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

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pR _prtgii h (5.39) where R is the shell's radius of curvature. P I I I 00 Fig. 5.28. Determining the Fig. 5.29. Equilibrium of a, axial force of a "conical shell." shell element. Membrane stresses ar and a are the reason foi' the appearance of deformation. The greatest stresses a lead to shell deformation in a radial direction: pr % R 2 5 401 ) B! tg ~ .( Radial displacements toward an increase in-the shell's radius' of curvature R are assumed positive. Pressure p acting on the internal surface of the shell from the center to the periphery is also assumed positive. As in a cylindrical shell, we express al' strains and internal forces in terms of full radial displacements of w. Thus, the relative deformation in a circular direction is' 55 rtgf 558
Squrvature variation along the generatrices is d 2 tL' * dr 2 Curvature variation in a circular direction, connected with the variation in the shell's radius of curvature R because of a turn of the elements by angle dw/dr, I dw "r dr Theilast expression is derived in the following manner. initial curvature of the shell in a circular direction is 1/R = 1/r Ug 0. Due to the turn of the generatrix by angle dw/dr, the rad.us of curvature acquires a new value: The rsinOrsInO ; dw cos~+Cos 0 dr fi hence t•he variation in curvature is : ~~~~k ;-•--=. 1 Idw . S RHoU R r dr pi We shall disregard the curvature varia tion because of dplacm,,r~t I Full circular normal stresses are i rtgO0 linear bending momenrts are D , +k) D j AI&=D (kv+ jikrj=L?[ i (5. ..15 * I
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FTD:-MT-24-1462-71 FOREIGN TECHNOLO
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tUNCLASSIFIED - Security Ct-9-1uifl
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t IABLE OF CONTENTS U. S. Board on
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5.2. Ion motors ...................
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II jah _X JOLIGAETECbtSODN USA N NL
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,.is the calculation Of thermal str
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S1 In stress analysis the calculati
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"I 3 f !7 2 II 3 I 44; a ' 3 I 4 2
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)I requires special protection of t
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electrical power of the power insta
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Extraterrestrial motors in power fr
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S1' , . that a part operatesbefore!
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Fig. 1.3. Diagram of an ERE with me
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Table 1.3 shows the working media,
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I I The schematic of a nuclear ther
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Fig. 1.5. converter. Diagram of an
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The advantage of this arrangement i
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A complex system or any part of it,
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I I Stages and content of operation
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'the use of earlier systems and uni
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Structural diagram of operations Th
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. . . . . __.. . . . . .. .. . . .
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-- indication of state, transmissio
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Stages ERE, I. Analysis of the tech
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Space vehicle (SV) jParts jettisone
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Spc veil (SV)!- 0 4. ho 0. 4)Z - H4
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~tto 4- jo 0o (utd~nb 'Sa vtho- 4)i
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'Li However, 'this list can be chan
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- S developed. Or course, there are
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Sthat From the design and operation
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As the number or tests builds up-an
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II P 'Po. = -ý SFig. 1.20. Curves
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Stress is the intensity of the inte
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strength criterion only when even s
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JV Strength- reserve is the ratio o
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'2 1 I III I, . - I - S We know tha
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i J However, when the operating tim
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Plastic deformations in the latter
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Let us examine the basic design rel
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I I The constants B and n are deter
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Along with equation (1.18) we use e
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Iftesting continues, as shown in Fi
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I I Based on the known deformation
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6%Fx (a) Fig. 1,31., Uniaxial (a) a
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The element is in plastic state (1
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Total operating time of the sample
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I:! Substituting expression (1.35)
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Function B(T) is found after determ
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first We shall express stresses in
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etween it and the stressed state of
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a) b) c) Fig. 1.36. Determining the
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other conditions being equal, the c
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The fuel elements also rest on a li
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As the reflector and moderator in t
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Let us examine the examples of weld
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Between these shells passes a fluid
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The procedure for welding a two-lay
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A fuel element is a closed pressuri
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1 2A S(a) II • • /Fig. 2.8. Con
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The reflector material 5 (beryllium
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Figure 2.12 is a sketch of a fast n
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I. ! ~ ~~. . ........... li .... I
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I jZ ICIS qo 'Im klol
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THERMAL STRESSES IN FUEL ELEMENTS T
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Ora-O"when r=a; when r=b. (2.8) Sub
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I The exponential logarithmic depen
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I I of the cylinder between two adj
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EuI~, 21,2 Eat, • bb 2-(1 ---xInb
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-a - Fig. 2.18. Thermal stresses in
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I a It is necessary that n > 1l. If
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The locus of points equidistant fro
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Equations of equilibrium for an axi
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Fig. 2.23. Equilibrium of a shell e
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:I I I I The first equilibrium equa
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The wall stress of this sphere is d
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I These formulas enable us to plot
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. . . S_.. I i. stresses. Maximum i
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Shells in the reactors which we sha
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axial stresses. Simplicity fully Ju
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abl-ab (R+AR)d-•Rdf AR ab Rd? R (
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V 1! II Point 3 corresponds to the
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SI Now we seek the pressure of the
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!I As is apparent from Fig. 2.39, t
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I I I I '' 9 capacity of a shell in
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SI a i f fit~ Z.rl -= •.r nl--~ ~
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We plot the unknown curve p = f(AR)
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-.. -, 7 ''°-^ ...... I}" L7,50s.
