滑块式分拣机分拣道岔的数学模型设计.pdfVIP

J u n 2 0 1 2 机床与液压 Hy d r o me ch a t r o n i cs En g i n e e r in g Vo 1 40 No 1 2 DOI 1 0 3 9 6 9 j is s n 1 0 0 1 3 8 8 1 2 0 1 2 1 2 0 0 9 M a t he ma t ica l M o de l S t ud y o n S o r t in g Tr a ck o f S l id in g S ho e S o r t e r W ANG Xia o me i ZHU Xin ca i DI NG Yo u q in g ZHOU Xio n g J C h o n g q in g U n i v e r s it y o f S cie n ce a n d T e ch n o l o g y C h o n g q in g 4 0 1 3 3 1 C h in a 2 C h o n g q in g U n i v e r s it y of T e ch n o l o g y C h o n g q i n g 4 0 0 0 5 4 C h in a 1 I nt r o d uct io n Ab s t r a c t Th i s p a p e r b r i e f l y d e s c r i b e s t h e ch a r a ct e r i s t i c s a n d b a s i c s t r u ct u r e o f s l i d i n g s h o e s o rt er B a s e d o n t h e d y n a mi c a n a ly s i s o f t h e s o r t i n g o p e r a t i o n t h i s p a p er e s t a b l i s h e s a n o v er a l l d e s i g n i d e a o f s o rt i n g t r a ck ma t h e ma t i ca l mo d e 1 Th r o u g h t h e c o mp a r i s o n o f t h r e e k i n d s o f s t a rti n g s e g me n t ma t h ema t i c a I mo d e ls t h e d e s i gn s ch e me o f t h e s o rt er i s d e t e r mi n e d B y u s i n g t h e s i mi l a r p r i n c i p l e s t h e ma t h e ma t i c a l mo d e l o f t h e e n d s e g me n t i s d e s i g n e d a n d wh i ch o f t h e mi d d l e s e g me n t i s c o n s t r u ct e d F i n a l ly t h e mo u n t i n g lo c a t i o n o f t h e wh o l e s o rti n g t r a c k i s d e t e r mi n e d a n d t h e ma t h e ma t i c a l mo d e I o f s o rt i n g t r a c k f or s l i d i n g s h o e s o rt er i s t h e r e b y e s t ab l i s h e d K e y wo r d s s o rt i n g ma ch i n e s li d i n g s h o e s o rt e r s o r t i n g t r a c k ma t h e ma t i c a l mo d e l S l id in g s h o e s o r t e r wh ich is v e r y imp o r t a n t i n t h e l o g i s t ics s y s t e m o f mo d e m d ig it a l e q u ip me n t is a hi g h s p e e d a u t o ma t e d p a r ce l s o rtin g ma chi ne I n t h e U n it e d S t a t e s E u r o p e J a p a n a n d o t h e r d mr e l o p e d co u n t r ie s t h e a u t o ma t ic s o rtin g ma ch in e is i n co n mo n u s e W it h t he r e q u ir e me n t s o f h ig h q u a l i t y do me s t ic s e r v ice s a n d t h e d e l iv e r y v o l u me in cr e a s in g s h a r p l y t h e ma n u a l s o rti n g is n o t a bl e t o me e t t h e r e q u ir e me nt s o f l a r g e s ca l e d is t r i bu t io n Be ca u s e t h e a ut o ma t i c s o rtin g t e ch n o l o g y h a s a d v a n t a g e s o f hi g h s o rti n g s p e e d hi g h e ffi cie ncy a n d l o w e r r o r a t e it h a s a h u g e ma r k e t in C hin a S l id in g s h o e s o rte r is a d a p t e d t o s ma l l me d i um s iz e it e ms a n d me e t s s mo o t h e f f i cie n t a n d fle x ib l e s o rti n g r e qu i r e me n t s I t s a p pl i ca t io n i s e x t r e me l y e x t e n s iv e Th e o v