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1
HIGH SPEED DYNAMO ELEOTEIO MAOHINEBY
BY
H. M. HOBART, B.Sc.
M. INST. C.E., MEM. A.I.E.E., M.I.E.E. AND
A. G. ELLIS, Assoc. A.I.E.E.
ASSOCIATE CITY AND GUILDS OF LONDON INSTITUTE
FIRST EDITION
FIRST THOUSAND
NEW YORK
JOHN WILEY & SONS
London: CHAPMAN & HALL, Ldhted
1908
COPYRIOHTRD, 1906, BY
H. M. HOBART AJfD A. 6. ELL.I8 Entered at Stationers* Ball
StanbopepteM
P. H. CILSON COMPAHY
BOSTON. U.S.A.
125005
DEC l-i 1908
PREFACE.
With the recent extensive introduction of high speeds with steam turbines and hydraulic turbines, the importance of thoroughly inves- tigating the influence of such speeds on the design of dynamo elec- tric machinery is quite obvious, and has been the primary motive in writing the present treatise. The influence of the rated speed is, however, so closely associated with that exerted on the design by the rated output and pressure, that we have found it necessary to care- fully consider all three factors.
It would be very difficult by customary methods, to disentangle the consequences of these various influences, but by the novel methods to which we have resorted, a clear comprehension of the subject, and the deduction of perfectly definite conclusions have been made practicable. Incidently we should like to call attention to these designing methods as affording fairly certain means of arriv- ing at a more satisfactory design than is likely to be obtained by the use of less practical and less logical methods.
Developments in the design and construction of this class of machinery have been very rapid, and considerable progress has been made even during the last few months: The designs and construc- tions described in this treatise comprise, not only the standard methods by which the especial conditions imposed by high speeds are being met, but also various recent propositions which have not yet withstood the test of time.
The detailed studies of the influences of the various elements in the design, especially of the rated speed, indicate the lines which must be followed, not only in the electromagnetic design, but also in dealing with the constructional problems.
In the preparation of this treatise courtesies have been extended to us by many manufacturing firms, both in their corporate capacity, and through their officials or designers, and we wish to cordially
iii
iy PREFACE.
express our appreciation of these courtesies. We believe the follow- ing to be a complete list:
Messrs. AUgemeine Elektricitats Gesellschaft. British Thomson Houston Company. British Westinghouse Company. Brown Boveri & Co. Brace Peebles & Co. Brash Electrical Engineering Company. Bollock Electrical Manufacturing Company. Dick, Kerr & Co. Galvanische Metal Papier Fabrik. General Electric Company, U. S. A. Kolben & Co.
The Felton-Guillaume, Lahmeyer Co. Le Carbone Company. Morgan Crucible Company. National Carbon Company. Oerlikon Company, Parsons & Co. Bateau Turbine Company. Richardson, Westgarth & Co. Joseph Sankey & Co. Scott & Mountain. Siemens Dynamo Works, Ltd. Siemens Schuckert Works.
The following Engineering and Scientific Societies, and technical periodicals have permitted us to make use of certain materials from their publications :
The Institution of^ Electrical Engineers.
The American Institute of Electrical Engineers.
Electrical Review (England) .
Electrical Review (New York).
Electrical Engineering.
Electrical Times.
Electrician.
Electrical World.
Elektrotechnische Zeitschrifl.
Elektrotechnik und Maschinenbau.
Street Railway Journal.
H. M. H.
A. G. £.
CONTENTS.
PART I. GENERAL CONSIDERATIOH&
CHAPTER I.
PAOK.
Introductort 1
CHAPTER II. Design CosFFiaENTS for Dynamo Electric Machinery 6
CHAPTER III. Criteria for Heating and for Temperature Rise 27
CHAPTER IV. Materials for Construction of High Speed Electric Machines . 45
PAKT n.
ALTERN AXm 6 CURRENT GENERATORS.
CHAPTER V. Pressure Regulation of Alternating Current Generators ... 65
CHAPTER VI.
General Considerations Relating to the Influence of the Rated Output and Speed on the Design of Alternating Current Generators 88
CHAPTER VII. General Procedure in Alternator Design 103
vi CONTENTS.
CHAPTER VIII.
PAGE.
Study op the Influence op the Speed and the Number op Poles
ON Designs for 400 kva. Alternators . ' 131
CHAPTER IX.
Study of the Influence of Speed, Number op Poles and Frequency ON Outline Designs for 3000 kva. Alternators, for Various Speeds 156
CHAPTER X.
High Speed Designs for a Rated Output of 6000 kva. and a
Study of Large Designs in General 197
CHAPTER XI. Construction of High Speed Alternators 219
CHAPTER XII. Stresses in Rotating Field Systems 305
PART m.
CONTINUOUS CURRENT GENERATORS.
CHAPTER XIII.
General Considerations Relating to the Influence of the Rated Output, Voltage, and Speed, on the Design of Continuous Current Generators 319
CHAPTER XIV.
A Method of Determining the Leading Dimensions of Large High
Speed Continuous Current Generators 334
CHAPTER XV.
A Set of Preliminary Designs for Continuous Current Gene- rators FOR Various Rated Outputs and Speeds for the Most Favourable Voltages for these Outputs 364
CONTENTS. vii
CHAPTER XVI.
PAOK.
A Comparative Study or the Designs Set Forth in the Two Pre- ceding Chapters 378
CHAPTER XVII. Troublesome Ratings and Proposals for Their Designs 3d4
CHAPTER XVIII. . CoNSTRUcmoN OP High Speed Continuous Current Generators . . 412
CHAPTER XIX. Brushes and Brush Gear for High Speed Generators 468
LIST OF ILLUSTRATIONS.
FIO. PAGE.
1. Curves showing relation of rated speeds and rated outputs for steam
turbines and other prime movers 3
2. Curve showing relation of rated speeds and rated outputs for de Laval
turbines 3
3. Output coefficients of low and moderately low speed alternators .... 10
4. Output coefficients of alternators 11
5. Output coefficients of alternators 12
6. Output coefficients of alternators 13
7. Output coefficients of continuous current machines 14
8. Output coefficients of continuous current machines 15
9. Output coefficient curves for 500 volt continuous current machines at
different speeds and outputs 16
10. Weight factors of alternators 18
11. Weight coefficient — total weight -s- DJl^ for alternators 19
12. Weight coefficient — total weight -5- D^Xg for high speed alternators . . 21
13. Weight coefficient — total weight -h D^}g for slow speed alternators . . 22
14. Relation between total weight of alternators and DXg 23
15. Relation between total weight and D^)ig for small slow speed alternators . 24
16. Relation between total weight and iy}g for large slow speed alternators . 25
17. Relation of weight to J^Xg in continuous current machines at different
speeds 26
18-21. The armature heating coefficient for the alternating current generators
specified in Chapters VII-X, calculated according to the four methods
as set forth in Table 4 32
22 and 23. The armature heating coefficients for the continuous current
generators specified in Chapter XV, calculated according to the two
methods set forth in Table 7 37
24. Temperature tests of field spools. (Reproduced by permission from the
Joum. /. .B. J?., vol. 38, p. 421) 42
25-32. Curves showing effect of grade of armature laminations on cost and
quality of continuous current generators for 1000 kw., 1000 volts, and
various rated speeds 46
33. Ratio of Total Works Cost of 1000 kw. continuous current dynamos with
special and ordinary grade laminations 47
34-41. Curves showing effect of grade of armature limitations on cost and
quality of 3000 kva. alternators for various rated speeds 48
iz
X LIST OF ILLUSTRATIONS.
Fia. pA.a».
42. Ratio of Total Works Cost of 3000 kva. alternating current generator with
special and ordinary grade armature laminations 49
43-50. Curves showing effect of grade of armature laminations on cost and quality of 400 kva. alternators for various rated speeds. (The points ® relate to the rotating armature designs of column D of specification on pp. 131-135) 51
51. Ratio of Total Works Cost of 400 kva. alternating current generator wit!i
special and ordinary grade armature laminations. (Point A relates to
a rotating armature design) 52
52. Epstein sheet iron tester 52
53. Wound sample of Epstein iron tester 53
54. Curves showing the energy losses in armature stampings (thickness 0.4 to
0.5 mm.). For periodicity of 50 cycles and for different densities . . 55
55. Curves showing the effect of the thickness of the stampings on the figure
of loss (watts per kg. at a periodicity of 50, and a density of 10,000) for stampings by Messrs. Sankey of Belston, England 56
56. Saturation curves used in designing the magnetic circuit of electric
machines 59
57. 57 A and 58. Vector diagrams relating to pressure regulation 69
59. Slot of 3000 kva. alternator 71
60. Saturation curves for 3000 kva. 3-phase 750 r.p.m. 8-pole 50 cycle 11,000
volt alternator 75
61. Alternator magnet cores 76
62. Straight line saturation curves 81
63. Saturation curves showing the effect of the radial depth of the air gap
upon the regulation of a 6000 kva. 3-pha8e 6-pole 750 r.p.m. 37.5 cycle 11,000 volt alternating current generator 83
64. Curves showing relation between regulation and relative proportions of
air gap and iron ampere turns for a 600 kva. alternator 84
65. Curves showing relation between field excitation radial depth of air gap
short circuit current and regulation for 6000 kva. alternator 85
66. Behrend's curve, showing comparative weights of 1000 kw. 3-phasc 25-
cycle generators at different rated speeds 93
67. 1375 kva. 3-phajBe 64-pole 94 r.p.m. 50-cycle 5500-volt alternating current
generator 94
68. 1500 kva. 3-phajBe 6-pole 1000 r.p.m. 50-cycle 11, 000- volt alternating
current generator 94
69. Curves showing air gap diameter for 25-cycle polyphase alternators as a
function of the rated output for various speeds 104
70. Curves showing air gap diameter for 50-cycle polyphase alternators as a
function of the rated output for various speeds 105
71. Curves showing values of K, the "voltage coefficient," in the E.M.F.
formula 112
72. Outline of field of 650 kva. alternator 114
LIST OF ILLUSTRATIONS. xi
no. PAOB.
73. Curve showing thickness of armature slot insulation for alternating cur-
rent generators 117
74. Armature slot for 650 kva. alternator 118
75. Curves for estimating the total armature core loss in alternating current
generators 119
76. Saturation curve for 650 kva. 3-phase 4-pole 1500 r.p.m. 50-cycle 500- ^
volt alternator . . • 123
77. Outline drawing of assembly of 650 kva. 1500 r.p.m. 50-cycle 4-pole
3-phaBe alternating current generator 126
77 A. Outline drawing of assembly of 650 kva. 1500 r.p.m. 50-cycle 4-pole
3-phase alternating current generator 127
78. Outline drawings of 400 kva. 3-phase 50-cycle alternators for various
speeds facing 131
79. 400 kva. 4-pole 1500 r.p.m. 50-cycle 3000-volt alternating current
generator 132
80. D)ig and D^lg for 400 kva. alternators 138
81. Specific electric and magnetic loadings a and /9 and output coefficient
^ for 400 kva. alternators 139
82. Losses and efficiencies for 400 kva. alternators 140
83. Air gap and iron ampere turns in per cent of total field ampere turns, and
ratio of field ampere turns to armature ampere turns for 400 kva. alternators 142
84. Armature and field strengths, depth of air gaps, and kilowatts per pole
for 400 kva. alternators 143
85. Weight and cost of effective material for 400 kva. alternators 144
86. Total net weight and weight coefficients for 400 kva. alternators .... 145
87. No load saturation curves of 500 kva. 3600 r.p.m. 60 cycle 2-pole 4000
volt alternator 148
88. Curves of iron loss for various voltages on open circuit for 500 kva. 3000
r.p.m. 60 cycle 2-pole 4000 volt alternator 149
89. Curves of short circuit, armature PR^ and load iron loss on short circuit
for 500 kva. 3000 r.p.m. 60 cycle 2-pole 400 volt alternator 150
90. Curves for losses and efficiency of 500 kva. 3600 r.p.m. 60 cycle 2-pole
400 volt alternator 151
91. Saturation curve for 400 kva. 3-phase 2-pole 3000 r.p.m. 50 cycle 550
volt alternator (rotating field) 153
92. Saturation curve for 400-kva. 3-phase 2-pole 3000 r.p.m. 50 cycle 550
volt alternator (rotating armature) 154
93. Outline drawings of 3000 kva. 25 cycle 11,000 volt alternating current
generators at various rated speeds from 750 r.p.m. 4 poles to 83 r.p.m.
36 poles facing 169
94. Outline drawings of 3000 kva. 25 cycle 11,000 volt alternating current
generators at various rated speeds from 750 r.p.m. 4 poles to 83 r.p.m.
36 poles facing 169
95. D}g and E^lg as function of rated speed for 3000 kva. 25 cycle designs . 171
xii LIST OF ILLUSTRATIONS.
FIO. PAOB.
96. Specific electric and magnetic loading a and fi for 3000-kva. 25 cycle
S-phase alternator 172
97. Losses for 3000 kva. 25 cycle 3-pha8e alternator 173
98. Flux per pole and total flux for ^000 kva. 25 cycle 3-phase alternator . 174
99. Armature strength and total flux for 3000 kva. 25 cycle 3-phase alter-
♦ nator 175
100. Air gap depth and armature strength for 3000 kva. 25 cycle S-phase
alternator 176
101. Weight and cost of effective material for 3000 kva. 25 cycle S-phase
alternator 178
102. Total net weights and weight coefficients for 3000 kva. 25 cycle 3-pha8e
alternators 180
103. 104 and 106. Outline drawings of 3000 kva. alternators facing 189
104. 105 and 106. Outline drawings of 3000 kva. 50-cycle alternators, facing 189
107. DXQf D^Xg and output coefficient for 3000 kva., 50-cycle, 1 -phase alter-
nator 188
108. Specific magnetic and electric loading, fi and a, and for 3000 kva. 50-
cycle 3-phase alternators 189
109. Losses for 3000 kva. 50 cycle 3-phase alternator 190
110. Weight and cost of effective material for 3000 kva. 50-cycle 3-phase
alternator 191
111. Total net weight and weight coefficient for 3000 kva. 50-cycle 3-pha8e
alternator 191
112. Curves showing weight and cost of effective materials of 3000 kva. 25
and 30 cycle 3-phase alternators for various rated speeds 192
113. Curves showing total net weight of 3000 kva. 25 and 50-cycle 3-phase
alternators for various rated speeds 193
114. Weight and cost of effective material for 3000 kva. 25 and 50 cycle
3-phase alternator 194
115. Total net weights for 3000 kva. 25 and 50 cycle 3-phase alternators . . 195
116. Outline drawings of 4, 6 and 8-pole, 750 r.p.m., 6000 kva. alternators 198
117. Saturation curve for 4-pole 750 r.p.m., 6000 kva. alternator 199
118. Saturation curve for 6-pole 750 r.p.m., 6000 kva. alternator 200
119. Saturation curve for 8-pole, 750 r.p.m., 6000 kva. alternator 201
120. a, P and ^ for 6000 kva. designs 205
121. Curves of flux and armature strength in 6000 kva. designs 206
122. Curves for armature strength and depth of air gap for 6000 kva. designs 207
123. Curves for weight and cost of effective material for 6000 kva. altematore 208
124. Curves for the total weight and for the weight coefficients for 6000 kva.
alternators 209
125-127. Outline drawings for 1500, 3000, and 6000 kva. 8-pole 750 r.p.m.
50-cycle alternators 210
128. D*;i(7 and DA^ for 11, 000- volt 3-phase 8-pole 50-cycle alternators ... 214
LIST OF ILLUSTRATIONS. xiii
PIG. PAOK.
129. Annature ampere turns and kva. per pole and air gap length and ratio
of field to armature ampere turns for 11000- volt 3-phase 8-pole 50-cycle
alternators 215
130. Weight and cost curves for ll,000-volt3-phase 8-pole 50-cycle alternators 215
131. Total net weights and weight coefficient for 11, 000- volt 8-pole 50-cycle
3-phase alternators 216
132. Total weight of machines and weight and cost of effective material per
kva. for 11, 000- volt 8-pole 50-cycle 3-phase alternators 217
133. Open type stator frame 219
134. Alternator with open frame — (Allgemeine Electricitats Gesellschaft) . . 220
135. Section of Westinghouse turbo-alternator stator 221
136. Section of B. T. H. turbo-alternator stator 221
137. Section of ribbed stator frame 221
138. Enclosed frame for forced ventilation — Lahmeyer Company 222
139. Group of Lahmeyer turbo-alternator stators 223
140. C. E. L. Brown's ventilating scheme for turbo-generator 224
141. Oerlikon Company's ventilating scheme for turbo-generators 224
142. Oerlikon Company's ventilating scheme for a turbo-generator 225
143. Oerlikon Company's ventilating scheme for a turbo-generator 225
144. Lower half of frame of 1100 kw. 1500 r.p.m. alternator — Oerlikon Co. . 226
145. Lower half of frame of 1100 kw. 1500 r.p.m. alternator — Oerlikon Co. . 227
146. Assembling upper half of armature of 1100 kw. 1500 r.p.m. alternator . 228
147. Turbo-alternator with forced ventilation. (Built by Messrs. Siemens
Bros., Ltd.) 229
148. Section of an Allgemeine Electricit£lts Gesellschaft turbo-alternator,
water-cooled 230
149. Spiral coil 230
150. Lap coil 230
151. Single-phase whole coiled winding 231
152. Single-phase half coiled winding 232
153-156. Elements of alternating current armature landings 233
157. Sections of armature end windings 234
158. Woimd bipolar armature of Oerlikon 400-kw. 5000-volt 42-cycle 2520-
r.p.m. turbo-alternator with a 2-pole 2-phase whole coiled, sextuple
coil spiral winding 235
159. Armature of Westinghouse 5500-kw. 4-poIe 1000-r.p.m. 33-cycle 11,000-
volt turbo-alternator with a 4-pole 3-phase half coiled octuple coil
spiral winding 236
160. Winding armature of 5500 kw. Westinghouse alternator 237
161. Armature winding of 1500-kw. 1000 r.p.m. 6-pole 50 cycle British
Thomson-Houston Curtis turbo-alternator 238
162. Armature winding and slot of 1500 kw. British Thomson-Houston alter-
nator 239
163-165. Methods of retaining end windings of turbo-alternator armatures . 240
xiv LIST OF ILLUSTRATIONS.
FIG. PAOB.
166. Method of retaining armature windings of 3000 kva. 4-pole alternator —
, (G. E. Co. of America) 241
167-168. Methods of retaining armature end windings 242
169. Turbo-alternator armature of Lahmeyer Company showing arrange-
ments for securing end windings 243
170. Winding a 2-pole B-phase armature — Bruce Peebles & Co 244
171. Armature of 5000-kw. S-phase 10,500-volt 1000-r.p.m. 50-cycle alter-
nator — Brown Boveri & Co 245
172. Armature of 3000-kw. single phase 3000-voIt 45-cycle 1360-r.p.m. alter-
nator — Brown Boveri & Co 246
173. Armature of 1000-kw. 370-volt 1500-r.p.m. 50-cycle alternator —
Brown Boveri & Co 247
174-176. C. E. L. Brown's cylindrical slotted rotating field constructions
(from D. R. P. 138,253 of 1901) 248
177. Finished rotor of a Brown Boveri turbo-alternator 250
178. Finished rotor of Lahmeyer turbo-alternator 251
179. An instance of an early Oerlikon type of ring wound field 252
180. Rotating armature of an early type of 200 kw. polyphase alternator built
by the Oerlikon Company 253
181. Unwound field of 250 kw. Oeriikon alternator 253
182. An Oerlikon 4-pole rotating field wound. (End shields removed.) . . . 254
183. Finished rotor of bipolar 2-phase 400-kw. 5000-volt 42-cycle 2520-r.p.m.
Oerlikon alternator 255
184. Laminations for rotating fields of Oerlikon high speed alternators . . . 255
185. A Westinghouse 2-pole field structure . 256
186. A Westinghouse 4-pole field structure 257
187. End bell of Westinghouse rotor 257
188. Bipolar laminated field — Westinghouse Company 300-kva. 3000-r.p.m.
6600-volt 50-cycle 3-phase 258
189. Turbo-alternator field — Walker compensated type 3-phase 650-kva.
25-cycle 1500-r.p.m 258
190. Walker compensated type field for 3000-kva. 3-phase 25-cycle 750-r.p.m.
6600-volt alternator 259
191. 2-pole rotating field for 500-kw. A.E.G. alternator 260
191A. Section of coil retaining wedges of A.E.G. rotor 260
192. Rotor of A.E.G. turbo-alternator showing field coils in place 261
192A. Complete rotor of A.E.G. turbo-alternator 261
193. Smooth core rotor of the American General Electric Company's 4-pole
9000 kva. 750 r.p.m. alternator 262
194. Finished rotor of the American General Electric Co.'s 4-pole, 9000-kva
alternator 262
195. Bullock Co.'s smooth core rotating field construction 263
196. A Siemens-Schuckert rotating field for bipolar alternator 264
LIST OF ILLUSTRATIONS. xv
FIO. PAGE.
