Unit II DC Machines

1IFETCE/EEE/M.SUJITH/III YEAR/VI SEM/EE 2355/DEM/VER 1.0

DC MACHINES

Output Equations Main Dimensions - Magnetic circuit calculations Carters Coefficient - Net length of Iron Real & Apparent flux densities Selection of number of poles Design of Armature Design ofcommutator and brushes performance prediction using design values.

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IFETCE/EEE/M.SUJITH/III YEAR/VI SEM/EE 2355/DEM/VER 1.0

DC MACHINESLIST OF SYMBOLS:

D = stator bore or armature diameter, m L = stator core length, m p = number of poles Z = Total numbers of armature conductors Iz = current in each conductor(Ia/A) , A E = induced EMF, V P = machine rating (power output),kW Pa = power developed by the armature, kW Q = kVA rating of the machine = flux per pole, Wb = pole pitch ( D/p), m Total Electric loading = p ; Total Magnetic loading = Iz Z Specific Electric loading = ac = Iz Z / D (amp.conductor/m) Specific magnetic loading = Bave = p/ DL (Wb/m2 )

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CONSTRUCTION OF A D.C MACHINE

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COMMUTATOR OF A D.C MOTOR

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D.C MACHINES-CONSTRUCTION D.C Machines used for industrial electric drives have 3 major parts

namely,i. Field system,ii. Armature, andiii. Commutator.

The field system is located on the stationary part of the machinecalled the stator and consists of ,i. main poles- are designed to produce the magnetic flux.ii. Interpoles placed in between the main poles& are

employed to improve the commutation.iii. frame or yoke- provides mechanical support to the

machine and also serves as a path for flux.

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The armature is the rotating part (or rotor) of a d.c machine andconsists of,i. Armature core with slots andii. Armature winding accomodated in the slots.

The conversion of energy from mechanical to electrical or vice-versa takes place in the armature.

The commutator is mounted on the rotor of the machine. The commutator and brush arrangement works like a

mechanical dual converter.

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OUTPUT EQUATION

The output equation relates the power developed in armature to the main dimensions and speed of the machine.

The main dimensions of a d.c machine are,i. Armature diameter (D) andii. Armature length (L).

Power developed in armature, Pa = Co D2 L n. Output coefficient, Co = 2 Bav ac x10-3

maximum gap density, Bg= Bav/kf= Bav/

Co in terms of Bg is given by, Co = 2 Bg ac x10-3

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Power developed by the armature, Pa is different from the rated power output P, of the machine.

The relationship between the two are,Pa = P/ for generatorsPa = P for motors

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CHOICE OF ARMATURE LENGTH:The factors to be considered for the choice of armature

length are,i. Costii. Ventilationiii. Voltage between adjacent commutator segmentsiv. Specific magnetic loading.Maximum value of armature core length,

Lmax = 7.5Tc Nc BavVa

Where Tc = turns per coilNc = no.of coils between adjacent segmentsBav = specific magnetic loadingVa = peripheral speed

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MAIN DIMENSIONSCHOICE OF ARMATURE DIAMETER:

The factors to be considered for the choice of armature length are,i. Peripheral speedii. Pole pitchiii. Specific electric loadingiv. Induced emf per conductorv. Power output.

Maximum value of armature diameter, Dmax= Pa x10-3

ac ez

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CHOICE OF SPECIFIC MAGNETIC LOADING:The choice of average gap density or specific magnetic loadingdepends upon the following:

Flux density in the teeth. Frequency of flux reversal. Size of the machine.

Large values of flux density results in increased field mmf. Highervalue of field mmf increases the iron loss, copper loss & cost of copper.

If frequency of flux reversal is high, then the iron loss in the armaturecore & teeth would be high.

It is possible to use increased value of flux density as the size of themachine increases.

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CHOICE OF SPECIFIC ELECTRIC LOADING:The choice of specific electric loading depends on the following:

Temperature rise. Size of the machine. speed of the machine. Armature reaction. Voltage. Commutation.

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The general relations

Flux () = (MMF/ Reluctance) , Wb ;

Reluctance(S) = (l /a) , A/Wb ;

Permeance = ( 1/S) , Wb/A ;

where l = length of the flux path, m ;

A = area of cross section for the flux path, m2 ; = permeability = o r ;o = absolute permeability = 4 x 10 -7 H/m and r = relative permeability.

