Design and Stress Analysis of Extraterrestrial ... - The Black Vault

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,.is the calculation Of thermal strer--in the tubes of' the radiators, cooling the panels and ribs, and in the cylindrical and conical shells. Considerable attention is given to the calculation of thermal streiS in the electrodes of motors and parts of the feed system. In the appendix is given) information on the rupture strength of the materials most widely used in extraterrestrial engines. This book is a ianual for senior students in courses of related *•specialties. It can also be useful to engineers and designers who work in the sphere of space technology. 30 tables, 350 illustrations, bibliography of 52 titles. k 41T-M-41427
'.PREFACE This manual is written in accordance with the program of a course in the design of extraterrestrial electric rocket engines (ERE), and is to be read in schools of higher educaticn. In the press a number of problems connected with ERE have been widely discussed. However, the questions examined in this book of their design, strength, vibrations, have not as yet been properly systematized and much time shculd be spent on their study. In this manual vie-have made an attempt at the systematic presentation of the indidted information. In its preparation the authors took ii:to account the fact that the students are already familiar with courses on the strength of materials and the theory of extraterrestrial electric rocket engines. The book consists of five chapters. Chapter I presents general information on extraterrestrial engines and requirements imposed'on them; ERE classification is given, there fundamental and structural diagrams are presented, and also the general problems of reliability and strength are examined. Chapter II contains fundamental information on design and stress analysis of the ERE power generator. The greatest attention is here given to nuclear reactors; their classification, structural diagram, and design of separate units and parts are examined. FTD-MT-24-1462-71 viii
Page 2 and 3: FTD:-MT-24-1462-71 FOREIGN TECHNOLO
Page 4 and 5: tUNCLASSIFIED - Security Ct-9-1uifl
Page 6 and 7: t IABLE OF CONTENTS U. S. Board on
Page 8 and 9: 5.2. Ion motors ...................
Page 10 and 11: II jah _X JOLIGAETECbtSODN USA N NL
Page 14 and 15: S1 In stress analysis the calculati
Page 16 and 17: "I 3 f !7 2 II 3 I 44; a ' 3 I 4 2
Page 18 and 19: )I requires special protection of t
Page 20 and 21: electrical power of the power insta
Page 22 and 23: Extraterrestrial motors in power fr
Page 24 and 25: S1' , . that a part operatesbefore!
Page 26 and 27: Fig. 1.3. Diagram of an ERE with me
Page 28 and 29: Table 1.3 shows the working media,
Page 30 and 31: I I The schematic of a nuclear ther
Page 32 and 33: Fig. 1.5. converter. Diagram of an
Page 34 and 35: The advantage of this arrangement i
Page 36 and 37: A complex system or any part of it,
Page 38 and 39: I I Stages and content of operation
Page 40 and 41: 'the use of earlier systems and uni
Page 42 and 43: Structural diagram of operations Th
Page 44 and 45: . . . . . __.. . . . . .. .. . . .
