S t a n i s ł a w T O R
D e p a r t m e n t of M a c h i n e r y B u i l d i n g a n d A v i a t i o n R Z E S Z Ó W U N I V E R S I T Y O F T E C H N O L O G Y
C O M P U T E R A I D E D D E S I G N O F T R A N S M I S S I O N P O W E R S Y S T E M O F T H E R O A D B U I L D I N G M A C H I N E S
S u m m a r y . W h e n d e s i g n i n g the p o w e r t r a n s m i s s i o n s y s t e m s of b u i l d i n g m a c h i n e s it is n e c e s s a r y to k n o w the d y n a m i c loads.
W e c a n d e t e r m i n e t h e s e loads by m e a n s of s i m u l a t i o n c a l c u l a t i o n s on t h e c o m p u t e r s - u s i n g c o m p u t e r a i d e d design.
S i m u l a t i o n c a l c u l a t i o n s a r e c a r r i e d out for the a d e q u a t e m a t h e m a t i c a l mo d e l s , w h i c h c h a n g e t h e i r fo r m s a c c o r d i n g to the o p e r a t i o n c o n d i t i o n of the p o w e r t r a n s m i s s i o n system.
T h e p r o gram, d e v e l o p e d by the a u t h o r , of s u c h c a l c u l a t i o n s c a n go into c o m p l e x C A D p r o g r a m or be a s u p p o r t s o f t w a r e for C A D in t r a d i t i o n a l d e s i g n i n g .
1. I n t r o d u c t i o n
W h e n d e s i g n i n g the e l e m e n t s of m a c h i n e s it is n e c e s s a r y to k n o w the d y n a m i c loads. D e t e r m i n a t i o n of t h e s e loads b y the t r a d i t i o n a l d e s i g n m e t h o d s is not p o s s i b l e a n d t h e y a r e e s t i m a t e d by m u l t i p l i c a t i o n of s t a t i c loads by d y n a m i c loads factor. Then, the r e s u l t s of c a l c u l a t i o n s a r e v e r i f i e d b y t h e m e a n s of m e a s u r e m e n t on the real o b j e c t - a f t e r the p r o t o t y p e has b e e n p r o d u c e d .
U s i n g c o m p u t e r a i d e d d e s i g n (CAD), t h e s e loads c a n be r e l a t i v e l y p r e c i s e l y d e t e r m i n e d by the m e a n s of d i g i t a l s i m u l a t i o n c a r r i e d out for p r o p e r l y f o r m u l a t e d p h y s i c a l a n d m a t h e m a t i c a l m o d e l s w h i c h in c a s e of p o w e r t r a n s m i s s i o n s y s t e m s can c h a n g e t h e i r f o r m s on e a c h p h a s e of th e i r o p e r a t i o n , such as: st a r t i n g , e n g a g i n g , s l i p a n d the like. T h e d e s c r i p t i o n of some e l e m e n t s of such a p r o c e d u r e will be s u b j e c t of the p r e s e n t paper.
2 . -G e n e r a l a l g o r i t h m of the m e t h o d
W e c a n d e t e r m i n e the d y n a m i c loads s o l v i n g an e q u a t i o n of m o t i o n of s y s t e m ’s e l e m e n t s , i n c l u d i n g m a c h i n e s t r u c t u r e , t a k i n g into c o n s i d e r a t i o n e x t e r n a l r e a c t i o n a n d the f a c t o r s r e l a t e d to the po w e r t r a n s m i s s i o n s y s t e m a n d its c o n trol. S o l v i n g the e q u a t i o n of m o t i o n - the m a t h e m a t i c a l m o d e l , we c a n a l s o s t u d y the o t h e r d y n a m i c p h e n o m e n o n such as loads d i s t r i b u t i o n for the i n d i v i d u a l d r i v i n g axles, d e t e r m i n e the c o u r s e of d r i v i n g force, d e t e r m i n e a m p l i t u d e - f r e q u e n c y c h a r a k t e r i s t i c s , s t u d y the e f f e c t of the f a c t o r s , w e can i n t e r s t e d in, s u c h as e.g. the t u r n - o n time of c o n t r o l c l u t c h e s - th e i r c h a r a k t e r i s t i c s on the v a l u e of d y n a m i c loads.
In o r d e r to c a r r y out the c a l c u l a t i o n it is n a c e s s a r y to k n o w the p a r a m e t e r s of m a t h e m a t i c a l mo d e l s u c h as m a s s m o m e n t s of inertia, t o r s i o n a l r i g i d i t y c o e f f i c i e n t s , d a m p i n g c o e f f i c i e n t s , p e r f o r m a n c e c h a r a c t e r i s t i c s of e n g i n e a n d h y d r o k i n e t i c t o r q u e c o n v e r t e r , etc.
