PREDICTION OF THE CUTTING TEMPERATURES OF TURNING STAINLESS STEEL WITH CHAMFERED CUTTING EDGE NOSE RADIUS TOOLS

Transcription

1 Journal of Matrial Sin and Enginring with Advand Thnology Volum, Numbr, 00, Pag 5-43 PREDICTION OF THE CUTTING TEMPERATURES OF TURNING STAINLESS STEEL WITH CHAMFERED CUTTING EDGE NOSE RADIUS TOOLS Dpartmnt of Mhanial and Eltro-Mhanial Enginring National Ilan Univrity No., Shn-Lung Road I-Lan City, 60 Taiwan, R.O.C. -mail: Abtrat Tmpratur of th arbid tip urfa, whn turning tainl tl with a hamfrd main utting dg no radiu tool ar invtigatd. Th mounting of th arbid tip in th tool holdr i ground to a no radiu a maurd by a toolmakr miroop, and a nw utting tmpratur modl dvlopd from th variation in har and frition plan ara ourring in tool no ituation ar prntd in thi papr. Th fritional for and hat gnratd in th bai utting tool ar alulatd by uing th maurd utting for and th thortial utting analyi. Th hat partition fator btwn th tip and hip i olvd by th invr hat tranfr analyi, whih utiliz th tmpratur on th P-typ arbid tip urfa maurd by infrard a th input. Th tip arbid urfa tmpratur i dtrmind by finit lmnt analyi (FEA), and ompard with tmpratur obtaind from xprimntal maurmnt. Good agrmnt dmontrat th auray of th propod modl. Kyword and phra: tainl tl, turning, FEM, tmpratur of tainl tl, hamfrd main utting dg. Rivd Otobr 30, Sintifi Advan Publihr

2 6. Introdution In mtal utting, at lat on fifth of all appliation ar turning opration. Th utting ffiiny inra ignifiantly, if th mahin tool and th utting tool ar uitably ltd. Suitabl tool nd uffiint hardn and hould b of appropriat gomtry. Bid th utting vloity and utting dpth, th rat of fd play an important rol in an ffiint utting opration. A for th othr utting variabl, an optimal hoi of id rak angl ( α ), and of th no radiu of th tool influn th utting quality. In gnral, tainl tl hav high vioity, poor hat ondutivity, and ar apt to ohr to a tool during utting, thu it i diffiult to ut thm (Divin JR [6]). Narly, all th work applid in th pro of mtal utting i onvrtd into hat a frition i ovrom, and utting tmpratur i an important paramtr in th analyi of mtal utting. Th hat i diipatd by th four omponnt involvd in proing th matrial: th utting tool, th workpi, th hip formd, and th utting fluid. Mot of th hat gnratd om from hip formation, with mot of thi hat pad into th hip, whil om of th hat i ondutd into th workpi. Turning i ntial for tainl tl mahining, partiularly for autniti tainl tl, whih lad to th formation of built-up dg during utting. Howvr, it i diffiult to mahin tainl tl. Th utting tool war rapidly bau of high utting tmpratur, and trong adhion at th tool-hip intrfa and tool-workpi matrial intrfa (Trnt [9]). Analyi of th thrmal fild in mtal utting ha bn a topi of rarh intrt for many yar. Obviouly, it i nary and ignifiant to tablih th natur and ditribution of th mtal-utting tmpratur. Many xprimntal thniqu for mauring th mtalutting tmpratur an alo b found in th litratur (Boothroyd [], Lhok and Shin [], Amdt and Brown [], Kato t al. [9], Wright [4]). Th drawbak of th many implifid aumption aoiatd with th analytial olution wr ovrom by th finit lmnt analyi (FEA) of Tay t al. [8]. FEA onidr th variation in vloity, train, and train rat of diffrnt dformation zon, trating th tool hip and workpi ombination a a ingl ontinuum.

