ÿþA k a d e m i a G ó r n i c z o - H u t n i c z a
i m . S t . S t a s z i c a w K r a k o w i e
I n |y n i e r i a M a s z y n i U r z d z e D
A n a l i z a d y n a m i c z n a m e c h a n i z m u j a z d y s u w n i c y
P r o j e k t w y k o n a B:
M a c i e j P a l u s z e k
R o k I I I
G r u p a 7 A
R o k a k a d e m i c k i : 2 0 1 4 / 2 0 1 5
D a t a w y k o n a n i a w i c z e n i a : 1 7 . 1 1 . 2 0 1 4
6
N a z w a p a r a m e t r u / T e m a t
4 0 0 0 0
M a s a p o d n o s z o n a [ k g ]
4 4 0
M a s a z b l o c z a [ k g ]
1 7 0 0 0
M a s a w ó z k a [ k g ]
9 2 8 0
O p ó r j a z d y [ N ]
2 3
M o c s i l n i k a [ k W ]
7 1 5
O b r o t y s i l n i k a [ o b r / m i n ]
1 5 , 6
P r z e Bo |e n i e r e d u k t o r a
0 , 9 4
S p r a w n o [ r e d u k t o r a
0 , 5
Zr e d n i c a k o Ba j e z d n e g o [ m ]
0 , 1 5
M o m e n t b e z w B. b b n a h a m . [ k g m ]
0 , 8 5
M o m e n t b e z w B. s i l n i k a [ k g m ]
0 , 1 0 5
M o m e n t b e z w B. s p r z . s . [ k g m ]
0 , 5 6
M o m e n t b e z w B. s p r z . w - b 1 [ k g m ]
0 , 5 6
M o m e n t b e z w B. s p r z . w - b 2 [ k g m ]
8 0
Zr e d n i c a w a Bu [ m m ]
2 8 0 0
D Bu g o [ w a Bu [ m m ]
2 1 6
M o m e n t h a m u l c a [ N m ]
0 , 0 0 5
L u z z r e d u k o w a n y [ r a d ]
3 0 9
M a s a k o Ba [ k g ]
S c h e m a t m e c h a n i z m u .
1 . S c h e m a t o b l i c z e n i o w y .
R O Z R U C H ( D A N E N O M I N A L N E )
2 . R ó w n a n i a r u c h u .
5Ø@Ü1 - 5Ø<Ü1 " 5Øß1 - 5ØXÜ " 5Øß1 - 5Øß2 - ! " 5Øß1 - 5Øß2 = 0
( ) ( )
5Ø@Ü2 - 5Ø<Ü2 " 5Øß2 - 5ØXÜ " 5Øß1 - 5Øß2 - ! " 5Øß1 - 5Øß2 = 0
( ) ( )
5Ø@Ü1 5ØXÜ " "5Øß ! " "5Øß
5Øß1 = - -
5Ø<Ü1 5Ø<Ü1 5Ø<Ü1
5Ø@Ü2 5ØXÜ " "5Øß ! " "5Øß
5Øß2 = - -
5Ø<Ü2 5Ø<Ü2 5Ø<Ü2
5Øß1 = 5Øß1
5Ø@Ü1 5ØXÜ " "5Øß ! " 5Øß1
5Øß1 = - -
5Ø<Ü1 5Ø<Ü1 5Ø<Ü1
5Øß2 = 5Øß2
5Ø@Ü2 5ØXÜ " "5Øß ! " 5Øß2
5Øß2 = - -
5Ø<Ü2 5Ø<Ü2 5Ø<Ü2
3 . O b l i c z e n i a :
a ) o b l i c z a n i e m o m e n t u b e z w Ba d n o [c i z r e d u k o w a n e g o n a w a B J z r 1