e r a l l s t r u ct u r e o f t h e s l id i ng s h o e s o rte r is s h o wn in Fig 1 Re ce iv e d 2 01 2 0 4 0 8 WANG Xia o me i E ma il w a n g x mah c y a h o o co m cn l 2 3 1 s u p p ly s y s t e m 2 r a c k a n d t r a ck 3 t r a n s mis s io n s y s t e m 4 r e co v e r y t r a ck 5 co n v e y e r 6 s o r t in g s y s t e m 7 r e ce iv in g t r a c k F ig 1 Ov e r a l l s t r u ct u r e d ia g r a m o f s l id in g s h o e s o e r S o rtin g s y s t e m i s t h e co r e o f s l id i n g s ho e s o rt e r I t ma in l y co n s is t s o f s o rtin g t r a ck a nd d iv e rte r Fi g 2 s ho ws t h e s t r u ct u r e d ia g r a m o f t h e s o rtin g s y s t e m I n o r d e r t o a ch ie v e t h e o b j e ct o f s t a b l e s o rtin g t h e s o r t in g t r a ck g u id e s t h e s h o e s t o mo v e in a cco r da n ce wit h a d e s i g n e d l o cu s I n o r d e r t o e n s ur e t h a t t h e s ho e s ca n s mo o t hl y co mp l e t e t h e s o rti ng t a s k in hi g h s pe e d s t a t e wh e n t h e s ho e s mo v e i n t h e s o rtin g t r a ck t he s o r t in g t r a ck ma t h e ma t ica l mo d e l ca n b e g ua r a n t e e d t o p r o d u ce t h e p o s s i b l e s ma l l imp a ct f o r ce b e t we e n s o rtin g t r a ck a n d g u ide wh e e l s a n d b e t we e n s h o e s a n d it e ms Ob v i o u s l y t h e d e s i g n a b o u t ma t h e ma t ical mo d e l o f 5 2 Hy d r o me ch a t r o n ics En g in e e r i n g s o r t in g t r a ck is v e r y cr it ica 1 2 3 1 s o r t in g t r a ck 2 1 in e a r t r a ck 3 d iv e r s io n b l o ck F ig 2 S o r t in g s y s t e m s t r u ct u r e d ia g r a m 2 Ov e r a l l d e s ig n id e a o f s o r t in g t r a c k ma t he ma t ica l mo de l Th e k no wn t e ch n ica l p a r a me t e r s in t h e d e s ig n a r e a s f o l l o w s v e l o cit y o f co n v e y e r 2 m s ce n t e r d is t a n ce o f a d j a ce n t s l a t s 0 1 9 2 m e f f e ct i v e w i d t h o f s l a t 0 8 m a n g l e o f r e ce i v in g t r a ck o 2 8 ce n t e r d is t a n ce o f a d j a ce n t r e ce i v in g t r a ck s 1 0 m d ia me t e r o f g u i d e wh e e l 1 4 0 mm 1 s l id in g s h o e 2 s l a t 3 g u id in g w h e e l F ig 3 S l id in g s h o e ins t a l l a t io n d ia g r a m I n Fig 3 t h e s l id i ng s h o e is y o k e d t o t he s l a t s o t h e s h o e ca n a l wa y s ma in t a in t h e h o ri z o n t a l l in e a r v e l o cit y o f 2 m s t h a t is s y nch r o n o u s wit h t h e s l a t T he r e f o r e ma t h e ma t ica l mo d e l o f s o r t in g t r a ck s h o ul d e n s u r e t h e d y na mic p a r a me t e r s in d ir e ct io n a s s h o wn b e l o w t 2 t t 2 m s a t 0 I n o r d e r t o f a ci l it a t e t h e t h e o r e t ica l a n a l y s is t h e d e s ig n us e s g u id e wh e e l ce n t e r l o cu s in s o r t in g t r a ck t o e s t a b l is h s o rtin g t r a ck ma t h e ma t i ca l