. Sten VELCHEV,. Ivn KOLEV, 3. Ksii IVANOV EMPIRICAL MATHEMATICAL MODELS OF THE DEPENDENCE OF THE SPECIFIC CUTTING FORCE ON THICKNESS OF CUT IN TURNING -3. DEPARTMENT OF MACHINE TOOLS & MANUFACTURING, ANGEL KANCHEV UNIVERSITY OF RUSE, 8 STUDENTSKA STR., 77 RUSE, BULGARIA ABSTRACT: Bsed on te nlysis of te teoetil odels fo deteining te seifi utting foe, boundy onditions of its deendene on te tiness of ut e offeed. Hyotetil gi eltions of te seifi utting foe vesus te tiness of ut wit its nge in lge te fo bittle nd dutile woiee teil e offeed in ddition wit ossible yotetil teti odels fo oxition of tese eltions. Exeientl ese of te influene of te tiness of ut on te seifi utting foe in tuning of diffeent woiee teils is done. By tetil oessing of te exeientl dt, te suggested yotetil tetil odels e gined nd nlyzed nd s te best new eiil tetil odel of te deendene of te seifi utting foe on te tiness of ut is eoended tis one wi is wit te best dequy nd uy. Te devitions between te vlues of te seifi utting foe eeived fo lultions by te teti odels bsed on efeene dt nd te vlues eeived fo te suggested new odel ve been exloed. It tuns out tt in soe ses fo soe woiee teils tese devitions e 4-5% nd oe. In onsequene, wen lulting te utting foes in tuning by su etods signifint eos n be eeived. KEYWORDS: seifi utting foe, tiness of ut, yotetil odel, eiil odel, uy of odels INTRODUCTION Te foule fo lulting te utting foes fo vious utting oetions ost often e bsed on te Kintzle tetil odel [], deived fo exeientl ese. Tis odel of te in utting foe in tuning n be esented s: F =.. b., () wee. is te bsi vlue of te seifi utting foe t te noinl oss-setionl e of te ut A =. b =. =, b - te widt of ut, - te tiness of ut, - te exonent Te tetil odel of te seifi utting foe n be exessed using owe funtion =... () Te vlues fo. nd deend on te tye nd te enil oeties of te woiee teil. Tese vlues fo vious teils nd t vious utting onditions e ublised in seilized nd efeene litetue [,3,4,5]. Coetion oeffiients e estblised fo lultion of te utting foes t diffeent onditions nd fo diffeent utting oetions, Tese oeffiients te into ount te influene of te e ngle γ, te utting seed v, te tool we, te tye of utting oetions, et. Fleise et l [6] oose to ly foul () fo ioining ( = µ) of steel AISI 45, AISI nd o-ion by estblising oetion oeffiient tt tes into ount te influene of te utting edge dius. In te efeene boo [7], fouls fo lultion of te utting foes in tuning of vious wo teils e given wen v =onst nd onstnt ote utting onditions: x y F F F = C. F. f (3) Hving in ind tt te det of te ut influenes ootionlly ( x F = ) nd tt te det is ootionl to te feed f, te seifi utting foe is lulted using odel (): F C F = = = y.., (4) F. f wee C F =., = y F. oyigt FACULTY of ENGINEERING HUNEDOARA, ROMANIA 33
ANNALS OF FACULTY ENGINEERING HUNEDOARA Intentionl Jounl Of Engineeing Te odel () of te seifi utting foe is often used in diffeent studies of te utting foes. Fo exle, Adi et l [8] use it fo te tngentil nd dil seifi utting foes (lled utting foe oeffiients in tis tile) in fln illing of luiniu lloy 6-6-T6. Te se odel fo tese seifi foes is used by Diez Cifuentes et l [9] in illing of luiniu lloy AL-74, s well s by Ait et l [] in ult-eision end-illing of bittle teil (glss). Te extoltion of te vlues of in tuning, lulted using foul () t sll tiness of ut, n led to onsideble eos. Results of onduted esees tt y be seen in [3] sow tt wit deesing of te tiness of te ut te intensity of its influene on te seifi utting foe gows wi is exessed wit te gowt of te owe index. So it is suggested tt te nge of tiness of ut fo to µ is divided into tee sub-nges wee. nd e deteined fo e one of te. Ote eiil tetil odels fo oxition of te = f ( ) deendene e lso suggested. Te deendenies of te tngentil t nd te dil seifi utting foes on te feed e toot f t, te utting