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Adaptive Control System for Optimizing the ECG Process under the Overcut Constraint
Adaptive Control System for Optimizing the ECG Process under the Overcut Constraint M. Shpitalni, Y. Koren, E. L e n z (1); Technion-Israel Institute of Technology 'he o f the main l i m i t a t i o n s i n Peripheral r l e c t r o rhenical SrindinQ f c r c \ i s the ov-rcut n'lenmmon. The dominant naraneters which govern the dimensions o f tlle l o m e t r i c a l overcut are the voltaqe and the feedrate. T\is paper deals w i t b the developlent o f an m a i i i c a l model sihich descrihes the overcut as a function o f the doninant parameters. Pased on t h i s rode1 an adpative control system was b u i l t and e x n e r i w n t s i n n r o f i l e Deripheral CCI; were c a r r i e d out. 4 comparison o f the r e s u l t s obtained w i t h and without the adaptive control system i s oresented as well as the r e l a t i o n s h i p between the side and botton overcuts. 4ccordinq t o the a h v e an adantive s t r a t e w t o control the ieometrical overcut i n P r o f i l e FCG i s suggested.
THE ECG W C E S S The Flectro Chemical c r i n d i n q (FCSl nrocesr has heen described i n d e t a i l hv other authors [l-a]. l n t h i s oaner we s h a l l b r i e f l y surmarize the o r i n c i n l e s o f the nrocess concentratinq on the nerioheral FCG and qive special a t t e n t i o n t o the overcut nhenomenon and other aspects of the nrocess on which oiir ontimal adantive control system *#as hased. The material removal i n the FCI: proces i s based on the n r i n c i n l e o f anodic d i s r n l r i t i o n A i r r i m p l e c t r n l v s i s ctnhined w i t h a n ahrasivp w i n d i n n oneratinn. I n the p l e c t m l y s i s orocess. the workpiece i s used as the anode while the qrindinq $,theel i s iused as the crlt+nde; \otb o f then are, o f course. e l e c t r i c a l conductnrs. The e l t t r i c tension hetween the two electrodes i s insured by a " . C . fqenerallv r e c t i f i e d ' binger sunnlier. The anode i s held a t a n o s i t i v e p o t e n t i a l r e l a t i v e t o the cathode, which i s p r a c t i c a l l y ?rounded. 1 s a l t s n l i i t i o n (usiiallv consistinq o f 'la'ln , K'lO and t h e i r huffers, 'oa'V and PI0 \ i s inserted i n t o the 31an bhween the two electrodes2in order2to create the w r k i n 0 zone (sometimes c a l l e d the imrkinq qaol i n which the elect'ol v s i s nrocess takes nlace. fi fundanental descrintlon o f the V G setup i s shown i n Fiq. 1.
menon i s l i m i t e d i n i t s 'dimcnsions and decays as the overcut increases. As a conseauence, a meaninqful qeometrical deviation between the qround n r o f i l e and the qrindinq wheel n r o f i l e can e a s i l y be obtained. Yoreover. the electrochemical etchinq occurs both on and underneath the surface causinq geometrical overc u t and s e l e c t i v e l y etchinq the subsurface layers destroyinq t h e i r Qualities. The iindersiirface selective etchinq occurs p a r t i c u l a r l y i n qrindinq o f comnosite materials and r e l a t e s t o a sinqle "preferred" nhase l i k e the Co Dhase I n the case o f sintered carbides [S.fil .The qeanetrical overcut effects, on the other hand, are usually emnhasized i n q r i n d i n n o f more homoqeneous materials l i k e steels. I n t h i s p a w r the discussion i s l i m i t e d t o the q e a e t r i c a l effects o f the overcut ohenomenon. The overcut ohenanenon i s affected by almost a l l the oarameters and variahles involved i n the FCG process r71, heqlnninq w i t h the qrindinq machine, the power sunplier. the qrindinq wheel (type, q r a i n size, and o r o f i l e l and the workpiece fmaterfal, pretreatments and shape) through the e l e c t r o l y t e (type. ph. pressure. temwrature. and concentration) and endinq w i t h the feedrate. the voltage across the electrodes and the depth of qrindinq. "lany investiqators were aware o f the fact t h a t for a c e r t a i n machine and a qlven setup and job, the dominant narameters are the feedrate and the vol taqe across the electrodes. THE AIV OF THE WRK
r
Although not many o f the investiqators studied the prohlem o f the overcut r7.81. vet. i t i s well-known t h a t the overcut i s one o f the main l i m i t a t i o n s o f the hiqh-potential nrocess - the p e r i pheral n r o f i l e d FCG. Vast o f the research exnresses i n one way o r another the importance o f beinq able t o nredict, control o r reduce t h i s phenmenon.
flB W
Fiq. 1 : Fundamental descrintion o f the FCG nrocess The e l e c t r o l y s i s process i n which atoms frnm the m e t a l l i c workniece move i n t o the s o l u t i o n i s described f o r Ferum. as an examole, hy eqs. (1-5). Anode : Cathode:
tt
Fe
* Fe
2tJ2fl
2 211'
211' + 21 Solution:
+ 2i t
-L
2(nH)-
H7t
Fett + Z(W)-+Fe(Wi)2t
and total1y:Fe t 2H2n
+
H2t+Fe(WJ)2r
(1) (2)
(3) (4)
(51
The e l e c t r o l y s i s process, which i s usually qoverned by Faraday's law of e l e c t r o l y s i s , i s distiirhed by the hydroqen produced beside the cathode as well as by the nassive layer (sometimes c a l l e d the anodic l a y e r ) which coats the anode. Roth o f these phenaena d i s t u r b the motion o f the charqed ions i n t o and i n the s o l u t i o n and f i n a l l v ston the anodic dissolution. It i s the qrindinq wheel's task t o renlace the e l e c t r o l y t e i n the workinq zone as well as t o scrape o f f the passive layer.
It i s mentioned many times [7,8,9], t h a t i n order t o minimize the overcut dimensions, one should increase the feedrate and decrease the e l e c t r i c tension between the electrodes. That t r i v i a l s o l u t i o n a c t u a l l y means an increase i n the ahrasive comnonent o f the process a t the expense o f the electrochemical one, and leads t o conventional abrasive qrindinq. Fuch a s o l u t i o n can i n no way be an Index o f nerfornance when dealinq w i t h an electrochemica l process. I n our opinion the process should onerate on the optimal l o c i (as described hv the authors r l n , l l l and w i l l be b r i e f l y repeated herafter) w i t h the additional constraint o f a qiven maximum permitted overcut. In other words, the ootimal working p o i n t (UP) on the oatlmal l o c i should be defined and determined by the maximum n e n i t t e d overcut.
The development o f such an adaptive strateqy, self-defined and converging t o the optimal operatinq p o i n t i s the goal o f t h i s work. The system should converqe from any s t a r t f n q o o i n t (YP) t o the o p t i m l operatinq n o i n t ('JP) f o r any qiven task and independently of the threesome: the workpiece. the qrfndlnq wheel, and the e l e c t r o l y t e . THF EC6 r)PTIttIZATION
A t the f i r s t staqe an ontima1 control system was b u i l t based
on the concept o f maximizinq the removal r a t e under desired and proqraimnable constraints. The control olane I s defined by the two daninant and Independent control parameters: the feedrate Vf and the operating voltage I). The working reqion i s bounded by
TYE nVFQCUT PHENOMFYW: one o f the nain l i m i t a t i o n s of the FCG process (OX.) ohenomenon. The overcut may he defined as uncontrolled electrochemical o v e r d b o l v i n q o f the The phenomenon ocrurs beneath and on the sides o f wheel during and irmediately a f t e r qrindinq. The
Annals of the ClRP Vol. 30/1/1981
i s tbe overcut undesirpd and workniece. the n r i n d i n q overcut nheno-
The f i v e constraintscreate f i v e extremal ooints of which three, have a o r a c t i c a l meaninq. Point A: l i e s i n the I n t e r s e c t i on between the power and the m i n i m a l t a g e constraints. The material removal r a t e (MRR) i s maximized under the l i m i t a t i o n o f being pure abrasive. Point A i s therefore dlstinquished by: very l o w electrochemical e f f i c i e n c y , hiqh wear r a t e b,Q,r,
97
%asurin : The bottom o v e r c u t w produced durinq the FCC oneration was meas:red on h a l f o f the workpiece width x = x ( r e l a t i v e t o the zone t h a t was wound without the electrocheniEa1 comnonent! alonq the l o n q i t u d i n a l axis [feed d i r e c t i o n ) hy a T a l l w i n Surface Analyzer w i t h v e r t i c a l maqnification o f x l W . The r e s u l t s obtained are sumnarized i n Tahle 1. Table 1: The hottom overcut. i n the peripheral ECG. vs. the adjusted voltaqe for d i f f e r e n t constant feedrates.