197. A method of clamping field coils. (General Electric Company of
America.) 264
198. Definite pole rotor for 6-poIe 5000 kva. 5000 r.p.m. alternator for Twin
City Rapid Transit Company. (General Electric Company of
America.) 265
199A and B. Angle brackets for retaining field coils 265
200. Subdivided field coil 266
201. 4-pole rotating field for 1500 kw. 1500 r.p.m. Bruce Peebles alternator . 267
202. General arrangement of 3000 kw. Dick Kerr turbo-alternator 268
203. Complete rotor of a Dick Kerr turbo-alternator 269
204. Methods of attaching pole cores and pole shoes 270
205. General arrangement of 4000 kw. 3-phase 400 r.p.m. 60 cycle 2400 volt
alternator designed by Rushmore 271
206. Assembled field core of 4000 kw. alternator, designed by Rushmore . . 272
207. Wound field of 4000 kw. alternator, designed by Rushmore 273
208. Field coil retaining pieces for Westinghouse 3750 kw. 20-pole 3-phase
2200 volt, 30 cycle 1000 r.p.m. alternator 274
209 and 210. Field magnet stampings of Westinghouse 3750 kw. 20-pole
alternator 275
211. General arrangement of 1200 kva. 3-phase 1500 r.p.m. 4-pole 50 cycle
1155-2000 volt Oerlikon turbo-alternator facing 275
212. General arrangement of 250 kva. 3-phase 3000 r.p.m. 2-poIe 50 cycle
Oerlikon turbo-alternator facing 277
213. 1000 kva. 5200 volt 1500 r.p.m. Oeriikon single-phase turbo-generator 279
214. General arrangement of 1000 kva. 1500 r.p.m. 4-pole 50 cycle 5200 volt
single phase Oerlikon turbo-alternator facing 283
215. Stator and rotor lamination of 1000 kva. single phase turbo-alternator .
facing 283
216. Characteristic curves of 1000 kva. 5200 volt 50-cycle single phase Oerlikon
alternator 283
217. General arrangement of 1000 kva. 1500 r.p.m. 2000 volt standard
3-pha8e alternator — Brown Boveri & Co facing 285
218. General arrangement of 1500 kva. 1000 r.p.m. 6-pole British Thomson-
Houston alternator 285
219. Stator frame of British Thomson-Houston Company's 1500 kva. turbo-
alternator 286
219A. Armature laminations of British Thomson-Houston Company's 1500
kva. turbo-alternator 286
220. Rotating field construction of 1500 kva. British Thomson-Houston
turbo-alternator 288
220A. Field collector, rings of 1500 kva. British Thomson-Houston turbo- alternator 289
221. 1500 kva. 1000 r.p.m. British Thomson-Houston Curtis turbo-alternator 290
222. Rotating field of 1500 kva. British Thomson-Houston turbo-alternator . 291
xvi LIST OF ILLUSTRATIONS.
FIG. PAOB.
223. Saturation curve of 1500 kw. 3-pha8e 11,000 volt 50 cycle 1000 r.p.m.
British Thornton-Houston turbo-alternator 294
224. General arrangements of 500 kw. 3-phaae 4-pole 1500 r.p.m. 50 cycle
550 volt Scott and Mountain turbo-alternator 295
225. Armature winding diagram and details of slot of 500 kva. S-phase turbo-
alternator 296
226. Rotor lamination of 500 kva. Scott and Mountain turbo-alternator . . 297
227. Heyland's 600-kw. 2-pole 3000 r.p.m. 330-volt 50-cycIe S-phaae self-
compounding alternator 302
227 A. Diagrammatic sketch of Heyland's self-compounding alternator . . . 303
228. Rotating field for 4-pole 50-kva. alternator 307
229. Rotating field for 6-pole 1000-kva. alternator 312
230. Total Works Cost of 500 kw. 250 volt continuous current generator for
various rated speeds 320
231. Curve of relation of minimum T.W.C. to speed for 250 volt continuous
current generators 321
232. Total Works Cost curves for 500 kw. 250-volt continuous current machines 323
233. Sketches showing outlines of 500 kw. 250-volt machines for various
rated speeds and designed on three different principles 325
234. Magnet pole sections and perimeters 330
235. Curve showing the effect of the shape of the magnet core on the weight
of the magnetizing copper required 331
236. Curve showing the value of " K " in the formula il ^ '" K" X f^g X
R X F X 10-« for estimating the reactance voltage 335
237. Reactance voltage curves for various 6-pole 1000 r.p.m. designs for
various armature strengths 338
238. Reactance voltage curves for 6-pole 1000 r.p.m. designs for various
diameters 340
239. Curves showing suitable armature ampere turns per centimetre of per-
iphery for continuous current machines for 500 volts 341
240. Output coefficients of continuous current dynamos 343
241. Reactance voltage curves for 6-pole 1000 r.p.m. designs for various out-
puts and diameters 346
242. Design chart for determining preliminary dimensions and reactance
voltages for 6-pole continuous current dynamos at various rated speeds and outputs facing 347
243. Reactance voltage curves for 6-pole designs for >i^ « 30 347
244. Reactance voltage curves for 6-pole designs for >i^ — 30 348
245. Design chart for preliminary dimensions and reactance voltages, r, of
1000 r.p.m. continuous current dynamos with various numbers of poles facing 349
246. Reactance voltage curves for 1000 r.p.m. designs for various numbers of
poles and various gross core lengths facing 349
LIST OF ILLUSTRATIONS. xvii
VIO. PAGE.
247. Design chart for continuous current generators for obtaining the pre-
liminary dimensions and the reactance voltages for any rated outputs and speed facing 349
248. Design chart for obtaining preliminary dimensions and reactance volt-
ages of 125 r.p.m. continuous current dynamos with various numbers
of poles facing 349
249. Design chart for obtaining preliminary dimensions and reactance volt-
ages of 250 r.p.m. continuous current dynamos with various numbers
of poles facing 349
250. Design chart for preliminary dimensions and reactance voltage of 1000
r.p.m. continuous current dynamos with various numbers of poles . . 349
251-255. Curves relating to preliminary designs for 500 kw. 250 volt continu- ous current machines for various speeds plotted from schedules in Tables 48 to 53 facing 353
256. Data of 500-kw. 250-volt designs at different rated speeds selected from
curves in Figs. 251-255 355
257. Curves relating to preliminary designs, for 250, 500 and 1000-volt 500-kw.
continuous current generators for various rated speeds .... facing 361
258. Curves showing technical data of fifteen 250-kw. continuous current
generators plotted from designs given in Table 55 facing 361
259. Curves showing technical data of fifteen 500-kw. continuous current
generators plotted from designs given in Table 56 facing 361
260. Curves showing technical data of fifteen 1000-kw. continuous current
generators plotted from designs given in Table 57 facing 361
261. Outline sketches of 250-kw. 250-volt continuous current dynamos for
rated speeds ranging from 125-3000 r.p.m 365
262. Outline sketches of 500-kw. 500-volt continuous current dynamos for
rated speeds ranging from 125-2500 r.p.m 366
263. Outline sketches of 1000-kw. 1000-volt continuous current dynamos for
rated speeds ranging from 125-2000 r.p.m 367
264. Outline sketches of 250, 500 and 1000 kw. dynamos (Figs. 261, 262, 263
brought together) facing 373
265. Values of "K" in the formula Total Works Cost in dollars = /C X D X
(iflf + 0.7 t) 373
266-269. Graphic determination of Total Works Cost of 250 kw. continuous
current dynamos for various rated speeds 374
270, 271. Graphic determination of effective costs and effective weights of
250-kw. 250-volt continuous current dynamos at different rated speeds 375 272-274. Graphic determination of reactance voltage, armature heating and
full load efficiency of 250 kw. 250 volt continuous current dynamo
for various rated speeds 376
275. Curves showing effective weight, cost of effective material and Total
Works Cost of 250, 500 and 1000 kw. continuous current dynamos for various rated speeds facing 377
276. Curves showing technical data of 250, 500 and 1000 kw. continuous cur-
rent dynamos for various rated speeds facing 377
xviii LIST OF ILLUSTRATIONS.
FIO. PAQK.
277. Curves showing in comparison the technical data obtained from the
designs by chart method in Tables 55, 56, and 57, Chapter XIV, and designs given in specification in Table 58 of Chapter XV 383
278. Curves showing values of reactance voltages, volts per segment, and
commutator peripheral speeds for 45 preliminaiy designs for contin- uous current generators of various rated outputs, voltages and speeds 385
279. Curves showing values of Total Works Cost in dollars and total weight
in kilograms for 45 preliminary designs for continuous current genera- tors of various rated outputs, voltages and speeds 386
280. Curves showing values of armature ampere turns per pole, flux per
pole in megalines and cycles per second for 45 preliminary designs for continuous current generators of various rated outputs, voltages and speeds 387
281. Curves showing heating constants expressed in watts per sq. dcm. of
surface for armature, commutator and field spools for 45 preliminary designs for continuous current generators of various rated outputs, voltages and speeds 388
282. Curves showing conmiutator diameter, length of segment and width of
segment insulation for 45 preliminary designs for continuous current generators of various rated outputs, voltages and speeds 389
283. Curves showing values of brush PR loss, brush friction loss and total
commutator loss for 45 preliminary designs for continuous current dynamos of various rated outputs, voltages and speeds 390
284. Curves showing values of armature PR loss, armature iron loss and
total armature loss for 45 preliminary designs for continuous current generators of various rated outputs, voltages and speeds 391
285. Curves showing values of armature loss, commutator loss, field loss,
friction loss and total losses for 45 preliminary designs for continuous current generators of various rated outputs, voltages and speeds , . 392
286. Curves showing values of full load, half load and quarter load efficiencies
for 45 preliminary designs for continuous current generators of various rated outputs, voltages and speeds 393
287. Various designs for a 1000 kw. 1000 r.p.m. 1000 volt dynamo, with
various reactance voltages 396
288. Suggested arrangement for the 1000 kw. 6-pole, 1000 volt 1000 r.p.m.
C.C. generator, having an extended armature core for the interpoles . 401
289. Proposed method for obtaining good commutation 402
290. Diagrammatic 2-pole representation of rotary converter scheme for a
continuous current turbo-generator 406
291. Vector diagram for alternating current generator 408
292. Excitation regulation curves for 1000 k.w. alternator 408
293. Excitation regulation curves for 1000 kw. alternator 409
294. General arrangement of high speed continuous current generator —
1000 kw. 6-pole 1000 r.p.m 413
LIST OF ILLUSTRATIONS. xix
wn, PAOB.
295. Outline sketches of 1000 kw. 1000 r.p.m. continuous current generator
with commutator dimensions proportioned for various voltages em- ploying ordinaiy carbon brushes 414
296. Outline sketches of a 1000 kw. 1000 r.p.m. continuous current gener-
ator, for different voltages, showing reduced commutator lengths effected by the use of special brushes 416
297. Armature of Parsons' first turbo-dynamo 419
298. Armature for Oerlikon 200 kw. 220-250 volt 3000 r.p.m. continuous
current generator 419
299. Field system for Oerlikon 200 kw. 220-250 volt 3000 r.p.m. continuous
current generator 420
300. Method of holding down end connections by means of metal end-bells . 421
301. Method of reducing centrifugal force at the surface of end connections . 421
302. Sketch showing typical high speed commutator construction 422
303-304. Methods used for interlocking commutator segments 423
305. Method for obtaining improved commutator ventilation where sufficient
diameter is obtainable 423
306-^307. Ventilated conmiutator patented by Siemens Bros., D3mamo Works t
limited 424
307A and B. Miles Walkers' Commutator Construction 425
308. Brown Boveri 250 kw., 2700 r.p.m., 150-volt turbo-generator . . facing 427
309. Field frame and core, without windings, of a 135 kw. Brown Boveri
continuous current 3000 r.p.m. turbo-generator 428
310. Field frame, core and windings, of a 135 kw. Brown Boveri continuous
current 3000 r.p.m. turbo-generator 429
311. Finished armature and commutator of a Brown Boveri 135 kw. continu-
ous current generator at 3000 r.p.m 430
312. Armature of Richardson Westgarth and Brown Boveri 's 1000 kw. 550
volt 1250 r.p.m. 4-pole continuous current turbo-generator 432
313. Richardson Westgarth and Brown Boveri 1000 kw. 1250 r.p.m. 4-pole
continuous current turbo-generator 432
314. Large steam turbine unit installed at the Rhenish Westphalian Works
at Essen, consisting of a 10,000 h.p. turbine coupled to a 5000 kw. alternator and a 1500 kw. continuous current generator 433
315. Armature of a 1500 kw. continuous current generator belonging to the
set shown in Fig. 314 434
316. Curves plotted from Table 70 showing total weight of continuous current
, kilowatts X 100
turbo-generators m terms of -— : — 435
Revs, per nun.
317. Curves plotted from Table 71 showing floor space required by continu-
ous current turbo-generators of various outputs 436
318. 500 kw. 1500 r.p.m. 250 volt continuous current turbo-generator built
by Siemens Bros. Dynamo Works 438
319. 750 kw. Siemens continuous current generator for turbine drive with
commutator poles. Speed 1600 r.p.m 440
XX LIST OF ILLUSTRATIONS.
no. PAOC.
320. General arrangement of 750 kw. 250 volt, 1500 r.p.m. continuous current
generator facing 441
321. Diagram of winding for auxiliary field circuit connections of 750 kw.
high speed continuous current generator 442
322. British Westinghouse Company's 375 kw. 2500 r.p.m. 250 volt continuous
current turbo-dynamo with rotating portion removed 446
323. 200 kw. 2000 r.p.m. 110 volt continuous current turbo-dynamo built by
the British Westinghouse Company 447
324. 20 kw. continuous current turbo-generator by the A.E.G 451
325. 100 kw. continuous current turbo-generator by the A.E.G 451
326. Field system of an A.E.G. turbo-generator showing shunt coils and Deri
winding in place 452
327. 100 kw. 3000 r.p.m. 125 volt turbo-generator by the Rateau Turbine
Company of Chicago 453
328. 100 kw. turbo-generator by the Rateau Turbine Company of Chicago . 454
329. Radial type of homopolar generator 456
330. Axial type of homopolar dynamo 456
,331. Noeggerath's 500 kw. homopolar dynamo 457
332. Armature of 500 kw. Noeggerath homopolar generator 458
333. Efficiency curves of 300 kw. 500 volt homopolar dynamo 459
334. Armature slot for 1000 kw. continuous current generator 461
335. Commutator segment for 1000 kw. continuous current generator . . . 462
336. Variation of contact resistance with brush pressure for a soft carbon . . 472
337. Variation of contact resistance with brush pressure for a hard brush
employed in service where heavy pressure is required 473
338. Variation of contact resistance with peripheral speed of commutator . . 474
339. Curves for establishing brush friction loss at commutator for a brush
pressure of 0.1 kg. per sq. cm 476
340. Noeggerath's tests of voltage drop between copper brushes and a cast
steel ring 481
341. Total losses in the steel slip rings of Noeggerath 's 400 kw. homopolar
machine 481
342. Burleigh's construction for compound brushes 482
343. Variation of contact resistance and voltage drop with current density
for Moiiganite brushes 484
344. Curves for obtaining the commutator losses with Morganite brushes, facing 485
345. Typical arrangement of brush gear for pilot brushes 485
346. Brown Boveri brush gear for turbo-generators, showing pilot brushes . . 486
347. Brush contact losses for Bronskol and carbon brushes 488
348. Methods of attaching flexible connectors to carbon brushes 490
349-352. Types of spring pressure brush holders 492
353. Morgan Crucible Company's spring brush holder for high speeds .... 494
354. Section of the Morgan Crucible Company's pneumatic brush holder . . 494
355. Morgan Crucible Company's pneumatic brush holder 496
"HIGH SPEED DYNAMO ELECTRIC MACHINERY."
LIST OF SPECIFICATIONS OF DESIGNS GIVEN IN THIS TREATISE.
Part II. ALTERNATma Current Generators.
|
Kva. |
Phase. |
Pole*. |
R.P.M. |
Cycles. |
Volte. |
Chapter. |
Page. |
|
1375 |
3 |
64 |
94 |
50 |
5500 |
VI |
95 |
|
1500 |
3 |
6 |
1000 |
50 |
11000 |
VI |
95 |
|
650 |
3 |
4 |
1500 |
50 |
500 |
VII |
127 |
|
400 |
3 |
64 |
94 |
50 |
3000 |
VIII |
133 |
|
400 |
3 |
4 |
1500 |
50 |
3000 |
VIII |
133 |
|
500 |
3 |
2 |
3000 |
50 |
550 |
VIII |
133 |
|
500 |
3 |
2 |
3000 |
50 |
550 |
VIII |
133 |
|
3000 |
3 |
4 |
750 |
25 |
11000 |
IX |
168 |
|
3000 |
3 |
6 |
500 |
25 |
11000 |
IX |
168 |
|
3000 |
3 |
8 |
375 |
25 |
11000 |
IX |
168 |
|
3000 |
3 |
12 |
250 |
25 |
11000 |
IX |
168 |
|
3000 |
3 |
24 |
125 |
25 |
11000 |
IX |
168 |
|
3000 |
3 |
36 |
83 |
25 |
11000 |
IX |
168 |
|
3000 |
3 |
4 |
1500 |
50 |
11000 |
IX |
184 |
|
3000 |
3 |
6 |
1000 |
50 |
11000 |
IX |
184 |
|
3000 |
3 |
8 |
750 |
50 |
11000 |
IX |
184 |
|
6000 |
3 |
4 |
750 |
25 |
11000 |
X |
201 |
|
6000 |
3 |
6 |
750 |
37.5 |
11000 |
X |
201 |
|
6000 |
3 |
8 |
750 |
50 |
11000 |
X |
201 |
|
1500 |
3 |
8 |
750 |
50 |
11000 |
X |
211 |
|
1000 |
3 |
4 |
1500 |
50 |
2000 |
XI |
276 |
|
250 |
3 |
2 |
3000 |
50 |
XI |
277 |
|
|
1000 |
1 |
4 |
1560 |
50 |
5200 |
XI |
278 |
|
1500 |
3 |
6 |
1000 |
50 |
11000 |
XI |
284 |
|
500 |
3 |
4 |
1500 |
50 |
550 |
XI |
298 |
Part III. Continuous Current Generators.
|
Kw. |
Poles. |
R.P.M. |
Volte. |
Chapter. |
Page. |
|
10 8 |
125 250 |
||||
|
250 |
6 6 4 2 14 10 |
500 1000 2000 3000 125 250 |
250 |
XV |
368 |
|
500 |
8 6 4 4 |
500 1000 2000 2500 |
500 |
XV |
368 |
|
1000 |
16 12 8 6 4 |
125 250 500 1000 2000 |
1000 |
XV |
368 |
|
1000 1000 |
6 |
1000 1500 |
1000 550 |
XVII XVII |
398 405 |
|
750 750 375 |
4 6 4 |
1600 1500 2500 |
500 250 240 |
XVIII XVIII XVIII |
441 445 448 |
HIGH SPEED DYNAMO ELECTRIC MACHINERY.
PART I — GENERAL CONSIDERATIONS.
CHAPTER I.
INTRODUCTORY.
In the early days of the development of dynamo electric machinery, when designs of only yery small output came into consideration, it was found that with increase in the rated speed, the "weight eflS- ciency" and the "cost efficiency" of dynamo electric generators con- tinued to increase up to the limit to which it was found practicable to increase the speed with due consideration to the design of the prime mover. In order to obtain these advantages of high speed it was very customary to drive the electric generator by belting or by ropes, at a speed considerably higher than that of the engine from which it was driven. The disadvantages of rope or belt driving led, notably in England, to the development of the so-called "high speed" engine to which the generator was directly coupled. As development proceeded, the most customary rated capacity required for a single generating set, rapidly increased, and while the higher speeds con- tinued to be found advantageous for alternating current generating sets, even when of large rated capacity, it gradually became apparent that for continuous current generating sets of large rated capacity, such disadvantages relating to commutation and ventilation attended the design, that but little if any advantage remained from the use of high speeds. It has finally come to be realized by those best informed, that in the case of continuous current generators for the customary voltages of from 500 to 650 volts, there is, for each rated
2 INTRODUCTORY.
capacity, a limiting speed beyond which the design becomes not only less satisfactory, but also more expensive.
The impression which nevertheless still prevails in less well informed circles, that continuous current generators are especially adapted to high speed work, and that the development of low sj)eed engmes is not in the interests of the best dynamo design, but is a concession to the advantages of low speed for engines, is far from correct. Low and high speed steam engines have their respective merits and demerits: the same is true of low and high speed dynamo electric machinery, and it is fomid necessary to consider each case very carefully. It may be said in general that, up to a certain limit, a machine for a given capacity and voltage, and of a given degree of excellence, will be cheaper the higher the speed; but for speeds above that limit, the machine will be more expensive. Hence it may be said that for each rating there is a particular speed which is the most economical and satisfactory speed. Analogous considerations lead the steam engineer to prefer a particular speed for a steam engine of a given rated output. Just as the experience of each steam engineer with the type of engine with which he has been chiefly engaged leads him to an individual opinion as to the most favourable speed for a steam engine of a given capacity, so one finds considerable difference of opinion among designers of electrical machinery as to the most favourable speeds for continuous current djoiamos.