roo d e 1 Be ca u s e o f t h e ch a n g e s i n t he d ir e ct io n o f mo t io n t he a cce l e r a t io n o f s h o e s in e v it a b l y a ccu r s a n d t h u s i mp a ct s a t t h e b e g in n in g a n d e n d o f t h e s o rti ng t r a ck I n o r d e r t o s mo o t h l y g u id e it e ms t o wa r d r e ce iv e r s in h ig h s pe e d s t a t e t h e d e s ig n o f s o rtin g t r a ck ma t he ma t ica l mo d e l s ho u l d e n s u r e t h a t t h e s h o e s a ccu r a t e l y s mo o t h l y a nd r a p id l y d iv e rt a n d t h e n ma in t a i n u n if o r m mo t io n a f t e r e n t e ri n g t h e s o rtin g t r a ck wh i ch ca n r e d u ce imp a ct no is e a n d imp r o v e t h e wo r k in g l i f e o f t h e wh o l e e q u ip me n t T he r e f o r e t h e mi dd l e l O C U S o f s o rtin g t r a ck ca n b e d e s ig n e d t o a s t r a ig h t l i n e Aco r d in g t o t h is id e a t h e dy n a mic a n a l y s is a b o u t s o rtin g t r a ck ma t h e ma t i ca l mo d e l ca n be d iv i d e d in t o t h r e e s e c t io n s in cl u d in g s t a rtin g s e g me n t mid d l e s e g me n t a n d e n d s e g me n t S o rtin g t r a ck ma t h e ma t ica l mo dl e d i a g r a m i s s h o wn in Fig 4 Fig 4 S o in g t r a ck ma t h e ma t ical mo d e l d ia g r a m I n Fig 4 mi d dl e s e g me n t P3 P4 is a s t r a ig ht l in e wh o s e s l o p e is t a n 28 28 i s t he s a me a s t h e a n g l e o f r e ce iv in g t r a ck Th e d y n a mic p a r a me t e r s i n mid d l e s e g me n t P3 P4 a s f o l l o ws t 2 m s t f dy d 酬 y d t a n 2 8 d t t d 一 d 一 一 t a n 2 8 2 t a n 2 8 1 0 6 3 m s a t 0 3 De s ig n a n d ca l cu l a t io n o f ma t h e ma t i ca l m o de l in s t a r t ing s e g m e nt As s h o wn i n Fig 4 p o in t P1 in s t a rtin g s e g me n t o f s o rtin g t r a ck is co n n e ct e d wit h l o we r h o r i z o n t al l in e a r t r a ck a n d p o in t P3 is co n n e ct e d wi t h mid d l e s e g me n t Th e r e f o r e f r o m p o in t P1 t o p o i n t P 3 t w h ich is t h e v e l o cit y i n Y d i r e ct io n is ch a n g e d f r o m 0 t o 1 0 6 3 m s a n d a t w h ich i s t h e a cce l e r a t io n i n Y d ir e ct io n is ch a ng e d fro m 0 t o 0 I n o r d e r t o r e d u ce t h e imp a ct p r o d u ce d fro m d iv e r s i o n t h e d e s ig n s h o u l d a v o i d t h e s t e e p ch a ng e o f s t a rtin g s e g me n t l o cu s Mo r e o v e r in o r W ANG Xia o me i e t a l Ma t he ma t ica l Mo d e l S t u d y o n S o r t in g Tr a ck o f S l id in g S h o e S o r t e r 53 d e r t o a v o id a l t e r n a t in g im p a ct a t o f s t a rt in g s e g me n t s h o u l d b e d e s ig ne d f o r p o s it i v e I n a d d i t io n a y t i s d e s ig n e d t o b e s y mm e t r i ca l in o r d e r 吕 t o s im p l if y t h e d y n a m ic a n a l y s is T h u s a t a n d y t s ch e m e d ia g r a m ca n b e d e s ig n e d a