3.5
12.5 *Yf
14
11
(nnls), Ihn(v),
aY (mn 1(1-2)
EMPIRICAL MODEL
Fig. 2: Descrlption o f the constraints and the extremal noints on the control plane. o f the grinding wheel, very l o w overcut ( i f any). qood surface f l n i s h . and q u i t e l o w MRR. Point R . ( o r p o i n t 9 i n cases where the power i s l i m i t e d by the operator due t o f r a q l l e n a t e r i a l , etc.): being able t o move on the sparking constraint (by chanqi n q the l i m i t l e v e l ) . Point 9 c a n ' t be characterized by any q u a l i t y except t h a t i t always represents the maximum uQR. The material i s removed by a combined operation o f hoth the abras i v e and electrochemical components. Point C: Unlike p o i n t R . p o i n t C i s s t a t i c and defined hy the i n t e r s e c t i o n o f two cons t a n t and f i x e d constraints: the maximal voltage and the sparki n g l i n e . Point C, therefore, represents the s i t u a t i o n ( i n general) of maximum WR i n the maximal tenslon and under the sparklng constraint. This p o i n t i s dlstinquished by hiqh electrochemical e f f i c i e n c y . low wheel wear and r e l a t i v e l y hiqh overcut. Point C1: i s the operating n o i n t and i s f r e e t o m v e alonq the optimal frame (0)CRA. I n a m a j o r i t y o f o r a c t i c a l cases, C would be between m i n t s R and C. I n p r o f i l e grindins i n parti! cular. one would p r e f e r t o work i n the area o f Point C i n order t o prevent superfluous wear on the qrlndinq wheel. I t was shown hy the authors r i l l t h a t the sparkinq l i n e (and p r a c t i c a l l y a l i n e near the sparking l i n e whose distance from the sparking l i n e i s predetermined by the operator) together w i t h the power l i m i t a t l o n produce the ootimal workinq loci.
The reader should . .. - be aware o f the f a c t t h a t the moment we accept the sparking and the power constraints t o define the optimal l o c i . the two dominant parameters - operatinq voltage and feedrate are no longer independent. For each adjusted voltage U there I s only one adapted ontlmal feedrate. rh the other d n d . f o r each f i x e d feedrate there i s a t l e a s t one optimal voltaoe. A t the desian phase. the f i r s t s t e ~must be t o f i n d out tke degree o f influence o f chanqinq each'of the two parameters on the overcut. For t h a t nuroose, a peripheral ECG w l t h zero depth o f grinding was selected as a nreliminary study case.
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Although i t can be e a s i l y seen t h a t the most dominant parameter r e l a t i n g t o the bottom overcut i s the adjusted voltaqe. and although one may e a s i l y conclude t h a t i n an adantive cont r o l system i t would be natural to f i t the feedrate t o the adjusted ( o r operating) voltage. yet, there are s t i l l some qood reasons t o construct a made1 describing the overcut behavior. a. The r e s u l t s ohtained from the model can be used as i n i t i a l conditions f o r the adantive control system. b. T r i a l and e r r o r methods can be used accordinq t o the model i n cases where an adaptive control system i s not available. c. A mathematical model can he accurately analvzed t o define the degree o f influence o f each paraneter on the overcut. d. Ry s t a t l s t i c a l analysis, on the other hand, we can deternine t o what extent the phenanenon i s described hy the model.
It can be shown t h a t the r e s u l t s ohtained i n the exoeriment are described by: 6y = K. EXP (bo t bU l, t h2vf\ (6) where: 6 (mn 10- 2 ) by(-); bl(V)K
4 i(mn
T bottom overfut ; b2 (mn/s)- coefficients
la2)-
dlriension f a c t o r
Y r i t i n g eq. (6) i n l i n e a r form by takinq I n of both sides:
(7)
I n (ay) = bo t bl Um t h2Vf By means o f regression and l i n e a r curve f i t t i n q we qet: b = 0.641 b! = 0.163 (V1-l b; = -1.621'(k/s)-'
.
According t o W. (6) and the coefficients ( 8 ) . iso-overcut Curves Can be calculated. quch calculated l i n e s and the Pract i c a l r e s u l t are shown i n Fiq. 3.
,""
*
1
9
4
E W IPWJT I n order t o emohasire the geometrical overcut and minimize the influence o f tbe qrindinq wheel wear on the results, steel (4340) workpieces and diamond wheels were selected. The clqathon Electrolytic-125F grinder w i t h wheel power o f 2HP and constant r o t a t i o n speed o f 5000 r.p.m. was used. The power supplier was the E l y f o r n Ely 3QO generator ( f u l l wave r e c t i f i e r w i t h maximal output power o f 2.2 t 3 J emltted a t nominal rated voltaqe l e v e l s o f 7.5, 10, 12.5 and 1%'). As an e l e c t r o l y t e , we used a water s o l u t i o n o f c m e r c i a l s a l t f424, hy weight rlafln ; 42*. ClaYn ; and 16% anti-corrosion additions) w i t h density 3 0 f 1.04 gr?cm3. The d r i v e system was based on a stepping motor mounted d i r e c t l y t o the worktable lead screw causinq movement o f 0.0159 mn oer pulse. FIRST STAGE EXPERIMENTS
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PLANAR PERIPHERAL ECG
Type o f grinding:plinar peripheral ECG Grinding wheel: DD l ~ - l ~ / M6125 , nm, 7 mn i n width Horkpiece: s t e e l (4340). 59 mn lenqth, 5 mn width Depth o f grinding: zero Adjusted voltage: 7.5, 10. 12.W Constant feedratrs: 0.16-1.28 mn/s i n steps o f 0.16 mn/s Phcedure: A f t e r 35 m o f ECG along the workpiece. the elect r i c a l power was stopped and the grlnding process was continued without the electrochemical component but w l t h the same feedrate.
98
---Fig. 3: Calculated i s o - o v e n u t l i n e s and exuerimental r e s u l t s .
ANALYSIS
.rxperinent W s c r i n__ t ion :
Rased on the r e s u l t s and some s t a t i s t i c a l i n v e 3 t l m t i o n (analysis o f varlance and f a c t o r i a l analysis for 3 desiqn), imoortant conclusions can be reached.
?n eac+ t e s t (setup\ there were 4 3m wide worknieces. 6ach o f the four was assiqned a "man numeral (Flrl. 4 ) . The mrknieces were held 6.y ba sunnnrts fone on eacb side\ each of '.n 4 d t h to inslire s t a h i l i t v f o r the F I X nneratlnn. Tn each tested qroun. 4 irooves w i t h d i f f e r e n t adjusted voltane lJm t.fere rlmunrt. 4s a reference rlmove. one o f the A grooves rlrminrt without tension ( I =q. wits used. Frm the four worknieces 3 were randrmlv se1ectePand m - z v t r w i .
--------I---
a. The r e s u l t s confirm the assumntlon t h a t the bnttam overcut increases when increasinrl the adjusted voltaqe and decreases when increasinq the feedrate. This phenomenon i s confirmed a l l over the investiqated reqion. h. The influence o f the adjusted v o l t a q r i s much more s i q n i f i c a n t than t h a t o f the feedrate. The influence o f the adjusted voltaqe decreases i n low voltaqe levels (hl (I = -h V 1. h u t f o r prac0.5mnIs. t i c a l representative conditions, l.e.mlt,,, = ?'l4 and V the proportion i s changed h It = -3h2Vf where the miius siqn Indicates opposite lnfldeflces. c. From analysis o f variance (Table 2) we see t h a t the b o t t m overcut i n the case o f Derinheral FCG w i t h zero deoth of qrlndi n g i s r e a l l y dominated by the adjusted voltaqe and the feedrate. A l l the other Darameters concerned taken together have a n e g l i q f b l e influence and the variance r a t i o i s ahout 286. Table 2: Analysis o f Variance SnllRCE
W R E F OF FQEFWY
SUM 4F S'IIARES
KA'I S'IJASF
53.885 About reqr. TOTAL
0.157
18
59.190
21
2.574 0.009
I n ~ $ s1 t a t i s t l c a l camnutations the feedrate" was taken i n m 14 1 s and the varlance r a t l o i s : 2.57410.904 = 286
*
A l l c a p u t a t i o n s are r e l a t e d t o I n (6y).
d. Rased on f a c t o r l a l analysis f o r 3* desiqn r i l l . we can see t h a t the mutual influence and the cross e f f e c t s between the adjusted voltage and the feedrate ( l i n e a r and quadratic! are very s n a l l and p r a c t i c a l l y n e g l i q l b l e . Telylnq on the above analysis, three imnortant operatlonal conclusions r e l a t i n g t o the optlmal adaptive control system may be reached.
a. The adjusted voltaqe I s the nost domlnant narameter.
It I s therefore essential t o q r i n d under a constant v o l t a l e l e v e l i n order t o ensure and achleve: the desired overcut. a more uniform overcut and surface. a b e t t e r c o r r p l a t l o n 4 t h the modrl and a b e t t e r r e p e a t a h i l i t v . This l a s t n o l n t n r a c t i c a l l v wans small standard deviation over a hatch. ksuminq normal d i s t r l h u t l o n and dmandinq: (?\ the nmqrarned nernitted overcut R,, i s qiven hv:
where: a,x: 5
n
nermitted overcut 1 maxinum nract4cal1v ohtained overcut
- estinated standard deviation orohability
-
It can e a s i l y be seen fra en. ll'(l t e a t decreasinq the standard devlation enahles one t o increase the nroqrarmed overcut without hreakinq the severe constraint o f the laxinurn nermitted overcut. Teerefore. the adjusted voltaqe n i r l h t he Increased causinq r e ductlnn i n the wheel w a r as a consenuence. b. It i s necessarv t o continuouslv adant the feedrate t o the adjusted voltaqe i n order t o keep the nrocess on the ootimal l o c i , nrevent arcinq (over feedrate) o r over electrochemical etchlnq (lad feedratel. c. The adantlve control s v s t m t h a t was developed hv the authors w l t h r l l l o r without rli' the control loon f o r the wheel nower l i n i t a t i o n can he used as the adantinq (feedrate t o the adjusted voltaqe\ u n i t I n the whole svsten. 4WlA'lZF ~
T F SV
-
I n the second exnerimental staqe. t e s t s r e l a t l n q d i r c c t l v t o n r o f i1e rC6 were nerfnrmed
.