Page 46 and 47: -- indication of state, transmissio
Page 48 and 49: Stages ERE, I. Analysis of the tech
Page 50 and 51: Space vehicle (SV) jParts jettisone
Page 52 and 53: Spc veil (SV)!- 0 4. ho 0. 4)Z - H4
Page 54 and 55: ~tto 4- jo 0o (utd~nb 'Sa vtho- 4)i
Page 56 and 57: 'Li However, 'this list can be chan
Page 58 and 59: - S developed. Or course, there are
Page 60 and 61: Sthat From the design and operation
Page 62 and 63:
As the number or tests builds up-an
Page 64 and 65:
II P 'Po. = -ý SFig. 1.20. Curves
Page 66 and 67:
Stress is the intensity of the inte
Page 68 and 69:
strength criterion only when even s
Page 70 and 71:
JV Strength- reserve is the ratio o
Page 72 and 73:
'2 1 I III I, . - I - S We know tha
Page 74 and 75:
i J However, when the operating tim
Page 76 and 77:
Plastic deformations in the latter
Page 78 and 79:
Let us examine the basic design rel
Page 80 and 81:
I I The constants B and n are deter
Page 82 and 83:
Along with equation (1.18) we use e
Page 84 and 85:
Iftesting continues, as shown in Fi
Page 86 and 87:
I I Based on the known deformation
Page 88 and 89:
6%Fx (a) Fig. 1,31., Uniaxial (a) a
Page 90 and 91:
The element is in plastic state (1
Page 92 and 93:
Total operating time of the sample
Page 94 and 95:
I:! Substituting expression (1.35)
Page 96 and 97:
Function B(T) is found after determ
Page 98 and 99:
first We shall express stresses in
Page 100 and 101:
etween it and the stressed state of
Page 102 and 103:
a) b) c) Fig. 1.36. Determining the
Page 104 and 105:
other conditions being equal, the c
Page 106 and 107:
The fuel elements also rest on a li
Page 108 and 109:
As the reflector and moderator in t
Page 110 and 111:
Let us examine the examples of weld
Page 112 and 113:
Between these shells passes a fluid
Page 114 and 115:
The procedure for welding a two-lay
Page 116 and 117:
A fuel element is a closed pressuri
Page 118 and 119:
1 2A S(a) II • • /Fig. 2.8. Con
Page 120 and 121:
The reflector material 5 (beryllium
Page 122 and 123:
Figure 2.12 is a sketch of a fast n
Page 124 and 125:
I. ! ~ ~~. . ........... li .... I
Page 126 and 127:
I jZ ICIS qo 'Im klol
Page 128 and 129:
THERMAL STRESSES IN FUEL ELEMENTS T
Page 130 and 131:
Ora-O"when r=a; when r=b. (2.8) Sub
Page 132 and 133:
I The exponential logarithmic depen
Page 134 and 135:
I I of the cylinder between two adj
Page 136 and 137:
EuI~, 21,2 Eat, • bb 2-(1 ---xInb
Page 138 and 139:
-a - Fig. 2.18. Thermal stresses in
Page 140 and 141:
I a It is necessary that n > 1l. If
Page 142 and 143:
The locus of points equidistant fro
Page 144 and 145:
Equations of equilibrium for an axi
Page 146 and 147:
Fig. 2.23. Equilibrium of a shell e
Page 148 and 149:
:I I I I The first equilibrium equa
Page 150 and 151:
The wall stress of this sphere is d
Page 152 and 153:
I These formulas enable us to plot
Page 154 and 155:
. . . S_.. I i. stresses. Maximum i
Page 156 and 157:
Shells in the reactors which we sha
Page 158 and 159:
axial stresses. Simplicity fully Ju
Page 160 and 161:
abl-ab (R+AR)d-•Rdf AR ab Rd? R (
Page 162 and 163:
V 1! II Point 3 corresponds to the
Page 164 and 165:
SI Now we seek the pressure of the
Page 166 and 167:
!I As is apparent from Fig. 2.39, t
Page 168 and 169:
I I I I '' 9 capacity of a shell in
Page 170 and 171:
SI a i f fit~ Z.rl -= •.r nl--~ ~
Page 172 and 173:
We plot the unknown curve p = f(AR)
Page 174 and 175:
-.. -, 7 ''°-^ ...... I}" L7,50s.
