Skip to main navigation Skip to main content
  • E-Submission

JKSPE : Journal of the Korean Society for Precision Engineering

OPEN ACCESS
ABOUT
BROWSE ARTICLES
EDITORIAL POLICIES
FOR CONTRIBUTORS
REGULAR

Application of Bat algorithm for Improvement of Surface Integrity in Turning of AISI 304 Austenitic Stainless Steel

Journal of the Korean Society for Precision Engineering 2021;38(4):237-244.
Published online: April 1, 2021

1 Hanoi University of Industry, 298, Cau Dien Street, Bac Tu Liem District, Hanoi Vietnam JFIFddDuckydqhttp://ns.adobe.com/xap/1.0/ Adobed     ! 1AQa"q 2#w8B36v7XRr$9bCt%u&Ws'(xy4T5fH  !1AQaq"2B Rbr#u67Ѳ3sTt5v8Sc$4ĂCÔ%UӅFV ?_Aנj- H>>,m*>fzp"TrKkr^r.|_&]|*vPuܶvoQ1mwVJUhu-I"=LniAƕ8"۲ k*ҿ[yu:.vUQ+)%F DHyVBk>Hy8jݹ q~9D4KRmzQ)^ʔ.J%k_tVi5NTjg!'ky|5asOȻ)R۸ߩFMԿ3L4j6dڜ#NIwUF]JqB/(FafJRzq3\G՛ ?~\ 6)6W4m[O^L0E&rRMض*C .]Unl-1 1r#Rj/&QɈ׉˩s6Rj=5Tg.y.·Pӡ:JJS:C8-2u]d&vUz;7p9 5VnL֢"y)">iי(IDDd| Yj0; LRfS:ktYK%*N2^m|&dğth":ey)uPQZW)gcC3Pv&MMWd&Ŵ۲mvTRoժM03*F3Yd6\8,\hݻ kߔi<k NTwSԪmljj[>->ptU%'LR>&EBH$MQAUx[$Z6vi&_a.KIQ{hyƒ j"JOC9eFҝfj;˚Ω<[3_m% lQ@4g=5$(J]Yc-OMq<Ǎ wSzڗ)k$7VIP붾ͯnV+卵*t]iЎD31~SA1éC2u)ʼnQn-Uoi3:grI8ؓWm*G zܕ)ZקJ}Y YlGeJ6cB2I NS3Q>k=KTBT]W6+SOXQgGR? telˊ%-Re\hѯ2TF"C/OJΩ6r[N.0{SpljjX1“jOsӥ;ҭhe}xu`Ք&.)yO̒ Fߑ.$Qw;9Iw2o+RVJMSOj[SoҌZ%;`d$blQ{Ro{Imڌ>3egf\O֝Uzx"䢸g+mv%Gʆ:|V[N'&ס-ޝ'kfE|K,G&˳98Juin/\\Qݿ̋v~Ǩ!rtWU d|E߫R4d}.qPw*Ӭv5YEcn~f5c%MTMkb-F>5JT,})QHg%{("ӔȸWMsYyWNRrkkJr0XドnͫT}r-jj,Ŕʍ\Q2Ri>v$5!]"JB2WɅ)]VԜUc8i|.jeRO6^V.¸ Q&#|ܶ-*uOG%JAtRZRr]FFG\۩w+?'zչSѧt jz>KW&ot{7P&2D;&\\>Q2JzܗAKSfeNn[jRrԕf6,q,F1tRfԗ>vֶևj-&R'Zi2=xv~Elbsvm8=ӛ"ū񕜈BȩlWau[]ٷBߨF~J!|Ipr3R̴#Yp)={7:G{+:\W}n|Q#%)7^-h"Ƒq:M*%J&$T軨I333׎g_- ucBwwjp[6i25$̏bU’ٱRv?G\~#Iͪb7<<}Ezt" q_Inw,7-d,G÷%T* Wg1"䥱kq/A.,_KhqŒxwvo u2ۥۧ.bQ}XκA$֣ +K״ZUNmڸII{.v{5z5ѮRme[moyƾd~cRݾK'j.\i&/S6f|b=5: p!6i_ 4j6=.si˧eƾtS^c.Y^RJVS-Vi3,esi08?H$GvZgg?gi䤟2adw릿:"۪lkSN>q-4kI܋ێe̊qۅgDoѨ9; #T.Q;7#~_Ufstb_'w~Xw1Xk,vcOt._}v}8"(4Z\ۘgk?J?bm_c!g{HZV]Fkk%~gEt)b秴vΰB|꽸}mp~E6ݹv;7P٤v+ri*3Ԣ|'O14_~7nP{7ZU\Vű[ +7󖱅o#:ǥŬ\|3r%TJX]V7ez¨Y]lc|O3V! R zbJ'PnGqVJ"19WVeOF埜EaEJωqCN5Z g-9[S<$sUK5b|7sn\7x qmv##FF\ w[=-43$^ooVSiXօv7iB۴yg>]Vf"r$J3""32!Zh[K%7GvNLs+4nB/B{vlsobJaҺJR:0g%&zR\ S3T[&ִor*ⷳc3ʊO[iozW٨%$gn:ܶWwFBԹjHP&z u&F2\f;ipW73 [; '_̽b;vib!oec dC-tS__$Xs]l9&z$2/N>%'[}b{h/{`{Ji׉׏ YJB/X%}.|+{(S:qz]4_Kѵo`^tY_4S#* ^zvݾMr+TrkQ g.8Ͽ^i>ӈǙvix>$o( ^qt*&t1oJVu-ql5U6jCЉmĻ*"?JT=K'O/|=Vo}l0b}}f?X[?/\JSBe,kP8ETJ==?.p5ފgbU9}ǶdNKk—_$8̸͓ۍ8Di\BԿ-1v{FF]|.^ۅ{vl12׏z7-R7wE?\nh\jN/Kձr_oBw"N QMBZqe-m:ӨSn6j4%!hQ;sv'm4kcM=!8\m[M4{SMliۇ%eֽR&N:{2A8)THLK3Zj[jPBx#BگMf:G1\`edcʮ?|w(-̮vXt,bW2;.ιNHRR#YwTM"<;mk\.foIDjmlJ;vxy7o7i\,KQŊ9d^Mmgc L*.T6tLeIuOH3SJQ3=F/ʿ<9\JM6mN6=<{xkP!F1QR[I$6ُimXu2An2yԒMU q f[IB-'䤯jYm52&JG\zд\~vdg QtHGXw&1Lw+nDEdC1w|YJmvP)HZ>i0BPβә?R:QO["]I_Jʏۍ>QKyu^bycBq4lXF~l [\*N>-J6,Gq(Zr5h]CwYӤU~ʶߑ u*SIv%ZfJ7)! FS*s_\|IŸZ)J ]ܜi4"z[+Z,MOZ))}|Ʀ(RUNIII.S'ˍO~˨rn}M)xxӕ0 eyҵ7YMAB]ӣU:/ѭ*6bcwP͵ "+qēVjŹO|GtY4V j[mLV M -m>",B$ GD1~j6O4|LxnNmqATNR3ε|DŽa[fmn-ڭ+FiK7Pcm;r5 l8r{#-]'nrFh2ruycb;pW=njRqRJ(d mnpckNnʹ+6]tz~E=ʕ l ZZ5jSi3#47.Lcfe`9؏v囜.F\-UZ:*0_<Νu9Lӵm&)_3\^ҹ3"1n1v_|uRʞͫr'iȧN_kH׺8xXrj=\МH)V\ˬ.Xʸ oVRC}ySU9/OBY먌5 ٿwޞ)rw8Ӫi5*5ZΗcGƱ !ZۄlmpjJ -l <R̵/JAպZuq\IdUS 48wXJJtcg4cI~aqߓwŷrm-v)G7yS^7H^-\mŌAq|"m9IBnF㏉9[N+mmy/!KKۉ%n +BdddfFF6FQRN-U5;Sv'm4kcM=Mn)\qιqUd9F%",6MGdT%-+~ f%+y֛^3SrF>6lc(֪vۊN;g._0Sѧ]ETWرkQKzGe9ʨsKA"yC y2\[5 rԭ7Gk5Mzw_4sM3hxЊ'oÍ5jsub )ͪ~tR2H]R͍>̋m6=%(˿(Wrr-܅y5(ܔJ޺YunW̹븹NsqK ]/QR#"ZMDfD|43Qw|._ԡSqTZBg??O Ϥ)/E_U|i}2 9Z?¹0:x'3,whǣ?C y-A~=daJј&M?D1_PS+Oi&;a @;Dž7[ zZC"bv:jjMQk$M RԸ3uA\=wI.AwC"^.{?-\NSiˏ"b}T/}q/ o.1M}R%:-ZniʒL$SgrBW*,Mw'N\ɇ{s\j]VryG'8f`}'N<*/`U숻z CwHq18J+vԕKss4R53/&XTt1bZƟo\=%nO)h$rBi-nKĪ^ ջڜlwkYm[̑+/QrZo%TQ;TLs($2C:s.%+eoNttq۰kK7O0m_t_pZ1SsSM7"mevFZ[w -FJ*T*jФQRg BSu|]g:ɵzjqwmltL.e3sRMچkSmjkmWœިm++¦'tILk*բQ D,PB\lI[9{%Gb R6öۍmX-MaʉA931cs..G4CujQտ[9 }G-xwl)IQz j Ó"rqe&=]꾧֎c)<kӳ+0JrRR3'TnXi^xMF Bު*tIL.[h"2"nKzZe'ZV/RrNYz]8죝n]Ķܩ>^Ժ]u-7^\mZjܣ9+Rmn ߑv?oꋘ?&ƪy^N4o=3-ؔ̿*`}V݁ ƒPu8%$ ݗ]wt;\y\>='OjPIp/nJU8{϶FNMsf"ίNqƹ(+ ݮF2Km |jܴZs%zf*eȫ?]4)I۵nR&FX + [jDh(#哑9q9Eծj8noǕZf\J-l&Z˫}`ӎhyrΉn\űn]9pʌӣ"׮Wt?N4_I_~54#/my1Xr*척aS#DT >q ssΛW;3oUaJSRMDgQnt:Ql,/ ܷfRqiM Ȼ>Cob;A>ڦWقM9X~/!'MW.}Vrߔꔵ!5|iB(0-zF=}okڢE$^wW~nokY߮\6՜̌{i-AF*9)\t9IV6۸5ZUF6R$ŨQIq砳YUZ]eyv >hI櫥N )&l JulwE1GDOuFN2| }馥uC1rޫV+^gdb&W[4<^e4YW,d|htͮsUM)۸8:{3d{AѢ)~ \#J=NdƮꮓ90 |1K$v*?мS ]i$J,C,SG?/_՜pMSƯM|mG1V1$~K>CSvkuj=&) -,yLjuFHK{c駗.SOua;BrSqj-ۍZ#'Jys7[g2z/.u4+XV2VQ.ޕ)$"(%)#Z7suZ%j }BǬݕe)Jvz8zJf:hIN|svO1O#IEcۍjݽ:SdὮvu^@:o^5cs>i/VqmVm]ؔܢn6'vޑ̗J4Wn@OlKbX ;n:hgJ9ŻyǑz8f܌q&Y fN0N;[69 rbׅC2/#kE l&2~èMR.*%g=Ft.%؝e8<.e=Uv{~㻏"EˑnvDѭ͜Lu3u0:U֝$[M5<:oi+V4V9 6nXvx&_ q Qqw3W:uϔ2yb/(ɳ|5zQiJ#r|Hw#.W?4aDŲ\ugWG;Cw鐢K|xg)##=O.dF˟jMUvWĻsr.z]kPc9"]R)mkfOd*uYf١RsB Aîh=k]ʳUrrZsq`d#r$/Ը3o^&lRWȍyuW̦Y4QDUMJ65ƒ[+ygk XK_±k#y:8(TJOSQhJt2.DR}"5[) r)6V6u5k:eXZmv𭤔!푊Q[qQ}ҹLE- 8qIZG|UM4j}Mܕ[Vwm{} Naqµ"ԈM zOpKѰ?IAD3Ir0'/q1itoB5{%wkOBn-ۜduqIzYK60{+DʕܞqIt";r1mG/\/ym[6JƫR \L=S=OT@Ix[TMm{>ݾտ֒ݸӉLYIx>+"JVNzx||5rI?C{oz8۹e\R-^\A2F R+N9 vlT]"ۭ d)t֞i #E2jB@׵=#/N+!