PREPARED BY: GUIDED BY: H.V.DATANIYA SIR

 Magnetization curves  Calculation of MMF for airgap  Calculation of MMF for teeth

 Magnetization curve of a magnetic material is the relation between the magnetic flux density ( B ) in wb/ m 2 or tesla and the magnetizing force H in ampere turns (AT) per meter length.  These curves are used for finding the MMF or ampere turns in any part of a magnetic circuit.

 From these curves we can find the magnetizing force necessary to produce certain flux density in a magnetic material.  Magnetic curves are also called as B-H curves.  If the magnetic field intensity in the core is increased current, the flux density in the core will change.

 For low value of H, the flux density increases almost linearly. However, for higher values of H, the change of B is non-linear.  The magnetic material shows the effect of saturation.  The reluctance of magnetic path is dependent on the flux density B.  Reluctance S is low when B is low and high when B is high.

 The magnetizing force H produces a magnetic flux density B, i.e. B is directly proportional to H.  B/H = constant = µ  B= µ o µ r H tesla  Where, µ= absolute permeability of medium  µ o= permeability of free space  µ r= relative permeability of medium

Total MMF or ampere turns required = MMF required for iron parts + MMF required for airgap Usually the MMF required to overcome the reluctance of iron parts is very small at compared to MMF required for airgap. Therefore the length of airgap, should be small as possible.

 To calculate the MMF required for the airgap, the following factors/points must be considered. 1. Length of airgap is not constant over whole of pole pitch. The length of airgap at the pole tips is more than that at the centre of the pole shoe. Due to this, the flux density towards the pole tips will reduce. There fore the average value of flux density must be taken in to account to calculate the MMF required for the airgap.

The ratio of average flux density over the pole pitch to the maximum flux density in the airgap is called field factor kf. k f = B av / B max = pole arc / pole pitch There fore effective area of airgap Ag e = gap area x field form factor Ag e = t p L K f Where, L = gross length of armature

Reluctance of airgap with sloted armature will be more as compared to smooth armature machines, because the length of airgap will increase due to slots on the armature. The reluctance of airgap with smooth armature S g1 = l/µ 0 A = lg / µ 0 t s L

Fig: Air gap with smooth armature Fig: Air gap with slotted armature Fig: Air gap with slotted armature and fringing effect

Therefore effective slot pitch T se = b t = t s – b s where, b s = width of slot b t = width of tooth There fore the reluctance of airgap with slotted armature, S g = l g / µ o t se L = lg / µL(t s – b s )

 Therefore, the flux of one slot pitch will be distributed over width = ( b t + £b s ) = t’ se  Effective slot pitch in this case, t’ se = b t + £b s = b t + b s + £b s – b s = ts - b s ( 1- £)  Thus, reluctance of airgap with slotted armature and considering fringing of flux.

S g2 = l g / µ o t’ se L = l g / µ o L [ t s – b s ( 1 - £ )] = l g / µ o L [ t s – k cs b s ]  Where k cs is called as carter’s gap coefficient and depends upon the ratio of slot width of airgap length. k gs = t s / t s – k cs b s  k gs is known as the gap contraction for the slots.

 The ratio K gd = L / L – k cd n d b d  K gd is called gap contraction factor for ducts.  Therefore, total gap contraction factor k g = k gs x k gd  Effective length of airgap l ge = k g l g

At g = H g x l gd At g = B g / µ 0 x k g l g = 1 / 4x3.14 x K g B g l g At g = K g B g l g

 The exact calculation of the ampere turns necessary to establish the flux in the teeth is difficult due to the following problems : 1. The teeth are wedge-shaped or tapered. Tapered teeth results into varying flux density over the length of teeth. 2. The teeth are normally working at such a high flux density that their permeability is very small and as a result, a small portion of the airgap flux is diverted and passed through slots.

The MMF required for the tapered teeth can be calculated by following methods : I. Graphical method II. Simpson’s rule III. B t1/3 method for flux density at 1/3 rd section.

 This method is applicable to teeth having small taper. In this method, values of ‘at’ i.e. ampere turns per metre are found at three equidistance points i.e. two ends and at the middle along the height of tooth.  At m = a t 1 + 4at 2 + at 3 / 6  Total MMF = mean value of ampere turns per metre * hifht of teeth

Where at1, at2 and at3 are the value of ampere turns per mwtre at the tip, middle and bottom cross- sections respectively. AT 1 = at m x h t AT 1 = at m x d s

This method is very simple as compared to other methods. Bt 1/3 = flux density at 1/3 height from the narrow and At 1/3 = ampere turns per metre corresponding to bt 1/3, which can be obtained from ‘B-at’ curve. Total MMF for teeth AT 1 = at 1/3 x height of tooth = at 1/3 x ht AT 1 = at 1/3 x ds

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