Fxperinent Conditions: type o f qrindlnq: D r n f l l e nerlnheral FCG qrlndlnq Wheel : 9D 100-100/*', 7 m width deoth o f qrlndlny: 1.6 rm qrlndlnq n r o f i l e : "ectanqular 1 . 6 ~ 7mn w i t h rounded corners workpiece: Weel 434'7, 3 rn wldth r e s u l t s : n t l e a s t ti r e s u l t s f o r each tested mcdn, conditfon adjusted voltaqe: 7.5. 1'7, 12.5" 1511 w i t h current l i m i t a t i o n 1 f-edrates: Znnstant 0.1Q. Q.16, 0.24, 0.32. Q . A n mls, and varlable feedrate ohtained hy the adantive control u n i t .
Flq. 4: Qescrintion o f the n r o f i l e rlrinrlinq t e s t . The side and hottam overcuts were neasured hy a n r o f i l e nroj e c t o r (Johnes t I-ansonl v i t h maqnification o f X50. For each qroove hnth the reference I r n f i l e and the tested one r e r e dram. Data Collection: ~--__--The measurlnq method and the data c o l l e c t l n q nrocedure ~ I l l For each tested qmove and oneratinn cnnd i t i o n ( c e r t a i n adjustet' voltaoe and fendrate!a s i x r o u tahle was completed. For each case. the l e f t and r i q h t slde overcut dimensions wrr I n A i c a t d a t fiinctinn o f t C - hrinbt. n f tC - w z w l n q n o l n t Y. 6 s mentioned heenre, each set o f 4 ~ m - k nieces was qround a t a constant q i v m fecnrat? under three d i f ferent non-zero adjusted voltaqes, and a reference qroove was qround without tension. The wnrkniece was mounted on the s l i d i n q t a h l e of the p r o f i l e projector and the reference qroove was confed on t o a trancnarent naper. T'le workpiece was then moved hy the tahle u n t i l the n r o f l l e o f the tested nrnnve was alirlned as s r x n e t r l c a l l v as possible w i t h the reference qroove. 'ceasurinq horizontal and v e r t l c a l axes on each side (denoted hy X , Y Xq. Y ) o f the conied qroove r a r e drawn. The o r l q i n o f each o f L * tRem was well-defined hy the Intersection o f the measured nrof i l e and the reference one. The bottom and slde overcuts were meastired a t defined noints alonn these axes and were r e l a t e d t o then. b e t o errors which occurred durlnq the measurinq nrocess and caused by the allqnnent nrocedure. the need f o r correction o f the r e s u l t s was essential. The correction was perfanned by a mathematical nrocedure o f centerinq the r e s u l t s without l o s i n q the s t a t i s t l c a l d l s t r l h u t l n n . nnce the centerinq oneration had been cmnleted, the source of the r e s u l t s , i n the sense o f l e f t and L indexes were o r r l q h t side, was innored. Therefore the omitted and x and .y were referrcd t o as the measurenent axes i n qeneral he h r i e f l v sumarized.
.
The Side
nvercut:
The measured side overcuts f o r t e s t s nerformed w i t h d i f f e r e n t adjusted voltaqes and w i t h d l f f e r e n t constant feedrates are shown I n Flq. 5 for y=lm. Fach drawn n o l n t i s the mean o f 6 measured overcuts. The r e s u l t s obtalned f o r 3 wide range o f feedrates were Dut on a s m i - l o q a r l t h i c scale as function o f the operatlnq voltaqe only accordlnq t o the eouatlon: 6x = h4FXP(bl
II\
(11)
where: 6
(mn 10- 2 )
hx(m bO(V)-
lljlJ! -
-
the side overcut coefficlent coefficlent ooeratlnn voltaqe ( d i f f e r s fra the adjusted voltaqe by the proqramnahle narameter nU(ll=llm-~U))
-
99
Vised on the e x n e r i n r n t s c a r r i e d out, t + e r e were some exnectat i o n s concerninq the s i d e overcut which would he ohtained under the o p t i i a l adantive c o n t r o l . a. t b - k i n q w i t h cnnstant tension instirps qood w e d i c t i o n o f t h e overcut dimensions and r e o e t i t i o n o f performance. h. The d i s t r i h u t i o n o f the nvercut nver a hatch would he reduced and t h e surface would he innroved. c. Chanqinq the feedrate d u r i n q t h e ECC nrbcess would h a r d l y a f f e c t the dimension of t h e overcut o r i t s character. d. fis t h e i n f l u e n c e o f t h e feedrate on the overcut i s m a l l , t h e t i n e d u r i n q which t h e wheel i s Over t h e workniece w i l l a l s o have a l o n influence on t h e overcut. T t i s expected, therefore, t h a t the"wal1s"would he more i r n r i i h t . -he qrooves as conied from the p r o f i l e n r o j e c t o r are shown i n Fiq. 6. P r o f i l e s ohtained w i t h and w i t h o u t t h e adantive c o n t r o l are comnared
.
2
0
10
8
Ulr:
Tahle 4 : Somoar4son of the r e s u l t i n g s i d e overcut w i t h and w i t h o u t t h e adantlve c o n t r o l sys em. "f Xx(y=l \ s
Fiq. 5: T k s i d e overcut vs. t h e o n e r a t i n i voltaqe f o r d i f f e r e n t feedrates and v=l .M.
(mn/S\
('1)
This equation i s o f t h e sane form as en. ( 6 ) which descrihes t h e bottom overcut. The d i f f e r e n c e hetween t h e two eouations i s t h a t i n eq. (11) t h e influence o f t h e feedrate was i m o r e d i n order t o meet t h e demands o f the o o t i q a l adantive c o n t r o l conceot. h mentioned hefore, t h e feedrate w u l d a u t m t i c a l l v he adaoted' t o t h e adjusted voltane. n l t h o u i h t h e feedrate was n o t taken i n t o consideration. r e l a t i v e l v hiq6 renression c o e f f i c i e n t s were achieved, as shown i n Tahle 3. Table 7: Coefficients and reqression f a c t o r ohtained i n d l f f p r m t measurins heio'rtz v Y
!n)
(4'71Q-z\
h Jl
17.4
I
1
I
- IIC-
(n l Q - 2 )
18.33 7 .13 17.33 ld.17 13.83
3 .4'7 3 .23 2 .77
6.00 9 .67
1
0.10
(m 11-2)
I
2 .14
2:11
rc
(-\
I
Q.2
1.35
Q.2
'7.71
" w i t h t h e adaptive c o n t r o l u n i t
1.4
1.47
q.22
0.87
0.6
1.54
n.23
q.37
4y examininq the s i d e overcut ohtained we may conclude t h a t the overcut was s i g n i f i c a n t l y reduced hy u s i n q t h e adantive nntimizinq systm.
1 .Q
1.6
1.24
rJ.W
The dependence o f the s i d e overcut on t h e feedrate i n t h e hiqher m i n t s (near the o r i q i n a l surface) v i s very I n w . I b e reqresstan c o e f f i c i e n t increases w i t h the h e i i h t o f t h e msasiirini d n t . The s i d e overcut hehaved i n t h e same way as the hottom overc u t i n t h e p l a r a r n e r i o h e r a l FCC, b u t i t s denendence on the It operatinq voltaqe i s stronqpr (6 =1.23 aqainst h =0.16?). i s obvious therefore, t h a t the sldr overcut and !he bottom o v e r r 4 c u t are n o t indeoendent. The slooe o f t h e overcut f u n c t i o n was a l l aroiind h =1.23 and o n l y I n the case where yx0.2 'near t h e cnrner) b.raslhl d i f f e r e n t and decreased t o 1.2.
The Rottom Overcut The dimension o f t h e bottom overcut. i t s u n i f o r m i t y , d i s t r l h u t i o n and r e o e a t a h i l i t y over a batch were the main c h a r a c t e r i s t i c s we were i n t e r e s t e d i n . The w x i m a l bottom overcut ( 6 \ was always ohtained i n t h e h a l f o f t h e workpiece w i d t h CXd( a 7 . 5
nm.) F.s before, i n t h e f i r s t stage t h e cases o f constant feedrate f o r d i f f e r e n t o p e r a t i n g voltaqes were investioated. The bottom overcut f o r these t e s t s i s described i n Fiq. 7 on a semi-loqarit h i c scale accordinq t o eq. (12). t h i s equation i s s i m i l a r t o eq. ( 6 ) which s a t i s f i e d t h e bottom overcut f o r zero dent4 o f q r i n d i n q n e q l e c t i n q t h e feedra t e i n f l uence.
(hill)
Oy = F b.,XP
(12)
The ohtained c o e f f i c i e n t s accordlnq t o t h e l e a s t square anproxiw t i o n were: h = 2.Q5 (m l Q - 2 \
hl) = 0.20 (Vl-'
w i t h reqression f a c t o r o f r'zQ.77
lJ Fiq. 6:
Q v e K u t t h a t has been conied f r r m t h e p r o f i l e o r o j e c t o r : (a)ll =12.5v llf=n.lF.m/s (h) Tame as ( a ) f o r 4 d i f f e r e n t Darts ( c ) Um=12.5v w i t + b.C.
