Alfred Still.

Principles of electrical design; d. c. and a. c. generators online

. (page 17 of 30)
Online LibraryAlfred StillPrinciples of electrical design; d. c. and a. c. generators → online text (page 17 of 30)
Font size
QR-code for this ebook


91 " "
92 "
92 " "


y>.


%


Full load





CHAPTER X

PROCEDURE IN DESIGN OF D.C. GENERATOR-
NUMERICAL EXAMPLE

61. Introductory. Since the procedure about to be followed
in working out a numerical example in dynamo design is not
likely to meet with the approval of every practical designer, it
is well to remember that an attempt is here made to base the
work on fundamental principles and show how these principles
may be applied in the detailed design of dynamo-electric
machinery. The method here presented is one that will yield
very satisfactory results when developing new types of machines,
or when no account need be taken of existing patterns or tools.
The practical designer is usually compelled to use stock frames
and armature punchings, and adapt these to the requirements
of the specification. He must effect some sort of compromise
between the ideal design and a design that will comply with
manufacturing conditions. In the method here followed, the
assumption is made that the designer is given a free hand to
produce a machine that shall, in all respects, be suitable for
the work it has to perform, and of which the cost and efficiency
shall be generally in accordance with present-day requirements.
The various steps in the electrical design of a D.C. generator will
be followed in logical sequence, and if the work appears unneces-
sarily detailed and drawn out, it must be remembered that
the method has an educational, apart from a practical, value;
it illustrates the application of theoretical principles to a con-
crete case, and shows how the practice of engineering is largely
a matter of scientific guesswork. The experienced designer will
be able to skip many of the intermediate steps here purposely
included; because he will be able to rely on the engineering judg-
ment he has acquired during years of practice in similar work.
The point that must never be lost sight of is that, when an engi-
neer makes a guess in respect to a dimension or any quantity
of doubtful or indeterminate value, he is always able to check

199



200 PRINCIPLES OF ELECTRICAL DESIGN

the accuracy of his estimate by satisfying himself that the
results obtained accord with the known laws of physics.

Since the design of commutating poles was treated at some
length in the chapter on commutation (see Art. 51, Chap. VIII),
it is proposed to select for the purpose of illustration a machine
of comparatively small output, and endeavor to obtain satis-
factory commutation without the addition of interpoles.

62. Design Sheets for 75-kw. Multipolar Dynamo. The
particulars contained in the following design sheets are more
than sufficient for the needs of the practical designer; but they
serve a useful purpose as a guide in making the calculations.
The items are numbered for easy reference, and it will be found
convenient to calculate the required dimensions and quantities
generally in the order given, although the particular arrange-
ment here adopted need not be adhered to rigidly. Two columns
are provided for the numerical values, and they are supposed
to be filled in as the work proceeds. The first of these columns
is to be used for assumed values or preliminary estimates; while
the last column is reserved for the corrected final values.

The actual calculations will follow the design sheets, and
they will be shown in sufficient detail to be self-explanatory.
The calculation of items of which the numerical values are ob-
viously derived from previously obtained quantities will not
always be shown in detail. The design sheets should be fol-
lowed item by item, and where the method of calculation is
not clear, the succeeding pages may be consulted for explanations
and references to the text.

The machine to be designed is for a continuous output of
75 kw. The terminal voltage on open circuit is 220; but it is
required to raise this to 230 at full load in order to compensate
for loss of pressure in cables between the dynamo and the place
where the power is utilized. The machine is therefore over-
compounded. It is to be belt-driven at a constant speed of
600 revolutions per minute. The temperature rise is not to
exceed 40C. after a full-load run of not less than 6 hr. duration.

All numerical calculations have been worked out on the slide
rule, and scientific accuracy in the results is not claimed.



PROCEDURE IN DESIGN OF D.C. GENERATOR 201

DESIGN SHEET FOR CONTINUOUS-CURRENT GENERATOR



SPECIFICATION


Symbols


Preliminary
or assumed
values


Final
values


1 Kw output






75


2. No-load terminal voltage






220


3 Full-load terminal voltage






230


4. Speed, r p m






600


5. Permissible temperature rise


T =




40C


PRELIMINARY ASSUMPTIONS AND CALCULATIONS

6 Number of poles
7. Frequency
8. Per cent, armature surface covered by poles
9. Specific loading of armature
10. Type of armature winding (series or multiple)
11. Apparent air-gap density (open circuit)
12. Line current
13. Armature current (per circuit)
14. Armature diameter (inches)
15. Peripheral velocity (feet per minute)
16. Total number of face conductors
17. Armature ampere-turns per pole
18. Length of air gap. ... . .