seed v, te dil det of ut e, nd te xil det of ut wen end illing of luiniu lloys e oxited by Wng nd Cng [] using line funtion. Wen v = onst, e = onst, nd = onst te eqution loos lie: i = i i. f t, i { t, } (5) Te oxition of tis se is ute enoug beuse duing te exeients te ftos do not vy u. In tis odel te tiness of ut is indietly esented. Duing illing it is vible but te vege tiness unde given iustnes e ootionl to te feed. Wen eseing te in utting foe in fe illing of steel AISI 5 Andeson et t [] use tetil odel of te seifi utting foe C (lled utting esistne in tis tile) tt loos lie: C C = + C, (6) wee C nd C e onstnts deived fo te utting foe dt. Bsed on exeientl studies of te utting foes in otogonl tuning of steel AISI 45, Conzlo et l. [3] deive tis odel of te in utting foe: F / = +. f (7) Sine in tis se f =, nd using foul (7), one n deive odel lie (6) fo te seifi utting foe = F /(. ). Su odel fo te in seifi foe n lso be deived fo te fouls by Ding et l [4] fo te utting foes in end illing of d steel AISI H3 t v = onst, = onst nd e = onst. Te deendene of te tust foe nd toque on te feed f (/ev), dill diete d () nd sindle seed n () in dilling of oi oosite using HSS dill e eseed by Jybl et l [5]. Te deendene of te toque M = f ( f, d, n) is oxited by seond-degee olynoil wi wen d = onst nd d = onst is: M = b + b. f + b. f (8) If te toque is exessed by te seifi utting foe. f. d M = = b + b. f + b. f. Ten te odel of te seifi foe is = + +. f, (9) f wee, wen ting into onsidetion te dt fo [5], >, >, >. Te deendenies, oosed by Cng et l [6], of te nol n, dil nd tngentil t seifi utting foes in bll end illing of luiniu lloys on te feed e toot f t nd te dness of teil d e oxited by tid-degee olynoil. Wen d = onst te odel is: 3 i = C i C i. ft + C 3 i. ft C 4 i. ft ; i { u,, t} () Te eltionsi between e-sled unut i tiness t n nd log-sled nol seifi utting foe n in end illing of luiniu lloy is oxited by Yun et l [7] using Boltzn funtion A A ln( n ) = ( ) + A t x /, () n dx + e wee te oeffiients A > A > ; x < ; dx >. Te boveentioned estblises tt wen oosing tetil odel fo oxiting te exeientl deendene of te seifi utting foe n eiil o sould be lied. In onsidetion is ten te ysil ntue of te deendene of etin ete on te ftos tt influene it, nd not te bsi equieent wen oosing tetil odel fo dequte 34 Toe IX (Ye ). Fsiule 3. ISSN 584 673
ANNALS OF FACULTY ENGINEERING HUNEDOARA Intentionl Jounl Of Engineeing esenttion of te exeientl deendeny. Tis eiil o llows fo te lultion of te seifi utting foe wit stisftoy uy ving liited vition of te influening ftos. Otewise te esults y ve substntil eos. Te uent ese is to ieve oe ute lultion of te utting foes using new eiil tetil odels fo te seifi utting foe bsed on te ysil ntue of te influene of te tiness of ut. Aolising tis gol fes viety of obles tt need solving: nlysing te teoetil deendenies of te seifi utting foe nd bsed on te enil ntue of te oess of utting substntiting te yotetil gil deendenies of te seifi utting foe on te tiness of ut in wide vition nge of its vlues; suggesting vious tetil odels fo ossible oxition of tis deendene fo vious wo teils; n exeientl ese of te deendene of te seifi utting foe on te tiness of ut fo vious wo teils; deiving nd eseing of te suggested eiil odels of tis deendene; ese of te devition of seifi utting foe vlues by oing te esults of te suggested new tetil odels bsed on efeene dt oed to deteine tose vlues using te new tetil odels wi e oosed nd efeed to s te best oding to ysil nd sttistil itei. HYPOTHETICAL MATHEMATICAL MODELS It is neessy to nlyze te esults of te teoetil studies, onduted fo estiting utting foe in ode to oose te ind of te eiil tetil odels tt deteine te deendene between te seifi utting foe nd te tiness of ut bsed on te ysil ntue of its influene in wide nge of vition. Te in gol of tese esees is to nlytilly