Adaptive Control Optimization for Grinding

8/13/2019 Adaptive Control Optimization for Grinding

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- ~ , ,.. . , rvt r80-WA/PROD-12E AMERICAN SOCJETY OF MECHANICAL ENGINEERS

45 E 47 St. New York N.Y. 10017The Socoety shall no1 be respOnsible lor statement or opinions advanced in papersn a.scusson at meeti 9S of the Society or ol Its Oivrsions or SeciiOr>$. Ot pointed .nits OUDitcations. o scussJOn is printed only il .. peper s publiShed in ASME.J


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and

Prh = 13.8 (-;rd,.t:tblPpt = 0.96 bu

2)(;' )

P. / = Ct + C27rnudu.ft d.)d, 112ut112nu.-t/' bA 4)where d . . is t he workpiece diameter lmml. b is the grindinl( width(mm). t; is the radial infeed velocity (mm/sl. t, is the peripheral wheel"elocity (m/s). "" ' is the rotational speed of the workpiece (rev/sl, andd . is the equivalent diameter (mm) which for external cylindricalgrinding is given by:

d _ d.du- d .where d is the wheel diameter. The express ion for P,.h in eq. :l is basedon a constant specitic chip formation energy of 1:1. . /mm'1 which isgenera lly valid for grinding of both plain carbon and alloy steels ofvarious compositions and heat treatment. The quantity within theparentheses is the vol umetric removal rate. The plowing componentPpt in equation (3) is based on a constant tangential plowing force perunit width which is also relatively insensitive to the particular steelbeing ground. The sliding component in equatinn ( -I I is due to rubbingof the wear flats on the abrasive grains against the workpiece and. assuch. is proportional to the fraction A of the wheel surface consistingof dulled flat area. The quantity within the parentheses in equatio n( -I ) is the frictional shearstress between the wear tlats and the workpiece which includes a factorC plus an additicnal term proportionalto C arising from the curvature difference between the wheel and theworkpiece. For a particular case of grinding on AISI 1090 hot rolledsteel. the constants are C1 = 7.55 x tQ-3 and C2 = 2.10 x tQ-3 [lll:these constants will scale up or down accordingly depending on theparticula r wheel-workpiece combination. With these particular valuesof C and C2, the wheel can be considered to have an "effective wearflat area" which may be larger or smaller than the actual wear flat area.Therefore. the expression for P,, with these C1 and C2 values can betaken as generally valid for grinding of different steels when A is interpreted as an "effective" rather than an "actual" wear flat area.

Grinding Burn Constraint. One main limitation to the removalra te for grinding of steels is workpiece burn. On the basis of a heattransfer analysis and experimental measurements. it has been shownthat burning occurs when a critical grinding zone temperature isreached [12 1. The corresponding threshold grinding power (Watts )for workpiece burn can be written in terms of the grinding parametersas:

Pb = 19.5 d .. utb + 12.8 bd, 1' 4ut 114n.w 4d,..112 (5)with the grinding parameters in the same units as in equations (2-4).This burning prediction has been shown to be a l i d for both straightsurface and externa l cylindrical grinding is in the form of a powerfunction relationship between the ratio of voiUI netrical removal rateper unit width Zlb to wheel velocity u, :

(6)or since Z = -;rdu.Ufb

R. =Ro ( U f ) 7)with the constants R0 and x evaluated c c o r d i n ~ to the surface finishfor a given amount of ma terial removal after dressing. The exponent 1x typically ranges from 0.4 to 0.6, although both Roand x are reducedby extended sparkout at the end of the grinding cycle before disengaging the wheel from the workpiece.

Dressing. The manner in which the wheel is dressed can greatlyinfluence grinding performance [15. 161. With finer dressing (e.g . linerdressing lead or dressing depth with a single point dresser , the wheelis duller Oarger A l thereby raising the grinding power in equation (2),but the surface finish is better. This tradeoff between grinding powerand surface finish indicates that there should be an optimum dressing2

condition fo r a maximum removal rate subject to burning and surfacefinish constraints. For single point dressing, which is used in t hepresent study, the surface finish has been found to have a powerfunction dependence on the dres.ing lead d and dressing depth ad[161. which when comb ined with equation (6) gives:

Ra =R adY fd : - ( z )'bv, (8)where R;, is a constant. Ty pical values for the dressing parameterexponents are .v = 0.25 and z = 0.60. which indicates that the dressinglead has a much bigger int1uence than the dressing depth on $Urfacefinish. A direct relationship has also been found between the effecti,ewear tlat area and these dressing parameters [ il. althou (h the needto use such a predictive equat ion is avoided with the present grindingoptimization syst.em.Optimization Strategy

The performance index of the grinding process is t he volumet ricremoval rate which for external cyclindrical grinding can hewritten:9 )

The objective of the oprimization is to maximize Z subject to theco nstraints of wo rkpiece burn and surface finish requirements. Forany part icular optimization. the workpiece diameter d. is nearlyco nstant and the grinding width b is fixed. so the performance indexcan be simply taken as the radial infeed velocity Uf. The optimizationproblem therefore can be written:

Maximize UfSubject to: P S Pb

Ra S Rax OJIn the present ca> I. it can be shown [181 that for a specified wearflat area A there is a p articular combination of Uf and n". which willsa tisfy equation (ll l, and this is the optimal working point (Uf*, nu.lfor a given equivalent diameter. wheel diameter, and wheelspeed. Thecollection of all the op timal points for various wear flat areas definesan optimal locus in the L f n. plane [til. Several examples of optimalloci are shown in Fig. : for a number of equivalent dia meters with .= 30m/sand d, = -140 mm. which corre spond to wheel velocity andwheel diameter of the present grinding system. Any point on an optimallocus is the optimal operating point for a particular wear flatarea. optimal points further out along the locus at larger removal ratesco rrespond n to sharper wheels (smaller effective wear flat areal. Thecomp ete erivation of t he optimal locus relationship is presented inreference [1 il.