s s h o w n i n F ig 5 a b c r e s p e ct iv e l y 0 t l t s O t I t s a Fig 5 吕 O t l t 2 0 t s t 2 0 f f s b 吕 t 1 t s O t I t s c Acce l e r a t io n a n d v e l o cit y s ch e me d ia g r a m o f s t a r t in g s e g me n t in d ir e ct io n T hr o u g h p r e l i mi na r y a n a l y s is o f Fig 5 a b c it i s f 0 u n d t h a t a in s ch e m e b is min imu m wit h in t h e s a me p e ri o d o f t 2 wh ich b e s t me e t s t h e r e q u ir e me n t o f r e d u cin g i mpa ct Th e r e f o r e t h e ma t h e ma t ica l mo d e l in s t a rt in g s e g me n t is d e s ig n e d a s s ch e m e b Acco r d in g t o t h e k n o wn p a r a me t e r s r e s p o n s e t ime o f d i v e r s io n s h o u l d b e l e s s t h a n 8 6 ms 0 1 9 2 1 0 0 0 4 0 2 2 8 6 G e n e r al l y r e s p o n s e t im e o f e l e ct r o ma g n e t ic p a rt s is n o t l e s s t h a n 1 0 0 ms s o t h e d iv e r t e r t h a t is l o ca t e d i n s t a r t in g s e g me n t o f s o r t in g t r a ck is e q u ip p e d wi t h p n e u ma t i c t r a ns mis s io n d e v ice I n o r d e r t o e ffe ct i v e l y a n d a ccu r a t e 1 v d i r e ct g u id in g w h e e l s t o w a r d s o rt in g t r a ck s h o u l d co n s i d e r t h e l l o win g f a ct o r s d e s ig n m o v e m e n t b e t w e e n a d j a ce n t g u i d e w h e e l s a n d d i v e rs io n b l o ck ca n no t o ccu r i n t e r f e r e n ce t e r r e s p o n s e t i m e o f d i v e r e a s y in s t all a t io n T h r o u g h t h e co mp a ri s o n o f s e v e r al t ime s ch e me s t h e d e s ig n s e l e ct e d t 2 e q u M t o 0 0 5 9 s T h u s t h e p r o j e ct e d l e n g t h o f s t a rt in g s e g me n t in d ir e ct io n is 1 1 8 mm t t 2 2 0 0 5 9 m 0 1 1 8 m 1 1 8 mm T h u s t h e d i a g r a m o f a cce l e r a t io n ma t h e ma t ica l mo d e l in s t a r t in g s e g me n t ca n b e s h o wn a s Fig 6 An aly z in g f r o m F ig 6 t h e d y n a mi c e q u a t io n s o f s t a rt in g s e g me n t a r e p r e l imin a ri l y e s t a b l i s h e d a s f o 1 1 o ws o tI t 0 0 0 5 9 1 At p o in t P1 t 0 0 y t 0 t 0 Y 0 At p o i n t P3 t 0 0 5 9 s 0 y 0 1 06 3 m s 0 0 0 29 5 0 0 59 0 t s F ig 6 Acce l e r a t io n ma t h e ma t ica l mo d e l d ia gra m in s t a r t in g s e g me n t S u b s t it u t in g t h e s e k n o w n d y n a mi c p a r a me t e r s in t o e q u a t i o n s 1 t h e r e s u l t s a r e o b t a in e d a s f o l l o w s a4 一 2 5 8 8 9 2 3 3 05 4 9 o g 2 o t 1 o t 0 0 Th e r e f o r e t h e d y n a mic e q u a t i o n s o f s t a r t in g s e g me n t a r e s h o wn a s l l o ws 4 I 一 一 莘 5 4 Hy d r o me ch a t r o n ics En g in e e r in g r y t 一2 5 8 8 9 2 t 3 0 5 4 9 t v t 一 1 0 3 5 5 6 8 t 9 1 6 4 7 t L a t 一3 1 0 6 7 0 4 1 8 3 2 9 4 t t 0 0 0 5 9 2 Be ca u s e o f 2 t s o t 0 5 x Ma t he ma t ica l mo d e l o f t h e s t a r t in g s e g me n t o f s o r t in g t r a ck