lulte te utting foes by using enil oeties of te ined teil nd soe etes of te oess of utting, nd eting diffeent yoteses bout te defotion of te ut duing te i fotion oess. Te esulting teoetil odels e vey diffeent fo one note. Soe teoetil foule fo deteining te in seifi utting foe e sown in Tble. Tey e deived fo te foule fo deteining te in seifi utting foe ( = F (. b) ) suggested by diffeent esees of D odel fee otogonl utting wit one se lne. It ust be noted tt wile deteining using odels,, 3 te foes on te jo fln of te tool ve not been ten into onsidetion. Tey e ignoed due to tei insignifint vlue, wi is llowed t lge tiness of ut, lene ngles nd n unwon tool wit dutile teils. Tble. Soe teoetil tetil odels fo lultion of te seifi utting foe Teoetil tetil odel Auto/Soue τ φ.os( ρ γ + γ ). = H. Enst, M. E. Ment 94 [8] sinφ.os( φ + ρ γ ). = ( ot gφ + tg ) τ φ C z 3. sin ρ ( λ.os( ρ γ ) 4. γ. N. N. Zoev, 956 [9] ε =,85. HV A. M. Rozenbeg, A. N. Eein, 956 [] = R e γ = + γ α n λ (osγ + μγ.sinγ ) = F / b ( ) α μ α α N. γ V. D. Kuznezov, V. A. Kivouov 954 [] Sybols: τ φ se stengt on te se lne; ρ γ ngle of fition between i nd fe; γ e ngle; φ se ngle; C z onstnt ngle fo wo teils; HV Vies dness of i; ε se stin; R e yield stengt in oession; λ i lengt oession tio; F α N jo fln eendiul foe; n exonent; μ α oeffiient of fition between jo fln nd tnsient sufe. Te teoetil foule used to lulte te seifi utting foe is inute nd too olited fo til lition visulize te enis of oess of utting. Wit wide vitions of te tiness of ut te fition foe on te jo fln is not to be ignoed nd te seifi utting foe is viewed s oosite foe (see Model 4, Tble ): = γ + α, () wee γ - te oonent wi is foed by te nol foe nd te fition foe on te e; α te oonent foed by te fition on te jo fln. Te vible intensity of te influene of te tiness of ut n be exlined nd te liits of its vition n be deteined using te esults fo te teoetil esees tt te into onsidetion te ysil ntue of fotion of te seifi foe. Wit slle tiness of tiness of ut dutile utting lsti teils te oonent of te seifi utting foe γ ineses oding to te teoetil odels -4 (Tble ). Tis is due to te inese of te i lengt oession tio λ nd tus te onventionl se ngle φ deeses. Te oonent of te seifi utting foe α ineses signifintly fste wi is due to te slle oss-setionl e. Te fition foe on te jo fln s deteined vlue, oyigt FACULTY of ENGINEERING HUNEDOARA, ROMANIA 35
ANNALS OF FACULTY ENGINEERING HUNEDOARA Intentionl Jounl Of Engineeing wi does not deend on te tiness [9] (odel 4 Tble ). Te ovell seifi foe ineses wit eve gowing intensity nd wen tends to zeo te seifi foe sould be n indefinite lge vlue (fig. ): Wit, (3) Wit n inese of te oonent α deeses nd t lge tinesses it s insignifintly sll vlues. Te oonent of te seifi foe γ oding to te se teoetil odels deeses beuse λ deeses φ ineses, nd te fition ngle ρ γ deeses. At tinesses of given wo nd tool teils te i lengt oession tio is onstnt vlue Figue. Hyotetil gil deendenies of te seifi utting foes γ, α nd on te tiness of ut: ) Dutile teils; b) Bittle teils ( onst ) λ nd tus φ onst. Tis leds to te ssution tt wen te tiness s signifintly ig vlues ten te seifi utting foe is onstnt vlue (fig.)., onst =,. (4) Wen utting bittle teils te oonent α nges siilly to te nge of te tiness. Wen utting dutile teils te nge of γ is bsed on te vying degees of lsti defotion of te ut nd is inly due to te seondy lsti defotion due to te fition on te e. Wen utting bittle teils te lsti defotion is oo ( λ ). Tus it n be sid tt fo n idelly bittle teil (fig. b): γ onst =,. (5) A new ete, is used wen studying te seifi utting foe. It n be lled liit seifi utting foe nd is teisti oety of given wo teil. It deends ostly on te e ngle wen n unwon tool is used. Su n ssution is onfied by soe exeientl studies. Fo exle wen tuning steel SM45C Lee et l. [] ve obtined