The optimal locus provides a convergence path to the optimalworking point provided that the grinding power can be measured online [1 l. At the optimal working point. the equality P =Pb prevails.Starting from some initial point on the op timal locus where P


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0

> 0

f

0 wm

s 30 tft/sds 440 mm

2 3 4 (rev/s)

Fig. 2 Examples ol opt lmalloei in U.. r - n,. p

Op ti ma llocus

5 6

Fi; . 3 llluS1ralionof optimal loeus ~ wHh machW. tool limitations irl ., - n.pla ne

if P > Pb the optimal working point can be rt-ached by backing offalon ( the optimal locus until P = Pb.The surface finish constraint can now also be induded in the optimiz.ation problem together with the burning constraint according

t.O the optimization problem in equation (10). As the removal rate is:ncreased by proceeding out along the optimal locus as describedabove. the surface finish becomes rougher ( 'f:e eq1uation (7)). Thesurface finish constraint may be reached prior 1o t he burning limit1 R ~ = Rax and P


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, ---- ------,I COMPUTER IIIIIIIIIII ~ ~ ~ ~ A ~ D ~ C J = ~_ jT

Fig. 5 n ~ i n e adaptive control sySiem: 1 - 1 ~ n g mote< inteed drive: 21nteed controlhandwh : 3-grinding wn-.1 mote


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If,' I

J I.: ~ < ) \l I ;; V Iil ; l.(\ T, \ . I.S .._I a>12

Jea4 0

0 () 2D 3 0 4 0 2 0 0 () 2 0 3 0 0 () 2D 0 I() 2() 0 I ) 2DTo - ltl(a)

0 I() 2D 1 2 1 2r ..... {)(b)

Fig . 6 Dynamic response of system tor lous gains K and K2: 32AJ8VBE whHI,SAE 1045 stHI worl


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Table I Grinding OptimizationIllustration32A46K8 VBE wheel, SAE 4340 steel workpiece (240 Sri nell)d 5 440 ""' d,; 110 nn, b 32 ""' 0 .2 om radial re m was developed which optmizes both : rinding and r e s ~ i n g parameters for plunge grinding osteels. The system based upon a pract ical optimization ~ t r a e ~desi:med to maximize remo,al rate u b j e c t tn constraint..< on wmkpiecburn and surface In sh. althou (h other machine tool limitations aralso considered. The design and operation of a pilot ACO ( rindinsystem was described and ,orne illustrative results were presentewhich demonstrate how the ~ s 1 e m con,er) es towards the optimconditions. This ACO concept offers the advantage of heinl( relativestraightforward to implement. requiring the addition ol a smacomputer. power sensnr. and interface to the bas ic grinding machinAn exist ing CNC' grinder can he upgraded wan AC'O system usinthe present concept with only the addition ol a power sensor and somadditional software in corporating the optimal control st rate (y.Re fe rences

1 Kuren. Y . and llPnl'ri. .J.. Su mt'mal Cllntr >l / Jfadl illP TtmKhanna Puhl ihe rs. Ddhi. India. 1 1:..;. Ch . 9.: Wada. R.. and Kuctama. H .. :\ctaptl\1' Con tr ol in n n c l i n ~ : Hu lf -JapS,cil' t . ; PrPlalkin. S .. :-;p. A. i.\tt-; .J ' t-:nu. Jor Ind . \'ul. ltJU. 1\171 .2 9 ~ -In Ma lkin. S.. :u>ci Murra_. T .. Compari""' uf i n ~ l e Point and H u t aOressinj uf C : r i n d i n ~ Wheels." l 'mc f tj th s . tlt .- \m('Tf(' (l l l .\(otafw.,rkiRe.worch Cunjctrl'trc ,., . \mherst. ~ l a s . " Hf';;, pp . : ";):S- : :) : t17 :--talkin. :> and Koren. Y . "S trate)(ICS to Optimize c;rindinl and r e s sParamet er . fu r Maximum R moval Hme: lu apprar.111 :VIavne. R. \\" . nd :".1alkin. =- .. ..Op;::nizaruul =>fOperating P a r a m e t ~fn r c:rinding nl S ~ t d , _ ' A.'.Hf: . . ui t - : n ~ t n t < r i n ~ j r fndustn. \'ul. 9S. 1 1pp. 111 11'- 10:;2.19 Knren. Y . f ) , . , i ~ n ntTounputer Cun trollir :--tanutacru rin)l SystemTran

Adaptive Control Optimization for Grinding

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