3 PREDICTION OF THE CUTTING TEMPERATURES 7 Finit lmnt modl (FEM) imulation i found to b uful for tudying th utting pro and hip formation. FEM ar widly ud for alulating th tr, train, train rat, and tmpratur ditribution in th primary, ondary, and trtiary ub-utting zon. A FEM ombind with invr mthod of thrmolati-plati matrial undr larg dformation for obliqu utting i prntd. Singamnni [7] dmontratd that th mixd finit and boundary lmnt modl that an timat utting tmpratur i impl, ffiint, and at th am tim, ay to implmnt. Th tmpratur ditribution i onitnt with prviou onluion, with th pak tmpratur on th rak fa at om ditan from th utting dg, and it alo onform to th ratr war phnomnon. Fuh and Chang [8] and Chang [5] prntd a FEM modl that orrlat loly with th xprimntal valu, and prdit valu of th utting for and utting tmpratur in turning tainl tl with a harp hamfrd utting dg tool. Analyi of th thr-dimnional utting tmpratur with a no radiu tool ha rivd xtniv attntion. Howvr, th utting tmpratur of no radiu tool wr xludd from th diuion. Th aim of thi papr i to larify th tmpratur of tainl tl with th hamfrd main utting dg no radiu tool.. Thortial Analyi Th FEM wa firt applid in th 970, gratly improving th auray of imulation (Fang and Zng [7]). Klamki [0] firt introdud th appliation of FEM in th fild of mahining. Lajzok [] dvlopd a implifid orthogonal utting modl from th hip gomtry and tool for obtaind from hi xprimnt, whil nglting th prn of hip. Uui and Shirakahi [3] firt aumd th har utting angl, hip gomtry, and flow lin in ordr to prdit fator uh a tr, train, and tmpratur. Shamoto and Altinta [5] dmontratd that th mhani of obliqu utting ar dfind by fiv xprion. Thr of th xprion ar obtaind from th gomtry of obliqu utting, and th rmaining two ar drivd by applying ithr maximum har tr or minimum nrgy prinipl. Sin tmpratur i of fundamntal importan in mtal utting opration, many attmpt

4 8 hav bn mad to prdit it. Som work imply u th rlationhip btwn th work don, and th volum of mtal involvd in th pro to obtain an avrag tmpratur. Othr u omputr to driv th tmpratur ditribution. Howvr, th mthod for mauring tmpratur in mtal utting hav not bn improvd muh, o it i diffiult to prov th thortial rult in a pri mannr. Th nrgy har plan onvrion in mtal utting tak pla mainly in thr rgion, th primary dformation zon and th ondary dformation zon, a third hat our dvlop in mot pratial a at th war land on th flank of th tool. It i alo alway af to aum, a a firt approximation, that all of th work don during th dformation pro gt onvrtd into hat (Shaw [6]). Mot of th hat gnratd at th har plan go into th hip and lav th problm zon. A portion of thi hat ntr th workpi. Th main part of th hat gnratd ha littl influn on th prforman of th tool, in th hip lav th ontat ara vry quikly. Uui and Hirota [0], [], and Uui t al. [] ud an itrativ thniqu to find th hip flow dirtion that minimizd th um of har and frition nrgi. Thy did o by alulating th har nrgy of a ri of paralll fftiv har plan (oniting of th utting vloity and hip flow vtor) along th ativ utting dg. Chang [5] prntd a modl for harp tool with a hamfrd main utting dg that an prdit th utting tmpratur. A thr-dimnional utting modl with a no radiu tool i a impl a inluding main and front utting dg, a hown in Figur,, and 3. Prdition of th utting tmpratur and for with hamfrd main utting dg no radiu tool dpnd on no radiu R, utting dpth d, fd rat f, utting pd V, firt-id rak angl α, ondid rak angl α, paralll bak rak angl α b, id utting dg angl C, and th nd utting dg angl C. Th pro for driving th har plan A and frition plan Q ar dividd into gmnt with tool no radiu, rat of fd, and dpth of ut a hown in Figur 3. Th ara of th har plan A and th projtd ara Q of th variou a ar obtaind a follow.

5 PREDICTION OF THE CUTTING TEMPERATURES 9 Figur. Bai modl of th hamfrd main utting dg tool, f < R, R 0.

6 0 Figur. Bai modl of th hamfrd main utting dg tool, f > R, R 0.

7 PREDICTION OF THE CUTTING TEMPERATURES Tabl. Tool gomtry pifiation (hamfrd main utting dg) Sid utting dg angl C No. of tool Sid rak angl, ( α α ) α, α r, r No roundn (R) 0º 0º, 0º (0º, 0º ) 0., 0.3, 0.5, and 0.8(mm) 0º 0º, 0º (0º, 0º ) 0., 0.3, 0.5, and 0.8(mm) 0º 3 30º, 30º (30º, 30º ) 0., 0.3, 0.5, and 0.8(mm) 30º 4 0º, 0º (0º, 0º ) 0., 0.3, 0.5, and 0.8(mm) 30º 5 0º, 0º (0º, 0º ) 0., 0.3, 0.5, and 0.8(mm) 30º 6 30º, 30º (30º, 30º ) 0., 0.3, 0.5, and 0.8(mm) 40º 7 0º, 0º (0º, 0º ) 0., 0.3, 0.5, and 0.8(mm) 40º 8 0º, 0º (0º, 0º ) 0., 0.3, 0.5, and 0.8(mm) 40º 9 30º, 30º (30º, 30º ) 0., 0.3, 0.5, and 0.8(mm) Notation: tool holdr and tip Carbid tip (Sandvik P0).. Shar ara of th utting pro with a hamfrd main utting dg no radiu tool () Th no radiu of th tool (R) i mallr than th rat of fd ( f ), R < ( f o C ) ( + in( C C )) (Figur ). Th har plan A inlud both th ara of A, A3, A, and th ylindrial ara A, formd by th tool no radiu (Fuh and Chang [8]). A = A + A + A3 + A, () A = 0.5 [ 4a n ( a + n ) ] /, () A π + C C = ( / o η ) ( f o C R + R o Φ ) d, 0 (3) A3 = f o C[ ( d R + R in C )/ o Cf ( o C tan η' + in C )] {( o α in φ ) [ tan η o η' o α in αb / ( + tan α ) ] /( o η ' in φ o α o α )}, ot φ b (4)