deendenies of te seifi utting foe (lled seifi utting enegy in tis tile) on te feed, sown on Fig.. Te eiil tetil odels tt Figue. Seifi utting enegy fo oxite te deendene of te seifi utting foe on SM45C []; KA, KC nd MC tyes i foes of inset TNMG 648; te tiness of ut in wide nge of vition ust oly V utting seed; D det of ut. wit te liit onditions (3) nd (4). Te tetil odel () olies wit ondition (3) but wen it does not oly wit ondition (4), i.e.. Futeoe it n t exess te vible intensity of in logiti oodinte syste beuse d ln / d ln = = onst wi does not onfo to exeientl dt. Mtetil odel (5) does not oly wit bot onditions - wen f t, i = i = onst nd wen f t, i <. Te odel (6) stisfies bot onditions: wen, C nd, C = C. It is neessy to veify tis odel fo vious wo teils. Te odel (9) olies ondition (3), but does not oly wit ondition (4), nd odel () olies only wit ondition (4). It is x / dx estblised tt wen n ln n = ( A A ) ( + e ) = onst, odel () does not oly wit ondition (3). Wen n ln n = A, i.e. ondition (4) is fulfilled. Tble. Hyotetil Mtetil Models Mtetil odels Conditions.... > ; = + + > ; > + +. > ; = + > + 3. 3 = + > ; > + > ; 4. 4 = e > ; e < > ; 5. 5 = + > ; + > 36 Toe IX (Ye ). Fsiule 3. ISSN 584 673
ANNALS OF FACULTY ENGINEERING HUNEDOARA Intentionl Jounl Of Engineeing Te tetil odels tt oxite yotetil gil deendenies of te seifi utting foe on te tiness of ut (fig. ) nd tt oly wit onditions (3), (4) nd (5) e osen fo []. Soe of te e odified bsed on stutue (tble ). A tetil odel s to be seleted toug tetil oessing of exeientl dt fo obtining te oeffiients of tese odels nd sttistil nlysis of te esults. Tis odel sll oxite te deendene of te seifi utting foe on te tiness of ut wit te best dequy nd uy. RESEARCH METHODOLOGY DETERMINING THE SPECIFIC CUTTING FORCE Fo e test te seifi utting foe is lulted using te following foul: = F Ae f f, N /, (6) wee F, N, is te in utting foe, deteined exeientlly; A e f f is te effetive osssetionl e of ut,. If wen deteining duing tuning te noinl oss-setionl e of ut is A =. f, nd not te tul A e f f < A, wit otively lge feeds f, sll dets of ut, nd one diuses ε soe signifint istes n be de. Teefoe it is neessy to deteine eisely te effetive oss-setionl e of ut. An o to deteine te widt b nd its vege tiness = f. s to be doted wen eseing te deendene ( ) RESEARCH METHODOLOGY DETERMINING THE DIMENSIONS OF CUT Deending on te utting onditions te det of ut, te feed f nd te geoety of te tool te tool utting edge ngle κ nd ino utting edge ngle κ nd te one dius t te ti ε tee e fou ossible sees of utting duing tuning. Hee will be eviewed te deteining of te eleents of te oss-setionl e of ut in two of tese sees te (fig. 3 ) fist see is obtined wen olying wit te following onditions: > ε ( osκ γ ), f ε sinκ, (7) nd te seond see (fig. 3 b) olying wit > ε ( osκ γ ), f > ε sinκ. (8) Tese sees te ost fequently et in tie nd e tus used in te exeientl esees efoed. Wen utting is done using uved utting edges, sevel oes fo deteining te widt of ut e eoended oding to ISO 3/3 984/E: b = AC o oding to [] Figue 3. Sees of ut. а) wit b = AB stigt nd uved es of te + BC (fig. 3). Fo te uent study ets: jo utting edge nd wit uved e of te ino utting b = AC = AG + CG (9) edge; b) wit stigt nd uved wee AG = ; es of te jo utting edge CG = [ P ε ( osκ )] ot gκ + ε sinκ nd te ino utting edge. Te effetive oss-setionl e of ut in bot sees is deteined wen te e of te ti A A A is subtted fo te noinl oss-setionl e of ut A f E n =.. Te e A A A is E deteined using foule tt e not quoted ee. A eff = An A, () AA E Wen duing utting tee e uved utting edges, te tiness of ut in te diffeent oints of te utting edge is vible. Teefoe, it is eted to deteine te vege tiness of ut []: = Aeff / b,. () Te ext vlue of te tul det of ut is needed to deteine te diensions of te osssetion A nd b. Tt is wy te diete of te wo sufe D is esued wit ioete wen beginning te test. Te diete d of te ined sufe is esued fte te test is done. Wen ting into ount te ougness of te sufe nd ignoing its identl oonent, te tul det of ut is deteined using te following foule: D d f = +, (fig. 3, ) it f, / ev () 8 D d wee y E is lulted by te given foul. RESEARCH CONDITIONS ε = + ε y E, (fig. 3, b), (3) Te exeientl esees e done using te wo teils: AISI bon steel W-.C, CuSn7P,7 bonze, luiniu lloys AlCu4,5Mn,5Mg,6 nd gey ion GG5. oyigt FACULTY of ENGINEERING HUNEDOARA, ROMANIA 37