Magnetizing force (H)= mmf per unit length

= flux x reluctance per unit length

= x(1/length)x (length /a) = x (1 /a)

= B/ . (where B=( / a)

(or ) B = H

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Magnetic circuit

calculations

Magnetic flux density

Reluctance for Air gap

In smooth armature

Open armature

slots

MMF for air Gap

-Smooth Armature-Open armature

slots

MMF for teeth

-Graphical Method-3 Ordinate method

-Bt1/3 Method


Reluctance of air gap in machines with smooth armature

Reluctance of air gap in machines with open armature slotsWithout Fringing effect With Fringing effect

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0

0

an

. . .sec . . . . .

gg

s

g

g

s

lS

LyS reluct cel airgaplength

permeabilityLy area of cross tion of airgap over one slot

0 ( ).

gg

s s

g

lS

L y ww slot width

0 ( )' .

gg

s cs s

cs

lS

L y k wk carter s coefficient slots


Gap contraction factor for slots

Gap contraction factor for ducts

Stator slot pitch

Rotor slot pitch

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's s

gss cs s s

y yky k w y

gdcd d d

LkL k n w

sss

DyS

2 gsr

r

D ly

S

. .. .

. . .

. . .

os

or

s

r

w stator slot openingw rotor slot openingS no of stator slotsS no of rotor slots


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Carters coefficient

Carters coefficient for stator slots

Carters coefficient for rotor slots

Gap contraction factor for stator slots

Gap contraction factor for rotor slots

11 (5 / )css g os

Kl w

11 (5 / )csr g or

Kl w

ssgss

ss css os

yKy k w

srgsr

sr csr or

yKy k w

..

slot openinggap length


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MMF for Air Gapmmf of air gap with smooth armature

mmf of air gap with open armature= gap expansion factor

Field form factor = air gap density over the pole pitchmaximum flux density in the air gap

800,000g av gAT B l

800,000g av g gAT B l kgk

avf

g

BkB

fpolearck

polepitch av av

gf

B BBk


MMF CALCULATION FOR TEETH

Mmf required for teeth depends on area of cross section of tooth and flux passing through it

The area of cross section depends on dimensions of tooth which in turns depends on type of slots

Due to non uniform dimensions of the teeth, the following problems may be occurred

(i) The teeth are tapered. The path of flux is not constant and gives different values of flux density over the length of teeth

(ii) The sloth provides the parallel path for the flux, shunting the tooth .teeth normally worked in saturation region and therefore their permeability is low, the flux goes down to depth of the slots

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There are 3 methods employed for the calculation of MMF required for the teeth:-Graphical methodThe graph between the flux density and distance from the root of the tooth is drawn

Total mmf for tooth is

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tt t

Bn A

. . .t mean t mean sAT at l at d

length of tooth slot depth


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There are 3 methods employed for the calculation of MMF required for the teeth:-

Three ordinate method(Simpsons rule)This method is based on assumption that the curve relating mmf per metre, at with flux density is a parabolaat1= at for the root of toothat2=at for the center of toothat3=at for the tip of tooth

Mmf required for the tooth

1 2 346mean

at at atat

t mean t mean sAT at l at d


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There are 3 methods employed for the calculation of MMF required for the teeth:-

Bt1/3 Method(most simplest method)

The method is based upon the assumption that value of mmf per metre, at obtained for flux density at a section one third of tooth height from the narrow end is the atmeanTotal mmf for tooth

1 13 3

t t s

t s

t

s

At at l at d

l dl teethlengthd slotdepth


NET LENGTH OF IRON The length of the core is divided into packets of about 40 to 80 mm

width separated by vent spacers.

Vent spacers form ventilating ducts through which is air circulated andwidth normally varies from 8 to 10mm.

(Iron space factor) Stacking Factor: Ratio of actual length of iron in astack of assembled core plates to total axial length of stack.

Gross iron length = core length length of ventilating ducts

Net iron length

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s d dL L n w

[ ]i i d dL k L n w


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REAL AND APPARENT FLUX DENSITIES

The flux entering in to armature from air gap flows in teeth

If the flux density in teeth is high, mmf acting on the teeth is high

Always = Real flux < apparent flux density

Real flux density

Apparent flux density

. . . ..app

total flux in slot pitchBtooth area

. . ..real

actual flux in toothBtooth area


The apparent flux density

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. . . . .. . . . .

( )

.

. . &

av

s i as i a

i i

i a

i i

a areal

a i

i areal a

i a

app real a

Total flux over a slot pitchBIron area over a slot pitch

A A

A AAB

A A

w k t B BA A

B B B K


Ai= tooth width x net iron length = wtLiAa= total area iron area=Lys - wtLi

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. ( . )

. ( . )air area over slotk

iron area over tooth

& 0.9

( 1)

.1.

