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BY (11) 8346
(13) C1
(46) 2006.08.30
(19)
(12)
7
(51) G 01M 1/00, 1/32
(54)
(21)
(22) 2003.06.12
(43) 2004.12.30
(71)
:
(72)
: a 20030590
(73)
(BY)
;
;
:
:
(BY)
(56) RU 2163008 C2, 2001.
RU 2185609 C2, 2002.
SU 1013784 A, 1983.
JP 57083746 A, 1982.
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(BY)
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BY 8346 C1 2006.08.30
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BY 8346 C1 2006.08.30
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BY 8346 C1 2006.08.30
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ω
ω'
ϕ
ϕ,
,
.2 ϕ
.2 ,
,
.1 .2 .2 ε
t
ϕ,
-
.3 -
. 1).
:
1.
:
(
)(
OXYZ
. 1).
,
.
O1X1Y1Z1,
.
X1 ,
,
∆α = 2π/15 = 360°/15 = 24° (
2.
. 1).
r
2h.
3.
ω = ω'⋅ϕ,
ϕ,
. ϕp = 2πNp.
2L
X X1
,
ω' = dω/dϕ ≈ ∆ω/∆ϕ.
ω
ω = f(t).
αi
αi,
∆ϕ (
ϕ
. εi =
N .
ϕ,
,
dω dϕ
= ωi ⋅ ω' .
⋅
dt dϕ
)
ω = f(ϕ)
ε = f(ϕ)
.
ωmax
ω' = const = ωmax/2πNP.
ϕ.
ω = f(ϕ),
ω =0
X1(X).
Np,
,
ε, . ϕω=const = 2π⋅Nε=0 ,
,
,
ϕi ,
.
Nε=0
ϕ = 2π⋅N ,
ω
∆α = αi+1-αi.
.
-
ωi
∆α,
ϕi
,
,
ϕi
.2 .
3
ω' = dω/dϕ ≈ ∆ω/∆ϕ
αi
.2 ,2
2 .
∆ϕ
:
,
,
-
ω = ω'⋅αi.
,
∆α (
-
)
2π.
t
-
BY 8346 C1 2006.08.30
15
t 2 π = ∑ (∆t )i .
i=1
,
.
=
+
,
ε=0
ε=0
+
.
.
4.
ϕi
αi,
2π
-
Np, Nε=0, N
5.
,
ε=0,
.
αi.
.1
[3] . 738
OXYZ
RBx, RBy
RAx, RAy
ϕi
-
,
.
741
(
.
. 1):


R Ay + R By − P = 0

.
y
y
2
R A h − R B h − ω J yz + J xz ε = 0 
− R xA h + R xB h + ω2 J xz + J yz ε = 0
R +R = 0
x
A
x
B
Z1,
.
,
.1
OX1Y1Z1
β.
X(X1)
(1)
Y1Z1
.
.
.
OXYZ,
β
.
.
.
OX1
β
OX1Y1Z1
OXYZ
0.
R +R −P =0
y
A
.
OX1Y1Z1
[3] . 744
(2)
OXYZ
Jxy = 0; Jzx = 0; Jyz
(2)
(1)
x
x
RA + RB = 0
y
B
R Ay h − R yB h − ω 2 J yz = 0
− R xA h + R Bx h + J yz ε = 0
3
3 ,
3
ε
R xA = J yz
2
R xB = − J yz

( )

( )


.
( )


( )


ε
2
R Ay =
2
P  J yz ω 
1
+
2 
2hP 
R By =
2
P  J yz ω 
1
−
2 
2hP 
4
(1)
(à) 

(á) 
.
(a ) 
(~
a )
3
(3)
:
(4)
-
BY 8346 C1 2006.08.30
ω = const,
(3)
. ε = 0,
:
(à) 

(á) 
.
(a ) 

(~
a )
R xA + R xB = 0
R +R −P =0
y
A
y
B
R Ay h − R By h − ω 2 J yz = 0
− R xA h + R Bx h = 0
ω = const,
(5)
:


( )


( ) .