Page 176 and 177:
I" Table 2.2. (Cont d) (1) V(. )3 (
Page 178 and 179:
W/ dr (2.48) "The sign is negative
Page 180 and 181:
Ve designate th6 relaitie -momenits
Page 182 and 183:
a a I a A4l "• dr; P= pr dr idy;
Page 184 and 185:
'(2.61) or in shortened form, V 2 V
Page 186 and 187:
4i In this case, the constant C2 in
Page 188 and 189:
will be If the external force is co
Page 190 and 191:
I W -P [(a2 -I a +(•1 -r2)In a ("
Page 192 and 193:
+) If we find that Wmax • h, the
Page 194 and 195:
I I W c I , I- a , I. ' We cut the
Page 196 and 197:
- (0,,i66.0,239. 10-6-0,484.0,33. 1
Page 198 and 199:
-n I I I I Pig, 2.56. Determining t
Page 200 and 201:
In some cases, it is assumed that t
Page 202 and 203:
6e, I Smat a a SI r.+0P6h2a .. 'fro
Page 204 and 205:
In designing a source it is necessa
Page 206 and 207:
removal, for example, in a containe
Page 208 and 209:
- 2d I I I ______ -. - I 2o ( 'I Z
Page 210 and 211:
Ir dp;- N,= N, .(-N,,lr d$ + d (3,I
Page 212 and 213:
It is perfectly obvious that the el
Page 214 and 215:
dr dr, dMr, dr2 d, d2or 1 3 dr dr "
Page 216 and 217:
I ! i I I The quality of the device
Page 218 and 219:
The mirror surface, in this case, i
Page 220 and 221:
Fig. 2.69. Thermal trap with contro
Page 222 and 223:
i ffased on this factor, fuel eleme
Page 224 and 225:
In extremely small pores (pore c) t
Page 226 and 227:
why fuel elements with a solid elec
Page 228 and 229:
Peazeemnl (l) Fig. 2.73. A regenera
Page 230 and 231:
I. II As a result' of the- process,
Page 232 and 233:
'4I '21
Page 234 and 235:
U k IIl + (n2lpiim)() Fig. 2.78. Co
Page 236 and 237:
I I I I Figure 1.3 shows one of the
Page 238 and 239:
• C a is the axial velocity of th
Page 240 and 241:
Figure 3.1 shows working blades of
Page 242 and 243:
Fig. 3.11. Union of disk with shaft
Page 244 and 245:
I *1 warping, the material of the h
Page 246 and 247:
(a) (b) Fig. 3.6. Dry-fri'ction bea
Page 248 and 249:
ing groove, and through the incline
Page 250 and 251:
I '' S Albng with the variation in
Page 252 and 253:
Friction and wear in such a bearing
Page 254 and 255:
The transition from the oversaturat
Page 256 and 257:
O a) CO- 4) U'% 0 4Z Oo .~ 0 t'24a)
Page 258 and 259:
I _____ ', "I I The Na-K pump consi
Page 260 and 261:
E- W2l.i rx.
Page 262 and 263:
w is the angular velocity of disk r
Page 264 and 265:
; I ' | * * I I j I l7 I II I' *
Page 266 and 267:
and, finally, dPa 2.ir( 2r a dr z z
Page 268 and 269:
Flexural stresses at any point' of
Page 270 and 271:
Another means of unloading consists
Page 272 and 273:
0 I I I In cae wetakii CO/7eHU~e *1
Page 274 and 275:
Determining the frequencies of inhe
Page 276 and 277:
Differentiating this equation, we f
Page 278 and 279:
Equation '(3.?5) is a differentiale
Page 280 and 281:
Functions S, T, U and V during diff
Page 282 and 283:
1 JVQP (3.30') Fig. 3.24. Forms of
Page 284 and 285:
Then the bendinv moment is t ! ! EI
Page 286 and 287:
'!..... " - ;-~ .- .-.. ~ - - J I T
Page 288 and 289:
Figure 3.25 shows the operation of
Page 290 and 291:
2 I ' whe, For plottfng the donvert
Page 292 and 293:
satisfies the bounaary conditions o
Page 294 and 295:
- o0 CC 0 CL P% c - t- -. C4 t C Ci
Page 296 and 297:
The angular velocity w Aof natural
Page 298 and 299:
I. Each of the harmonics of the ang
Page 300 and 301:
At each of the points of interse-ti
Page 302 and 303:
The actual frequency of natural ben
Page 304 and 305:
