,,,
- , , . . .
() , : , , , .
, , :
, ;
, , , , ;
, , ;
, ;
;
;
( 120 ./.) ( 200 ./.) , ;
, 360;
, .. ( ..).
, .
, , . "Wesscam" () 1 ( ), 2, 4 ( {}).
, , . . , , .. .
1, 2, 4 . -05. .
1 . (10 /) .
2 ( ). 30 /. , .
4 . 60 /., , , . .
, :
100 /;
c;
- .
, :
, ;
, ;
;
;
.
.
, , . , . [3] , . .
. , , . , .
, , .. , . , .
:
, , ;
.
, , , . , , [8,9], . .
.
+60...-80 ., .
.
- . . , - . .
, , , , . , . , . .
, , . .
. , , . , - 3 , , .
. , . . , , . , .
30 %. .
, .
.
- , .
, .
, . DERIVE.
.
.1.
X0,Y0,Z0 - .
X1,Y1,Z1 -
.
X2,Y2,Z2 - .
Qij - j- i-
.
wij - j- i- .
wij' - j- i- .
Ji - i-
.
Jij - .
Mij -
j- i- .
a - Y1.
a' -
Y1.
a'' - Y1.
b - Z2.
b' - . Z2.
b'' - Z2.
i- :
dQxi/dt - Qyiwzi + Qziwyi = Mxi
dQyi/dt - Qziwxi + Qxiwzi = Myi
dQyi/dt - Qziwxi + Qxiwzi = Myi
:
) :
dQy1/dt - Qz1wx1 + Qx1wz1 = My1
) :
dQx2/dt - Qy2wz2 + Qz2wy2 = Mx2
dQy2/dt - Qz2wx2 + Qx2wz2 = My2 (1)
dQz2/dt - Qx2wy2 + Qy2wx2 = Mz2
X1, Y1, Z1 :
Qx1 = Jx1wx1 - Jxy1wy1 - Jxz1wz1
Qy1 = Jy1wy1 - Jyx1wx1 - Jyz1wz1 (2)
Qz1 = Jz1wz1 - Jzx1wx1 - Jzy1wy1
X2, Y2, Z2 :
Qx2 = Jx2wx2 - Jxy2wy2 - Jxz2wz2
Qy2 = Jy2wy2 - Jyx2wx2 - Jyz2wz2 (3)
Qz2 = Jz2wz2 - Jzx2wx2 - Jzy2wy2
-, - .1, :
) :
wx1 = wx0cos(a) - wz0sin(a)
wy1 = wy0 + a' (4*)
wz1 = wx0sin(a) + wz0cos(a)
wx1' = wx0'cos(a) - wz0'sin(a)
wy1' = wy0' + a'' (4*')
wz1' = wx0'sin(a) + wz0'cos(a)
) :
wx2 = wx1cos(b) + wy1sin(b)
wy2 = wy1cos(b) - wx1sin(b) (5*)
wz2 = wz1 + b'
wx2' = wx1'cos(b) + wy1'sin(b)
wy2' = wy1'cos(b) - wx1'sin(b) (5*')
wz2' = wz1' + b''
2- (5*) , :
wy1=wx1tg(b)+wy2/cos(b)
2- (5*') , :
wy1'=wx1'tg(b)+wy2'/cos(b)
, , wy2, wz2, wy2', wz2' , .. , :
wx1 = wx0cos(a) - wz0sin(a)
wy1 = wx1tg(b)+wy2/cos(b) (4)
wz1 = wx0sin(a) + wz0cos(a)
wx1' = wx0'cos(a) - wz0'sin(a)