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I" Table 2.2. (Cont d) (1) V(. )3 (
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W/ dr (2.48) "The sign is negative
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Ve designate th6 relaitie -momenits
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a a I a A4l "• dr; P= pr dr idy;
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'(2.61) or in shortened form, V 2 V
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4i In this case, the constant C2 in
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will be If the external force is co
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I W -P [(a2 -I a +(•1 -r2)In a ("
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+) If we find that Wmax • h, the
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I I W c I , I- a , I. ' We cut the
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- (0,,i66.0,239. 10-6-0,484.0,33. 1
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-n I I I I Pig, 2.56. Determining t
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In some cases, it is assumed that t
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6e, I Smat a a SI r.+0P6h2a .. 'fro
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In designing a source it is necessa
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removal, for example, in a containe
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- 2d I I I ______ -. - I 2o ( 'I Z
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Ir dp;- N,= N, .(-N,,lr d$ + d (3,I
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It is perfectly obvious that the el
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dr dr, dMr, dr2 d, d2or 1 3 dr dr "
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I ! i I I The quality of the device
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The mirror surface, in this case, i
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Fig. 2.69. Thermal trap with contro
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i ffased on this factor, fuel eleme
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In extremely small pores (pore c) t
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why fuel elements with a solid elec
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Peazeemnl (l) Fig. 2.73. A regenera
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I. II As a result' of the- process,
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'4I '21
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U k IIl + (n2lpiim)() Fig. 2.78. Co
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I I I I Figure 1.3 shows one of the
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• C a is the axial velocity of th
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Figure 3.1 shows working blades of
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Fig. 3.11. Union of disk with shaft
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I *1 warping, the material of the h
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(a) (b) Fig. 3.6. Dry-fri'ction bea
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ing groove, and through the incline
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I '' S Albng with the variation in
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Friction and wear in such a bearing
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The transition from the oversaturat
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O a) CO- 4) U'% 0 4Z Oo .~ 0 t'24a)
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I _____ ', "I I The Na-K pump consi
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E- W2l.i rx.
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w is the angular velocity of disk r
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; I ' | * * I I j I l7 I II I' *
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and, finally, dPa 2.ir( 2r a dr z z
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Flexural stresses at any point' of
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Another means of unloading consists
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0 I I I In cae wetakii CO/7eHU~e *1
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Determining the frequencies of inhe
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Differentiating this equation, we f
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Equation '(3.?5) is a differentiale
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Functions S, T, U and V during diff
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1 JVQP (3.30') Fig. 3.24. Forms of
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Then the bendinv moment is t ! ! EI
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'!..... " - ;-~ .- .-.. ~ - - J I T
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Figure 3.25 shows the operation of
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2 I ' whe, For plottfng the donvert
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satisfies the bounaary conditions o
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- o0 CC 0 CL P% c - t- -. C4 t C Ci
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The angular velocity w Aof natural
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I. Each of the harmonics of the ang
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At each of the points of interse-ti
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The actual frequency of natural ben
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1 I i , II ' t S S "•< i, I S, 3.