ANNALS OF FACULTY ENGINEERING HUNEDOARA Intentionl Jounl Of Engineeing Te exeients e done on lte odel SU5 wit tooling: Inset SNMG4-MR, GC45 o gde; tool olde PSBNR55M (SANDVIK Coont), utting edge ngle κ = 75 ; ino utting o edge ngle κ = 5 ; one dius ε =.. A tee-oonent dynoeti syste wit sensitiveness of.5 μ of te indutive tnsdues IWT of VEB RFT Geny nd univesl esuing devie N3 IEMI, ve been used to esue te utting foes. Tble 3 sow te utting onditions. Tble 3. Cutting onditions Det of Binnel Tiness of Nube Wo Cutting seed ut Feed dness ut of tests Mteil v,/ in HB (noinl) f, / ev,, n. Steel AISI W-.C 8 9..8.4.4.93. Gey ion GG 5 56 55..8.4.4.93 3. Bonze CuSn7P.7 93 8..8.74.4.575 4. Aluiniu lloy AlCu4.5Mn.5Mg.6 7..8.74.4.575 DETERMINING THE COEFFICIENTS OF THE MATHEMATICAL MODELS Te deteintion of te tetil odels oeffiients tt oxite te deendene of te seifi utting foe nd te sttistil nlysis is done toug oessing of te exeientl dt using oute og eted eseilly fo te uose [3]. Te oeffiients of tetil odels, nd 3 (Tble ) e deteined toug te lest sques etod (LS Metod). Mtetil odel 4 is libelised toug ting double logit nd odel 5 toug ting single one. Te initil vlue of te oeffiient < i nd itetion e osen. On e ste toug LS Metod te oeffiients,, nd te su of te sques of te eos S in e deteined. Vlid vlues of te oeffiients nd e tose fo wi S in s te sllest vlue. Te signifine of te odel oeffiient is estited by te Student s t - iteion nd te unifoity of te disesions by te Con s G iteion. Te Fise iteion, te oeltion oeffiient R nd bsolute vlue of te xil eltive eo Δ x % e used to estite te dequy, te uy nd te effiieny of te tetil odels. Te Fise iteion is used in two vints: ) F = F = s / sb F α, ν, ν (4) b) Fo bette editbility oeties of te odel, te F - iteion sould be sevel ties (oe tn 4 ties) gete tn te itil vlue F α, ν, ν, wee α is te signifine level, nd ν nd ν e te degees of feedo [4]. F = F = s s (5) Te disesion of eoduibility s, esidul disesion s b nd te disesion in eltion to te en vlue of te seifi utting foe s e lulted toug nown foule. All tests e eeted tee ties. Te tul det of ut, te effetive osssetionl e of ut, te widt nd te vege tiness s well s te seifi utting foe fo e test wee lulted by using te seilly eted fo tt uose oute og. RESULTS AND ANALYSES / 4 F, ν, n α ν Te estblised deendenies of te seifi utting foe on te tiness of ut fo e teil nd e test e sown in fig. 4. In te e of sll tinesses (. ), te seifi utting foe deeses intensively wen te tiness ineses fo ll eseed wo teils. Wit gete tinesses of ut te seifi utting foe deeses less intensively nd is lose to onstnt vlue. Fo te dutile teils bonze nd luiniu lloy te deese stts wen te tiness. nd fo steel. 6. Fo bittle teil st ion, te seifi utting foe vies insignifintly fo tiness of =. is lost onstnt. 38 Figue 4. Vition of te seifi utting foe on te tiness of ut. а) steel (AISI W-.C), gey ion (GG5) б) bonze (CuSn7P.7), luiniu lloy (AlCn4.5Mn.5Mg.6) Toe IX (Ye ). Fsiule 3. ISSN 584 673
