Modeling and Injection Rate Estimation of a Piezo Injector for CRDI Diesel Engines

C o p y r ig h t 2 0 0 5 K S A E 1 2 2 5 - 6 3 8 2 / 2 0 0 5 / 0 7 4 - 1 3 T r a ns a c tio ns o f K SA E , V o l. 1 3 , N o . 2 , p p .9 3 -1 0 0 (2 0 0 5 )

N o m e nc lature^{1 )}

! : a re a , M^

B : v is c o u s fric tio n c o e ffic ie n t

#_D : d is c h a rg e c o e ffic ie n t

$_ : e le c tric d is p la c e m e n t, _#M

%_ : e le c tric fie ld , _6M

& : fo rc e , .

M : m a s s , KG

*T o w h o m c o rr e s p o n d e n c e s h o u ld b e a d d re s s e d . m s u n w o o @ h a n y a n g .a c .k r

0 : p re s s u re , 0A

1 : v o lu m e tric flo w ra te , _{M S}

3_ : s tra in

4 : s tre s s , 0A

6 : v o lu m e , _M

V : v o lta g e , 6

X : d is p la c e m e n t, M o r s ta te v a ria b le : b u lk m o d u lu s o f fu e l, _.M

 : d e n s ity o f fu e l, KGM^

*

Modeling and Injection Rate Estimation of a Piezo Injector for CRDI Diesel Engines

Sunwoo Kim Namhoon Chung Myoungho Sunwoo^*

Department of Automotive Engineering, Hanyang University, Seoul 133-791, Korea (Received 6 September 2004 / Accepted 25 November 2004)

A b s trac t : S trin g e n t e m is s io n re g u la tio n s a n d in c re a s in g d e m a n d s o n re d u c tio n s o f n o is e a n d v ib ra tio n o f c o m m o n ra il d ire c t in je c tio n (C R D I) d ie s e l e n g in e s le a d to th e a d v e n t o f p ie z o -a c tu a te d in je c to rs . C o m p a re d w ith s o le n o id -a c tu a te d in je c to rs , p ie z o -a c tu a te d in je c to rs g e n e ra te g re a te r fo rc e a n d g iv e fa s te r re s p o n s e tim e , re s u ltin g in m o re a c c u ra te a n d fa s te r in je c tio n s . T h e a c c u ra te a n d fa s t re s p o n s e o f a n in je c to r c a n o ffe r a n o p p o rtu n ity to c o n tro l th e c o m b u s tio n p ro c e s s a n d p o llu ta n t fo rm a tio n . In th is s tu d y , th e m a th e m a tic a l m o d e l o f a p ie z o -a c tu a te d in je c to r is d e v e lo p e d . A n e s tim a to r o f th e in je c tio n ra te o f th e p ie z o -a c tu a te d in je c to r is d e s ig n e d b a s e d o n th is m o d e l. T h e s lid in g m o d e th e o ry is a p p lie d to th e e s tim a to r d e s ig n in o rd e r to o v e rc o m e m o d e l u n c e rta in tie s . T h e in je c to r m o d e l a n d th e e s tim a to r a re v e rifie d b y th e in je c tio n e x p e rim e n ts in a n in je c to r te s t b e n c h . T h e s im u la tio n a n d th e e x p e rim e n ta l re s u lts s h o w th a t th e p ro p o s e d s lid in g m o d e o b s e rv e r c a n e ffe c tiv e ly e s tim a te th e in je c tio n tim in g a n d th e in je c tio n ra te o f th e p ie z o -a c tu a te d in je c to r.

K e y w o rd s : C R D I( ), P ie z o in je c to r( ), In je c tio n ra te ( ), S lid in g m o d e

o b s e rv e r( )

S ubs c ripts : c o n tro l c h a m b e r

, : n e e d le , n e e d le s e a t re s p e c tiv e ly : p o p p e t v a lv e

: p ie z o : s p rin g : s a c c h a m b e r

: v a lv e p is to n o r v a lv e c h a m b e r

1 .

C O2

, P M (p a rtic u la te m a tte r), N O x (id le )

.

.^{1 )} (c o m m o n ra il)

.

(ra il) (fu e l a c c u m u la to r)

.