ĕhx}I!cM`ąZ*ŻɄҒ߮Y.Z}='/oۙ3IpW̮hT7cTSuz9>B}΄&h!>lӵn~j˅IvU.'v'CSZw8QK3G> ,J59ٷ+HSg䧎hJdzvwv-cvxS5[̊n~ؿ%ַX?O0\6ne 6kn9.ϯ} *h 8_QhLݣ7q +=XBҲ5?[[)+F`=4 }B,sNg==u*Nj9k_GJ)+R~GSPBȒZ:(K]heL=vKPӢwq(NrG^ثϣ?#tC?.ͼ[ۅo؞y#%ǛjVyLSw%T*s92JTM%"YkQО.q)gCͲn8cgi6j1MѾ[{9h^vƘǚםidfi.^RHmg&rׇz:}݃}xT$ضk'5s-狶,\vpbPD،=Okf.c#cdz2FK5T!&)|ntD<+OŹU i-G[EE*FDfeaf2QƤM\UG_{ǹm%\yrGy:.\4wjPGUJޕUV7Do\7Vy_13w;[?c]H\$IJ,*L]3b%L{y.JRKG2sq,B6T}(#nW|km+q5] r㪍bJ@y{byz,b踊3ϻJ,'^xd،)JVw#.Vټc''ÝպWtbRؒJz۠8!o9IۄS95E9ؔ-e9JR{dmnッ<[~n${~Њ$W?&ՐY_? #a.ߑv?oꋘ?&ơ|y^N4o=3t=~7!/M3>n8W홎2M`Qx+ z qy8%]7_~540ۦ彷]Wq CѡwkďyF5Dum_}~P(5.(X,K9vᯐ?leB9;Jhm#3{CxGE-S{;@Fz˙]=O'!ɿ]' r`:7'2bЖ>Iy,/eTy/V<.H?UYY{\^#ѣr9^7?xoRȆ7EoS_&??zϾM?(~Q-K&>"~aߨ t7Emsϛ+?;fCr)fY+>z$tIkjn_>vnrֳki-˹l= t;'EyC¥|/BLwBJdgjۛ$s S1|ɍV%JI6KvəhzIlBYɒ|0"Sy0F>eo5W)O+X˻u';v)2vVq۳kۮws?UʑBǴYO漪e2MIjPAک\b1)DDؚKm6ZWΨgȕ۶yjڳ 2ضN[C[|r@9Jfo<_eI7q.|cÊV߷:i.:$ȋ)1%%)ADZCEBxJ0MJۥy(bNsKM9k43IwNt.\%N簤I'.j|ƃ2$grBEٌ\}9:v*!n7M(ɽ]7c@XxƱԨ37īf62cTTfFK]9wntQHͮvٱI/f|j=7}\_V5U^+:uljSȃY(XI.ȱmo1甅jڎIZ2>#\*:gY|4k\8ZwSqtyA!+];бޞKծË¥e)#5ap.QK^8VdU{*ѽL\=qmjnB5>{ Ӟ`v±5 ^k&O~Oshɷ,;6nOW>u6{RqS`)S%jp\ipdEBLfTWy$GIYw~䲭J.1vSY5z.V>^+Ǎvc.I[R{QsNR3ӎfhd>y?UJ*}~[e\i5U^͛E]G_FS(Iɿ]i8:4zj~շsW,ˆsy:%O}iur]iF5~3M:Ӟ#N06)4ߧgdawIotiz:1r5YDZLHBSi;NQc44la=Y kQIT*ըl:tq2(է9VO4뒳܂~2rq'nrVZŦ[t7\oլfb/mlpc.I8콚q^1iE~䰳mi[dۧw֤ICfdFeCsg:i| 6擣׋* 96lust^{%99UNRvaMܽo ammi$em4D6DD\nA%$$#}۷/ݕr99JMն[oT޲E"KTaP+HGkŴj5TM5xƱOS-k`ۛkٝWz;{kS}F;~q|~^_|euwnE'pSupUP)V]vE+t =ZRaVdG6= *.ϼnj9:UɷbېmF_tޫgHjVS'śǕًdkkѻ_]Kv?nT>)^e=Ar1'3ԔILyD?:-^in):{7.؂\.:V }#뺾.3r̸*xbFM aȵz 6SQ:ײj[ 8nn iFMw rR"5M5I旘35f^j='j:nNW.ʭocZvZKV^ɚJ.cM1ZI7E'6rg탸5oZ=[m Z`\hbMUR١Ȗĉ):Jin!_7Dй+f̷eKҷvͨBPR(V`y6tw*MRΝcB.ڭTnc;P$8nFvm4(D(R#R-L -2:FP lxZKQc6I("Km%$E, 78uXIFA$RQI$JbInG]c[ֹ:ZM+n^')JmJMJRu{e)7jQDw~%yQl}BZujSSf۩QZ+Dzhd5o%BIc'GZ?}΍:>Ɵivז-%݌J5MqGWTVʦh݇ܟ~Օ_6 n'{3~mϬj'J11OȻn߃r Qr\3y٘+WӍ'WxEs^O3 o~[|7>]]H9݇ZomT@]?5B:Z߂'`V_+/MSKX߆ޠk3?o7y:4R/7þ] iG߬aBRU&?r&/} cQߥGj2?C5Yśe7hU=?+ x龳f-܈czW^7p%-(\D4h{UK&ӡn^m]Fݢ:`δvj俜F+) y[{{ 7 tu>gvrěOj'5 iRg[ͶFjGe n~qT$ci ۚ0oԹc*jL[sVWqj\ݻ&6"WoK:cnWmrv)o>66(F>=W^bf#c zzʞtپy%mՉPël e}J.\Zk4ttt>oEM=q)hJjI=ͥ(%]脼_88ф;͛gWG;Cw~˘$4=uWdĜTثNDkiQL9U*O"4XP`02,Ge-k5$h>ܼ]3vr6!9RQPIVSnM(ۓ{>;/Qͱv{3&-[rc)ܚI$n{Sv3[j00)-D3z}MRzVQпj,T[uVs0\}Sid;r(ݝJ>æʺL&c[jPK0~d(FKÝW\m]GTcF|Iׁ)I3~#oX%vҦEݑؼ5Żv2qAZTE^..M{ʐfȏ2##.R}*KʛZz^ӞN*lPťLf\G6[WVQquV]XAi)5J!,$iJ6o$tPZc;Kjx_n3`qIelV~vLy{fn匋Ѿn%;zV.n'-ұdd2߽1bZksPe3TI9)$ԩIN9Vơ\=2885N\ p)/a柛w9g_lױo8ݷ iixJV& ғRi{N^_oAŮE6Y7I$Nk$|Q)-*4Z)^¸%4Qm [I%.c-OV+C֧R#%ѨCe3i;w$G+_dy| Fzj$DI(=OA gj%v/]8qԯNIS*֩',Q%\44ZZ%D|Ǧʴ6&vֵI$%8(ԬƾS&#Z. }6z?b/|Jl{ץv&mpx4Z$”ڝ4-H%dGKfM:sKSRWeJAn]>s6应-W9'H]'uȫYvgK^\czp|My\鏩w/ËQ.)]\QiS`8uL뚛̸=J"ܻi\å'-)54Ue]:K\퓡vK xwBqrH\*֕TnzC.mT=t-H]SČ~Nu╏NÅ3f|͡G~B+Xm[Q7U{9"~jgK Zoʰ7"qJ,ekSeNGgϳ] ^.6:s}_,%eRg<5⿨z{ZPun#jRІ.6g T.!]xa c#jN$Zpl̋H WZu8WmMRýsĮ?Mco~sx TU҆Q :KDG4n42.<3/'^?6/ܠڒ^yrrÿr2\D}}B]^E~^T cɛ7϶Y[<֞[7d}2%QPqOLEQR\CIsj1?\}%tJ0e~ *sk"*)&ۓEi#{1J8Hrt|'ܝRr8)=ƔN'RVz:cf]F7bZyZUȘ4x8,#JG̒?.W9XnO]KO]%]ƻ O5Γ/3qÓj؍/r̺rƵ 5\&m6h.xoeX[=<3%< lZ"2h\Z[&jW3ejm?k&[]ųj+{N{66leu_+lj]q* 7g*knأYv= q ەdxЬZ|%GUrQ3jLŒqET]1% qkXYūYc[7Ś]QY\jko\</Lc7+'hMSUc6qXyؙ~6#ѯv.0$BQi5YyIhɍiy=KD!n3Vm[V%W-B%swa97ajۗ m+9~]fKq|Ddaˑ0A]_v޺mM5* F-BYHJ5}q>ʉ.6hyDmpD׬'-_v5;5[8K[viJ.3dR:oYHHh9I7:۽fi+wm^ [)odPѱ52CZUJicSw\&_s0uBȍh32džzQflcd^m|7GѹE!fO5]]H9݇ZomT@]?5B:Z߂'`V_+/MSKX߆ޠk3?o7y:4R/7þ] iG߬aBRU&?r&/} cQߥGj2?C5Yśe7hU=?+ x龳f-܈czW^7p%5|Y:SJE\U-(a_cƣUǽXXKiȞNlmۊڭڄR!**ܤMeȽ$|X5(Ź\rJ~ܮ]>'HB0cp XFr_c?f?7<ukSgov¥iG>>䙗i.+t+bOjIܶ . i^:nm}s}(3>NZ$2Qg([".>i.ƾ)B̋M8+"- >eE6DݥJnJˣt׻ 5.˅nJGwZD~!i۶a,Db3ZQ3O#KO5/֍ozuK'GbRi᝘NV_ҝcvם ZoX}F6z 7e5_e:ۓj=AB+iܔERadMBq*ԯ DwI/Gy*mĥiRKg6skY/#SN4e$-yXM YL?^ĸNNӪ{$r1JJRSLO]Aqm>V/s[~i/j+m>z}eI"Qvp]{ZԼ:{vPAG2=T͡@ڐ#u"E*>C;o$~C#_d/HBq^YRٽzIKbOm\~żjFFGdiQ(*/i*#.FF]©m=BmpQQQSP&Ҫ!T&^>:y)$ˑÐFčI Bӡ-t!bM WҦŶ'UZ=}zvn~oT/\ǒ'nr8 AJIӆz<^uߖ4eFC1i+v!3qNyߕni?4JZlmYFXFۼO0B\m[ tʄU3s"Sr(NJ;SKW72L4̏BVdf^Ҹj\]ȱ۪(ӷm?J-KEmWڽ^4<8qu%9pŹW~877ܾeVгS(յe^C]yX͹! םm4FGȋ\y'Z FX7e)|Gjt߹#gb\ŧq_([R8[qU$Z (ʻezV2V!iQ,i$JE˂٩ a(GK'O{vnBvryRd-RK4=qxZJMl_CuuIz @Rt㮽޳!|68\-l[џ84-2Pu" RJ_^OL>G1~XnBŬw6J0*Uvlږ1N G1q9IUm*'oWu][&UyYZbBZRZNfEJf"+2nF~Eû7n1xv.RUM$6 lAxSQJ&n5ܞwlEói"#>4׿Q.nEq7Oko[1wg8ZQwZYiqtm&~">Bo?w͡ni2峋NCEy Ҕ+%ZJ ʩq*fpˤl,~^Mχk1+:ݕ z&Y`KLӪУDr3[*Z :(SL&ݻ۬Vqsyԭs x|iI߽zZrg.:mp%6ԜvgmpIUt;QbS.Է) ǨKSV,*lڌ|5Jt3#NP.=+OZ~/G سIgbꥹJnl_DUM\iM!֔wVZuԺ,yV.Q>f v:݇WiaŸN5Ҕ[M7SsrvǣrMW= \8ZW-jsnڕ.ZnF2qt ً[ٻޘY۷Zm"Jxr&NAfA-݌to9s359݆mZ+N1-qS$D=17 x׵+%_ ve4ir6Z$FDڗnFtOr'7'{9C˨ꤡaYoace{Refnft RR"4%ʌm:Sj3)OdInTO>X'vxV#jܮw9Fog;5.~Y5\~18YQܹvj4+~t7S ﬕs %^۵ڴDZV69R^Y+rj$ԇoJKR5wB9C>Y:l+EǎS{ʲ{T6Wi* ^^9k/y/Cs\g*qڵgn4T8mERr|Ti+iPe;;.i\EBEJ 丬i9ɧM-ԼsGDrZ>r#R>~X9y4b棇9JwV۔%m(b[Tjvl}۩~nDԺ{Zo-YuK1vx.nWuO+jN [ٮ0%"΢CdTJK-RަH"$I(*ve &҉FzB,_Vpqp9m8werv')E;o&QE׵^d9˦j\_,ڵugZȻ̧8k+jK{wmr@3ӭ2 wFkzFVqs1؛.v'I%$[iT]D5Dl2 nk7qUxԫLS+sا3/ΖeZYK<["%-g/kRs:f3;*E ت wJ%)5&+&rw*霣i|sMҴ|;R+fm䡩.!**dӶ-6s6,]zAXMWjmnz%SJߴm2UXw7MQ%<!tKys#P,W>s;3IYwx<+i_\\\U6 u7P|xbn_k&ӓVOe䦒 VUr,-㘘"-LZeOSҠթrEvq8Kf%5%&K"#%vD/.ZYYŏ+p$nZkvއuW9㓱Z G wYIFyf)?