0
2
Fiq. 7: rlottom overcut feedrates.
100
i
4
VS.
8
u
I2
aoplied voltaqe f o r different fixed
Table 5:
Cornoarison o f the r e s u l t i n q h o t t o r avercut w i t h and w i t h o u t the adantive c o n t r o l system
F
(X’X
(d 10% 12.5 12.6 12.6* 1Q.l 1 D.l 19.1 10.1 10.1*
7.4
Q.lQ
30.00
.15
16.67 a .50 17.m lA.9Q 2fl.67 2‘1.67 12.75 11.67 5.73
- nc-
0 .I0
9 .16
I
9.24 9 .32 - AC0.10
a
7 .6*
I
-4C-
.m
9 .67 3 .75
I
s frm ~ n - ~ ) 5.37 7.33 ‘1.51 fi.26 2.28 2.73 4.50 2.31 2.88 2.q7 1.55 4.23 2.87
*under adaptive c o n t r o l
I n r e l a t i o n t o t h e bottom overcut, i t can be seen t h a t working on t h e o p t l n a l l o c i s i q n i f i c a n t l y reduced b o t h the overcut i t s e l f and the standard deviatlon.
c
Fig. 10: fivercuts w i t h and w i t h o u t t4e adantive c o n t r o l .
Fig. 8:
Typical h o t t m overcut f o r d i f f e r e n t adjusted voltaqes under adaptive c o n t r o l .
Typical bottom overcut surfaces obtained hy a T a l l y s u r f ( w i t h v e r t i c a l m a q n i f i c a t i o n o f XlQ0 and h o r i z o n t a l naqni f i c a tion o f X2Ql w l t h and w i t h o u t t h e adaptive c o n t r o l svstem a r e n r e sented i n Figs. 8,?. Jn these f l g u r e s the s i q n i f i c a n t c o n t r i b u t i o n of t h e adaptive c o n t r o l i s well-seen. I n Fiq. l Q , two h a l f photograohs o f the qround groove, one under the adantive c o n t r o l and t h e o t h e r u i t h o u t adaptive c o n t r o l are presented. Dote were qrQUnd w i t h the sane adjusted voltage. Il-=12.5V. There i s a c l e a r coflnection between the bottom and s i d e overcuts. The i n v e s t l o a t i n n of t h e c o r r e l a t i o n hetween them i s o u t o f t h e scope o f t h i s work. Rut It should he noted t h a t i t c l e a r l y seem t h a t t h e bottom overcut i s m r e s e n s i t i v e t o chanqes i n t h e feedrate.
The Optimal Ada@ive Control qystem t
i
tonceot: the concent a c c o r d i n i t o which the ootimal adanv e m system was developed and b u i l t was:
a. The adjusted voltaqe should n o t he cllanqrd d u r i n g the q r i n d i n g operatloo. b. The adjusted voltaqe should he chanqed i f necessary i n t h e I n t e r v a l s between q r i n d i n q o f two cansecutive stenoinq workpieces accordinq t o t h e measured and nermitted o v r r c u t . c. The feedrate should he continuouslv and a u t a n a t i c a l l y adapt i v e l y chanqed by t h e o o t i n i z l n q u n l t i n order t o keen the worki n g p o i n t on the o o t i n a l l o c i . The system mav he t r e a t e d as a double adaotive c o n t r o l system as i t includes t w o adaotinq loons. The f i r s t adapts the feedrate t o t h e adiusted v o l t a q r i n o r d e r t o meet t h e optimal l o c i . T M s nhase i s w r f o n e d continuously, a u t o m a t i c a l l v and o n - l i n e . The second loop chanqes the adiusted voltaoe as d i c t a t e d hy the adaotive s t r a t egy
.
Oescri t i o n The optimal adaotive c o n t r o l svstem i s pres e n t k l The system c o n s i s t s of two loops. The f i r s t one i s t h e feedrate adanter. The ooerator d e t e n i n e s t h e distance o f the operatinq l o c i from t h e w a r k i n a l i n e by sel e c t i n q DU. (Decmended values a r e between 0.5 and 9.75 v o l t s ) .
.
I
4
F i g . 9: Typical bottom overc u t w i t h V =0.16 m/s obtalned fir d i f f e r e n t
L W PASS FILTER
I vtIf
“n.
F i q . 11 : The optimal adaptive c o n t r o l system.
101
The system would converqe t o the ooeratlnq voltaqe I1 which should he equal t o I l r e f . As the oower sunplier i s r e c t i f i e d a lowpass f i l t r a t i o n was needed. The c o n t r o l l e r (a special nume r i c a l c o n t r o l l e r was designed f o r t h i s puroose) emits pulses t o the d r i v i n q system w f t h the freauency proportional t o the required feedrate. The actual oneratinq voltaqe II d i f f e r s from the adjusted one U due t o the feedrate V (causlnn a voltaqe drop). % r i n g the"gr1nding operation thefadjusted vol taqe IJ i s held constant. A f t e r the qrindinrl ooeration had been terfilinated. the overcut was measured and the adjusted voltage IJ, for the following workpiece was determined accordinq t o the strateqy t o he described hy the second adaotive loon. Suqqested Strategy The proqramned overcut should be determined accordinq t o eq. ( l a ) I n order t o insure t h a t QgYo f the parts w i l l be qround w i t h smaller overcut than the maximum n e n i t t e d one. 4 dead zone i n which I1 would n o t he chanqed was defined. The dead zone i s used as a m f i l t e r which prevents the control s y s t m from following the d i s t r i b u t i o h o f the obtained overcuts. The a l q o r l t h f o r correctlnq the adjusted voltaqe I s based on the measured overcut and the approximate r e l a t i o n which descrlbes the overcut of a l l types !nC) and given hy: 'lC= boEXP(bllJm) As has been shown. b i s almost constant f o r the bottom overc u t a l l over the warping reqlon. Therefore, i f index n denotes the next p a r t and 1 denotes the previous one, the r e l a t i o n between the next and orevious overcuts i s qlven hy eq. (15) and the c o e f f i c i e n t ho vanishes. ')C EXP [bl(Um-l~,l)]
The control plane was defined hy the trio most d a i n a n t oarameters o f the nrocess, i.e. tbe oneratlnq voltaqo and tbe feedrate. The wnrkinq area vas bounded hv thP sparkini. the power and the machine constraints. Sonseouentlv, the ootimal oneratlnq l o c i was defined. Desiilt s obtained w i t h the o n t l n a l control system fvariahlp faadrate\ were compared w i t h the r e s u l t s ohtained w i t h constant feedrates. The c a p a r i s o n showed a s i q n l f i c a n t reduction i n the overcut and a qreat imnrovement i n the d i s t r i h u t l o n and unlformi*y of the orocess under the ontimal control. The behavior o f the overcut alons tbe optimal l o c i ams described and an adaptive control s t r a t e i y t o l i m i t and control the overcut was suqqested. DEFEWJCES 1. C.L. Faust and J.A. Gurklis: "Electrochemical Yachininq and Electrochemical Grinding ,I' PSM, International Conference on Yanufacturinq Techno= l358. 2. L.V. Colwell: " b Physical rodel o f the Electrochemical Grinding Process." MM. International Conference on Yanu facturing Technology, 'Vchiian. Sept.. 1967. po.365-382. 3. Q.R. Cole: "An E x p e r i r y t a l I n v e s t i q a t i o n of the FLectrol y t i c Grindinq Process, r\SW Trans. on Industry, 1961, OP. 104-201. 4. J . Hopenfeld and 0.Q. Cole: "Electrochemfcal Yachinlnq " r e d i c t i o n and Correlation o f Process Variables." y .4 J Trans. on Industry, 1966. pD.155-461.
5.
o r : the next adjusted voltage should he: (1K) For the case stud+ed. the mean value o f h was 0.23. I n order t o always stay on the safe side two qain Jalues o f h should be used. I.le selected h t o he 0.26 when increasinq the adjusted voltage and 0.22 whea decreaslni i t . The p r i n c i n l e of convergence i s shown i n Fiq. 12.
-
-
Levinqer: "Electrochemical qrindinq o f T - C o Cemented Thesls. Haifa. Technion, 1077. Carhides." Y.Q.
P.
5. 9. Levinqer and
$. %ilkl;: 'JC-to Cemented Carhfdes.
"Flectrochemical Grindlnq o f Paper '10. 77-1#/PRnD-26.
ASME
7. Y . Geva: "Furface I n t e q r i t y i n the clectrochenical Grindinq Process," 9 . k . Thesis, Technion, Haifa, 1977.
8.
A . k d d a n and C.F. M b l e : "Pe;ipheral and clectrochemical Grindinq w i t h a Fanned !+heel, Proc. o f the 13th Internationa l V D R Conf., qiwninqham. cent. 1972.
9. M. Geva. E. Lenz and 5. Vadiv: "Peripheral Electochenlcal Grindinq o f 5intered Carbides Effect on Wrface Flnish," Wear. Val. 38, 1976. pp.325-339.
TI).
-
Y. Shpitalnl, Y. Koren and E. Lenz: "Adaptive Control of the ECG Drocess." Proc. o f theCI9P (Yanufacturinq Systems), Vol. 7. Yo. 3 . 1078.