T h e s e p a r a m e t e r s c a n be d e t e r m i n e d a l r e a d y in the d e s i g n p h a s e . A s a g e n e r a l rule, a l r e a d y at t h e b e g i n n i n g of d e s i g n we d e t e r m i n e the p o w e r of m a c h i n e ' s d r i v i n g motor, the c h a r a c t e r i s t i c of h y d r o k i n e t i c t o r q u e c o n v e r t e r , c a p a c i t y of b u c ket, l i f t i n g c a p a c i t y of m a c h i n e , p a r a m e t e r s of t y r e a n d the like.
T h e o t h e r p a r a m e t e r s of the m o d e l - s u c h as t o r s i o n a l r i g i d i t y c o e f f i c i e n t - w e c a n d e t e r m i n e by m e a n s of c a l c u l a t i o n b a s i n g o n the k n o w n d e p e n d e n c e s or w e can a s s u m e on the b a s i c of r e l a t i v e d i m e n sions. G e n e r a l b l o c k d i a g r a m of the m e t h o d is s h o w n in F i g . l . , w h i l e the initial f o r m of p h y s i c a l m o d e l - F i g . 2.
A s it has b e e n a l r e a d y d e s c r i b e d in the i n t r o d u c t i o n , b o t h p h y s i c a l and m a t h e m a t i c a l m o d e l s c h a n g e t h e i r f o r m s on e a c h p h a s e of o p e r a t i o n of the p o w e r t r a n s m i s s i o n s y s t e m e.g.: the e n g a g i n g is f o l l o w e d by the c h a n g e of p h y s i c a l a n d m a t h e m a t i c a l m o d e l - r e d u c t i o n of the d e g r e e of f r e e d o m of the s y s t e m [5] , a f t e r the s l i p of the w h e e l s in r e l a t i o n to s u b s t r a t e t h e c o n d i t i o n of e n g a g i n g of the p o w e r t r a n s m i s s i o n s y s t e m w i t h the l o a d e r ' s s t r u c t u r e c h a nge, a n d the like; t h e r e f o r e in e v e r y s t e p of i n t e g r a t i o n the c o n d i t i o n s d e t e r m i n i n g the a s s u m p t i o n of the mod e l a d e q u a t e for c a l c u l a t i o n m u s t be c h e c k e d . A f t e r e a c h c h a n g e of m o d e l it is n e c e s s a r y to v e r i f y the a n g u l a r p a t h e s [5] In o r d e r to c o n t i n u e the c a l c u l a t i o n s on the n e w m o d e l .
dote» boo© I catalogue of pro- due t* power Ind©x, own ox per Ione«
•ntry assumption© capacity* power, driving fore©*
parameters of th© hydrok I net Ic torque converter*
transmission ratio* parameter of th© tyre* speed
t ~
•laboratlon of mathematical and physical models*
adequate for phenomenons In question* for instance:
load distribution* dynamic loads* gaI lop* runlng ...
calculation or assumption of parameters of the mode I
digital simulation* calculation of dynamic loads*
In the transmission assembly* velocity* acceleration
strenght calculation of the t p s elements*
dimensioning TPS elements* calculation of actual parameter of the model
verification calculation© TPS elemsnts optimization* technical documentation
construction and experimentation on the prototype date base I I
formulas* nomograms*
tables for deter
mining parameters of the model
data base I I I computer program«
I Ibrary
Fig.l. G e n e r a l b l o c k d i a g r a m of C A D m e t h o d for p o w e r t r a n s m i s s i o n s y s t e m s of b u i l d i n g m a c h i n e
l a i V i / l o )
J o J*i Mt2Ci3
j J
2
J a J * J s ^ J JeM ,Js
Jj j=L
*2
'Hg H
11
' / / / 7 7 7 7
W
F i g . 2. P h y s i c a l m o d e l of loader T P S d u r i n g start m o v i n g by c l u t c h i n g in d i r e c t i o n c l o u t c h
3. N u m e r i c a l f o r m u l a t i o n of s e l e c t e d t r a n s i e n t s t a t e s o c c u r r e d in p o w e r t r a n s m i s s i o n s y s t e m of b u i l d i n g m a c h i n e s
W i t h the c h a n g e of the f o r m of m o d e l the d i s c o n t i n u i t i e s of the d e s c r i b i n g f u n c t i o n o c c u r r e s u l t i n g in s p e c i f i c p r o b l e m s c o n c e r n i n g t h e i r d i s c r i p t l o n . T h e s e t r a n s i e n t s t a tes, s u c h as e.g. e n g a g i n g , s t a r t i n g , r u p t u r e of the whee l s ' a d h e s i o n to s u b s t r a t e a n d the like, h a v e to be c o r r e c t l y n u m e r i c a l l y f o r m u l a t e d .