8 A = 0.5( W o α ) tan C. (5) Th frition ara of th utting ro tion Q i qual to Q + Q + Q3. { f [ d.5 f in C o C R( in C o C )] Q = 0 [ π / 4 + tan( C C )/ 0.5( C C )] 0.5{ f o C R R [ + tan [( C C ) ]]} [ tan( C C )/( o α o α )]}, (6) Q = W o α [( d / o C W o α tan C )/ o αb ], (7) [( W o α tan C )/ αb ] ( 3 Q3 = 0.5 o Q i th ara of triangl DD ' Y ). (8) Exprion for f, a, n,,, g, η ', d, and Φ ar hown in Appndix A ; th angl Φ and η ' ar dfind in Figur. () Th no radiu of th tool (R) i largr than th fd rat ( f ), R ( f o C )/( + in( C C )) (Figur ). Aordingly, th dpth of ut (d) an b ubdividd into thr part a, (a) d > R, (b) d = R, and () d < R (Figur 3a, 3b, 3) (Fuh and Chang [8]). (i) d > R, Φ A = A + A + A3 + A = fi ( Φ) d + fii ( Φ) d + A3 + A, Φ Φ Φ0 { [ d R( in C )] f o C tan η ' f in C o C } A3 = 0.5f A b (Figur 3a) (9) { o α in φ [ in φ in η ( in α + o α ot φ ) in α ] } / /( o η ' in φ o α o α ), (0) b = 0.5( W o α ) tan C. (5) b

9 PREDICTION OF THE CUTTING TEMPERATURES 3 Whn d R( in C ), Q = Q + Q +. Q Q3 / = 4 { R tan [( 0.5f /( R ( 0.5f ) ] [ + 0.5f ( R f ) / + f ( d R)]} ( o α o α ), () / b Q = W o α [( d / o C W o α tan C )/ o αb ], (7) [( W o α tan C )/ αb ] ( 3 Q3 = 0.5 o Q i th ara of triangl DD ' Y ). (8) (ii) d = R, A = A + A + A3 + A4 + A = Φ fi Φ Φ ( Φ) d + fii ( Φ) d + fiii Φ3 Φ3 Φ0 ( Φ ) d + A + A, (Figur 3b) () 4 { 0.5( d R + R in C ) /[ in φ o α in( η C )] A 4 = ' + {[ o α in φ ][ in η ( in α + o α ot φ ) in α ] } / /( o α b oc ), (3) b A = 0.5( W o α ) tan C. (5) Funtion of f ( Φ), f ( Φ), and f ( Φ) and th variabl Φ, and Φ 3 ar givn in Appndix B. (iii) d < R, I II III, Φ A Φ = A + A + A = fi ( Φ) d + fii ( Φ) d + A3, Φ Φ Φ0 (Figur 3) (4) A = 0.5( W o α ) tan C. (5) Q = Q + Q + Q3, / = {[ R tan f /( 4R f ) / ] + 0.5f ( R f ) Q 4

10 ( d R) f + d( R d) [ f d + R [ d f in( tan d( R d) /( R )] / ]}, d (5) Q = W o α [( d / o C W o α tan C )/ o αb ], (7) [( W o α tan C )/ αb ] ( 3 Q3 = 0.5 o Q i th ara of triangl DD ' Y ). (8) Figur 3(a). d > R.

11 PREDICTION OF THE CUTTING TEMPERATURES 5 Figur 3(b). d = R. Figur 3(). d < R. Figur 3. Bai modl of th hamfrd main utting tool no radiu tool, ( a) d > R, ( b) d = R, and ( ) d < R ( f > R, R 0 ).