: 1 1

i f f

a o real

real app a

real app o real

real app o real s

ss

i t

a s s t i ss

i t i t i

L S L SwhereB atB B B kB B at kB B at k

Lytotal areak kiron area L w

A L y w L LyNote K kA w L w L


SELECTION OF NUMBER OF POLES: Selection of no.of poles depends on,

i. Frequencyii. Length of commutatoriii. Weight of iron partsiv. Labour chargesv. Weight of coppervi. Cross over & distortion of field form.

The no.of poles are chosen such that the frequency lies between 25 to 50 Hz.

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ADVANTAGES OF LARGE NUMBER OF POLES:The large number of poles results in the reduction of the following: Weight of armature core and yoke. Cost of armature and field conductors. Overall length and diameter of the machine. Length of commutator. Distortion of field form under load conditions.

DISADVANTAGES OF LARGE NUMBER OF POLES:The large number of poles results in increase of the following: Frequency of flux reversals. Labour charges. Possibility of flash over between brush arms.

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GUIDING FACTOR FOR CHOICE OF NO.OF POLES: The Frequency should lie between 25 to 50 Hz. The value of current per parallel path is limited to 200 amps, thus

the current per brush arm should not be more than 400 amps.Current per parallel path = Ia/P for lap winding.

=Ia/2 for wave winding.Current per brush arm = 2Ia/P for lap winding.

=Ia for wave winding.where, P= number of poles.

The armature mmf should not be too large.The normal values ofArmature mmf/pole are listed in the table:

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If there are more than one choice for no.of poles which satisfies theabove 3 conditions, then choose the largest value for poles.Thisresults in reduction in iron and copper.

Output (kW) Armature mmf/pole (AT)

Upto 100 5000 or less100 to 500 5000 to 7500

500 to 1500 7500 to 10,000

Over 1500 Upto 12,500

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SEPARATION OF D AND L:In D.C machines the separation of D and L depends onPole proportionsThe ratio of is usually between 0.64 to 0.72 (L/)Square pole (L/) choose as 0.7 and practically the value of (L/) is 0.7 to 0.9Moment of inertiaHigh inertia machines may required for impact load applications machines designed with larger diameterPeripheral speed.Should not exceed 30m/sVoltage between adjacent commutator segments.Maximum voltage between segments

Limiting values Bgm=1.2wb/m 2 , Va=30m/s, Ecm=30, Tc=1, L=0.4m

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2cm gm a cE B LV T


ARMATURE DESIGN

Design of armature winding involves:1. Choice of armature winding2. Number of armature conductor3. Number of armature coils4. Number of armature slots5. Cross section of armature conductors6. Armature voltage drop7. Depth of armature core

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CHOICES OF ARMATURE WINDING :DC machines employ 2 general types of double layer windings. They are: Simplex lap winding.

Progressive lap winding Retrogressive lap winding

Simplex wave winding.

These 2 types of windings primarily differ from each other in thefollowing factors:

The no.of coils between positive & negative brushes, i.e., no.ofparallel paths.

The manner in which the coil ends are connected to the commutatorsegments.

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COMPARISON OF LAP AND WAVE WINDING LAP WINDING WAVE WINDING

1.The number of parallel paths is = the no. of poles. (A=P)2.Equaliser connections have to be employed.3.It is used for large capacity machines when the current rating is >400A. 4.Current through a conductor is Ia/P.5.For a specified voltage rating, the no. of armature conductors required is P/2 times that of wave winding.

1.The number of parallel paths is two.2.Equaliser connections not needed.3.It is used for small and mediumcapacity machines .

4.Current through a conductor is Ia/2. 5.For a specified voltage rating, the no. of armature conductors required is 2/P times that of lap winding.

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LAP WINDING WAVE WINDING

6.Since the lap winding has large no. of conductors, the area required for insulation is moreand so the slot area will be large. Also the no. of coils will be large & cost will be high.

7.For a specified current rating the area of cross section of the conductor is 2/P times that of wave winding.

6.Since the wave winding has less no.of conductors, the area required for insulation is less and so the slot area will be less. Also the no.of coils will be less & cost will be less.

7.For a specified current rating the area of cross section of the conductor is P/2 times that of lap winding.