ƎUm5ԉ/'k84{KO:rQI}XRuԪ|*lu)3qZ[mSm5R3".Xcَ5c®ࢫI*۳~wRϿQWޝ(EJrri&ۥ^ʶ齲Im|[yb;mnm֩uiܘq>E+Ikx߄3r33-5𹻖09ϖ9[Tz~mr5NsWl$oPusޛ^{Z;);sڹf\3oٹZmԉ/'k84{NO:rQIBø8Bݱ3n֤DiK4u& ofSȒܩx<˘|N0Fչ]qsp"}! QWw@t4ӭ+cO5%]'*{eM߲DRO1y*q8w++e!c߶ܪlZWّM欼 CQ̼빶lX{vib/V/ ai;x6~]+z]MWB>re-:lgk}պ!#9?%܋V-c[z!W?c7YNm/jRr[HOzԻefճ0q15Zp#rkQQ0tU-AmڵP/cȕ?0cZYj;:0ZM=D6g ?'UN+ձ[K ܖB2'xq9{|۫N0ku 7xaj;n\ 2[VznMlWiKbSk))f..)Km)&bGZ=>OR܍W:j'rM'wYz&/鶧{Sʵb"vջq[I-ՌZH._x*BagC'T(Q:$ͳQcMCKy?3g'ߝqnT);qs #ؤZ}OOI:cfnc8W~qy.;^pVl]Hԓ>^H^@7-AA܃nmL(uWܻS߿ Td95Bdh4t6*dDh!EhI[iŨ\L.&Nc ܮf^;$R)\rip9I|ٺ?#R.ZDZ;/]nݻqs\QE9M&Bd ]N mN*D>tgbK>+ˏ.!23]BȔR1ɝ^j'k2ƮqBQq[$di]icV/e`޵B.FIIJqbi>Ӥ|p; 6${)RU>_e}^dzdfzi %ekRVUS?6'hׂ)5.\+qUgzE2C˷ecŏ^֔ibk shesFWJ#~> Wk~ݨ}ڶ>ơǚ)׽ZƉo~B-ڼrvoE:Ʃ3ۣK7+Y`WirS):{>ڛ}:wԨ(J_";6R%[u&ƫdZ_\'np| RJwNeTW,=rrbnkڄ[M3ܴz)3- R.?:okۼ0TU'w{6&w7j1z3ON'fGoO?)S_bQ_¿R(^ԴԴG.EtMڇ&RUiW uQjU> Kiu1d<ѥIQ'RQ1:O/lŗᏩiʂv&Jc{D5 Tt)1.n[n۶X}RjqnOʽ(~[Ns{ސ⛌uO,kgo֢dRNQȄ .'6W!׌P朼tdZjFGE"]K@'i۪N;sI[{SOzk>`rRR+!σj8&TjlvA̷Q?HyjyLHNտJMjܶT۽lG?SnKN%<‘ nq[N0Sq[Ta(&t(|HGO~gvkݻTR4&Z$#ViOY1r$6YF?e4U/Mvxų:zbU^gQQ+NW_'4jfz^c'#`rvrڡ(IJ/J ݦ6 ]-CW |_{v*_q3^DZ}Ic6Uڌ8p7{crZq5ki`)mU6|-Z5^iEz3P=:Cu7DF'k%}<C-޹ֲ̱#\,(f88%X-N(ck0VLR~} G"-8ӏ/ϰKq?(#nrVTmZ;zióM4 m |UT'C^_1X.gXM{%ʤd 4\ovN":"y-,T)fLQgۢr=/CƹǨJVr[a+!rT|%Y\ٱzsS>jͱ.oOc6f$q% ǒGo;n[];ߎjrk{~\VۓNIGn:iqxo |~t5)Rxעri{Vi&NUOl_ѮMfsޕkЄay.0P{7N((BaIP$ K"U6Gl ݙqJRu+qN$ m#*p<|{:>-Ev=86N*MM긭U*uѾ?/^o7;'u,h4݌xښRM:5.(/ \իU.{F^rmF-Jɷ.>Q"[4xT^OZ~mK}T0ݛ^SAo9u?lX(' qj%=X}"^e4wˠ|rܫ 6I\Ķ;Ӻw!'ڍWg{ i U_9Avhۣƾ+:vs/MK[ɭīe{`Zgb}r[i'GE2J7Nez579wRq+Un ]J.cJ4M:h箽Wxxm^ pc\wcN%'My $$| :$Fqɏ¾^қP9J6Wxvu}ݵP>Z'FFdg"-; [¢cmWkÎT8nG%ݣ7*\խCLRYZͤiD&J#'ehbSyXK|y*ӞpS̍R`[pTr/Eg)K+92{_ n3zwz'oŸۤ+sOj J:`T>Cf*lwd\fYOP"R E֢̔L4ɥ :;.b(B02rJ蠟9>V'9M%)IqnhP<%,r'P/vNSwr#w"ݨaqc(|{kd=^0jTMR2ULNz|.<|^PfY22##!,K~E BEJۜ&jRNsHަޛg\r,v؜.jK3)[EJ2ii{KEiHP^&]Gn8x=K}Wx/KI9-ϵwQ%spܾ[^R}S3$qvq8M[ ozKxcqmJ/ӿ{_}7&ݨ\f6ZSyQz& 7ۉ[8~UNn|nkiTB+4RI8'Nc%tn{!]Ȋo.nEmʱn𵵥J A+wy#+ikǒڂ;՛s85'KmE:Ђu""Iģ5p=БbTY-ͽڔ詻ngL2Q}$de# fs^o{DUUsfwӶ;s1T,ǤtޒQ\෼J=.tKU,7čJ5 N$y3kdSMQU~mO[03 $zAڟsF5^뜞"Կ QHmrR"ӳηer+ҔZ]hE-6Jmt'ޒ=O[sQj)6K}?e4v_KfZheޓ=BV[bY}lݒTTЬ{ȫvO_qpRApVŗ 6ju=*BR)g "O1yhb=tqJ gtm\b3RY+JQ^Ō֍\յ\>+uSi{=x ^w;uӘ#ĸzLn*$anok߷CBӷ}5Yqvdž<( "_OWit5:EZj2 B ρ1̊fi[n!HQF82q1牙nqnEpT(2RMoM4ϳOu ':֧_Xjsg jP^(ڙ{2%E͖j^}ZU[Q$'U) <܂%!s"m R'G5M0<+zM6qYm$ڕ$3ǧH]?o2N<8F1̻r_my[Rf59NjpzBnl7*{.QP 3N&^BLJPjAHCK2Q}$#~YMq8 k(MFMU)8MEqTy+Tʞ-ar5yܕOXw!e;q-Jqܶ䓊Y:LC UE{/t>r"lI9)3KJjϤA 6SEE$d߇3KG*En|P\ԭTn6I-ƍKTj<1H_zwGr19wF N8ݝ+a9ɫM6mhePi%mmD! """"""*1bRKrD"vnrM۫mmĽm]ӡiG~e"˩ lhRTMk^MX["Jݱk7_ޕ*DqĒ&flՒ}`W}~SմZ{ĕ~wm*/{{ѹ_-0ط#P]xlڱ~Tn5wi*lڪ (JxioϏbqKYR|!|KN53 OS222$jzww%i}>N)E+rۥ7c$Ofl/LNث\6H9: FY󡈾I)fB֔JI_ ֣^: 9mY{66㒢7Uj]:.-os[R&gMF3˸#໹kmjq^8W"PΦURjʄWa˧T!͋ lW48JB2ko+ /Nw QwQzQ ے%$ޓ7^YL|r7!v%Trܥ &|M8~ybrn[RV gSn{{*#2#ԽᢏӴHak" ӌcwҜw&RJ07ױ>Ļ =^ BɆ)v32.M1=#6%̠tҤnzqMwԣ~s*%-j|_m*.Yx9Sz=)qE4 3pk+,`=kNRڥ=B=nŔNAx)Q$ԩȧ4z3t#Z2lҮYn$S%y- JzGpu|LBV7ZW#;Wwipܷ%(6jFG5#{$D"uۭ~]֫SrD܃fҎӾ+Tu>-ZTQ& N|$沸ii>eRWݳu'[O̻j8JۻEѩ[]vni= ڒ,[_%kC7I3Nv$4ɎЈeٸoUu:[}Do5|zNq=Tre%ɧ6&~DȍF]ƞG5q m]/w/ \ʲr8=oʔe9U(W"|S]uZd#?Se[W"ֿh][-7Nu:T=)R}.;ml*5Dlf $fF(̏T hiIUU4Szɕ t(%_|2 ~6eM;TƗK[f&]LK^CE2[ȏBOd;Mi|cx,^6;sیGpQ\NuJIFTJ~đArh* B"$H쉩eXPRj?sl"ԥ)su]xpԴY%VESH"ЋJǰ K&5^Ukzׄ8kEgS2h&Se\ Yl]WҶp-ZUvi7QS:4byqOo+[̺腋[6-_Fo.6[7$p&^ _GZԸߍkc.qqoI[9m߸YxOZЦ1uoiSH)P9Uʄjcq= S>֙NeR><;+ڌk%_qT].srNO?s[=vH[]RZHRMtᩗVؾ:/~u)ԍdg%=edVrISb{6vSu=(ܥ)mTv/J}̇8 S3ad:^hBSf؉OɔLhI_1d8,L><_A0y3rXq"'(۱;mFNII.v5_(^q~X>y{3צ I*Vܛv/jW' T'NR'j%ꔩ:mJ3SB}΋!-H-RJBТQoedi9tjENenPpke.%4]#{:>mkEɱdYWl\\\'nRM4&U>?Ќˉk÷!𴪛]]5}UqG~ݏI"O~s6(Ļ)qO~h}uԕd}Q~G,oE!&G&/]_H-O=o{k\̭bkv.Ô܈+;arZx)m?M\3lU$mk-CFXjTv6u' g:Vn_*qk:VC A%'4JV%EY)#BғO4<e׿jQQ]yUr4=wm[K1r׵%Iũ-O}|kC;/VcݩWZ)EHdžTru]8hgĵ-;=>U_ InvTm_jBM+QiF"9*{DI/iuo(=TzϖmPQl_v4z>T*ȴ>YF;ε\t]EH4ꌇ[VrLzef 2T^V>g2~kg5~Nק;{~Z~W}&ŒBӿS2$J?~(Yœ"˲ߩ\O]: J׉ښT{mmIѩn3˧)4LdFZ/zUG>U> n 5& ϴ-KJi2o]uKljvK3$bԔҚV旧iY5.ίfi96v7!v))FJM4{jG~Jt/lUE%pTAFe4qQk\ve۽/u/Im+W')v{\-E|Pms7߮DZRr۞/mu*1ՙaB܆ -xg3#6ۥtRogʌU)׎]ZҞNnŞr}F1Nnޞ;cZ{N}ۿMiuxʉ*3qi'9KHQ$WJxXyرŔe~[v5~/jN9Q4o6rJv FrdxM*iRjMzUinHdн7ᾞS=S'7 } ̽zt7K|_g J=Lq+/Bw_\ۧx\HJUPzQ<hqF[V0x==CsU7q|^ {)Iq38$_A(VgcKu06Ƅ"%i~_ˉk QCܣB8Ku/񋇵u([w}$F|8TՠI.E !;RJ^}MɒD_q2];Ɖ{5}*n7nEInO{Mwv}&q+v [V}Ĝ@%>#dXQ$f;iep.GquixVt x6bj͵mlKقQ[T]zs/&yەnM'W}!Fp_d^Tu N{ɻ'l{խ2.sTu{W^H&;1s)Pӛ6>$mě;Łnj= fLT)>׸+qReɴ[UR\L*P/!$Ӊ3Q 'K=m~6XqW3^W+ųO_[F$rR*u"T%@O +%# ]˽!aܽz{ͷvQh쩎]hGތ5ɇ*DzJDRNLi 4:{~2FmXY-zzĽ^f=]uū{/+&c:Ma{ĝDp2m܍kHș/(--m_vݮK(V{R}.k&yƴ7i^4@3f sK3^Ř˸B=]?gt5KbZB<e;kQLpxuWC}n 5ҴepB##~q= `x]KWF {GfŲ}?G.I9pjWkU]>={7q{kO/^I3==f1ɏ%nnʫ/Zu_yXN<57ۍ'vy/"8넭M2eԷ&Y,в33%IkjMr7xf nmQkX4踼>a-GcIeތw&U=-:qnW)z¥j :WqSZvԒ#j"KrIU)%qrmRoDGQ~SYRsu*V)  ,/x)MFD6O#]z 96[Ui(JRfw'y$GeUީkdMF-ݻ98F2d[o{Rn0n-xsV6Dh|Eb2E:KCOӪv4SJCr"J!!m,hRLD| ZYFm/X~ΧfrN&4Ƒ=Z9Mh.Mܵw/BdrܥniŪ8ɧ|y%œ[M=_tj?F!z5\evM:\ ~F-sg钬OWq“iiȍ<Gi%%n2rqͻllƑ)okw7}\Uk-:&fj솘XerV9yZuʼşdFC=rmo%~ZN78X(N)_7.Εn1MpJ}62jjJdI";R5&iLԸc:jmqiQj$ujp\{;v5B񥍪Xn Ą4qOERjzN(Ga٠䌡)p*v(J7#ZۻZ8O W uONb+^Qipv9GvֽƼϯrYƖKGJQDNPhRJjᡧC"21"9ѓS1;R_O7/WGz)8fE%F2ukmvSov/iZ&/]~KmI[:^~ͤ\kMi稜\ywJt3W7 8Ʒ~ݥeFgѼw"8VVSج\뻆}ݭ/J6Q)d|)zU3>k\L=;ow֯gN3pKѫ|wmkZ$z^2R:E)f>ς нd|#׆?