12 6.. Enrgy mthod to prdit th frition utting for In thi papr, w noti that () R < ( f o C ) /( + in( C C )), () R ( f o C )/( + in( C C )) will b tudid in futur. Th har nrgy pr unit tim U, and th frition nrgy pr unit U f an b dtrmind by th following quation. That i, U U f = F V = τ A o α V / o( φ α ), (6) = F V = τ in β o α Q V / [ o( φ + β α ) o( φ α )], (7) in whih F = τ A, V = V o α / o( φ α ), V = V in φ / o( φ α ), rprntd by U = U + U f. (8) Th valu of A ar alulatd aording to Equation ()-(5), and th valu of Q ar alulatd from Equation (6)-(8). Th xprimntal valu of α, β, φ, and τ ar obtaind a follow: α rprnt th fftiv rak angl, that i, α = in ( in αn o i + in η in i ), β i th frition angl, whih qual to xp ( 0.848α 0.46 ), φ i th fftiv har angl and qual to ( 0.58α.39 ) propod by Uui t al. [], τ i th har tr, whih qual to αMN (tainl tl) (Chang [4]), and η i th hip flow angl, whih an b dtrmind by onidring minimum th nrgy U min and aording to th omputr flow hart (Figur 4). All th angl ar xprd in radian for digital omputation. In th following, th utting for an b dtrmind by applying th propod quation VF U + U = m F H H = f U for U min in onjuntion with th nrgy mthod (R. E. M. mthod) (Ravindran t al. [4]), and V i th utting pd. Thrfor,

13 PREDICTION OF THE CUTTING TEMPERATURES 7 ( FH ) = Umin / V = { τ o α A / o( φ α ) + τ in β o α Umin Q [ o( φ α + β) o( φ α )]}. (9) / To obtain th valu of ( F H ) U from Equation (9), ( F ) min H U i min quatd to th prinipal omponnt of rultant utting for R t, whih onit of F and N. t t ( R ) = N o α o α + ( F ) in α = ( F ), (0) t H t whr th fritional for i dtrmind by b t Umin H Umin Ft = τ in β o α Q / [ o( φ + β α ) in φ ]. () Thrfor, N t i rwrittn a N t [( F ) ( F ) α ] / ( o α o α ). = in () H t Umin b Th valu of F T and F V ar dtrmind from th omponnt of N t and F t. That i, F F T V = N o α in α + F ( in η o α o η in α in α ), (3) t b t b b = N in α + F ( o η o α ), (4) t t whr N t, th normal for on th tip i a urfa with minimum nrgy; and ( R i th horizontal utting for in th horizontal plan. t ) H

14 8 Figur 4. Flow hart of th frition for and invr hat tranfr olution.

15 PREDICTION OF THE CUTTING TEMPERATURES 9.3. Solid modlling of arbid tip Th hamfrd main utting dg tool ha a mor omplx gomtry. To dvlop a 3D FEM for thrmal analyi, a olid modl of th tip an b tablihd in thr tp. Firt, th tip ro-tion profil (TCSP) prpndiular to th main utting dg wa maurd by uing a miroop, thn CAD oftwar, Solid Work TM, wa mployd to gnrat th tip body by wping th TCSP, along th main utting dg with th pifid pith. Finally, th tip main utting dg wa imulatd to rmov unwantd matrial, and rat a olid modl of turning tip gomtry, a hown in Figur Finit lmnt modl Th finit lmnt analyi oftwar Abaqu TM i ud in thi tudy. Th finit lmnt mh of th arbid tip i hown in Figur 5, whih wa modlld by 58,000 four-nod hxahdral lmnt. A hown in th top viw of Figur 5, 8 6 nod ar loatd on th projtd ontat lngth btwn th tool and th workpi, 3 6 nod ar loatd on th hamfrd width of th main utting dg, and 6 nod ar plad on th flank war. Th hould provid a raonabl olution in th analyi of tip tmpratur ditribution in turning. Th initial ondition of FEA ha a uniform tmpratur of 5ºC in th tip. Bau, th tip do not rotat in th xprimnt, fr onvtion boundary ondition i ud, whn applid to th urfa of tip ontat with th workpi. Figur 5. Solid modl of th hamfrd main utting dg tool.

16 30.5. Modifid arbid tip tmpratur modl Magnitud of th tip load i hown in th following Equation (5) and (6). whr A i th ara of frition for ation, K = U f / A, (5) A = L ( d + W + V ), (6) W i th tip hamfrd width, d i th utting dpth, war of th tip, and for implifiation, th valu of p b U f i th frition nrgy, V b i th flank V b i t to b 0.mm. L f i th ontat lngth btwn th utting dg and th workpi, a in Equation (7), (9), and (3), L P i th projtd ontat lngth btwn th tool and th workpi, a rfrrd to in Figur 6, and an b dtrmind by Equation (8), (30), and (3), a th following ondition. () R < ( f o C )/ ( + in( C C )), (Figur ) L f = = Ph + hj + ( jok + dg) / o α ( d R) / o C + R( π / C + C ) / o α + f o C / [ o( C C ) o α ] R tan C / o α, (7) Lp = [( d R) / o C + R tan C ] in C + 0.5R( π / C + C ) α o ( π / C ) + { f o C / [ o( C C ) α ] o R tan C / o α } o C. (8) () R ( f o C )/ ( + in( C C )), (Figur and 3) (i) whn d R( in C ), thn Lf = ph + hj + jok / o α = ( d R) o C + R tan C + R[ 0.5π C + in ( f / R )]/ o α, / (9) L P = [( d R) / o C + R tan C ] in C + R( 0. 5π C )

