1. = α β υ. , . 8.3. υ = π*d2*n2/60 ≈ 3,49 /; ( > 350 ), (8) , . :
υ = 1,15;
= 1,18*1,3*1,15 = 1,76.
2. :
εα = (0,951,6*(1/z1+1/z2))*(1+sβ)*sβ
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ZHβ =√ s2β/εα
, :
εα = (0,951,6*(1/60+1/160))*(1+s 8)*s 8 = 1,76
______________________________________ _
ZHβ =√0,99022/1,76 = 0,75
3. .
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σ = 1,18*ZHβ*√*1*/(d2w1*bw*sin2αw)*((u+1)/u)
αw ≈ α = 20 dw1 ≈ d1 :
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σ = 1,18*√2,1*105*138*103*1,76/(602*27*sin(2*20))*((2,7+1)/2,7) = 1048
> 1016 ;
: ([σ] σ)/[σ]*100% = 3%, . , [σ] σ.,
.
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σHmax = σH*√T/Tmax ≤ [σH]max
T = * Tmax. = 2,2, Tmax = 1 = 361*103 :
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σFmax = σF*T/Tmax ≤ [σF]max
, :
σFmax = 550*2,2*361*103/361*103 =1210 < 1430.
.
.
Ft = 2*T2/d2;
: Fa = Ft*tgβ;
: Fr = Ft*tgαw/cosβ;
, :
Ft = 2*361*103/160= 4523;
Fa = 4523*tg8 = 635,7 ;
Fr = 4523*tg20/cos8 = 1662 ;
.
.
1. [τ] = 12 ( .315 ):
_________________________ _____________________________________________
d = 3√T2/(0,2[τ]) = 3√361*103/(0,2*[12]) =53 ;
2. , .1, :
- d = 55 ;
- d = d 5 = 50 ;
- l = 160 ; la = lb = 80 ; = 160 .
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3. , , :
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FM = 125√T2 = 125*√361= 2375 .
4. :
- Ft2 = 2*T2/d2;
- : Fa2 = Ft2*tgβ;
- : Fr2 = Ft2*tgαw/cosβ;
, :
Ft2 = 2*261*103/160= 4513;
Fa2 = 4513*tg8= 634H;
Fr2 = 4513*tg20/cos8 =1658 ;
5. .
.
ΣF = 0; R + R Fr2 = 0;
ΣM = 0; R*l +Ma Fr2*la = 0;
= Fa2*d2/2; 2 R = (Fr2*la Fa2*d2/2)/l; 1 R = Fr2 R;
.
ΣF = 0; R + R Ft2 = 0;
ΣM = 0; R*l Ft2*la = 0;
2 R = Ft2*la/l; 1 R = Ft2 R;
.
ΣF = 0; R R F = 0;
ΣM = 0; R*l F *(l + ) = 0;
2 R = F *(l + )/l; 1 R = R F;
, :
R = (1658*80 634*361/2)/160 = 113,8 ;
R = 1658113,8 = 1544 ;
R = 4513*80/160 = 2257 ;
R = 4513 2257= 2257 ;
= 634*361/2 =114437;
R =2375*(160+160)/160 = 4750 ;
R = 4750 2375 =2375 .
6. ( ).
______________________________ ________________________________
R = √R2 + R2 + R = √15442 + 22572 + 2375 = 5109 ;
_______________________________ _________________________________
R = √R2 + R2 + R = √113,82 + 22572 + 4750 =7009 .
7. . : 1-1 , , 2-2 , .
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1-1 = √2 + 2 = √(Fr2*la*lb/l + Ma* la/l)2 + (Ft2*la*lb/l)2 + F**l/l
σ = 1-1/(0,1*d3);
τ = 2/(0,2* d3);
σ-1 = 0,4*σ;
τ-1 = 0,2*σ;
τ = 0,6*σ.
, :
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1-1 = √( 1658*80*80/160 + 114437*80/160)2 + (4513*80*80/160)2 + 2357*160*80/160 = 407304,7 *;
σ = 407304,7 /(0,1*603) = 18,9 ;
τ = 361*103/(0,2* 603) = 8,4 ;
σ-1 = 0,4*1600 = 640 ;
τ-1 = 0,2*1600 = 320 ;
τ = 0,6*1600 = 960 .
σD KτD. 1-1 : . σ/dσ = K1*K2*K3, 1 = 0,38 + 1,48*lgdk, 2 = 0,305 + 0,0014*σ, 3 = 0,65 + 0,014* ( = 15 ). dσ = 0,5*(1 + (d/7,5)-2ν), ν = 0,19 -1,25*10-4*σ.
