Afeasibilitystudyofon-linedrillwearmonitoringbyDDSmethodology

8/3/2019 Afeasibilitystudyofon-linedrillwearmonitoringbyDDSmethodology

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Int. J. M ach. To ol De s. Re s. V ol . 26. No. 3. pp. 245-2 57. 1986. 11112(I-7357/86$3.0ll+.l}l)Printed in Gre at Britain Pcrgamon Journals Ltd.

A F E A S I B I L I T Y S T U D Y O F O N - L I N E D R I L L W E A RM O N I T O R I N G B Y D D S M E T H O D O L O G Y

P U L A K B A N DY O PA D H YA Y ,* E V E RS M O L I N A G O N Z A L E Z , * R E N H U A N G t a n d S . M . W u *(Received 4 June 1985)

A h s t r a c t - - A n e w a p p r o a c h t o a c h i e v e o n - l i n e dr i ll l if e m o n i t o r i n g is i n t r o d u c e d u s i n g t h e D y n a m i c D a t aS y s t e m ( D D S ) m e t h o d o l o g y . C h a n g e s i n th e t h r u s t a n d t o r q u e o f t h e d r il l in g p r o c e s s w e r e i n v e s t i g a t e d . As t a t ic a n a l y s i s p r o v i d e d p o o r c o r r e l a t i o n a n d l o w s e n s i ti v i ty b e t w e e n a v e r a g e t h r u s t / t o r q u e a n d d r i ll f la n k w e a r .T h e d y n a m i c p a r a m e t e r s ( n a t u r a l f r e q u e n c i e s a n d d a m p i n g r a t io s ) o f t h e d r il l in g p r o c e s s w e r e s t r o n g l y re l a t e dw i t h th e a v e r a g e d r il l f la n k w e ar . H e n c e , a n e w p a r a m e t e r " N o r m a l i z e d D a m p i n g R a t i o " ( N D R ) w a s f o r m e df r o m t h e D D S a n a l y s is u s i n g t h e d y n a m i c p a r t o f t h e s i g n a l w h i c h c o r r e l a t e s w i t h d r i ll w e a r . T h e p o s s i b il i ty o fd e v e l o p i n g a n o n - l i n e d r i l l f l a n k w e a r m o n i t o r i n g s c h e m e u s i n g t h e N D R i n d e x i s p o i n t e d o u t .

1 . I N T R O D U C T I O NFR OM THE t i m e w h e n F . W . T a y l o r [1 ] fi rs t d e v e l o p e d t h e t o o l l i f e e q u a t i o n , s e v e r a la t t e m p t s w e r e m a d e t o i m p r o v e t h e T a y l o r 's e q u a t i o n b y in c o r p o r a ti n g t h e e f f e c ts o fd i f f e r e n t m a c h i n i n g v a r i a b l e s [ 2-- 4] a s w e l l a s s t o c h a s t ic n a t u r e o f t h e p r o b l e m [ 5 - 7 ].W i t h t h e i n t r o d u c t i o n o f a d a p t i v e c o n t r o l i n m a c h i n i n g , t h e c o n c e p t o f " o n - l i n et o o l - l i f e m o n i t o r i n g " c a m e i n t o l i g h t w h e r e t h e c u t t i n g t o o l - l i f e i s m o n i t o r e d a n de s t i m a t e d d u r i n g c u t t i n g u s i n g a p p r o p r i a t e t r a n s d u c e r s a n d s i g n a l a n a l y s i s d e v i c e s .B a s i c a l l y , t w o t y p e s o f o n - l i n e t o o l - l i f e m o n i t o r i n g s c h e m e s p r e v a i l :1. D i r ec t M e t h o d - - w h e r e t h e c o n d i t i o n o f t h e t o o l i s m o n i t o r e d i n t e r m s o f i ts p h y s i c a l

p a r a m e t e r s l i k e t o o l w e a r [ 8 , 9 ] .2 . I n d ir e c t M e t h o d - - w h e r e o t h e r p a r a m e t e r s s u c h a s t h r u s t , t o r q u e o r v i b r a t i o n i sm e a s u r e d o n - l in e a n d c o r r e l a t e d t o t h e p h y s i c a l c o n d i t i o n o f t h e t o o l [1 0 - 1 2 ] .

M o s t o f t h e s e m e t h o d s c a n s u c c e s s fu l ly d e t e c t a n d p r e d i c t s u d d e n f a il u re o f t h e c u t ti n gt o o l. H o w e v e r , t h e p r o b l e m t o m o n i t o r a n d f o r e c a s t th e t o o l l if e s ti ll re m a i n s , b e c a u s e o ft h e l a ck o f p r o p e r c o r r e l a t io n b e t w e e n t h e m e a s u r e d p a r a m e t e r a n d g r a d u a l to o l w e a r , a sw e l l a s u n a v a i l a b i l it y o f s i g n a l a n a ly s i s p r o c e d u r e s u i t a b l e f o r o n - l i n e u s e .W i t h t h e i n t r o d u c t io n o f t h e D y n a m i c D a t a S y s t e m ( D D S ) m e t h o d o l o g y , i t is p o s s i b let o i d e n ti fy t h e d y n a m i c s o f a c o n t i n u o u s s y s t e m b y d e v e l o p i n g a m a t h e m a t i c a l m o d e l i nt h e f o r m o f a l i n e a r d if f e r e n t ia l e q u a t i o n ( A p p e n d i x A ) .U n d e r p r a c t i c a l c i rc u m s t a n c e s , i t is m o r e c o n v e n i e n t t o r e c o r d a n d a n a l y s e t h e d i s c r e t ed a t a o b t a i n e d f r o m t h e s y s t e m . T h e d y n a m i c s o f a c o n t i n u o u s s y s t e m , s a m p l e d a tu n i f o r m s a m p l i n g i n t e r v a l, A , c a n b e r e p r e s e n t e d b y a s t o c h a s t i c d i f f e r e n c e e q u a t i o n i nt h e f o r m o f a t i m e s e r i e s [ 1 4 ] . T h e s e m o d e l s a r e k n o w n a s A u t o r e g r e s s i v e M o v i n gA v e r a g e ( A R M A ) m o d e l s o f o r d e r (n , m ) .O n c e t h e a d e q u a t e o r d e r o f th e A R M A m o d e l is f o u n d f ro m t h e d a t a , t h e d y n a m i cc h a r a c t e r i s ti c s o f t h e s y s t e m n a m e l y n a t u r a l f r e q u e n c i e s a n d d a m p i n g r a t i o s c a n a l s o b ei d en t if ie d . T h e A R M A m o d e l c a n p r o v id e f u r t h e r in f o r m a t io n s u c h a s d i s p e rs i o n o rp o w e r a t e a c h m o d e o f v i b r a ti o n , a n d f r e q u e n c y r e s p o n s e o f t h e s y s t e m in t e r m s o fa u t o - s p e c t r u m .T h e D D S m e t h o d o l o g y h a s b e e n a p p l i e d t o i d e n ti fy t h e d y n a m i c s o f m a c h i n i n gp r o c e s s e s o n - l i n e . A l s o t h i s t e c h n i q u e w a s u s e d t o m o n i t o r a s i n g l e p o i n t c u t t i n g t o o lw e a r [ 13 ] as w e l l a s d ri ll c o n d i t i o n m o n i t o r i n g b a s e d o n h o l e q u a l i t y [ 17 ]. I n b o t h c a s e s ,* U n i v e r s i t y o f W i s c o n s i n - - M a d i s o n , M a d i s o n , W i s c o n s i n 5 3 7 0 6 , U . S . A .t V i s i ti n g s c h o la r a t U W - - M a d i s o n f r o m N a n j i n g I n s t. o f T e c h n o l . , P e o p l e s R e p u b l i c o f C h i n a .