At this point it is desirable to consider the relation of the angular speed to the output, in prime movers of the types which are in general use for electric power generation purposes. The curves in Fig. 1 give a rough idea of the speeds of prime movers of the various types for rated outputs up to 6000 kw. In these rapidly developing lines of work, manufacturing concerns are constantly modif3dng their plans. Hence while the turbine curves in Fig. 1 reflect the general state of affairs, it would be imprudent to place reliance on the precise values to which the curves are plotted. The point to be observed from these curves is the large range of speeds lying between the speeds of steam turbines and the speeds of piston engines.
Speeds within this range are consequently not available for direct coupled electric generators, except when driven from hydraulic tur- bines. Such speeds are nevertheless often more suitable and eco- nomical for electric generators, as we shall see in the course of this work.
INTRODUCTORY.
|
2500 |
1 |
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1 |
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^IIMA |
V |
\ |
»t^ |
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|
1 |
\ |
^ |
hi |
|||||||||
|
(h 1/wv> |
\ |
\c |
^ |
^'^fr, |
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^ |
Wt |
"^4« |
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m ItfM |
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V |
Hfm |
|||||||||||
|
F= |
^.^ |
^©Ssss.' |
1000
9000 8000 4000
Output In Kilowatts
5000
6000
Fig. 1. — Curves showing relation of rated speeds and rated outputs for steam turbines and other prime movers.
Kg. 2 gives a corresponding curve for the de Laval turbine which has been plotted sepa- rately since the out- put for which this tjrpe of turbine is made does not usually exceed 200 kw. This limita- tion is chiefly due to the reduction gear which is employed to reduce the speed in the ratio of 10 : 1 . The pri- mary turbine spindle runs at speeds of from 10,000 R.P.M. to 30,000 R.P.M; the sec- ondary shaft to which the dynamos are coupled running at speeds ranging from 1000 to 3000 R.P.M. It is with the influence of the rated speed on the design and character- istics of electrical ma- chinery that we are here chiefly concerned.
It would probably have been more correct to enti- tle this treatise " The in- fluence of the rated speed and output on the design of electric machinery," for it is impracticable to advantageously discuss the influence of the speed without also discussing the influence of the rated output.
Two broad dividing lines are at once encoun- tered when approaching the subject, for a comparatively superficial examination reveals the three following facts :
|
80000 |
^ |
||||||||||
|
\ |
|||||||||||
|
^SSOOO 0 |
\ |
||||||||||
|
S |
V |
||||||||||
|
volutions pel |
^ |
V |
|||||||||
|
\ |
^ |
> „ |
|||||||||
|
^ |
f^^ |
LISJU |
|||||||||
|
& fllflflAO |
k |
|
|
||||||||
|
L |
|||||||||||
40
80 ISO
Outputin^llawatts
160
)»0
Fig. 2. — Curve showing relation of rated speeds and rated outputs for de Laval turbines.
4 INTRODUCTORY.
1. When not carried to excess, the lower the speed in revolutions per minute, the more satisfactory will be the results which may be obtained in designing continuous current dynamo electric ma- chinery.
2. When not carried to excess, the higher the speed in revolutions per minute, the more satisfactory will be the results which may be obtained in designing alternating current dynamo electric machinery.
For either one of these two classes of dynamo electric machinery, a machine for some particular rated output and voltage will yield satisfactory results for a minimum Total Works Cost when designed to operate at some particular speed in revolutions per minute. For higher and lower speeds, either the Total Works Cost will be greater for a given quality of performance, or the performance will be inferior for a given Total Works Cost.
3. Far a given rated output, this preferable speed wiU be much lower for a continuous current design than for an altera noting current design. ,
There are exceptions to all rules, nevertheless the above conclu- sions are of fairly general applicability. The working out of the large number of designs, of which the results are given in this treatise, was imdertaken largely with the object of attaining to greater pre- cision in our knowledge of the influence exerted on the design by these two factors of speed and output.
While a considerable knowledge on the part of the reader as regards the detailed steps employed in the design of electric machinery has often been assumed, the preparation of this treatise has afforded a favourable opportunity of setting forth a number of modified pro- cesses which we have found it useful to employ at various stages of the design. These processes are generally of an empirical natiu^, but readers conversant with the principles of the design of djmamo electric machinery may be glad to substitute them for the more elementary, although in some cases more complex, processes set forth in most text-books dealing with the subject.
In view of the broad demarcation to which we have alluded, we have devoted separate sections to the treatment of alternating current and continuous current machinery; but we have, for the sake of variety and also of departing from a meaningless tradition, given first place to the treatment of alternating current machinery.
Part I, entitled " General Considerations," contains Chapters I to
INTRODUCTORY. 6
IV which deal with matters common to both classes of machinery. Chapter IV on '' Materials " might profitably be again read after a perusal of the whole work, and especially of Chapters XI, XII, and XVIII which deal with the constructional problems. The question of materials is closely allied to the special types of construction employed and it was difficult to decide whether to place the chapter near the beginning or at the end of the book.
Part II, entitled ''Alternating Current Generators/' comprises Chapters V to XII which deal with alternating current machinery, and Part III, entitled *' Continuous Current Generators," comprises Chapters XIII to XIX dealing with continuous current machinery.
CHAPTER n.
DESIGN COEFFICIENTS FOR DYNAMO ELECTRIC MACHINERY.
Design Coefficients are of use in connection with the design of djmamo electric machinery as constituting convenient starting points on which to base a new design, or for purposes of comparisons between several designs. Such coefficients may embody relations between :
A. Dimensions and output — designated "Output Coefficients/'
B. Weight and dimensions or output — "Weight Coefficients."
C. Cost and dimensions or output — "Cost Coefficients."
A.
Output Coefficients.
The following output coefficients have been more or less exten- sively used:
|
(1) |
W D'igR |
W = rated output in watts. D = armature diameter at |
|
(2) |
W Dig |
air gap. ig - armature gross core |
|
(3) |
W |
length. |
|
Volume of active belt |
R - rated speed in R.P.M. |
(4) Specific Utilization Coefficients.*
Of the above, (1) is the most convenient and is the most exten- sively used. We shall designate this coefficient as simply the "Out- put Coefficient" and shall denote it by the letter $.
H^"'*' ^ = W^R
D and ig are expressed in decimetres, W in watts, and R in revolu- tions per minute.
* The specific utilization coefficientB which are developed in this Chapter were originally proposed by Dr. S. P. Thompson. See Seventh Edition (1904) of Dsmamo Electric Machinery, (E. & F.N. Spon. London.) Vol. I. p. 576.
6
OUTPUT CJOEFFICIENTS. 7
In the case of alternating current machines the output in volt amperes should be employed for W instead of the output in watts. This is equal to nVl where n denotes the number of pliases, V the voltage per phase, and / the current per phase.
We may obtain an insight into the inter-relation of these coeffi- cients and a comprehension of their significance, by developing cer- tain fundamental relations for dynamo electric machines. We shall at this point carry out such a development for alternating current machines. For continuous current machines the relations are pre- dsely similar.
The primary fundamental equation for alternating current ma- chines is
y^kTMN
where V = the voltage per phase,
k = the " voltage coefficient '' the values of which are given in Chapter VII, page 110. T = the niunber of turns in series per phase. N = the frequency in cycles per second. M = the magnetic flux entering the armature per pole in c. g. s, lines. If we also write
p = the number of poles.
/ = the full load current per phase.
R — the rated speed in revolutions per minute;
then multiplsdng both sides of equation (1) by the current /, we have
ri-'-MmZ p,
We have also the fundamental relation between the speed, fre- quency, and niunber of poles,
iV--2^ (3)
2 X 60 ^ '
8 DESIGN CJOEFFICIENTS FOR DYNAMO ELECTRIC MACHINERY.
^^^^^' Vi fcJ^/r X pR kXpMxITxR ...
• "2X60X10»" 120 X 10» . . . U
This equation shows that the output per phase VI depends on the three terms pM, IT, and R: pM is the total flux crossing the air gap from all poles from field sjrstem to armature, IT is the ampere turns per phase, which is equal to the total ampere turns on the armature for all phases divided by the number of phases, and R is the speed in revolutions per minute.
Thus for a given machine of given size (i.e., dimensions) the output will be practically proportional to the speed. Doubling the speed of a given machine doubles the frequency, which practically doubles the voltage, and, for a given current output, the output in kilo-volt- amperes will be doubled. Practical considerations which are set forth later in his treatise, occasion wide deviations from direct pro- portionality between speed and output. Conversely a machine for a given rated output will usually be smaller (in dimensions) the higher the speed. We may further develop equation (4) as follows: Let us designate, ^= the average magnetic flux density in the air gap, or the
"specific magnetic loading" of the armature. a = the ampere conductors per centimetre of armature peri- phery, or the "specific electric loading" of the armature, n = the number of phases. ^ is equal to the Total Flux divided by the total au* gap surface.
.'./?=» -^TT- «= -T-> for T, the polar pitch, is equal to — TzUAg T/gf p
a is equal to the total armature ampere conductors divided by the
armature periphery at the air gap = ir— •
M = BxXg. Also the armature ampere turns per phase,
2n
Substituting these in equation (4) we obtain
yj _kX pzXgp X TcDa X R 120 X 10» X 2n
OUTPUT COEFFICIENTS. 9
Multiplying by n we obtain the total output of the machine in volt amperes,
•""-^fif • •••••• <«
We also have t == — and substituting this in equation (5) we P obtain
= 0.041 X IQr'kiyXgapn .... (6)
h varies with the ratio of pole arc to pole pitch, and with the spread of the armature winding (see page 110), but if we take for the moment the constant value, k = 4.44, we have
nVI = 0.182 X lir^iy^Ra^ (7)
This is a rational formula connecting the output, speed, and the principal dimensions, or the cubical volume enclosed by the armature surface at the air gap which is proportional to D^^.
Prom equation (7), for a given rating and speed, it is seen that the dimensions (D^^) will be dependent on the two factors a and p — which are respectively the "density" of ampere conductors on the periphery of the armature, and the density of the flux in the air gap, — and clearly the higher the value of either or both of these factors, the smaller will be the machine. In practice the values for each of these are somewhat of the same order for all normally designed machines, their precise values depending on the conditions to be fulfilled by the particular case under consideration.
The values are limited by consideration of the permissible heating (the dimensions and surface of the machines must be sufficiently large to radiate the heat due to losses, without undue temperature rise), and by pressure regulation in the case of alternators and by commutation in the case of continuous current machinery.
If we transpose equation (7) we may obtain
nVI
0.182 X a^ X 10-*.
D'XgR
The expression on the left hand side is the output coefficient f as defined at the beginning of this chapter on pages 6 and 7.
10 DESIGN COEFFICIENTS FOR DYNAMO ELECTRIC MACHINERY.
Hence the value of ^ is
f = 0.182 Xap X l(r».
In commencing the carrying out of a design, it is convenient to assign an appropriate value to f and to derive from this the value of L^Xg and thence the chief dimensions.
We shall in later chapters give considerable attention to the coefficients a and ^ in connection with the various designs studied. For the present purpose we shall analyse the value of the output
|
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9 A |
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/ |
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|
1 |
^ |
/^ |
||||||||||
|
? |
||||||||||||
|
0.8 |
||||||||||||
|
fli |
||||||||||||
1000
aooo oooo
9000 3000 4000
Rated Output leva.
Fig. 3. — Output coefficients of low and moderately low speed altematon.
coefficient f, and the general influence on this value, exerted by the various factors in the design such as speed and frequency.
The curves which follow may be taken as giving rough but fairly rep- resentative average values for $ in normal designs, and also as indica- ting in what cases, and to what extent, higher values may be obtained.
OUTPUT COEFFICIENT OF ALTERNATORS.
The curves in Fig. 3 show the relation between the average output coefficient and the rated output of polyphase alternators. The data from which these curves are drawn is chiefly for low speed machines and the curves should be taken as roughly representative
OUTPUT COEFFICIENTS.
11
for low and moderately low speed alternators. The question of the influence of high speeds is considered farther on.
Fig. 4 shows the relation between the average output coeflS- cient and the air gap diameter for low speed and moderately low speed alternators. It is not difficult to obtain good designs with output coefficients higher than the values indicated by the curves in Figs. 3 and 4, but as these curves represent the bulk of the designs from which the analysis has been made, they will be con- sidered as representative values, and the further studies in this chapter will have reference to them.
|
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|
24 |
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|
^^^ |
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on |
^ |
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t? |
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<3 |
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1 A |
/ |
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^ |
^' |
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J |
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y |
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y |
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A fi |
'/ |
r |
||||||||||||||
|
A4 |
||||||||||||||||
|
• |
100 800 800 400 600 600 700
Gap Dlameterin Centimetres..
FlQ. 4. — Output coefficients of alternators.
It does not invariably follow that a higher output coefficient corre- sponds to a lower Total Works Cost, although generally speaking the higher the value of $ the lighter and cheaper the machine.
The curves of Figs. 3 and 4 should be taken as mean curves for machines within the average range of frequency, and as roughly indicating the influence of the latter on the value of the output coeffi- cient. Fig. 3 gives two curves for 25 and 50 cycle alternators respect- ively, showing the output coefficient plotted against the rated output. It will be noted that somewhat higher output coefficients are obtain-
12 DESIGN COEFFICIENTS FOR DYNAMO ELECTRIC MACHINERY.
able with lower frequencies. Fig. 4 shows corresponding cui-ves in which f is plotted against the air gap diameter for 25 and 50 cycle machines. Regarding the influence of the speed, although the weight of the machine is considerably reduced by the employment of high speeds (the weight being an inverse function of the speed for a given rated output), it is nevertheless not the case that high speeds permit of higher output coefficients. On the contrary, the output coefficients obtained with steam turbine alternators are considerably lower than for slow speed machines. This statement is borne out by inspection of any
|
&4 |
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|
2.0 |
jSI |
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V* |
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y |
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X ^ |
^ |
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|
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|
OA |
||||||||||||
1000 8000 8000 4000 6000 6000 Rated Oatpnt kva. FiQ. 5. — r Output coefficients of alternators.
turbo-alternator designs. It is due to the fact that the design of alternators for high speeds is a difficult problem, and larger dimensions than would otherwise be required are called for, chiefly on account of the question of heating. We have in Chapters VI, VIII, IX, and X studied more specifically the reasons for these results.
In Fig. 5 the upper curve applies to low speed machines, say below 300 R.P.M. The lower curve gives a rough idea of the average out- put coefficients for high speed machines above 300 R.P.M., and up to a maximum of 1500 R.P.M.
The low output coefficients for the high speed machines are apparent from these curves. In smaller ratings, the curves more nearly approach
OUTPUT COEFFICIENTS.
13
one another, as the high speeds are more favourable to small machines than to machines of large rating.
In Fig. 6 the output coeflScient is shown as a function of the air gap diameter for high and low speeds. The high speed curve, it will be seen, is above the low speed and it may be thought at first sight that this is contradictory to the curves in Fig. 5. This is not the case; the fact is that, for a given diameter, the high speed machine has a higher output coeflScient than the low speed. This is because for any given diameter a high speed machine would have a rated out-
|
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|
2.4 |
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20 |
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4 |
r |
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tr |
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1 1.6 0.8 |
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P |
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S^ |
^ |
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w |
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-^ |
^ |
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r |
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f |
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|
0.4 |
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100 200 800 400 500 600 700
Gap Diameter in CentimetreB
FiQ. 6. — Output coefficients of altematois.
put much greater than that of the corresponding low speed machine. Thus, for example, let us consider a 3000 kva. machine designed first for a speed of 100 R.P.M. and secondly for 1000 R.P.M. At 100 R.P.Mi the output coeflScient according to the upper curve of Rg. 5 would be about 1.95; and at 1000 R.P.M., from the lower curve of Fig. 5 the output coefficient would be 1.55. In such a pair of machines the air gap diameter would be about
600 centimetres for the 100 R.P.M., and 150 centimetres for the 1000 R.P.M.
(see curves in Pig. 70, Chapter VII).
14 DESIGN CJOEFFICIENTS FOR DYNAMO ELECTRIC MACHINERY.
Now from the curves of Fig. 6 the output coefficients corre- aponding to these diameters are respectively
2.0 for the low' speed machine of 600 centimetres diameter and 1.6 for the high speed machine of 150 centimetres diameter.
These figures are in good agreement with those obtained from the high and low speed curves of Fig. 5.
OUTPUT COEFFICIENT OF CONTINUOUS CURRENT MACHINES.
If, for continuous current machines, we carry out a similar inves* tigation, we arrive at the following expression for the output coeffi- cient:
e = 0.160 X ia-»a^.
|
^^^ |
. |
|||||||||||||||||||
|
3 |
_.^ |
— - |
|
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^ |
-^ |
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e 2 |
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1.4 1 '•' 1 ^'^ 1 0.8 t 0.6 O 0.4 0J8 |
^^ |
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t |
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i |
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f |
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10 90 80 40 60 |
||||||||||||||||||||
|
uatpui m Jiiio waits |
||||||||||||||||||||
900
400
600
1400
1600 180O
800 1000. 1900 Rated Ontpat Jta Kwb. Fig. 7. — Output coefficients of continuous current machines.
The numeral is in this case 0.160 against 0.182 for alternators. This is owing to the fact that the voltage coefficient k is 4.00 for continuous current machines while it was taken as 4.44 for alternators. It must not be taken from this that the values of ^ obtainable with contin-
OUTPUT COEFFICIENTS.
15
uous current machines are lower than those for alternating current machines. On the contrary, the very reverse is generally the case as will be seen from the curves which wiU be given.
That higher output coefficients may be obtained with continuous current macliines, signifies that the values of either a or ^, or both, are higher than in alternators. The difference is accounted for by the stringent restrictions, chiefly as regards pressure regulation, en-
80 180 160 900 840 280
Armature Diameter In CendiaetraB.
Fig. 8. — Output coefficients of continuous current machines.
880
countered in the case of alternators. Figs. 7 and 8 give curves for the average values of the output coefficient for continuous current machines plotted as a fimction of the rated output and diameter respectively.
In continuous current machines, it again appears that designs for higher rated speeds do not permit of such high values for $ as
16 DESIGN COEFFICIENTS FOR DYNAMO ELECTRIC MACHINERY.
lower speed designs. This is established by the studies in Chapters XV and XVI, and the quantitative relations obtained from these results are shown in the curves in Fig. 9. These curves show $ as a function of the rated output for rated speeds ranging from 125 to 2000 R.P.M.
The values indicated by these curves correspond to normal designs. Here again it does not follow that in all cases a high output coefficient corresponds to the most suitable or to the cheapest designs.
4i)
3.0
0
I
1.0
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250 500 750
Bareed Ontpat lalCllawatts
100
Fig. 9. — Output coefficient curves for 500 volts continuous current machines at different speeds and outputs.
It is desirable to point out in connection with the output coefficient that, while of great utility, it cannot be regarded as more than a nu- cleus from which to evolve a design. Employed with a clear imder- standing of this limitation, and with the reservation that its value must be adjusted according to the requirements of each individual design, the conception is of great utility to the designer.
In order to facilitate the intelligent use of the output coefficient,
OUTPUT COEFFICIENTS. 17
we have set forth the data and curves of this chapter. While the values and relations given in the curves are fairly representative and show the average magnitude of the influence of the various factors involved, they should not be rigidly adhered to in cases where the individual design shapes out best by departing from these values.
Methods of designing alternating and continuous current machines, using the output coefficient f as a basis, are set forth in Chapters VII and XIV respectively.
We have seen how the specific electric and magnetic loadings, a and P, are related to the output coefficient f , viz. that f is propor- tional to the product a/?. The study of the value of $ may be thus regarded as a study of the product afi, although the influence of the speed and output on each of these factors individually has not as yet been ascertained, but will, for alternators, be dealt with in Chapters VIII, IX, and X.
In choosing a value for c as a starting point for a design, the designer is really fixing a value for the product a/9 without assigning individual values to them. This determines the value of D^Xg, and the design may then be proceeded with in the manner outlined in Chapters VII and XIV.
In working out the further stages of the design the values of a and /9 will require to be determined, but it is often possible and desimble to vary considerably the values of a and /? relatively to one another, without changing the originally chosen value of f . For instance, an alternator which requires especially close voltage regulation will gen- erally have a low value for a but in many cases it may have the same value of $ as a more normal machine.
We have now considered the coeflScients (1) and (4) mentioned
W on page 6. The second coefficient mentioned there is ^t~ , which
has been known as the Steinmetz coeflScient. This coeflScient which we mil denote by ^ is closely related to the output coeflicient $. We have
^ D'XgR DXg DR DR'
Also the peripheral speed, S, in centimeters per minute, is equal to nDR.
18 DESIGN COEFFICIENTS FOR DYNAMO ELECTRIC MACHINERY.
Thus
and substituting this in the above equation, we have and the relation between the two coefficients is established.
8.0
8.0
1.0
|
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100
SOO 300
Diameter O fn.Centimetraa.
400
500
Fig. 10. — Weight factors of alternators.
B.
Weight Coefficients.