wy1' = wx1'tg(b)+wy2'/cos(b) (4')
wz1' = wx0'sin(a) + wz0'cos(a)
wx2 = wx1cos(b) + wy1sin(b) (5)
wx2' = wx1'cos(b) + wy1'sin(b) (5')
(2), (3) (1), :
Jy1wy1' + (Jx1-Jz1)wx1wz1 + Jzx1wx12 - Jxz1wz12 +
+ Jzy1wx1wy1 - Jxy1wy1wz1 - Jyx1wx1' - Jyz1wz1' = My1 (6.1)
Jx2wx2' + (Jz2-Jy2)wy2wz2 - 2Jzywy22 + Jyz2wz22 +
+ Jyx2wx2wz2 - Jzx2wx2wy2 - Jxz2wz2' - Jxy2wy2' = Mx2 (6.2)
Jy2wy2' + (Jx2-Jz2)wx2wz2 + Jzx2wx22 - Jxz2wz22 +
+ Jzy2wx2wy2 - Jxy2wy2wz2 - Jyx2wx2' - Jyz2wz2' = My2 (6.3)
Jz2wz2' + (Jy2-Jx2)wx2wy2 + Jxy2wy22 - Jyx2wx22 +
+ Jxz2wy2wz2 - Jyz2wx2wz2 - Jzx2wx2' - Jzy2wy2' = Mz2 (6.4)
(6.2), (6.3), (6.4) , (6.1) Y1. (6.1), (6.2), (6.3) A, B C, , :
My1 = A + B sin(b) + C cos(b) (7)
(7) A, B C y1.
y1=Jxz1{wx12-wz12}+
+Jxz2cos(b)wx22-Jyz2sin(b)wy22+
+{Jyz2sin(b)-Jxz2cos(b)}wz22+
+{Jyz2cos(b)-Jxz2sin(b)}wx2wy2+
+{Jxy2sin(b)+(Jx2-Jz2)cos(b)}wx2wz2+
+{(Jz2-Jy2)sin(b)-Jxy2cos(b)}wz2wy2+ (8)
+{Jx2sin(b)-Jxy2cos(b)}wx2' +
+{Jy2cos(b)-Jxy2sin(b)}wy2'-
-{Jxz2sin(b)+Jyz2cos(b)}wz2'+
+Jyz1wx1wy1-
-Jxy1wz1wy1+
+(Jx1-Jz1)wx1wz1 -
-Jxy1wx1'-
-Jyz1wz1'+
+Jy1wy1'
y1, Mz2 (4), (4'), (5), (5') , y1, Mz2:
MZ2={cos(2b)-2}cos(a)2tg(b)2Jxy2(wx02+wz02)+
+{2tg(b)2sin(b)2-2cos(b)2+4}sin(a)cos(a)Jxy2wx0wz0+
+{(Jy2-Jx2)/cos(b)-2Jxy2sin(b)(1+tg(b)2)}cos(a)wx0wy2+
+Jyz2wz0wz2(sin(a)-cos(a))/cos(b)-
-Jxz2wx0'cos(a)/cos(b)+
+{2Jxy2(sin(b)tg(b)2+sin(b))sin(a)+(Jx2-Jy2)sin(a)/cos(b)}wy2wz0+
+Jxz2wz0'sin(a)/cos(b)+
+{Jxz2-Jyz2}wy2wz2tg(b)+
+{(Jy2-Jx2)tg(b)+Jxy2(1-tg(b)2)}wy22-
-{Jxz2tg(b)+Jyz2}wy2'+
+Jz2wz2'
(9)
My1={[Jxz2(tg(b)4+2/cos(b)2-1)cos(b)3+Jyz1tg(b)+Jxz1]cos(a)2+
+[[(Jx1-Jz1)-Jxy1tg(b)]cos(a)-Jxz1sin(a)]sin(a)}wx02+
+{[[Jxy1tg(b)+(Jz1-Jx1)]sin(a)-Jxz1cos(a)]cos(a)+
+[Jxz2cos(b)3[2/cos(b)2+tg(b)4-1]+Jyz1tg(b)+Jxz1]sin(a)2}wz02+