24 5


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246 P. BANDYOPADHYAYe t a l .

the dynamics of the machining process was evaluated and successfully correlated to thephysical parameters of the system.In the present work, an analysis is carried out to correla te the flank wear of drills withthe dynamics of the drilling process using DDS methodology. The objectives of thepresent work is two-fold:1. To develop a simple and reliable criterion for drill life which can be measured and

monitored on-line.2. Also to investigate how the developed criterion change for different cuttingconditions, i.e. for different drill diameters and cutting speeds.

2. E X P E R I M E N T A T I O N

2.1. Experimental planFor the purposes of experimenta tion, the following criteria and operating conditions

are selected:(a) Tool l i fe cri terion--The average flank wear (Fig. 1) is used as the criterion to

characterize the drill condition.

A v e . f l a n k w e a r = - -B+C+D4

FIG. 1.

(b) Choice o f performance indice s--The static and dynamic components of boththrust and torque are used as indirect parameters to be correlated with averageflank wear of the drill.(c) Cutt ing condit ions--Three different sets of experiments were run to study theeffects of change in drill diameter and drilling speeds separately. The cuttingconditions are indicated in Table 1.

TABLE 1. CUT I~ING CONDITIONS

C a s e D r il l R P M F e e d r a t e D e p t h o fd i a m e t e r ( I P R ) h o l eI 3/8" 825 0.00 9 14'"II 3/8" 665 0.00 9 14'"I I I 1 /4" 825 0 .009 ~"


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A Feasibility Study of On-line Drill Wear 247( d ) M ater ia l and geom et ry - -T he c h o i c e o f w o r k p i e c e - t o o l m a t e r i a l c o m b i n a t i o n is

k e p t f i x e d i n a l l t h r e e c a s e s .T o o l m a t e r ia l - H S S ( H a r d n e s s 5 8 ~ 6 0 R C )T o o l g e o m e t r y - 1 18 p o i n t a n g l e , s t d . t w i s t d r i ll .W o r k p i e c e m a t e r ia l - G r a y C a st i r o n , 1 8 0 ~ 2 2 0 B H N .

2 . 2 . Experimental procedureI n a l l t h e t h r e e c a s e s , e x t e n s i v e t o o l l if e t e s ts w e r e c a r r i e d o u t i n a s i n g le s p i n d l e

d r il li n g m a c h i n e . T h e p r o g r e s s i v e w e a r w a s m e a s u r e d o f f - li n e a f t e r a c e r t a i n n u m b e r o fh o l e s w e r e d r i l l e d u s i n g a d r i l l p a r a m e t e r m e a s u r i n g m i c r o s c o p e . T h e t h r u s t a n d t o r q u es ig n al s c o m i n g f r o m a " K I S T L E R 9 2 7 1 A " t w o c h a n n e l d y n a m o m e t e r ( F ig . 2 ) w e r er e c o r d e d f o r t h e n e x t h o l e . T h e e n d o f d ri ll l if e is c h a r a c t e r i z e d b y t h e r a p i d g r o w t h i nf l a n k w e a r d u r i n g d r i l l i n g .

C "

k .Fir. 2.

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T h e r e c o r d e d s i g n al s a r e d i g it iz e d f o r o ff - li n e a n a ly s is . D D S m o d e l i n g t e c h n i q u e isu s e d t o a n a l y z e t h e d y n a m i c s o f th r u s t / t o r q u e s ig n a ls f o r e a c h c a s e a n d f o r e v e r y s t a g e o fw e a r , s o th a t a s u i ta b l e c o r r e l a t i o n b e t w e e n a v e r a g e f la n k w e a r a n d t h e d y n a m i c s o f t h es i g n a l c a n b e o b t a i n e d .2 . 3 . G row th o f dr il l fl ank w ear

T h e a v e r a g e f la n k w e a r i s c o m p u t e d b y m e a s u r i n g t h e w e a r a t e a c h s e c ti o n A , B , C


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248 P. BANDYOPADHYAY t at.a n d D ( F ig . 1 ) a n d t h e n t a k i n g t h e ir a r i th m e t i c a v e r a g e . T h e g r o w t h o f th e a v e r a g e f l a n kw e a r f o r a l l t h e c a s e s i s g i v e n i n F i g . 3 .F r o m t h is f ig u r e , it c a n b e s e e n f o r s a m e d i a m e t e r i n c a se s 1 a n d I I , t h e w e a r g r o w t hr a t e is f a s t e r f o r h i g h e r s p e e d . O n t h e o t h e r h a n d , f o r th e s a m e s p e e d i n c a se s I a n dI I I , t h e w e a r g r o w t h r a t e i s f a s t e r f o r s m a l l e r d i a m e t e r . A l s o , t h e c r i ti c a l w e a r v a l u e i sb i g g e r f o r la r g e r d i a m e t e r , b u t d o e s n o t c h a n g e m u c h f o r s a m e d i a m e t e r a n d d i f f e r e n ts p e e d s .

