, , . . , - ,
ri = m × zi / 2.
. . 15.1. , - . - , - . , , .
( ) : ( , .
. , :
, :
- ()
- .
.
. 16.1
- :
5%,
u1h = [ 1+ (z2 × z4)/(z1 × z3) ] × (0.95... 1.05).
- :
( ) ( ),
awI = awII ; awI= rw1 + rw2 = r1 + r2 ; awII = rw4 - rw3 = r4 - r3.
, xi = 0 rwi = ri = zi × m / 2.
r1 + r2= r4 - r3 Þ mI (z1 + z2) = mII × (z4 - z3).
|
|
, mI = mII = m,
z1 + z2 = z4 - z3 |
- ( k > 1):
aw.
,
max (da2,3 ) < lB2B3.
(ha*= 1, x2,3 = 0, 2 D y = 0)
max (da2,3 ) = max [(z2,3 + 2 × ha* +2 × x2,3 - 2 D y) × m ] = max[(z2,3 + 2) × m ].
lB2B3 = 2 × aw × sin (jh / 2) = 2 × (r1 + r2) × sin (p / k). = (z1 + z2) × m × sin (p / k).
max [(z2,3 + 2) × m ] < (z1 + z2) × m × sin (p / k).
sin (p /k) > max [(z2,3 + 2)/ (z1 + z2) ] |
- k > 1:
:
, - 1. , z1 z4 . , j h z1 . z1 z4 , .
Þj h= 2 × p / k
Þt 1 = 2 × p / z1
j h
j 1 = j h × u1h Þj 1 = 2 × p × u1h / k
t 1 j 1 Þ B = j 1 / t 1, B - .
B
2 ×p× u1h × z1 / (k × 2 ×p ) = B Þ
u1h × z1 / k = B. |
j h p ,
j h= 2 ×p / k + 2 ×p× = 2 ×p / k (1 + k × ).
, :
u1h × z1 / k (1 + k × ) = B. |
- :
, zi > zmin.
- :
, ,
z . . > 20, z . . > 85,zd = z . - z . . > 8. |
- .
R
R = min [ max (z1 + 2 × z2 ), (kK × z4) ], kK - , .
, , - . ( 1, 2, 5 6). . . , .
|
|
u14 h = (z2 × z4)/(z1 × z3) =[ u1h / (0.95... 1.05) - 1] = (B × D)/(A × C).
u14 h - A, B, C D. A z1 , B - z2 , C - z3 D - z4. , (B × D) / (A × C) u14 h.
B / A = z2 / z1 = 1... 6 - ,
D / C = z4 / z3 = 1.1... 8 - .
:
z1 + z2 = z4 - z3
a× (A + B) = b× (D - C).
, a b
a = (D - C), b = (A + B),
.
:
z1= (D - C) × A × q, z3= (A + B) × C × q,
z2= (D - C) × B × q, z4= (A + B) × D × q.
q - , 5 6.
, , 1, 2, 5 6. 3 () 4 () , . , 7. , R.
1. .
: , u1h = 13, k = 3.
: zi -?
:
u14 h = (z2 × z4) / (z1 × z3) = [ u1h / (0.95... 1.05) - 1] = 12 = (B × D)/(A × C) = 3 × 4 / (1 × 1) = 2 × 6 / (1 × 1)= 4 × 3 / (1 × 1) =...
:
z1= (D - C) × A × q = (4 - 1) × 1 × q = 3 × q; z1= 18 > 17;
z2= (D - C) × B × q = (4 - 1) × 3 × q = 9 × q; q = 6; z2= 54 > 17;
z3= (A + B) × C × q = (3 + 1) × 1 × q = 4 × q; z3= 24 > 20;
z4= (A + B) × D × q = (3 + 1) × 4 × q = 16 × q; z4= 96 > 85;
:
sin ( p / k) > max [(z2,3 + 2)/ (z1 + z2) ]
sin ( p / 3) > (54 + 2)/(18+54)
0.866 > 0.77 - .
:
(u1h × z1 / k) × (1 + k × p) = B;
(13 × 18/3) × (1 + 3 ) = - p.
. , !
R = (18 + 2 × 54) = 126.
:
z1= (D - C) × A × q = (6 - 1) × 1 × q = 5 × q; z1= 45 > 17;
z2= (D - C) × B × q = (6 - 1) × 2 × q = 10 × q; q = 9; z2= 90 > 17;
z3= (A + B) × C × q = (2 + 1) × 1 × q = 3 × q; z3= 27 > 20;
z4= (A + B) × D × q = (2 + 1) × 6 × q = 18 × q; z4= 162 > 85;
:
sin ( p / k) > max [(z2,3 + 2)/ (z1 + z2) ]
sin ( p / 3) > (90 + 2)/(45+90)
0.866 > 0.681 - .
|
|
:
(u1h × z1 / k) × (1 + k × ) = B
(12 × 45 / 3) × (1 + 3 ) = - .
!
R = (45 + 2 × 90) = 225.