ANNALS OF FACULTY ENGINEERING HUNEDOARA Intentionl Jounl Of Engineeing Te yotetil tetil odels given in Tble wee nlyzed in ode to oxite te exeientl deendenies of te seifi utting foe on te tiness of ut. Te esulting oeffiients fo tese odels of te exeientl dte wee tetilly oessed nd e given in Tble 4. Coosing tetil odel wi best oxites te exeientl dt is te olex. Te sttistil itei sould be lied wen te onditions given in Tble e fulfilled, s well s ondition wee n < n, (6) is te vege vlue of te seifi utting foe t xiu tiness of ut (n -t til). Tble 4. Coeffiients of te tetil odels, te sttistil itei nd te onditions Wo Mteil Mteti l Model F F R Conditions Adequy n n <а Δ x % Steel W-.C Gey ion GG 5 Bonze CuSn7P.7 Aluiniu lloy AlCu4.5Mn.5 Mg.6 83 95.83 -.58 89.7 9..994 - + - - 36 6.5-3.4 9.4.984 + + - - 73 3 494.836-5.4 9.4.966 + - 6-4 963.7.596 -.66 4 9..966 + + + 9.8 5 353 45..578 7 9..95 + + + 9.3 38 6.4 -. 8. 9..994 - + + - 77 9.7-49. 9.4.99 + + + 4.8 3.73-6.94 9.4.935 + - 38 - - 4 8,6 -.95 7. 9..974 + + +.7 5 87.35.39 3.9 9..98 + + + 7. 47 9.64.8 5.4..98 + + - - 48 5.3 -.6 9.8.977 + + - - 3 556.3-5.4 9.8.969 + + 357 - - 4 3.5 -.63 9.8..973 + + + 6.3 5 3 48..757 7...969 + + + 6.3 9..8 -.93...995 - + - - 969. 6.4-5. 9.8.99 + + - - 3 8.6-6.99 9.8.935 + - 9 - - 4 78.3.93.637 9..998 + + + 4.4 5 797.3 84. -.4 88..997 + + + 4.5 Wen evluting te odel s dequy to te Fise iteion F (vint ), ost of te odels e dequte but only fo itil vlues of te iteion t diffeent levels of signifine. Te seond vint b using Fise s iteion s been used so tt tee is genel evlution of te dequy. Its itil vlue is osen fo level of signifine α =. 5. Te vlues of te F iteion, its itil vlue F = 4 F α, ν ν, te oeltion oeffiient R nd te xil eltive eo Δ x % e given in Tble 4 nd e used fo te nlyzed tetil odels of te vious wo teils. In te Conditions, Adequy nd Condition (6) oluns lus o inus seifies if te onditions ve been et o not. Fo wo teil- steel AISI W.C, tetil odels 4 nd 5 oly wit ll onditions nd sttistil itei. Tey e lost equivlent, but odel 5 s slle xiu eltive eo. Fo gey ion GG5 odel does not oly wit te ondition < nd odel 3 is indequte. Aoding to te sttistil itei nd te eltive fult odel is te best one followed by odels 5 nd 4. It is eted tt te fition does not deend on te tiness of ut nd tt te ut of bittle teils is tuned into i wit insignifint lsti defotions. Ten te oonent of te seifi utting foe γ does not deend on te tiness nd te oeffiient exesses te liit seifi foe = γ = wile te oeffiient exesses te fition on widt of ut unit. Te best odel lied wit bittle teils is odel followed by odel 5 wit oeffiient =.39 wi is lose to = of odel. Fo te wo teil- bonze CuSn7P.7, odels 4 nd 5, wi e lost equivlent, olies wit te onditions nd te sttistil itei. Te se is estblised fo te ined teilluiniu lloy AlCu4.5Mg.6 Mn.5. Tis ese sows tt tetil odel, oesonding to odel (6) [], is suitble fo bittle teils - in tis se gey ion. Howeve, fute dditionl ese is needed to suot tis finding. Mtetil odels 4 nd 5 ove to be ost suitble fo dutile teils. Mtetil odel 5 n be eoended sine it exesses te ysil ntue of te foultion of te seifi utting foe in bette wy, nd odel is tiul se of odel 5. Teefoe, te exeientl tetil odel, tt oxites te deendene of te seifi utting foe on te tiness of ut in tuning n, be eesented in genel fo =..., (7) + oyigt FACULTY of ENGINEERING HUNEDOARA, ROMANIA 39,
ANNALS OF FACULTY ENGINEERING HUNEDOARA Intentionl Jounl Of Engineeing wee. = is oonent of. in,. = - oonent of. in =, = - exonent. Te vlues of. =,. nd fo te eseed ined teils e given in Tble5. Tble 5. Vlues of.,. Wo Mteil.. N/ N/ с.., N/ Steel AISI W-.C 353 45.578 758 Gey ion GG5 77 9.7. 