'~1- ! /[ . o . / ___ /__ /EE o.15~ O.lO3g / ~ - I 3 / 8 " ~ , 665rpm

0 . 0 { 5 [ / / / " - I 3 / 8 " ~ , 8 2 5 rp m- I o - I I / 4 " ( ~ , 8 2 5 r p mo I Y /Y t I I I l0 ~00 300 500T L 3 T L n T L 2

N u m b e r o f h o le s

FIG. 3.

2 . 4 . Analys i s o f s ta tic components o f thrus t and torqueT o f in d th e c o r r e l a t i o n b e t w e e n a v e r a g e f l an k w e a r a n d s ta ti c c o m p o n e n t o f t h ru s t /t o r q u e s i g n a l , t h e a v e r a g e v a l u e s o f t h r u s t a n d t o r q u e f o r a ll t h e t h r e e c a s e s u n d e rv a r i o u s l e v e l s o f w e a r w e r e c a l c u l a t e d a n d a r e s h o w n i n F i g s 4 ( a ) a n d ( b ) .(1 ) Average thrus t - - f rom F i g . 4 ( a ) , i t c a n b e s e e n f o r a l l t h e t h r e e c a s e s , t h e a v e r a g e

c o m p o n e n t d o e s n o t c h a n g e s ig n i fi ca n tl y w i t h w e a r . F o r e x a m p l e , i n C a s e I , t h ei n c r e a s e i n a v e r a g e t h r u s t w i t h w e a r i s o n l y a b o u t 7 % , w h i c h i s v e r y s m a l l .M o r e o v e r , t h e a v e r a g e v a l u e i s n o t n e c e s s ar i ly m o n o t o n i c a l l y i n cr e a s in g w i t h f l a n kw e a r , s h o w i n g t h e c o r r e l a t i o n i s n o t v e r y r e li a b l e .

(2 ) Average torque-- from F i g . 4 ( b ) , t h e s a m e t r e n d c a n b e o b s e r v e d f o r a v e r a g e t o r q u ei n a l l t h r e e c a s e s , w h i c h d i s p l a y e d s m a l l i n c r e a s e ( 5 - 1 0 % ) a n d p o o r r e l a t i o n w i t ha v e r a g e f l a n k w e a r o f t h e d r i ll .

I t m a y b e m e n t i o n e d t h a t s i m i l a r i n c o n s i s t e n t r e l a t i o n s h i p s w e r e o b t a i n e d b e f o r eb e t w e e n a v e r a g e t h r u s t / t o r q u e w i th d r il l f la n k w e a r [ 15 ]. I t w a s f o u n d t h a t t h e a v e r a g et h r u s t / t o r q u e v a r i e s d i r ec t l y w i t h th e h a r d n e s s o f t h e w o r k p i e c e m a t e r i a l, a n d c a n n o t b eu s e d a s a s u cc e ss f u l p a r a m e t e r t o p r e d i c t a v e r a g e t o o l f la n k w e a r . S i n c e , t h e w o r k p i e c em a t e r i a l h a r d n e s s v a r i e d f r o m 1 80 t o 2 2 0 B h n i n th e a b o v e e x p e r i m e n t s , t h e r e s u l t sr e f le c te d th e s a m e p h e n o m e n a .

3 . ANALYSIS OF DRILLING DYNAMICSS i n c e t h e a v e r a g e t h r u s t / t o r q u e c o m p o n e n t d i d n o t s h o w g o o d c o r r e l a t i o n w i t h d r i l l

w e a r , D D S a n a ly s is w a s c a r r i e d o u t t o i n v e st ig a t e t h e c h a n g e s i n d y n a m i c c o m p o n e n t s o ft h e s e s i g n a ls w i t h w e a r . B e f o r e t h e a n a l y s is o f t h e s i g n a ls , t h e d y n a m i c s o f t h e m a c h i n et o o l s t r u c t u r e a n d t h e d y n a m o m e t e r w e r e f ir st i d e n ti f ie d i n te r m s o f t h e ir n a t u r a lf r e q u e n c i e s . F o r t h i s p u r p o s e , i m p a c t t e s t s w e r e c a r r i e d o u t u s i n g a m o d a l l y - t u n e di m p a c t h a m m e r . F i g u r e s 5 ( a ) an d ( b ) s h o w t h e f r e q u e n c y r e s p o n s e o f t h e d y n a m o m e t e r


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in ax ia l and t or s iona l d i r e c t ions . The se nat ur a l f r e que nc ie s c or r e spond t o 350 and 600H z r e s p e c t i v e l y .

The nat ur a l f r e que nc y o f t he dr i l l he ad in t he ax ia l d i r e c t ion w as ide nt i f i e d us ing ap i e z o - e l e c t r i c a c c e l e r o m e t e r . F i g u r e 5 ( c ) s h o w s t h e a u t o s p e c t r u m o f t h e d r i l l h e a d ,s h o w i n g i t s n a t u r a l f r e q u e n c y c o r r e s p o n d s t o n e a r l y 7 5 H z .3.1. P rel iminar y tests fo r dril ling d ynam ics

T o a n a l y z e t h e d y n a m i c c o m p o n e n t o f t h e t h r u s t / t o r q u e s i g n a l s , t h e p r e r e c o r d e ds i g n a ls w e r e p l a y e d b a c k t o i d e n t i fy t h e d o m i n a n t m o d e s o f v i b r a ti o n u s i n g t h e s p e c t r u ma n a l y z e r a n d i d e n t i f y i n g t h e p e a k f r e q u e n c i e s . I n a l l t h e c a s e s , t h e m o s t d o m i n a n tf r e q u e n c i e s w e r e f o u n d a s f o l l o w s :

(a ) For thrust dynamics: T h e d o m i n a n t p e a k f r e q u e n c i e s a p p e a r a t d r i l l r o t a t i o n a lf r e que nc y m od e ( i . e . dr i ll r e v . pe r se c on d = 12 H z ) , ax ia l v ibr at ion o f t he he adand i t s f i r s t har monic s ( 75 H z and 150 H z ) and ax ia l nat ur a l f r e que nc y o f t hed y n a m o m e t e r ( 5 8 0 H z ) .(b ) For torque dynamics: T h e d o m i n a n t p e a k f r e q u e n c i e s o c c u r a t t h e r o t a t i o n a lf r e q u e n c y ( 1 2 H z ) , t w i c e t h e r o t a t i o n a l f r e q u e n c y ( = 2 5 H z ) , a n d t o r s i o n a lv i b r a t i o n f r e q u e n c i e s o f t h e d y n a m o m e t e r ( 3 2 0 H z ) a n d p r o b a b l y t h e d r i l l h e a d( 1 2 0 H z ) .