(E C U ) (ra il p re s s u re ),

(in je c tio n tim in g ), (in je c tio n q u a n tity )

(in je c tio n ra te ) .^{2 ,3 )}

(s o le n o id ) (p ie z o )

.

, .

(p ie z o -a c tu a te d in je c to r) (s o le n o id -a c tu a te d in je c to r)

.

,

.^{1 )}

,

(fe e d b a c k

c o n tro l) .

.

2 .

2 - (2 -w a y v a lv e ) , F ig . 1

. 1 0 0 ~ 3 0 0

(c e ra m ic e le m e n t)

(p ie z o s ta c k ) ,

.

.^{4 )}

( c o n v e r s e p ie z o e le c tr ic e f f e c t) .

( p i e z o s t a c k ) (p o p p e t v a lv e )

. ( c o n t r o l c h a m b e r )

Valve piston Piezo stack

Push rod

Oring Push rod spring

Poppet Valve spring

Return line

Outlet orifice Inlet orfice

Control chamber Servo piston

Needle spring

Accumulator chamber

Needle valve

Injection nozzle

Fig. 1 Operation principle of a piezo injector

(a c c u m u la to r c h a m b e r)

.

3 .

(p ie z o - a c tu a to r m o d e l), (m e c h a n ic a l m o d e l)

(h y d ra u lic m o d e l) .

, .

.^{1 ,7 )}

. . . . .

.

3 .1 3 .1 .1

,

5 )

.

(1 ) (2 )

.^{6 )}

(1)

? (2)

, ,

, ? .

F i g . 2 1 0 0

Fig. 2 Schematic of a piezo stack

. V

, XV . ,

(3 ) .^{4 )}

(3)

(2 ) $ Q

. 3

, % V

(2 ) (4 )

.

? (4)

3 .1 .2

N e w to n 2 .

. , .

(5 ) .

(5)

,

(6 ) .

S u n w o o K im N am h o o n C h u n g M y o u n g h o S u n w o o

(6) , : c ro s s -s e c tio n a l a re a o f n e e d le v a lv e : c ro s s -s e c tio n a l a re a o f n e e d le s e a t 3 .1 .3

(c o n tro l v o lu m e )

. ,

, S a c (7 )

.^{1 0 )}

0?  6 1^IN1_ON6? (7)

, _<

K

3 .2

. F ig . 3 (a ) 6 0 0 b a r, 1 .2

m s

.

,

. 7 5 %

.

. 0 .8 m s

6 0 0 b a r

.

F ig . 3 ( b ) 4 0 0 b a r , 0 .3 m s

( p ilo t in je c tio n ) 1 .4 m s

( m a i n i n j e c t i o n )

.

0 1 2 3 4 5

0 10 20 30

Time [ms]

Inj. rate [mm3/ms]

Measured data Simulation result

Injection Command

(a) Rail pressure : 600 bar, injection duration : 1.2 ms

0 1 2 3 4 5

0 10 20 30

Time [ms]

Inj. rate [mm3/ms]

Measured data Simulation result

Injection Command

(b) Rail pressure : 400 bar, pilot injection duration : 0.3 ms, main injection duration : 1.4 ms

Fig. 3 Comparison between the measured and modeled injection rate

,

. 0 .1 m s .

. ,

(in je c tio n ra te m e te r) . F ig . 3 (a ) (b )

3 % .

M o d e lin g an d In je c tio n R ate E s tim atio n o f a P ie z o In je c to r f o r C R D I D ie s e l E n g in e s

,

.

4 .

4 .1

(s ta te v a ri-

a b le ) ,

.

,

.

(o b s e rv e r) .

, .

.

4 .2

. (L u e n b e rg e r)

8 )

9 )

. 8

, 2 1

. (8 )

,

(9 ) .

:?pF : 7 ⁽⁸⁾

, ^{: p ;X X X  X X X X X=} p ;Q X_V X?  0_{V V} 0_C X_N X_N?  0_S=

p

ppX>? ppFp FF:>7  KppSGNXNpX> 

ppX>? ppFp FF:>7  KppSGNXNpX> 

ppX>? ppFp FF:>7  KppSGNXNpX> 

(9)

^

. (1 0 )

(1 1 ) .

pX^ ppXN X>pp ⁽¹⁰⁾

pppX^? pprFN KppSGN X^p pppX^? pprF N KppSGN X^p pppX^? pprF_{ }N KppSGN X^p

(11)

, rF_I F_I: 7 N F_I:> 7

S ^{(1 2 )}

cI (1 3 )

.

