Unit II DC Machines

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DC MACHINES

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

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DC MACHINES LIST 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 Φ = flux per pole, Wb τ = pole pitch (π D/p), m Total Electric loading = pΦ ; Total Magnetic loading = Iz Z Specific Electric loading = ac = Iz Z / π D (amp.conductor/m) Specific magnetic loading = Bave = pΦ/ π DL (Wb/m2 ) 3

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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, and iii. Commutator. The field system is located on the stationary part of the machine called 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 and consists of, i. Armature core with slots and ii. Armature winding accomodated in the slots. The conversion of energy from mechanical to electrical or viceversa 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 

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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. ii.

  



Armature diameter (D) and Armature length (L).

Power developed in armature, Pa = Co D2 L n. Output coefficient, Co = π2 Bav ac x10-3 maximum gap density, Bg= Bav/kf = Bav/Ψ Co in terms of Bg is given by, Co = π2 Bg Ψ ac x10-3

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

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

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

Cost ii. Ventilation iii. Voltage between adjacent commutator segments iv. Specific magnetic loading. Maximum value of armature core length, Lmax = 7.5 Tc Nc BavVa i.

Where Tc = turns per coil Nc = no.of coils between adjacent segments Bav = specific magnetic loading Va = peripheral speed

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MAIN DIMENSIONS CHOICE OF ARMATURE DIAMETER: The factors to be considered for the choice of armature length are, i. Peripheral speed ii. Pole pitch iii. Specific electric loading iv. Induced emf per conductor v. Power output. Maximum value of armature diameter, Dmax= Pa x10-3

Π ac ez

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CHOICE OF SPECIFIC MAGNETIC LOADING: The choice of average gap density or specific magnetic loading depends 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. Higher value 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 armature core & teeth would be high.  It is possible to use increased value of flux density as the size of the machine 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 (Φ) = (MMF/ Reluctance) , Wb ; Reluctance(S) = (l /aµ) , 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 ; µ = permeability = µo µr ; µo = absolute permeability = 4π x 10 -7 H/m and µr = relative permeability. Magnetizing force (H)= mmf per unit length = flux x reluctance per unit length = Φx(1/length)x (length /aµ) = Φx (1 /aµ) = B/µ . (where B=(Φ / a) (or ) B = µH 16

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Magnetic circuit calculations

Magnetic flux density

Reluctance for Air gap

In smooth armature

Open armature slots

MMF for air Gap

MMF for teeth

-Smooth Armature -Open armature slots

-Graphical Method -3 Ordinate method -Bt1/3 Method

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Reluctance of air gap in machines with smooth armature Sg 

lg

0 Lys S g  reluct an ce lg  airgaplength

0  permeability Lys  area.of .cross.sec tion.of .airgap.over.one.slot Reluctance of air gap in machines with open armature slots Without Fringing effect With Fringing effect

Sg 

lg

0 L( ys  ws ) wg  slot.width

Sg 

lg

0 L( ys  kcs ws ) kcs  carter ' s.coefficient  slots 18

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Gap contraction factor for slots

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Gap contraction factor for ducts

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Stator slot pitch

D yss  Ss

Rotor slot pitch

ysr 

k gs

ys ys   y s  k cs ws ys '

k gd 

L L  kcd nd wd

wos  stator.slot.opening wor  rotor.slot.opening

D  2lg

S s  no.of .stator.slots

Sr

S r  no.of .rotor.slots 19

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• Carter’s coefficient 

slot.opening gap.length

• Carter’s coefficient for stator slots

• Carter’s coefficient for rotor slots

K css

1  1  (5lg / wos )

K csr

1  1  (5lg / wor )

• Gap contraction factor for stator slots K  gss

• Gap contraction factor for rotor slots K gsr

yss yss  kcss wos

ysr  ysr  kcsr wor 20

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MMF for Air Gap mmf of air gap with smooth armature AT  800, 000 B g

mmf of air gap with open armature k = gap expansion factor

l

av g

ATg  800, 000 Bav lg k g

g

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

polearc k f   polepitch

B av kf  Bg

Bav Bav Bg   kf 

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MMF CALCULATION FOR TEETH 





(i)

(ii)

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 The teeth are tapered. The path of flux is not constant and gives different values of flux density over the length of teeth 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 method The graph between the flux density and distance from the root of the tooth is drawn

Total mmf for tooth is

 Bt  nt A t

ATt  atmean  lt  atmean  d s 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(Simpson’s rule) This method is based on assumption that the curve relating mmf per metre, at with flux density is a parabola at1= at for the root of tooth at2=at for the center of tooth at1  4at2  at3 atmean  at3=at for the tip of tooth 6 Mmf required for the tooth

ATt  atmean  lt  atmean  d s 24

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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 atmean Total mmf for tooth At  at  l  at  d t

1

3

t

1

3

s

lt  d s lt  teethlength d s  slotdepth 25

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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 and width normally varies from 8 to 10mm.