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F i e . 5 .

From the prel iminary tests for various levels of dri l l f lank wear, i t was found that thedynam i c s c or r e spondi ng to the dr i l l r o tat i onal f r e que nc y and twi c e the r otat i onalfr e que nc y m ode s ar e qu i te s e ns it i ve to dr il l f lank we ar , be c a use the p e ak pat te r ns c hangeat the se f r e que nc i e s wi th we ar .3 . 2 . D D S a n a l y s i s

Si nc e the dynam i c s o f the thr us t and tor que s i gnal s c or r e spondi ng to the dr i l lr otat i onal f r e que nc y m ode and twi c e the r otat i onal f r e que nc y m ode ar e o f i n te r e s t tom oni tor the ave r age dr i l l f l ank we ar , a l l the s i gnal s we r e passe d thr ough an anal ogband-pass f i lt e r to ge t r id o f the o the r dynam i c m o de s . Th e se t t i ng o f the l ow e r and uppe rlimits of the band-pass fi l ter were 10 and 30 Hz in cases I and III, and 8 and 25 Hz forCase II . The f i l tered s ignals were digi t ized us ing a sampl ing interval of A = 0.01 s , andc o r r e sp o n d i n g N y q u i s t f r e q u e n c y o f 5 0 H z .


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A Feasib i l i ty Study of On- l ine Dri l l We ar 251D D S m o d e l i n g te c h n i q u e w a s u s e d t o e s t i m a t e th e d y n a m i c p a r a m e t e r s , f r o m 1 02 4

d a t a p o i n t s f o r e a c h s e t o f th e f i l t e r e d s ig n a l .3 . 2 . 1 . No r m al i z ed dam p i ng r a tio ( ND R) - - a new par am e t er f o r ana ly si s. S i n c e t h e

d y n a m i c s o f b o t h t h r u s t a n d t o r q u e s i g n a ls a r e e v a l u a t e d f o r e a c h l e v e l o f w e a r , a n e wp a r a m e t e r d e s i g n a t e d a s N o r m a l i z e d d a m p i n g r a t i o w a s f o r m e d t o q u a n t i f y t h e r e l a t i v ec h a n g e i n d r i l l i n g d y n a m i c s w i t h w e a r a t e a c h m o d e o f v i b r a t i o n . M a t h e m a t i c a l l y , N D Ri s d e f i n e d a s f o l l o w s :

N D R i j = (~j/~o) ( l )w h e r e ,~ij = d a m p i n g r a t i o a t i th v i b r a t i o n m o d e a n d j t h l e v e l o f d r i l l w e a r~io = d a m p i n g r a t i o a t i th v i b r a t i o n m o d e a n d n o d r i l l w e a r .3 . 3 . Dyn am ics o f thrus t s ignal

A R M A m o d e l s w e r e f i t te d t o th e s e d y n a m i c t h ru s t d a t a fo r th r e e d i f fe r e n t ca s e s a n ds e v e r a l le v e l s o f w e a r . I n a l l t h e c a s e s , t h e a d e q u a t e m o d e l w a s f o u n d t o b e A R M A ( 4 ,3 ) . T h e n a t u r a l f r e q u e n c i e s , a b s o l u t e d a m p i n g r a t i o s , N D R a n d d i s p e r s i o n v a l u e s fo r th et h r e e c a s e s a r e s h o w n i n T a b l e 2 .

TABLE 2. DYNA MIC CHARACTERISTICS OF THRUST SIGNAL FROM A R M A ( 4, 3 ) MODEL1st Mo de 2nd Mo de

Case . no . Average Freq . Dam p- ND Rl j D i sper - Freq . D amp- NDR2j Di sper -f lank (Hz) ing rat io s ion (Hz) ing rat io s ionw e a r ~ ( % ) ~ ( % )( r am)Case 1 0 13 .2 0 .0 36 2 1 .00 85 26.9 0 .1 18 1 1 .00 150.070 1 3. 0 0 .0 28 9 0 .80 83 26.8 0 .1 96 5 1 .66 17d=3/8"~b 0.127 1 3. 0 0 .0 33 8 0 .93 84 27.0 0 .1206 1 .02 15speed = 0 .133 13 .2 0 .0 47 6 1 .31 83 26.8 0 .1108 0 .94 17825 rpm 0 .155 12 .5 0 .2 48 7 6 .87 86 23.8 0 .6 41 0 5 .42 140.174 1 4. 2 0 .2 83 3 7 .82 87 26.8 0 .0 241 0 .20 13Case I I 0 10 .7 0 .05 61 1 .00 81 20.6 0 .1326 1 .00 100.059 1 0. 6 0 .0 64 9 1 .16 78 20.4 0 .1 41 7 1 .07 22d=3/8"~b 0 .088 10 .5 0 .0 67 2 1 .20 83 21 .1 0 .1 42 1 1 .07 17speed = 0 .123 10 .4 0 .0 73 6 1 .31 80 21.6 0 .1628 1 .23 20665 rpm 0.140 1 0 .6 0. 08 47 1.51 81 21.7 0.2372 1.79 190.179 1 0. 0 0 .1 76 7 3 .15 85 19 .1 0 .2204 1 .66 15Case I l l 0 12 .9 0 .043 1 1 .00 82 26 .2 0 .112 1 1 .00 180.076 1 2. 8 0 .0 78 3 1 .82 83 25.7 0 .1 32 2 1 .18 17d=l/4"d~ 0 .089 11 .8 0 .22 50 5 .22 84 24 .5 0 .18 31 1 .63 16spee d = 0 .110 12 .4 0 .2 26 9 5 .26 82 25.8 0 .1 18 2 1 .05 18825 rpm 0 .120 11 .3 0 .2 53 4 5 .88 85 24.6 0 .2 481 2 .21 150 .140 13 .5 0 .41 79 9 .70 87 27 .1 0 .16 31 1 .45 13