11. Y. Shpitalnl: "Adaptlve Control of the Etectrochemical Brindlng Pmfess," r).Sc. Thesis, TPchnion. Haifa, 1989.
I Fig. 12:
No11
-
The adaptive strateqy optimizinq the adjusted voltage.
SUHYARY An optimal adaptive control system based on three t e s t l e v e l s was presented. Tests i n Peripheral P r o f l l e FCG were c a r r i e d out and the behavior o f the bottom and side overcuts was investigated. Rased on the r e s u l t s an emnlrical model, which describes the d i f f e r e n t types o f overcuts was developed and tested. The model was found t o be easy t o construct. valuable. and accurate enough f o r adaptive control PurPofes.
102
THE ECG W C E S S The Flectro Chemical c r i n d i n q (FCSl nrocesr has heen described i n d e t a i l hv other authors [l-a]. l n t h i s oaner we s h a l l b r i e f l y surmarize the o r i n c i n l e s o f the nrocess concentratinq on the nerioheral FCG and qive special a t t e n t i o n t o the overcut nhenomenon and other aspects of the nrocess on which oiir ontimal adantive control system *#as hased. The material removal i n the FCI: proces i s based on the n r i n c i n l e o f anodic d i s r n l r i t i o n A i r r i m p l e c t r n l v s i s ctnhined w i t h a n ahrasivp w i n d i n n oneratinn. I n the p l e c t m l y s i s orocess. the workpiece i s used as the anode while the qrindinq $,theel i s iused as the crlt+nde; \otb o f then are, o f course. e l e c t r i c a l conductnrs. The e l t t r i c tension hetween the two electrodes i s insured by a " . C . fqenerallv r e c t i f i e d ' binger sunnlier. The anode i s held a t a n o s i t i v e p o t e n t i a l r e l a t i v e t o the cathode, which i s p r a c t i c a l l y ?rounded. 1 s a l t s n l i i t i o n (usiiallv consistinq o f 'la'ln , K'lO and t h e i r huffers, 'oa'V and PI0 \ i s inserted i n t o the 31an bhween the two electrodes2in order2to create the w r k i n 0 zone (sometimes c a l l e d the imrkinq qaol i n which the elect'ol v s i s nrocess takes nlace. fi fundanental descrintlon o f the V G setup i s shown i n Fiq. 1.
menon i s l i m i t e d i n i t s 'dimcnsions and decays as the overcut increases. As a conseauence, a meaninqful qeometrical deviation between the qround n r o f i l e and the qrindinq wheel n r o f i l e can e a s i l y be obtained. Yoreover. the electrochemical etchinq occurs both on and underneath the surface causinq geometrical overc u t and s e l e c t i v e l y etchinq the subsurface layers destroyinq t h e i r Qualities. The iindersiirface selective etchinq occurs p a r t i c u l a r l y i n qrindinq o f comnosite materials and r e l a t e s t o a sinqle "preferred" nhase l i k e the Co Dhase I n the case o f sintered carbides [S.fil .The qeanetrical overcut effects, on the other hand, are usually emnhasized i n q r i n d i n n o f more homoqeneous materials l i k e steels. I n t h i s p a w r the discussion i s l i m i t e d t o the q e a e t r i c a l effects o f the overcut ohenomenon. The overcut ohenanenon i s affected by almost a l l the oarameters and variahles involved i n the FCG process r71, heqlnninq w i t h the qrindinq machine, the power sunplier. the qrindinq wheel (type, q r a i n size, and o r o f i l e l and the workpiece fmaterfal, pretreatments and shape) through the e l e c t r o l y t e (type. ph. pressure. temwrature. and concentration) and endinq w i t h the feedrate. the voltage across the electrodes and the depth of qrindinq. "lany investiqators were aware o f the fact t h a t for a c e r t a i n machine and a qlven setup and job, the dominant narameters are the feedrate and the vol taqe across the electrodes. THE AIV OF THE WRK
r
Although not many o f the investiqators studied the prohlem o f the overcut r7.81. vet. i t i s well-known t h a t the overcut i s one o f the main l i m i t a t i o n s o f the hiqh-potential nrocess - the p e r i pheral n r o f i l e d FCG. Vast o f the research exnresses i n one way o r another the importance o f beinq able t o nredict, control o r reduce t h i s phenmenon.
flB W
Fiq. 1 : Fundamental descrintion o f the FCG nrocess The e l e c t r o l y s i s process i n which atoms frnm the m e t a l l i c workniece move i n t o the s o l u t i o n i s described f o r Ferum. as an examole, hy eqs. (1-5). Anode : Cathode:
tt
Fe
* Fe
2tJ2fl
2 211'
211' + 21 Solution:
+ 2i t
-L
2(nH)-
H7t
Fett + Z(W)-+Fe(Wi)2t
and total1y:Fe t 2H2n
+
H2t+Fe(WJ)2r
(1) (2)
(3) (4)
(51
The e l e c t r o l y s i s process, which i s usually qoverned by Faraday's law of e l e c t r o l y s i s , i s distiirhed by the hydroqen produced beside the cathode as well as by the nassive layer (sometimes c a l l e d the anodic l a y e r ) which coats the anode. Roth o f these phenaena d i s t u r b the motion o f the charqed ions i n t o and i n the s o l u t i o n and f i n a l l v ston the anodic dissolution. It i s the qrindinq wheel's task t o renlace the e l e c t r o l y t e i n the workinq zone as well as t o scrape o f f the passive layer.
It i s mentioned many times [7,8,9], t h a t i n order t o minimize the overcut dimensions, one should increase the feedrate and decrease the e l e c t r i c tension between the electrodes. That t r i v i a l s o l u t i o n a c t u a l l y means an increase i n the ahrasive comnonent o f the process a t the expense o f the electrochemical one, and leads t o conventional abrasive qrindinq. Fuch a s o l u t i o n can i n no way be an Index o f nerfornance when dealinq w i t h an electrochemica l process. I n our opinion the process should onerate on the optimal l o c i (as described hv the authors r l n , l l l and w i l l be b r i e f l y repeated herafter) w i t h the additional constraint o f a qiven maximum permitted overcut. In other words, the ootimal working p o i n t (UP) on the oatlmal l o c i should be defined and determined by the maximum n e n i t t e d overcut.
The development o f such an adaptive strateqy, self-defined and converging t o the optimal operatinq p o i n t i s the goal o f t h i s work. The system should converqe from any s t a r t f n q o o i n t (YP) t o the o p t i m l operatinq n o i n t ('JP) f o r any qiven task and independently of the threesome: the workpiece. the qrfndlnq wheel, and the e l e c t r o l y t e . THF EC6 r)PTIttIZATION
A t the f i r s t staqe an ontima1 control system was b u i l t based
on the concept o f maximizinq the removal r a t e under desired and proqraimnable constraints. The control olane I s defined by the two daninant and Independent control parameters: the feedrate Vf and the operating voltage I). The working reqion i s bounded by
TYE nVFQCUT PHENOMFYW: one o f the nain l i m i t a t i o n s of the FCG process (OX.) ohenomenon. The overcut may he defined as uncontrolled electrochemical o v e r d b o l v i n q o f the The phenomenon ocrurs beneath and on the sides o f wheel during and irmediately a f t e r qrindinq. The
Annals of the ClRP Vol. 30/1/1981
i s tbe overcut undesirpd and workniece. the n r i n d i n q overcut nheno-
The f i v e constraintscreate f i v e extremal ooints of which three, have a o r a c t i c a l meaninq. Point A: l i e s i n the I n t e r s e c t i on between the power and the m i n i m a l t a g e constraints. The material removal r a t e (MRR) i s maximized under the l i m i t a t i o n o f being pure abrasive. Point A i s therefore dlstinquished by: very l o w electrochemical e f f i c i e n c y , hiqh wear r a t e b,Q,r,
97
%asurin : The bottom o v e r c u t w produced durinq the FCC oneration was meas:red on h a l f o f the workpiece width x = x ( r e l a t i v e t o the zone t h a t was wound without the electrocheniEa1 comnonent! alonq the l o n q i t u d i n a l axis [feed d i r e c t i o n ) hy a T a l l w i n Surface Analyzer w i t h v e r t i c a l maqnification o f x l W . The r e s u l t s obtained are sumnarized i n Tahle 1. Table 1: The hottom overcut. i n the peripheral ECG. vs. the adjusted voltaqe for d i f f e r e n t constant feedrates.
3.5
12.5 *Yf
14
11
(nnls), Ihn(v),
aY (mn 1(1-2)
EMPIRICAL MODEL
Fig. 2: Descrlption o f the constraints and the extremal noints on the control plane. o f the grinding wheel, very l o w overcut ( i f any). qood surface f l n i s h . and q u i t e l o w MRR. Point R . ( o r p o i n t 9 i n cases where the power i s l i m i t e d by the operator due t o f r a q l l e n a t e r i a l , etc.): being able t o move on the sparking constraint (by chanqi n q the l i m i t l e v e l ) . Point 9 c a n ' t be characterized by any q u a l i t y except t h a t i t always represents the maximum uQR. The material i s removed by a combined operation o f hoth the abras i v e and electrochemical components. Point C: Unlike p o i n t R . p o i n t C i s s t a t i c and defined hy the i n t e r s e c t i o n o f two cons t a n t and f i x e d constraints: the maximal voltage and the sparki n g l i n e . Point C, therefore, represents the s i t u a t i o n ( i n general) of maximum WR i n the maximal tenslon and under the sparklng constraint. This p o i n t i s dlstinquished by hiqh electrochemical e f f i c i e n c y . low wheel wear and r e l a t i v e l y hiqh overcut. Point C1: i s the operating n o i n t and i s f r e e t o m v e alonq the optimal frame (0)CRA. I n a m a j o r i t y o f o r a c t i c a l cases, C would be between m i n t s R and C. I n p r o f i l e grindins i n parti! cular. one would p r e f e r t o work i n the area o f Point C i n order t o prevent superfluous wear on the qrlndinq wheel. I t was shown hy the authors r i l l t h a t the sparkinq l i n e (and p r a c t i c a l l y a l i n e near the sparking l i n e whose distance from the sparking l i n e i s predetermined by the operator) together w i t h the power l i m i t a t l o n produce the ootimal workinq loci.