:
z1= (D - C) × A × q = (3 - 1) × 1 × q = 2 × q; z1= 18 > 17;
z2= (D - C) × B × q = (3 - 1) × 4 × q = 8 × q; q = 9; z2= 72 > 17;
z3= (A + B) × C × q = (1 + 4) × 1 × q = 5 × q; z3= 45 > 20;
z4= (A + B) × D × q = (1 + 4) × 3 × q = 15 × q; z4= 135 > 85;
:
sin ( p / k) > max [(z2,3 + 2)/ (z1 + z2) ]
sin ( p / 3) > (70 + 2)/(18+72)
0.866 > 0.8 - .
:
(u1h × z1 / k) × (1 + k × ) = B
(13 × 18/3) × (1 + 3 ) = - .
.
R = (18 + 2 × 72) = 162.
. .
2. .
. 16.2 | : , u1h = 7; k = 3.: zi -?. |
. 17 u1h k.
:
z1 = 18 > 17.
:
u1h = (1 + z3 / z1 ) × (0.95... 1.05)
z3 = [u1h / (0.95...1.05) - 1] × z1
z3 = [ 7 / (0.95...1.05) - 1] × 18 = 108
:
z1 + z2 = z3 - z2
z2 = (z3 - z1) / 2 = (108 - 18) / 2 = 45
:
sin ( p / k) > max [(z2 + 2)/ (z1 + z2) ]
sin ( p / 3) > (45 + 2)/(18+45)
0.866 > 0.73 - .
:
(u1h × z1 / k) × (1 + k × ) = B
(7 × 18/3) × (1 + 3 ) = .
, z1
, .
3. .
. 16.3 | : , uh1 = -24; k =3.: zi -?. |
:
u1h= 1 / uh1
u14 h = (z2 × z4)/(z1 × z3) =[ 1 - u1h / (0.95... 1.05) ] = 25/24 = (B × D)/(A × C) = 5 × 5 / (4 × 6) = 5 × 5 / (6 × 4)= 25 × 1 / (12 × 2) =...
:
z1 + z2 = z4 + z3
:
a× (A + B) = b× (D + C).
a b:
a = (D + C), b = (A + B).
:
z1= (D + C) × A × q = (1 + 2) × 12 × q = 36 × q; z1= 36 > 17;
z2= (D + C) × B × q = (1 + 2) × 25 × q = 75 × q; q = 1; z2= 75 > 17;
z3= (A + B) × C × q = (12 + 25) × 2 × q = 74 × q; z3= 74 > 17;
z4= (A + B) × D × q = (12 + 25) × 1 × q = 37 × q; z4= 37 > 17;
:
sin ( p / k) > max [(z2,3 + 2)/ (z1 + z2) ];
sin ( p / 3) > (75 + 2)/(36+75)
0.866 > 0.694 - .
|
|
:
(u1h × z1 / k)? (1 + k × ) = B;
[18 / (-24 × 3)] × (1 + 3 ) = - =1.
. , .
R = (36 + 2 × 75) = 186.
, , , .
4. .
. 16.4 | : , u1h = 55; k = 2.: zi -?. |
:
u1h= 1 / uh1;
u14 h = (z2 × z4)/(z1 × z3) =[ 1 - u1h / (0.95... 1.05) ] = 54 / 55 = (B × D)/(A × C) = 6 × 9 / (11 × 5) = 18 × 3 / (55 × 1) =...
:
z1 - z2 = z4 - z3
:
a× (A - B) = b× (D - C)
a b:
a = (D - C), b = (A - B)
:
z1= (D - C) × A × q = (3 - 1) × 55 × q = 110 × q; z1= 110 > 85;
z2= (D - C) × B × q = (3 - 1) × 18 × q = 36 × q; q = 1; z2= 36 > 20;
z3= (A - B) × C × q = (55 - 18) × 1 × q = 37 × q; z3= 37 > 20;
z4= (A - B) × D × q = (55 - 18) × 3 × q = 111 × q; z4= 111 > 85;
:
sin ( p /k) > max [(z2,3 + 2)/ (z1 + z2) ]
sin ( p /2) > (37 + 2)/(110 - 36)
1.0 > 0.527 - .
:
(u1h × z1 / k) × (1 + k × ) = B;
[110 / (55 × 2)] × (1 + 3 ) = - .
. , .
R = (1.2 × 111) = 133.2, kK = 1.2.
, , , .
. , . ( ) - . (, ), . .
():
. , . , .
. (.16.5).
. 16.5
z2 z1
(w1 - wh) / (w2 - wh) = - z2 / z1
z4 z3
(w2 - wh) / (w3 - wh) = z4 / z3 .
, ,
[(w1 - wh) / (w2 - wh)] × [(w2-wh)/ (w3-wh)] = - z2 × z4 / (z1 × z3)
(w1 - wh) / (w3 - wh) = - z2 × z4 / (z1 × z3) = u13(h)
u13 (h) × w3 - u13 (h) × wh = w1 - wh
w1 - (1 + u13 (h)) × wh - u13 (h) × w3 = 0 |
, (, ) . , , . .16.6.
|
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. 16.6
16
1. ?(.1)
2. , (.1)
3. >2 (.2-3)
4. ? (.3)
5. (.4-6)
6. ?(.9-10)