Alternators. — The total net weight of an alternating current gen- erator may be roughly estimated either from the total weight of the effective material or from the air gap dimensions D and Xg. The latter method may be based on a term proportional to the surface, as DXg, or to the volume as D^Jig.
The weight of the effective material, by which is meant the field iron (poles and yoke) and copper, and the armature iron (lamina- tions) and copper, constitutes a fairly definite proportion of the
WEIGHT COEFFICIENTS.
19
total weight of the machme, if there is not an abnormal amount of material put into the frame and spider. We shall designate as the "weight factor*' the ratio of the total
60
I
90
1 "
10
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L_ |
1 |
1 4
DA^ (in Square Metres)
Pig. 11. — Weight coefficient — total weight -^ D^ for alternators.
net weight (excluding bed plate and pedestals) to the weight of the eflfective material.
A curve showing rough but representative values for the weight factor for normal alternators in terms of the armature air gap diameter is given in Fig. 10. On the curve are marked the points correspond- ing to seven machines obtained from actual figures for the total weight.
The niachines of small diameter have a lower factor than those
I
20 DESIGN COEFFICIENTS FOR DYNAMO ELECTRIC MACHINERY.
I
PS
• *
U
I 5
2
IS
•BUOX Uf
•j<nj«a n^]9IA
•saox u| |ii|j JO ^qai^M I«10X
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ajoo ssoio
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u\ paeds pa^irH
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OOO0OO««««««< 0xxxQQQQaa
OC9^«DOW30r«CO^OaOOO«Dr««000»OCOkOO*0
*o«>p<ao«Doooe>9«D coo 000*00 ^K»«ooaoci
aOOC4eOiOK^Oa»OaO«0»^aOe«i«<OOTH^O'«000
"To =;
c^**3«p^eo'^ao»r»oo»oo^oioo'^r»«oooo 09 9000 CO c<4coior>^a>oo«-4Csie9<^eoeooc4'-iO
0000^^0000000«-it^«OM>tOe9aO«000
«o^to<OdOOoe^<^co«paotsIi-«io«Di«io«o»oesie«s
00'-^lOi<<^rHSl^«0«DOC««^CO^Soe90 OOOOOOQO«0'<«<C<4000oS^^2^^lOOOOO«000
^QO<^^e^e^t^co o'»^ co^'^'oSSSeoSScsioio
«oo:2ssSoocoo«.ss§?8i^5S5«.c.«
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^~ 55 uT"
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SSSSS^SSSS^o^ootocooioc^aoaoo
C4 C4 C4 *^ *-4 iF^ lO CO C) f-i *^ ^ ^ CO CO ^ lO O CO
»o ■— — — —
*C t» O O O O to to lO to lO lO o o o o o«o * O to '^ C« CO to to to to 04 C4 04 C9 Ol C) to to to to to ^ * SS c^ 'm
^OOO^^^OO^OOt
>tou5oooooooi )r^r«to too too
•^ »-^ CO 1^ ^m
9 CO CO CO CO CO CO CO CO CO ^^
>tOdOOtOI^OOOaO
}«o^'«^ooototoor^ * v-H e« coco
«-^e^co^io«or«aooo«-^e9co-««<to«or«oooo»^e>9 co"
WEIGHT CX)EFFICIENTS.
21
with large gap diameters. This is due to the larger amount of electromagnetically non-effective material in machines of large diameter, as in the arms of the magnet wheel, and in the stator frame.
Small diameters are associated with high speed machines^ and thus the latter have generally a smaller weight factor and a smaller amount of non-effective material. The data relating to the points marked on the curve in Fig. 10 is given at the bottom of Table 1.
I"
|
c |
|||||||||||||
|
.\ |
3 |
< |
> |
||||||||||
|
X |
\ |
||||||||||||
|
^ |
\ |
||||||||||||
|
>?* |
X |
s^ |
• |
||||||||||
|
E |
0 |
^ |
"^ |
O |
O^ |
> |
|||||||
|
(s)^ |
^ |
||||||||||||
|
( |
"^ |
||||||||||||
|
• |
|||||||||||||
8 8 4
O^Xq (in Cubic Metres)
Fig. 12. — Weight coefficient — total weight -j- D'Xg for high speed alteraatora.
The upper part of this table relates to the alternator designs for which specifications are given in Part II.
The total weights of effective material in column 9 are obtained from the detailed designs in Chapters VII to X.
The total net weights are then obtained from this by multiplying by appriopriate values of the weight factor taken from the curve in Fig. 10 and entered in colunm 10.
22 DESIGN COEFFICIENTS FOR DYNAMO ELECTRIC MACHINERY.
In columns 14 and 15 are calculated the weight coefficients for the total weights per unit of D^Jig and of DXg, and in columns 12 and 13 the weights of effective material per unit of D^Xg and Dig. The latter coefficients do not vary over so wide a range as do the total weight coefficients, as in the latter, the additional variable, the weight factor, is introduced.
In Fig. 11 is plotted the weight coefficient, (total weight h- D^ff), as a function of Dig^ the different styles of points making a (fis-
ic
14
12
10
« 6
B
B ^^^
H^^-
B
10
15
20
25
30
85
40
D*A^ (in Cubic Metres) Fia. 13. — Weight coefficient — Total weight h- D^Xg for slow speed altematora.
tinction between the various designs. The [)oints for the machines in the lower part of Table I are marked thus jT]. This curve may be taken as suitable for both high and low speed machines, since the value of DXg is practically a constant for any given rated output and practically independent of the speed even in the largest ratings. The value of D^Xg, however, varies widely with the rated speed, for
WEIGHT CX)EFFICIENTS.
23
a given rated output, as will be seen from the relation embodied in the output coefficient
. w
since f does not vary widely for a given rated output.
Hence in high speed machines, we are confined to a compara- tively small range of values for IPXg, the maximum value being about 6 cubic metres. The range for slow speed machines extends
|
100 |
f |
|||||||||||||||
|
140 |
/ |
|||||||||||||||
|
J |
f |
|||||||||||||||
|
/ |
||||||||||||||||
|
190 K |
/ |
|||||||||||||||
|
/ |
r |
|||||||||||||||
|
o 100 |
i |
/ |
||||||||||||||
|
/ |
||||||||||||||||
|
/ |
||||||||||||||||
|
/ |
||||||||||||||||
|
^ 00 |
y |
/ |
||||||||||||||
|
40 |
J |
/ |
||||||||||||||
|
J |
/ |
|||||||||||||||
|
«0 |
^ |
/ |
||||||||||||||
|
> |
/ |
|||||||||||||||
|
/^ |
1 S 3
OAa Ob Sqnara Metres) Fio. 14. — Relation between total weight of alternators and Dig.
to as high as 40 cubic metres and hence we must take each class separately.
Fig. 12 shows the weight coefficients, (total weight -&- D^kg) plotted against iJ^ig for the high speed machines of Table I.
Fig. 13 gives a similar curve for slow speed machines obtained from an analysis of a large number of machines; by way of example the points corresponding to the machines in the lower half of Table I
24 DESIGN COEFFICIENTS FOR DYNAMO ELECTRIC MACHINERY.
have been entered. Prom the curves in Figs. 11, 12, and 13 we have derived, in Figs. 14, 15, and 16, curves showing the total net weight in terms of D\g and D^'^.
Continiums Current Machines. — For continuous current machines, a greater proportion of the total weight of material is effective, as there is no non-effective material corresponding to the armature frame in alternators, the magnet yoke of continuous current machines being self-supporting.
|
100 |
||||||||||||||
|
140 |
||||||||||||||
|
180 |
||||||||||||||
|
H o 5100 i 1 2 80 |
||||||||||||||
|
y |
y^ |
|||||||||||||
|
y |
y |
|||||||||||||
|
1 40 |
X |
y |
||||||||||||
|
y |
y^ |
|||||||||||||
|
y |
y |
|||||||||||||
|
y |
/ |
|||||||||||||
|
80 |
/ |
ir~- |
||||||||||||
|
\ |
% |
i |
I |
\ |
s |
7 |
D>Ai7 (in Oubio Metres) Fig. 15. — Relation between total weight and U^lg for small slow speed altematore.
Hence the values of the weight factor, as defined above, are less in the case of continuous current machines than for alternators. The average values of the weight factor for continuous current machines usually range from 1.3 to 1.5, the higher values applying again to machines of large diameter.
In this case the effective material includes the weight of the com- mutator segments.
Fig. 17 shows the relation between the total weight of continuous
COST COEFFICIENTS.
25
current machines and the value of D^Xj. The curves are plotted from an analysis of a large number of machines. Curves are given for 125, 500, and 2000 R.P.M., which roughly indicate the influence of the speed oh the relation of total weight to D^Xgf.
C.
Cost Coefficients.
The Total Works Cost of a machine may be roughly determined from the dimensions or weight, without recourse to detailed estimates of material and labour charges.
|
flJA |
||||||||||||||||
|
IMt |
â– ^ |
'^ |
||||||||||||||
|
120 |
,^ |
^ |
'' |
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|
1 |
^ |
y |
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|
/ |
X |
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|
i" |
/ |
r |
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|
/ |
r |
|||||||||||||||
|
/ |
/ |
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|
t. |
J |
/ |
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|
/ |
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|
dA |
||||||||||||||||
|
^ |
||||||||||||||||
|
9t\ |
||||||||||||||||
10
80
85
K. 80 25
D>A^ (in Cubic Metres) Fio. 16. — Relation between total weight and l^ljg for large slow speed alternators.
A method of estimating the Total Works Cost of continuous current machines from the air gap dimensions is given in Chapter XV. In this method the Total Works Cost is equal to
kDL or kD{\g + 0.7 t),
where L is the length of the armature over the windings (which may be taken as approximately equal U) Xg + 0.7 t), and k is the cost
26 DESIGN COEFFICIENTS FOR DYNAMO ELECTRIC MACHINERY.
coefficient, the value of which varies, although not widely, with the rated output and the peripheral speed.
A useful rough method consists in working from the cost per ton of total weight of machine. The value of this figure for both alter-
1
|
M |
||||||||||||||||||||
|
46 |
^ |
|||||||||||||||||||
|
^ |
y^ |
|||||||||||||||||||
|
in |
^ |
y^ |
||||||||||||||||||
|
y |
X |
|||||||||||||||||||
|
no |
^ |
y |
||||||||||||||||||
|
^'^ |
P |
y |
||||||||||||||||||
|
fa |
f' |
^ |
||||||||||||||||||
|
..*? |
^. |
^ |
y |
|||||||||||||||||
|
^ |
^ |
t |
k |
|||||||||||||||||
|
.5 |
c |
:^ |
/^ |
|||||||||||||||||
|
8 |
e |
^ |
'/ |
|||||||||||||||||
|
^ |
y/ |
|||||||||||||||||||
|
7 |
1 |
1000 8000 8000
Values of D^A^^ (in Decimetres)
Fia. 17. — Relation of weight to J^'kg in continuous current machines at different
nating and continuous current machines of other than small rated outputs, averages from $150 to $200 per metric ton of total weight. The cost per ton is lower the greater the total weight.
CHAPTER III.
CRITERIA FOR HEATING AND FOR TEMPERATURE RISE.
The ultimate temperature rise in a dynamo electric machine is pro- portional to the losses in the machine, and inversely to the radiating surfaces of the various parts of the machine in which the losses occur; i.e., the ultimate temperature rise is proportional to the watts lost per unit of radiating surface.
For the purposes of the present treatise, and in connection with the various designs worked out herein, we shall estimate the tempera- ture rise on the basis of the watts dissipated per square decimetre of radiating surface.
Armature Losses and Temperature Rise of Armature. — ^The various losses throughout an armature are capable of being esti- mated to a fair degree of accuracy, but the true radiating surface of an armature, more especially in view of the fact that the losses occur in both the copper and the iron, is rather an indefinite quan- tity.
The iron surfaces at the sides of the ventilating ducts and the winding surfaces at the ends of the armature coils are all exposed to the cooling air, but they contribute to the radiation of the heat to widely different extents.
In the case of armatures of great core length the core ducts may receive air at a higher temperature than that at which it passes the windings, and it is possible for the ducts near the centre of the core to contribute very little to the heat dissipation. Furthermore, the velocity of the cooling air may vary considerably in different parts of the machine.
The desirability of estimating the heating, on the basis of surfaces common to all dynamo machines, will be readily appreciated.
We give here four methods, A, B, C, and D, which may be con- veniently used for the purpose of estimating the temperature rise of armatures.
27
28 CRITERIA FOR TEMPERATURE RISE.
METHOD A.
A convenient basis for reference for armatures is the cylindrical surface at the air gap, extended to include the end connections of the windings. This surface comprises the armature core surface and the external surface of the end portions of the windings. Repre- senting by D the armature diameter at the air gap, and by L the length over the ends of the windings, this surface is equal to nX DX L.
The overall length L for ordinary continuous current barrel- wound armatures is usually approximately equal to {Xg -f 0.7t) where Xg denotes the armature gross core length and t denotes the pole pitch. Of this length, 0.7t is the part occupied by the end windings, which, according to this formula, project a distance equal to 0.35 of the pole pitch at each end. This is a very usual value in practice. The cylindrical surface over the winding is thus,
;r X 7) X (Agr -f 0.7t).
If D, Xg, and r are, for the purpose of these thermal calculations, taken in decimetres, the surface is in square decimetres, and this is the most convenient unit for expressing radiating surfaces. If the dimensions are taken in centimetres the surface must be divided by 100 to reduce it to square decimetres.
Denoting by W the total losses in watts throughout the arma- ture (copper and iron), then the value of the watts per square deci- metre of radiating surface as thus defined, is equal to
W
7cXDX{Xg + 0.7 t) '
and for a given armature, running at a given speed, the temperature rise is roughly proportional to the value of this expression.
For ventilated revolving armatures of ordinary design, the thermo- metrically determined temperature rise lies between 0.6 deg. Cent, and 1.6 deg. Cent, per watt per square decimetre. The temperature rise per watt per square decimetre may be designated the "Specific Temperature Rise," and we may write,
T (in deg. Cent.) ^ K X watts per square decimetre.
The value of K, the ** Specific Temperature Rise," is usually from 0.6 to* 1.6. This value applies to ordinary armatures having a peri-
ARMATURE LOSSES AND TEMPERATURE RISE. 29
pheral speed of some 10 to 25 metres per second and to the thermo- metrically determined temperature rise.
For a peripheral speed of twice this, say 35 metres per second, the value of K will be from 0.5 to 1, provided there is an eflScient flow of air through the armature core and windings.
In alternating current generators, it is more usual to have the arma- ture winding on an external stator. This circumstance does not materially affect the value of K so long as the ventilating facilities are ample and the rotor peripheral speeds are of the stated values.
In turbine dynamos the peripheral speed generally reaches 50 to 80 metres per second, and may, in exceptional cases, be as high as 100 metres per second in large alternators. The watts per square decimetre for such machines is high by reason of the small dimensions required at high speeds, and a much smaller value of K must be attained by some means in order that the temperature rise shall not be abnormal. It is thus a matter of the greatest importance that the armatures of turbo-dynamos shall be provided with a very liberal number of ventilating ducts and that no expedient means of improving the ventilation shall be omitted.
With armatures of this class and for the range of peripheral speeds quoted above, i.e., 50 to 100 metres per second, the specific tem- perature rise may be more of the order of 0.3 to 0.6 deg. Cent, per watt per square decimetre.
We may tabulate the following values for K in the formula T (in deg. Cent.) = X X watts per square decimetre.
TABLE 2.
Values of Specific (Thermometricallt determined) Temperature Rise in Terms of Peripheral Speed of Rotor.
Average Peripheral Speed.
Value of jr.
10 to 25 metres per second 35 metres per second . . 70 metres per second . .
0.6to 1.6 O.Stol.O 0.3 too. 6
These figures must be used judiciously and the individual circum- stances of any particular case must be given careful consideration. While the data serves to give a good general idea, especially for pur- poses of comparison, due regard must be paid to each case, especially
80 CRITERIA FOR TEMPERATURE RISE.
to the efifectiveness of the ventilating arrangements. If the latter be well designed, the lower values of the specific rise may be taken. In the case of those turbo-dynamos in which the air is forced through the machine by means of fans and cups on the rotor, as is now frequently being done, the lower values will often be attainable, but of course any such calculations are best substantiated by test results on the class of machine being dealt with. There is frequently but very restricted space available for providing access of air to the interior of the rotor ifa the case of turbo-generators, and hence in spite of their high peripheral speeds they are in many cases at a grave disadvantage as compared with large slow speed generators where the active mate- rial of the rotor is supported at the rim of a large, open spider.
For alternating current armatures, where the winding is carried out as a barrel winding, similar to a continuous current winding, the above method and constants will hold good. The peripheral speed will generally be that of the rotor within the stationary armature.
If the winding of an alternator is carried out as a coil winding, as is commonly the case with stationary armatures, the "length over the windings '' is indefinite, and consequently the cylindrical surface at the air gap is a much less definite conception. Nevertheless good results may be obtained even in these cases, by method A.
Various alternative methods are, however, available, and will now be briefly considered.
METHOD B.
One of these methods consists in using simply the armature core surface at the air gap, and the watts lost below that surface. This surface is simply 7:DXg, and the watts requiring to be dissipated by this surface consist of the armature iron loss (core and teeth) plus the losses in the embedded portions of the conductors. This latter is equal to the total copper loss minus the loss in the end windings.
On this basis the specific temperature rise generally has values about two thirds as great as the values given in Table 2 which are intended for use with method A, in which the heating coeflicient is calculated on the surface kD (Xg -f 0.7t).
Calculations by method B relate only to the heating of the arma- ture body, the radiating surface of the end windings not being taken into account. As these are, however, when correctly designed, usually subject to better cooling facilities than the body of the arma-
ARMATURE LOSSES AND TEMPERATURE RISE.
81
ture, it may often be assumed that their temperature rise will not exceed that of the armature body, and calculation on the latter will suffice in such cases.
METHOD C.
Another alternative consists in employing as the "equiva- lent" cylindrical surface, the value of the expression
D X (^9 + Kt)
where X is a coefficient depending mainly on the rated voltage and also to a certain extent on the value of t, the polar pitch. In Table 3 are given fairly representative values for K.
TABLE 3.
Values of K in the Expression D x (}<g + Kt) Repbesenting the Equiva- lent Cooling Surface of tue Armature of an Alternating Current ' Generator.
Rated Terminal Voltage.
1,000 or less
2,000 . . .
4,000 . . ,
6,000 . . .
8,000 . .
10,000 . . .
12,000 . .
20,000 . . .
Values of K. when
r the Pole Pitch
- 40 Cms.
(or Lras).
Values of K. when
r the Pole Pitch
-60 0ms.
(or More).
METHOD D.
Another coefficient which may be used for estimating the armature heating, is the watts per square (iecimetre of total boundmg surface, which (for stator armatures) is taken as consisting of the internal (air ga^p) and external cylindrical surfaces, and the surface of the two ends of the armature core.
This surface is equal to
»(D,+C)*,+-(Z),'-C),
82
CRITERIA FOR TEMPERATURE RISE.
where Z), and D are the armature external and internal diameters respectively, and hg is the gross core length.
Method A.—
Total Armatore Loaaea
F!g.l8
|
»0 160 |
||||||||||
|
o |
||||||||||
|
UO 80 40 |
♦ i |
• |
8 |
|||||||
|
f |
^ |
X |
||||||||
|
^ |
.• |
X |
||||||||
w
Method C -»
Total Armature Losses â– â– DCXflf+KT)
Fig.90
|
aw |
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|
« |
0 |
|||||||||
|
80 |
« |
, • |
o |
|||||||
|
K |
A |
8 |
) |
|||||||
|
40 |
X |
• |
• |
|||||||
w
40
100
|
Method B-^ |
atts Lost between Core hei |
sdi |
|||||||||
|
TO\g |
|||||||||||
|
Flfl:.19 |
|||||||||||
|
90O |
( " |
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|
4 |
• |
* |
|||||||||
|
X |
f\ |
||||||||||
|
• |
e |
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|
• |
|||||||||||
|
80 |
|||||||||||
|
40 |
|||||||||||
00
80 100
« ^v ^ r. - Total Armatare
Method D Total Surihce of
Armature Core
/lPig.2l
ISO
80
jfO
80
AbsdasM denote the Peripheral Speed of Rotor In Metere per Second.
I^ote:- In the above Figs, the Output of the Machines la represented as fbllows:- X-400kva O-650kva.. •-aOOOkva., O-6000 kva.. A-lgOOkva.
FiQS. 18-21. — The armature heating coefGcient for the alternating current gen- erators specified in Chapters VII- X, calculated according to the four methods as set forth in Table 4.
In all of these methods we may denote as the heating coeflScient,
T^^fttts loss
the quotient — zr—. ; — , i. e. the energy in watts requiring to be
radiatmg surface -i —^
dissipated per square decimetre of radiating surface. Thus the (ther-
mometrically determined) temperature rise is equal to the product of
the ** Specific Temperature Rise " and the " Heating Coefficient."
ARMATURE LOSSES AND TEMPERATURE RISE.