\ǔpV{;\$ƵE%-ͪm0S6[n< kE[}mvE4DDZ^$OZ0*$~XUv҅B@^?]so#%ojw;Y#SxxueBگy v^i-)s)zV jC{7Gt.w3v,ygg8s]aE_,*E tY5k٨h=o"m泏:\6w噓aiL׎n^c\75AGkЯ0Lf46َ`egZ˓p/k;̛]kq!ݸzpԭG"}R9Ve>ˏHUjJ-&7nrnwG*Xv\˱/vN}O)ʼn&CV͍f̵]r\PMB-6Du-#RͰtRN^)mT _}nSȕC*_xBuTkJW[`ɩ`ejvsngP ڻ.-WUtܑqԹQj)t;vN&RNũT+8%IXӃ5fK՛-d9 ]CƑm|nZ-6=Hz,*aEm W3VzRšdY~Xf׀Xx"]s;)5u*ُHB BRGS6bݶؿ 9j[1*jױga7oX CUI%0v#~\-O-Ꙛuɷ쏪&5mY٦M`LJ2qK~HZbr =N'YobI. (^ ׾{_ ?OJ`S`3BN[}5w6:ǵ/iSlt=4F*d&T4y/#. ɵim5Uֲf 眕6Y7 fơ=3dϕq뚩$qTM-%r!$@A? ޾V0c~{[{;򥧅a~ڵ»&ڄv1ek=wb MLkNAԬw-x>~/r=e73VeVN)K%Sښe"+3uXuچrn ֺVzscJ峻m}vb㶓n\YbIUBT%*,0nov=;z꣓S/nSXSpl##k9mXGrZv^Gde!ŷRԠzQyjC]`gToPov{j~KRBMY}i[߶9KL2ԉO0K#m>wB[ٍ+n[[b٦DX ݲpo] [\m5qdT()mo4Oy9Ie b][wղmM~vmi۱~t \}$яimRk(L c Cvk7r9_r1 ;zv|F@KyZ[&jEji/"6$69ml#e]9s\{ScL}Ȣؿ0q/nZ*t,CLoD߉Njǚy=Pgmu6^]l-["çUʖMlʍp-"qmU>۷uFOJ%Ǔkx 'g=睋k[3u,{³WɘݪF]ՍeFX"Oy\,cچ=w/gn Ļ]#2? vqy-gXnR.^}ݺFs{ŝG]}e|#0mjx"ƬWكm?rgU^xVB":Dt>@LRbun~ݭ,w+v⪕;\U(RYa61>#Jm˞Μ9g9XKaG='u8gf}'qy#ɉw J]We.ʲ-<+&q%s?2dњztҼn`cΤmmqMdz O[-ߩӲ&;[tmܝVnr">{x<8U+p:Ig]zjGkt,uzf}dؠoJaکqEq -(:d<պ=eKy[˗^%ZXkX[C2߱\ITTLGzANM￵i]K>UsOGDDD.ZF6* ҃V Zhz{'xp^`wo8r0h ZmJ5"jb[l=yUu7-;7IT%:jFjߖm0tzU'K)څNۧYJ)4IQ}^KWm7kSP>q;ނ#)'n7&׊r?óM{IwR\j2Qn[v pe#/tAF\ϵ225q֒om6z})6҅*oqDsMf CNIN=T S2t,_ѧ}kveMF0J\Rnnݙܹy[rUc-j{yGtkQ%s]5qB.Nw.JN1LvR Ui5J ZESQԙr):MJ+g}χ!2;q([jAud][ljVK3$ײSJI=/|&tl'*n۽f.frܥ jQO8>&Z];.|7T/C}$ڋUmP2Reҭ8hFF\L 3~e v\۫]ݝNmrnB%*]Z«hKc=BTLG :V74$=Ǘy+EX'4tn(I:Ѝ;Df8c,k1%dJ6.j6ź{N~l6&*fœI7 WAlGOu-ҢH,,(ǔe뿋쩨kM܍ZſgRvQ' 9)?n|er˭|I|-fGK.rΛp8XV1%K6mvG+tc+qE&ǸC_Nm:l=_/m5^[dߌڇ.c<%:)tQ$Ow~-aY;UJ>=F)2[nk؆?훐M=l6[4(O.]2#-H^n#->&mp5~Fӛ+|| S,xag%qkEUzUgæBhߕP(7]kFnq?֖CpruZ6*rEڊtS|*tI*E}7R<,nUU֫^I7Q*mSly%rdȓd8hE<9oHhMfNSRj[i7D[Rj݊+kდq{"$$H?p\̅S?㭻;t~R߁)^/>Qj`yt[w ԛ;²~+ߔ_ YW~|o]?x^ᯛ `ʼn;g)T@vWn]>&4lp+$D̢1l|ȨF%-}.9[}w~ ԠLM9hСablfe&QoW!s?wjLK?s7yO>(=C~_nyǜu?v3vyo oI@qV-jeES^[9WoSܝh"l2C1a͔CiJ@3:Pճw=/7ovuk+\V;lDgն<[A+rX~d;m!_s8ݖ׷;;.0llUC+?i#_crʙ1~C.\–q ul8Hܶ2m`ܻM3Tov|Bs rɵ"oLS- DКw=Tv@f'6|YlD͓Y%׵-#Ѯo%:&!3o%\J<02;K87>^vgƓ# ;ݝmz^Y6=PS39U%~ &f# }o!muH;ʲŇ˷yvP+&.7e[3'vR4Yj̗IZ`e˽3o[WU{ m[sUbۋZǾۆl6~9'V*.\S2<Sd*zY[aŶ`]C$n.v^Ʌ dng>ەZ,Mmϑ :n6nϦezWqUJ4! ۇ4R! =>>Fn|Q[{pRO17ƕ~._I''00k=b՛o}Osðc2'o\3}ݭQ^2 . R1yKȣtAݿ-uܾw!`?1Whn|gzUo[ECWwjUIן)^h#1ɭ!/Z np;o;ΗŻkXs."6E`Z1 עӐ9Kl8qd q} 2Stt;#j>;խabONŗ=fwP1j)l6J̶|gV2`y/0E˛6+ԫ1? 6}KW c\KoKͨ2ۅFw–s*TԞLיuDx .kCzWXhy۶gLu|%TnupǺl-S* PRaLnT+c+*xl.v!.U=|; !_L̎뱚U=4hm:ٯ"y)$:>%(n}X'p[ȴ ^˒4kƓmzDx \ 'NqamP7nyN݅=j7%McSڵj%STy qXymvCg{w/w=wSW5r̹u erծˊsOm=DhEҚRb#n)QOxtվQwe]I}wCa'"[ۂ-z}2UuKP$㜉ԧ:mc<Ý>RoL?wu|%ҷ&K y_!y9 ??:tq3(UU-lkS'ɸ@jdzQˬR] EVPW1DJq2n:,c|ǻ̑;y{X,ۂ.u.b˕u.tKBjQ"[S園S`ٮdNبeJ&9Ơ ~0a(Vm٘L+Jr*vڑE( x0+tp˕ n';wm-ޜMOxX>{#2%jgb2M[`K*\5@8l'e=0u+w ֘鳾{y܀:R*Ya]"Ӧ%ktynlۣ65,3gU}{GYrb;ge'TKwǘ.,rpܚV]Tr,!dp /ԺU,xՉ>s׽~W5oTh yx?xrrx?)?ilbT׬,z$Ԏ.UH٠\U1pU:]JwSrGZq8àd驐,N67QYBӢD㏙W!Q25ϸo9ms-7-%3CihO.J鯽-;MZM8ku-7k9S$8]q2E(}bۏI[DKOK}3KUB^u %Y,u.-&f#]'܆o$x`Yu,dzwM;#oKxn;\[d7}Rb+*Y䛂ZuBӱl{j0O̓}LhK;[aֶaGL{Cb#S.T[>߃F]NK"u^LUʐ_ykW?!GRj29͖qa'0[npcDvV)qz9R)PۨM^aJx W] r>];eN3vxdmĘ(5W2K1䪖weF{mE/QP6\u54x5[hۮ-Nk”i[lUgL]J}5 S:EhiUrgHl!ŒJ$pe=q^b͵Q' ?6|R\,JA ڵ"TDꈭ:ymg`B5t%M] <N_zv2_Ortٵ/i/ReӮ*7[qүqEG* m"[I:6e^p"I$jԴęh!m)]GZkcjS!{e^z}+Cѥ9;R|/ֱeiUԏCNu2Zhcٗg$ݭwvr P8*7/Lk~I'Km1+MW%Bk|oOm>-#qj*|Dbѱkn|n{v#jĮqNpMIUm(7Liz;{ҜݞڝVƚVϬ+sO!OstGvxӉ']uӎ4g_ 1^-8ۦ k!)Ύ5O;YSB#2Zzχ;<.ֵOtge~.(RC#wFZeGZٸ6FFJ4e2ˇpJT$[wgV)q6muDGJ56q\I!̗ y/I~RtJ9kJ]Iy*'FN0s.[l!fw'y(7$œ WƫgyΙdMEU JQJv̋vmrۖ.jWR_M֨djYgSj0^\y'EoECjm$ IƩK>Z28J2TiJ2N#}.s cArl嫶nB.FIJ.)۔\ZiM>/hLĸ=C1s[?YMqp|94- 鮝𦔽/k^#NT(Y LS$6˩}{;5 )B۷W$qpN)qqoot}ZDVә;7TiK|6f3h$dԄ}fqݡ>Nb򗉉+ͶO]>ߡ_VtYf79ڰիF sq~prս|QM)g%l0ocJȨHz V;Bb/kLAcfPJ,ԭ{ƍgpjNR6VSI*$!yV足jᇑ.](EܣqM\qJ2eZT).<9UB/(B0j)mtKEj#׿fDI-=rZړj|'Nڤ]k*i$5qt"ݙPM6E4ke^Z8ۏhz$Q(R Ay2zfRñnpnkbkI:=j &ΝșW?׵d{+ύM'??XqeeĽ.[o=UxFS=ӷdZwenՄ]_X=ĭVa* pKs0ބۍfJ3 gz̚i|wnxtjc¼5${(1fXQ65ȼb̶Zkn>%FQMJXӡ{TZEVNᖣimT/37cNJUPnP҂ZOE~"-Rc4^b- FEͧtf5[)S!OZIښݲ͑;tvܡ+N)AR=hCNn;wL16-:特7M$=Tҕ-.R[HٷnXk sn[ҞD-0WS9p9:-Ϸ-jѬNu{ҹfv)[Ľvwfg(ٷfe+0mYj8Q1\ݧg]Eǎvڿc!4#j5̋C2"}BRriFp7=ô\TZ:\BLfj#I22װ<;صZl j 6:l"6]۸ K'6RTѯ^ئOԓV\?$x7s#r:Oh{ց=MmuHԷd{pN /܅:UE#Yy+(SgQ(Щ)RHzw>^Ѿݻ>mK&^ '$Jۻ&w%F|xfz%˳ L~3N?Cy9 v w/{ƿ kz3x> sXv}vP"@WyC z`'톽Dw%-tt yVY\wmuPYQA0iG-2JP,6/gˢ]u.-n!Zw.N7Q]Df}Q0({a\@=i_X7gFǘ8^⻲}G MZ1)WEfO12G+=-B@z\`||w6ċj߬m}UwRox֢I &c~XGP6Qndpvܻul'V7^FJt^{b^B(L~sѣ6@߿^xqU!ڙ5|Vpvef-uӥ^3  FSDɯKD%0r}FF穛r7 +o"V8tv̖NQU!5uFd"bCr^bJ=֤fM#ʳԷP0O-9xRBm\=`r-:;~3Tl(nXtXi%2Vٛ#vwqƴ`L@"H‹qW.j,JM5B[)WܺUeZFqc'V˷1W7V̾-MHФwn8N;HPSdݷC7&2j.W\τGŎ'Vb]c.x+Rx1%C2T{myg[qU|+m:M:շ8҉yWd)ՋWS%%:iqlʹmGwݹ WnNŤѩ5(9hTٵDdGUi-)vSs2 2{OnT$Xck n:¶(lASLeȔBjμPpTb2~N2~%^k[ܗ[Jzs0ӓHBKq[}JَA-$dFQgjxxFv4r/x*Rm% `4J(&iv7SkԲmSH1YWmx 8n.k']:Z˭_W >ڃXЩ. jTq%Aā[E}amc]D:rmHRiu:uӚӢ\p(5-q%e)(۬ҖȽIf<߽pr&ݫVfY91q2ĭEQgYbTGQ&,yL+N$[q*RVۉQ=FuTܻ>f>f㋳8N6$܌n)9&»iˤsX,݅܍ȩv+sRTpO}d?Wn/Inpȸ%O]StQO|v5\}7Zwb.AIVK^:wb{[uݯcytO߶S<{8KSRׁH̏N7ۚ[xkwYy_'ZӵF+>쌛ZUĦreE9F[24De{}@:ExWs-\ǻ7K-\JNvEk%:s˙#κ].oͳ;լ7wB6nwu:$L; DkI#Wz.:Xp(˅v$Sq,wn\qIN-e<5Oe+vuYTpcojUI_ާP8 O 7&VL8z$_B-H-[uh]T{|8=qVRN-:Ij:7PUtXϷmy鉿:RIM~33ӸS2#׳GdŲ5+/Bx{(WzȨ5Y㞎#|˖+ ط.