P =
/ =
r =
Q =

B 8 -

7 =

Ic =
D =
v =
Z =

5 =


4
20
0.72
475

8,000

83.4
19.63

350
3,650
228


4
20
0.72
461
lap.

326
82.6
19.5
3,070
342
3,565
0.25


19. No-load flux per .pole (maxwells)
20. Pole pitch (inches)
21. Pole arc (inches)
22. Area under pole face (square inches)
23. Axial length of armature (gross)


* =

T =*

la =


6,290,000

11.05
122
11 1


6,430,000
15.34
11

11


24. Axial length of pole face
25. Cross-section of each armature conductor (square
inches)




10.6
0402


10.5
0.039


26. Dimensions of armature conductor (inches)






!4X$i


27. Number of slots




57


57


28. Number of inductors per slot




6


6


29. Slot pitch (inches)


X =




1.076


30. Slot width (inches)


8 =




0.5


31. Slot depth (inches)
32. Tooth width, top (inches)
33. Tooth width, average (inches)


d =




1.0
0.576
0.521


34. Tooth width, bottom (inches)
35. Number of radial cooling ducts
36. Width of duct (inches)
37. Net length of armature (inches)
38. Net tooth section under pole (average)
39. Apparent flux density in teeth (open circuit)

ARMATURE LOSSES AND TEMPERATURE RISE (FULL LOAD)
40. Length mean turn of armature coil (inches)


n =
l n =


3

9.1
48.6
20,500


0.466
3
0.4
9

48.1
20,700

43 3


41. Ratio of active to total copper






337


42. Resistance of one turn (ohms)






00132


43. Resistance of one path through armature (ohms)






0564


44. Resistance of armature (ohms)






0141


45. IR drop in armature (volts)






4.7


46. IR drop in series coils (main field) (volts)




1.6





202 PRINCIPLES OF ELECTRICAL DESIGN

DESIGN SHEET FOR CONTINUOUS-CURRENT GENERATOR. Continued





Symbols


Preliminary
or assumed
values


Final
values


47. IR drop in interpole winding
48. IR drop (total) at brush-contact surfaces (volts) . . .
49. I 2 R loss in armature winding




2
1 570


2.25
1 540


50. I Z R loss to be radiated from armature core
51. Full-load useful flux per pole


4>


530


6 970 000


52. Flux density in armature core below teeth






15 000


53. Full-load apparent tooth density (mean value)
54. Radial depth of armature stampings below teeth
(inches)


Rd~


22,400


4


55. Internal diameter of armature core (inches)
56. Weight of iron in armature core below teeth (pounds)
57. Weight of iron in teeth (pounds)
58. Iron loss in core (watts) at full load
59. Iron loss in teeth (watts) at full load.
60. Total iron loss at full load
61. Total watts to be radiated from armature core
62. Cooling surface of active belt (square inches)




1,284
390
1,674
2,204


9.5
428
75
1,284
360
1,644

675


63. Cooling surface of inner bore (square inches)






329


64. Cooling surface of ducts and ends (square inches) . .






1,820


65. Temperature rise of armature (degrees Centigrade) .
STUDY OF FLUX DISTRIBUTION IN AIR GAP

66. Permeance per slot pitch at center of pole face
67. Equivalent air gap (inches)
68. Drawing of pole to scale and measurement of flux
paths


T =
P\ =

d e =

Fig 78


37


98
0.307


69. Permeance curve for air gap
70. Calculation of actual tooth densities in terms of air-
gap densities, and plotting curve connecting these
values.
71. Saturation curves for air gap, teeth, and slots for a
number of points on armature surface
72. Open-circuit m.m.f. curve. .
73. Open circuit flux distribution curve A
74. Required area of flux curve A