(Iron space factor) Stacking Factor: Ratio of actual length of iron in a stack of assembled core plates to total axial length of stack. Gross iron length = core length – length of ventilating ducts

Ls  L  nd wd Net iron length

Li  ki [ L  nd wd ] 26

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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

Breal

actual. flux.in.tooth  tooth.area

Apparent flux density

Bapp

total. flux.in.slot. pitch  tooth.area

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The apparent flux density

Total. flux.over.a.slot. pitch Bav  Iron.area.over.a.slot. pitch s i  a   (s  i  a ) Ai Ai

i a   Ai Ai a Aa  Breal  . Aa Ai  i a   w.k .t  Breal  & Ba   Ai Aa   Bapp  Breal  Ba K IFETCE/EEE/M.SUJITH/III YEAR/VI SEM/EE 2355/DEM/VER 1.0

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k

air.area (over.slot ) iron.area (over.tooth)

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

Li  S f L & S f  0.9 whereBa  o atreal Breal  Bapp  Ba k Breal  Bapp  o atreal k Breal  Bapp  o atreal ( ks  1) total.area Lys ks  1  k   iron.area L i wt Aa Ls ys  wt Li Lys Note : K     1  ks  1 Ai wt Li wt Li 29

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SELECTION OF NUMBER OF POLES:  Selection of no.of poles depends on, i. Frequency ii. Length of commutator iii. Weight of iron parts iv. Labour charges v. Weight of copper vi. 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 of Armature mmf/pole are listed in the table:

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Output (kW)

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Armature mmf/pole (AT)

Upto 100

5000 or less

100 to 500

5000 to 7500

500 to 1500

7500 to 10,000

Over 1500

Upto 12,500

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

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SEPARATION OF D AND L: In D.C machines the separation of D and L depends on Pole proportions ratio of Ψ is usually between 0.64 to 0.72 (L/τ) Square pole (L/τ) choose as 0.7 and practically the value of (L/τ) is 0.7 to 0.9 The

Moment of inertia High inertia machines may required for impact load applications  machines designed with larger diameter

Peripheral speed. Should not exceed 30m/s Voltage between adjacent commutator segments. Maximum voltage between segments

Ecm  2 Bgm LVaTc

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

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ARMATURE DESIGN Design of armature winding involves: 1. Choice of armature winding 2. Number of armature conductor 3. Number of armature coils 4. Number of armature slots 5. Cross section of armature conductors 6. Armature voltage drop 7. 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 the following factors:  The no.of coils between positive & negative brushes, i.e., no.of parallel paths.  The manner in which the coil ends are connected to the commutator segments.

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COMPARISON OF LAP AND WAVE WINDING LAP 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.

WAVE WINDING 1.The number of parallel paths is two. 2.Equaliser connections not needed. 3.It is used for small and medium capacity 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

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

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

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NUMBER OF ARMATURE CONDUCTORS Generated emf in the armature

E  V  I a rm ( generator ) E  V  I a rm (motor ) where v  ter min al.voltage rm  int ernal.resis tan ce I a rm  int ernalvoltagedrop number.of .armature.conductors.is.given.by Ea Z  np

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NUMBER OF ARMATURE COILS   

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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

Ec  2Tc N c Bav LVa 

Maximum at load

Ec  2Tc N c Bgm LVa (lap ) Ec  Tc N c Bgm LVa ( wave) IFETCE/EEE/M.SUJITH/III YEAR/VI SEM/EE 2355/DEM/VER 1.0

NUMBER OF ARMATURE SLOTS Factors to be considered when selecting the number of armature slots  Mechanical difficulties  Cooling of armature conductors  Flux pulsation  Commutation Guiding 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 ½ )  Commutation (Slots per pole must be > 9for better commutation process)  Suitability of winding (lap or wave)

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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

Diameter of armature in m

Slot depth in mm

0.15

22

0.40

42

0.20

27

0.50

45

0.25

32

0.30

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ARMATURE VOLTAGE DROP 

Length of mean turn of armature winding

Lmt  2 L  2.3z  5d s 

Projection of coil outside the core



Resistance of each conductor



Resistance of each parallel path



Armature voltage drop

Ls  0.3z  1.25d s

1  Lmt  . 2 as

z  Lmt  . a 2az

 I a ra

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DEPTH OF ARMATURE CORE 

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

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Area of armature core



1 a   2

Depth of armature

c 1  Ac   .  Li  d c Bc 2 Bc

1  dc  2 Li Bc IFETCE/EEE/M.SUJITH/III YEAR/VI SEM/EE 2355/DEM/VER 1.0

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= 60–80 % 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

I b  2 I a / P (lap ) I b  I a ( wave)



Total brush contact area per spindle

Contact area of brushes in a spindle ab =contact area of each brush nb =no. of brushes per spindle 

Ab  I b /  b

Ab  nb ab 46

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tb  (1to3)  c



Thickness of brush



Width of brush



Length of commutator

Ab ab wb   nb t b tb

Lc  nb ( wb  cb )  c1  c2

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

Pbf   Pb ABVc

Pb=brush contact pressure on commuator N/m2 AB=pAb for lap winding ; AB=2Ab for wave winding ; Vc=peripheral speed of commutator m/s ; μ =coefficient of friction 47

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

Commutator peripheral speed



Number of brushes per spindles

Vc   Dc n

I brush.area nb  Ib 

Actual commutator pitch

 Dc c  (always c  4mm) C C=no. of commutator segments=no. of coils

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LOSSES AND EFFICIENCY IN DC MACHINES I2R losses : copper loss in

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. i)

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PERFORMANCE PREDICTION USING DESIGN VALUES.     

   

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 = ψ π D/p In the design process, choose of poles based on f & Ib and then calculate D and L.

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