JOJ
■(•ma -bfi Jod^ i|L
|< 0 X X X
»3®>o^»o^eoeocowcoco — ^ — "^
D <0 ^ CO ^ CO
*('ui(j *be) 9J03 ojn^vnuy
•(•ma 'bS ■'»<I
csig^cog<i^iie^c^e^c^c^e<ii
s§gsss§5:sssssssfcg
*bg) eavjjng 8unv(I>«H
>OQOQOOQOQPOOQQaO^
aoieMjdza u} jg jo ani«A
•(•nia -bg j»d
iSS^SSSSSo838SSgia3^$
•RlltMfconM aj «PW>H
5wSi-iSoSSSeori'-'W 5^<ooot»t^r^t*co^^c<i-Hi-H
t^t^^»OCOQOQOOC^COCO«ar^t^>OOi
•(•tna 'bg Jiod
SS§S::22§SSSgS88SSSS
•(* ro + ^Y) (Tf (ma
?8S82§
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S'cO^ACDCs'kQCOi-lC^QC^oiocOXQ
I
I
I
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t>>i9XO)ClQCD'^QOOOO^COCOXO)^
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t^t^t^iogJoB65c5wcocoTjiu5«5»Hiooo
'puooog jod MioXo a} iC9Pipo(J9 j
SwSSSSSc5^c5cJc5SSSSS
•9inniw jod rao|9niOAeH «1 P09dg p99«H
SsSSSpSSSSt^oSSoSc
t^t«*t^t^O«5 .H 01 CO u5 1^ £>• wi t
*«Aq a| ^ndino po9«S
8
•iOqom^ 991I9i9J9H
84
CRITERIA FOR TEMPERATURE RISE.
In the diagrams in Figs. 18 to 21 we have for a number of the authors' alternator designs, particulars of which are given in subse- quent chapters, plotted the heating coeflScients as a function of the peripheral speeds of the rotor.
TABLE 5.
The ARifATURE Heating Coefficients for Twenty-nine Alternating Current Generators Based on Three Different Methods of Calculating the Radiating Surface.
|
i |
e |
Method A. |
M^LhoU B. |
Method C. |
|||||||||
|
a 1 9 |
1 1 |
CBS |
5 I a 1 |
1 |
|||||||||
|
1 5r, |
^<3 |
II 1! |
ii -E 5 1^ |
li |
§1 |
I* |
li 1 |
||||||
|
s |
o |
OQ 1 |
1^ |
s |
< |
{5^ |
^-\^s |
9 Qb |
^ s |
WpP |
|||
|
1 |
1 |
& |
9 1 |
to. |
a. |
ft. 45 |
loii |
0^ 0.8 |
1 78 |
lOOOw 0 |
|||
|
I |
80 |
600 |
20.4 |
530 |
20.4 |
5 |
73.5 |
65 |
64 |
||||
|
II |
100 |
770 |
38 |
2,400 |
20.8 |
6 |
131 |
46 |
00 |
r>7 |
I.O |
152 |
39.4 |
|
III |
250 |
375 |
42 |
2,200 |
28 |
14 |
314 |
44 |
183 |
74 |
1.0 |
365 |
38.4 |
|
IV |
250 |
3000 |
81 |
2,080 |
78.5 |
14 |
187 |
73 |
100 |
138 |
0.8 |
200 |
70 |
|
V |
2*>o| cm |
28.3 |
3,600 |
28.3 |
16 |
170 |
m |
11:^1 142 |
1.2 |
210 |
76 |
||
|
VI |
300.^fHH) |
72 |
• • . |
72 |
16.5 |
163 |
100 |
91 ISO |
. . . |
. . • |
|||
|
VII |
350 :iQm |
67.5 |
33.8 |
18 |
204 |
90 |
173 |
106 |
, . , |
||||
|
VIII |
375 oiM) |
36.4 |
3,600 |
36.4 |
20 |
Old |
i.'2 |
800 |
25 |
||||
|
IX |
4m sm) |
113 |
2,000 |
94 |
20 |
257 |
'78 |
WVl |
150 |
0.8 |
275 |
73 |
|
|
X |
500;3(HH) |
89 |
550 |
89 |
25 |
230 |
109 |
117 214 |
0.7 |
226 |
110 |
||
|
XI |
fiOOiriiW |
89 |
550 |
51.3 |
25 |
376 |
67 |
217 100 |
0.7 |
380 |
66 |
||
|
XII |
1000 |
I'm) |
82.5 |
82.5 |
45 |
356 |
126 |
ir.n |
27;^ |
. . . |
, , , |
||
|
xin |
1000 |
1.5{M) |
71 |
5,200 |
71 |
45 |
430 |
105 |
2!H |
153 |
i!i |
506 |
89 |
|
XIV |
12t>0 |
1.500 |
67.5 |
2,000 |
67.5 |
51 |
356 |
143 |
2:^0 |
220 |
0.8 |
375 |
136 |
|
XV |
um m) |
42 |
. . . |
42 |
60 |
503 |
119 |
I^.^O |
170 |
. . . |
|||
|
XVI |
1500 ICKK) |
61 |
61 |
64 |
360 |
177 |
2[ HI |
â– 120 |
|||||
|
XVII |
1500 lOOO |
64 |
li'ooo |
64 |
64 |
396 |
161 |
224 JHG |
i^e |
620 |
ios |
||
|
XVIII |
ISWL^OO |
100 |
8,000 |
100 |
76 |
600 |
12(1 |
'A-2A;i:h |
1.3 |
850 |
90 |
||
|
XIX |
1800UKH) |
64 |
11,000 |
64 |
79 |
396 |
200 |
22JH->0 |
1.6 |
620 |
127 |
||
|
XX |
2000 |
7r.o |
68 |
6,000 |
58 |
80 |
875 |
91 |
I)!i5 |
115 |
1.1 |
990 |
81 |
|
XXI |
•2im |
nio |
44.5 |
11,000 |
53 |
97.5 |
875 |
111 |
urn |
174 |
1.7 |
1320 |
74 |
|
XXII |
3500 |
12fH) |
86.5 |
5,000 |
108 |
122 |
980 |
125 |
r;50 |
1-SS |
1.2 |
1200 |
102 |
|
XXIII |
37fiO |
2.V) |
42.5 |
2,200 |
88 |
131 |
1300 |
100 |
UT^ |
2(J3 |
0.8 |
1380 |
95 |
|
XXIV |
'Mm |
3^0 |
39 |
3,500 |
39 |
131 |
806 |
164 |
5S5 |
224 |
1.2 |
950 |
138 |
|
XXV |
5(KM) |
5nr) |
57.5 |
115 |
150 |
1350 |
111 |
S;iO |
ISO |
. . . |
. . . |
||
|
XXVI |
50(Â¥) |
5m |
62 |
9,000 |
125 |
150 |
1600 |
M |
96a |
ir* |
\A |
1500 |
100 |
|
XXVII |
S'lOO |
100() |
90 |
134 |
165 |
1300 |
127 |
7f*0 |
â– ?in |
||||
|
XXVIII |
irm |
M) |
50 |
12,000 |
100 |
215 |
2380 |
90 |
1550 140 |
\.7 |
3550 |
'60 |
|
|
XXIX |
7500 |
250 |
50 |
12,000 |
100 |
215 |
2380 |
m |
1550 |
140 |
1.7 |
3550 |
60 |
In this table the heating coefficients (B) are based on the approxixnate total losses in the annature, no deduction being made for the losses in the end windings as in Table 4.
AHMATURE LOSSES AND TEMPERATURE RISE. 86
The data from which these curves have been plotted are set forth m Table 4.
In this table are given the leading particulars of these machines, and in the colimm marked w are given, in kilowatts, the total elec- trical losses in the armature. Column a represents the radiating surface calculated from the expresssion D {Xg -h 0.7t).
The corresponding heating coeflScient is marked and the re-
a
suits are plotted in Fig. 18, also marked A. Columns b and c in Table
4 similarly represent the radiating surfaces nDXg, and ttD (Xg -{- Kr)
and the results are plotted in Figs. 19 and 20 respectively. Colunm
d in the- same table refers to the total radiating surface of the
armature core, including the end surfaces as well as the internal and
external cylindrical surfaces. The results are plotted in Fig. 21.
Published data of other designers' machines is too meagre to per- mit of corresponding analyses. With an endeavour, however, to take such designs into consideration. Table 5 has been prepared.
In this table are calculated the rough approximate values above referred to, for three of the heating coefficients, for the twenty-nine alternators of which further data is given in Table 16, on p. 98.
In these designs a very rough approximation to the total arma- ture losses was obtained from the assumptions contained in Table 6.
TABLE 6.
Mean Values for Armature Losses in Alternators, in Per Cent of Rated
Output.
Rated Oatput kw.
Total Armature Losses in Per Cent of Rated Output.
UptoSOOkw. . . 500 to 1000 kw. . 1000 to 2000 kw. . 2000 to 4000 kw. . 4000 kw. and over
5.0% 4.5% 4.0% 3.5% 3.0%
While weight must not be attached to any individual value in Table 5, the matter of interest is the order of magnitude of the coeffi- cients. Neglecting those values which are unduly high or low, the general order of magnitude of the figures is fairly uniform, when taken in conjunction with the corresponding outputs and peripheral speeds.
86 CRITERIA FOR TEMPERATURE RISE.
In slow speed designs, where the losses are more concentrated in the *' active belt/' i.e., at the air gap periphery of the armature, the watts per square decimetre of that surface is the more rational coeflScient to take out. But in high speed machmes, where owing to the small number of poles, the armatures are of great radial depth, the bulk of the losses occur in the armature iron, and the watts per square decimetre of the total external armature surface becomes a more real conception.
Of course none of these coefficients are true thermal constants, as no account is taken in any of them of the exposed surfaces in the ventilating ducts. A method which takes account of the ventilat- ing ducts is suggested later in this chapter on page 38.
In certain types of machines, it is very useful to calculate still another heating coefficient; that is, the total losses in both rotor and stator, divided by the air gap surface, as calculated by any of the foregoing methods; that is, we can divide the total electrical losses by any of the following surfaces:
(A) TiDiXg + 0.7r)
(B) TcDXg
(C) 7cD{Xg + Kt).
Machines for which this course is to be especially recommended, are those in which both stator and rotor are provided with distributed windings. This applies at once to induction motors and to turbo- alternators having a smooth cylindrical rotating field construction with distributed field windings.
Continuous Current Machines. — From the collection of prelim- inary continuous current designs which the authors have worked out and tabulated in Chapter XV, the armature heating data of Table 7 has been compiled. The curves in Figs. 22 and 23 correspond to this data.
For continuous current machines, the most rational heating coef- ficients are employed in Methods A and B. As in the case of the alternators, coefficient A is obtained by dividing the total arma- ture losses by the cylindrical air gap surface taken over the ends of the windings, and coefficient B represents the watts lost between the armature core heads, divided by the cylindrical air gap surface, also taken between the core heads. For both these methods, the units
CONTINUOUS CURRENT MACHINES.
87
|
1 |
S |
|||||||||||||||
|
6 |
Method B:- Watto Lost between Conk rDXg |
g |
||||||||||||||
|
% |
Q |
|||||||||||||||
|
X |
||||||||||||||||
|
< |
) |
S |
||||||||||||||
|
r r\ |
^ |
|||||||||||||||
|
i-\j |
||||||||||||||||
|
^ |
^ |
o |
||||||||||||||
|
c |
s |
|||||||||||||||
|
v^ |
i § i n II > |
|||||||||||||||
|
•'* |
o |
|||||||||||||||
|
X |
• |
O |
â– g 3 + S Iq
3 ••
g § i I 1 g
X • O
1
g
6 .a â– 8
2»)9mp9a 'b8 J^ ntVAk. v] )a9p0doo Dnn^aH Mmvauy 3in eioaop 89i«tznao
I ft
« s
^ i
.§3
f
I 1
I
38
CRITERIA FOR TEMPERATURE RISE.
are, as before, chosen to give the resulting heating coefficient in watts per square decimetre.
With regard to the remaining methods, C has no application to continuous current machines, as present practice is not concerned with the high voltages obtaining in alternators. It is sufficient in all cases, to take K equal to 0.7. Consequently Method C becomes identical with Method A-
Method D is generally unsuitable for application to high speed continuous current machines, owing to the fact that the internal cylindrical surface of the laminations very seldom contributes appre- ciably to the radiating surface of the armature.
The laminations are often mounted directly upon the shaft, and longitudinal tunnels stamped in the laminations provide a path for the air and link up with the ducts between the laminations.
TABLE 7.
The Armature Heating Coefficientb for the CoNnNuous Current Genera- tors Specified in Chapter XV. Calculated According to the Two Methods A and B.
|
Kated Speed in Bers. ^l ute. |
Fre- quency in Cycles per Second. |
Arma- ture Speed in Metres per Second. |
Method A. |
Method B. |
||||||
|
Bated Output in Kilowatts |
Total Arniap ture lx>88 in Kilo- watts. IT. |
Radi- ating Surface +0.7 T). |
1 Heating Coeffi- cient, (Watts per Sq. Dm.). |
Loss within Arma- ture Core- heads in Kilo- watts. |
Badl- ating Surface wxg. |
Heating Coeffi- cient, (Watts per Sq. Dm.). |
Desig- nating Symbol for Curves in Figs. 22 and 23. |
|||
|
a. |
lOOOtff. a |
IT,. |
b. |
lOOOiTi. b |
||||||
|
125 |
10.5 |
10 |
14.4 |
280 |
51 |
6.8 |
132 |
52 |
X |
|
|
250 |
16.8 |
15 |
11.2 |
200 |
56 |
6.4 |
104 |
62 |
X |
|
|
250 • |
500 |
25.0 |
23 |
9.6 |
160 |
60 |
6.3 |
70 |
90 |
X |
|
1000 |
50.0 |
40 |
8.9 |
125 |
72 |
6.0 |
50 |
120 |
X |
|
|
2000 |
66.6 |
57 |
7.4 |
90 |
82 |
5.4 |
40 |
135 |
X |
|
|
3000 |
50.0 |
62 |
6.9 |
93 |
74 |
4.9 |
39 |
125 |
X |
|
|
125 |
14.7 |
14 |
•22.8 |
430 |
53 |
13.9 |
210 |
66 |
||
|
250 |
21.0 |
21 |
19.5 |
320 |
60 |
12.2 |
150 |
81 |
||
|
500 ' |
500 |
33.3 |
31 |
17.7 |
240 |
74 |
12.3 |
112 |
120 |
|
|
1000 |
50.0 |
50 |
16.3 |
190 |
86 |
12.7 |
90 |
140 |
||
|
2000 |
66.6 |
70 |
15.3 |
160 |
95 |
12.8 |
79 |
150 |
||
|
2500 |
83.0 |
75 |
13.65 |
140 |
96 |
12.4 |
90 |
138 |
0 |
|
|
/ |
125 |
16.7 |
20 |
42.5 |
700 |
61 |
26.4 |
320 |
83 |
Q |
|
250 |
25.0 |
30 |
37.0 |
550 |
68 |
20.9 |
230 |
90 |
0 |
|
|
1000 . |
500 |
33.3 |
40 |
31.5 |
390 |
80 |
21.6 |
190 |
114 |
O |
|
1000 |
50.0 |
53 |
24.6 |
270 |
91 |
17.5 |
158 |
no |
0 |
|
|
^ |
2000 |
66.6 |
74 |
24.7 |
260 |
95 |
22.8 |
165 |
138 |
6 |
|
For Graphic I |
tesults |
secfigu |
ire |
22 |
23 |
INFLUENCE OF THE ROTOR CORE DUCTS. 89
Influence of the Rotor Core Ducts. — All the preceding data is necessarily crude in that no direct account is taken of the propor- tions and number of ventilating ducts. Obviously there should enter into the formulae, terms related to the rate of flow of air through these ducts, and to the extent and nature of the surfaces swept by this air. One of the authors' assistants, Mr. E. Goad, has, at their request, worked out the following method, which involves a quantity which may be designated the "Ventilation Coefficient" of the machine. The method as here described is planned, in the first instance, for the stator armatures.
To Determine the Ventilation Coefficient of a Machine. Let n = the number of ducts.
a = the width of each duct in centimetres. H = the number of slots. t =» minimmn width of tooth in centimetres.
The area for the passage of air through the ducts = nwHt square centimetres. Since the volume of air which passes through the ducts is proportional to the peripheral speed, the volume of air which passes through the ducts per second will be proportional to:
SXnXaXHxt,
where S = the peripheral speed of the rotor in metres per second. Let Dj = the external diameter of the armature in centimetres. D = the air gap diameter in centimetres. Then the area of one side of one armature lamination
= 7 (Dj* — D*) square centimetres. 4
Therefore the total area of duct surface exposed to the air passing through the ducts is equal to
2 X n X j(Z),' - Z)*) - ^^^^ (Z)j» - D») square centimetres.
Assuming that a unit volume of air carries away with it a definite quantity of heat, whatever its velocity, the temperature rise will be inversely porportional to the volume of air passing per second through the ducts. The temperature rise is also inversely propor- tional to the surface exposed to the air. Therefore if we multiply the volume of air per second by the exposed surface we obtain a coefficient to which the temperature rise is inversely proportional.
40 CRITERIA FOR TEMPERATURE RISE.
This coefficient, which may be tenned the ventilation coefficient, combines the two chief components tending to promote ventilation, and is numerically equal to
tL^^ (D7 - Z)») X S X n X a X ff X ^ - 1 (D* -D')xSXaXHxtXn\
As an example of the method of calculating and using the venti- lation coefficient, let us consider the case of a 970 kva. alternator.
The following are the chief dimensions (in centimetres) with which we are concerned in the present investigation.
Rated output — kva 970
Number of phases 3
Number of poles 4
Revolutions per minute 1500
Periodicity — cycles per secrond 50
Rated voltage 450
External diameter of armature laminations (DO 128
Diameter of armature at air gap (D) 75
Gross length of armature core (^gf) 74
Number of ventilating ducts (n) 9
Width of each duct (a) 1.0
Net length of armature core (X?i) 58
Ratio of - 0.78
Number of slots {E) 60
Dimensions of slots 2.3 dia.*
Slot pitch 3.93
Width of tooth (0 1.63
Peripheral speed of rotor in metres per second (*S) 60
Following the method of procedure outlined above, the smallest area for the passage of air through the ventilating ducts is equal to noHi = 9 X 1 X 60 X 1.63 = 880 square centimetres. The periph- eral speed (5) is equal to 60 metres per second, and the total cooling surface provided by the ducts is equal to
t^ {D^ - Z)») = ?^ (128» - 75') = 152,000 square centimetres.
Hence the ventilating coefficient is equal to
880 X 60 X 152,000 = 8 X 10*.
* The armature slots of this machine are of circular section and semi-enolosed.
FIELD CX)ILS. 41
This quantity 8 X 10" is proportional to the amount of heat that is dissipated by the passage of air through the ventilating ducts. The annature losses in this machine are equal to 29,600 watts, and the resulting temperature rise was ascertained to be 53 deg. Cent, on the annature iron, 50 deg. Cent, on the armature winding, and 43 deg. Cent, on the magnet winding. All these are thermometrically determined. The radiating surface of the armature core, calculated according to method D, is equal to 640 square decimetres. The heating coefficient is equal to ^|f^-^ or 46 watts per square deci- metre. This is equivalent to ||, or 0.88 watts per square decimetre per deg. Cent. A stationary piece of iron that is not ventilated will dissipate only about 0.15 watt per square decimetre per deg. Cent.; we must conclude therefore that the remainder constituting 83 per cent of the total heat is dissipated through the direct agency of the drculating air.
In this machine (^:J| X 29,600) or 5000 watts would be dissipated by the action of radiation alone, and the fact that the remaining 24,600 watts are dissipated, for the same temperature rise, is due to the efficacy of the ventilation scheme. There should therefore be some direct connection between the amount of this extra heat and the ventilating coefficient 8 X 10*.
For a first approximation, it may be said that a ventilating co- efficient of one million would correspond to a dissipation of about ^%Vf ^r, say, 3 watts. A large number of actual machines should be analysed before placing much reliance on this figure.
Field Coils. — For an ordinary field coil, when stationary, and in the presence of a stationary armature, the thermometrically deter- mined specific temperature rise is from 4 to 5 deg. Cent.* per watt per square decimetre taken on the basis of the external exposed cylindrical surface of the coil.
If the coil is in the presence of a rotating armature, this figure may,
♦ Goldschmidt (Jaum» I. E, E, vol. 34, p. 660) gives 15 deg. Cent, per watt per square decimetre, but this is based on the whole surface of the coil (internal and external) for medium sized semi-enclosed machines, and the rise is measured by re- sistanoe increase, which is often some 50 to 70 per cent greater than that observed by the thermometer. Dr. S. P. Thompson, in the discussion on this paper, gave a figure of 3.5 deg. Cent, due to Esson, 4.2 deg. Cent, due to the OerUkon Co., and 7.1 deg. Gent, due to Neu and Levine, the latter being by resistance measurement, and all being reckoned on the external cylindrical surface of the coil. See also Rayner, *' Report on Temperature Measurements at the National Physical Labora- tory," Jaum, /. E. £., vol. 34, p. 613.
42
CRITERIA FOR TEMPERATURE RISE.
for peripheral speeds above 17 metres per second, be reduced to the extent of some 25 per cent to 50 per cent, the smaller figures applying to cases of small winding depth and well ventilated coils and high speeds.