1 I i , II ' t S S "•< i, I S, 3.
Page 306 and 307:
(In view of the smallness of angle
Page 308 and 309:
dr dr r d• _._._.• .d~t 1 •t-
Page 310 and 311:
7WI - For conical disks equation (3
Page 312 and 313:
Hyperbolic disks. If the, thickness
Page 314 and 315:
o•/. or Oer 17,0 5,0 16,0-2 4,5 5
Page 316 and 317:
- 0CX=, 9 - 280- 270- 110 0,15 __ -
Page 318 and 319:
11 0,7 2,- 7,5 - '2,4- a'l 0,5 02 0
Page 320 and 321:
55- . \, 105 50-100 45 ' 95 S85 "J
Page 322 and 323:
Let us examine two cases: disk) and
Page 324 and 325:
4. 100 0,6- WoO, ~: 1 0,94 493,8 3,
Page 326 and 327:
0,7 3,3 -3,3 0,6 -3,2 0,15 3,0 2,9
Page 328 and 329:
f~rc 200 -PC.; 190 40 170 30 I/t 0,
Page 330 and 331:
a) arB 0 if the disk does not bear
Page 332 and 333:
I I I I II I , Substituting this so
Page 334 and 335:
Z= lz 1 x _-, 9 S1- 0,TF,1 o~ 5o o
Page 336 and 337:
ii 0,1 42 0,3 ,4 0,50q6 0,7 08 0,9
Page 338 and 339:
The expression for a* is obtained f
Page 340 and 341:
, The'actual stresses on the bounda
Page 342 and 343:
ý4.1 j L. - - c* m oc ~ .7 lira___
Page 344 and 345:
C,4 C4C4 I IC4) CI tz +3Il + + CC.)
Page 346 and 347:
C.. C4 0 C4 C I -T I -J . C :.d C?3
Page 348 and 349:
Widely used methods are those based
Page 350 and 351:
Solving the last equation relative
Page 352 and 353:
Substituting the difference (awl -
Page 354 and 355:
0 g h•con- - o7 g , 0,7 .Op • o
Page 356 and 357:
iJ relaxation) occurs and with stea
Page 358 and 359:
In the examired theory during plast
Page 360 and 361:
Let, us p w I I ! • Let, us proce
Page 362 and 363:
Rupture sets in only when plastic f
Page 364 and 365:
£@ 1 hdr .1 (o) hr r(3.102) Usuall
Page 366 and 367:
I Since the shaft is elastic, then,
Page 368 and 369:
I I SI hence r M! rad/s ,(3.104) de
Page 370 and 371:
y ii y0 \ 1 0-1 H t ieemNw idn 5ai7
Page 372 and 373:
Critical angular velocities- of a s
Page 374 and 375:
We assume that the disk and shaft a
Page 376 and 377:
Expanding the determinant of (3.113
Page 378 and 379:
y=aP-P+a, 2 M; a 21aiP+a22M# (3.119
Page 380 and 381:
(1) ((2) O~7~C.• o~P'7t7- A O6/UC
Page 382 and 383:
Wihen X = w, forward synchronous pr
Page 384 and 385:
we find For forward synchronous pre
Page 386 and 387:
•+ , , ; Im• S, -I i I I- I' su
Page 388 and 389:
When analyzing the natural frequenc
Page 390 and 391:
Vz 7M 7 ' z (KR--K-) z z (R (3.137)
Page 392 and 393:
The concept of forced vibrations. t
Page 394 and 395:
Resonance modes can be shown on the
Page 396 and 397:
' C Yon no'. ern12 •. -p. 4 a..(a
Page 398 and 399:
I ~ I 'Existing methods of damping
Page 400 and 401:
Vibrations in rotors on hydrostatic
Page 402 and 403:
SQTi •-fT 1 (O,0625VI)Y+1-0, 1-(p
Page 404 and 405:
During the forward speed of the piv
Page 406 and 407:
~t The coefficients of hydraulic fr
Page 408 and 409:
of forces in the absence of pivot v
Page 410 and 411:
To solve the problem of the vibrati
Page 412 and 413:
I I k i = Ib the projections of dis
Page 414 and 415:
3 The general solution to (3.160) c
Page 416 and 417:
(3.166) Thus, near the boundary of
Page 418 and 419:
2 1z or 2.. .• .. :. • C .2,e.