The reader should . .. - be aware o f the f a c t t h a t the moment we accept the sparking and the power constraints t o define the optimal l o c i . the two dominant parameters - operatinq voltage and feedrate are no longer independent. For each adjusted voltage U there I s only one adapted ontlmal feedrate. rh the other d n d . f o r each f i x e d feedrate there i s a t l e a s t one optimal voltaoe. A t the desian phase. the f i r s t s t e ~must be t o f i n d out tke degree o f influence o f chanqinq each'of the two parameters on the overcut. For t h a t nuroose, a peripheral ECG w l t h zero depth o f grinding was selected as a nreliminary study case.
-
Although i t can be e a s i l y seen t h a t the most dominant parameter r e l a t i n g t o the bottom overcut i s the adjusted voltaqe. and although one may e a s i l y conclude t h a t i n an adantive cont r o l system i t would be natural to f i t the feedrate t o the adjusted ( o r operating) voltage. yet, there are s t i l l some qood reasons t o construct a made1 describing the overcut behavior. a. The r e s u l t s ohtained from the model can be used as i n i t i a l conditions f o r the adantive control system. b. T r i a l and e r r o r methods can be used accordinq t o the model i n cases where an adaptive control system i s not available. c. A mathematical model can he accurately analvzed t o define the degree o f influence o f each paraneter on the overcut. d. Ry s t a t l s t i c a l analysis, on the other hand, we can deternine t o what extent the phenanenon i s described hy the model.
It can be shown t h a t the r e s u l t s ohtained i n the exoeriment are described by: 6y = K. EXP (bo t bU l, t h2vf\ (6) where: 6 (mn 10- 2 ) by(-); bl(V)K
4 i(mn
T bottom overfut ; b2 (mn/s)- coefficients
la2)-
dlriension f a c t o r
Y r i t i n g eq. (6) i n l i n e a r form by takinq I n of both sides:
(7)
I n (ay) = bo t bl Um t h2Vf By means o f regression and l i n e a r curve f i t t i n q we qet: b = 0.641 b! = 0.163 (V1-l b; = -1.621'(k/s)-'
.
According t o W. (6) and the coefficients ( 8 ) . iso-overcut Curves Can be calculated. quch calculated l i n e s and the Pract i c a l r e s u l t are shown i n Fiq. 3.
,""
*
1
9
4
E W IPWJT I n order t o emohasire the geometrical overcut and minimize the influence o f tbe qrindinq wheel wear on the results, steel (4340) workpieces and diamond wheels were selected. The clqathon Electrolytic-125F grinder w i t h wheel power o f 2HP and constant r o t a t i o n speed o f 5000 r.p.m. was used. The power supplier was the E l y f o r n Ely 3QO generator ( f u l l wave r e c t i f i e r w i t h maximal output power o f 2.2 t 3 J emltted a t nominal rated voltaqe l e v e l s o f 7.5, 10, 12.5 and 1%'). As an e l e c t r o l y t e , we used a water s o l u t i o n o f c m e r c i a l s a l t f424, hy weight rlafln ; 42*. ClaYn ; and 16% anti-corrosion additions) w i t h density 3 0 f 1.04 gr?cm3. The d r i v e system was based on a stepping motor mounted d i r e c t l y t o the worktable lead screw causinq movement o f 0.0159 mn oer pulse. FIRST STAGE EXPERIMENTS
-
PLANAR PERIPHERAL ECG
Type o f grinding:plinar peripheral ECG Grinding wheel: DD l ~ - l ~ / M6125 , nm, 7 mn i n width Horkpiece: s t e e l (4340). 59 mn lenqth, 5 mn width Depth o f grinding: zero Adjusted voltage: 7.5, 10. 12.W Constant feedratrs: 0.16-1.28 mn/s i n steps o f 0.16 mn/s Phcedure: A f t e r 35 m o f ECG along the workpiece. the elect r i c a l power was stopped and the grlnding process was continued without the electrochemical component but w l t h the same feedrate.
98
---Fig. 3: Calculated i s o - o v e n u t l i n e s and exuerimental r e s u l t s .
ANALYSIS
.rxperinent W s c r i n__ t ion :
Rased on the r e s u l t s and some s t a t i s t i c a l i n v e 3 t l m t i o n (analysis o f varlance and f a c t o r i a l analysis for 3 desiqn), imoortant conclusions can be reached.
?n eac+ t e s t (setup\ there were 4 3m wide worknieces. 6ach o f the four was assiqned a "man numeral (Flrl. 4 ) . The mrknieces were held 6.y ba sunnnrts fone on eacb side\ each of '.n 4 d t h to inslire s t a h i l i t v f o r the F I X nneratlnn. Tn each tested qroun. 4 irooves w i t h d i f f e r e n t adjusted voltane lJm t.fere rlmunrt. 4s a reference rlmove. one o f the A grooves rlrminrt without tension ( I =q. wits used. Frm the four worknieces 3 were randrmlv se1ectePand m - z v t r w i .
--------I---
a. The r e s u l t s confirm the assumntlon t h a t the bnttam overcut increases when increasinrl the adjusted voltaqe and decreases when increasinq the feedrate. This phenomenon i s confirmed a l l over the investiqated reqion. h. The influence o f the adjusted v o l t a q r i s much more s i q n i f i c a n t than t h a t o f the feedrate. The influence o f the adjusted voltaqe decreases i n low voltaqe levels (hl (I = -h V 1. h u t f o r prac0.5mnIs. t i c a l representative conditions, l.e.mlt,,, = ?'l4 and V the proportion i s changed h It = -3h2Vf where the miius siqn Indicates opposite lnfldeflces. c. From analysis o f variance (Table 2) we see t h a t the b o t t m overcut i n the case o f Derinheral FCG w i t h zero deoth of qrlndi n g i s r e a l l y dominated by the adjusted voltaqe and the feedrate. A l l the other Darameters concerned taken together have a n e g l i q f b l e influence and the variance r a t i o i s ahout 286. Table 2: Analysis o f Variance SnllRCE
W R E F OF FQEFWY
SUM 4F S'IIARES
KA'I S'IJASF
53.885 About reqr. TOTAL
0.157
18
59.190
21
2.574 0.009
I n ~ $ s1 t a t i s t l c a l camnutations the feedrate" was taken i n m 14 1 s and the varlance r a t l o i s : 2.57410.904 = 286
*
A l l c a p u t a t i o n s are r e l a t e d t o I n (6y).
d. Rased on f a c t o r l a l analysis f o r 3* desiqn r i l l . we can see t h a t the mutual influence and the cross e f f e c t s between the adjusted voltage and the feedrate ( l i n e a r and quadratic! are very s n a l l and p r a c t i c a l l y n e g l i q l b l e . Telylnq on the above analysis, three imnortant operatlonal conclusions r e l a t i n g t o the optlmal adaptive control system may be reached.
a. The adjusted voltaqe I s the nost domlnant narameter.
It I s therefore essential t o q r i n d under a constant v o l t a l e l e v e l i n order t o ensure and achleve: the desired overcut. a more uniform overcut and surface. a b e t t e r c o r r p l a t l o n 4 t h the modrl and a b e t t e r r e p e a t a h i l i t v . This l a s t n o l n t n r a c t i c a l l v wans small standard deviation over a hatch. ksuminq normal d i s t r l h u t l o n and dmandinq: (?\ the nmqrarned nernitted overcut R,, i s qiven hv:
where: a,x: 5
n
nermitted overcut 1 maxinum nract4cal1v ohtained overcut
- estinated standard deviation orohability
-
It can e a s i l y be seen fra en. ll'(l t e a t decreasinq the standard devlation enahles one t o increase the nroqrarmed overcut without hreakinq the severe constraint o f the laxinurn nermitted overcut. Teerefore. the adjusted voltaqe n i r l h t he Increased causinq r e ductlnn i n the wheel w a r as a consenuence. b. It i s necessarv t o continuouslv adant the feedrate t o the adjusted voltaqe i n order t o keep the nrocess on the ootimal l o c i , nrevent arcinq (over feedrate) o r over electrochemical etchlnq (lad feedratel. c. The adantlve control s v s t m t h a t was developed hv the authors w l t h r l l l o r without rli' the control loon f o r the wheel nower l i n i t a t i o n can he used as the adantinq (feedrate t o the adjusted voltaqe\ u n i t I n the whole svsten. 4WlA'lZF ~
T F SV
-
I n the second exnerimental staqe. t e s t s r e l a t l n q d i r c c t l v t o n r o f i1e rC6 were nerfnrmed
.