Éh 2 ÉS 2 Éh 2
J z r =ð =ð ( J h +ð J S +ð J s p ) ´ +ð 2 J s p 1
1
2 2 2
J z r =ð ( J h +ð J S +ð J s p ) ×ði 2 +ð 2 J s p 1 =ð ( 0 , 1 5 +ð 0 , 8 5 +ð 0 , 1 0 5 ) ×ð1 ×ð1 5 , 6 2 +ð 2 ×ð 0 , 5 6 =ð 2 6 9 , 9 6 0 [ k g m 2 ]
1
b ) o b l i c z e n i a m o m e n t u b e z w Ba d n o [c i z r e d u k o w a n e g o n a k o Bo j e z d n e J z r 2
m Q +ð m Q 0 +ð m w 2 k
Ék 2 Ék 2 Ék ×ð D 2
J z r 2 =ð =ð 2 ( J s p 2 +ð J k ) +ð ×ð
2 2 2 4
( m Q +ð m Q 0 +ð m w ) ×ð D 2
k
J z r 2 =ð 2 ( J s p 2 +ð J k ) +ð
2
1 D 2 1 0 , 5 2
2
k
J k =ð m k ×ð =ð ×ð3 0 9 ×ð =ð 9 , 6 5 6 [ k g m ]
2 4 2 4
( 4 0 0 0 0 +ð 4 4 0 +ð1 7 0 0 0 ) ×ð0 , 5 2
2
J z r 2 =ð 2 ( 0 , 5 6 +ð 9 , 6 5 6 ) +ð =ð 3 5 9 0 [ k g m ]
4
c ) o b l i c z a n i e m o m e n t u o d s i l n i k a M 1
M 1 =ð1 , 5 ×ð M s i l ×ði
P 3 0 P
M s i l =ð =ð
É Àn s
3 0 P i 3 0 ×ð 2 3 ×ð1 0 3 ×ð1 5 , 6
M 1 =ð1 , 5 ×ð ×ð1 0 3 =ð1 , 5 =ð 7 1 8 8 , 0 1 6 [ N m ]
Àn s À ×ð7 1 5
d ) o b l i c z a n i e m o m e n t u o d o p o r ó w j a z d y M 2
D k 0 , 5
M 2 =ð w ×ð =ð 9 2 8 0 =ð 2 3 2 0 [ N m ]
2 2
e ) o b l i c z e n i a m o m e n t u p r z y h a m o w a n i u M 1 h
M 1 h = M h ×ð i = 2 1 6 ×ð 1 5 , 6 = 3 3 6 9 , 6 [ N m ]
f ) o b l i c z e n i a w s p ó Bc z y n n i k a s p r |y s t o [c i w a Bó w k
À ×ðd 4 G À ×ð0 , 0 8 0 4 ×ð8 0 ×ð1 0 9
k =ð 2 =ð 2 ×ð =ð 2 2 9 7 8 5 , 0 6 3 [ N m ]
3 2 ×ðl 3 2 ×ð 2 , 8
g ) o b l i c z e n i a w s p ó Bc z y n n i k a t Bu m i e n i a h
h = 0 . 0 0 5 · k = 0 , 0 0 5 ×ð 2 2 9 7 8 5 = 1 1 4 8 , 9 2 5 [ N m ]
4 . P r z e b i e g m o m e n t u .
5 . P r z e b i e g p r d k o [c i .
M a s a p i e r w s z a :
M a s a d r u g a :
6 . W y z n a c z o n e a n a l i t y c z n i e w s p ó Bc z y n n i k i r ó w n a D r u c h u .
5Ø<Ü1 = 2 8 8 , 8 5 7 5ØXÜ5ØTÜ5ØZÜ2
5Ø<Ü2 = 3 5 9 0 5ØXÜ5ØTÜ5ØZÜ2
5Ø@Ü1 = 7 1 8 8 , 0 1 6 5ØAÜ5ØZÜ
5Ø@Ü2 = 2 3 2 0 5ØAÜ5ØZÜ
5ØXÜ = 2 2 9 7 8 5 , 0 6 3
! = 1 1 4 8 , 9 2 5
7 . P o r ó w n a n i e w s p ó Bc z y n n i k ó w w y z n a c z o n y c h i z p r o g r a m u .