17 PREDICTION OF THE CUTTING TEMPERATURES 3 o[( 0.5π C )/ + αr in f / R o[ in ( f / R )/ ]. (30) (ii) d < R( in C ), thn L f = R( θ + θ ) = R[ in ( f / R )[ o ( R d) / ], R (3) ( f / R ) o[ in ( f / R )] / + R o (( R d) R) L P = R in / o[ in ( R d) / ] /. (3) (a) (b) Figur 6. Calulation of ontat lngth (a) L f, (b) L P btwn utting tool and workpi at f > R, R 0. T T T T ρ = k + k + k, (33) t x y z whr ρ i th dnity, i th thrmal ondutivity, and k i th hat apaity. Th boundary ondition on th quar urfa at th utting dg, oppoit from th turning tip, alo aumd to b maintaind in turning, i aignd to b 5ºC. Th hat gnratd in turning i applid a a lin load on th main utting dg. Th ontat btwn tool and hip i wid in tainl tl mahining aording to Equation (7) and (8). Compard with th 0.36mm fd pr rvolution, th haratriti lngth of th lmnt at tip and utting dg i muh largr, around 3.9mm.

18 3 Thi allow th u of lin hat flux at th utting dg in FEA. In hat gnration, th utting dg i aumd to b prftly harp; th frition for i multiplid by th hip vloity to giv th lin hat gnration rat, q f on utting dg. q = F V (34) f f Auming that, K i th hat partition fator for dtrmining th ratio of hat tranfrrd to th tool, th hat gnration rat, q tool on ah utting dg i:. q tool = Kq f. (Li and Shih [3]) (35) In thi tudy, K i aumd to b a ontant for all utting dg. Th invr hat tranfr mthod i mployd to find th valu of K, undr rtain turning pd..6. Invr hat tranfr olution and validation Th flowhart for invr hat tranfr olution of K wa obtaind by th Abaqu TM olvr and i ummarizd in Figur 4. By auming a valu for K, th patial and tmporal tmpratur ditribution of th tip an b found. Th invr hat tranfr mthod i mployd to olv K by minimizing an nrgy funtion on th tip urfa i dtrmind by Equation (34) and (35), a hown in Figur 5. Uing an timatd valu of K, th hat gnration rat i alulatd and applid to nod on th tip main and nd utting dg. Th dirpany btwn th xprimntally maurd tmpratur by infrard pyromtr j by tim t, i i T j t i xp n nj i t t Obj( K ) = ( i i T xp t ) j Tj, (Li and Shih [3]) (36) i= j= whr n i i th numbr of tim intant during turning, and n j i th numbr of thrmooupl ltd to timat th objtiv funtion. Aftr finding th valu of K, th FEM an b mployd to alulat th tmpratur at loation of thrmooupl not ud for invr hat tranfr analyi. Th tool tip tmpratur prditd from th FEA i ompard with xprimntal maurmnt to validat th auray of th propod mthod.

19 PREDICTION OF THE CUTTING TEMPERATURES Exprimntal Produr Th xprimntal t-up i hown in Figur 7. Th mahin tool ud for th tt i th Vitor, lath. In Figur 7, th workpi i hld in th huk of th lath, and th uttr i mountd on a dynamomtr (Kitlr typ 957B) to maur th thr-axi omponnt for. Th for ignal ar rordd through harg amplifir and A D onvrtr. An infrard dttor i utilizd to monitor th utting tip, and th tmpratur aquird i tord in th omputr. All th maurd data ar rordd by a data aquiition ytm (Kithly Mtrobyt Da-600), and analyzd by th ontrol oftwar (Eayt). Th workpi ar tainl tl, SUS 304 of 65mm in diamtr; and 500mm lngth ut from th am bar ar ud. Th ompoition of workpi i C = 0.05%, Mn =.7%, P = 0.34%, S = 0.4%, Si = 0.9%, Ni = 9.4%, Cr = 8.45%, 68HB. Th utting tool ud in th xprimnt ar Sandvik p0, typ SP (Brook [3]). Carbid-tippd tool with following angl ar ud: bak rak angl = 0º, id rak angl = 6º, nd rlif angl = 7º, id rlif angl angl = 9º, nd utting dg angl = 70º, id utting angl = 0º, 30º, and 40º, and no radiu = 0.~ 0.3mm. Tool haratriti inlud WC 69%, TiC 5%, TaC 8%, Co 8%, 3 HV = 740, dnity = 0.3g / m, thrmal ondutivity = 5W/m K, and hat apaity = 0J/Kg K. Th tool gomtri ar ummarizd in Tabl. Th xprimntal tt wr ondutd undr th following ondition: dry utting; utting vloity 40-48m/min; utting dpth and mm; fd rat 0.33mm/rv; th tool holdr bing vrtial to th workpi; and protruion of tool tip from th dynamomtr bing 30mm. For ah tool onfiguration, th workpi i turnd to b a lngth of 40mm in th fd dirtion. Th data ar rordd thr tim at diffrnt tion, and avrag valu ar takn. Th hap of th main and th ondary tip ar obrvd. Blok diagram of prforman ar drawn, a hown in Figur 4.