Let c o n s i d e r - for i l u s t r a t i o n - t h r e e cases.
3.1. E n g a g i n g
In the b u i l d i n g m a c h i n e s the h y d r o m e c h a n i c a l p o w e r t r a n s m i s s i o n s y s t e m s , c o n t r o l l e d b y t h e m u l t i p l e - p l a t e f r i c t i o n c l u t c h , a r e m a i n l y U6ed.
T i m e t0 ~ w h e n the c l u t c h p l a t e s c o m e i n t o c o n t a c t (Fig. 3) is a s s u m e d to' be the po i n t of the b e g i n n i n g of e n g a g i n g (moment of f r i c t i o n Mc+ 0), w h i l e t i m e - as the e n d of e n g a g i n g w h e n the a n g u l a r
v e l o c i t i e s of a c t i v e a n d p a s s i v e p a r t of the c l u t c h a r e equal, i.e.!
W z <
1
>w h e r e : - a n g u l a r v e l o c i t y of t h e c l u t c h ' s a c t i v e part - a n g u l a r v e l o c i t y of the c l u t c h ' s p a s s i v e part
a û
yi
F i g . 3. C o u r s e of the e n g a g i n g . a - p h y s i c a l m o d e l
b - d e t e r m i n a t i o n of the po i n t of e n g a g i n g
T h e r e f o r e , w h e n m a k i n g the i n t e g r a t i o n of d i f f e r e n c i a l e q u a t i o n w e h a v e to e x a m i n e the c o n d i t i o n (1) in e v e r y s t e p of the in
t e g r a t i o n .
A s it is s e e n f r o m F i g . 3, e v e n w i t h the small s t e p of i n t e g r a t i o n of d i f f e r e n t i a l e q u a t i o n the " o m i s s i o n " of the p o i n t of e n g a g i n g can h a p p e n , i.e. the s i t u a t i o n w h e n for:
w h i l e f o r t»t2:
(2)
T h e s y s t e m b e c o m e s d i v e r g e n t , f u r t h e r c a l c u l a t i o n s are i m p o ssible. So, w e h a v e to c o r r e c t the s t e p S of i n t e g r a t i o n . T h e m o s t e f f e c t i v e w a y c o n s i s t s in it that w e h a l v e the b a s i c i n t e g r a t i o n s t e p a n d e x a m i n e the d i f f e r e n c e for the t i m e t x* S / 2 .
If this d i f f e r e n c e is p o s i t i v e , t h e n w e d e v i d e the i n t e g r a t i o n s t e p
b y f o u r a n d a g a i n c a l c u l a t e the d i f f e r e n c e 2 for the time t1+3/4fl’, etc., till the c h a n g e of s i g n o c c urs. A f t e r t h e c h a n g e of s i g n of the d i f f e r e n c e w e h a l v e the last s t e p a n d s u b s t r u c t f r o m the last time.
W e p r o c e e d this w a y till the s t a t e of e q u a l i t y of a n d is r e a c h e d , for the a s s u m e d n u m e r i c a l a c c u r a c y .
3.2. St a r t i n g .
T h e t y r e d d r i v e n w h e e l is i n f l u e n c e d by the b a s i c lo a d s shown in F i g . 4.
a } tO cD
M n = 0
Q ^ Q
R ^ 7 7 /
\ M n
7 7 7 R
F i g . 4. B a s i c loads i n f l u e n c i n g t y r e d d r i v e n w h e e l
F r o m the p o i n t of v i e w of i n t e r a c t i o n of the p o w e r t r a n s m i s s i o n s y s t e m - wh e e l a n d l o a d e r ' s s t r u c t u r e , w e d i s t i n g u i s h t h r e e bas i c s t a t e s :
a) - s t a t e of s t a r t i n g w h e n M„<R-e^v b) - s t a t e of s t a r t i n g w h e n M ^ R - e ^ c) - s t a t e of m o t i o n w h e n
D u r i n g s t a r t i n g the a r m of r o l l i n g r e s i s t a n c e t o r q u e c h a n g e s its v a l u e f r o m e*0 at Ma- 0 to « “«»ax at the m o m e n t w h e n i.e. at the m o m e n t of st a r t i n g .
W e can d e t e r m i n e the real v a l u e of the a r m of r o l l i n g r e s i s t a n c e t o r q u e d u r i n g s t a r t i n g f r o m the e q u i l i b r i u m c o n d i t i o n :
R-e~Mn (4)
W e put v a l u e of e, d e t e r m i n e d f r o m the above, into the p r o p e r d i f f e r e n c i a l e q u a t i o n of the m a t h e m a t i c model.
F u l f i l m e n t of the propel c o n d i t i o n of t h e s y s t e m (3) d e t e r m i n e s the s e l e c t i o n of the a d e q u a t e model.
