1
STATEMENT OF THE PROBLEM
DESIGN #1: DESIGN OF AN ARMATURE OF A DC GENERATOR
PROBLEM: Design an armature of a DC generator having the following specifications:
1) Full load output 1550 kW
2) Open circuit / No load Voltage 750 V
3) Full load Voltage 660 V
4) Ratio of pole arc to pole pitch (r) 0.64
5) Speed (N) up to 500 rpm
6) Winding Simplex Lap Winding
2 DESIGN SHEET FOR ARMATURE OF D-C GENERATOR (PART – 1)
ITEM NO. SPECIFICATION: 1550 kW ; 660/750 Volts ; 500 rpm SYMBOL Preliminary or Assumed Values Final Values
ARMATURE CORE AND WINDING
1 Number of Poles - - - P 12 12 Frequency, Hz - - - ƒ - - - - 50 2 Ratio of pole arc to pole pitch - - - r 0.64 0.64 3 Specific Loading - - - q 1,055 1,055 4 Apparent Air-gap flux density (open circuit) - - - 62,550 70,706.506
5 Line Current (full load) - - - I - - - - 2,348.485 6 Type of Winding - - - - - - - - - - - lap 7 Armature current per circuit - - - Ic 392.59
8 Output factor (laD2) - - - - - - - 44,481.004 50,682.602
9 Armature diameter, in - - - D 57.34 57.34 10 Peripheral velocity, fpm - - - 7,509.72 7,509.72
11 Total number of face conductors - - - Z 484 484
12 Number of slots - - - S - - - - 20 13 Number of conductors per slot - - - - - - - - - - - 24 14 Axial length of armature core; gross, in - - - la 13.53 15.415
15 Flux per pole (open circuit) - - - 16.363 x106
16 Pole pitch, in - - - 15.012 17 Pole arc, in - - - 9.61 18 Area covered by pole face (rτla), sq in - - - - - - - 130.023 148.138 19 Dimensions of armature conductors, in. units - - - - - - - - - - - (0.185x0.345) 20 Slot pitch, in - - - - - - - 9.007 21 Slot width, in - - - s - - - - 0.8 22 Slot depth, in - - - d - - - - 1.104 23 Tooth width, in. At top - - - t - - - - 8.207 At root - - - - - - - - - - - 7.86 Average - - - - - - - - - - - 8.034 24 Number of radial ventilating ducts - - - -- - - n - - - - 1 25 Width of radial ducts, in - - - - - - - - - - - 0.375 26 Net length of armature core, in - - - ln 12.103 13.837
27 Net tooth section under pole, at center, sq in - - - - - - - 103.718 118.577 28 Apparent density in teeth under pole, at center, sq in - - - 157,770.458 91,999.51
29 Length per turn of armature coil, in - - - -- - - - - - - - - - - 68.602 30 Resistance of one turn, ohms at 60°C - - - - - - - - - - - 0.000422 31 Resistance of armature, ohms - - - - - - - - - - - 0.0085 32 IR drop in armature, volts - - - - - - - - - - - 6.674 33 I2R loss in armature winding, watts - - - - - - - - - - - 31,441.889 34 Estimated full-load flux per pole - - - - - - - - - - - 16.661x106
35 Flux density in armature core below teeth - - - - - - - 76,000 76,002.571 36 Internal diameter of core stampings, in - - - - - - - - - - - 39.572 37 Weight of iron in core (without teeth), lb - - - - - - - - - - - 4,484.022 38 Weight of iron core in teeth, lb - - - - - - - - - - - 665.487 39 Total weight of armature stampings, lb - - - - - - - - - - - 5,149.509
3 DESIGN OF ARMATURE CORE AND WINDING
Item1: Number of poles (P) and frequency (ƒ)
Referring to Art. 3, for an output of 1550 kW, a speed of up to 500 rpm and 12 poles would be suitable for this trial design, therefore,
ƒ = ( ) = 50 Hz
Item 2: Ratio of Pole Arc to Pole Pitch
Refer to Art. 2. Since the machine will be provided with commutating poles, a suitable value for this ratio is;
r = 0.64
Item 3: Specific Loading (q)
, , , , , , – , q = 1,055
Item 4: Apparent Air-gap Flux Density, open circuit (Bg’’) , ,
, ,
, , ’’ – , Bg’’ 62,550
Item 5: Line Current , Full Load ( IL )
IL = = , , = 2,348.485 Amp
Item 6: Type of Winding
Simplex Lap Winding
Refer to Art. 6. Since the current per path should not exceed 250 to 300 amp, lap winding with two parallel paths could be used for this trial design.