+{(Jx1-Jz1)cos(2a)+[1-tg(b)4-2/cos(b)2]Jxz2cos(b)3sin(2a)-
-[Jyz1tg(b)+2Jxz1]2sin(a)cos(a)-
-Jxy1tg(b)cos(2a)}wx0wz0+
+{[Jxy2sin(b)cos(b)(tg(b)2+1)+(Jx2-Jz2)]cos(a)}wx0wz2+
+{[Jxz2sin(b)cos(b)+Jxz2sin(b)3/cos(b)+Jyz2]cos(a)+
+[Jyz1cos(a)-Jxy1sin(a)]/cos(b)}wx0wy2-
-{[Jxz2sin(b)cos(b)(1+tg(b)2)+Jyz2]sin(a)+
+[Jyz1sin(a)+Jxy1cos(a)]/cos(b)}wz0wy2+
+{-[tg(b)2+1]sin(b)cos(b)Jxy2+(Jz2-Jx2)]sin(a)}wz0wz2+
+{[Jx2sin(b)cos(b)(1+tg(b)2)+Jy1tg(b)-(Jxy1+
+Jxy2)]cos(a)-Jyz1sin(a)}wx0'+
+{[-Jx2sin(b)cos(b)(1+tg(b)2)+(Jxy1+Jxy2)-
-Jy1tg(b)]sin(a)-Jyz1cos(a)}wz0'+
+{Jyz2sin(b)-Jxz2cos(b)]wz22-
-{Jxz2sin(b)+Jyz2cos(b)}wz2'+
+{(Jx2-Jy2)sin(b)+Jxy2cos(b)(tg(b)2-1)}wz2wy2+
+{Jx2sin(b)2/cos(b)-2Jxy2sin(b)+Jy2cos(b)+Jy1/cos(b)}wy2'
.
(9) , 2.
.2.
:
Jx1 = -------//------ Jx2= 2000 2 = 0.2 2
Jy1 = 1500 2 = 0.15 2 Jy2= 9500 2 = 0.95 2
Jz1 = -------//------ Jz2 = 10000 2 = 1 2
Jxy1 = Jyx1 = 0 Jxy2 = Jyx2 = 0.0085 2
Jxz1 = Jzx1 = 0 Jxz2 = Jzx2 = 0.023 2
Jzy1 = Jyz1 =1500 2 = 0.15 2 Jzy2 = Jyz2 = 0.04 2
.
wx0 = 1 / wy2 = 2 /
wy0 = 1 / wz2 = 2 /
wz0 = 1 / wy2' = 3 /2 (10)
wx0'= 0,2 /2 wz2' = 3 /2
wy0'= 0,2 /2
wz0'= 0,2 /2
:
a = 2 . 120 . (10)
b = 1 . 60 .
MOMIN 1.
-:
1) ;
2) ;
3) ;
1) ,
.. :
wx0 = wy0 = wz0 = wx0' = wy0' = wz0' = 0 (11)
a 0; b 0; wy2 0; wz2 0; wy2' 0; wz2' 0
(11) (9), :
MZ2=+{Jxz2-Jyz2}wy2wz2tg(b)+
+{(Jy2-Jx2)tg(b)+Jxy2(1-tg(b)2)}wy22-
-{Jxz2tg(b)+Jyz2}wy2'+
+Jz2wz2'
MY1=+{Jyz2sin(b)-Jxz2cos(b)}wz22-
-{Jxz2sin(b)+Jyz2cos(b)}wz2'+
+{(Jx2-Jy2)sin(b)+Jxy2cos(b)(tg(b)2-1)}wz2wy2+
+{Jx2sin(b)2/cos(b)-
-2Jxy2sin(b)+Jy2cos(b)+Jy1/cos(b)}wy2'
, (10), :
) Y1: y1 = + = 5.68 + 0.14 = 5.82 .
a = 0.067 .
b = 1 .
wy2 = -2.0 /.
wy2' = 3.0 /2.
wz2 = 2 /.
wz2' = -3.0 /2.