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NUMBER OF ARMATURE CONDUCTORS

Generated emf in the armature( )( )

min .int . tan

int. . . . . .

a m

a m

m

a m

a

E V I r generatorE V I r motorwherev ter al voltager ernal resis ceI r ernalvoltagedropnumber of armature conductors is given by

EZnp


NUMBER OF ARMATURE COILS Single turn coils used for lap windings Multi turn coils used for wave windings The number of turns per coils and number of coils are so chosen that

the voltage between adjacent commutator segments is limited Normally the maximum voltage between adjacent segments at load

should not exceed 30V Average voltage between adjacent segments at no load

Maximum at load2c c c av aE T N B LV

2 ( )

( )c c c gm a

c c c gm a

E T N B LV lapE T N B LV wave


NUMBER OF ARMATURE SLOTSFactors to be considered when selecting the number of armature slots Mechanical difficulties Cooling of armature conductors Flux pulsation CommutationGuiding factors for choice of number of armature slots Slot pitch (25mm to 35mm) small machines -20mm Slot loading = No of conductors in slot x current per conductor(not exceed 1500 ampere conductor) Flux pulsation (slot per pole is integral plus ) Commutation (Slots per pole must be > 9for better commutation process) Suitability of winding (lap or wave)


SLOT DIMENSIONS

SLOT AREA = CONDUCTOR AREA / SLOT SPACE FACTOR Slot space factor lies in range of 0.25 to 0.4 The dimensions of tooth should be chosen such that the flux density of

tooth doesnot exceed 2.1wb / m2

Guideline for choosing the slot depth

Diameter of armature in m

Slot depth in mm

0.15 220.20 270.25 320.30 37

Diameter of armature in m

Slot depth in mm

0.40 420.50 45


ARMATURE VOLTAGE DROP

Length of mean turn of armature winding

Projection of coil outside the core

Resistance of each conductor

Resistance of each parallel path

Armature voltage drop

2 2.3 5mt sL L z d

0.3 1.25s sL z d

1 .2

mt

s

La

.2

mt

z

Lza a

a aI r


DEPTH OF ARMATURE CORE

Flux in the armature =(1/2) flux per pole

Area of armature core

Depth of armature

12a

1 .2

cc i c

c c

A L dB B

12c i c

dL B


TYPES OF COMMUTATION: The phenomena of commutation is affected by the resistance of the

brush, reactance emf induced by leakage flux and rotational emf induced by armature flux.

Brush materials- Hard Carbon(20-30m/s), Metal graphite(20-30m/s), Electro graphite(30-60m/s), Natural Graphite (50-60m/s)

Based on the factors affecting the commutation, the process of commutation is classified into:

Resistance commutation. Retarded commutation. Accelerated commutation. Sinusoidal commutation.

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DESIGN OF COMMUTATOR AND BRUSHES

The number of commutator segments is equal to the number of coils. The commutator diameter Dc= 6080 % of the armature diameter (D). The peripheral speed is limited to 15m/s to 30m/s Each brush should not carry more than 70A Current carried by brush

Total brush contact area per spindle

Contact area of brushes in a spindleab =contact area of each brushnb =no. of brushes per spindle

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2 / ( )( )

b a

b a

I I P lapI I wave

/b b bA I

b b bA n a


Thickness of brush

Width of brush

Length of commutator

Cb= clearance between the brushes (usually 5mm)C1=clearance allowed for stagering the brushes (10mm for small machine

and 30mm for large machine)C2=clearance for allowing end play (10mm to 25mm)

Brush friction loss

Pb=brush contact pressure on commuator N/m2AB=pAb for lap winding ; AB=2Ab for wave winding ; Vc=peripheral speed of commutator m/s ; =coefficient of friction

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(1 3)b ct to

b bb

b bb

A awn t t

1 2( )c b b bL n w c c c

bf b B cP P A V


Commutator peripheral speed

Number of brushes per spindles

Actual commutator pitch

C=no. of commutator segments=no. of coils

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c cV D n

.brush areab

b

InI

( 4 )cc cD always mmC


LOSSES AND EFFICIENCY IN DC MACHINES

I2R losses : copper loss in

i) Armature ii) Field iii) Inter pole winding

Rotational losses :i) Friction & windage losses (bearings & commutator)ii) Iron loss

a) Hysteresis loss .b) Eddy current loss.

For the calculation of copper losses , the total length and area cross section of each of the windings should be first calculated.

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Peripheral speed, v 45 m/s Frequency of flux reversal, f 50 Hz Current per brush arm 400 A Armature MMF per pole 7000 A The MMF required for the air gap = 50% of the

armature MMF. Gap contraction factor = 1.1 The current per brush arm (Ia) = 2Ia/p For square poles: L = D/p In the design process, choose of poles based on f & Ib and then

calculate D and L.

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PERFORMANCE PREDICTION USING DESIGN VALUES.


Unit II DC Machines

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