( ) 


R xA = R xB = 0
R Ay =
.ε=0
(5)
2
P  J yz ω 
+
1
2 
2hP 
2
P  J yz ω 
R = 1 −
2
2hP 
y
B
(6)
(4)
J yz =
P l
r 
 −  ⋅ sin 2β
2g  3 4 
2
2
:
(R xA )Ò =

(a ) 


(á) 

.
(a ) 



(~
a )

εP  l 2 r 2 
 −  sin 2β
4g  3 4 
(R xB )Ò = −
εP  l 2 r 2 
 −  sin 2β
4g  3 4 
ω2  l 2 r 2  
P
 −   sin 2β
(R ) = 1 +
2  2hg  3 4  
y
A Ò
(R yB )Ò =
ω2  l2 r 2 
P
 −  sin 2β
1 −
2  2hg  3 4 
(RAx) , (RAy)
6.
∆ϕi
.2
,
7.
ϕi
(RBx) , (RBy)
∆αi.
-
αi.
β
(7)
(7)
(7)
β .
:
(a ) 

( )
.
( )
( ) 
(R XA ) = A sin 2β A
(R ) = B sin 2βB
X
B
(R YA ) = C sin 2βA
(R YB ) = D sin 2βB
5
(8)
BY 8346 C1 2006.08.30
(7)
A=
(8)

(a ) 


(á) 

.
(a ) 



(~
a )

εP  l 2 r 2 
 − 
4g  3 4 
εP  l 2 r 2 
B = −  − 
4g  3 4 
P  ω2  l 2 r 2 
 − 
C = 1 +
2  2hg  3 4  
P  ω2  l 2 r 2 
 − 
D = 1 −
2  2hg  3 4  
(8)
(9)
:
.
(10)
(RAx) , (RAy)
(10)
(RBx) , (RBy)
:
(R A ) 2 

A 2 + C2 
.
2 
(
R
)
β B = 2 arcsin 2 2 B 2 
B + D 
β
β
β,
β A = 2 arcsin 2
(11)
(7).
,
(10)
.
-
,
(
,
,
-
.)
.
.3
,
RA
RB
).
rAK
8.
L1
rB K
mA
L2,
(
.
. 3):
r = (L + L1 ) tgβ A 
.
rBK = (L + L1 ) tgβB 
K
A
(12)
R AK
9.
mA mB
[3] . 736:
R KA = m A (ω2 x mA + εy mA )
,
R KB = m B (ω2 x mB − εy mB ) 
xmA, ymA, xmB, ymB (
10.
(12):
6
mB
RBK ,
-
(13)
.
. 3).
-
BY 8346 C1 2006.08.30
x mA = rAK cos α = [(L + L1 )tgβ A ] cos α 

y mA = rAK sin α = [(L + L1 )tgβ A ] sin α 

x mB = rBK cos α = [(L + L1 )tgβ B ] cos α 
y mB = rBK sin α = [(L + L1 )tgβ B ] sin α 
(14)
11.
(13):

ω2 x mA + εy mA 

R KB
T

mB =
ω2 y mB + εx mB 
R
m TA =
K
A
(15)
(RA)
(10)),
(15)
(R A )

ω x mA + εy mA 

(R B )

mB ≈
ω2 y mB + εx mB 
0
∆αi (
-
2
(16)
(16)
. 1).
.
.
:
mA ≈
12.
2π
13.
(RB) (
α
(14)
mTA
mTB , m A
mB
,
-
,
.
14.
(
. 3)
-
,
.
15.
.
16.
,
.
,
:
1.
,
-
(
-
).
2.
(
)
.
3.
,
,
,
.
4.
.
-
(
)
,
-
,
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,
,
:
(
,
)
,
.
7
-
BY 8346 C1 2006.08.30
:
1.
.,
1986. - . 69-91.
2.
.
2163008,
3.
.
742-744.
4.
.,
..:
.
G 01
.-
..,
:
, 1964. - . 547-658,
.
,
, 1998. - . 370-390.
.3
.
,
.
,
1/00, 2001.
.2
220034, .
.:
, 20.
8
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