Design Sheet of Armature for Dc Generator

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

7) Tolerance

± 10 %

1

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

P ƒ r q

Number of Poles - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Frequency, Hz - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

2

Ratio of pole arc to pole pitch - - - - - - - - - - - - - - - - - - - - - - - - - - - -

3

Specific Loading - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

4

Apparent Air-gap flux density (open circuit) - - - - - - - - - - - - - - - -

5

Line Current (full load) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

6

Type of Winding - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

7

Armature current per circuit - - - - - - - - - - - - - - - - - - - - - - - - - - - -

8

Output factor (laD2) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

9

Armature diameter, in - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

10

Peripheral velocity, fpm - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

11

Total number of face conductors - - - - - - - - - - - - - - - - - - - - - - - - -

12

Number of slots - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

13

Number of conductors per slot - - - - - - - - - - - - - - - - - - - - - - - - - -

14

Axial length of armature core; gross, in - - - - - - - - - - - - - - - - - - - -

15

Flux per pole (open circuit) - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

16

Pole pitch, in - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

17

Pole arc, in - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

18

Area covered by pole face (rτla), sq in - - - - - - - - - - - - - - - - - - - - -

19

Dimensions of armature conductors, in. units - - - - - - - - - - - - - - -

20

Slot pitch, in - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

21

Slot width, in - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

22

Slot depth, in - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

23

Tooth width, in.

I - ----Ic - ----D Z S - ----la

- ----- ----s d t

At top - - - - - - - - - - - - - - - - - - - - - - - - - - - - - At root - - - - - - - - - - - - - - - - - - - - - - - - - - - - Average - - - - - - - - - - - - - - - - - - - - - - - - - - - -

24

Number of radial ventilating ducts - - - - - -- - - - - - - - - - - - - - - - - -

25

Width of radial ducts, in - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

26

Net length of armature core, in - - - - - - - - - - - - - - - - - - - - - - - - - - -

27

Net tooth section under pole, at center, sq in - - - - - - - - - - - - - - - -

28

Apparent density in teeth under pole, at center, sq in - - - - - - - - - -

29

Length per turn of armature coil, in - - - - - - - - -- - - - - - - - - - - - - - -

30

Resistance of one turn, ohms at 60°C - - - - - - - - - - - - - - - - - - - - - -

31

Resistance of armature, ohms - - - - - - - - - - - - - - - - - - - - - - - - - - -

32

IR drop in armature, volts - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

33

I2R loss in armature winding, watts - - - - - - - - - - - - - - - - - - - - - - -

34

Estimated full-load flux per pole - - - - - - - - - - - - - - - - - - - - - - - - - -

35

Flux density in armature core below teeth - - - - - - - - - - - - - - - - - -

36

Internal diameter of core stampings, in - - - - - - - - - - - - - - - - - - - -

37

Weight of iron in core (without teeth), lb - - - - - - - - - - - - - - - - - - -

38

Weight of iron core in teeth, lb - - - - - - - - - - - - - - - - - - - - - - - - - - -

39

Total weight of armature stampings, lb - - - - - - - - - - - - - - - - - - - - -

- ----- ----n - ----ln - -----

---------------------------------------------

12 - -------0.64 1,055 62,550 - -------- -------392.59 44,481.004 57.34 7,509.72 484 - -------- -------13.53 16.363 x106 15.012 9.61 130.023 - -------- -------- -------- -------- -------- -------- -------- -------- -------12.103 103.718 157,770.458 - -------- -------- -------- -------- -------- -------76,000 - -------- -------- -------- --------

12 50 0.64 1,055 70,706.506 2,348.485 lap 50,682.602 57.34 7,509.72 484 20 24 15.415

148.138 (0.185x0.345) 9.007 0.8 1.104 8.207 7.86 8.034 1 0.375 13.837 118.577 91,999.51 68.602 0.000422 0.0085 6.674 31,441.889 16.661x106 76,002.571 39.572 4,484.022 665.487 5,149.509

2

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, Ic =

,

(

) = 392.59 Amp 3

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

=

And the Slot per Pole (

= 20 slots

) would be,

⁄

Item 13: Number of Conductors per Slot ( CS )

Item 14: Axial length of Armature Core ( la ) Solving for

, , (

) 4

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

( (

)

) (

) 5

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,

6

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 10 % tolerance, a 50 cycles should be below 138,600

of 126,000

and applying the

.

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.

.

/(

)

7

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

(

)

,(

)(

)-

8

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,

( ,

,

,

,

) .

/

9

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 airgap 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

, , 10

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

41

Average volts per turn of armature winding

42

Number of turn between bars

43

Total number of Commutator bars

44

Bar pitch, in

45

Width of copper bar (on surface), in

46

Radial depth of bar, in

47

Current density at brush-contact surface, amp per sq in

48

Contact area per brush set, sq in

49

Brush arc (circumferential width), in

50

Axial brush length (total) per set, in

51

Number of brushes per set

52

Axial length of Commutator, in

53

Brush-contact drop, volts

54

Brush-contact loss, watts

55

Brush-friction loss, watts

56

Total brush loss, watts

57

Drawing to scale giving leading dimensional of Armature and Commutator

Dc ------------------------------------------------------------Lc -------------------------------

--------------------------------------------------------40 19.63 ---------------------------------------------------------------Fig. II

36.45 37.19 1 239 0.479 0.449 3.43 40.061 19.6 1.0 19.6 31.36 22.85 2.3 9,096.684 12,684.355 21,781.039

11

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 0.03 = 0.449in at the Commutator surface.

Bar Pitch ―

, therefore, 479―

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,

12

Item 47: Current Density at Brush-Contact Surface (

)

The Current Density over the Brush Contact Surface is about 30 to 50 preliminary value.

, taking 40

as

Item 48: Contact Area per Brush Set ( ( ⁄ )(

) (

)

)

Item 49: Brush Arc (Circumferential Width) 1.0 inch 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 Length of the Commutator Face must allow for the following: a. Brush holder and clearances =

⁄

⁄ in Carbon Brushes, the Axial

⁄

b. Staggering of (+) and (-) Brushes = ⁄ c. End clearance for Brushes = 1 in d. End Play = ⁄ 13

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 ( )(

)(

9,096.684 +

,

)( ,

,

)

⁄

,

Item 56: Total Brush Loss

,

Item 57: drawing to Scale giving leading Dimensions of Armature and Commutator

√ √

,

14

15