97 3 Bonze CuSn7P.7 3 48..767 369 4 Aluiniu lloy AlCu4.5Mn.5Mg.6 797 84..637 88 ACCURACY OF THE EMPIRICAL MATHEMATICAL MODELS Tis ese is t estiting te uy of soe eted eiil odels of te seifi utting foe on te tiness of oding to efeene dt given in. Te odels ve been ed s A[4], (SANDVIK Coont), B [] nd C [7]. Te suggested new odels of tese deendenies e eted s te best ones bsed on tis estition. Te seifi utting foe, wi deends on te tiness of ut, fo ll teils, is lulted by using te following foul (odel A):,4 =.,4, (8) wee., 4 is te bsi vlue of te seifi utting foe wit tiness of ut =, 4, given in tbles; Te exession in te bets is oetionl oeffiient: = (,4 / ), (9) Ten =.,4.. (3) In (odel B) te seifi utting foe dt is given in tble. Te vlues of., 4 fo vious teils n be ten dietly s well s te owe. If., 4 is eted s bsi Tble 6. Vlues of vlue lulted using foul (4) of tetil odels A, B nd C odel С, te seifi utting foe is lso lulted using foul (3) nd te oetionl oeffiient using foul (9). 3 Wo Mteil Steel AISI W-.C Gey ion GG5 Bonze CuSn7P.7 A[4].5.8.5 B[].8..7 C[7].7.5.34 Te vlues of odels А, В Al-lloy 4 nd С e given in Tble 6. AlCu4.5Mn.5Mg.6.5.5.3 Te seifi utting foe oding to te best suggested odel (7) n lso be lulted using foul of tye (3): =..4., (3) wee.. 4 is deteined s odel (7) wen =. 4 nd = /.. 4. So tt te bsi vlue of te seifi utting foe is eliinted beuse it diffes fo teils enil teistis, it is eted tt it will ve onstnt vlue fo ll eseed odels (..4.. 4 = ). Tus te uy of te esetive odel is estited egdless of te seifi bsi vlue of te utting foe. Te diffeene between te eiil odels oding to efeene dt nd te suggested new ones desibing te deendene of seifi utting foe on te tiness of ut is deteined using te following foul: Δ = % = %. (3) Te lultions e done fo soe tinesses of te ut =. 5. tt oxitely oesonds to te ost widely used feeds duing tuning f =. 7. 3 /. Te deendene of te devitions Δ of te vious odels on te tiness of ut fo te diffeent teils is sown in fig. 5. Fo bon steel te sllest devitions e ieved using te C odel (-9.3 3.7 %), wi e lge in te B odel (-8.5. %) nd te lgest ones using te A odel (-7..7 %). Genelly te devitions e eltively sll nd e oble to te eltive eo of te suggested new odel. Fo bonze tee e signifint devitions. Te sllest devitions e te ones fo te B odel (-..9), lge e in te A odel (-7. 33.3) nd te lgest in te C (- 4.4 6. %). Fo te woiee teil luiniu lloy te odels A nd B ve te sllest devitions (- 3.9 7.) nd C s te lgest (-8. 9.9%). 3 Toe IX (Ye ). Fsiule 3. ISSN 584 673
ANNALS OF FACULTY ENGINEERING HUNEDOARA Intentionl Jounl Of Engineeing Sizble devitions lso ou wit te woiee teil gy ion. Te C odel s te sllest devitions (-7.9 8.3%) nd te A odel s te lgest ones (-.9 36.6%). Te devitions of te suggested odels fo te seifi utting foe oding to efeene dt fo bonze, luiniu lloy nd st ion e too lge nd y led to signifint eos if used to lulte te utting foes. CONCLUSIONS Te following onlusions n be de fo te nlysis tt s been done: ) Liit onditions ve been defined bsed on te teoetil deendenies of te seifi utting foe nd te ysil ntue of te utting oess enis. Te tetil odels used to oxite te deendene of te seifi utting foe on te tiness of ut wit wide nge vition ust oly wit tese liit onditions. b) Hyotetil gil deendenies f ( ) = fo dutile nd bittle wo teils nd yotetil odels fo te oxition of tese deendenies tt oly wit te liit onditions defined ve been suggested. ) A new ete of te seifi utting foe s been suggested liit seifi utting foe tt would ou fo vey lge tinesses of ut ( ), teisti fo etin wo teil. d) New tetil odels ve been eed nd suggested toug exeientl studies nd tetil oessing of te exeientl dt by Figue. 4. Deendenies of te devitions of te using sttistil nd ysil itei tt bette tetil odels oding to efeene dt oxite te deendene of te seifi utting on te tiness of ut: а)aisi W-.C steel; b) foe on te tiness of ut wit wide nge bonze CuSn7P.7 ; ) luiniu lloy vition fo ining vious teils duing AlCu4.5Mn.5Mg,6 ; d) gey ion GG5 tuning. e) Desite te liited volue of exeientl studies te suggested yotesis tt wit vey lge tinesses ( ) te seifi utting foe is onstnt vlue fo etin utting onditions n be ffied. f) Te exeientl tests onfi te tesis tt fo bittle teils te deese of te seifi utting foe is ostly due to te deese of its oonent wi is esult of te jo fln fition