Z
W s p ó Bc z y n n i k W y z n a c z o n y
p r o g r a m u
I 1 [ k g m 2 ] 2 5 3 , 9 2 8 8 , 9
I 2 [ k g m 2 ] 1 1 0 2 , 2 3 5 9 0
M 1 [ N m ] 6 7 5 6 , 7 4 7 1 8 8 , 0 2
M 2 [ N m ] 2 3 2 0 2 3 2 0
k 2 2 9 8 1 5 2 2 9 7 8 5
h 1 1 4 9 , 0 7 1 1 4 8 , 2 6
8 . O d c z y t a n y c z a s u s t a l e n i a .
5ØaÜ5ØbÜ5Ø`Ü5ØaÜ = 0 , 8 6 5Ø`Ü
9 . O b l i c z o n a n a d w y |k a d y n a m i c z n a .
5Ø9Ü5ØZÜ5ØNÜ5ØeÜ
5ØCÜ = = 1 , 9 0 9
5Ø9Ü5ØbÜ5Ø`Ü5ØaÜ
R O Z R U C H ( M O C S I L N I K A X 1 0 )
4 . P r z e b i e g m o m e n t u .
5 . P r z e b i e g p r d k o [c i .
M a s a p i e r w s z a :
M a s a d r u g a :
8 . O d c z y t a n y c z a s u s t a l e n i a .
5ØaÜ5ØbÜ5Ø`Ü5ØaÜ = 0 , 7 9 4 5Ø`Ü
9 . O b l i c z o n a n a d w y |k a d y n a m i c z n a .
5Ø9Ü5ØZÜ5ØNÜ5ØeÜ
5ØCÜ = = 1 , 7 8 7
5Ø9Ü5ØbÜ5Ø`Ü5ØaÜ
R O Z R U C H ( M O C S I L N I K A / 1 0 )
4 . P r z e b i e g m o m e n t u .
5 . P r z e b i e g p r d k o [c i .
M a s a p i e r w s z a :
M a s a d r u g a :
8 . O d c z y t a n y c z a s u s t a l e n i a .
5ØaÜ5ØbÜ5Ø`Ü5ØaÜ = 1 , 1 5Ø`Ü
9 . O b l i c z o n a n a d w y |k a d y n a m i c z n a .
5Ø9Ü5ØZÜ5ØNÜ5ØeÜ
5ØCÜ = = 2 , 2 1
5Ø9Ü5ØbÜ5Ø`Ü5ØaÜ
H A M O W A N I E ( D A N E N O M I N A L N E )
4 . P r z e b i e g m o m e n t u .
5 . P r z e b i e g p r d k o [c i .
M a s a p i e r w s z a :
M a s a d r u g a :
6 . W y z n a c z o n e a n a l i t y c z n i e w s p ó Bc z y n n i k i r ó w n a D r u c h u .
5Ø<Ü1 = 2 8 8 , 8 5 7 5ØXÜ5ØTÜ5ØZÜ2
5Ø<Ü2 = 3 5 9 0 5ØXÜ5ØTÜ5ØZÜ2
5Ø@Ü1 = 7 1 8 8 , 0 1 6 5ØAÜ5ØZÜ
5Ø@Ü2 = 2 3 2 0 5ØAÜ5ØZÜ
5ØXÜ = 2 2 9 7 8 5 , 0 6 3
! = 1 1 4 8 , 9 2 5
7 . P o r ó w n a n i e w s p ó Bc z y n n i k ó w w y z n a c z o n y c h i z p r o g r a m u .