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(In view of the smallness of angle
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dr dr r d• _._._.• .d~t 1 •t-
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7WI - For conical disks equation (3
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Hyperbolic disks. If the, thickness
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o•/. or Oer 17,0 5,0 16,0-2 4,5 5
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- 0CX=, 9 - 280- 270- 110 0,15 __ -
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11 0,7 2,- 7,5 - '2,4- a'l 0,5 02 0
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55- . \, 105 50-100 45 ' 95 S85 "J
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Let us examine two cases: disk) and
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4. 100 0,6- WoO, ~: 1 0,94 493,8 3,
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0,7 3,3 -3,3 0,6 -3,2 0,15 3,0 2,9
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f~rc 200 -PC.; 190 40 170 30 I/t 0,
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a) arB 0 if the disk does not bear
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I I I I II I , Substituting this so
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Z= lz 1 x _-, 9 S1- 0,TF,1 o~ 5o o
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ii 0,1 42 0,3 ,4 0,50q6 0,7 08 0,9
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The expression for a* is obtained f
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, The'actual stresses on the bounda
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ý4.1 j L. - - c* m oc ~ .7 lira___
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C,4 C4C4 I IC4) CI tz +3Il + + CC.)
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C.. C4 0 C4 C I -T I -J . C :.d C?3
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Widely used methods are those based
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Solving the last equation relative
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Substituting the difference (awl -
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0 g h•con- - o7 g , 0,7 .Op • o
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iJ relaxation) occurs and with stea
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In the examired theory during plast
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Let, us p w I I ! • Let, us proce
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Rupture sets in only when plastic f
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£@ 1 hdr .1 (o) hr r(3.102) Usuall
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I Since the shaft is elastic, then,
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I I SI hence r M! rad/s ,(3.104) de
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y ii y0 \ 1 0-1 H t ieemNw idn 5ai7
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Critical angular velocities- of a s
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We assume that the disk and shaft a
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Expanding the determinant of (3.113
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y=aP-P+a, 2 M; a 21aiP+a22M# (3.119
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(1) ((2) O~7~C.• o~P'7t7- A O6/UC
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Wihen X = w, forward synchronous pr
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we find For forward synchronous pre
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•+ , , ; Im• S, -I i I I- I' su
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When analyzing the natural frequenc
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Vz 7M 7 ' z (KR--K-) z z (R (3.137)
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The concept of forced vibrations. t
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Resonance modes can be shown on the
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' C Yon no'. ern12 •. -p. 4 a..(a
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I ~ I 'Existing methods of damping
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Vibrations in rotors on hydrostatic
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SQTi •-fT 1 (O,0625VI)Y+1-0, 1-(p
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During the forward speed of the piv
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~t The coefficients of hydraulic fr
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of forces in the absence of pivot v
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To solve the problem of the vibrati
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I I k i = Ib the projections of dis
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3 The general solution to (3.160) c
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(3.166) Thus, near the boundary of
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2 1z or 2.. .• .. :. • C .2,e.
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I 3.2. THERMOEMISSION ENERGY CONVER
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STRUCTURAL DIAGRAMS AND DESIGN OF C
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In the creation of the design serio
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I £ The nortcoming in this design
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'I, Fig. 3.92. Overall view of reac
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Figure 3.93 is a diagram of an elec
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We shall set up one of 'he shell se
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E3 e 2 , --e 1 , o A= B 3 , 0 --E 1
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worst efficiency. In the table the
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7,7 417 1 2 Fig. 3.96. Diagram of a
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A thermoelectric converter consists
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I 1A 7ý,, -- Fig. 3.101. Controlla
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Photoelectric Converters In a photo
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of 140 W with allowance for all los
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Radiator coolers are divided into s
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2 A Fig. 4.2. A conical flexible un
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Folding conical, radiators. As seen
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* ,. I- ] 2 : I KEY: ()aA (V)w °+
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point does not exceed the temperatu
Page 458 and 459:
The subscript "cep" e ~'~;+ f~dx. 0
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-- - ' 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-
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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
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which is done by introducing into t
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-.............. . a U-shaped jacket
Page 484 and 485:
The mechanical strength of heat exc
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All the welding seams on the pipes
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I I! .jn the design of a heat excha
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.The following types of corrosion a
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To •clean lithium q the oxygen an
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t I * I where p is the permissible
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Additional tensile (compressive) st
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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
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when ).
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Axial displacement of compensator:
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CHAPTER V MOTORS 5.1. PLASMA MOTORS
Page 516 and 517:
Pulsed pinch plasma motor This inot
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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 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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