Fxperinent Conditions: type o f qrindlnq: D r n f l l e nerlnheral FCG qrlndlnq Wheel : 9D 100-100/*', 7 m width deoth o f qrlndlny: 1.6 rm qrlndlnq n r o f i l e : "ectanqular 1 . 6 ~ 7mn w i t h rounded corners workpiece: Weel 434'7, 3 rn wldth r e s u l t s : n t l e a s t ti r e s u l t s f o r each tested mcdn, conditfon adjusted voltaqe: 7.5. 1'7, 12.5" 1511 w i t h current l i m i t a t i o n 1 f-edrates: Znnstant 0.1Q. Q.16, 0.24, 0.32. Q . A n mls, and varlable feedrate ohtained hy the adantive control u n i t .
Flq. 4: Qescrintion o f the n r o f i l e rlrinrlinq t e s t . The side and hottam overcuts were neasured hy a n r o f i l e nroj e c t o r (Johnes t I-ansonl v i t h maqnification o f X50. For each qroove hnth the reference I r n f i l e and the tested one r e r e dram. Data Collection: ~--__--The measurlnq method and the data c o l l e c t l n q nrocedure ~ I l l For each tested qmove and oneratinn cnnd i t i o n ( c e r t a i n adjustet' voltaoe and fendrate!a s i x r o u tahle was completed. For each case. the l e f t and r i q h t slde overcut dimensions wrr I n A i c a t d a t fiinctinn o f t C - hrinbt. n f tC - w z w l n q n o l n t Y. 6 s mentioned heenre, each set o f 4 ~ m - k nieces was qround a t a constant q i v m fecnrat? under three d i f ferent non-zero adjusted voltaqes, and a reference qroove was qround without tension. The wnrkniece was mounted on the s l i d i n q t a h l e of the p r o f i l e projector and the reference qroove was confed on t o a trancnarent naper. T'le workpiece was then moved hy the tahle u n t i l the n r o f l l e o f the tested nrnnve was alirlned as s r x n e t r l c a l l v as possible w i t h the reference qroove. 'ceasurinq horizontal and v e r t l c a l axes on each side (denoted hy X , Y Xq. Y ) o f the conied qroove r a r e drawn. The o r l q i n o f each o f L * tRem was well-defined hy the Intersection o f the measured nrof i l e and the reference one. The bottom and slde overcuts were meastired a t defined noints alonn these axes and were r e l a t e d t o then. b e t o errors which occurred durlnq the measurinq nrocess and caused by the allqnnent nrocedure. the need f o r correction o f the r e s u l t s was essential. The correction was perfanned by a mathematical nrocedure o f centerinq the r e s u l t s without l o s i n q the s t a t i s t l c a l d l s t r l h u t l n n . nnce the centerinq oneration had been cmnleted, the source of the r e s u l t s , i n the sense o f l e f t and L indexes were o r r l q h t side, was innored. Therefore the omitted and x and .y were referrcd t o as the measurenent axes i n qeneral he h r i e f l v sumarized.
.
The Side
nvercut:
The measured side overcuts f o r t e s t s nerformed w i t h d i f f e r e n t adjusted voltaqes and w i t h d l f f e r e n t constant feedrates are shown I n Flq. 5 for y=lm. Fach drawn n o l n t i s the mean o f 6 measured overcuts. The r e s u l t s obtalned f o r 3 wide range o f feedrates were Dut on a s m i - l o q a r l t h i c scale as function o f the operatlnq voltaqe only accordlnq t o the eouatlon: 6x = h4FXP(bl
II\
(11)
where: 6
(mn 10- 2 )
hx(m bO(V)-
lljlJ! -
-
the side overcut coefficlent coefficlent ooeratlnn voltaqe ( d i f f e r s fra the adjusted voltaqe by the proqramnahle narameter nU(ll=llm-~U))
-
99
Vised on the e x n e r i n r n t s c a r r i e d out, t + e r e were some exnectat i o n s concerninq the s i d e overcut which would he ohtained under the o p t i i a l adantive c o n t r o l . a. t b - k i n q w i t h cnnstant tension instirps qood w e d i c t i o n o f t h e overcut dimensions and r e o e t i t i o n o f performance. h. The d i s t r i h u t i o n o f the nvercut nver a hatch would he reduced and t h e surface would he innroved. c. Chanqinq the feedrate d u r i n q t h e ECC nrbcess would h a r d l y a f f e c t the dimension of t h e overcut o r i t s character. d. fis t h e i n f l u e n c e o f t h e feedrate on the overcut i s m a l l , t h e t i n e d u r i n q which t h e wheel i s Over t h e workniece w i l l a l s o have a l o n influence on t h e overcut. T t i s expected, therefore, t h a t the"wal1s"would he more i r n r i i h t . -he qrooves as conied from the p r o f i l e n r o j e c t o r are shown i n Fiq. 6. P r o f i l e s ohtained w i t h and w i t h o u t t h e adantive c o n t r o l are comnared
.
2
0
10
8
Ulr:
Tahle 4 : Somoar4son of the r e s u l t i n g s i d e overcut w i t h and w i t h o u t t h e adantlve c o n t r o l sys em. "f Xx(y=l \ s
Fiq. 5: T k s i d e overcut vs. t h e o n e r a t i n i voltaqe f o r d i f f e r e n t feedrates and v=l .M.
(mn/S\
('1)
This equation i s o f t h e sane form as en. ( 6 ) which descrihes t h e bottom overcut. The d i f f e r e n c e hetween t h e two eouations i s t h a t i n eq. (11) t h e influence o f t h e feedrate was i m o r e d i n order t o meet t h e demands o f the o o t i q a l adantive c o n t r o l conceot. h mentioned hefore, t h e feedrate w u l d a u t m t i c a l l v he adaoted' t o t h e adjusted voltane. n l t h o u i h t h e feedrate was n o t taken i n t o consideration. r e l a t i v e l v hiq6 renression c o e f f i c i e n t s were achieved, as shown i n Tahle 3. Table 7: Coefficients and reqression f a c t o r ohtained i n d l f f p r m t measurins heio'rtz v Y
!n)
(4'71Q-z\
h Jl
17.4
I
1
I
- IIC-
(n l Q - 2 )
18.33 7 .13 17.33 ld.17 13.83
3 .4'7 3 .23 2 .77
6.00 9 .67
1
0.10
(m 11-2)
I
2 .14
2:11
rc
(-\
I
Q.2
1.35
Q.2
'7.71
" w i t h t h e adaptive c o n t r o l u n i t
1.4
1.47
q.22
0.87
0.6
1.54
n.23
q.37
4y examininq the s i d e overcut ohtained we may conclude t h a t the overcut was s i g n i f i c a n t l y reduced hy u s i n q t h e adantive nntimizinq systm.
1 .Q
1.6
1.24
rJ.W
The dependence o f the s i d e overcut on t h e feedrate i n t h e hiqher m i n t s (near the o r i q i n a l surface) v i s very I n w . I b e reqresstan c o e f f i c i e n t increases w i t h the h e i i h t o f t h e msasiirini d n t . The s i d e overcut hehaved i n t h e same way as the hottom overc u t i n t h e p l a r a r n e r i o h e r a l FCC, b u t i t s denendence on the It operatinq voltaqe i s stronqpr (6 =1.23 aqainst h =0.16?). i s obvious therefore, t h a t the sldr overcut and !he bottom o v e r r 4 c u t are n o t indeoendent. The slooe o f t h e overcut f u n c t i o n was a l l aroiind h =1.23 and o n l y I n the case where yx0.2 'near t h e cnrner) b.raslhl d i f f e r e n t and decreased t o 1.2.
The Rottom Overcut The dimension o f t h e bottom overcut. i t s u n i f o r m i t y , d i s t r l h u t i o n and r e o e a t a h i l i t y over a batch were the main c h a r a c t e r i s t i c s we were i n t e r e s t e d i n . The w x i m a l bottom overcut ( 6 \ was always ohtained i n t h e h a l f o f t h e workpiece w i d t h CXd( a 7 . 5
nm.) F.s before, i n t h e f i r s t stage t h e cases o f constant feedrate f o r d i f f e r e n t o p e r a t i n g voltaqes were investioated. The bottom overcut f o r these t e s t s i s described i n Fiq. 7 on a semi-loqarit h i c scale accordinq t o eq. (12). t h i s equation i s s i m i l a r t o eq. ( 6 ) which s a t i s f i e d t h e bottom overcut f o r zero dent4 o f q r i n d i n q n e q l e c t i n q t h e feedra t e i n f l uence.
(hill)
Oy = F b.,XP
(12)
The ohtained c o e f f i c i e n t s accordlnq t o t h e l e a s t square anproxiw t i o n were: h = 2.Q5 (m l Q - 2 \
hl) = 0.20 (Vl-'
w i t h reqression f a c t o r o f r'zQ.77
lJ Fiq. 6:
Q v e K u t t h a t has been conied f r r m t h e p r o f i l e o r o j e c t o r : (a)ll =12.5v llf=n.lF.m/s (h) Tame as ( a ) f o r 4 d i f f e r e n t Darts ( c ) Um=12.5v w i t + b.C.
0
2
Fiq. 7: rlottom overcut feedrates.
100
i
4
VS.