Fig. 79

Fig. 82
Fig. 83
Fig. 79




106 3


75. Corrected open-circuit m.m.f. curve
76. Corrected flux curve A to check with required area
(item 74)


Fig. 83
Fig 84




107


77. Maximum value of armature ampere-turns per pole
(item 17) .






3 565


78. Resultant m.m.f. curve to get flux curve B


Fig. 83






79. Flux curve B. Measured area =


Fig. 84




99.5


80. Required area of full-load flux curve C =






115


81. Estimated additional field ampere-turns to bring up
area of flux curve from area of B curve to required
area of C curve
82. M.m.f. curve for flux curve C
83. Full-load flux curve C


Fig. 83
Fig. 84




900











PROCEDURE IN DESIGN OF D.C. GENERATOR 203

DESIGN SHEET FOR CONTINUOUS-CURRENT GENERATOR. Continued



COMMUTATOR DESIGN


Symbols


Preliminary
or assumed
values


Final
values


84. Diameter of commutator (inches)
85. Peripheral velocity (feet per minute)
86. Volts per turn of armature winding (average value).
87. Number of turns between bars
88. Total number of commutator bars
89 Bar pitch (inch)


^ =




13.5
2,130
2.87
1
171
0.247


90. Thickness of mica insulation between bars (inch) . .
91. Width of bar (on surface) (inch)
92. Radial depth of bar (inch)
93. Average current density over brush-contact sur-
face (amperes per square inch)
94. Contact area of brushes (all + brushes (square
inches)) . .


M =


35
9.32


0.032
0.215
1.75

36.2
9


95. Contact area per brush set (square inches)
96. Circumferential width of brush (inch)
97. Brush width referred to armature surface (inch).. . .
98. Total axial brush length, per set (inch)
99. Number of brushes per set
100. Axial length of commutator surface (inches)

CALCULATION OF FLUX REQUIRED IN COMMUTATING ZONE

101. End flux (maxwells)
102. Equivalent slot flux (two slots)
103. Total flux entering teeth in commutating zone. . . .
104. Average flux density of commutating field
105. Calculated density at beginning of commutation . .
106. Calculated density at end of commutation . .


*.=
*..=


4.66
7*


4.5
0.75
1.083
6
4
7*

31,300
11,730
54,760
712

586
838


107. Permissible departure from ideal values of flux
density, -f- or (gausses)






1,720


COMMUTATION LOSSES AND TEMPERATURE RISE

108. Brush pressure, pounds per square inch
109. Resistance per square inch of contact surface
110. Total brush resistance (full-load conditions)
111. Total voltage drop at brush-contact surfaces
1 12. J2/2 loss (watts)
113. Friction loss (watts)
114. Total commutator loss (watts)




730


1.5
0.025
0.00556
2.25
744
324
1,054


115. Total cooling surface (square inches)
116. Temperature rise of commutator (degrees Centi-
grade


T




"470.8
48.4


POLE CORES AND FRAME
117. Leakage coefficient (assumed)




1.2




118. Flux density in pole core (full load)






16 500


119. Cross-sectional area of pole core (square inches)






78 54


120. Pole-core width \ ,.
> diameter (inches)






10


121. Pole-core length (axial) /
122. Pole length (radial) (inches)






7


123. Flux density in frame (yoke ring)






15 000


124. Cross-sectional area of frame (square inches)






43.2



204 PRINCIPLES OF ELECTRICAL DESIGN

DESIGN SHEET FOR CONTINUOUS-CURRENT GENERATOR. Continued





Symbols


Preliminary
or assumed
values


Final
values


125. Frame width (axial) (inches)






13


126. Frame thickness (at center) (inches)






3.5


128. Calculation ami plotting of saturation curve for the
complete magnetic circuit

FIELD WINDINGS

129. SI per pole for total magnetic circuit (no load) . . .
130. SI per pole for total magnetic circuit (full load) . .
131. SI per pole to compensate for distortion and
demagnetization


Fig. 87




5,930
7,850

400


132. SI per pole in shunt field at full load






6 200


133. Thickness of shunt winding (inches)




2


2


134. Length of winding space for shunt coils (inches) . .
135. Size of shunt field wire (circular mils)




5

4 880


5

5 178


136. Shunt field current (full load)






4 56


137. Number of turns per pole in shunt winding
138. SI in series winding, per pole . . .






1,360
1 650


139. Series field current. ...




326


300


140. Number of turns of series wire, per pole
141. Size of series field wire (square inches)
142. Resistance of series field (hot) .