|e<o/rߔX>7s}VE.OVti׽ .5nNJO"95{#q}Ay9do]R"M6z\tnNS-D!@3N_jicWsy*5uٮRcWv/.,j}=S)j5C^> Ie =gu9ӛqjtz]۪TMoߧI!Ǧ¶m:,"[L!{qAv-o 3{"KʼnrIkfٶj2ƙ؄S`7` k6jzޞ?e5G&6uʷ2%ԒRKE*G\Npom F/V |C0.q_eenƣ<5Oh'67ɪn[SĽ{ڔjǘzs;~׌(ۂ`ܢ1ƣ` _l9Va6%UQWh~P~\F^ZHR@:ۧCJ{ôGeBh;~ۧnU J\O+n2 RҠ)ng}Kh{5+S×ܛ.1ZjG)iRȤIN 4%{oΜ/eO[Nffd ĹK?nnԼMqX'܌nZvq<ķbFnͪaQ`5 s,M_լ?-@_{w{ӺձJ}GF[%v\5[ŒGkOw/ΜM9rjË%2+rd~+󲕛C9U۳r[aJǭm|˒LAʨSCq[XMۺoubfp:t+ΤĻo ][ zt-*67kvS7D·MMCQXm;)܎n_h%]4ܙnRk!]ڵsDUF"`R, &#R_*[z*ZqFXɻ]7|۵w+'pFDەs=r./ᐚm3Hשy yD"jHCr':sA65نѮ^o1V/ f;nFr3VM)e*- s D'H݅fӧ\*޷[k<7u<-]֍Q8R h|p=WlW3s%Q %3l}@U-K6f-NϿu|ڴmWN׮[׸F*mW\%r! C78:޳vBG7ŵ.JթԚ2x)ST!řn~9 W:Wpܢ件{xf8ٳwKE ҰWxVB\qBZ 2wMb[lGSnyԚ~z9ZmያvoN2Afnݽjf>)j3 !;gOYʹK" Wftڎ+׭b*2ϻK>ۢӱeyԪXISUm[z+ugX%0lϏnvg!;t{BqPj>PyvR7Cj]O%+ݲ :qiMj6W}3vC/R=4Som]ŗ=ю, TF6U_-\6MyskwMr&Q\wjKܩyMϣUj0*}RZܷSdY3>Zjqj6TgzpA/M`/Cmл,޻feE[/+uk^Vs1W$G(JsW2ٰu*߻q*Y޵.Wi:ur5T),=0uRmho.twܖiYwrWHntvEj8qhf`Ͻpf(R&>Ki%I7$QӖm-2 ~yߗQ-앑/ x[k8nw.c㩵k}]FkbJl:{.(˩n0Hqvαp7 귎.Gupx[N`Yq'+ruU7[ү+>!xrȫoSo]OC# d^Q]\>!ƛGw^Mx"-+%vdX-:M2UR%d>%l ioSu6lsj7D P>XxHz Ukà(n^Q V>5cVtWj SEiJdznyej[lE' 3kuٌNn4JW)gB {4 j6&]' m-(ZMEz8cz>WZ6#7+[,MR-Z!4ܓtCyE|umj1ƽvƷV\;%>Q :#Le(iVz5 4ũۤUWxX ^(ҔsլB2w-V ^R+; ˂M\z+Uwr+RWY⺧~ Q*JcYSNSλUd8in=v K낫k\IRרSUaCFmϿ5̗P|u ZTԕ}>oYѲ1sfP+sQkX8Gb~6r,s>^\,mGL+7[n-E\.Fqḕcl*Jmjb5 ,m]c}NXfeVlǸJ5eˡ$4%g~N p4Y*WwW٧<8v#;qԩTut,m"#Y D\5V`\\Lȋ];LȇiS6ϝZ l>LruR\v=ǘϔDg=ԈdFZ+M{=|,[;0>RiSi4,S5}yxw&(E7&fݙ4UՕ! ~'Id)]ǽu2K-fޭ \08Vڅ쓬=Vy^^ IhyKR-B#Ըr=]mܻӾ'*Umkoy rTqT_i,/8Q^<ݤ|4ԻO(܄"'5N~#m.(Ҿ2i6Uev&I*<}҄$eNtÛzyWJubW^iBW.܅Wڮg]irO6Ve90sgv.+sV޿aޔ[p?3q*FutUo*eL\KM'EG*ZcAFfG5J 5jj=MJ3OK:k˝'NMB7m3uFҕ\-Ywg%PRqMIyZGY9|μvn߻5cWݷa^+X֥vnݘ\v7m>Fgzv"-;Ew֝}1|RjN𿊀7g#֟*GQQ|#/bo]p$>_Un9гUbn9׃ErQBU-^vDmVh'<R[fdHT]*~}3j;nvjc7s-rӳ Y8[n[1pJx kX[Jk9Mn!_Nю6x:iZ˦U |߉^Ԛ݃hYxk &U^bwKk.[jE+P(˞=9j@snCv7%c_7=xǁ<l {t'酚+1F‹l׭:ݻILruǶkL-L(K0L1&>wXB(pm;1fpnlp֓%Skidkt(U +xulo'/ڕeN r=^pZZ:Pnj8Hf"48ijY[ N[yZٻ+=  ø:3 ?^ܷ^Sr#YK[UF?CuhC b]GM')mڏsNrܗI]ljq6VB. W,UK"YX5{c >Iqā> T:n!,5l2VzCl|+I[*SrjnS6٨y+x,@>П.g+!rn9>N|W>OZT_ut Y""v7|sfި;Pclm EùN,{'fNT%U&LfH8~1v>Il}统u6P˗c(WV~H^bMU.o*oOF0N:_:6Smr_.b+|ݶYY غF,mwjv>f*>QM뭱Sd:`N{l/⎱;n-z~"Gze퇎J5S KG9!Gn;N1 ݎ h6m|S?ɂ5'WOÞ 7|7^ao @mxGmi^jϽ>01Mf0լD3-2T. VXR"ɥV Kl J O7|u?bvа;6.eߓ|[1bmRr,eRz`z 6܎-ͨku͹Fː dPhYgZUj}nvX;z=gVեTv_J }\1n7w2J?ޘγc\E 1Aޑzq;\r]]\Y&[nsNei\uURje*Qk2CSl*xJz-xٶlm+|UjUؓ`Ladqiĩ!Gd\W~fz;Tn*PdRM&T4`չSWq5k훶(N"Ӎ% V]֦wb.nUO!u*J&Oӕ2e|Z=eV쫚΅g#+/RW:طnbi*Wyo)p{:ETKؚR(RY+r웓r(IF) VmȵNB:h Q1ғ|u8E]{,'$-TR[j49l*3"I鯴zhd>Q+\BkNF=.$ZR4Nwհ(IpNi.(Gi33#33e$FXK*NdWrud[r{xnk$v2ıh+J1TQ[#JQl[tRO]LHKٮ NӍnF񨔤֞Em'MILB"ԋ%dBŋ+p̿_17jzT~4pc Vo\ƹb9Rq-'1j;8ܗ)hE%DZKS<璸Bu*%*Yw5ڻ9ۣ^z4U; Ñk\U(o~G?VUĎ:?P?_F_Kߤ~ᓾI |pr.Ok\SklRhҪz{­P .}SktZ7UQ4ڌIM8̈eaӊJZ%FFZu,KZvln廐SNFIVtuNi?CM5]+Ph,{jN JSR$IS^tSUVrORYu.9WyP6 [Kiu m!X|]Y79ӄ)\ģ)pbڳr%*&ꑶ_-H*dzk)1 V3')UAϹٶWRxe'պn۫h7AR9 EAJeGLms!%D| A 5]/Q3eb̄vnVn%za\m kZnv([emqrIҕij|""><hjJשvvǕ|Pޟs}V~2&Z?+2N&Z4w@)4iSڪ_>/JN9Hiۏuf8'It[ȲR.hZ$ȋ_Y ~U<UUO*6b)Ovzڜj\R̋.$FsQuҊj^נ䈈y<zZIuP[}Qm=C?zN(Exqu/kn S-FzKZzOסӽjJ\)F3b!r5ٝ|;6 o=-3*λ]αb\abqRi-w޵⦪~b8Kpo)Z=>)ғ"5/GTZLE-輵f7ݘ۹~+&+w/7GFI:l33fg.N~۲\2|*cnermnnM+Fq"ѪIz%j =YW8@~gc/~?N'?)«qȸs➟n=k" X“m֮VreMh2[uݖ] *FܖN)MȐ`f0 g,C9̑o;ddudJ=In13:ݒvvdMUEJLp^,6t-@͐9'{7m{-3,>hnF;ѰM)->>+Ěz!R* :`e--m7nB\u{b U>[8֪]6^ߤLʦ\DFNo$$dͶlgno8OrsQ\l̯hRo8tuNo+ CTxu!2[>ctFpeޓƻֶR"3QrQuOѳgwQr;S~)6HhZw/GgVTmUf_yt7%$];zLWF̰xy2Ʉu!MCmš_0[W6jf#a-KLi+3Q7c^qg%s<1aYIQeZf+}>;S6L0]Yu_h9߻<ƅpmiM$AVvŚ,*#t2.8Y)-Zhshü97/#Oro"u^/uFgWɺ,p:6a,^x%$Yve^3PƗMnTP&yS}OJ '덫MH^:rXԴJۋ/rI;S*,+yz1hv)Qw^ڍJ2oL׊q(\fDj:^T%vOadɂnS}ZO)N*λdaȜkG_PIEO}нa(^iQX᯦-7^)%g'SJx(.S9zVɴZ{E ))ۅi/s7 VIV-|sj0*UBTHIqRf>FP$KqN0 R̻8j\GcC}IUz\i 6F)Q{Gҧ3qSzKj-Az VЛS-zy:8*mNk|D鿓ND2u+0Yŝ7kqm·?8Ib]u>˗^_>(]vӋzv+ݩ){vZrJ2RQ몋C$z [,pp,8mڊbR]Il .f~d/ݓs㓓mͶ{mgjQwn=Oic9ܚm4Q/6ݨ[TƧ?nԶoytf{@AzT{e{[O'ZRZt~AGD?s3􌿂ՉIw'|~U\ w~di:Kޱ)U/sU%njѩ&GSP^ǝd)..!^U` 1wX[aԇSxoFV6_扐)T 2Mfd=ۖͭiZ7KK Bi9%7@<3<ճԻU,},a}FRqɛr i@ONJvK KLN M, ʖv0n-]DwlI-X6ܶ$Jʴh5O+mOI+Ra瞠\ MG7BفjYo1#͖0V`Ѱ2M?c8>-Crt*JkIGS:e#hPKx[鱼>{5m;wcն&>j-M֥^َ) 6yȜl_w{-ō̱r> U=]iw3)r*]:K]6BdCTZ|>gf}LW}[$'Y5 &c -j.z6R 67MԷFMnÌwI7w5E}o޽+K ֵy4܌ȥW"COyR[q5Ӱ͙f[v"_#q{MV6܍3"u9BK(41ӯqˇc${ߝCi6I(OmθzҜ5k^:>Jzw.>qV8{vU[ڶEm|DžBz].KHjI]x;Mɗ{m,qZXr忇2u^RO2Z}ZێS[2Jen!*NDcrBUً4<ǼMҲs1Zw57c3&ĖڻzmP*FuJG1-dN:|OU}ҵgi2t~F^^Z.VxjvŧnNNh<:]^~NN+ge^g.SԔGFe߯'[vn'(ScJ]kܗ7eJOlRrfziݮq̋S"\*U<*W]k$FջV}? 7g#֟*GQQ|#/bo]p$>_Un9;l S VvQU%OLU{οmU6bZ1MTx%!֙Q7, J=!3 ;Q,ڌ;6ͱ݅q^&ߔ·n #WbwӖX.HtG)N&d̵zpI,n cu ޖUj+VXUp[w]N o.J6Z8Ts&utxln;~HPHS/xw`G\ʡ¿rj Z^vt"[L:SD\h0sUwR,}[x^X,R2Vn< ]2YDr[SRKs8tXb̷G?Ps Tv 3be,zVz D[/I.KOEQrm'$7|[J>r S`5յwT#\w1FTz\Ԛ &"ׅhSHrD\'r]~/>p;:Piuu:"9ő=tTaS7V2rӷk7mb[^WmPp*[y.Þ6f]cizJCgRR@UVl큝.WJP1N{/\whZ ػϧӱE7|E֫Sί.x-Y&pi%v''-x6r'Ws*6=DwwUu]=C?MK [yrtܒG$!WGqJ*%SAz ED[^)/tė/g=#Omd.|^n/sl׉g DZqemqowݮRzUܜ=ڽ-o/Iۖ;qVʘgPp|mm;6zGl9.8pwWgsJ2qPbe}}UpNjٯ}7TMQKrؽtEx%v w߾8%|j;~|}pK]ơ/ w߾8%|j;~|}pK]ơ/ w&~e_H 8PL7:%ʭ5Kw&U2vwR_+rm'}C7#rWoO&HoG?M$UR7{FU]u ;# !Wk`|W>׹潇9Vn)6)*ҹ{%qV4q>W1vi#T"Qk&GwxcJBJ- Ϸ^ˁxkU}ԣ/3.;]J=<*)cS)ROK9H=,r zX @)cS)Da^ԽQ gxJI=w֣gf*TRj