T h e f o l l o w i n g o b s e r v a t i o n s c a n b e m a d e f r o m t h e a n a l y s is s h ow n i n T a b l e 2 :( 1 ) I n al l t h e c a s e s , t h e A R M A ( 4 , 3 ) m o d e l s r e f l e c t t w o m o d e s o f v i b r a t i o n c o r -

r e s p o n d i n g t o t h e d r i l l r o t a t i o n a l f r e q u e n c y a n d t w i c e t h e r o t a t i o n a l f r e q u e n c y .( 2) T h e v i b r a t i o n a t t h e r o ta t i o n a l f r e q u e n c y m o d e i s m o r e d o m i n a n t b e c a u s e i t

c o n t r i b u t e s t o n e a r l y 8 0 - 8 5 % o f t h e t o t a l p o w e r o f th e f i l t e r e d t h r u s t d y n a m i c s .( 3) A l s o , th e ' N D R ' v a l u e s c o r r e s p o n d i n g t o t h e r o t a t io n a l f r e q u e n c y m o d e i n c r e a s e s

w i t h i n c r e a s e i n d r il l f l a n k w e a r f o r a ll t h e t h r e e c a s e s . F i g u r e 6 ( a ) s h o w s h o w" N D R " a t t h is f ir st m o d e c h a n g e s w i t h i n c r e a s e i n d r i l l w e a r . I t c a n b e s e e n t h a ta t t h e e n d o f t o o l l if e , t h e N D R v a l u e c h a n g e s a b o u t 8 t i m e s f o r C a s e I , w h e r e a s


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A Feasibility Study of On-line Dr ill Wear 253

(4 )

it c h a n g e s a b o u t 3 a n d 1 0 t i m e s f o r C a s e s I I a n d I I I r e s p e c t i v e l y . T h i s s h o w s t h a tt h e p a r a m e t e r NDR for thrust i s r e a s o n a b l y s e n s i t i v e t o d r i ll w e a r . A l s o , t h es e n s i t i v i t y i n c r e a s e s a t h i g h e r s p e e d s ( f r o m C a s e s I & I I I ) .T h e A R M A s p e c t r u m p l o ts fo r th e t h r e e c a s e s a r e s h o w n i n F ig u r e 6 ( b ). I t c a n b es e e n f r o m t h e s e p l o t s t h a t t h e p e a k a t t h e r o t a t i o n a l f r e q u e n c y m o d e ( i .e . 1 3 H z f o rC a s e s I a n d I I I , a n d 1 0 . 6 3 H z f o r c a s e I I ) g r a d u a l l y d a m p e d o u t w i t h i n c r e a s e i n dr il lf l a n k w e a r .

3 . 4 . Dynam ics of torque signalA R M A m o d e l s w e r e a l s o f it te d f o r t h e d y n a m i c t o r q u e s ig n al s a n d A R M A ( 4, 3)

m o d e l w a s a l so f o u n d a d e q u a t e i n a ll t h r e e c a s e s. T h e n a t u r a l f r e q u e n c ie s , d a m p i n gr a t i o s, N D R a n d d i s p e r s i o n v a l u e s a r e i n d i c a t e d in T a b l e 3 .

TABLE 3. DYNAMIC CHARACTERISTICS OF TORQUE SIGNAL FROM A R M A ( 4, 3 ) MODEL

1st Mode 2nd ModeCase no . Average Freq . Damp- N D R 1 j Disper- Freq . Damp- ND R 2) Disper-flank (Hz) ing ratio sion (Hz) ing ratio sionwear ~ (%) ~ (%)(ram)Case 1 0 13 .2 0 .01 86 1 .00 81 26 .8 0 .00 09 1 .00 190 .070 1 3 .3 0 .01 54 0 .83 79 26 .8 0 .00 19 2.11 21d=3/8" (b 0 .127 1 3. 2 0 .0 18 2 0 .98 83 26 .8 0 .00 21 2 .33 17speed = 0 .133 13 .3 0 .0141 0 .76 85 26 .7 0 .00 27 3 .00 15825 rpm 0.155 13 .4 0 .1 47 9 7 .95 84 26.9 0 .0 15 5 17.22 160 .1 74 1 2 . 6 0 . 1 3 3 3 7 .1 6 8 6 2 3 . 5 0 . 1 2 8 3 1 4 2 . 55 14

Case II 0 10 .6 0 .0 07 6 1 .00 85 21.6 0 .0 01 3 1 .00 150.059 10 .8 0 .0 09 4 1 .24 82 21.4 0 .0 02 8 2 .15 18d= 3/8" + 0 .088 10 .5 0 .0 07 2 0 .95 80 21.7 0 .0 04 8 3 .69 20speed = 0 .123 10 . 7 0 .00 64 0 .84 83 21 .3 0 .00 84 6 .46 17665 rpm 0.140 1 0. 8 0 .0 35 9 4 .72 84 21.6 0 .0 14 5 11.15 160 .1 79 1 0 . 8 0 . 0 0 8 3 1 .0 9 8 7 2 2 . 3 0 . 1 9 2 8 1 4 8 . 3 0 13Case l I I 0 13 .8 0 .01 67 1 .00 79 26 .8 0 .00 07 1 .00 210.076 1 3. 3 0 .0 26 8 1 .61 81 26.6 0 .0 00 8 1.17 19d - 1 /4" (b 0 .089 13 .3 0 .0 10 7 0 .64 83 26 .7 0 .0 02 3 3 .28 17speed = 0 .110 13 .4 0 .0 29 4 1 .76 86 26.8 0 .0 02 5 3 .57 14825 rpm 0 .120 13 .5 0 .01 98 1 .18 88 26 .7 0 .00 35 5.00 120 .140 13 .5 0 .01 52 0 .91 89 28 .4 0 . 1 0 7 3 153 .28 11

T h e f o l lo w i n g o b s e r v a t i o n s w e r e m a d e f r o m T a b l e 3 :( 1) L i k e t h ru s t , t h e t o r q u e d y n a m i c s al so s h o w e d t w o m o d e s o f v i b r a t io n a t t h e

r o t a t i o n a l f r e q u e n c y a n d t w i ce t h e r o t a ti o n a l f r e q u e n c y m o d e . T h e v i b r a t io n a t t h er o t a t i o n a l f r e q u e n c y m o d e c o n t r i b u t e s 8 0 -- 8 5% , a n d t w i c e t h e r o t a ti o n a l f r e q u e n c ym o d e c o n t r i b u te s 1 5 - 2 0 % o f t h e t o ta l p o w e r o f t h e f il te r e d t o r q u e d y n a m i c s .