The general magnitude of the effect of the peripheral speed of the armature on the temperature rise of field coils is very clearly brought
Thermal Test of Field Spool shown in Fig. >•
Duration of Test «8 hours
Watts dissipated in Spool throughout Test » 48
Peripheral Speed of Armature
0 Meters per Second
10 Meters per Second
I
t
H
11
MMv^
I,
1-
M«aii
RmtU
I
riM of T>mp- by ^RwUtmfto = 47 ° of Maximum 'to Mau^ jTl3~f '
rt
J_L
n;
li 10 S Position of Layers
|
1 |
||||||||||||
|
f' |
rM |
., |
||||||||||
|
s" |
,/ |
BP |
N |
|||||||||
|
S» |
a^ |
r* |
^ |
L |
" |
- |
||||||
|
L |
||||||||||||
|
\ |
||||||||||||
|
a** |
M |
â– 4 |
ri..rf|1Wp, |
>V |
-«t'\ |
|||||||
|
Sia |
Iklk |
oMUulBaB to It |
-i4-u 1 1 |
|||||||||
|
1 |
Id |
i |
4i |
T |
3ot |
Potition of Layers
FiQ. 24. — Temperature tests of field spools. (Reproduced by permission from the Joum, I. E, E., vol. 38, p. 421).
out by the test results for a field coil of a certain four pole contmuous current machine. These results are plotted in Fig. 24. The coil was wound with 38 layers of No. 21 B.W.G. ; connecting leads were brought out every two layers, so that the resistance of 19 sections of the coil could be independently determined by means of their rise in resistance. Two separate tests were made, one with the
FIELD COILS. 48
armature stationary, and the other with the armature revolving at a peripheral speed of 10 metres per second. We see from Fig. 24 that when the armature was at rest, the layer next to the magnet core and the outside layer had practically the same temperature, but that when the armature was running at a peripheral speed of 10 metres per second, the outer layer had a much lower temperature than the layer next the magnet core.
In both tests, however, it should be noted that the temperature at the middle of the winding is considerably higher than the tempera- ture of either the internal or the external surfaces.
WTien the armature was stationary the ratio of the maximum temperature rise to the mean temperature. rise was 1.13, and when the armature was rotating, this ratio was about the same figure, being actually 1.15.
But another relation that is very striking, is that of the maximum temperature to the temperature at the external surface. This works out at 1.4 and 1.95 respectively, for the teste when the armature was stationary and revolving. The fact that the internal temperature of a coil may rise to a value twice as great as that which would be indicated by a thermometer laid on the external surface, ought to impress engineers with the importance of determining all rises of temperature of coils by means of the alteration in resistance. This is the more important in view of the importance of avoiding liability to deterioration of the insulation on the field conductors.
Some teste made by Dettmar in 1900 on the effect of temperature on the cotton coverings of copper wires showed that, in the course of time, a temperature of less than 100 deg. Cent, caused decided deterio- ration of the cotton coverings. The more recent teste of the National Physical Laboratory of Great Britain ^ on large numbers of insulating materials, showed that in the case of all these materials, deterioration ultimately set in at a temperature of not over 125 deg. Cent., and in most of these materials the temperature at which deterioration occurred was considerably below 125 deg. Cent.
These curves and values for the distribution of temperature in an ordinary field coil emphasize the importance of ventilating the field spools by subdividing them into two or more parte with concentric air channels between them. Field coils for modem machinery should be constructed in this manner, which ensures a more uni- * See Joum. L E. E., vol. 34, p. 613.
44 CRITERIA FOR TEMPERATURE RISE.
form distribution of temperature throughout the depth of the coil, and also a considerably lower average temperature for a given ex- penditure of copper or a smaller weight of copper for a given mean temperature rise.
In the case of turbo-alternators, the field windings usually form part of the rotating system and the methods of winding and fixing the coils depart considerably from the ordinary field coil construc- tion. Among the various constructions employed for turbo-alternator fields (which are described in a subsequent chapter), the types vary from the ordinary , compact field coil, through variations and develop- ments from this, to a thoroughly distributed field winding in slots similar to those on an armature, which is employed with the smooth cylindrical type of rotating field.
It is necessary to consider each case or type individually, with due regard to the velocity of the moving windings, the distribution, and conductivity of the coil and of the material in contact therewith, and also the ventilating provisions.
For an ordinary field coil rotating at a mean peripheral speed of about 40 metres per second, the specific temperature rise at the centre of the body of the coil, may be from 15 to 30 deg. Cent.
In turbo-alternators, the number of poles is generally few, being determined by the frequency and speed, from 2 to 8 being practically the limits. With such fields carried out with the definite pole con- struction, there is plenty of space between the poles and free access to the cooling air. When the field winding is carried out in slots on a cylindrical core it may be treated as equivalent to a wound armature from the heating standpoint although it is not generally so well ventilated. In such machines it is instructive to calculate the heat- ing coefficient mentioned on p. 36 of this chapter, viz. the total stator and rotor losses per square decimetre of air gap surface.
CHAPTER IV.
MATERIALS FOR CONSTRUCTION OF HIGH SPEED ELECTRIC
MACHINES.
Armature Core Plates. Oore Loss. — A number of groups of designs of alternating and continuous current dynamos are analysed in later chapters of this treatise. These designs show conclusively that one of the most striking characteristics of high speed dynamo electric machines of large rated outputs is the very large percentage of the total internal loss constituted by the core loss. In the case of turbo-alternators the core loss frequently amounts to two thirds and more of the total loss, and in many cases it cannot be materially reduced. In slow speed alternators of the same rated capacity, on the contrary, the core loss is more of the order of 50 per cent or less of the total internal loss.
During the last two years there have been placed on the market some grades of sheet iron which, in practice, permit of reducing the core loss for a given design to some 60 per cent to 70 per cent of the amount when the more customary grades of sheet iron are em- ployed. Unfortunately the price of the low loss material is at present from two to three times that of the material customarily employed for armature cores. In view, however, of the reduction of loss, and consequently also of heating, and of the improved efficiency at all loads, the low loss sheets are to be recommended for the armatures of high speed alternating current machinery in spite of the high price.
The use of this iron may often also assist the designer of high speed contirmous current machinery, for the question of heating has to be handled with much greater care in the design of high speed than in the design of low speed continuous current machines. As to the cost of the sheets, this, while high, will not so greatly affect the total cost of the design of these machines as might at first be thought would be the case, for it is a characteristic of high speed continuous current dynamos that the cost of the electromagnetic material is generally a somewhat less percentage of the Total Works
45
46
MATERIALS FOR (X)NSTRUCnON.
AnuUar* Lamlnatioaia of Ordiaaxy
Ond« SIMM Iron at iOO doUan per Tod.
Vlff.tt
|
ng |
tt |
|||||||
|
^^ |
||||||||
|
40 |
r-1 |
^ |
||||||
|
«N |
||||||||
500 iOOO 1500
Flff.M
1°
;fe:
600 1000 1500
FIff.Sl
|
av |
||||||||
|
fO |
||||||||
|
10 |
^ |
1:1. |
^ |
E2^ |
^ |
if^r |
F= |
|
|
•0 |
^ |
|||||||
|
<x |
^Ar |
matt |
" ^ |
La. |
aina |
tiooa |
||
|
_,^ |
_! |
-Z |
Anmfcnra Laminatioaa of a Qpeolal <*Lov L(Ma" Shastlraa at ftO doUara per Ton.
JV.»
80| r
M
M
•oA,
Tig, 90
500 1000 UOO
|
n,.M |
||||||||
|
> |
||||||||
|
40 |
^ |
,^ |
& |
^ |
n |
S^ |
i^^ |
ij- |
|
^ |
^ |
Acn |
«tD |
• I |
amf |
wtl |
mi- |
|
500 IOOO 1500
AbaoiMaa denote Rated Speed la SevolntiotuperMlBota.
Figs. 25-32. — Curves showing effect of grade of armature laminations, on cost and quality of continuous current generators for 1000 kw., 1000 volts, and various rated speeds.
ARMATURE CORE PLATES.
47
i.20r
Cost than is the case with the low speed machinery. Thus quite a considerable increase in the outlay for core plates will in many cases only entail a fairly small percentage increase in the Total Works Cost. This is clear from the curves in Figs. 25 and 26 relating to designs for 1000 kw., 1000 volt continuous current dynamos for various speeds, and in which respectively the customary and the low-loss grades of core plates are employed.
We see from the curves that the Total Works Cost of the designs is only increased by some 5 per cent to 10 per cent by the substitution of the superior grade core plates. The consequent improvement in the quality of the design is generally somewhat greater the higher
the rated speed. This is seen from the curves in Figs. 27 and 28, in which the core loss is plotted as a percentage of the total internal loss. Thus the higher the rated speed the greater is the desirability of employing the low loss iron, although in the case of continuous current machines the gain is by no means great. Figs. 29 and 30 show the relative heating coeffi- cients for the armatures in the two cases and Figs. 31 and 32 the costs of the armature laminations and of the total effective material as a per- Fig. 33 shows the ratio between
^
I
o 01.05
&
1.00"
|
^^ — — — < |
|
600 1000 1500
RoEtod 8|ieed In Revs, per Mbnite
Fig. 33.— Ratio of Total Works Cost of 1000 kw. continuous current dynamos with special and ordinary grade laminations.
centage of the Total Works Cost.
the Total Works Cost in the two cases.
In high speed alternators, the core loss assumes much greater pro- portions than in continuous current macliines. This is largely due to the armature being external to the rotor, and of the great radial depth of the laminations as a consequence of which the weight of laminations for given air gap dimensions, D and Xg, is much greater than in the case of an internal armature.
Figs. 34-42 show in detail the manner in which the cost, losses, and heating for a group of 3000 kva. 25 cycle alternators at different rated speeds are affected by the use of the special low loss steel laminations. Further details of these machines are given in Chapter IX.
48
MATERIALS FOR CONSTRUCTION.
Is
li
I
II
2^
A.-Armaiure Grade ShM%
loot of Ordtnjuy BtMi at 9100 per Ton
Flg.M
|
FIS.S8 |
Kg. |
SO |
||||||||||||||||
|
140 |
180 |
|||||||||||||||||
|
W 40 |
||||||||||||||||||
|
^-o |
â– HI |
|||||||||||||||||
|
O |
xr^ |
5**" |
â– ^ |
40 |
««•<: |
^ |
-- |
.^ |
||||||||||
|
O |
-cy- |
Jir' |
||||||||||||||||
|
« |
w |
4fl |
M) |
0( |
N) |
« |
10 |
S( |
W |
4( |
» |
« |
M) |
80 |
|
m |
I1g.40 |
|||||||
|
«0 |
||||||||
|
40 |
SS |
!tiv-, |
''£. |
|||||
|
"S?' |
terial |
|||||||
|
20 |
C- |
y |
r |
|||||
|
■«^ |
f^ |
_La |
»inMio2 |
lo |
||||
|
o* |
^ |
-J |
â– â– |
400 800 WO
B .- Anaatant Laninattona of Special Grade Low Loea Sheet U»A a» t8B0 perToB
Fig. 95
too 400 600 »0
|
ncM |
nc.s7 |
~ |
||||||||||||||||
|
80 |
0 |
80 |
||||||||||||||||
|
/>- |
-o |
-o |
||||||||||||||||
|
J |
^' |
40 |
/^ |
^ |
^^ |
|||||||||||||
|
— ^ |
/ |
|||||||||||||||||
|
40 |
||||||||||||||||||
|
80 |
||||||||||||||||||
|
_J |
||||||||||||||||||
|
K |
W |
4( |
K) |
« |
w |
« |
« |
N) |
4( |
w |
800 |
800 |
too 400 000
Abeciaeae denote Bated Speed in Rerolntions per JCtnate.
Figs. 34-41. — Curves showing effect of grade of armature laminations on cost and quality of 3000 kva. alternators for various rated speeds.
ARMATURE CORE PLATES.
49
|
ija) |
"~~~" |
^ |
=^ |
|||||
|
^1 15 |
y |
|||||||
|
1 |
/' |
|||||||
|
i ^1 10 |
/ |
|||||||
|
/ |
||||||||
|
2 1-05 |
"^ |
|||||||
|
1 1.00 |
||||||||
_ ^ 200 400 600 800
Rated Speed in Beva. per Minute
Fig. 42. — Ratio of Total Works Cost of 3000 kva. alternating current generator with special and ordinary grade armature laminations.
In these figures the various quantities are plotted against the rated speed of the machine.
Fig. 34 sho\vs the Total Works Cost of the machine, the cost of the effective material and the cost of the armature laminations
for ordinary grade stampings. In Fig. 35 are shown similar curves for the same machines when built with the low, loss sheet steel stampmgs. Figs. 36 and 37 give the iron loss as a percentage of the total electrical losses. Figs. 38 and 39 show the armature heating coefficient. In Figs. 40 and 41 are plotted the costs of the eflfective material, and of the armature laminations as a percent- age of the Total Works Cost of the machme. Fig. 42 shows the ratio of the estimated Total Works Costs of a machine with Jow loss iron to the Total Works Cost of a machine built with stampings of ordinary grade iron.
All the above curves are based on the assumption that the same weight of material is used in both cases; the improvements effected by employment of special low loss steel, lying in the direction of the quality of the design and not of the cost.
In general it may be seen from the curves that in the case of alternators, the higher the speed the greater is the percentage core loss, and the greater also is the percentage cost of the armature laminations. The result is that though it is particularly desirable to use the low loss steel at the high speeds yet, at the same time, the extra cost involved by the use of this expensive material becomes considerably greater.
Thus in Fig. 42 the ratio of the Total Works Cost for the two cases rises to as high a value as 1.2, at the highest speed. This is due to the large proportion of the total weight of the machine which the armature laminations constitute in the case of alternators for high speeds and with few poles.
A similar set of curves are shown in Figs. 43-51 deduced for the 400 kva. 50 cycle alternators described in Chapter VIII.
60 MATERIALS FOR CONSTRUCTION.
The same quantities are plotted in these figures. The range of speed is much greater, and the ratio of Total Works Costs rises to the value of nearly 1.3, that is, the cost of the machine is increased by nearly 30 per cent by the employment of the special grade iron for the armature laminations. This high figure is here due to the fact that it relates to a 2-pole design in which the armature iron consti- tutes a very great percentage of the total weight.
It is, nevertheless, especially in 2-pole designs that the use of a low loss iron is most important, as such machines are at best of but poor quality and in such cases the improvement in quality is justi- fied even at the expense of considerable increase in the Total Works Cost.
We see then from the above that the employment of special grade steel for the armature laminations of alternators is, so far as relates to expense, less extravagant, the slower the speed, but that it is more desirable, or even indispensable, so far as relates to the quality of the results, the higher the speed.
The reason for the considerable increase in the Total Works Cost which the use of special grade steel effects in the case of alternators is simply due to its high price. When the use of such material has become more common, the price will be brought more into line with that of the present ordinary grades of steel, and its use for high speed alternators will become general.
In the designs set forth in this treatise we have based our esti- mates on the use of the customary grades of core plates. In so far as the low loss core plates are employed instead, the designs will be improved. But the designs will even then be none too good, for in the design of extra high speed electrical machinery, there is no option but to sail closer to the wind than in designing machines for less extreme speeds, so that the increased margin afforded by the use of this low core loss material is very welcome.
The "figure of loss" is the most useful term in which to express the quality of sheets as regards core loss. This term is defined by the Verband Deutscher Elektrotechniker as the total iron loss in watts per kilogram, as measured by means of a wattmeter on a sample made up of at least four different plates. The sample shall weigh at least 10 kg. and the loss in watts per kilogram shall be determined at a temperature of about 30 deg. Cent, for a maximum induction of 10 kilolines per square centimetre and a periodicity of
ARMATURE CORE PLATES.
61
I I
B
I
I*.
I
Anaatore Lunluittona of Ordimurjr
gnde.ah«et itMl ariOO doOcn
per Ton.
F{ff.iS
VitM
60 ^
M
<f
to
o
1000 am 8000
W(g.i7
uo
FigM
|
(> |
|
|
JTo il-E« |
taL««*M- |
|
io |
|
|
\^ |
t^lMtfcwj. |
|
pv^ |
• |
1000 1000 8000
Armatnre LamiiiAtloiui oft Special
*<low lo«" glwet atMl at 850 dolUn
per Ton.
RgM.
^^^5
1000 8000 9000
11g.4A
|
M |
A |
Y' |
-^ |
â– ^ |
{ |
|||
|
y |
/ |
|||||||
|
/ |
/ |
|||||||
|
T |
||||||||
|
0 |
||||||||
1000 8000 8000
Flg.l8
«w — -.
80
40
fig.fiO
Absoissae denote Rated Speed In Revolutions per Minute.
Fiaa 43-50. — Curves showing effect of grade of armature laminations on cost and quality of 400 kva. alternators for various rated speeds. (The points ® relate to the rotating armature designs of column D of specification on pp, 133-137.)
62
MATERIALS FOR COxXSTRUCTION.
1.2
1
o H
o
o 1.1
1.0
1000 sooo aooo
Rated Speed in Revs, per Minute
Fig. 51. — Ratio of Total Works Cost of 400 kva. alternating current gen- erator with special and ordinary grade armature laminations. (Point A relates to a rotating armature design.)
50 complete cycles per second. As normal thicknesses shall be
taken 0.3 mm. and 0.5 mm., deviations from the normal thick- ness shall not exceed 10 per cent. The measurements shall be made I ^_3l I I I I I I I I ^^ ^ magnetic circuit composed ex- clusively of iron or steel, of the quality to be tested, and built in accordance with the conditions set forth below. As specific weight of the iron, 7.77 shall be taken in all cases where more precise data is not available. The iron loss shall be measured by the Epstein method in accordance with which the mag- netic circuit is constructed of four cores, each having a length of 500 mm., a breadth of 30 mm., and a weight of at least 2.5 kg., thus
making a total weight of at least 10 kgs. for the four cores. The
individual sheets are insulated from
one another by Japanese paper in such
a manner that they are at no point in
contact with one another. The four
cores constitute a rectangular circuit,
as shown in Fig. 52, and are secured
in ix)sition by wooden clamps at the
four corners. At the butt joints they
are separated from one another by
press-spahn of 0.15 mm. thickness.
In building together the circuit, care
must be taken that the cores fit. well
with one another. As indications
that this is the case may be men- tioned the deadening of the noise
when magnetised, and the obtaining
of a minimum deflection on the ammeter in the magnetising
circuit. The magnetising coils are constructed on bobbins, with internal
dimensions of 38 nmi. X 38 mm. and a length of 435 nun. Each of
Fig. 52.
Epstein sheet iron tester.
ARMATURE CORE PLATES. 68
the four bobbins contains 150 turns of copper of a cross section of 14 sq. mm. It is suggested in the rules that the winding may con- veniently consist of two round wires each of 3.5 mm. diameter and wound in parallel. Originally it was thought preferable to build up these Epstein samples to a weight of 20 kgs., but this weight has ulti- mately been reduced to 10 kgs., which is now standard. A photograph of a wound sample is shown in Fig. 53.
Fig. 53. — Wound sample of Epstein iron tester.
The most customary standard size in which sheet steel for armatures is delivered, is in plates measuring 1 metre X 2 metres. Plates of larger dimensions are generally only supplied at higher prices, and a longer time is required for providing them. It has thus become fairly general practice when armature cores of diameters in excess of 1000 nmi. are required, to build them up from segments whose max- imum dimensions do not exceed the dimensions of sheets of this standard size.
It is therefore customary to consider 990 mm. as the largest diam- eter of armature in which complete disks shall be employed.
The "figure of loss" for ordinary sheet iron ranges from 1.5 to 4 watts per kg. From the standard conditions of density (10 kilolines per square centimetre) and frequency (50 cycles per second) at which (F) the "figure of loss" is expressed, the loss in watts per kilogram at any other density (B) and frequency (N) may be approximately esti- mated as follows:
54
MATERIALS FOR CONSTRUCTION.
Let L equal the loss for any other than the normal values of B and N (i.e., at values other than -B = 10 and N = 50), for an iron whose
Q
figure of loss is equal to F. Then L
X N X F ^ 0.002
lOX 50
X C X N X F, where C is a factor depending on the density B. Let- ting K - 0.002 X C, we have L ^ K X N X F. Values for K for any density, B, may be taken from Table 8.
TABLE 8.
|
Values op iC in the |
. Formula L ^ K X N X F, pob Obtaining the Core Loss |
||
|
IN Watts Per Kilogram. |
|||
|
Deneityln Kilolines per Square Centi- |
Multiplier to Obtain the Watts per kg. from Figure of T<088 and |
Density in Kilolines per Square Centi- metre. |
Multiplier to Obtain the Watts per kg. from Figure of Loss and |
|
me re. |
Periodicity. |
Periodicity. |
|
|
B |
K |
B |
X |
|
4 |
0.0046 |
13 |
0.0296 |
|
5 |
0.0066 |
14 |
0.0336 |
|
6 |
0.0088 |
15 |
0.0380 |
|
7 |
0.0114 |
16 |
0.043 |
|
8 |
0.0136 |
18 |
0.050 |
|
9 |
0.0168 |
20 |
0.060 |
|
10 |
0.0200 |
22 |
0.070 |
|
11 |
0.0236 |
24 |
0.080 |
|
12 |
0.0268 |
The watts per kilogram for customary material for a thickness of some 0.4 to 0.5 millimetre and at a periodicity of 50 cycles per second, is plotted as a function of the density in curve A of Fig. 54. Curve B of this same figure corresix)nds to one of the low loss materials. The figures of loss for these two materials are indicated in the curves, and in these tests were respectively 3.3 and 1.6.