Page 420 and 421:
I 3.2. THERMOEMISSION ENERGY CONVER
Page 422 and 423:
STRUCTURAL DIAGRAMS AND DESIGN OF C
Page 424 and 425:
In the creation of the design serio
Page 426 and 427:
I £ The nortcoming in this design
Page 428 and 429:
'I, Fig. 3.92. Overall view of reac
Page 430 and 431:
Figure 3.93 is a diagram of an elec
Page 432 and 433:
We shall set up one of 'he shell se
Page 434 and 435:
E3 e 2 , --e 1 , o A= B 3 , 0 --E 1
Page 436 and 437:
worst efficiency. In the table the
Page 438 and 439:
7,7 417 1 2 Fig. 3.96. Diagram of a
Page 440 and 441:
A thermoelectric converter consists
Page 442 and 443:
I 1A 7ý,, -- Fig. 3.101. Controlla
Page 444 and 445:
Photoelectric Converters In a photo
Page 446 and 447:
of 140 W with allowance for all los
Page 448 and 449:
Radiator coolers are divided into s
Page 450 and 451:
2 A Fig. 4.2. A conical flexible un
Page 452 and 453:
Folding conical, radiators. As seen
Page 454 and 455:
* ,. I- ] 2 : I KEY: ()aA (V)w °+
Page 456 and 457:
point does not exceed the temperatu
Page 458 and 459:
The subscript "cep" e ~'~;+ f~dx. 0
Page 460 and 461:
-- - ' P l -- u -A - a .' • U1 1.
Page 462 and 463:
AL Fig. 11.11. Determining thermal_
Page 464 and 465:
In the cross section of pipes and r
Page 466 and 467:
o> . .. Fig. 4.14. Stress diagrams
Page 468 and 469:
1 I I I Thermal stresses in a a, fl
Page 470 and 471:
We shall use Hooke's law for a two-
Page 472 and 473:
i.e., the plate bends along a spher
Page 474 and 475:
then "- D(0 + ) B& 3 ( +,u) aAt EAh
Page 476 and 477:
Then instead of At(z) we shall writ
Page 478 and 479:
Heat exchangers in which the heat t
Page 480 and 481:
which is done by introducing into t
Page 482 and 483:
-.............. . a U-shaped jacket
Page 484 and 485:
The mechanical strength of heat exc
Page 486 and 487:
All the welding seams on the pipes
Page 488 and 489:
I I! .jn the design of a heat excha
Page 490 and 491:
.The following types of corrosion a
Page 492 and 493:
To •clean lithium q the oxygen an
Page 494 and 495:
t I * I where p is the permissible
Page 496 and 497:
Additional tensile (compressive) st
Page 498 and 499:
Calculation formulas are valid unde
Page 500 and 501:
The compliance parameter is determi
Page 502 and 503:
-KI 1- SI ' 2I -log VJ L0 Fig. 4.38
Page 504 and 505:
Case 3. The shell is loaded simulta
Page 506 and 507:
The value of n for thin cylindrical
Page 508 and 509:
In the general case, critical time
Page 510 and 511:
when ).
Page 512 and 513:
Axial displacement of compensator:
Page 514 and 515:
CHAPTER V MOTORS 5.1. PLASMA MOTORS
Page 516 and 517:
Pulsed pinch plasma motor This inot
Page 518 and 519:
In the plasma generator unit the ev
Page 520 and 521:
If an external magnetic field is cr
Page 522 and 523:
forces Fig. 5.5. acting Simplified
Page 524 and 525:
Z I . . .. . . Pulsed plasma face-t
Page 526 and 527:
The grain of the working medium is
Page 528 and 529:
J 4J 0 0 514 ~
Page 530 and 531:
I I Forces T e, while acting normal
Page 532 and 533:
where D - 12 "). Let us return to e
Page 534 and 535:
It is significant also that when n
Page 536 and 537:
where B is a coefficient; n is the
Page 538 and 539:
Bend w is an elastic bend of the sh
Page 540 and 541:
Thus, a linear law of temperature g
Page 542 and 543:
;' -- e--- 1= - (20MO cosVxJr- Q 0
Page 544 and 545:
Table 5. 1. 3x __ _ _ V I '0 I ! 0
Page 546 and 547:
Hence generalized stress is SV2= f
Page 548 and 549:
Let us 3train a free shell loaded w