is a s s h o wn b e l o w y x 一1 6 1 8 0 8 x 3 8 1 8 6 x 0 0 1 l 8 3 B y e q u a t io n s 2 t 0 0 2 9 5 s a 2 7 0 4 m s t o o l a r g e which is cl o s e r t o 0 t h e b e t t e r S o t h e d e s ig n o f t o o l o n g e n d s e g me nt is a l s o ha s i t s d r a w b a ck s Th r o u g h t h e co mp a ri s o n o f s e v e r a l t ime s ch e me s t h e d e s i g n s e l e ct s t 2 e q u a l t o 0 3 s I n o r d e r t o s i mp l i f y t he d y n a mic a na l y s is a n d ca l cu l a t io n UV t h a t is t h e s e co n d co o r d in a t e s y s t e m s ho u l d b e e s t a b l is he d a t p o in t P4 1 ine a r t r a ck N 4 D e s i g n a n d cu a t i 0 n o f m a t h e m a ti ca l F i g 8 E n d se gm e n f o f so rti n g trac k a n d li n e a r mo d e l in e nd s e g me nt An a l y z in g f r o m Fi g 4 p o in t尸4 a t t h e e n d s e g me nt o f s o rtin g t r a ck is co n n e ct e d wi t h t h e mid d l e s e g me n t a n d p o in t P6 is co n n e ct e d wit h t h e u pp e r h o riz o n t a l l i n e a r t r a ck t is ch a n g e d f r o m 1 0 6 3 m s t o 0 a n d a is ch a n g e d f r o m 0 t o 0 R e s e m b l e d t h e a n a l y s i s pri n cip l e o f t he s t a r t i ng s e g me n t a cce l e r a t io n ma t h e ma t ica l mo d e l d ia g r a m in t h e e n d s e g me n t is de s ig n e d p r e l imi n a r il y a s s h o wn i n Fig 7 a P m s 0 t l t 2 P F ig 7 Acce l e r a t io n ma t h e ma t ica l mo d e l W he n it e m e n t e r s in t o r e ce iv in g t r a ck t h e s l id in g s h o e s w il l mo v e t o wa r d u p p e r l i n e a r t r a ck d u e t o in e r t ia Th e r e f o r e t h e us e o f d iv e r t e r is u n n e ce s s a r y in t h e e nd s e g me n t S o t he in t e r f e r e n ce b e t we e n a d j a ce n t g u i d i n g w h e e l s a n d d iv e r s io n b l o ck d o e s n o t e x is t I n o r d e r t o r e du ce t h e impa ct p r o d u ce d b y d i v e r s i o n t h e e n d s e g me n t ca n b e d e s ig n e d t o b e s l ig h t l y l o n g e r a n d fla t t e r I n a d d it io n in t h e int e r s e ct io n o f t h e e n d s e g me n t o f s o r t i ng t r a ck a n d u pp e r l in e a r t r a ck a s s h o wn in Fi g 8 co n t o u r MN ca n n o t be f o r me d Ana l y z in g f r o m F ig 7 a f t e r p o in t M s l id in g s h o e s wil l mo v e t o wa r d u pp e r l in e a r t r a ck d u e t o in e r t ia a t p o in t M The r e f o r e co n t o u r MN s h o u l d n o t b e t o o l o n g a n d t h e a cce l e r a t i o n a t p o i n t M s h o u l d n o t b e I n F ig 7 wh e n s e l e ct in g t 2 t o be 0 3 s r e s e m b l e d t h e d y n a mi c a n a l y s is o f s t a rti ng s e g me n t t h e d y na mic e q u a t i o n s o f e n d s e g me n t a r e s h o wn a s f o l l O WS r 1 9 6 9 3 t 一1 1 8 1 6 t 1 0 6 3 t v v t 7 8 7 7 0 t 一3 5 4 4 7 t 1 0 6 3 a v t 2 3 6 3 1 I t 一7 0 8 9 4 t t 0 0 3 4 Be ca us e o f U 2t s o