- y1 , ;
- y1 , ;
:
=2.38 %
) Z2: z2 = + = 7.67 + 0.33 = 8.0 .
a = 0.067 .
b = 1 .
wy2 = 2.0 /.
wy2' = -3.0 /2.
wz2 = -2 /.
wz2' = 3.0 /2.
:
=4.2 %
2) ,
.. :
wy2= wy2'= wz2 = wz2' = 0; a 0; b 0; (12)
wx0 0; wy0 0; wz0 0; wx0' 0; wy0' 0; wz0' 0
(12) (9) :
MZ2={cos(2b)-2}cos(a)2tg(b)2Jxy2(wx02+wz02)+
+{2tg(b)2sin(b)2-2cos(b)2+4}sin(a)cos(a)Jxy2wx0wz0+
-Jxz2wx0'cos(a)/cos(b)+
+Jxz2wz0'sin(a)/cos(b)+
MY1={[Jxz2(tg(b)4+2/cos(b)2-1)cos(b)3+Jyz1tg(b)+
+Jxz1]cos(a)2+
+[[(Jx1-Jz1)-Jxy1tg(b)]cos(a)-Jxz1sin(a)]sin(a)}wx02+
+{[[Jxy1tg(b)+(Jz1-Jx1)]sin(a)-Jxz1cos(a)]cos(a)+
+[Jxz2cos(b)3[2/cos(b)2+tg(b)4-1]+Jyz1tg(b)+
+Jxz1]sin(a)2}wz02+
+{(Jx1-Jz1)cos(2a)+[1-tg(b)4-2/cos(b)2]Jxz2cos(b)3
sin(2a)-[Jyz1tg(b)+2Jxz1]2sin(a)cos(a)-
-Jxy1tg(b)cos(2a)}wx0wz0+
+{[Jx2sin(b)cos(b)(1+tg(b)2)+Jy1tg(b)-(Jxy1+Jxy2)]cos(a)-
-Jyz1sin(a)}wx0'+
+{[-Jx2sin(b)cos(b)(1+tg(b)2)+(Jxy1+Jxy2)-Jy1tg(b)]sin(a)-
-Jyz1cos(a)}wz0'+
:
) Y1:
y1 = + = 0.154 + 0.551= 0.705 .
a = - 0.82 .
b = 1 .
wx0 = wz0 = 1 /.
wx0' = wz0' = 0.2 /2.
wy0 = 0.167 /c.
wy0' = 0.167 /2.
:
= 78.14 %
) Z2:
z2 = + = 0 + 0.07= 0.07 .
a = - 0.785 .
b = 1 .
wx0 = wz0 = 1 /.
wx0' = wz0' = 0.2 /2.
wy0 = 0.167 /.
wy0' = 0.167 /c2
:
= 100 %
3) .
(9).
MZ2={cos(2b)-2}cos(a)2tg(b)2Jxy2(wx02+wz02)+
+{2tg(b)2sin(b)2-2cos(b)2+4}sin(a)cos(a)Jxy2wx0wz0+
+{(Jy2-Jx2)/cos(b)-2Jxy2sin(b)(1+tg(b)2)}cos(a)wx0wy2+
+Jyz2wz0wz2(sin(a)-cos(a))/cos(b)-
-Jxz2wx0'cos(a)/cos(b)+
+{2Jxy2(sin(b)tg(b)2+sin(b))sin(a)+(Jx2-
-Jy2)sin(a)/cos(b)}wy2wz0+
+Jxz2wz0'sin(a)/cos(b)+
+{Jxz2-Jyz2}wy2wz2tg(b)+
+{(Jy2-Jx2)tg(b)+Jxy2(1-tg(b)2)}wy22-
-{Jxz2tg(b)+Jyz2}wy2'+
+Jz2wz2'
MY1={[Jxz2(tg(b)4+2/cos(b)2-1)cos(b)3+Jyz1tg(b)+
+Jxz1]cos(a)2+
+[[(Jx1-Jz1)-Jxy1tg(b)]cos(a)-Jxz1sin(a)]sin(a)}wx02+