( 2 ) U n l i k e t h r u s t , th e " N D R " v a l u e s a t t h e d r il l r o t a t i o n a l f r e q u e n c y m o d e d o n o ts h o w a n y d e f i n i t e r e l a t i o n s h i p w i t h d ri ll f l a n k w e a r .

( 3) H o w e v e r , t he " N D R " v a l u e s a t t w i c e t h e r o t a t i o n a l f r e q u e n c y m o d e s h o w e d ad e f i n it e r e l a t i o n s h i p w i t h d ri ll f l a n k w e a r . T h e c h a n g e o f N D R v a l u e s w i t h w e a r a tt h is s e c o n d m o d e f o r a ll t h r e e c a s e s a r e p l o t t e d i n s e m i - l o g s c a le i n F ig . 7 ( a ) . I t c a nb e s e e n t h a t a t th e e n d o f d r il l l if e , t h e N D R v a l u e c h a n g e s a s m u c h a s 1 40 t o 1 5 0t i m e s i n d i f f e r e n t c a s e s , s h o w i n g t h i s p a r a m e t e r i s h i g h l y s e n s i t iv e t o d r il l f l a n kw e a r .

( 4 ) A l s o t h e A R M A s p e c t r u m p l o t s f o r a ll t h r e e c a s e s a r e s h o w n i n F i g . 7 ( b ) . T h e s ep l o t s a l s o s h o w t h a t a t t w i c e t h e r o t a t i o n a l f r e q u e n c y m o d e , t h e p e a k g r a d u a l l yg o e s d o w n w i t h dr il l w e a r s h o w i n g t h e i n c r e a se i n d a m p i n g .


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11/13

A Fe a s i b i l i t y S t u d y o f O n - l i n e D r i l l W e a r 2 5 54. G E N E R A L O B S E R V A T I O N S A N D P H Y S IC A L I N T E R P R E T A T I O N

4 . 1 . C o m m e n t s o n t h e D D S r es u lt sF r o m t h e a n a l y si s o f t h r u st a n d t o r q u e d y n a m i c s , t h e f o l lo w i n g g e n e ra l o b s e r v a t i o n sc a n b e m a d e :

( 1) T h e N o r m a l i z e d D a m p i n g R a t i o ( N D R ) v a l u e s a t t h e r o t a ti o n a l f r e q u e n c y m o d e o ft h e t h r u s t s i g n a l a n d a t tw i c e t h e r o t a ti o n a l f r e q u e n c y m o d e o f t h e t o r q u e s i g na ls h o w g o o d c o r r e l a t i o n w i t h w e a r . H o w e v e r , t h e N D R v a l u e s f o r t h e t o r q u ed y n a m i c s i s f a r m o r e s e n s i t i v e t o d r i l l w e a r a s i t c h a n g e s 1 4 0 - 1 5 0 t i m e s i nc o m p a r i s o n t o 3 - 1 0 ti m e s c h a n g e i n th r u s t d y n a m i c s . H e n c e , i t s e e m s j u s t i fi e d t ou s e t h e N D R v a l u e s o f t h e t o r q u e s ig n al a s a b e t t e r p e r f o r m a n c e i n d e x t os u c c e s s f u l ly m o n i t o r d r il l f la n k w e a r .( 2) T h e f r e q u e n c y a t w h i c h th e d a m p i n g r a ti o s ar e to b e m o n i t o r e d i s i n d e p e n d e n t o fd r il l d i a m e t e r , w o r k p i e c e a n d t o o l m a t e r i a l , a n d f e e d r a t e . I n f a c t, i t c a n b e d i r e c t l yc a l c u l a t e d f r o m t h e s p e e d o f t h e d r i l l i n g o p e r a t i o n . H e n c e , t h e r e s u l t s a r e f a i r l yg e n e r a l a n d c a n b e e a s i ly i m p l e m e n t e d f o r t h e p u r p o s e s o f o n - li n e d r i ll - w e a rm o n i t o r i n g .(3 ) A l s o f rom Fig . 7 ( a ) , i t can be seen tha t once the c r it i ca l w ear l imi t is r eac hed , t heN D R v a l u e s f o r t h e t o r q u e d y n a m i c s i n c r e a s e s e x p o n e n t i a l l y , r e f l e c t i n g t h e r a p i dw e a r g r o w t h o f th e d r i ll a t t h e e n d o f it s li fe . A s a r e s u l t , t h is N D R v a l u e c o u l db e u s e d a s a p h y s i c a l p a r a m e t e r t o p r e d i c t t h e e n d o f t h e d r i l l l i f e .( 4 ) F r o m T a b l e s 2 a n d 3 , t h e a b s o l u t e d a m p i n g r a t i o ( ~ i) v a l u e s at t h e r e l e v a n t m o d e s ,h a v e s i g n i f i c a n t d i f f e r e n c e s f o r t h e t h r e e d i f f e r e n t c a s e s u n d e r s e v e r a l l e v e l s o fw e a r . T h i s s h o w s th e e f f e c t s o f d if f e r e n t d ri ll s iz e s a n d s p e e d s o n t h e s e p e r f o r m a n c ei n d e x v a lu e s . H o w e v e r , b y n o r m a l iz i ng t h e d a m p i n g r a ti o s ( i. e . N D R v a l u e s ) , t h e s ee f f e c t s a r e r e d u c e d t o a g r e a t e x t e n t a n d p r a c t i c a l l y s a m e t r e n d c a n b e s e e n i n a l lt h r e e c a s e s ( s e e F i g s 6 ( a ) a n d 7 ( a ) ) .

