m

Let current is increased by ∆I so there is increase in field strength by ∆H and flux density by ∆B. Due to ∆B change there is change in the flux ∆ ϕ.

∆ ϕ = ∆B × a  … (B = Flux / Area)

Now change in flux causes induced e.m.f. in coil according to Faraday's law.

e = - N (dϕ / dt) = -N (∆B × a / dt)

Supply voltage has to overcome this hence

V = -e = N (∆B × a / dt)

Power supplied

This is energy supplied within time dt.

Energy supplied for one cycle can be obtained by integrating above expression.

E = a × l × ʃ HΔB joules

Here ʃ is nothing but integration of the areas enclosed by strip H AB for one cycle i.e. the area enclosed by hysteresis loop for one cycle.

And a × l = Volume of the material.

Energy supplied during one cycle in joules = Volume × Area of the hysteresis loop

When 'H' is increased from zero to maximum, energy is supplied while when 'H' is reduced energy is recovered. But all the energy is not recovered.

So net energy absorbed by material during one cycle appears as hysteresis loss.

Energy per unit volume per cycle = Hysteresis loss per unit volume.

Hysteresis loss in joules/cycle/m³ = Area of the hysteresis loop.

Energy supplied per unit volume = Area of the hysteresis loop

If the hysteresis curve is drawn with scale as,

1 cm = x ampere-turns/metre of H and 1 cm = y teslas for B

Then the hysteresis loss can be calculated as,

Hysteresis loss/cycle/m3 = [x × y × Area of hysteresis curve in cm2]

In practice the hysteresis loss is calculated with reasonable accuracy by experimentally determined mathematical expression devised by Steinmetz, which is as follows

Hysteresis loss = K_h (Bm)^1.6 f × Volume watts

where K_h = Characteristic constant of the material

B_m = Maximum flux density and f = Frequency in cycles per second

b. Practical Use of Hysteresis Loop

• As we have seen that hysteresis loss is undesirable as it produces heat which increases temperature and also reduces the efficiency.

• In machines where the frequency of the magnetization and demagnetization cycle is more, such hysteresis loss is bound to be more.

• So selection of the magnetic material in such machines based on the hysteresis loss. Less the hysteresis loop area for the material, less is the hysteresis loss.

Key Point: So generally material with less hysteresis loop area are preferred for different machines like transformer cores, alternating current machines, telephones.

Shapes of hysteresis loops for different materials are shown in the Fig. 1.18.2.

The Fig. 1.18.2 (a) shows loop of hard steel, which is magnetic material.

The Fig. 1.18.2 (b) shows loop of cast steel.

The Fig. 1.18.2 (c) shows loop of permalloy (Alloy of nickel and iron) i.e. ferromagnetic materials.

The Fig. 1.18.2 (d) shows loop for air or non magnetic material.

 • The materials iron, nickel, cobalt and some of their alloys and compounds show a strong tendency to move from weaker to stronger portion of a non-uniform magnetic field. Such substances arecalled ferromagnetic materials.

• The hysteresis loss is proportional to the area of the hysteresis loop. For ferromagnetic materials the hysteresis loop area is less as shown in the Fig. 1.18.2 (c) thus hysteresis loss is less in such materials.

• In nonmagnetic materials, the hysteresis loop is straight line having zero area hence hysteresis loss is also zero in such materials.

2. Eddy Current Loss

• Consider a coil wound on a core. If this coil carries an alternating current i.e. current whose magnitude varies with respect to time, then flux produced by it is also of alternating nature. So core is under the influence of the changing flux and under such condition according to the Faraday's law of electromagnetic induction, e.m.f. gets induced in the core. Now if core is solid, then such induced e.m.f. circulates currents through the core. Such currents in the core which are due to induced e.m.f. in the core are called as eddy currents. Due to such currents there is power loss (12R) in the core. Such loss is called as eddy current loss. This loss, similar to hysteresis loss, reduces the efficiency. For solid core with less resistance, eddy currents are always very high.

• The Fig. 1.18.3 shows a core carrying the eddy currents. 

Eddy current loss depends on the various factors which are

i) Nature of the material ii) Maximum flux density iii) Frequency iv) Thickness of laminations used to construct to core v) Volume of magnetic material.

• It has been found that loss can be considerably reduced by selecting high resistivity magnetic material like silicon. Most popular method used to reduce eddy current loss is to use laminated construction to construct the core. Core is constructed by stacking thin pieces known as laminations as shown in the Fig. 1.18.4. The laminations are insulated from each other by thin layers of insulating material like varnish, paper, mica. This restricts the paths of eddy currents, to respective laminations only. So area through which currents flow decreases, increasing the resistance and magnitude of currents gets reduced considerably

• The loss may also be reduced by grinding the ferromagnetic material to a powder and mixing it with a binder that effectively insulates the particles one from other. This mixture is then formed under pressure into the desired shape and heat treated. Magnetic cores for use in communication equipment are frequently made by this process.                                                                                                               This loss is quantified by using the expression,

 Eddy current loss = Ke (Bm)2 f2 t2 x Volume watts

where, Ke  = A characteristic constant of material

Bm = Maximum flux density                                                                        

 f = Frequency

t = Thickness of the lamination

Ex. 1.18.1 A cylinder of iron or volume 8x 10-3 m3 revolves for 20 minutes at a speed 3000 rpm in a two pole field of flux density 0.8 Wb.m2. If the hysteresis coefficient of iron is 753.6 joule/m3, specific heat of iron is 0.11, the loss due to eddy current is equal to that due to hysteresis and 25% of the heat produced is lost by radiation, find the temperature rise of iron. Take density of iron as 7.8x 10 kg /m3. AU : May-19, Marks 13

Sol. : An armature undergoes one magnetic reversal after passing under a pair of poles. Thus in one  revolution, it undergoes P/2  number of magnetic reversals.

Review Questions

 1. Derive the expression for the hysteresis loss per unit volume. AU : Dec.-10, Marks 8

2. Explain the practical significance of hysteresis loop.

3. Explain the power losses that occur in a magnetic material when it undergoes cyclic magnetization. AU : May-11, Marks 10

4. What is eddy-current ? Explain in detail the eddy current loss. AU : May-11, Dec. 15, Marks 6

5. Specify the causes for hysteresis and eddy current losses in electrical machines. Also suggest the methods in construction to minimize the above losses. AU : May-15, Marks 8

6. Explain the losses in magnetic materials. AU : Dec.-12, May-16, Marks 16