0.25


5H

0028


143. Cooling surface of field coils (one pole) (square
inches)






680


144. Surface temperature rise of field coils (degrees
Centigrade) . .


T




43


145. Current in diverter..






30 56


146. Resistance of diverter. .






0275


EFFICIENCY

147. Corrected value for tooth loss at full load
148. Calculation of efficiency at M, li, H, 1, and 1H,
full-load output






360


149. Plotting of efficiency curve ...


Fig 88















63. Numerical Example Calculations. Items (6) and (7):
Number of Poles. Refer to table in Art. 20 (page 81). Usual
number; 4 or 6. On page 78 in same article, the frequency is
stated to be generally between 10 and 40. With four poles,

r 4 600 . . . ,

/ = 2 X ^TTT, which is satisfactory.

Item (8): Ratio of Pole Arc to Pole Pitch. Refer Art. 19,
pages 74 and 76. Since there are no interpoles, we shall make
r = 0.72.

Item (9) : Specific Loading. Refer Art. 19, pages 74 and 76.
For 75-kw. machine, try q = 475.



PROCEDURE IN DESIGN OF D.C. GENERATOR 205

Item (10): Type of Winding. Refer Art, 23, page 84. In
this case some doubt exists as to whether a wave or lap winding
should be adopted. If the pressure were higher say 500 volts
a series, or two-circuit, winding would be preferable. With
only 220 volts to be generated, we shall adopt a simplex multiple
winding which, with our four-pole machine, will give us four
armature circuits in parallel.

Item (11): Apparent Air-gap Density. Refer to the table on
page 75 in Art. 19, and select B g = 8,000.

Items (12) and (13): Line Current = 7500 % 3 o = 326 amp.
The current in each armature conductor will be one-quarter
of this (Art. 23, page 87) if we neglect the shunt exciting
current. The shunt excitation of a 75-kw. machine might
amount to 2.3 per cent, (see Art. 58, page 192), so that the

OOf!

full-load current per conductor will be -j- (1 + 0.023) = 83.4

amp., approximately.

Item (14): Armature Diameter. Using the output formula
(43) as developed in Art. 19 (page 74), we have:

_ 75,000 X 60X10*

tflj 6.45 X 7T 2 X 8,000 X 475 X 0.72 X 600 "

Referring now to page 77, we can use formula (46) to get l a
in terms of D. The ratio l a /r t for an economical design of
machine of this size and number of poles, will probably have a
value between 0.5 and 0.8. For a square pole face,

t = rr. . r . o.72

r r

and this seems a good proportion to aim at, especially as it will
allow of cylindrical pole cores being used. With the square
pole face,



l a = = 0.567D
whence



na _. _

" 0.567 ' 7 ' 5e
and

D = 19.63 in.

Let us therefore decide upon armature punchings of 19.5 in.
external diameter.



206 PRINCIPLES OF ELECTRICAL DESIGN

Item (16): Number of Inductors. Refer Art. 18, page 72,
and Art. 19, page 74.

_ TrDq TT X 19.5 X 475 .

Z = Y^ = ~ ^5~i - = 350 (approximately)

l c OO.4

Item (17) : Full-load Armature Ampere-turns.

Z/ c _ 350 X 83.4
(SI). == 2^ : 2X4 3 ' 6c

(18): Lenpto of Air Gap. Refer Art. 36, page 119.

= - 228; or (say) * in -



Item (19): Maxwells per Pole. Refer formula (38), Chap. IV,
page 72.

The flux per pole on open circuit, if Z has the value as calculated
for item (16), is

220 X 60 X 4X 10 8
* - 4X600X350 = 6 ' 290 ' 000 maxwells '

Item (20) : Pole Pitch. Refer Art. 19, page 74 and Art. 20,
page 78.

7TX19.5 ,_-.
T = - - = 15.34 in.

Item (21) : Pole Arc. Refer Art. 19, page 74.

r X r = 15.34 X 0.72 = 11.05, or (say) 11 in.
Items (22), (23) and (24): Dimensions of Air Gap.