#Hoi Tran Viet / E-mail: hoitv@haui.edu.vn, TEL: +84-973383303
• Received: January 11, 2021   • Revised: March 2, 2021   • Accepted: March 8, 2021

Copyright © The Korean Society for Precision Engineering

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

  • 77 Views
  • 0 Download
  • 1 Crossref
  • 1 Scopus
next
  • Improving product quality is a crucial factor in determining the competitiveness and business efficiency of enterprises. This study investigates the influence of the cutting parameters, including the cutting speed, the depth of cut, and the feed rate on the surface roughness and the residual stress during the turning of AISI 304 austenitic stainless steel. Moreover, the work aims to determine optimal cutting parameters to satisfy both surface roughness and residual stress requirements. The mathematical model of the relationship between the machining parameters and the performance characteristics was formulated based on the response surface methodology (RSM) and the Box–Behnken design of the experiments. Pareto optimal solution applying natural-inspired algorithm (Bat Algorithm) is proposed to solve the bi-objective optimization problem to obtain the lowest surface roughness and minimal residual stress. The optimum cutting parameters selected by the manufacturing planners from the Pareto optimal fronts are calculated to comply with the production requirements.

MOBA

Multi-Objective Bat Algorithm

ANOVA

Analysis of Variance

AISI

American Iron and Steel Institute

RSM

Response Surface Methodology

Ra

Surface Roughness

σ

Residual Stress

Vc

Cutting Speed [m/min]

f

Feed Rate [mm/rev]

ap

Depth of Cut [mm]

p

Probability of Significance

F

Variance Ratio

MS

Mean of Squares

SS

Sum of Squares

DF

Degree of Freedom
AISI 304 is the most common among grades of the austenitic stainless steel family, which accounts for roughly 72%. It has been widely used in high technology industries and chemical foods due to excellent corrosion resistance and high strength in high-temperature conditions.1 AISI 304 austenitic stainless steel is regarded as a difficult-to-machine material due to its low thermal conductivity, toughness, gumming, easy work hardening, and high built-up edge, leading to poor surface integrity, increased tool wear and low productivity.2 As a matter of fact, surface integrity is an essential criterion for evaluating a part's corrosion resistance and fatigue strength. More specifically, it is the surface roughness and residual stress which are two critical indicators of surface integrity determine the product's cost and quality.3 Improving surface integrity, therefore, is a requirement of the production and also a significant challenge for selecting technology parameters to satisfy customer requirements.4 Recently, researchers have been trying to develop new algorithms to optimize the machining process to ensure the above criteria simultaneously. Also, there has been a growing trend towards the application of nature-inspired algorithms to solve optimizations effectively. Yang proposed many nature-inspired algorithms, such as genetic algorithm (GA), particle swarm optimization (PSO), ant colony optimization (ACO), firefly algorithm (FA), cuckoo search (CS) and bat algorithm (BA).5
GA was applied to predict the surface roughness when milling and drilling. The test showed that the minimum surface roughness predicted by GA is lower than the results measured from the experiment, regression model and response surface method.6,7 Likewise, when turning AISI 304, tool wear estimated by the utilization of GA is lower than that calculated by applying traditional optimization techniques.8 Zhou, et al. also used the GA-GBRT technique to predict the surface roughness and optimize Ra and MRR simultaneously during the turning of AISI 304.9 The results indicated that increasing the machining efficiency requires a slight rise of the cutting speed and depth of cut. Kumar deployed a Pareto optimal solution based on the GA to identify optimum real-time condition, thereby simultaneously ensuring productivity and quality.10 When comparing the optimal results of surface roughness between GA and PSO, Ahmad, et al. emphasized that PSO brought about the lower optimal surface roughness in a shorter time than GA.11
On studying the algorithm used for soft computation in mechanical machining such as turning, milling, drilling and grinding, Chandrasekaran, et al. indicated that PSO with an unsophisticated mathematical structure was more efficient than GA in many circumstances.12 Besides, PSO combined with Pareto optimal solution was employed to find the minimum surface roughness and maximum plastic deformation layer thickness.13
When investigating optimization algorithms applied in many fields, BA is more novel, more simple and more robust than PSO.14,15 In multi-objective optimization, BA was also evaluated to be more effective than PSO, NSGA III.16
Based on the above literature review, it is noted that the metaheuristic algorithms have proved their superiority when solving the problem of multi-objective optimization in machining. BA has been proposed to be more effective in terms of a quick convergence rate, the optimal point's focus, and escape from local extremes. Therefore, this study focuses on two objectives. Firstly, RSM was used to develop the mathematical models of the relationship between cutting speed, feed rate, and depth of cut with two output indicators, including surface roughness and residual stress. Secondly, Pareto optimal solution based on applying BA was exploited to improve surface integrity when turning AISI 304 austenitic stainless steel. This paper’s findings were expected to help production planners choose the most suitable set of cutting parameters to meet customer requirements.
2.1 Materials and Processes
The experiment was conducted on Mori Seiki SL-253 CNC lathe, with a maximum spindle speed of 4,000 rev/min and a rated power of 28 kVA as shown in Fig. 1.
Fig. 1

Mori Seiki SL-253 CNC lathe

KSPE_2021_v38n4_237_f001.jpg
Mitutoyo Surftest SV-2100 surface roughness tester was used to determine surface roughness as shown in Fig. 2. The surface roughness of each experiment was the average value of the three measurements at three different points on the surface of each sample.
Fig. 2

Mitutoyo Surftest SV-2100 surface roughness tester

KSPE_2021_v38n4_237_f002.jpg
Residual stresses were determined through the X-Ray diffraction method (XRD) on a Rigaku D/Max 2,500/PC diffractometer as shown in Fig. 3. The X-Ray results were analyzed and calculated in combination with Williamson-Hall method to determine residual stress values.17
Fig. 3

XRD system for measuring residual stress

KSPE_2021_v38n4_237_f003.jpg
The experiments were carried out with the cutting tool Sanvik DCMT 11 T3 04-MF 2220 coated with CVD Ti (C, N) + Al2O3 + TiN.
AISI 304 austenitic stainless steel was chosen for the experiments. Tables 1 and 2 show the material's chemical composition and physical properties.
Table 1

Chemical composition of AISI 304 austenitic stainless steel

Table 1
Composition C Cr Ni Si Mn P S
wt% 0.07 18.49 8.15 0.57 0.76 0.03 0.009
Table 2

Physical properties of AISI 304 austenitic stainless steel

Table 2
Specific heat
capacity
[J·kg-1·K-1]
Elastic
modulus
[GPa]
Coefficient
of thermal
expansion
[10-6·K-1]
Thermal
conductivity
[W·m-1 K-1]
Density
[g/cm3]
500 200 17.3 16.3 7.93
2.2 Design of Experiments
The experimental tests were carried out by employing Box-Behnken design (BBD) with three levels for each factor and the least total number of samples compared to central composite design (CCD) with 15 experiments.18,19 Based on the recommendations by the manufacturer of Sandvik Coromant and the results of the survey experiments, the ranges of cutting parameters and levels were selected as shown in Table 3 below.
Table 3

Cutting ranges and levels

Table 3
Cutting parameters Level
1 2 3
Cutting speed Vc [m/min] 230 260 290
Feed rate f [mm/rev] 0.08 0.14 0.20
Depth of cut ap [mm] 0.10 0.25 0.50
RSM was then applied to develop a mathematical model of the relationship between independent inputs and output indicators.
Based on the number of operating variables investigated in this study, the experimental results obtained were fit for the second-order polynomial regression model19 using Eq. (1).
(1)
y=c0+i=1Ncixi+i=1Nciixi2+i,j=1,i<jNcijxixj
where y is the response function, ci, cii, cij are the coefficients of quadratic and linear constraint conditions, xi, xj are independent values.
The results of surface roughness and residual stress measurement are shown in Table 4. It can be seen that surface roughness and residual stress are in the range of (0.44-1.72) μm and (125.9-240.8) MPa respectively.
Table 4

Experimental results

Table 4
No. Vc
[m/min]
f
[mm/rev]
ap
[mm]
Ra
[μm]
σ
[MPa]
1 290 0.2 0.25 1.58 201.6
2 260 0.14 0.25 0.73 125.9
3 260 0.14 0.25 0.73 125.9
4 230 0.2 0.5 1.72 240.8
5 230 0.14 0.1 0.93 136.3
6 260 0.08 0.5 0.45 143.1
7 260 0.2 0.1 1.55 233.3
8 260 0.14 0.25 0.73 125.9
9 260 0.08 0.1 0.44 131.7
10 230 0.2 0.25 1.66 204.5
11 290 0.14 0.1 0.87 172.5
12 290 0.08 0.25 0.48 166.7
13 230 0.14 0.5 0.85 226.5
14 230 0.08 0.25 0.64 143.2
15 290 0.14 0.5 1.02 148.3
3.1 Analysis of Variance (ANOVA)
ANOVA determines the input parameters' significance level and their contribution to the outputs. ANOVA shows that a model is considered to be significant if the P-Value is less than 0.05, i.e., the significance of the model is at a 5% significance level as suggested by Kao and Green.20 In this study, Minitab software version 18 was used for the ANOVA. Tables 5 and 6 show the results of ANOVA fo Ra and σ respectively.
Table 5