\ATien the laminations are built up together, as in a finished machine, the actual core loss per kilogram is considerably greater than would correspond to the results obtained on samples as plotted in Figs. 54 and 55, from tests by the Epstein method or its equivalent.
Measurements of the core loss of actual machines do not show so . great a gain from the use of low loss iron as are indicated by meas- urements on samples. It is found that the low loss iron may be relied upon to reduce the core loss in the actual machines to some 60 per cent to 70 per cent of the loss with the customary grades of core plates.
This lower degree of superiority may be ascribed largely to the eddy current losses due to filing the slots of the assembled armature and to eddy current losses in various solid parts as also in the armature
ARMATURE CORE PLATES.
65
conductors. These additional (or "parasitic") losses will not be decreased through the use of the better quality of core plates, and hence they tend to mask the advantage to be gained by employing it. The residual gain is, however, ample justification for employing the low loss material in extra high speed alternators, notwithstand- ing its great cost, as the difficulties associated with such designs justify resorting to any sound expedient not leading to prohibitive Total Works Cost.
|
/ |
|||||||||||||||
|
7 |
/ |
||||||||||||||
|
/ |
|||||||||||||||
|
6 |
/ |
||||||||||||||
|
ff K |
/ |
||||||||||||||
|
/ |
f |
||||||||||||||
|
i |
/ |
||||||||||||||
|
t |
/ |
/ |
|||||||||||||
|
1. |
/ |
iBll |
ore |
of |
y |
r |
|||||||||
|
^ |
/ |
r |
/ |
7 |
|||||||||||
|
A |
y |
/ |
/ |
/ |
|||||||||||
|
y |
/ |
A |
n?j |
Bcnci |
of |
||||||||||
|
J |
X |
^ |
X |
r^!^ |
1. |
||||||||||
|
A |
X' |
,^ |
^ |
||||||||||||
|
B |
|||||||||||||||
|
i |
t |
i |
Den |
w |
Ls |
aioi |
nes |
1 perl |
0 3g.( |
^^ |
2 |
1 |
4 |
Fig. 54. — Curves showing the eneigy losses in armature stampings (thickness 0.4 to 0.5 mm.)' For periodicity of 50 cycles and for different densities.
The core loss varies with the thickness of the plates, and the curves in Fig. 55 (taken from test results supplied by a large dealer in core plates) give approximate data of the extent of the influence of the thickness. The term "Stalloy" appended to the lower curve is merely a trade name applied to a particular brand of low loss core plates. Other dealers in armature core plates supply brands with substantially identical properties, and there are beginning to be heard reports of even better results.
The eddy current loss depends on the specific resistance of the
66
MATERIALS FOR CONSTRUCTION.
iron, a high resistance iron showing a lower eddy current loss. This property has been utilized to produce the "low loss" sheet steels which have appeared during the last year or two. The properties of such steel alloys embody a high specific resistance — up to 45 microhms per cubic centimetre and more, with very slight inferiority in mag- netic permeability. The core loss for such an alloy is plotted in the lower curve of Fig. 54, from which it will be seen that the loss as measured on samples for this alloy, is some 50 per cent of that obtained with ordinary iron.
|
5 |
|||||||||||||
|
^ |
y |
||||||||||||
|
Ki |
-vi |
r |
r— |
||||||||||
|
5 |
X |
y |
|||||||||||
|
i |
|||||||||||||
|
I ^9 |
— — "• |
^"^^ |
|||||||||||
|
— |
jt. |
ftoV |
— - |
' |
|||||||||
|
o ' |
-.— — ' |
tl^ — |
|||||||||||
|
ll |
|||||||||||||
0.1
0.2 0.3 0.4 0.5
Thicknen of Stampings In mm.
0.0
0.7
Fig. 55. — Curves showing the effect of the thickness of the stamping? on the figure of loss (watts per kg. at a periodicity of 50, and a density of 10,000) for stampings by Messrs. Sankey of Belston, England.
If we produce the cui-ves in Fig. 55 until they cut the vertical axis, as indicated by the dotted lines, we obtain a theoretical value for the figure of loss when the laminations are infinitely thin; in such a case, however, the electrical resistance to the eddy currents would be infinitely great, and the energy wasted in such currents would be infinitesimal. Hence we can obtain some idea of the amount of the hysteresis component of the losses; the figure of loss for the "Lohys" grade is about 2.45 watts per kg. at the limit, and on the other hand the '*Stalloy " brand has a figure of loss of only about 1.5 watts per kg. Thus not only do these low loss steels have greatly reduced eddy currents due to their high specific resistance, but the hysteresis loss is also materially decreased.
PERMEABILITY OF MAGNETIC MATERIALS.
Such a low loss steel may be utilized in high speed machines by retainmg the same weight of iron, and thus reducing th loss and the heating, or by retainmg the same core loss and heatmg and thus reducing the weight. If the design is sufficiently good from the thermal standpomt, the latter plan may be advisable, but it would depend on the relative cost in each case. The price of ordinary grade sheets ready for stamping is at present from $70 to $100 per ton, and for the low loss iron from $180 to $220 per ton.
In the case of a 4*pole 650 kva. alternator deagned in Chapter Vn, the magnetic cross section in the armature is 1540 square centi- metres and the weight of armature stampings is 2.34 tons. At a density of 8,000 lines per square centimetre and a frequency of 50 cycles, the loss per ton is 7 kw. and the total core loss 16.4 kw. As the heating coefficient of this machine is not excessive (80 watts per square decimetre of air gap surface) it is not necessary to decrease the core loss, and the armature laminations might be replaced by low loss iron at a density of 12 kilolines, which would require a magnetic cross section of only 1030 square centimetres. The weight would then be 1.55 tons and the loss per ton 10.5 kw., giving a total loss of 16.3 kw., which is the same as before. With the low loss iron the external diameter of the armature stampings would be reduced from 128 to 115 centimetres, and consequently a smaller frame could be employed with somewhat less material. For these two cases, how- ever, the cost of the stampings will be some $210 and $350 respec- tively, so that the outlay for core plates is some $140 greater.
In the case of bi-polar alternators, we have seen that the heating coefficient is rather high, and very efficient ventilation is called for. The bulk of the armature losses is comprised in the iron loss, which reaches some 90 per cent of the total armature loss. Advantage may in these cases be taken of a low loss iron by substituting stamp- ings of the same magnetic density and the same total weight, which would give a diminished core loss and heating. As a case in point, let us consider the 400 kva. 2-pole alternator, for which data is given in Chapter VIII. The heating coefficient for this machine is 152 watts per square decimetre. A comparison between the design as it stands and as it would be with special iron is set forth in Table 9 on page 58.
Permeability of Magnetic Materials. — For the designer, the most convenient method of showing the relative permeability of the various magnetic materials, is by means of saturation curves showing
/
/
/
/ 68
MATERIALS FOR CONSTRUCTION.
the excitation required for unit length of the material at different induction densities. Saturation curves for cast iron, cast steel, and armature laminations are shown in Fig. 56. While it is quite possible to obtain materials having a somewhat higher permeability than is indicated by these curves, there is always an element of uncertainty, owing to variations in the composition of the material. It is there- fore not expedient to base designs on the higher values obtainable,
TABLE 9.
Comparison op Costs op Armature op 400 Kva. 2-Pole Alternators.
• Magnetic cross section — sq. cms
Flux density — kilolines per sq. cm
Frequency
Kilowatts per ton
Weight — tons
Totw core loss — kilowatts
Total armature losses (iron and copper) . . Heating coefficient — watts per sq. dm. of irD^
Full load efficiency (cos ^ « 1 )
(Dost of stampings
|
Ordinary Iron. |
Special Iron. |
|
2050 |
2050 |
|
8.2 |
8.2 |
|
50 |
50 |
|
7.4 |
4.9 |
|
2.32 |
2.32 |
|
17.2 |
11.5 |
|
19.96 |
14.26 |
|
152 |
108 |
|
94.5% |
95.5% |
|
$210 |
$500 |
unless the material is carefully tested before use and the poorer samples ruthlessly rejected. The curves in Fig. 56, however, have been carefully prepared with a view to ensuring conservative results.
Materials for Rotors. — Rotating armatures for continuous current machines are of laminated construction and there is no particular difficulty in obtaining homogeneity.
The stresses in a rotating armature for a continuous current machine are not generally excessive, as continuous current machines do not usually run into large sizes. Further, the windings are thoroughly distributed, which relieves the system of the stresses due to large concentrated masses of copper. With rotating fields the stresses are generally of greater magnitude, being in some cases of such values that the unavoidable working stress does not permit of a safety factor of much more than 2, referred to the elastic limit.
In view of this, the material must, regardless of cost, be of the best quality procurable as regards strength and homogeneity. Hence for all high speed machines, except perhaps for those of small size, castings should generally be avoided. The material for rotating fields
MATERIALS FOR ROTORS.
may be either steel forgings, pressed steel, or sheet steel stafl according to the type of construction employed. ,
The safety factor obtained depends on the size and speed of the machine. Were it practicable to employ extra high strength steels, such as are used in rotating disks for steam turbines, considerably higher safety factors could be allowed. Such high strength steels are obtained by the addition of suitable small percentages of foreign materials — such as carbon, nickel, manganese, and chromium.
10 8O3O4O506O7ObO90l0O
Ampere Tarns per Centimeter
Fio. 56. — Saturation curve used in designing the magnetic circuit of electric
machines.
These substances, when used in the proportions required for impart- ing sidtable mechanical properties, unfortimately impair the per- meability and magnetic properties of the steel.
It will be of interest to give a few notes on materials of great mechanical strength. Stodola in "Die Dampfturbinen" quotes figures supplied by the Krupp Works at Essen. For turbine disks, a nickel steel is recommended of some 9 tons per square centimetre breaking strength with 12 per cent elongation, and an elastic limit of 6.5 tons per square centimetre. Nickel steel of greater strength
60
MATERIALS FOR CONSTRUCTION.
/ (though with less percentage elongation), is available, and with
forged pieces of small dimensions a breaking strength of over 20 tons per square centimetre, and an elastic limit of over 6 tons per square centimetre can be obtained. An average of 6 tests showed a break- ing strength of 18.1 tons per square centimetre, and an elastic limit of 13.2 tons per square centimetre with a mean elongation of 6 per cent. Messrs. Krupp's opinion is that where there is no reversal of the direction of the stress, it is permissible to work up to one third of the elastic limit, and ultimately perhaps even higher. Doctor Riedler and Professor Stumpf consider that from 2 to 2J as a safety factor is admissible.
With forgings of ordinary steel, such as is permissible for rotating fields, the average breaking stress in tension is about 4.7 tons per square centimetre, and the elastic limit is 3.5 tons per square centi- metre as set forth in Table 11 on pages 62 and 63. Hence allowing a safety factor of 2.5 on the elastic limit, a value of 1.4 tons per square centimetre for working stress in tension is obtained.
The peripheral stress in a rotating cylinder is given by the expres- sion . _ dv^
' "" 98,100'
Where / is the peripheral stress in tons per square centimetre, due to centrifugal force, d is the density of the material in grams per cubic centimetre, and v is the peripheral speed in metres per second.
TABLE 10.
The Limitinq Peripheral Speed for Materials of Different Strength.
Material.
Wrought iron . . .
Cast iron
Cast steel .... Forged steel. . . . Cast copper . . . Rolled copper . . . Hatd drawn copper Cast brass .... Gun metal .... Phosphor bronze . . Manganese bronze . Delta metal (cajst) . Cast aluminium . . Wood — Pine . . .
Peripheral Speed in Metres per Second for Peripneral Streseea £qual to
Ultimate Strength. Elastic limit.
220 130 220 240 130 155 210 140 159 210 230 240 220 260 to 370
160
00
150
170
'so
75 125
i26
MATERIALS FOR ROTORS.
61
This approximates to / = O.OOOOSv' for materials of the same specific gravity as steel and iron.
Hence for a stress of 1 ton per square centimetre, the correspond- ing peripheral speed will be about 110 metres per second. A periph- eral speed of 100 metres per second is rarely exceeded in alternator designs, and considerably lower speeds are highly desirable.
From this relation we are able to calculate the speed corresponding to the breaking stress and the elastic limit. These limiting speeds for various materials are set forth in Table 10, the ultimate strength and elastic limit being taken from Table 11.
The windings, whether on rotating armatures or fields, are generally 80 disposed as to minimise the stress on the copper as far as prac- ticable. The centrifugal forces of windings distributed in slots are taken up by slot wedges of bronze or gun metal„ or, if the stresses are low, oak or maple wood. The end covers for armature windings and also for field windings of fields of the smooth cylindrical type, may be of phosphor bronze, manganese bronze, or nickel steel.
Table 11 gives for a number of materials, including all those re- ferred to above, data for the average working and breaking stresses and for the elastic limits.
There has been a general impression that the low loss sheet steel, of which considerable data has been given in this chapter, is rather inferior as r^ards mechanical strength, and that this inferiority might stand in the way of its use in rotors where the highest obtain- able mechanical strength is of prime importance. While this work has been going through the press we have had pointed out to us that, at any rate in the case of certain of these new low loss sheet steels, this is not the case, and there have been supplied to us the following comparative figures for physical tests of **Stalloy" and of ordinary soft steel.
|
Stalloy. |
Ordinary Armature Quality. |
|
|
Maximum load in tons per sc). in RUiitip limit in tons t>er so. in |
32 26 10% |
18 10 |
|
E^lonoffttion on 4 in |
18^ |
|
|
10/f> |
Messrs. Joseph Sankey & Sons, the manufacturers of stalloy, also point out that, realizing that low hysteresis is not of much conse-
62 MATERIALS FOR CONSTRUCTION.
quence in the rotor, they have been making a special quality of steel purely with respect of mechanical strength, for which the figures are approximately as follows:
Maximum load in tons per s(]. in 25
Elastic limit in tons per sq. in 17
Elongation on 4 in 10%
The manufacturers do not guarantee the magnetic quality of this latter material. With stalloy, however, it would appear from the figures that both high meclumical strength and good magnetic qual- ity are secured.
MATERIALS FOR ROTORS.
63
k
u
JJJi
Sill
d d
o 00 . CO o o . . .CO 00 ^ ; ci fM 00 : : d
f-H C* 1-I 1-I 1-I
OQ
1
I
ij
CO CO • ^
d Sd d
CO "*
• ddo
• 1-I i-i«5
i
I
CO ^ CO ^' 1-4 csi "*' 1-4 1-< -^ -^ c^ ^ CO o d d »o f-i ^ ^d
^ ^ o
U
1-it^^ coN'*'*eo'^«o^^co3 5 00 -S^
4 .a
t^CVIXwcOOO AOCO Ab«C0C0h«O 00 C» t>- S
t^t^t^^t^lodododooodododxc^it^od t^od d d
Id 55
X C» C4 CO 1-H h« fM
icococo^cocococooc^co ddddddddddddddd
gs m
CO
dd
8
o
64
MATERULS FOR CONSTRUCTION.
I I
go.
2.3
â– .
S o*
00 1-< b* a CO N CO 1-I .«5«o . . ; . . . .o dodddddd do d
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8S^5SSfeS :f:S : : : : : 3^%
^ 1-H fH ^ oo o»-i 'oo ooo
d
epQ Q CO +»»C
00 0& rH o ?5 00 eo o6 ;OOs ; ; ; ; i'^23'^ d d 00 d c^ 1-4 •**< iH 'lowi d .d
o
8gSSS5S3SS§^f:S$8 : : : :i|§
d
di-4o6do<c^ioc^csi>ciocoi-< • • • -o-^o
ga? ... .8 :;::;:: : ; ; ;*
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oo.»o...oeo.o
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wdc^eo • -T-id^-iT-i • • -T-ioood • • • ■^ N
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a a So op 2 B^S'x^^s
PART II — ALTERNATING CURRENT GENERATORS.
CHAPTER V.
PRESSURE REGULATION OF ALTERNATING CURRENT GENERATORS.
For the purpose of studying the influence of various factors on the regulation, and in calculating the regulation for most of the designs worked out, we shall in this treatise follow the method set forth in a paper in which one of the present authors collaborated, and which was read before the American Institute of Electrical Engi- neers* in 1905. We shall not enter in detail into the theoretical basis of this method, but shall give an outline sufficient for purposes of calculation.
The pressure regulation of an alternator is preferably specified as the percentage by which the terminal voltage rises when the load is decreased! from full load to no load without changing the speed or the field excitation. This may be termed the ''inherent regulation" and is generally specified for full load at unity power factor, and for full load at 80 per cent power factor. The two values are termed respectively *' The inherent regulation at unity power factor" and "the inherent regulation at a power factor of 0.8." The full load current at other than unity power factor is to be taken at the value corresponding to unity power factor; i.e., the kilovolt- amperes and not the kilowatts is taken as the basis of rating of alternators.
The customary values of the inherent regulation range from 4 per cent to 7 per cent for a power factor of 1.0 and from 15 per cent to 22 per cent for a power factor of 0.8. The British Engineering Standards Conmiittee recommend 6 per cent on full non-inductive
♦ Ppoc. American IruttttUe of Electrical Engineers, vol. xxiii, p. 291, "A Contribu- tion to the Theoiy of the Regulation of Alternators," H. M. Hobart & F. Punga.
t This is the most common and the distinctly preferable specification, but an alter- native occasionally employed is to specify the percentage drop in voltage when the load is increased from xero to full load, the excitation and speed being maintained constant.
65
66 PRESSURE REGULATION.
load and 20 per cent on full inductive load with a power factor of 0.8, as maximum values.
It is sometimes useful to also specify the "excitation regulation," which is defined as the percentage increase in the field current to maintain normal terminal voltage when the load is increased from zero to full load. The excitation regulation ranges from 10% to 15% on non-inductive load, and from 25% to 35% on inductive load with a power factor of 0.8, for normal machines.
In pre-determining the pressure regulation of an alternator, the quantity requiring to be ascertained is the additional field ampere turns necessary at rated load to maintain the normal terminal volt- age, and it is with the estimation of this quantity that pressure regu- lation calculations are chiefly concerned. These additional ampere turns consist of three components whose respective functions are:
I. To counteract the demagnetising ampere turns of the arma- ture due to the current at the rated load.
II. To make up for the pressure drop due to the reactance and resistance of the armature winding.
III. To provide for the increase in magnetic leakage, brought about by the increased magnetomotive force, which increases the total flux in the magnet cores and hence the flux density and ampere turns required for the magnet cores and yoke.
I. The Demagnetising Ampere Turns.
The demagnetising component of the armature ampere turns is given by the expression
D ^ KB ni sin ^'
where D is expressed in ampere turns, and :
X = a coefficient depending on the ratio of pole arc to pole
pitch, B = the breadth factor of the winding. ni = the armature ampere turns per pole for all the phases. if/ =» the angle between the pole centre and the position of the armature conductor when it carries maximum current. This may be termed the ** internal phase angle." 1. The values of K are as follows:
Ratio of pole arc to pole pitch Value of X
THE DEMAGNETISING AMPERE TURNS.
67
2. The values for B, the "breadth factor," depend on the dis- tribution of the winding, and are given in Table 12.
TABLE 12.
Breadth Factor of Armature Coils.
|
Pereentaffe of Pole Pitch Covered by One Side of the Armature Coil. |
Values for B, the " Breadth Factor." |
|
20 per cent 33 per cent 40 per cent 50 per cent 60 per cent 80 per cent 100 per cent |
0.99 0.95 0.94 0.90 0.86 0.76 0.64 |
Single-phase windings cover from 20 per cent to 100 per cent of the pole pitch according as they are concentrated or thoroughly dis- tributed windings.
Two-phase windings generally cover 25 per cent of the pole pitch on either side of a coil of one phase, the whole coil thus covering one half of the pole pitch, and thus having a breadth factor of 0.90.
The commonest three-phase winding is the 2-range winding (which is half coiled, i.e. has one coil per phase per pair of poles, see p. 231, Chapter XI), and with this winding, a single coil of one phase covers one third of the pole pitch on either side, and thus has a breadth factor of 0.95. Three-phase distributed wave windings also spread 33 per cent of the pole pitch on either side of the winding of one phase under a pole.