Item 7: Armature Current per Circuit ( Ic )
Ic = ( )
From Art. 47, % of excitation for 1000 and larger is 0.3 to 0.4, thus, 0.3 may be used.
Then,
4 Item 8: Output factor ( IaD2 )
IaD2 = ( ) = , , , ( , )( , )( ) - = 44,481.003 in3
Item 9: Armature Diameter (D)
Using a rectangular pole face, where k = 0.71
la = ( ) = ( ) ( ) ( ) = 0.236 D Hence,
D = √ , ⁄ = 57.34 in.
Item 10: Peripheral Velocity (fpm)
=
( )( )
= 7,509.72 fpm
Item 11: Total number of Face Conductors (Z)
= ( )( , )
= 484 conductors
Item 12: Number of Slots (S)
Assuming that there are 24 conductors per slot
=
= 20 slots
And the Slot per Pole ( ) would be,
⁄
Item 13: Number of Conductors per Slot ( CS )
Item 14: Axial length of Armature Core ( la ) Solving for ,
,
5 Item 15: Flux per Pole, Open Circuit ( )
From Voltage Equation for dynamo;
Solving for , ( )( ) ( )( ) , ,
Item 16: Pole Pitch ( )
( )
Item 17: Pole Arc ( r )
Item 18: Area covered by Pole Face ( )
( )
Item 19: Dimensions of the Armature Conductors Assuming k = 700,000
= + = , , , = 2,540.94 Then,
Area of Cross Section = =
, = 0.155
Referring to Appendix I (Wire Table, bare and DCC Copper Ribbon), an insulated copper conductor having a cross sectional area of 0.184 has a thickness of (t=0.185) and width of (w=0.345)
respectively.
Item 20: Slot Pitch ( )
( )
Item 21: Slot Width ( )
Insulation thickness = 27 + = 27 + = 49 mils or 0.049 in ( ) ( ) ( )
6 Item 22: Slot Depth ( )
( ) ( ) ( ) ( )
Fig. I Arrangement of Conductors in Slot (Scale: NTS)
Item 23: Tooth Width ( ) At Top, At Root, ( ) , (
Therefore the Average Tooth Width is,
7 Item 24: Number of Radial Ventilating Ducts
Refer to Art. 16. Not more than three ducts should be necessary in an armature 9 to 11 in long, with each duct ⁄ in. wide.
Therefore,
Use one (1) radial ventilating duct.
Item 25: Width of Radial Duct ( )
⁄ in or 0.375 in Item 26: Net length of Armature Core ( ln )
Refer to Art. 16.
( ) , ( )-
Item 27: Net Cross Section of Teeth Under Pole
( ) ( ) ( ) ( ) (
) ( )
Item 28: Apparent Density in Teeth Under Pole ( ) ( ) , , , But referring to the table on number 17, a 50 cycles have a of 126,000
and applying the
10 % tolerance, a 50 cycles should be below 138,600 .
Since the preliminary value of is above the upper limit, therefore, it will be necessary to correct
(increase) the length of the armature core to bring the Flux Density down to a reasonable figure. Assuming = 138,000
Net Cross Section of Teeth = , , , = 118.577 Net Length Armature is.
8 To solve for the new and final value of ,
Then, ( )( ) , ( )( ) , , , , ( ) ,
Now both have an acceptable values wherein both values are within 10 % tolerance.
Item 29: Number of Radial Ventilating Ducts By referring to Art. 16, sin ( ) Then, ; cos d ( ) ( ) Therefore,
Total Length per Turn = Ic + 2 Ia = ( )
Item 30: Resistance of one turn, Ohms at 60
( )
9 Item 31: Resistance of Armature, ( )
( ) (
)
Finally, the Total Resistance in the Armature
( ) Item 32: IR Drop in Armature
Item 33: I2R Loss in Armature Winding
( )( ) ,
Item 34: Full load Flux
Assuming a brush contact drop of 2 volts, and a series field and commutating-field drop of about one-half that in the armature winding, the total generated voltage at full load must be,
= 672.011Volts
Therefore, the Full Load Flux must be,
(
)
, , .
/
10 Item 35: Flux density in Armature Core below Teeth
From Art. 17, the suitable density for a frequency of 50 Hz is 76,000. Bearing in mind that the air-gap is into two equal parts below the teeth, the armature flux is one-half of the total flux. Therefore, density in core is 76,000 ⁄ .