+{[[Jxy1tg(b)+(Jz1-Jx1)]sin(a)-Jxz1cos(a)]cos(a)+
+[Jxz2cos(b)3[2/cos(b)2+tg(b)4-1]+
+Jyz1tg(b)+Jxz1]sin(a)2}wz02+
+{(Jx1-Jz1)cos(2a)+[1-tg(b)4-2/cos(b)2]Jxz2cos(b)3
sin(2a)-[Jyz1tg(b)+2Jxz1]2sin(a)cos(a)-
-Jxy1tg(b)cos(2a)}wx0wz0+
+{[Jxy2sin(b)cos(b)(tg(b)2+1)+(Jx2-Jz2)]cos(a)}wx0wz2+
+{[Jxz2sin(b)cos(b)+Jxz2sin(b)3/cos(b)+Jyz2]cos(a)+
+[Jyz1cos(a)-Jxy1sin(a)]/cos(b)}wx0wy2-
-{[Jxz2sin(b)cos(b)(1+tg(b)2)+Jyz2]sin(a)+
+[Jyz1sin(a)+Jxy1cos(a)]/cos(b)}wz0wy2+
+{-[tg(b)2+1]sin(b)cos(b)Jxy2+(Jz2-Jx2)]sin(a)}wz0wz2+
+{[Jx2sin(b)cos(b)(1+tg(b)2)+Jy1tg(b)-(Jxy1+Jxy2)]
cos(a)-Jyz1sin(a)}wx0'+
+{[-Jx2sin(b)cos(b)(1+tg(b)2)+(Jxy1+Jxy2)-Jy1tg(b)]
sin(a)-Jyz1cos(a)}wz0'+
+{Jyz2sin(b)-Jxz2cos(b)}wz22-
-{Jxz2sin(b)+Jyz2cos(b)}wz2'+
+{(Jx2-Jy2)sin(b)+Jxy2cos(b)(tg(b)2-1)}wz2wy2+
+{Jx2sin(b)2/cos(b)-2Jxy2sin(b)+Jy2cos(b)+
+Jy1/cos(b)}wy2'
.
) Y1:
y1 = + = 8.1 + 1.65 = 9.75
a = 0.776 .
b = 1.0 .
wy2 = -2 /.
wy2' = 3 /2.
wz2 = 2 /.
wz2' = -3 /2.
wx0 = wz0 = 1 /c.
wx0' = 0.2 /c2.
wz0' = - 0.2 /c2.
wy0 = 0.167 /c.
wy0' = 0.167 /c2.
:
= 16.9 %
) Z2:
z2 = + = 11.6 + 0.361 = 11.96
a = -0.785 .
b = 1.0 .
wy2 = 2 /.
wy2' = -3 /2.
wz2 = -2 /.
wz2' = 3 /2.
wx0 = wz0 = 1 /c.
wx0' = wz0' = - 0.2 /c2.
wy0 = 0.167 /c.
wy0' = 0.167 /c2.
:
= 3.02 %
.
, (), - (), . , , .
, . - , (), . , ( ) .
, . - . , , .
, . .
.
1) .1.
.1.
. , .
, , . , .
2) . .2.
.2.
, , - .
( ), . .
, , ( .1), . . , (D) ( (17)10-3 [-1]) . D110-6510-5,
.1 .2 180. 360, , 90 . , , - .
.2 . , , .
1) .3.
.3
, .2. DA1 DA2 . 1 . U1 DD1 , U2, U1 U1, U2. U1 U2 DD2 ( Ȕ), , U1, U2. f , DD3 U1, U2 .
U1 U2, 0 180.
2) , , , (.4.) [15,94].
U1 U2 DD1...DD5 R1,R2,C1. DD1...5 , U . DA3 - . U1, U2 180.
.4.
, [15]. 60.
Copyright (c) 2024 Stud-Baza.ru , , , .