4 .2 . P hy s ic a l in te rpre ta t ionT h e i n c r e a s e o f d a m p i n g r a t i o a t th e r o t a t i o n a l f r e q u e n c y m o d e f o r t h e t h r u s t s i g n ala n d t w i c e t h e r o t a t i o n a l c u t t i n g f r e q u e n c y m o d e f o r t h e t o r q u e s i g n a l w i t h t h e i n c r e a s e i nd r il l f la n k w e a r c a n b e p h y s i c a l ly e x p l a i n e d a s f o ll o w s :

( 1) W i t h t h e g r o w t h o f f la n k w e a r , t h e f ri c ti o n b e t w e e n t h e w o r k p i e c e a n d t h e t o o li n c r e a s e s , w h i c h i n t u r n i n c r e a s e s t h e d a m p i n g o f t h e c u t t i n g p r o c e s s .( 2 ) S i n c e th e d r i ll h a s tw o c u t t i n g e d g e s , t h e d y n a m i c s o f t h e t o r q u e s i g n al in t h er o t a t i o n a l d i r e c t i o n i s a f f e c t e d m o r e b y d r i l l f l a n k w e a r a t t w i c e t h e r o t a t i o n a lf r e q u e n c y m o d e ( i . e . t h e f o r c i n g f r e q u e n c y ) i n t e r m s o f i n c r e a s e d f r i c t i o n a n dd a m p i n g .( 3 ) H o w e v e r , f o r t h e th r u s t d y n a m i c s in t h e a x ia l d i r e c t i o n , t h e r o t a t io n a l f r e q u e n c ym o d e i s a f f e c t e d m o r e w i t h w e a r , b e c a u s e t h e d y n a m i c c u t t i n g f o r c e f o r t h e t w oe d g e s i n t h i s a x i a l d i r e c t i o n a d d u p a t t h i s p a r t i c u l a r f r e q u e n c y .

I n c i d e n t a l l y , t h e i n c r e a s e o f d a m p i n g r a t i o w i t h t h e i n c r e a s e o f t o o l w e a r h a s b e e nr e p o r t e d b e f o r e f o r t u r n i n g o p e r a t i o n s [ 1 3 , 1 6 ] . S o t h e p r e s e n t a n a l y s i s a g r e e t h e s a m ep h e n o m e n o n f o r d r i l l i n g .

4 .3 . F e a s i b il i ty f o r o n - l i n e d r i l l l if e m o n i t o r i n gF r o m t h e a b o v e a n a l y s i s , it is e v i d e n t t h a t i f t h e N D R v a l u e a t t w i c e th e r o t a t i o n a lf r e q u e n c y m o d e f o r t h e t o r q u e s i g n a l c a n b e c o m p u t e d o n - l i n e , t h e s t a t e o f t h e d r il l i nt e r m s o f a v e r a g e f l an k w e a r c a n b e m o n i t o r e d a n d e x a c t t im e t o r e p l a c e t h e t o o l c a n b ep r e d i c t e d .


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25 6 P. BANDYOPADHYAY et al.

Thi s s c he m e c an be e as i l y i m pl e m e nte d us i ng a m i c r opr oc e s sor and sof twar e us i ngDDS m ode l i ng te c hni que . The s i gnal c an be c o l l e c te d fr om a su i tab l y de s i gne d tor quese nsor , and the n passe d thr ough a band pass f i l t e r , be for e fe e d i ng i n to the m i c r o-pr oc e s sor . In the m i c r opr oc e s sor , the data wi l l be sam pl e d and DD S m e tho dol o gy w i l l beuse d to c a l c u l ate the natur al f r e que n c i e s and "ND R" va l ue s o f the s i gnal. Co m p ar i ng the"NDR" value wi th i ts predetermined cr i t ical value can predict the condi t ion of the dr i l lon- l i ne .

5 . C O N C L U S I O N S1 . A ne w c on c e pt o f on- l i ne m oni tor i ng of dr il l f lank we ar by r e la t i ng i t to the dynam i c s

of the thrust or torque s ignal i s introduced.2 . D D S m e thod ol og y c an be use d to suc c e s sfu l ly c har ac te r iz e the se si gnal dynam i c s i n

terms of natural frequencies and damping rat ios .3. Th e damping rat ios at the dri ll rotat iona l frequ ency for the thrust dyn am ics and at

twi c e the r otat i onal f r e que nc y for the tor que dynam i c s show good c or r e l at i on wi thave r age f l ank we ar for d i f fe r e nt dr il l s i z e s and spe e ds . H ow e ve r , the s e ns i t iv i ty o f thetor que dynam i c s dam pi ng r at i o i s m uc h h i ghe r ( i nc r e ase 140-150 t i m e s ) andr e c o m m e n d e d f o r o n - l i n e u s e .

4. From the s tat ic analys i s , the average thrust and torque pro vided poo r corre la t ionand l ow se ns i ti v i ty (on l y 5 -10% i nc r e ase ) wi th dr il l f lank we ar . He nc e , the y ar e notgood pe r for m anc e i nd i c e s for dr i l l we ar m oni tor i ng .

5 . A n e w p a r a m e t e r, d e s ig n a t e d a s " N o r m a l i ze d D a m p i n g R a t io " ( N D R ) i s f o r m e d t obe use d as a r e l i ab l e pe r for m anc e i nde x for dr i l l we ar m oni tor i ng . Al so , thenor m al i z at i on he l ps i n nu l l i fy i ng the e f fe c t s o f d i f fe r e nt ope r at i ng c ondi t i ons anddri l l s izes on this performance index value .

6 . F i na l ly , it s e e m s feas i b l e to de ve l op a m i c r oc om pute r base d s im pl e dr il l f lank we a rm o n i t o r in g s c h e m e u s in g t h is t o r q u e d y n a m i c s N D R i n d e x f o r o n - li n e p u r p o s e s .

R E F E R E N C E S[1] F. W. TAYLOR, A S M E J . 2 8 , 3 1 - 3 5 0 ( 1 9 0 6 ) .[2] Y . S. LEE, J . E n g n g In d . T r a ns . A S M E , 1 0 5 1 ( 1 9 7 1 ) .[3] C. RUBENSTEIN,J . Eng ng I nd . Trans . ASM E, 221 (1976) .[4] A. BHAXTACHARVA,A . G H O SH a n d I . H A M . J . E n g n g I n d . T r a n s . A S M E 109 (1970) .[5] S. RAMALINGAMand J . D. WATSON, J . Engng hTd . Trans . AS M E 519-531 (1977) 193--2(19 (1978) .[6] S. M. Wu, J . E n g n g I n d . T r a ns . A S M E B 8 6 , 101)5 (1964 ).[7] K. HITOMI, N. NAKAMURA an d S. INOUE. J . Eng ng hzd . Trans . A S M E 101, 185-190 (1979) .[8] K. YAMAZAKI, A . YAMADA e t a l. , Ann CI RP 23 (1974) .[9] A. J . WILKINSON, P r o c . I E E E , 18, (1971) .[10] K. TARAMAN, R. SWANDO an d W. YUMAUCm, Re l a t i o n s h i p b e t we e n t o o l f o r c e a n d f l a n k we a r , S M E