3.3. S l i p
At the m o m e n t w h e n the v a l u e of the d r i v i n g t o r q u e e x c e e d s the v a l u e of the t o r q u e r e s u l t i n g f r o m the a d h e s i o n of the w h e e l s to s u b s t r a t e , b o t h the s l i p a n d the c h a n g e of the m a t h e m a t i c a l m o d e l will occur. That c h a n g e is c o n d i t i o n e d b y the d e p e n d e n c e :
s t a t e w i t h o u t s l i p 1. Ma-R -ei. R-u
(5)
s l i p 2 ,Ma-R -t»R -u
where: e - real v a l u e of the a r m of r o l l i n g r e s i s t a n c e torque, u - a d h e s i o n c o e f f i c i e n t of the w h e e l to s u b s t r a t e
a s s u m i n g the m o d e l of C o u l o m b f r i ction.
F i l f i l m e n t of o n e c o n d i t i o n out of (5) c a u s e s t r a n s i t i o n to the p r o p e r m a t h e m a t i c a l mode l .
C h e c k i n g of the c o n d i t i o n s t a k e s p l a c e in e v e r y s t e p of i n t e g r a t i o n .
F i g . 5. A n a l i t i c a l t o r q u e m o m e n t c o u r s e s , d u r i n g o v e r l o a d
a - d y n a m i c loads c a l c u l a t e d d u r i n the start w i t h full s l i d i n g in the h y d r o k i n e t i c t o r q u e c o n v e r t e r ,
b - as above, w i t h c a r r y i n g up fr o n t d r i v i n g a x l e
4. C o n c l u s i o n
O b t a i n e d r e s u l t s of the d e s c r i b e d m e t h o d - t a k e n b y w a y of e x a m p l e the c u r v e in F i g . 5. - v e r i f i e d d u r i n g m e a s u r e m e n t s o n the real o b j e c t , a r e s a t i s f a c t o r y .
D e v e l o p e d p r o g r a m s 0 DUN 1 , D 0 U N 2 , O D L U T F O R a l s o e n a b l e to st u d y the o t h e r d y n a m i c p h e n o m e n a in the p o w e r t r a n s m i s s i o n s y s t e m of w h e e l e d loaders, s u c h as: o v e r l o a d s in the c y c l e s s i m u l a t i n g o v e r l o a d s , e f f e c t of c l e a r a n c e s , c h a n g e of t r a v e l l i n g d i r e c t i o n w i t h o u t c o m p l e t e s t o p p a g e of the m a c h i n e a n d the like.
T h e p r o g r a m s , e n a b l i n g s t u d y the o t h e r p h e n o m e n a , s u c h as: snaki n g , c i r c u l a t e power, p o r p o i s i n g , etc, a r e in the c o u r s e of their d e v e l o p m e n t .
R E F E R E N C E S
[1] B a r a n I., M a r c h e l e k K. : R e d u k c j a s t o p n i s w o b o d y u k ł a d ó w d y s k r e t n y c h . M e c h a n i k a t e o r e t y c z n a i s t o s o w a n a , t o m 9.
zesz . l . P W N W a r s z a w a 1971.
[2] O s i e c k i I.: E l e m e n t y m o d e l o w a n i a w d y n a m i c e m a s z y n . D y n a m i k a m a s z y n . P A N O s s o l i n e u m . W a r s z a w a 1974.
[3] S w i ą t o n i o w s k i A.: A n a l i z a w s p ó ł z a l e ż n o ś c i p o m i ę d z y d r g a ni a m i w a l c a r k i a p r z e b i e g i e m pr o c e s u . Z e s z y t y N a u k o w e A G H n r 26 K r a k ó w 1991.
[4] P i e c z o n k a K. : O b c i ą ż e n i a u k ł a d u n a p ę d u j a z d y ł a d o w a r e k ł y ż k o w y c h p r z y r o z r u c h u . P r a c e n a u k o w e IKiEM. P o l i t e c h n i k a W r o c ł a w s k a 18 i 24. W r o c ł a w 1974.
[5] T o r S.: M o d e l o w a n i e n a E M C z j a w i s k d y n a m i c z n y c h w u k ł a d z i e n a p ę d o w y m ł a d o w a r k i k o ł o w e j . P r a c e N a u k o w e C P B P 0 2 . 0 5 P o l i t e c h n i k a W a r s z a w s k a 1990.
[6] W i l s o n W.K.: P r a c t i c a l S o l u t i o n of T o r s i o n a l V i b r a t i o n s P r o b l e m s . V o l u m e one. C h a p m a n a n d H a l l Ltd, L o n d o n 1956.
R e v i s e d by: Stanisław W o j c i e c h