20 34 Figur 7. Exprimntal t-up. 4. Rult and Diuion Th tmpratur maurd by infrard on th tip urfa i ud a input for th invr hat tranfr mthod to prdit th hat flux on th hamfrd main utting dg no radiu tool. Thi mthod dtrmin th hat partition fator by uing th optimization mthod. An infrard (IR) pyromtr ytm i dvlopd to maur th tmpratur during turning with a no radiu hamfrd main utting dg tool. For knowing th tmpratur of utting tool, and how thi hamfrd main utting dg no radiu tool dra th tmpratur of th tool tip urfa, i indiatd in th following. A mntiond by Li and Shih [3], aording to Equation (35) and (36), th flowhart for invr hat tranfr olution of K i dribd in Figur 4. Th rult obtaind from th finit lmnt analy ar hown in Figur 8-, and dribd a follow: () Figur 8 how th utting tmpratur v. utting tim for diffrnt valu α, α, and C with hamfrd no radiu tool at d =.0mm, f = 0.33mm/rv, V = 0m/min, and R = 0.mm. Figur 9 how th utting tmpratur v. C, for diffrnt valu R with hamfrd no radiu tool at α = 30, α = 30, d =.0mm, f = 0.33mm/rv, V = 0m / min, rptivly. Figur 0 how th utting tmpratur v, R for diffrnt valu α, α, and C with hamfrd no radiu tool, at d =.0mm, f = 0.33mm/rv, and

21 PREDICTION OF THE CUTTING TEMPERATURES 35 V = 0m/ min. Figur how th utting tmpratur of hamfrd utting dg no radiu inrt at C = 30, R = 0.3mm, α = 30, and α = 30, d =.0mm, f = 0.33mm/rv, and V = 0m/ min. () For a ontant no radiu R, Figur 8 and 9 how that inraing th id rak angl, α α, and C, rdu th utting, tmpratur. Th raon i that, th ontat lngth btwn th hip and th tool i hortnd, thu, auing th fftiv rak angl, fftiv har angl to inra and th frition for to dra. (3) A n in Figur 8 and 9, th utting-dg tmpratur of th hamfrd main dg no radiu tool at C 30, α = 30, and = α = 30 th lowt, whil th hight i C = 0, α = 0, and α = 0, and th tmpratur do not xd 400 C. (4) From Figur 9 and 0, for C = 30, α = 30, α = 30, and R = 0.3mm, it an b n that, th utting tmpratur i th lowt, bau th ara of har and frition ar th mallt, but th fftiv rak angl and th fftiv har angl ar both th largt, and th invr data orrlat loly with th xprimntal valu. (5) From Figur 0, for ontant C, a th no radiu (R) inrad from 0.3mm to 0.8mm, th utting tmpratur inrad, but it drad a R inrad furthr from 0. to 0.3mm. Whn R = 0.8mm, th ara of har and frition ar th largt, and probably du to th fft of hattr lading to untabl utting for. (6) Figur how that th utting tmpratur of hamfrd utting dg no radiu inrt i lo to that n in Figur 9 and 0.

22 36 Figur 8. Cutting tmpratur v. utting tim for diffrnt valu α, α, and C, with hamfrd no radiu tool at d =.0mm, f = 0.33mm/rv, V = 0m/min, and R = 0., rptivly (tainl tl). Figur 9. Cutting tmpratur v. C for diffrnt valu R, with hamfrd no radiu tool at α = 30, α = 30, d =.0mm, f = 0.33mm/rv, V = 0m / min (tainl tl).