T e c h n i c a l P a p e r , N o . M R 7 4 ( 1 9 7 4 ) .[11] P. MA~T1N, B. MUTELS an d J. P. DRAIPEI~,P r o c . 1 5 t h . M T D R C o n f . p p . 2 5 1 - 2 5 7 ( 1 9 7 5 ) .[ 12 ] K . W . Y EE a n d D . B L O M Q U m A n o n - l in e m e t h o d f o r d e t e r mi n i n g t o o l we a r b y t i me d o m a i n a n a l y s i s, S M E

t echnica l paper , N o . M R 8 2 - 9 0 1 ( 1 9 8 2 ) .[13] S. M . PANDH, H. SUZUKI an d C . H . KIaANG,A S M E J . M ec h . D e s. 102, 233--241 (1980).[14] S. M. PANDIT and S. M. W u. T i m e S e ri e s a n d S y s t e m A n a l y s i s w i t h A p p l i c a t i o n s , J o h n W i l e y , N e w Y o r k ,( 1 9 8 3 ) .[15] N. H. COOK an d K . SUBRAMAINIAN,J . Engn g I nd . Trans . AS M E 2 9 5 - 3 0 1 ( 1 9 7 7 ) .[16] J . TULSTY, T. MORJWAK1 an d B. S. GOEL , P r o c . N A M R C I V , 287 (1976) .[17] T. RADnAKRISnNAN, Dri l l po in t geometry opt imizat ion and on- l ine moni tor ing o f dr i l l condi t ion , P h . D .Disser ta t ion , M echanica l Eng ineer ing , U nivers i ty o f W iscons in - M adison , 1980.

A P P E N D I X ATt tE PARAMETRIC epresenta t ion of the dynamics of a sys tem in c o n t i n u o u s t i me d o ma i n ma y b e wr i t t e n a s :

( D " + c ~. , i D '~ i + o L , , 2 D " ~- + . . . . . . + o q D + o q , ) X ( O

- ( b , , , D ' " + b . . ~ D ' " ~ + . . . . . . + b . ) Z ( O ( AI )F [ Z ( t ) ] = 0 : E i Z ( t ) Z ( r - u ) ] = a ( u ) , r :


13/13

A Fe a s i b i l i t y S t u d y o f O n - l i n e D r i l l W e a r 2 5 7

w h e r e . X( t ) i s t h e s y s t e m r e s p o n s e ; Z ( t ) i s t h e w h i t e n o i s e ; ~ (u ) i s t h e d i r a c d e l t a f u n c t i o n ; E d e n o t e s t h ee x p e c t a t i o n o p e r a t o r ; c to , a l . . . , c t, ,_ , a r e a u t o r e g r e s s i v e a n d b ~ , b 2 . . . . . b ,, a r e m o v i n g a v e r a g e p a r a m e t e r s .A l s o s uc h m o d e l s a re d e n o t e d a s C o n t i n u o u s A u t o r e g r e s s iv e M o v i n g A v e r a g e A M ( n , m ) m o d e l s .T h e a b o v e c o n t i n u o u s s y s t e m ( A 1 ) s a m p l e d a t u n i f o r m s a m p l i n g i n t e r v a l s , A . c a n b e r e p r e s e n t e d b y as t o c h a s t i c d i f f e r e n c e e q u a t i o n i n t h e f o r m o f a t i m e s e r e i s .(1 - + , B - ~2 B2 - . . . - d~, ,B")X, = (1 - 0 j B - 0 2 B 2 " - . . . - O,, ,B")a,

E[a,] = 0 ; E[a,a, -k] = 5ktr,, 2 (A 2)w h e re X , is s y s t e m r e s p o n s e , a , is w h i t e n o i s e , + ~ . ~b2 . . . . + , , a r e a u t o r e g re s s i v e a n d 0 ~ , 0 2 . . . . . 0 ,, , a r e m o v i n ga v e r a g e p a r a m e t e r s . E q u a t i o n ( A 2 ) i s c a l le d U n i f o r m l y S a m p l e d A u t o r e g r e s s i v e m o v i n g a v e r a g e m o d e l o fo r d e r n , m ; a n d i s d e n o t e d b y A R M A ( n ,m ) .T h e a d e q u a t e o r d e r o f t h e A R M A ( n , m ) m o d e l c a n b e f o u n d u s i n g s o m e s t a t i st i ca l c r i t e r ia ( f o r d e t a i ls ) r e f e rt o [ 1 4 ]) . O n c e t h e a d e q u a t e m o d e l i s f o u n d , i t i s p o s s i b l e t o id e n t i f y t h e d y n a m i c c h a ra c t e r i s t i c s o f t h e s y s t e m i nt e r m s o f n a t u r a l f r e q u e n c i e s a n d d a m p i n g r a t i os . F o r e x a m p l e , i f t h e s y s te m h a s a n u n d e r d a m p e d m o d e . i t c a nb e g i v e n b y

l / [ l n ( 4h* )]2 [ ( ~ -+h* ' ~12~o,k = - ~ + c o s- ' \ 2 ~ ] ] (A 31

;k = J [ l n (XX*)]2 (A4 )Y r , ( ~ , + ~ , * ) 1 2tln(X~,*)l2 + 4 [ co s 2 ~ S ' ]where , co , ,k a n d ~ k a r e t h e n a t u r a l f r e q u e n c i e s a n d d a m p i n g r a t io o f t h e k - t h m o d e o f v i b r a t i o n , k a n d h * a r e ap a i r o f c o m p l e x c o n j u g a t e c h a r a c t e r i s t i c r o o t s w h i c h c a n b e o b t a i n e d f r o m t h e f o l l o w i n g e q u a t i o n

h " - ~ qb/h - j = 0 . ( A 5 )j = l

A l s o . t h e n o r m a l i z e d p o w e r s p e c t r u m d e n s i t y c a n b e f o u n d f r o m t h e m o d e l p a r a m e t e r s a n d i s g i v e n b y

2 o " 2S Of t ~ . . . . .'Y o

1 - k'~~ ~bk -j2kTrfA 2

1 - ,~ , +k e - j 2k'~1a 2 (A6 )

w h e re f is t h e f r e q u e n c y o f H z , % i s t h e v a r i a n c e o f X , .

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Afeasibilitystudyofon-linedrillwearmonitoringbyDDSmethodology

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