* = = 786 gq cm

B g 8,000 = 122 sq. in.

whence l a = 12 Ki = 11.1, and the axial length of pole face will
be something less, or (say) 10.6, to avoid the large amount of
flux which would otherwise curve round into the flat surface of
the core discs, where it would cause eddy currents. These axial
dimensions, both of armature and pole shoe, are, however, sub-
ject to correction after the actual winding details have been
settled; because the practical considerations may lead to a
change in the number of inductors (Z), and a corresponding
change in the amount of flux entering the armature.



PROCEDURE IN DESIGN OF D.C. GENERATOR 207

Item (25): Cross-section of Armature Conductors. By formula
(51), page 97.



QQ \

whence area of cross-section = ' 7 . = 0.0402 sq. in.

Z,(Ji O

Items (26) to (31): Conductor and Slot Dimensions. It is neces-
sary to find by trial the best arrangement of slots and conductors
to provide approximately 350 inductors (item (16)). The number
of slots per pole should not be less than 10 (Art. 23, page 84
and Art. 26, page 93), and there must be an even number of
conductors in each slot. A winding consisting of 44 or 45 slots,
each with eight conductors, would be a possible arrangement;
but the slot pitch would be large with so few slots. It would
seem advisable to have a winding with six conductors per slot.
The number of slots would then be approximately, 35 % = 58.3.
Either 14 or 15 slots per pole would be suitable for a parallel
winding; but since it is usual to provide the armature punchings
of four-pole machines with an uneven number of slots, so that
the armature core can be used for a two-circuit winding, we
shall adopt a winding of 57 slots with six conductors per slot,
making the corrected value of Z = 57 X 6 = 342

The slot pitch (refer Art. 25, page 92), is,



Oi

The number of teeth between pole tips is,
15.34 - 11



1.076



= 4.03



Had this figure been less than 3.5 (see Art. 26, page 93), it
might have been advisable to increase the number of teeth, or
widen the space between pole tips.

In order to determine the actual dimensions of the armature
conductors, it will be found convenient to assume, a width of slot.
This should be about one-half the slot pitch, or, say, 0.5 in.
(see Art. 25, page 92). If we adopt the arrangement of con-
ductors in the slot shown in Fig. 77, the width of each conductor
will be one-third of the total width available for copper. The
cotton covering on each conductor would add, say, 16 mils total
to its thickness; and the slot insulation will be about 0.035 in.



208



PRINCIPLES OF ELECTRICAL DESIGN



thick (see Art, 28, page 96). The space left for copper is
therefore 0.5 - (0.07 + 0.048) = 0.382; and the width of each
conductor is one- third of this amount, or 0.127. Let us make
this J in. (0.125). The depth of the (rectangular) conductor

0402

= 0.322, or, say, % 6 in. (0.312).



will be



These are the



0.125

dimensions called for under item (26); and the corrected value
for item (25) is 0.312 X 0.125 = 0.039 sq. in.
The required slot depth is made up as follows:

Hard-wood wedge, which should be about 0.200 in.

Insulation above, below, and between the coils

= 3 X 0.035 0.105 in.

Cotton covering on wires (twice 0.016) 0.032 in.

Copper . 0.624 in.



0.961 in.
or, say, 1 in. for the dimension d in Fig. 77.

Before finally adopting these dimensions, it will be necessary

to see that the flux density
in the teeth is not excessive
(item (39)).

Items (32) to (34) : Tooth Di-
mensions. The width of tooth
at the top is t = X s = 0.576.

The circumference of the
circle through the bottom of
the slots is TT X 17.5; and since
the slots have parallel sides, the
width of tooth at the root is
TT X 17.5




FIG. 77. Arrangement of conduc-
tors in slot



57



- 0.5 = 0.466.



Items (35) and (36) : Cooling Duds. Refer Art. 33, page 105.
Not more than three ducts should be necessary in an armature
11 in. long. Each duct might be 0.4 in. wide.
Item (37): Net Length of Armature. Refer Art. 31, page 103.

l n = 0.92 (11.1 - 1.2) = 9.1 in.