ANOVA results for surface roughness

Table 5
Source DF Seq SS Contribution [%] Adj SS Adj MS F-Value P-Value
Model 9 2.83234 99.49 2.83234 0.31470 109.05 0.000
Vc 1 0.08893 3.12 0.00109 0.00109 0.38 0.566
f 1 2.45459 86.22 2.01253 2.01253 697.39 0.000
ap 1 0.00763 0.27 0.00356 0.00356 1.23 0.317
Vc 2 1 0.08038 2.82 0.05363 0.05363 18.58 0.008
f 2 1 0.17579 6.18 0.19252 0.19252 66.71 0.000
ap 2 1 0.00770 0.27 0.01057 0.01057 3.66 0.114
Vc*f 1 0.00114 0.04 0.00086 0.00086 0.30 0.609
Vc*ap 1 0.01384 0.49 0.01590 0.01590 5.51 0.066
f *ap 1 0.00235 0.08 0.00235 0.00235 0.81 0.408
Error 5 0.01443 0.51 0.01443 0.00289
Lack-of-Fit 3 0.01443 0.51 0.01443 0.00481
Pure error 2 0.00000 0.00 0.00000 0.00000
Total 14 2.84677 100.00
Table 6

ANOVA results for residual stress

Table 6
Source DF Seq SS Contribution [%] Adj SS Adj MS F-Value P-Value
Model 9 22657.0 91.62 22657.0 2517.45 6.07 0.031
Vc 1 984.6 3.98 196.5 196.47 0.47 0.522
f 1 10297.3 41.64 4976.1 4976.09 12.00 0.018
ap 1 1211.0 4.90 70.1 70.05 0.17 0.698
Vc 2 1 1620.0 6.55 1638.4 1638.43 3.95 0.104
f 2 1 3376.4 13.65 2598.1 2598.06 6.27 0.054
ap 2 1 1709.7 6.91 1162.7 1162.71 2.80 0.155
Vc*f 1 97.0 0.39 78.7 78.69 0.19 0.681
Vc*ap 1 2731.4 11.04 3241.7 3241.69 7.82 0.038
f *ap 1 629.4 2.55 629.4 629.45 1.52 0.273
Error 5 2072.7 8.38 2072.7 414.53
Lack-of-Fit 3 2072.7 8.38 2072.7 690.89
Pure error 2 0.0 0.00 0.0 0.00
Total 14 24729.7 100.00
From the ANOVA tables, it is clearly stated that the feed rate is the parameter that most affects the surface roughness and residual stress with the contribution percentages of 86.22 and 41.64% respectively. Regarding P-Value, the cutting speed (0.566 for Surface Roughness and 0.522 for Residual Stress) and depth of cut (0.317 for Surface Roughness and 0.698 for Residual Stress) do not present any statistical significance on the two responses. This results are consistent with previous studies. Theoretically, the surface roughness is primarily a function of the feed rate and nose radius.21 Moreover, the higher the feed rate is, the greater the tensile residual stress on the surface is generated.22 Specifically, a rise in chip thickness leads to an increase in the temperature in the cutting zone, and the level of plastic deformation or hardening.
3.2 Develop Regression Equations
Based on Eqs. (1), (2) and (3) for prediction for surface roughness and residual stress were respectively formed as shown below.
(2)
Ra=12.11-0.0818Vc-11.57f-3.69f+0.000149Vc2+64.68f2+1.460ap2+0.0079Vcf+0.01002Vcap+2.27fapRsquare=99.49%
(3)
σ=1559-11.99Vc-665f+1066ap+0.0260Vc2+75154f2+484ap2-2.40Vcf-4.52Vcap-1177fapRsquare=91.62%
The Rsquare values (91.62 and 99.49%) for the quadratic and power models are high enough to obtain reliable estimates. Fig. 4 shows the normal probability plot of the residuals with values of surface roughness and residual stresses for normal distribution. Indeed, it can be seen that the points evenly distributed are skewed towards both sides in a straight line, which demonstrates the proposed model is sufficient to show the suitability.
Fig. 4

Normal probability plots for Ra and σ

KSPE_2021_v38n4_237_f004.jpg
3.3 Optimization of Responses
The objective of the present study is to minimize the surface roughness and residual stress simultaneously. The mathematical formulation of the current optimization problem can be stated as follows:
Minimize F(x) = {f1, f2}
f1=12.11-0.0818Vc-11.57f-3.69f+0.000149Vc2+64.68f2+1.460ap2+0.0079Vcf+0.01002Vcap+2.27fapf2=1559-11.99Vc-665f+1066ap+0.0260Vc2+75154f2+484ap2-2.40Vcf-4.52vcap-1177fap
where cutting parameters lower and upper bounds:
230m/minVc290m/min0.08mm/revf0.2mm/rev0.1mmap0.5mm
To optimize the multi-objective function, the article proposes to use the BA.

3.3.1 Bat Algorithm

The bat algorithm (BA) is one of the nature-inspired algorithms proposed by Yang in 2010 based on the bats’ hunting behavior.23 In this algorithm, the bat’s position represents a solution. The algorithm’s goal is to find the best solution in all of the bat’s positions, including exploitation procedure and exploration procedure, such as:
- Exploitation procedure: The frequency fi, velocity vi and position xi of the ith bat at the iteration (t + 1) are defined by Eqs. (4), (5) and (6).
(4)
fi=fmin+fmax-fminβ
(5)
νit+1=νit+xit-x*fi
(6)
xit+1=xit+νit
where, fmin, fmax are the minimum and maximum frequency of the bat populations, β ∈ [0,1] is a uniformly distributed random value and x* is the best location (Solution) after the tth iteration.
Exploration procedure: Random walks among bats are created around the best optimal to prevent getting block at a locally optimal solution by Eq. (7).
(7)
xnew=xold+εAt
where, ε ∈ [-1,1] is a random number, At is the average loudness of all the bats at tth iteration.
The loudness Ait and the rate rit of pulse emission have to be updated during the optimal search process, according to Eq. (8).
(8)
Ait+1=αAit,rit+1=ri01-exp-τtwhere, 0<α<1, τ are constants

where, 0 < α < 1, τ are constants

3.3.2 Multi-Objective Bat Algorithm (MOBA)

This paper proposes a Pareto optimal concept, formulated by Vilfredo Pareto in the XIX century,24 using the BA to simultaneously optimize surface roughness and residual stress. The flow chart of the BA is shown in Fig. 5.
Fig. 5

Flow chart of Pareto optimal using BA

KSPE_2021_v38n4_237_f005.jpg
Parameters of the MOBA used in MATLAB are presented in Table 7.
Table 7

Parameters of the MOBA

Table 7
Parameters Values
Loudness, A 0.8
Pulse rate, r 0.8
Minimize frequency, fmin 0
Maximize frequency, fmax 2
Number of iteration, t 1,000
Bat population, n 100
Number points of Pareto, N 1,000
Fig. 6 shows the formation of Pareto optimal front that consists of the final set of solutions. The final optimum (Vc, f, ap) and their corresponding Ra and σ are shown in Table 8.
Fig. 6

Pareto front points

KSPE_2021_v38n4_237_f006.jpg
Table 8

Optimal solutions achieved by MOBA

Table 8
No. Vc
[m/min]
f
[mm/rev]
ap
[mm]
Ra
[μm]
σ
[MPa]
1 252.779 0.100 0.201 0.516 117.987
2 261.006 0.080 0.258 0.430 124.112
3 258.689 0.088 0.235 0.453 120.366
4 257.074 0.092 0.226 0.468 119.189
5 254.277 0.098 0.210 0.500 118.099
6 259.661 0.085 0.243 0.443 121.630
7 256.727 0.093 0.223 0.472 118.929
8 257.665 0.090 0.229 0.461 119.616
9 255.833 0.095 0.219 0.481 118.571
10 262.242 0.080 0.302 0.427 126.941
The Pareto optimal frontier points show that for each point corresponding to one set of parameters (Vc, f, ap), it is impossible to find another set of parameters (Vc, f, ap) for surface roughness to reach expected value that the residual stress is lower than the value on the Pareto front or vice versa, the residual surface stress is the desired value for which the surface roughness is lower than the present value. Indeed, in Table 8, if the parameter set includes Vc = 257.665 m/min, f = 0.090 mm/rev, ap = 0.229 mm, on the Pareto front, Ra = 0.461 μm, σ = 119.616MPa. This means that if Ra is expected to reach 0.461μm, it is impossible to choose any other sets of parameters (Vc, f, ap) so that σ is lower than 119.616 MPa.
Hence, based on specific requirements, the appropriate machining parameters are selected. For example, when required to achieve a lower surface roughness, the cutting parameters Vc = 262.242 m/min, f = 0.080 mm/rev, ap = 0.302 mm are chosen. The residual stress and surface roughness obtained then are σ = 126.941 MPa and Ra = 0.427 μm respectively. When a lower residual stress is required, the cutting parameters Vc = 252.779 m/min, f = 0.100 mm/rev, ap = 0.201 mm are selected. The residual stress and surface roughness are σ = 117.987MPa and Ra = 0.516 μm respectively.
This result is significant when compared to traditional optimization methods. RSM itself also finds the optimal set of parameters. Still, RSM gives only one result which is not as good as the result found by the BA. At the same time, Pareto optimal solution based on BA provides manufacturers with countless optimizations for different requirements.
3.4 Confirmation Test
With the predicted results found, it is necessary to conduct a confirmation experiment. One set of cutting parameters Vc = 257.665 m/min, f = 0.090 mm/rev, ap = 0.229 mm is selected for the verification experiment. According to the results shown in Table 9, it is possible to indicate that the prediction results are in good agreement with the experimental results with the error rate of only from 1.7 to 2.4%.
Table 9