Page 550 and 551:
tt Solution is sought from formula
Page 552 and 553:
The value of wp is found from formu
Page 554 and 555:
We determine 1.29 1.29 D' Eh3 1,45
Page 556 and 557:
Table 5.2. CT- p ,INI'•I.R 1. po-
Page 558 and 559:
. sin ir P ( 2P2C 4 ) + eP cos ,x (
Page 560 and 561:
,_ . l90 _. h-ID NI -rcz Lit 'w. a)
Page 562 and 563:
Computation of w'" is made in ,line
Page 564 and 565:
Table I 5.3. (2(2) (1 l10 _ _ _ _ _
Page 566 and 567:
We integr'ate this equation once mo
Page 568 and 569:
Table 5.4. _ _ _ () Kit)I ) (3) ( U
Page 570 and 571:
These formulas show that on the fre
Page 572 and 573:
pR _prtgii h (5.39) where R is the
Page 574 and 575:
K i... Linear shearing forces, obta
Page 576 and 577:
1.1: deformation correspondz to-the
Page 578 and 579:
The assumed law of At enables us to
Page 580 and 581:
'I Thus, the solution to the nonhom
Page 582 and 583:
The diagram of the shell is shown i
Page 584 and 585:
Tne z?.ell dimension~, in our probl
Page 586 and 587:
Stresses in a circular diret.ion or
Page 588 and 589:
w lW 2- W- =--, (); r- '=r g "I ; r
Page 590 and 591:
I, * I I Suzt-ttuting conditions (5
Page 592 and 593:
-7 The obtained equation is a homog
Page 594 and 595:
PRINCIPAL AND OF MOTORS STRUCTURAL
Page 596 and 597:
The ionizer unit consists of the io
Page 598 and 599:
-ii 4 I medium 6 and heater 7. The
Page 600 and 601:
!8 41 C Fig. 5. 37. The positive io
Page 602 and 603:
Soldering the porous plate with the
Page 604 and 605:
I I I . 1 2 Fig. 5.39. Design of io
Page 606 and 607:
i,, 1B) 6".R1 Fig. 5.41. Plate elec
Page 608 and 609:
electrons from the cathode and then
Page 610 and 611:
Stress analysis of motor elements A
Page 612 and 613:
A- Fig. 5.47. Motor unit design. 4z
Page 614 and 615:
Let us project all forces acting on
Page 616 and 617:
I- (' l1dx dy '-7dx =0; Ox=O Rý tg
Page 618 and 619:
I The quaotity Scx consists of thre
Page 620 and 621:
The angle of shift is the variation
Page 622 and 623:
V Iv Yvox a, R&tgo Ox Oy z 2Ow+ 2 0
Page 624 and 625:
7 3- h 2 h 2 iY dz; 1Y=- -h'2 -h 2
Page 626 and 627:
F 2Ea / 2r 3 + a3 , A G _ L(aa3) 0
Page 628 and 629:
I dimension r, dr. We apply to the
Page 630 and 631:
We drop • from equations (5.86) -
Page 632 and 633:
1-IL'L + z A. 2 o,-1_€ ('~-1,2-lm
Page 634 and 635:
Function F(r) can be found from the
Page 636 and 637:
We integrate this equation twice. T
Page 638 and 639:
Here A 1 = (2)/(3,)(z + 1)(z + 3);
Page 640 and 641:
- Absolutely flexible membrane If a
Page 642 and 643:
2500- 2000 1500 -/ 1000 Y - 500 4j-
Page 644 and 645:
Movement of the bellows also depend
Page 646 and 647:
Is The coefficient kla! calculated
Page 648 and 649:
Fig. 5.65. Stress analysis of a bel
Page 650 and 651:
Table A.l. Mechanical properties of
Page 652 and 653:
.(ii (2) A, 6r,/M,.ajpa £'40- 6 dH
Page 654 and 655:
A shortcoming of graphite is the no
Page 656 and 657:
0 (1) (2) 40 6-16- i!• 2 [K1/MM 2
Page 658 and 659:
E ( dafi/MM 1 2 U) 2_ou . Iv 5000 1
Page 660 and 661:
I I I3 Table A.3. (Continued)' (1a)
Page 662 and 663:
Table A.11. Characteristics of niob
Page 664 and 665:
Table A.5. Mechanical properties of
Page 666 and 667:
Tungsten and its alloys Figure A.16
Page 668 and 669:
, - ,, I Table A.8. Modulus of elas
Page 670 and 671:
Bibliography 1. A it;ý' Ip e e Bn.
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Design and Stress Analysis of Extraterrestrial ... - The Black Vault

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