Z
W s p ó Bc z y n n i k W y z n a c z o n y
p r o g r a m u
I 1 [ k g m 2 ] 2 8 7 , 2 2 8 8 , 9
I 2 [ k g m 2 ] 1 1 0 2 , 2 3 5 9 0
M 1 [ N m ] 3 5 8 4 , 6 8 7 1 8 8 , 0 2
M 2 [ N m ] 2 3 2 0 2 3 2 0
k 2 2 9 8 1 5 2 2 9 7 8 5
h 1 1 4 9 , 0 7 1 1 4 8 , 2 6
8 . O d c z y t a n y c z a s h a m o w a n i a i c z a s u s t a l e n i a .
5ØaÜ5ØbÜ5Ø`Ü5ØaÜ = 0 , 8 2 5Ø`Ü 5ØaÜ!5ØNÜ5ØZÜ = 6 , 5 5Ø`Ü
H A M O W A N I E ( M O M E N T H A M U L C A X 1 0 )
4 . P r z e b i e g m o m e n t u .
5 . P r z e b i e g p r d k o [c i .
M a s a p i e r w s z a :
M a s a d r u g a :
8 . O d c z y t a n y c z a s h a m o w a n i a i c z a s u s t a l e n i a .
5ØaÜ5ØbÜ5Ø`Ü5ØaÜ = 0 , 2 5 5Ø`Ü 5ØaÜ!5ØNÜ5ØZÜ = 5 , 2 5Ø`Ü
W N I O S K I
J e [l i p o r ó w n a m y w y n i k i o t r z y m a n e m e t o d a n a l i t y c z n j a k i t e z p r o g r a m u m o |e m y z a u w a |y ,
|e r ó |n i s i o n e n i e z n a c z n i e z w y j t k i e m z r e d u k o w a n e g o m o m e n t u b e z w Ba d n o [c i I 2 , g d z i e
r ó |n i c a m o |e w y n i k a p r z e d e w s z y s t k i m z b Bd u p r o g r a m u j a k i b Bd u o b l i c z e n i o w e g o .
W t r a k c i e a n a l i z y w y k r e s u p r d k o [c i r o z r u c h u z a u w a |y m o |n a , |e p o u r u c h o m i e n i u s i l n i k a ,
p r d k o [ w ó z k a p o c z t k o w o o s c y l u j e , a n a s t p n i e w z r a s t a l i n i o w o d o p e w n e j w a r t o [c i . J e s t t o
s p o w o d o w a n e k o By s a n i e m s i p o d w i e s z o n e j p o d w ó z k i e m m a s y .
P r z y 1 0 - k r o t n y m z w i k s z e n i u m o c y s i l n i k a , c z a s u s t a l e n i a r o [n i e , c o j e s t w y w o Ba n e
z w i k s z o n y m m o m e n t e m r o z r u c h o w y m s i l n i k a i w k o n s e k w e n c j i p o w o d u j e g w a Bt o w n i e j s z e
r u s z e n i e w ó z k a . G d y m o c s i l n i k a z m n i e j s z y m y 1 0 - k r o t n i e , t o b d z i e o n a n i e w y s t a r c z a j c a d o
w p r a w i e n i a u k Ba d u w r u c h i m a s a 2 n a w e t n i e d r g n i e .
A n a l i z a w y k r e s u h a m o w a n i a w s k a z u j e n a t o , |e p o d c z a s h a m o w a n i a p r d k o [ w ó z k a u l e g a
w a h a n i o m . S p o w o d o w a n e t o j e s t z m i a n o b c i |e n i a u k Ba d u . G d y w a h a n i a u s t a j p r d k o [ j e s t
l i n i o w a . J e [l i z w i k s z y m y m o m e n t h a m o w a n i a t o c z a s h a m o w a n i a s i s k r ó c i a l e c z a s u s t a l e n i a
z p o d o b n y c h p o w o d ó w j a k p o p r z e d n i o z o s t a n i e w y d Bu |o n y .
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