S  X^p_ (12)

DTD ^ 

 

 S^  SS?

pppppppppppppppppppppppppppppppppppppppp X^p_IrF_INK_ISGNX^p_ Nc_I£S£

(13)

KI (1 4 ) .

KI cI£^rFI£ ⁽¹⁴⁾

(1 4 ) X^p_ 0

. :T

.

5 .

F ig . 4 (in je c to r te s t b e n c h )

.

. 1 0 0 ~ 1 4 0 0 b a r

(p u ls e g e n e ra to r) (in je c to r d riv e r)

.

. O N O S O K K I

F J 4 0 0 P IE Z O M E C H A N IK

. .

Fig. 4 Experimental setup of injector test bench

6 .

,

. F ig . 5

,

. F ig . 5 (a ), (b ), (c ) (d )

1 .2 m s ,

4 0 0 , 6 0 0 , 8 0 0 , 1 2 0 0 b a r . F ig . 5 (e )

(f) 1 .4 m s 0 .3

m s

4 0 0 , 6 0 0 b a r .

F ig . 5 (a ), (b ) (c ) ,

1 0 %

(o v e rs h o o t) . F ig . 5 (b )

6 0 0 b a r

.

. 1 2 0 0

b a r F ig . 5 (d )

.

(in te rn a l le a k a g e )

(c a v ita tio n )

. F ig . 5 (e ) (f)

. 3 %

.

.

7 .

(fe e d b a c k c o n tro l)

,

.

. . 1 )

0 50 100 150

Voltage [V]

0 2 4 6 8

Charge [×10-4C] M e a sure d

Estim a te d

0 1 2 3 4 5

0 10 20 30 40

Tim e [m s]

Inj. rate [mm3/ms]

M e a sure d Estim a te d Ra il pre ssure : 400 ba r Inje ction dura tion : 1.2 m s

0 50 100 150

Voltage [V]

0 2 4 6 8

Charge [×10-4C]

0 1 2 3 4 5

0 10 20 30 40

Tim e [m s]

Inj. rate [mm3/ms]

M e a sure d Estim a te d

M e a sure d Estim a te d Ra il pre ssure : 1200 ba r Inje ction dura tion : 1.2 m s

(a) Rail pressure of 400 bar, injection duration of 1.2 ms (d) Rail pressure of 1200 bar, injection duration of 1.2 ms

0 50 100 150

Voltage [V]

0 2 4 6 8

Charge [×10-4C]

0 1 2 3 4 5

0 10 20 30 40

Tim e [m s]

Inj. rate [mm3/ms]

M e a sure d Estim a te d

M e a sure d Estim a te d Ra il pre ssure : 600 ba r Inje ction dura tion : 1.2 m s

0 50 100 150

Voltage [V]

0 1 2 3 4 5

0 10 20 30 40

Tim e [m s]

Inj. rate [mm3/ms]

0 2 4 6 8

Charge [×10-4C] M e a sure d

Estim a te d

M e a sure d Estim a te d Ra il pre ssure : 400 ba r P ilot dura tion : 0.3 m s M a in dura tion : 1.4 m s

(b) Rail pressure of 600 bar, injection duration of 1.2 ms (e) Rail pressure of 400 bar, pilot injection duration of 0.3 ms, main injection duration of 1.4 ms

0 50 100 150

Voltage [V]

0 2 4 6 8

Charge [×10-4C]

0 1 2 3 4 5

0 10 20 30 40

Tim e [m s]

Inj. rate [mm3/ms]

M e a sure d Estim a te d

M e a sure d Estim a te d Ra il pre ssure : 800 ba r Inje ction dura tion : 1.2 m s

0 50 100 150

Voltage [V]

0 1 2 3 4 5

0 10 20 30 40

Tim e [m s]

Inj. rate [mm3/ms]

0 2 4 6 8

Charge [×10-4C] M easured

Es tim ated

M easured Es tim ated Ra il pre ssure : 600 ba r P ilot dura tion : 0.3 m s M a in dura tion : 1.4 m s

(c) Rail pressure of 800 bar, injection duration of 1.2 ms (f) Rail pressure of 600 bar, pilot injection duration of 0.3 ms, main injection duration of 1.4 ms

Fig. 5 Comparison between the measured and estimated electric charge and injection rate

S u n w o o K im N am h o o n C h u n g M y o u n g h o S u n w o o

.