, ,
( )( , ) And the final value of Flux Density in Armature Core below Teeth is,
, , ( )( ) , Item 36: Internal Diameter of Core Stampings
( ) ( ) Item 37: Weight of iron Core
The weight of a cubic inch of Iron is 0.28 lb, and the total weight of iron Core below the Teeth will be,
,( ) ( )
( ) . / *, ( )- ( ) + ,
Item 38: Weight of iron Teeth
( ) ( )( ) ( )
Item 39: Total Weight of Armature Stampings
,
11 DESIGN SHEET FOR ARMATURE OF D-C GENERATOR (PART – 2)
ITEM NO. SPECIFICATION: 1550 kW ; 660/750 Volts ; 500 rpm SYMBOL Preliminary or Assumed Values Final Values
COMMUTATOR AND BRUSHES
40 Diameter of Commutator, in Dc - - - 36.45
41 Average volts per turn of armature winding - - - - - - 37.19
42 Number of turn between bars - - - - - - 1
43 Total number of Commutator bars - - - - - - 239
44 Bar pitch, in - - - - - - 0.479
45 Width of copper bar (on surface), in - - - - - - 0.449
46 Radial depth of bar, in - - - - - - 3.43
47 Current density at brush-contact surface, amp per sq in 40 40.061
48 Contact area per brush set, sq in - - - 19.63 19.6
49 Brush arc (circumferential width), in - - - - - - 1.0
50 Axial brush length (total) per set, in - - - - - - 19.6
51 Number of brushes per set - - - - - - 31.36
52 Axial length of Commutator, in Lc - - - 22.85
53 Brush-contact drop, volts - - - - - - 2.3
54 Brush-contact loss, watts - - - - - - 9,096.684
55 Brush-friction loss, watts - - - - - - 12,684.355
56 Total brush loss, watts - - - - - - 21,781.039
57 Drawing to scale giving leading dimensional of
12 DESIGN OF COMMUTATOR AND BRUSHES
Item 40: Diameter of Commutator (Dc)
From Art. 14, a diameter of Commutator not exceeding 80 % of the Armature Core Diameter is generally found practical, although a reasonably good rule to follow is to make . Thus,
This is 63.57 % of the core diameter and makes the peripheral velocity, = 0.6357 x 7,509.72 = 4,773.929 fpm
Item 41: Average Volts per Turn of Armature Winding
⁄ ( ) ⁄
Item 42: Number of Turns between Bars
One (1)
Item 43: Total Number of Commutator Bars
( ) ( )
Item 44: Bar Pitch
( )
Item 45: Width of Copper Bar (On Surface)
Using in mica for insulation, the width of copper bar Bar Pitch ― , therefore, 479― 0.03 = 0.449in at the Commutator surface.
Item 46: Radial Depth of Bar
Since the Peripheral Velocity is less than 4,500 fpm, the Radial Depth of the Commutator Segment should be about,
13 Item 47: Current Density at Brush-Contact Surface ( )
The Current Density over the Brush Contact Surface is about 30 to 50
, taking 40
as
preliminary value.
Item 48: Contact Area per Brush Set
( ⁄ )( )
( )
( )
Item 49: Brush Arc (Circumferential Width)
1.0inch
Item 50: Axial Brush Length per Set
Item 51: Number of Brushes per Set The actual area per Brush Set is,
From Art. 34, the usual width of Brush is something between the limits ⁄ in and ⁄ in., and as a further check on the desirable dimensions, the width should not exceed one-tenth of the pole pitch referred to the Commutator surface. Thus, use a Brush of ⁄ in. width.
Then,
⁄
The Current Density will be increased slightly to;
(
)
Item 52: Axial Length of Commutator (Lc)
In addition to the 19.6 in which must be provided for the four ⁄ in Carbon Brushes, the Axial Length of the Commutator Face must allow for the following:
a. Brush holder and clearances = ⁄ ⁄ b. Staggering of (+) and (-) Brushes = ⁄ c. End clearance for Brushes = 1 in
14 Total Length will be,
Item 53: Brush Contact Drop
Referring to Fig. 38, the Brush Contact Drop for Hard Carbon at about 40. is 2.085 volts. Allowing the 10 % of roughness, chipping and irregularities, thi drop will be about
2.3 volts.
Item 54: Brush Contact Loss
Brush Contact Drop x P x Ic = 2.3 (12 x 329.59) = 9,096.684 watts
Item 55: Brush Friction Loss
For a peripheral speed greater than 4,000 fpm, use c = 0.25 for hard carbon; P = 2 ⁄
,
( )( )( )( )
, ,
Item 56: Total Brush Loss
9,096.684 + ,
,
Item 57: drawing to Scale giving leading Dimensions of Armature and Commutator
√
√ ,