23 PREDICTION OF THE CUTTING TEMPERATURES 37 Figur 0. Cutting tmpratur v. R for diffrnt valu α α, and, C, with hamfrd no radiu tool at d =.0mm, f = 0.33mm/rv, and V = 0m / min, rptivly (tainl tl).

24 38 Figur. Tmpratur of hamfrd utting dg no radiu inrt at C 30, R = 0.3mm, α = 30 and α = 30, d.0mm, = f = 0.33mm/rv, and V = 0m/ min (tainl tl). = 5. Conluion Good orrlation wr obtaind btwn prditd valu and xprimntal rult of for and tmpratur during mahining tainl tl with hamfrd main utting dg harp tool (Chang [5]). A nw modl for no radiu tool with hamfrd main utting dg ha bn dvlopd by inluding th variation in frition plan ara. In thi modl, th nrgy mthod i alo mployd for mor aurat prdition of utting for. Th FEM and invr hat tranfr olution for tool tmpratur in tainl tl turning i obtaind, and ompard with xprimntal maurmnt. Th good agrmnt dmontrat th auray of propod modl. Thi modl an b xtndd to th on-lin ontrol domain in addition to th fator of tim and thrmal fft.

25 PREDICTION OF THE CUTTING TEMPERATURES 39 Additionally, thi nw no radiu tool modl uing th variation in frition ara that our in no radiu tool an b applid to auratly prdit th utting for and th tmpratur of th tool tip urfa. Aknowldgmnt Th work wa upportd by National Sin Counil of Taiwan (R.O.C.) undr grant numbr NSC 008--E Rfrn [] G. Amdt and R. H. Brown, On th tmpratur ditribution in orthogonal mahining, Int. J. Mahin Tool and Manufatur, Dign, Rarh and Appliation 9 (966), [] G. Boothroyd, Tmpratur in orthogonal mtal utting, Pro., Int. Mhanial Enginring 77 (963), 7-3. [3] K. J. A. Brook, World dirtory and handbook of hard mtal, 5th dition, Intrnational Carbid Data Hand Book, Unitd Kingdom, D (99), [4] C. S. Chang, Turning of tainl tl with worn tool having hamfrd main utting dg, Int. J. Mahin Tool and Manufatur, Dign, Rarh and Appliation 38 (998), [5] C. S. Chang, Prdition of th utting tmpratur of tainl tl with hamfrd main utting dg tool, J. Matr. Pro. Thnol. 90(-3) (007), [6] C. A. Divin JR, What to onidr in hooing an alloy, mahining tainl tl, Amrian Soity for Mtal (ASM), U.S.A., (975), 9-3. [7] G. Fang and P. Zng, Thr-dimnional thrmolati-plati oupld FEM imulation for mtal obliqu utting pro, J. Matr. Pro. Thnol. 68 (005), [8] K. H. Fuh and C. S. Chang, Prdition of th utting for for hamfrd main utting dg tool, Int. J. Mahin Tool and Manufatur, Dign, Rarh and Appliation 35 (995), [9] S. Kato, Y. Yamaguhi, Y. Watanab and Y. Hiraiwa, Maurmnt of tmpratur ditribution within tool uing powdr of ontant mlting point, ASME, J. Eng. Ind. 98 (976), [0] B. E. Klamki, Inipint Chip Formation in Mtal Cutting a Thr Dimnional Finit Analyi, Ph. D. Dirtation, Univrity of Illinoi at Urbana, Champaign, 995.

26 40 [] M. R. Lajzok, A Study of Som Apt of Mtal Cutting by th Finit Elmnt Mthod, Ph. D. Dirtation, NC Stat Univrity, 980. [] C. E. Lhok and Y. C. Shin, Invtigation on utting tmpratur in turning by a tool-work thrmooupl thniqu, ASME, J. Manufaturing Sin and Enginring 9 (997), [3] R. Li and A. J. Shih, Invr Hat Tranfr Solution in Tool Tmpratur Titanium Drilling, Mhanial Enginring, Univrity of Mihigan-Ann Arbor, 005. [4] A. Ravindran, G. V. Rklaiti and K. M. Ragdll, Rgion-Elimin. Mthod, Enginring Optimization, Mthod and Appliation, Wily-Intrin, Nw York, U.S.A., (984), [5] E. Shamoto and Y. Altinta, Prdition of har angl in obliqu utting with maximum har tr and minimum nrgy prinipl, Tran., ASME, J. Manufaturing Sin and Enginring (999), [6] M. C. Shaw, Mtal Cutting Prinipl, Oxford Univrity Pr, Nw York, (984), [7] S. B. Singamnni, A mixd olution for thr-dimnional tmpratur ditribution in turning inrt by uing finit and boundary lmnt thniqu, J. Matr. Pro. Thnol. 66 (005), [8] A. O. Tay, M. G. Stvnon, Davi G. d Vahl and P. L. B. Oxly, A numrial mthod for alulating tmpratur ditribution in mahining from for and har angl maurmnt, Int. J. Mahin Tool and Manufatur, Dign, Rarh and Appliation 6 (976), [9] E. G. Trnt, Mtal Cutting, Buttrworth & Co. Ltd., Sond Edition, England, (984), [0] E. Uui and A. Hirota, An nrgy approah to mhani of thr-dimnional mtal utting, Pro. Int. Conf. on Prodution Enginring, Japan Soity of Priion Enginring (974), [] E. Uui, A. Hirota and M. Mauko, Analytial prdition of thr-dimnional utting pro, Part, Bai utting modl and nrgy approah, Tran., ASME, J. Eng. Ind. 00 (978), -8. [] E. Uui and A. Hirota, Analytial prdition of thr-dimnional utting pro, Part, Chip formation and utting for with onvntional ingl-point tool, Tran., ASME, J. Eng. Ind. 00 (978), [3] E. Uui and T. Shirakahi, Mhani of mahining-grom driptiv at prditiv thory, on th art of utting mtal -75 yar latr a tribut to F. W. Taylor, ASME PED-7 (98), [4] P. K. Wright, Corrlation of tmpring fft with tmpratur ditribution in tl utting tool, ASME, J. Eng. Ind. 00 (978), 3-40.