t 0 5U U 1 2 3 1 一1 4 7 7 U 0 5 3 2 U U 0 0 6 5 5 De s ig n a n d ca l cul a t io n o f ma t he ma t ica l mo de l in mid d l e s e g me n t As me n t io ne d e a r l ie r t h e mid d l e s e g me n t P3 P4 s h o u l d b e de s ig n e d a s a s t r a ig ht l i ne wh o s e s l o p e is t a n 28 P3 P4 is co n n e ct e d wit h t h e s t a r t in g s e g me n t P l P 2 P 3 m d t h e e n d s e g me n t P 4 P 5 P 6 a n d t hu s a co mpl e t e s o rtin g t r a ck is co n s t i t u t e d T he ma t he ma t ica l mo d e l o f s o r t in g t r a ck wh ich is e s t a b l is h e d b y u s in g gu id in g wh e e l ce nt e r l o cu s in s o rti ng t r a ck i s s h o wn in F ig 9 By u s in g s o me r e l e v a n t d a t u m me n t i o n e d a b o v e t h e l o cus e q u a t io n o f t h e mid d l e s e g me n t P3 P4 ca n b e r e p r e s e nt e d a s b e l o w t a n 2 8 一0 1 1 8 0 0 3 1 4 0 5 3 2 一0 0 3 1 4 0 1 1 8 1 2 6 4 T he u p p e r l imit i ng v a l u e o f me n t io n e d a b o v e is o b t a in e d by a na l y z in g f r o m Fi g 9 Th e d e t a il e d a n a l y s e s a r e s ho wn a s f o l l o ws 1 0 t a n 28 0 5 31 7 Th e r e f o r e t h e co o r d in a t e v a l u e in Y d ir e ct io n o f p o in t W is 0 8 0 0 5 31 7 0 26 8 3 W ANG Xia o me i e t al Ma t he ma t i ca l Mo d e l S t u d y o n S o r t in g Tr a ck o f S l id in g Sh o e S o rte r 55 1 o m q 8 0 l I I 1 4 s I 0 2 6 8 3 I I 0 0 3 1 3 7 l 0 0 5 6 36 1 2 6 36 1 5 6 36 x m F ig 9 S o r t i n g t r a ck ma t h e ma t i ca l mo d e l o f s l i d i n g T h e p r o j e ct e d l e n g t h in d ir e ct io n o f W is 0 4 4 5 6 m An d t h e co o r d in a t e v alu e in d i r e ct io n o f P o in t W is 0 1 1 8 0 4 4 5 6 0 5 63 6 T h e n t h e co o r d in a t e v alu e s o f p o in t W a r e d e t e r min e d t o b e 0 5 6 3 6 0 2 6 8 3 I n a d d i t io n t h e p r o j e ct e d l e n g t h i n Y di r e ctio n o f the e n d s e g me n t P 4 P 5 P 6 is 0 3 t a n 2 8 0 1 5 9 5 m T h e r e s u l t s h o w s t h a t t h e p o in t w h ich is p r o j e c t e d b y p o i n t P5 in d i r e ct i o n is s u p e r p o s e d w it h p o i n t P5 Th e r e f o r e the co o r d i na t e v a l u e o f p o in t P5 in d ir e ct io n i s 1 0 0 5 6 3 6 1 5 6 3 6 Th e n t h e co o r d in a t e v alu e o f p o i n t P4 in d i r e ct io n is 1 5 6 3 6 0 3 1 2 6 3 6 An d t h e co o r d i n a t e v a l u e o f p o i n t P4 i n Y d ir e ct io n is t h a t 0 8 0 一 O 3 t a n 2 8 0 6 4O 5 Th e co o rdin a t e v alu e s o f p o in t P4 a r e t h u s d e t e r min e d t o b e 1 2 6 3 6 0 6 4 0 5 T h r o u g h t h e a b o v e a n aly s is t h e s o rt in g t r a ck ma t h e ma t ical mo d e l o f s l id in g s h o e s o r t e r i s s e t up a s 滑块式分拣机分拣道岔的数学模型设计 王晓梅 朱新才 丁又青 周雄 s h o wn in Fi g 9 6 Co n cl u s io n s S l i di ng s h o e s o rte r is a n o v e l a ut o ma t i c s o rtin g e q ui pme n t whi ch me e t s