Demonstrative Video
Armature Windings
dc machines have closed circuit windings
Alternator windings are open, no closed path for the currents in the winding itself
One end is joined to neutral and other brought out (Y-connected)
two sides of any coil should be under two adjacent poles, i.e. coil span = pole pitch
winding can either be single layer or double layer
Winding is so arranged in different armature slots, that it must produce sinusoidal emf.
the complete slot is containing only one coil side of a coil
also referred to as
Consider- single-layer, one-turn, full-pitch, 4-pole, 12-slots
3 slots/pole or 1 slot/pole/phase and pole-pitch = 3
For max. emf, 2-sides of a coil should be 1 pole-pitch apart (\(180^{\circ}\) electrical)
\(R\)-phase: slot no.1 \(\Rightarrow\) 4,7 \(\Rightarrow\) 10
\(Y\)-phase: slot no.3- \(120^{\circ}\) afterwards
(3 slots = \(180^{\circ}\) \(\Rightarrow\) 2 slots = \(120^{\circ}\))\(B\)-phase: slot no. 5 \(\Rightarrow\) 8,11 \(\Rightarrow\) 2
The ends of the windings are joined to form a \(Y\)-connection
Concentric or Chain winding
Number of slots = 2 \(\times\) No. of coils = No. of coil sides
polar group of each phase is \(360^{\circ}\) (electrical) apart
necessary to use two different shapes of coils to avoid fouling of end connection
Since polar groups of each phase are \(360^{\circ}\) apart, all such groups are connected in the same direction
disadvantage- short-pitched coils cannot be used
Double-layer winding
either wave-wound or lap-wound
simplest and most commonly used
No. of slots is multiple of no. of poles and the phases. E.g. 4-pole, 3-phase may have 12, 24, 36, 48 etc. slots (multiple of 12 = 4 \(\times\) 3)
No. of slots = No. of coils (of the same shape).
Thus, each slot contains two coil sides, one at the bottom and other at top of the slot. The coils overlap each other.
4-pole, 24-slot; \(\Rightarrow\) pole-pitch = \(24/4=6\)
For max. emf, coils should be full-pitched
means one side of coil in slot no. 1 the other at 7, the two slots being one pole-pitch or \(180^{\circ}\) apart
Each phase has \(24/3=8\) coils
Winding for one phase is shown:
The complete wiring diagram for 3-phase:
Short-Pitch Winding
So far full-pitched coils i.e one pole-pitch = \(180^{\circ}\) is discussed
Full-pitched: coil sides in slots 1 and 7
Short-pitched or fractional-pitched: placed in slots 1 and 6, i.e. coil-span = 5/6 of a pole-pitch
Falls short by 1/6 pole-pitch = \(180^{\circ}/6 = 30^{\circ}\)
save copper of end connections
improve the waveform of the generated emf (sinusoidal) and distorting harmonics are eliminated
Due to elimination of high frequency harmonics, eddy current and hysteresis losses are reduced thereby increasing efficiency
Total voltage is somewhat reduced
Induced voltage in two sides of short-pitched coils are slightly out of phase, their resultant vectorial sum is less than their arithmetical sum
is defined as \[\boxed{=\dfrac{\mbox{vector sum of the induced emf per coil}}{\mbox{arithmetic sum of the induced emf per coil}}} < 1\]
Let \(E_s\) be induced emf in each side of the coil. Then for full-pitched total induced emf = \(2E_s\)
If short-pitched by \(30^{\circ}\) then resultant emf \[\begin{aligned} E & =2E_{s}\cos30^{\circ}/2=2E_{s}\cos15^{\circ}\\ k_{c} & =\dfrac{\mbox{vector sum}}{\mbox{arithmetic sum}}=\dfrac{E}{2E_{s}}=\dfrac{2E_{s}\cos15^{\circ}}{2E_{s}}=\cos15^{\circ}=0.966 \end{aligned}\]
In general, if the coil span falls by an angle \(\alpha\) (electrical) then \(k_c=\cos \alpha/2\)
\(\alpha\) is known as chording angle and the winding employed short-pitched coils is called chorded winding
Note: The value of \(\alpha\) will usually given in question, it not, then assume, \(k_c=1\)
Distribution/ Breadth factor/ Winding factor/ Spread Factor
In each phase, coils are not concentrated or bunched in one slot, but are distributed in a number of slots to form polar groups under each pole
The coils/phases are displaced from each other by a certain angle
Result is emfs induced in coil sides constituting a polar group are not in phase but differ by angular displacement of the slots
3-\(\Phi\), 4-pole, 36 slots \(\Rightarrow\) 9 slots/pole \(\Rightarrow\) 3 slots/pole/phase
Here, angular displacement between any two adjacent slots = \(180^{\circ}/9=20^{\circ}\) (elect.)
If three coils were bunched in one slot, then total emf induced in three sides of the coil would be the arithmetic sum of the three emfs i.e. = \(3E_s\), where \(E_s\) is emf induced in one coil side
Since the coils are distributed, the individual emfs have a phase difference of \(20^{\circ}\) with each other
\[E=E_{s}\cos20^{\circ}+E_{s}+E_{s}\cos20^{\circ}=2.88E_{s}\]
The distribution factor \(\left(K_d\right)\) is defined as \[=\dfrac{\mbox{e.m.f. with distributed winding}}{\mbox{e.m.f. with concentrated winding}}\]
In the present case \[K_d = \dfrac{\mbox{e.m.f in 3 slots/pole/phase}}{\mbox{e.m.f in 1 slots/pole/phase}} = \dfrac{E}{3E_s} = \dfrac{2.88E_s}{3E_s} = 0.96\]
\[\begin{array}{cl} \beta= & \mbox{Angular displacement betw. slots}\\ n= & \mbox{No. of slots/pole}\\ m= & \mbox{No. of slots/pole/phase}\\ m\beta= & \mbox{phase spread angle} \end{array}\]
\[\boxed{\beta = \dfrac{180^{\circ}}{\mbox{No. of slots/pole}} = \dfrac{180^{\circ}}{n}}\]
\[\begin{aligned} K_{d} & =\dfrac{\mbox{vector sum of coils emfs}}{\mbox{arithmetic sum of coil emfs}} =\dfrac{E_{r}}{mE_{s}}\\ & =\dfrac{2r\sin m\beta/2}{m\times2r\sin\beta/2}\\ & \boxed{K_{d} =\dfrac{\sin \left(m\beta/2\right)}{m\sin\left(\beta/2\right)}} \end{aligned}\]