27 PREDICTION OF THE CUTTING TEMPERATURES 4 Appndix A. Variabl for th tool with no radiu, and whr that no radiu i mallr than th fd ( R 0, R < f ), f = f W o α, (A) a = { f o C R[ + tan( C C ) / ]} / { o αb + [ tan α in αb + tan( C C )] } /( oα oαb ), (A) n { f o C R[ + in( C C )] /( o η ' in φ )}, = (A3) / b = ( + g g in α ), (A4) = { f o C R[ + tan( C C )/ }{ tan η o αb [ α in α + tan( C C ) o α ]/ ( o α o α ), tan b b (A5) g = { f o C R[ + in( C C ) ot φ tan α ]} / o η ', (A6) η' = tan [( tan η in α tan αb ) o αb / o α ], (A7) d = R / in φ{ o ( η' Φ ) + [ o φ in( η' Φ ) + / o αb in φ ( in αb o Φ tan α( in αb + ) in Φ ) } / dφ, (A8) Φ = π / + C + C. (A9) B. Funtion f ( φ) and th variabl Φ, Φ, and Φ 3 for th tool with no radiu, and whr th no radiu i largr than th fd rat, ( R 0, R > f, d > R, and d = R ). ( Φ) = [ f + R ( Φ + C )]{ in( η ' + C ) ot [ tan ( f + R o( Φ C )) f I o + /( R in( Φ + C ))] + o( η ' + C ) + o( η ' + C )} R { ( f + R o( Φ + C ))[ in( η ' + C ) o( η ' + C )ot

28 4 [ tan ( f + R o( Φ + C ))/ o( η' + C )ot [ tan ( f + R o( Φ + C ))/ R in( Φ + )]]] } /, C (B) fii ( Φ ) = / in( η ' + C ){ R in( Φ + C ) + f in( η ' + C ) o C / o η ' + R in( η ' Φ ) o C / o η ' } R / o η ', (B) f ( Φ ) = [ d R + R in( Φ + C )/ in( η ' + C )], (B3) III Φ = π / + tan f /( 4R ) /, (B4) C f Φ = η' in {( f / R ) in( η' + C ) + in η' }, (B5) {( / R) [ f in( η ' + C ) + ( R o ' / o C ) Φ3 = η' + in η ( d o η ' / o C ) R in( η ' + C ) / o C ]. (B6) C. Funtion f II ( Φ) and variabl Φ 0 and Φ for th tool with no radiu, and whr th no radiu i largr than th fd, ( R 0, R > f, d < R ). f ( Φ) = R in( η ' + C ){ in( Φ + C ) in( Φ + C )} + f ( ), (C) II / I Φ + in [( R d) / ], Φ0 = C R and (C) Φ i dtrmind o a to atify th following quation. (C3) Nomnlatur F HH Final modifid horizontal utting for. F P Plowing for (N). F F t Shar for (N). Frition for (N). F W Additional for du to war (N). L f Lngth of ontat btwn tool and work pi (mm).

29 PREDICTION OF THE CUTTING TEMPERATURES 43 L p Projtd lngth of ontat btwn tool and work pi (mm). R No radiu. σ y Yild normal tr ( MN/mm ). τ y Yild har tr ( MN/mm ). τ Shar tr ( MN/mm ). R T T Main utting dg radiu (mm). Cutting tim (min). Tmpratur ( C). g