Item (38) : Net Cross-section of Teeth under Pole. The cross-
section of iron in the teeth under one pole, at a point halfway
up the tooth, is,

9.1 X 0.521 X X 0.72 = 48.6 sq. in.



PROCEDURE IN DESIGN OF D.C. GENERATOR 209

Item (39): Flux Density in Teeth. Refer Art. 31, page 102,
and Art. 32, page 104. Before calculating the flux density in
the teeth, it is necessary to correct the figure for flux per pole
(item (19)), because the number of face conductors (Z) has been

changed. Thus,

350
$ = 6,290,000 X = M30,000 maxwells.



The apparent flux density at the center of the tooth, under
open-circuit conditions, is therefore,



= 20,500 gausses.

Referring to the table on page 104, it will be seen that a maximum
tooth density of 22,000 is permissible when the frequency is 20.
We do not yet know what will be the actual flux density at the
root of the teeth under full-load conditions; but it is not likely
to be excessive, and we may proceed with the design.

At this stage it might be well to alter the gross length of the
armature core from 11.1 to exactly 11 in., reducing the net
length accordingly. This will account for the corrected values
of items (37) to (39) in the last column of figures of the design
sheets.

Item (40): Length per Turn of Armature Coil. Referring to
Art. 30, page 97, we have,

1.15s 1.15X0.5
sma= ~X~ ~L076~
whence

a = 32 20'
and

cos a = 0.845



By formula (52), page 98,

_ 2 X 15.34
le ~ 0.845



+ 4 + 3 = 43.3 in.



Item (41) : Ratio of Copper in Slots to Total Armature Copper.
Refer Art. 34, page 109.

2l a 22



2l a + le 22 + 43.3



= 0.337



Items (42) to (45) : Armature Resistance. Refer Art. 30, page
97. The total length of one turn of the armature winding is



14



210 PRINCIPLES OF ELECTRICAL DESIGN

65.3 in., and by formula (21) page 83, the resistance at about
60C. will be

&. Pv Q

R = - 7 = 0.00132 ohm.

0.039 X 10 6 X -

7T

There are Z/2 or 171 turns in the armature winding, and there-
fore 171/4 = 42.75 turns in series in each armature circuit.
The value of item (43) is therefore 42.75 X 0.00132 = 0.0564
ohm; and of item (44), one-quarter of this amount, or 0.0141
ohm. The IR drop in armature winding is 0.0564 X 83.4 = 4.7
volts, or 2.04 per cent, of the full-load terminal voltage. This
compares favorably with the approximate figures given on
page 99.

Item (46) : Pressure Drop in Series Winding. Refer Art. (43)
page 139. We may assume this voltage drop to be one-third
of 4.7 or, say, 1.6 volts.

Item (48): Pressure Drop at Brushes. Refer Art. 53, page
179. Assume two volts.

Items (49) and (50) : Watts Lost in Armature Windings. Total
PR = El = 4.7 (83.4 X 4) = 1,570 watts. Item (50) is the
portion of this total loss which occurs in the "active" copper
of the armature; its value is,

1570 X 0.337 = 530 watts,

wherein the factor 0.337 is item (41) of the design sheets.

Item (51) : Flux Entering Armature at Full Load. Refer Art.
43, page 135.

The volts to be developed at full load are,

230 + 4.7 + 1.6 + 2 = 238.3
The full-load flux must therefore be,

238 3
6,430,000 X - = 6,970,000 maxwells.



Items (52) to (55): Flux Density in Armature Core. Internal
Diameter. Usual flux densities for different frequencies are
given in the table in Art. 32 (page 104). A density of 14,000
gausses would be satisfactory; but since the losses in the teeth
are likely to be below the average because a 1-in. depth of
slot is small for a machine of this size a density of 15,000 may



PROCEDURE IN DESIGN OF D.C. GENERATOR 211

be tried. Bearing in mind that the maximum flux in the arma-
ture core is one-half of the total flux per pole, we have,

3>
RdXlnX 6.45 X 15,000 = ^

whence

6,970,000

d ~ 2 X 9 X 6.45 X 15,000 ~

Item (56): Weight of Iron in Core. The weight of a cubic
inch of iron is 0.28 Ib. and the total weight of iron in the core



Online LibraryAlfred StillPrinciples of electrical design; d. c. and a. c. generators → online text (page 17 of 30)