8
u
I2
aoplied voltaqe f o r different fixed
Table 5:
Cornoarison o f the r e s u l t i n q h o t t o r avercut w i t h and w i t h o u t the adantive c o n t r o l system
F
(X’X
(d 10% 12.5 12.6 12.6* 1Q.l 1 D.l 19.1 10.1 10.1*
7.4
Q.lQ
30.00
.15
16.67 a .50 17.m lA.9Q 2fl.67 2‘1.67 12.75 11.67 5.73
- nc-
0 .I0
9 .16
I
9.24 9 .32 - AC0.10
a
7 .6*
I
-4C-
.m
9 .67 3 .75
I
s frm ~ n - ~ ) 5.37 7.33 ‘1.51 fi.26 2.28 2.73 4.50 2.31 2.88 2.q7 1.55 4.23 2.87
*under adaptive c o n t r o l
I n r e l a t i o n t o t h e bottom overcut, i t can be seen t h a t working on t h e o p t l n a l l o c i s i q n i f i c a n t l y reduced b o t h the overcut i t s e l f and the standard deviatlon.
c
Fig. 10: fivercuts w i t h and w i t h o u t t4e adantive c o n t r o l .
Fig. 8:
Typical h o t t m overcut f o r d i f f e r e n t adjusted voltaqes under adaptive c o n t r o l .
Typical bottom overcut surfaces obtained hy a T a l l y s u r f ( w i t h v e r t i c a l m a q n i f i c a t i o n o f XlQ0 and h o r i z o n t a l naqni f i c a tion o f X2Ql w l t h and w i t h o u t t h e adaptive c o n t r o l svstem a r e n r e sented i n Figs. 8,?. Jn these f l g u r e s the s i q n i f i c a n t c o n t r i b u t i o n of t h e adaptive c o n t r o l i s well-seen. I n Fiq. l Q , two h a l f photograohs o f the qround groove, one under the adantive c o n t r o l and t h e o t h e r u i t h o u t adaptive c o n t r o l are presented. Dote were qrQUnd w i t h the sane adjusted voltage. Il-=12.5V. There i s a c l e a r coflnection between the bottom and s i d e overcuts. The i n v e s t l o a t i n n of t h e c o r r e l a t i o n hetween them i s o u t o f t h e scope o f t h i s work. Rut It should he noted t h a t i t c l e a r l y seem t h a t t h e bottom overcut i s m r e s e n s i t i v e t o chanqes i n t h e feedrate.
The Optimal Ada@ive Control qystem t
i
tonceot: the concent a c c o r d i n i t o which the ootimal adanv e m system was developed and b u i l t was:
a. The adjusted voltaqe should n o t he cllanqrd d u r i n g the q r i n d i n g operatloo. b. The adjusted voltaqe should he chanqed i f necessary i n t h e I n t e r v a l s between q r i n d i n q o f two cansecutive stenoinq workpieces accordinq t o t h e measured and nermitted o v r r c u t . c. The feedrate should he continuouslv and a u t a n a t i c a l l y adapt i v e l y chanqed by t h e o o t i n i z l n q u n l t i n order t o keen the worki n g p o i n t on the o o t i n a l l o c i . The system mav he t r e a t e d as a double adaotive c o n t r o l system as i t includes t w o adaotinq loons. The f i r s t adapts the feedrate t o t h e adiusted v o l t a q r i n o r d e r t o meet t h e optimal l o c i . T M s nhase i s w r f o n e d continuously, a u t o m a t i c a l l v and o n - l i n e . The second loop chanqes the adiusted voltaoe as d i c t a t e d hy the adaotive s t r a t egy
.
Oescri t i o n The optimal adaotive c o n t r o l svstem i s pres e n t k l The system c o n s i s t s of two loops. The f i r s t one i s t h e feedrate adanter. The ooerator d e t e n i n e s t h e distance o f the operatinq l o c i from t h e w a r k i n a l i n e by sel e c t i n q DU. (Decmended values a r e between 0.5 and 9.75 v o l t s ) .
.
I
4
F i g . 9: Typical bottom overc u t w i t h V =0.16 m/s obtalned fir d i f f e r e n t
L W PASS FILTER
I vtIf
“n.
F i q . 11 : The optimal adaptive c o n t r o l system.
101
The system would converqe t o the ooeratlnq voltaqe I1 which should he equal t o I l r e f . As the oower sunplier i s r e c t i f i e d a lowpass f i l t r a t i o n was needed. The c o n t r o l l e r (a special nume r i c a l c o n t r o l l e r was designed f o r t h i s puroose) emits pulses t o the d r i v i n q system w f t h the freauency proportional t o the required feedrate. The actual oneratinq voltaqe II d i f f e r s from the adjusted one U due t o the feedrate V (causlnn a voltaqe drop). % r i n g the"gr1nding operation thefadjusted vol taqe IJ i s held constant. A f t e r the qrindinrl ooeration had been terfilinated. the overcut was measured and the adjusted voltage IJ, for the following workpiece was determined accordinq t o the strateqy t o he described hy the second adaotive loon. Suqqested Strategy The proqramned overcut should be determined accordinq t o eq. ( l a ) I n order t o insure t h a t QgYo f the parts w i l l be qround w i t h smaller overcut than the maximum n e n i t t e d one. 4 dead zone i n which I1 would n o t he chanqed was defined. The dead zone i s used as a m f i l t e r which prevents the control s y s t m from following the d i s t r i b u t i o h o f the obtained overcuts. The a l q o r l t h f o r correctlnq the adjusted voltaqe I s based on the measured overcut and the approximate r e l a t i o n which descrlbes the overcut of a l l types !nC) and given hy: 'lC= boEXP(bllJm) As has been shown. b i s almost constant f o r the bottom overc u t a l l over the warping reqlon. Therefore, i f index n denotes the next p a r t and 1 denotes the previous one, the r e l a t i o n between the next and orevious overcuts i s qlven hy eq. (15) and the c o e f f i c i e n t ho vanishes. ')C EXP [bl(Um-l~,l)]
The control plane was defined hy the trio most d a i n a n t oarameters o f the nrocess, i.e. tbe oneratlnq voltaqo and tbe feedrate. The wnrkinq area vas bounded hv thP sparkini. the power and the machine constraints. Sonseouentlv, the ootimal oneratlnq l o c i was defined. Desiilt s obtained w i t h the o n t l n a l control system fvariahlp faadrate\ were compared w i t h the r e s u l t s ohtained w i t h constant feedrates. The c a p a r i s o n showed a s i q n l f i c a n t reduction i n the overcut and a qreat imnrovement i n the d i s t r i h u t l o n and unlformi*y of the orocess under the ontimal control. The behavior o f the overcut alons tbe optimal l o c i ams described and an adaptive control s t r a t e i y t o l i m i t and control the overcut was suqqested. DEFEWJCES 1. C.L. Faust and J.A. Gurklis: "Electrochemical Yachininq and Electrochemical Grinding ,I' PSM, International Conference on Yanufacturinq Techno= l358. 2. L.V. Colwell: " b Physical rodel o f the Electrochemical Grinding Process." MM. International Conference on Yanu facturing Technology, 'Vchiian. Sept.. 1967. po.365-382. 3. Q.R. Cole: "An E x p e r i r y t a l I n v e s t i q a t i o n of the FLectrol y t i c Grindinq Process, r\SW Trans. on Industry, 1961, OP. 104-201. 4. J . Hopenfeld and 0.Q. Cole: "Electrochemfcal Yachinlnq " r e d i c t i o n and Correlation o f Process Variables." y .4 J Trans. on Industry, 1966. pD.155-461.
5.
o r : the next adjusted voltage should he: (1K) For the case stud+ed. the mean value o f h was 0.23. I n order t o always stay on the safe side two qain Jalues o f h should be used. I.le selected h t o he 0.26 when increasinq the adjusted voltage and 0.22 whea decreaslni i t . The p r i n c i n l e of convergence i s shown i n Fiq. 12.
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Levinqer: "Electrochemical qrindinq o f T - C o Cemented Thesls. Haifa. Technion, 1077. Carhides." Y.Q.
P.
5. 9. Levinqer and
$. %ilkl;: 'JC-to Cemented Carhfdes.
"Flectrochemical Grindlnq o f Paper '10. 77-1#/PRnD-26.
ASME
7. Y . Geva: "Furface I n t e q r i t y i n the clectrochenical Grindinq Process," 9 . k . Thesis, Technion, Haifa, 1977.
8.
A . k d d a n and C.F. M b l e : "Pe;ipheral and clectrochemical Grindinq w i t h a Fanned !+heel, Proc. o f the 13th Internationa l V D R Conf., qiwninqham. cent. 1972.
9. M. Geva. E. Lenz and 5. Vadiv: "Peripheral Electochenlcal Grindinq o f 5intered Carbides Effect on Wrface Flnish," Wear. Val. 38, 1976. pp.325-339.
TI).
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Y. Shpitalnl, Y. Koren and E. Lenz: "Adaptive Control of the ECG Drocess." Proc. o f theCI9P (Yanufacturinq Systems), Vol. 7. Yo. 3 . 1078.
11. Y. Shpitalnl: "Adaptlve Control of the Etectrochemical Brindlng Pmfess," r).Sc. Thesis, TPchnion. Haifa, 1989.
I Fig. 12:
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The adaptive strateqy optimizinq the adjusted voltage.
SUHYARY An optimal adaptive control system based on three t e s t l e v e l s was presented. Tests i n Peripheral P r o f l l e FCG were c a r r i e d out and the behavior o f the bottom and side overcuts was investigated. Rased on the r e s u l t s an emnlrical model, which describes the d i f f e r e n t types o f overcuts was developed and tested. The model was found t o be easy t o construct. valuable. and accurate enough f o r adaptive control PurPofes.
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