Results of confirmation test

Table 9
Experimental
result
Predicted
value
Experimental
value
Error
[%]
Ra [μm] 0.461 0.472 2.4
σ [MPa] 119.616 121.658 1.7
In this study, an experimental investigation was conducted to improve the surface integrity in terms of the surface roughness and residual stress when turning AISI 304 austenitic stainless steel. The following conclusions were drawn from the research.
ANOVA results showed that the feed rate had the most influence on surface roughness and residual stress.
Pareto optimal solution was employed based on the BA to optimize cutting parameters to minimize surface roughness and residual stress. Optimal results revealed the smallest roughness value is Ra = 0.427 μm; the minimum residual stress is σ = 117.987 MPa. The experimental confirmation results demonstrated that the Pareto optimal solution applying the BA was reliable and efficient.
Finding the optimal point on the Pareto front allows users to choose the optimal value for production requirements.
We would like to express our sincere thanks to the two anonymous reviewers for their valued comments. Also, we are very grateful to Department of Materials Science and Engineering, Pohang University of Science and Technology (POSTECH) and Vietnam-Japan Center, Hanoi University of Industry (HaUI) for supporting us to conduct such comprehensive experiments and accurate measurements.
  • 1.
    Karunya, G., Ravikumar, P., Geeta Krishna, P., and Shiva Krishna, P., “Optimization of the Surface Roughness by Applying the Taguchi Technique for the Turning of AISI 304 Austenitic Stainless Steel,” International Journal of Mechanical Engineering and Technology, Vol. 8, No. 8, pp. 694-701, 2017.
  • 2.
    Sushil, I., Amit, P., and Rohit, P., “Machining Challenges in Stainless Steel-A Review,” International Journal of Advance Research, Ideas and Innovations in Technology, Vol. 3, No. 6, pp. 1395-1402, 2017.
  • 3.
    Umbrello, D. and Filice, L., “Improving Surface Integrity in Orthogonal Machining of Hardened AISI 52100 Steel by Modeling White and Dark Layers Formation,” CIRP Annals, Vol. 58, No. 1, pp. 73-76, 2009.
    10.1016/j.cirp.2009.03.106
  • 4.
    Zerti, O., Yallese, M., Zerti, A., Belhadi, S., and Girardin, F., “Simultaneous Improvement of Surface Quality and Productivity Using Grey Relational Analysis Based Taguchi Design for Turning Couple (AISI D3 Steel/Mixed Ceramic Tool (Al2O3 + TiC)),” International Journal of Industrial Engineering Computations, Vol. 9, No. 2, pp. 173-194, 2018.
    10.5267/j.ijiec.2017.7.001
  • 5.
    Yang, X. S., “Nature-Inspired Optimization Algorithms,” Elsevier, 1st Ed., pp. 77-141, 2014.
    10.1016/B978-0-12-416743-8.00010-5
  • 6.
    Kilickap, E., Huseyinoglu, M., and Yardimeden, A., “Optimization of Drilling Parameters on Surface Roughness in Drilling of AISI 1045 Using Response Surface Methodology and Genetic Algorithm,” The International Journal of Advanced Manufacturing Technology, Vol. 52, Nos. 1-4, pp. 79-88, 2011.
    10.1007/s00170-010-2710-7
  • 7.
    Zain, A. M., Haron, H., and Sharif, S., “Application of GA to Optimize Cutting Conditions for Minimizing Surface Roughness in End Milling Machining Process,” Expert Systems with Applications, Vol. 37, No. 6, pp. 4650-4659, 2010.
    10.1016/j.eswa.2009.12.043
  • 8.
    Amin, A., Haji Subir, S. A. B., and Arif, M. D., “Optimization of Tool Wear Using Coupled RSM-GA Approach in Turning of Stainless Steel AISI 304 with Magnetic Damping of Tool Shank,” Advanced Materials Research, pp. 117-121, 2015.
    10.4028/www.scientific.net/AMR.1115.117
  • 9.
    Zhou, T., He, L., Wu, J., Du, F., and Zou, Z., “Prediction of Surface Roughness of 304 Stainless Steel and Multi-Objective Optimization of Cutting Parameters based on GA-GBRT,” Applied Sciences, Vol. 9, No. 18, Paper No. 3684, 2019.
    10.3390/app9183684
  • 10.
    Kumar, S. L., “Measurement and Uncertainty Analysis of Surface Roughness and Material Removal Rate in Micro Turning Operation and Process Parameters Optimization,” Measurement, Vol. 140, pp. 538-547, 2019.
    10.1016/j.measurement.2019.04.029
  • 11.
    Ahmad, N. and Janahiraman, T. V., “A Comparison on Optimization of Surface Roughness in Machining AISI 1045 Steel Using Taguchi Method, Genetic Algorithm and Particle Swarm Optimization,” Proc. of the IEEE Conference on Systems, Process and Control, pp. 129-133, 2015.
    10.1109/SPC.2015.7473572
  • 12.
    Chandrasekaran, M., Muralidhar, M., Krishna, C. M., and Dixit, U., “Application of Soft Computing Techniques in Machining Performance Prediction and Optimization: A Literature Review,” The International Journal of Advanced Manufacturing Technology, Vol. 46, No. 5, pp. 445-464, 2010.
    10.1007/s00170-009-2104-x
  • 13.
    Yue, C., Wang, L., Liu, J., and Hao, S., “Multi-Objective Optimization of Machined Surface Integrity for Hard Turning Process,” International Journal of Smart Home, Vol. 10, No. 6, pp. 71-76, 2016.
    10.14257/ijsh.2016.10.6.08
  • 14.
    Talal, R., “Comparative Study between the (BA) Algorithm and (PSO) Algorithm to Train (RBF) Network at Data Classification,” International Journal of Computer Applications, Vol. 92, No. 5, pp. 16-22, 2014.
    10.5120/16004-4998
  • 15.
    Khan, K. and Sahai, A., “A Comparison of BA, GA, PSO, BP and LM for Training Feed Forward Neural Networks in e-Learning Context,” International Journal of Intelligent Systems and Applications, Vol. 4, No. 7, pp. 23, 2012.
    10.5815/ijisa.2012.07.03
  • 16.
    Perwaiz, U., Younas, I., and Anwar, A. A., “Many-Objective Bat Algorithm,” PLoS One, Vol. 15, No. 6, pp. 1-20, 2020.
    10.1371/journal.pone.0234625
  • 17.
    Suryanarayana, C. and Norton, M. G., “X-Ray Diffraction: A Practical Approach,” Springer Science & Business Media, 1st Ed., pp. 63-237, 1998.
    10.1007/978-1-4899-0148-4_3
  • 18.
    Myers, R. H., Montgomery, D. C., and Anderson-Cook, C. M., “Response Surface Methodology: Process and Product Optimization Using Designed Experiments,” John Wiley & Sons, 4st Ed., pp. 369-542, 2016.
  • 19.
    Bezerra, M. A., Santelli, R. E., Oliveira, E. P., Villar, L. S., and Escaleira, L. A., “Response Surface Methodology (RSM) as a Tool for Optimization in Analytical Chemistry,” Talanta, Vol. 76, No. 5, pp. 965-977, 2008.
    10.1016/j.talanta.2008.05.019
  • 20.
    Kao, L. S. and Green, C. E., “Analysis of Variance: Is There a Difference in Means and What Does It Mean” Journal of Surgical Research, Vol. 144, No. 1, pp. 158-170, 2008.
    10.1016/j.jss.2007.02.053
  • 21.
    Tebassi, H., Yallese, M., Khettabi, R., Belhadi, S., Meddour, I., et al., “Multi-Objective Optimization of Surface Roughness, Cutting Forces, Productivity and Power Consumption When Turning of Inconel 718,” International Journal of Industrial Engineering Computations, Vol. 7, No. 1, pp. 111-134, 2016.
    10.5267/j.ijiec.2015.7.003
  • 22.
    Navas, V. G., Gonzalo, O., and Bengoetxea, I., “Effect of Cutting Parameters in the Surface Residual Stresses Generated by Turning in AISI 4340 Steel,” International Journal of Machine Tools and Manufacture, Vol. 61, pp. 48-57, 2012.
    10.1016/j.ijmachtools.2012.05.008
  • 23.
    Yang, X. S. and He, X., “Bat Algorithm: Literature Review and Applications,” International Journal of Bio-Inspired Computation, Vol. 5, No. 3, pp. 141-149, 2013.
    10.1504/IJBIC.2013.055093
  • 24.
    Coello, C. A. C., Lamont, G. B., and Van Veldhuizen, D. A., “Evolutionary Algorithms for Solving Multi-Objective Problems,” Springer, 1st Ed., pp. 141-205, 2002.
Bong Pham Van
KSPE_2021_v38n4_237_bf001.jpg
Associate Professor in the Department of Mechanical Engineering, Hanoi University of Industry, Hanoi, Vietnam. ASC Bong’s research interest is advance materials and optimization processing machining.
Hoi Tran Viet
KSPE_2021_v38n4_237_bf002.jpg
Ph.D. candidate in the Department of Mechanical Engineering, Hanoi University of Industry, Hanoi, Vietnam. He is interested in mechanical engineering, data analysis, simulation and optimization topics.

Download Citation

Download a citation file in RIS format that can be imported by all major citation management software, including EndNote, ProCite, RefWorks, and Reference Manager.

Format:

Include:

Application of Bat algorithm for Improvement of Surface Integrity in Turning of AISI 304 Austenitic Stainless Steel
J. Korean Soc. Precis. Eng.. 2021;38(4):237-244.   Published online April 1, 2021
Download Citation

Download a citation file in RIS format that can be imported by all major citation management software, including EndNote, ProCite, RefWorks, and Reference Manager.

Format:
Include:
Application of Bat algorithm for Improvement of Surface Integrity in Turning of AISI 304 Austenitic Stainless Steel
J. Korean Soc. Precis. Eng.. 2021;38(4):237-244.   Published online April 1, 2021
Close

Figure

  • 0
  • 1
  • 2
  • 3
  • 4
  • 5
Application of Bat algorithm for Improvement of Surface Integrity in Turning of AISI 304 Austenitic Stainless Steel
Image Image Image Image Image Image
Fig. 1 Mori Seiki SL-253 CNC lathe
Fig. 2 Mitutoyo Surftest SV-2100 surface roughness tester
Fig. 3 XRD system for measuring residual stress
Fig. 4 Normal probability plots for Ra and σ
Fig. 5 Flow chart of Pareto optimal using BA
Fig. 6 Pareto front points
Application of Bat algorithm for Improvement of Surface Integrity in Turning of AISI 304 Austenitic Stainless Steel
Composition C Cr Ni Si Mn P S
wt% 0.07 18.49 8.15 0.57 0.76 0.03 0.009
Specific heat
capacity
[J·kg-1·K-1]
Elastic
modulus
[GPa]
Coefficient
of thermal
expansion
[10-6·K-1]
Thermal
conductivity
[W·m-1 K-1]
Density
[g/cm3]
500 200 17.3 16.3 7.93
Cutting parameters Level
1 2 3
Cutting speed Vc [m/min] 230 260 290
Feed rate f [mm/rev] 0.08 0.14 0.20
Depth of cut ap [mm] 0.10 0.25 0.50
No. Vc
[m/min]
f
[mm/rev]
ap
[mm]
Ra
[μm]
σ
[MPa]
1 290 0.2 0.25 1.58 201.6
2 260 0.14 0.25 0.73 125.9
3 260 0.14 0.25 0.73 125.9
4 230 0.2 0.5 1.72 240.8
5 230 0.14 0.1 0.93 136.3
6 260 0.08 0.5 0.45 143.1
7 260 0.2 0.1 1.55 233.3
8 260 0.14 0.25 0.73 125.9
9 260 0.08 0.1 0.44 131.7
10 230 0.2 0.25 1.66 204.5
11 290 0.14 0.1 0.87 172.5
12 290 0.08 0.25 0.48 166.7
13 230 0.14 0.5 0.85 226.5
14 230 0.08 0.25 0.64 143.2
15 290 0.14 0.5 1.02 148.3
Source DF Seq SS Contribution [%] Adj SS Adj MS F-Value P-Value
Model 9 2.83234 99.49 2.83234 0.31470 109.05 0.000
Vc 1 0.08893 3.12 0.00109 0.00109 0.38 0.566
f 1 2.45459 86.22 2.01253 2.01253 697.39 0.000
ap 1 0.00763 0.27 0.00356 0.00356 1.23 0.317
Vc 2 1 0.08038 2.82 0.05363 0.05363 18.58 0.008
f 2 1 0.17579 6.18 0.19252 0.19252 66.71 0.000
ap 2 1 0.00770 0.27 0.01057 0.01057 3.66 0.114
Vc*f 1 0.00114 0.04 0.00086 0.00086 0.30 0.609
Vc*ap 1 0.01384 0.49 0.01590 0.01590 5.51 0.066
f *ap 1 0.00235 0.08 0.00235 0.00235 0.81 0.408
Error 5 0.01443 0.51 0.01443 0.00289
Lack-of-Fit 3 0.01443 0.51 0.01443 0.00481
Pure error 2 0.00000 0.00 0.00000 0.00000
Total 14 2.84677 100.00
Source DF Seq SS Contribution [%] Adj SS Adj MS F-Value P-Value
Model 9 22657.0 91.62 22657.0 2517.45 6.07 0.031
Vc 1 984.6 3.98 196.5 196.47 0.47 0.522
f 1 10297.3 41.64 4976.1 4976.09 12.00 0.018
ap 1 1211.0 4.90 70.1 70.05 0.17 0.698
Vc 2 1 1620.0 6.55 1638.4 1638.43 3.95 0.104
f 2 1 3376.4 13.65 2598.1 2598.06 6.27 0.054
ap 2 1 1709.7 6.91 1162.7 1162.71 2.80 0.155
Vc*f 1 97.0 0.39 78.7 78.69 0.19 0.681
Vc*ap 1 2731.4 11.04 3241.7 3241.69 7.82 0.038
f *ap 1 629.4 2.55 629.4 629.45 1.52 0.273
Error 5 2072.7 8.38 2072.7 414.53
Lack-of-Fit 3 2072.7 8.38 2072.7 690.89
Pure error 2 0.0 0.00 0.0 0.00
Total 14 24729.7 100.00
Parameters Values
Loudness, A 0.8
Pulse rate, r 0.8
Minimize frequency, fmin 0
Maximize frequency, fmax 2
Number of iteration, t 1,000
Bat population, n 100
Number points of Pareto, N 1,000
No. Vc
[m/min]
f
[mm/rev]
ap
[mm]
Ra
[μm]
σ
[MPa]
1 252.779 0.100 0.201 0.516 117.987
2 261.006 0.080 0.258 0.430 124.112
3 258.689 0.088 0.235 0.453 120.366
4 257.074 0.092 0.226 0.468 119.189
5 254.277 0.098 0.210 0.500 118.099
6 259.661 0.085 0.243 0.443 121.630
7 256.727 0.093 0.223 0.472 118.929
8 257.665 0.090 0.229 0.461 119.616
9 255.833 0.095 0.219 0.481 118.571
10 262.242 0.080 0.302 0.427 126.941
Experimental
result
Predicted
value
Experimental
value
Error
[%]
Ra [μm] 0.461 0.472 2.4
σ [MPa] 119.616 121.658 1.7
Table 1 Chemical composition of AISI 304 austenitic stainless steel
Table 2 Physical properties of AISI 304 austenitic stainless steel
Table 3 Cutting ranges and levels
Table 4 Experimental results
Table 5 ANOVA results for surface roughness
Table 6 ANOVA results for residual stress
Table 7 Parameters of the MOBA
Table 8 Optimal solutions achieved by MOBA
Table 9 Results of confirmation test