foe. Bsed on te study of te uy of te eiil tetil odels oding to efeene dt oed to te new eoended odels. It s been estblised tt fo soe odels nd soe wo teils te devitions e in soe ses insignifint but fo otes te devitions y e u to 4%-5%. As esult wen lulting te utting foes by using su odels soe signifint eos y ou. REFERENCES [.] O. Kinzle. Die Bestiung von Käffen und Leistungen n snenden Wezeuden und Wezeugsinen. VDI Z 94 (95)./, 99-35 (in Gen). [.] W. Degne, H. Lutze, E. Seil, Snende Foung : Teoie, Beenung, Ritwete, Münen, Wien, C. H. Velg, 993. [3.] G. Su, T. Stefele. Hndbu de Fetigungstene. Vol., Mosw, Msinostoenie, 985 (in Russin). [4.] SANDVIK Coont. TenilCuide.. [5.] W. König, K. Essel. Sezufise Sittftwete die Zesnung etllise Westofe. Velg Stleisen, Düsseldof, 973 (in Gen). [6.] J. Fleise, V. Sulze nd J. Koteneute. Extension of utting foe foule fo ioutting. CIRP J. Mnuf. siene Tenol.Vol., iss.. (9), 75-8. [7.] Refeene boo of te tenologist of ining. Vol.. Edited by S. Psov. Teni, Sofi, 99 (in Bulgin). [8.] K. Adi nd F. Isil. Mining tte in fln illing. Intentionl Jounl of Mine Tools nd Mnuftue, 5 (), 75-85. [9.] E. Diez Cifuentes, N. Peez Gi, M. Guzn Villenseno nd A. Vitn Idoie. Dyni nlysis of unout oetion in illing. Intentionl Jounl of Mine Tools nd Mnuftue, 5 (), 79-77. oyigt FACULTY of ENGINEERING HUNEDOARA, ROMANIA 3
ANNALS OF FACULTY ENGINEERING HUNEDOARA Intentionl Jounl Of Engineeing [.] M. Aif., M. Rn nd E.-Y. Sn. Anlytil odel to deteinte te itil feed e edge fo dutile-bittle tnsition in illing oess of bittle teils. Intentionl Jounl of Mine Tools nd Mnuftue, 5 (), 7-8. [.] M.-Y. Wng, nd H.-Y. Cng. A siultion se eo fo end illing AL66-T6. Int. J. Adv. Mnuf. Tenol. vol.,, 3, 689-696. [.] C. Andeson, M. Andeson nd J.-E. Stl. Exeientl studies of utting foe vition in fe illing. Intentionl Jounl of Mine Tools nd Mnuftue 5, (), 67-76. [3.] O. Gonzlo, J. Beistin, H. Juege nd C. Snz. A etod fo te identifition of te seifi foe oeffiients fo enisti illing siultion. Intentionl Jounl of Mine Tools nd Mnuftue, 5 (), 765-744. [4.] T. Ding, S. Zng nd Y. Wng. Eiil odels nd otil utting etes fo utting foes nd sufe ougness in d illing of AISI H3 steel, Int. J. Adv. Mnuf. Tenol., vol. 5 (), 45-55. [5.] S. Jybl, U. Ntjn. Otiiztion of tust foe, toque, nd tool we in dilling of oi-einfoed oosites using Nelde-Med nd geneti lgoit etods. Int. J. Adv. Mnuf. Tenol., vol. 5 (), 37-38. [6.] S. - T. Sing, C.-M.Tsi, A-C. Lee. Anlysis of utting foes in bll-end illing. Jounl of Mteils Poessing Tenology. Vol.47, (995), 3-49. [7.] W.-S. Yun, D.-W. Co. Aute 3-D uttung foe edition using utting ondition indeendent oeffiients in end illing. Intentionl Jounl of Mine Tools nd Mnuftue, 4, (), 463-478. [8.] G. Bootoyd, W. A. Knigt. Fundentls of Mining nd Mine Tools. Tid Edition, CRC Pess, Tylo & Fnis Gou. Bo Rton, 6, 573. [9.] Develoent of te Metl Cutting Siene, edited by N.N. Zoev, Mosow, Msinostoenie, 967, 46 (in Russin). [.] A. M. Vulf. Te utting of etls. Mosow, Msgiz, 968 (in Russin). [.] Y.-M. Lee, S.-H. Yng, S.-I. Cng. Assessent of i-being teistis using new i-being index. J. Mt. Po. Te. 73 (6), 66-7. [.] A. Mitov, P. Nenov, D. Minov nd T. Todoov. Aoxition of funtion wit one vible. VTU A.Knev, Rousse, 98 (in Bulgin). [3.] I. Kolev. Mtetil odels of seifi utting foe in tuning etodology fo deteining of oeffiients. Univesity of Ruse, Poedings. Vol. 49, boo, (), 4-8, (in Bulgin). [4.] N. De, H. Sit, Alied Regession Anlysis. Mosow, Sttisti, 973, 39 (in Russin). [5.] A. Mitov, D. Minov. Mtetil Metods of engineeing ese. V.T.U. A. Knev, Rousse, 985 (in Bulgin). ANNALS OF FACULTY ENGINEERING HUNEDOARA INTERNATIONAL JOURNAL OF ENGINEERING oyigt Univesity Politeni Tiiso, Fulty of Engineeing Hunedo, 5, Revolutiei, 338, Hunedo, ROMANIA tt://nnls.fi.ut.o 3 Toe IX (Ye ). Fsiule 3. ISSN 584 673