2 ) 8

.

3 0 ,

1 5 % ,

3 % .

3 )

.

4 ) 4 0 0 ~ 1 2 0 0 b a r

. 5 )

.

(M 1 -0 4 1 2 -0 0 -0 0 5 8 )

(M 1 0 4 2 6 0 1 0 0 6 -0 4 L 2 6 0 1 -0 0 6 1 5 )

, .

R e fe re nc e s

1 ) K . N a m , S . P a r k a n d M . S u n w o o , “ D y n a m ic M o d e l o f a n H S D I C o m m o n - r a il I n je c to r a n d I n je c tio n R a te E s tim a tio n ,” T r a n s a c tio n s o f K S A E , V o l.1 1 , N o .5 , p p .4 3 - 4 9 , 2 0 0 3 .

2 ) G . S tu m p p a n d M . R ic c o , “ C o m m o n R a il - A n A ttr a c tiv e F u e l I n je c tio n S y s te m f o r P a s s e n g e r C a r D I D ie s e l E n g in e s ,” S A E 9 6 0 8 7 0 , 1 9 9 6 .

3 ) W . B o e h n e r a n d K . H u m m e l, “ C o m m o n R a il I n je c tio n S y s te m f o r C o m m e r c ia l D ie s e l V e h i- c le s ,” S A E 9 7 0 3 4 5 , 1 9 9 7 .

4 ) N . J a lili, J . W a g n e r a n d M . D a d f a r n ia , “ A P ie z o e le c tr ic D r iv e n R a tc h e t A c tu a to r M e c h a - n is m w ith A p p lic a tio n to A u to m o tiv e E n g in e V a lv e s ,” M e c h a tr o n ic s , V o l.1 3 , p p .9 3 3 - 9 5 6 , 2 0 0 3 .

5 ) H . A d r ia e n s , W . L . d e K o n in g a n d R . B a n n in g ,

“ M o d e lin g P ie z o le c tr ic A c tu a to r s ,” I E E E / A S M E T r a n s a c tio n s o n M e c h a tr o n ic s , V o l.5 , N o .4 , p p .3 3 1 - 3 4 1 , D e c , 2 0 0 0 .

6 ) A n A m e r ic a n N a tio n a l S ta n d a r d : I E E E S ta n - d a r d o n P ie z o e le c tr ic ity , A N S I /I E E E S ta n d a r d 1 7 6 - 1 9 8 7 , 1 9 8 7 .

7 ) D . B a r a n o w s k i, W . K lu g l a n d D S c h o p p e ,

“ S im u la tio n a n d D e s ig n O p tim iz a tio n o f a C o m m o n R a il P ie z o I n je c to r f o r P a s s e n g e r C a r D I D ie s e l E n g in e s ,” F u e l I n je c tio n S y s te m s , p p .2 1 9 - 2 3 2 , 1 9 9 9 .

8 ) E . A . M is a w a a n d J . H e d r ic k , “ N o n lin e a r O b s e r v e r s - A S ta te - o f - th e - A r t S u r v e y ,” T r a n s . A S M E , J o u r n a l o f D y n a m ic S y s te m s , M e a s u r e - m e n t, a n d C o n tr o l, V o l.1 1 1 , S e p ., 1 9 8 9 .

9 ) J . E . S lo tin e , J . K . H e d r ic k a n d E . A . M is a w a ,

“ O n S lid in g O b s e r v e r f o r N o n lin e a r S y s te m s ,”

T r a n s . A S M E , J o u r n a l o f D y n a m ic S y s te m s , M e a s u r e m e n t, a n d C o n tr o l, V o l.1 0 9 , S e p ., 1 9 8 7 .

1 0 ) V . L . S tr e e te r a n d E . B . W y lie , F lu id M e c h a - n ic s , M c G r a w - H ill, N e w Y o r k , 1 9 7 9 .