# Hysteresis loss

1. Hysteresis loss:

• Below curie temperature (it is the rising temperature at which the given material ceases to be ferromagnetic, or the falling temperature at which it becomes ferromagnetic) all ferromagnetic materials exhibit the phenomenon called hysteresis which is defined as the lagging of magnet is at ion or induction flux density (B) behind the magnetising force (H) or it is that quality or a magnetic substance due to which energy is dissipated in it on the
reversal of its magnetism.
• Fig. 27 shows a typical hysteresis loop. It is a curve plotted between Band for various values of from a maximum value in the positive direction to maximum value in the negative direction and back again.
• Starting at zero with a coil wound round a toroid of unmagnetised iron, the magnetisation -H curve follows curve OD, If the m.m.f. is gradually reduced, the flux curve follows the line DE. As the m.m.f. is reversed the flux falls into the point L and thence to M. As the m.m.f. is returned to zero, the flux traces out the path MN. Then, as m.m.f. is again increased, curve NPD is followed; The area within the closed loop is a measure of energy lost during the cycle. This energy is, in effect, a frictional loss and shows up as heat in the material. The distance OE is a measure of the residual flux left in the closed magnetic circuit when the current is zero. It is known as Br’ the residual induction. Br
describes circuits in which there are no air gaps, e.g. the iron toroid, should not be confused with remanance, a more general term which refers to magnetic induction remaining in the magnetic circuit (usually in the air gap when one is present) after magnetising force has been removed.
• The distance OL is known as –HC, the coercive force, and is the value of the demanetising m.m.f. required to bring the residual or remanent magnetic induction to zero when such a loop is being traced out. • If a ferromagnetic substance is subjected to an alternating m.m.f., the first hysteresis loops traced out do not necessarily fall upon each other. When. successive loops retrace proceding ones, the material is said to be in a cyclically magnetised condition. For electro-magnet core materials, values of B; and – He are determined from a hysteresis loop taken when material is cyclically magnetised. Permanent magnet values, however are taken from the first hysteresis loop, since permanent magnets need be magnetised only once.
• The hysteresis loop equals the work which is necessary to/reverse the direction of magnetisation, The actual shape and area of loop depend on the internal structure and composition of the ferromagnetic substance.
• Thus work done (W) = (area of B-H loop) joules/m3/cycle.

It may be noted that while calculating the actual area, scales of B and H should be taken into consideration.

For Example, if scales are:

1 cm = x AT/m                              … for H

1 cm =y Wb/m2                            … for B

W = x.y (area of B-H loop) joules/m3/cycle.

–         Steinmetz developed an empirical relationship to express this loss in following terms.

Ph = KhfBmk                           … (14)

Ph = hysteresis loss in watt per m3 or per kg,

Bmax = maximum flux density, Wb/m2

Kh = hysteresis coefficient,

k = Steinmetz coefficient, and

f = frequency of magnetization, Hz.

The value of Steinmetz coefficient is approximately 2 for all modern magnetic materials.

Note. The transformers and generators cores and armatures of the electric motors etc. which are subjected to rapid reversals of magnetization should be made of such substances which have low coefficient in order to reduce the hysteresis loss.

Table 2. Hysteresis Coefficients

 S.No. Material Hysteresis coefficient Kh 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Cast iron Sheet iron Cast steel Hard cast steel Silicon steel (4.8% Si) Hard tungsten steel Good dynamo sheet steel Mild steel castings Nickel Permalloy 27.63 to 40.2 10.05 7.54 to 30.14 63 to 70.34 1.91 145.7 5.02 7.54 to 22.61 32.66 to 100.5 0.25  