3. The armature ampere turns per pole, m, may be designated as
the armature strength; the armature strength is in this treatise taken
equal to the number of turns per pole for all the (n) phases multiplied
Tni by (i) the ciurrent in the windings, and is thus equal to where T =
the total number of turns per phase, n ^ the number of phases, t « the current per phase, and p = the number of poles. Let us, for mstance, consider a 3-phase 3000 kva. 8-pole, 11,000 volt, 50 cycle, Y-connected alternator having 120 slots and 4 conductors per slot, The total number of conductors on the armature is 120 X 4 « 480,
68 PRESSURE REGULATION.
and the conductors per phase = ^^ = 160. T, the number of turns per phase, is thus equal to ^^ = 80. The voltage per phase equals,
lip = 6350. V3
The current per phase at full load is equal to
3,000,000 .ro rx6350 - '^ *'"P^'^'-
Hence for the armature strength we have
. Tni 80 X 3 X 158 .-.^ .
m =» = = 4740 ampere turns.
p 8
4. The ** internal phase angle '* <f>^ consists of three components
^' - ^ + a + /?.
<f> is the phase angle by which the current in the external circuit lags behind the terminal voltage. The power factor in the external circuit is equal to cos (f>.
a is the phase angle between the internal E.M.F. and the terminal E.M.F. and due to the armature reactance.
fi is the angular displacement of the magnetic centre of the field flux due to the distortion of the flux by the armature magneto- motive force.
The conditions in the alternator armature for a load having a power factor equal to cos <l>, are as represented in the vector diagram of Fig. 57 in which
OV « the terminal voltage per phase.
OC » the current in the armature windings, (and of course also in the external circuit) lagging by an angle ^ behind the terminal voltage OV.
OP « RV == the reactance voltage in the armature when carry- ing the current OC.
RE = the voltage drop by ohmic resistance.
OE =» the internal voltage per phase, generated in the armature by the flux crossing the gap. 4> =* angle VOC = phase angle between current OC and termi- nal voltage per phase OV. a « angle EOV = phase angle between internal E.M.F. per phase OE and terminal E.M.F. per phase OV.
CALCULATION OF <f>'
69
For a load of unity power factor, 4> » zero, and the conditions are as shown in Fig. 58.
Calculation of <l>\ — The Internal Phase Angle.
Of the three components <^, a, and fi:
(1.) ^ is known from cos <l>, the power factor.
(2.) The determiriatian of a: To determine a it is necessary to know the value of the reactance voltage(V) of the armature, and to be precise, also the resistance drop in the armature windings, the latter, however, generally exerting a far less influence on the final results than is exerted by the reactance voltage.
Fig. 58. Fi08. 57, 57A and 58. — Vector diagrams relating to pressure regulation.
The reactance voltage is equal to the reactance of the armature, multiplied by the current, thus:
V = (27:N1) X t, where
N « frequency in cycles per second. / = inductance of the armature winding in hemys. i « current in armature in amperes.
V « reactance voltage.
N and i being known, we can obtain v, the reactance voltage, as soon as we have determined /, the inductance.
70
PRESSURE REGULATION.
Estimation of Z, the Inductance of the Armature Windings in Henrys. — For ascertaining the inductance we require to know the number of lines linked with the armature conductors per ampere turn. With open straight-sided slots a sufficient approximation to the inductance of the embedded part may be obtained by an ele- mentary magnetomotive force calculation, thus:
Let D = depth of slot in centimetres.
d = depth above top of winding in centimetres. w = width of slot in centimetres.
Then the number of lines per ampere turn per centimetre of embedded length, for the case of the inductance of the winding in a single slot, may be taken as approximately equal to,
47r i(D -d) +d 10 w
0.63
D + d w
If the coil is spread over two slots, the length of the magnetic path through the air is doubled, and the number of lines per ampere turn per centimetre of core length is about one half the number for a single slot.
For the free length of the conductors, i.e., the parts not embedded in iron, the number of lines per ampere turn per centimetre may be taken as from 0.4 to O.8.*
As a rough approximation we may estimate the inductance of the free length on the basis of the following figures:
|
Niimb«r of Slots per Pole per Phase. |
Number of Lines per Am- pere Turn per Centimetre of "Free" Length. |
|
1 2 3 4 |
0.8 0.7 0.6 0.6 |
If we denote the total number of lines per ampere turn by Z, then we have for the 3000 kva. alternator which we have taken as example, Z = (free length in centimetres) X (0.5 to 0.8) + (the embedded length in centimetres) X (the lines per ampere turn per centimetre of embedded length).
* " Modem Commutating Dynamo Electric Machinery/' H. M. Hobart, Journal Institute Electrical Engineere, vol. zxxi, p. 170, 1901.
INDUCTANCE OF ARMATURE WINDINGS. 71
The inductance of a coil having t turns is equal to <* Z X 10^ and its reactance is equal to
27:Nt^ Z X 10-'.
The reactance per phase is the reactance per coU multiplied by the number of coils per phase. As an example let us return to the case of the 3000 kva. alternator mentioned on page 67.
A section of the slot is shown in Fig. 59.
Here D = 6.0,
d = 1.2, and w «= 2.1.
Consequently the number of c.g.s. lines per centimetre of embedded length is equal to
0.63(6:^_tl^^21g
The mean length of one turn » 516 centimetres. "Embedded" length per turn = 2Xn = 190 centimetres. "Free" length per turn « 356 centimetres.
The slots being open, no extra allowance is required for overhang of teeth. Hence the total number of lines per ampere turn per centimetre of embedded length r~7 Vg~ «2.16. ^ r^
Spread of coil (i.e., number of slots) = 5.
As there are 5 slots, the magnetic length of the leakage air path is approximately five times the magnetic length for one slot. The c.g.s. lines per I*""*"*
ampere turn per centimetre of embedded length Fio.69.
become approximately ^^-^ = 0.43, say 0.5. Slot of 3000 kva.
Hence we have: alternator.
c.g.s. lines per ampere turn for the free length = 0.5 X 356 = 178*. c.g.8. lines per ampere turn for the embedded length = 0.5 X 190 = 95. c.g.8, lines per ampere turn (Z) = 178 4- 95 = 273. Number of turns per coil (t) = 20.
Inductance of one coil in henrys (I) ^ e X Z X lOr* = 0.00109 and the reactance of one coil = 27ml = 2;r x 50 X 0.00109 = 0.342
72 PRESSURE REGULATION.
ohms. There are 4 coils per phase, therefore the reactance per phase is
0.342 X 4 = 1.37 ohms.
With full load current of 158 amperes, the reactance voltage per phase = 158 X 1.37 = 216. Expressed as a percentage of the terminal voltage per phase
[ — ^-p~ = 6350J, this is equal to^^rr X 100 = 3.4 per cent.
As the ohmic drop (ER of Fig. 57) is usually small compared with the reactance voltage and with the terminal voltage, we may neglect ER in estimating a. Consequently a is determined by the approximate relation
sin a « — cos 0,
when t; = reactance voltage, and V = terminal voltage.
This relation is apparent from the diagram in Fig. 57A in which the resistance drop ER has been neglected. The proof is as follows:
We have the angle BVH - KOR = ^ + a,
VH also ^^- = cos RVH = cos (^ + a),
.-. VH ^RVcos{<l> + a),
A • VH RV ,.^ .
and sm a = — - ^cos (<3& + a).
As a is exceedingly small compared with ^ we may take cos (^ + a) as approximately equal to cos <l>, and hence,
RV J. ^ . . . 1
sm a = ^Ty- cos 0 = — cos 0 approximately.
a could of course be scaled off from a diagram such as Big. 57, in which the various voltages are set out to scale, and there would then be no purpose in resorting to this approximation.
In the case we are considering, for full load at power factor 0.8, 0 = 37 degrees, the reactance voltage is 216, and hence,
216 cos 37^ ^ ^^^- '''' " ^ 6350 '^-^^^^^ whence a « 1.5 degrees.
INDUCTANCE OF ARMATURE WINDINGS.
78
(3.) The Determination of /?. We may determine the angle p from the distorting ampere turns. The equation for p, the degrees shift of the magnetic centre from midpole-face position is: —
a ^ Arm, distort, amp, turns per pole ^ ^ degrees. Air gap ampere turns on field per pole.
Table 13 shows the expressions for the general case of distorting and demagnetising ampere turns.
TABLE 13.
EXPRBBSION FOR DbMAONETISINO AND DlSTORTINQ COMPONBNTS OF ArMATURE
Ampere Turns.
|
RaUo of Pole Are to Pole Pitch. |
Armature Ampere Turns (Effectiye) per Pole. |
||
|
0.5. |
0.6. |
0.7. |
|
|
Demagnetifiing ampere turns . Distorting ampere turns. . . |
0.82 Bni sin 4>' O.llSnicos^ |
0.78 Bnt sin ^' 0.15Bntoo8^' |
0.75 Bnt sin ^ 0.20Bnico6^ |
In this table, ni denotes the effective armature ampere turns per pole, i.e., ni = (ampere turns per pole per phase) X (number of phases). B = the breadth factor already discussed on page 67.
The expression for the distorting ampere turns contains ^' which is equal to <^ -f a + /?. The value of this expression is not known until fi is determined. Hence in calculating the distorting ampere turns we must assume a preliminary value for /?, and if the calculated value of /? comes out sufficiently near the assumed value, the calcu- lation will stand, but if not, then the new value should be substituted and the calculation revised.
For example, in the case of the 3000 kva. alternator we are con- sidering, the ratio of the pole arc to the pole pitch is equal to 0.7, and the distorting ampere turns are ascertained from Table 13 to be:
0.20 B ni cos </>'
B = 0.95 (see p. 67) ni « 4740 (see p. 68) <^ = 37 degrees (see p. 72)
a = 1.5 degrees (see p. 72).
Assuming for p a trial value of 7 degrees, we have 0' - 37 + 1.5 + 7 = 45.5 degrees and cos ^' = 0.71.
74 PRESSURE REGULATION.
Hence the distorting ampere turns 0.20 X 0.96 X 4740 X 0.71 « 6500. The field ampere turns for the air gap for this design are 8100.
Whence /? - ^^^\ X 90 degrees = 7.2 degrees.
This value is so near the assumed value of 7 degrees that it is not necessary to re-calculate it, but if there were a wider difference, the value of /9 = 7.2 degrees should be substituted, giving <f/ = 45.7 and the calculation revised on this basis. We have now determined 0, a, and p, and from them, <f/, from which latter quantity the demag- netising ampere turns may next be calculated by aid of the expressions in Table 13. For the case under consideration the demagnetising ampere turns for cos <^ = 0.8 are
= 0.75 B ni sin 4/
= 0.75 X 0.95 X 4740 X 0.707
« 2400 (I)
Thus we have finally arrived at the value of Z), the demagnetising ampere turns, in the expression D =» KB ni sin <f/ on p. 66.
n. The Ampere Turns required for the Reactance Voltage.
The second component of the additional field ampere turns is required to make up for the sli^t loss of pressure due to the react- ance voltage. This component can be read ofif from the no load saturation curve. For the case under consideration, the no load saturation curve is given in Fig. 60. At unity power factor the component of the reactance voltage in phase with the terminal voltage is zero, and at any power factor, cos 4>y *he component is approximately v sin <3&, as may be seen from Fig. 57. We have:
i?sin^ = 216 sin 37° = 130,
and from the no load saturation curve of Fig. 60 the ampere turns
required for this voltage are found to be 280 (II)
The no load saturation curve can be readily drawn by working out the field ampere turns for the magnetic circuit at two voltages and drawing the curve through the two points obtained. One of the points should be worked out for the normal voltage of the machine and the other for a voltage some 20 per cent higher than normal voltage provided the flux densities are not too high on the satura- tion curves, as these curves are always imreliable at very high
AMPERE TURNS FOR REACTANCE VOLTAGE.
75
densities. In estimating the 20 per cent higher point; all the flux densities throughout the magnetic circuit are multiplied by 1.2, and the corresponding ampere turns for each part are taken from the appropriate saturation curve for the material.
When high densities are employed, as so often occurs, especially in
8000
4000
0000 8000 10000 laooo Ampere Tama per Pole.
14000 16000
Fig. 60.— Saturation curves for 3000 kva. 3-phase 750 R.P.M. 8-pole 50 cycle 11,000 volt alternator.
the armature teeth, the upper parts of the saturation curves are not reliable, and the following rough rule will be useful:
For wrought iron, stampings, or iron or steel forgings, for densities above 1&,000 lines per square centimetre, the percentage increase in ampere turns is from 8 to 10 times the percentage increase in flux density. Thus for a 20 per cent increase in density the increase in ampere turns will be 8 to 10 times 20 per cent, i.e. 160 per cent to 200 per cent, the higher value going with the higher saturations.
For example, let us take the armature teeth for the case in hand.
76 PRESSURE REGULATION.
The no load flux density in the teeth for 6350 volts, is 18,000, and at 1.2 times normal voltage ( = 7620 volts), the density is 1.2 X 18,000 = 21,600.
The ampere turns for teeth at normal voltage are 540, and at 7620 volts, will be 200 per cent greater, as the saturation is very high and hence the ampere turns are 3 X 540 = 1620.
m. The Ampere Turns for the increased Magnetic Leakage.
The third component of the additional ampere turns is required to make up for the increased magnetic leakage brought about by the higher magnetomotive force on the field magnets. An estimation of the leakage coeflScient is consequently necessary.
^, , I IE • X useful flux + leakage flux
The leakage coefficient = tt"^ — ^^
useful flux
The useful 'flux is the flux in the armature, and the useful flux + the leakage flux = the flux in the magnet cores and yoke. The leakage flux is approximately equal to
C X ^ ^^ "^ ^^^ X (Ampere Turns per Field Spool) a
for cores of rectangular cross section and
C X ^-^^ X (Ampere Turns per Field Spool) a
for cores of circular cross section. The small letters represent the dimensions of the magnet cores as in Fig. 61. C is a factor l3ring
between 2.4 and 3.4, the higher values applying in cases where the sides of the poles are close together and more nearly parallel with one another and where the pole tips are near together.
In high speed machines with few poles which are far apart at the tips,
Fia.61. — Alternator magnet cores. ,, , ^ .n i t^ ,i
the lower figure will apply. For the case through which we are working, we have A = 27, a « 20, 6 =» 140.
No load ampere turns on field = 9200, whence leakage flux « 4,600,000.
The useful flux required in the armature per pole at unity power
AMPERE TURNS FOR INCREASED MAGNETIC LEAKAGE. 77
factor is 34 megalines, and thus the leakage coefficient is equal to
34 + 4.6 , - . -3^ = ^•^*-
At the excitation necessary for normal voltage at full load and cos ^ = 0.8 the leakage coeflBcient is considerably greater on account of the greater magnetomotive force on the field, and the leakage flux will be increased in proportion to the field excitation.
In the case under consideration, we have already determined the demagnetising ampere turns and the ampere turns for the reactance voltage. These come to 2400 + 280 = 2680. As these constitute the bulk of the extra ampere turns, we may, for purposes of estimat- ing the increased leakage, take the total ampere turns at full load and cos ^ = 0.8 as 9200 + 2680 » 11,880, and at this excitation the leakage coeflScient will be
The extra flux, i.e., the leakage flux, only enters into the pole and yoke, and the densities in these parts only will be increased in the ratio \^ (or 3.5 per cent increase) and extra magnetomotive force will only be required for the pole and yoke. Hence in Fig. 60 we have plotted the no load saturation curve for the poles and yoke separately.
The increase of 3.5 per cent in density, corresponds to a voltage increase of 3.5 per cent of 6350 = 222 volts, which from the satura- tion curve for pole and yoke, requires 300 extra ampere turns (III).
We have now the three components I, II, and III. The total extra field ampere turns are thus 2400 -f 280 + 300 = 2980. The no load excitation is 9200 ampere turns, and thus the total field excita- tion required to maintain a normal terminal voltage of 6350 volts for rated load and cos (f) = 0.8, is 9200 + 2980 - 12,180 ampere turns. This gives us the extreme right hand point marked cos (f) = 0.8 on Fig. 60. This is a point on the saturation curve for full load at cos <l> = 0.8. The voltage corresponding to this excitation at no load is found from the no load saturation curve to be 7450 volts.
To this should be added the ohmic resistance drop which is / X /? = 158 X 0.126 - 20 volts, brmging the total up to 7450 + 20 = 7470
volts. 2^=7r = 1.18, consequently the inherent regulation at 0.8 power 6350
factor is equal to 18 per cent.
78 PRESSURE REGULATION.
REGULATION CALCULATIONS FOR FULL LOAD AT UNTTT POWER FACTOR.
At full load and unity power factor, the conditions are as repre- sented in Fig. 58, page 69. We have ^ = 0 and ^' - a + ^9.
a = tan-^ — = tan"* 0.034 =2^. 6350
The reactance voltage remains equal to 216 as before, and the vol- tage per phase is equal to 6350.
The angle <f/ will be small and for purposes of estimating p it will be sufficiently accurate to take cos <f/ as equal to 1.0, since for angles ranging from 0 to 20 degrees the variation in the cosine does not exceed 6 per cent.
The distorting ampere turns are now 0.20 X 0.95 X 4740 X 1.0 = 900 (see p. 73). The air gap ampere turns are 8100, whence,
Hence we have ^ = 2 4- 10 = IT.
The demagnetising ampere turns at unity power factor are
0.75 X 0.95 X 4740 X sin W (see p. 73) = 0.75 X 0.95 X 4740 X 0.21 = 720 ampere turns (I).
As the reactance voltage is in quadrature with the terminal vol- tage and consequently has no component in phase therewith, no extra field ampere turns are required to compensate for it. There will, however, still be a component required to provide for the increased leakage. This will amount to about 200 ampere turns and we must take it into account in estimating the increased leakage coeffi- cient. The excitation at full load and unity power factor will be approximately
9200 + 720 + 200 = 10,120.
The increased leakage coefficient for this excitation will be approxi- mately
This gives an increase in flux density in the poles and yoke of ^^^ » 1.5 per cent, which corresponds to an increase in voltage of
THE NO LOAD SATURATION CURVE 79
0.015 X 6350 = 84 volts. From the saturation curve for poles and yoke (Fig. 60) we find that this requires 150 extra ampere turns (III).
The total extra field ampere turns are thus I + III = 720 4- 150 =» 870. Adding this to the no load excitation of 9200 ampere turns we find that 10,070 ampere turns are required to give full terminal voltage at full load and unity power factor. This point is marked on Fig. 60 and is a point on the full load, unity power factor, satu- ration curve. The corresponding voltage on the no load satura- tion curve for an excitation of 10,070 ampere turns is 6750 volts.
—-—r = 1.063. Consequently at full load and unity power factor oo50
the inherent regulation is 6.3 per cent.
The IR drop which is practically in phase with the terminal voltage
and which amounts to 20 volts or 0.3 per cent, must be added on.
The total inherent regulation for full load and unity power factor is
thus 6.6 per cent, or say 7 per cent.
THE NO LOAD SATURATION CtJRVE AND THE SHORT-CIRCUn CHARACTERISTIC.
The regulation is closely dependent on the degree of saturation of the iron parts of the magnetic circuit and on the short circuit charac- teristic.
As regards the former, it may be said that the more highly saturated the magnetic circuit the closer is the regulation. The r^ulation is in this case improved by virtually bending the satura- tion curve over, i.e., by working the iron of the magnetic circuit very near its saturation limits. This procedure is advantageous in that it minimises the cross section of the magnetic paths, and consequently the total weight of iron in the machine. Furthermore, by saturat- ing the pole cores to a very high value, the mean length of one turn of the field winding is minimised, and consequently the weight of the field copper is reduced. It is a dangerous plan, however, since the material of the magnets (especially if cast) may turn out to be of inferior quality. Furthermore, should the machine be called upon to run at a voltage appreciably greater than the normal voltage, there will be difficulty, and perhaps impossibility, of getting sufficient flux through the machine for the high voltage, no matter how much the excitation is increased. The excitation regulation is also very great.
80 PRESSURE REGULATION.
With r^ard to these points, it is best practice to keep within reasonable flux densities, desirable values for which are given in Table 21, page 113, Chapter VII-
It is not so much the actual ampere turns expended on the iron, but rather the proportion which they bear to the total field ampere turns, or the ratio of iron to air gap ampere turns, which is of chief importance. The use of extra long air gaps will not necessarily be accompanied by a corresponding improvement in regulation; it is rather a matter of balance between the magnetomotive force for the air gap and for the iron; and as a matter of fact, in average cases at normal voltage, the ratio of iron ampere turns to air gap ampere turns ranges from 1:5 up to 1:7, i.e., the air gap absorbs from 80 per cent to 90 per cent of the total ampere turns. Such proportions are typical of a normal design so far as the regulation and the value of the short circuit current are concerned.
The short circuit current in the armature at any given field exci- tation is of such a value that the armature reactions just counter- balance the field excitation. The field excitation is oflFset by the armature demagnetisation and by the reactance drop in the arma- ture. The short circuit characteristic showing the relation between the field ampere turns with the armature current (i.e., the armature ampere turns) is approximately a straight line, and hence the short circuit current is practically proportional to the ratio of the field ampere turns per pole to the armature ampere turns per pole.
A "strong" armature is one in which, at rated load, the armatiu^ ampere turns are large in proportion to the field ampere turns. Conversely a "weak" armature is one in which, at rated load, the field ampere turns are large compared with the armature ampere turns.
The voltage regulation will of course be closer the less the armature demagnetisation, and as this depends for a given rating or current on the number of armature turns it may in general be said that the regulation with "strong" armatures is usually not so good as with "weak" armatures. Apart from the degree of saturation