, :
1 = 0,38 + 1,48*lg55 = 2,95;
2 = 0,305 + 0,0014*1600 = 2,5;
3 = 0,65 + 0,014*15 = 0,86;
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σ/dσ = 2,95*2,5*0,86 = 6,3;
ν = 0,19 1,25*10-4*1600 = -0,01;
dσ = 0,5*(1 + (55/7,5)-2*0,08) = 0,5.
σ = σ/dσ*dσ = 6,3*0,5 = 3,15. , ( . 15,2 ) σ = 2,2. σD σ, .. 3,15. Fσ = 1 0,22*(lg σ/20 1)*lgRz, Rz = 3,2 . V = 1 . σD = (σ/dς + 1/Fσ -1)/ V. , :
Fσ = 1 0,22*(lg1600/20 1)*lg3,2 = 0,89;
σD = (6,3 + 1/0,89 -1)/1 = 6,4.
1-1 .
τ/dτ ≈ 0,6*σ/dσ, Fτ = 0,575*Fσ + 0,425, τD = (τ/dτ + 1/Fτ -1)/ V , :
τ/dτ ≈ 0,6*6,3 = 3,78;
Fτ = 0,575*0,89 + 0,425 = 0,93;
τD = (3,78 + 1/0,93 1)/1 = 3,85.
, . ψσ = 0,02 + 2*10-4*σ = 0,02 + 2*10-4*1600 = 0,34; ψτ = 0,5*ψσ = 0,5*0,34 = 0,17; σ = σ =19,8 ; τ = τm = 0,5*τ = 0,5*8,4 = 4,2 .
(σm = 0):
Sσ = σ-1/(σD*σ + ψσ*σm) = 640/(6,4*19,8 + 0,34*0) = 5,1;
:
Sτ = τ -1/(τD*τ + ψτ*τm) = 320/(3,85*4,2 + 0,17*4,2) = 18.9;
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S = Sσ*Sτ /√S2σ + S2τ ≥ [S] ≈ 1,5
________________________________
S = 5,1* 18,9 /√5,1 2 + 18.92 = 4,92 > [S] ≈ 1,5
= FM*c = 2357*160 = 377120 *;
σ = /(0,1*d3); σ = 377120/(0,1*503) = 30,2 ;
τ = 2/(0,2* d3); τ = 361*103/(0,2* 503) = 14,4 ;
r = 1,25 . 15.1 t/r = (55 50)/(1,25*2) = 2 r/d = 1,25/50 = 0,02 σ = 2,0; τ = 1,65.
"dσ = 0,5*(1 + (d"/7,5)-2ν) = 0,5*(1 + (50/7,5)-2*0,08) = 0,5.
"dτ = 0,5*(1 + (d"/7,5)-1,5*2ν) = 0,5*(1 + (50/7,5)-2*1,5*0,08) = 0,501.
"σD = (σ/dς + 1/Fσ -1)/ V = (6,3+ 1/0,89 1)/1 = 6,42.
"τD = (τ/dτ + 1/Fτ -1)/ V = (3,78 + 1/0,93 1)/1 =3,85.
S"σ = σ-1/(σD*σ + ψσ*σm) = 640/(6,42*19,8 + 0,19*0) = 5,03;
S"τ = τ -1/(τD*τ + ψτ*τm) = 320/(3,85*14,4 + 0,17*14,4) = 5,52;
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S = Sσ*Sτ /√S2σ + S2τ ≥ [S] ≈ 1,5
________________________________
S = 5,03*5,52 /√5,03 2 + 5,52 2 = 3,7 > [S] ≈ 1,5
.
7. . [σ] ≈ 0,8*σ = 0,8*1400 = 1120 ; σ = 2*σ = 2*30,2 = 60,4 ; τ =2*τ =
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2*14,4 = 28,8 . σ = √(σ)2 +(τ)2 = √60,4 2 + 28,82 = 66,9 < [σ] = 480 . .
8. . . . 15.2 . l d = 55 .
J = π*d4/32 = 3,14*554/32 = 89,8*104 4.
:
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- Fr: = Fr*l2*l2b/(3**J*l) =1662*804/(3*2,1*105*89,8*104*160)=0,00075 ;
- = 0.
:
- Ft: =Ft*l2*l2b/(3**I*l) = 4523*804/(3*2,1*105*89,8*104*160)=0,002 .
:
- FM: = FM**la*(l2 a2)/(6**I*l) = 2357*160*80*(1602 802) /(6*2,1*105*89,8*104*160) = 0,0032 .
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: = √2 + 2 + = 0,0011, [] = 0,01*m = 0,01*1 = 0,01 > 0,0011 .