© Strojni{ki vestnik 50(2004)10,446-461 © Journal of Mechanical Engineering 50(2004)10,446-461 ISSN 0039-2480 ISSN 0039-2480 UDK 621.914:519.85 UDC 621.914:519.85 Izvirni znanstveni ~lanek (1.01) Original scientific paper (1.01) Sistem za spremljanje in optimiranje postopka frezanja z uporabo genetskih algoritmov A System for Monitoring and Optimizing the Milling Process with Genetic Algorithms Matja` Milfelner - Franci ^u{ V prispevku je predstavljen sistem za spremljanje in optimiranje postopka frezanja z oblikovnim krogelnim frezalom. Sistem združuje različne metode in tehnologije, to so: evolucijske metode, tehnologija obdelave, merilna in nadzorna tehnologija, inteligentna postopkovna tehnologija s podporo ustrezne programske in strojne opreme. Sistem za spremljanje in optimiranje postopka frezanja združuje sistem za spremljanje postopka frezanja in model optimiranja. Sistem za spremljanje postopka frezanja je namenjen spremljanju in zbiranju veličin odrezovalnega postopka z uporabo zaznaval in spremembo teh podatkov v numerične vrednosti, ki so izhodišče za optimiranje postopka frezanja z oblikovnim krogelnim frezalom. Z modelom optimiranja določamo rezalne parametre pri postopku frezanja na podlagi analitičnega modela rezalnih sil ter modela obstojnosti orodja z genetskim algoritmom. Sistem uporabimo za napovedovanje rezalnih sil, optimiranje rezalnih parametrov, zmanjšanje celotnega časa obdelave, povečanje natančnosti, zanesljivosti, produktivnosti in zmanjšanje stroškov obdelave. © 2004 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: optimiranje odrezovanja, sile rezanja, parametri rezanja, frezala oblikovna krogelna, algoritmi genetski) This paper presents a system for monitoring and optimizing the ball-end milling process. The system combines different methods and technologies, like evolutionary methods, manufacturing technology, measuring and control technology and intelligent process technology with the appropriate hardware and software support. The system for monitoring and optimizing the ball-end milling process combines the process monitoring system of the ball-end milling process and the optimization model. The monitoring system is designed for monitoring and collecting the variables of the milling process by means of sensors and the transformation of those data into numerical values, which are the starting point for the optimization of the ball-end milling process. The optimization model is used for the optimization of the milling parameters with genetic algorithms. The optimization is based on the analytical cutting-force model and the tool-wear model. The developed methods can be used for the cutting-force estimation and the optimization of the cutting parameters. The integration of the proposed system will lead to a reduction in the production costs and production time, flexibility in machining-parameter selection, and an improvement in product quality. © 2004 Journal of Mechanical Engineering. All rights reserved. (Keywords: optimization, cutting forces, cutting parameters, ball-end mill, genetic algorithms) 0 UVOD V prispevku je predstavljen razvoj sistema za spremljanje in optimiranje postopka odrezovanja, ki je prikazan na postopku odrezovanja materiala (jekel) z oblikovnim krogelnim frezalom. Postopek frezanja je eden izmed najpomembnejših in vsestranskih postopkov obdelave materiala, s katerim lahko obdelujemo zapletene površine in oblike izdelkov. Z združitvijo 0 INTRODUCTION This paper presents a system for monitoring and optimizing the machining process, which is shown in detail in the process of machining steels with ball-end milling. The milling process has become a very important and useful procedure for the manufacture of 3D surfaces of different shapes. Due to the widespread use of highly auto- 0 S3"in3(šul[M]! ms stran 446 Milfelner M., ^u{ F.: Sistem za spremljanje - A System for Monitoring sodobnih večosnih, frezalnih strojev z velikimi hitrostmi pa se je v proizvodnji pojavila zahteva po spremljanju in optimiranju postopka odrezavanja. Namen je razviti inteligentni sistem za spremljanje in optimiranje postopka frezanja, ki bo zbiral podatke med samim postopkom odrezovanja ter s pomočjo teh postopek optimiral. Z uporabo sodobnih metod umetne inteligence smo razvili model za optimiranje rezalnih parametrov na osnovi izmerjenih vhodnih parametrov. Sistem za spremljanje in optimiranje postopka frezanja z oblikovnim krogelnim frezalom temelji na vrednostih izmerjenih rezalnih sil z dinamometrom, analitičnemu modelu rezalnih sil, modelu obstojnosti orodja ter optimiranju rezalnih parametrov z genetskim algoritmom (GA). Sistem bo namenjen inžinerjem za določevanje optimalnih rezalnih parametrov z najmanjšim številom preizkusov ter za zagotavljanje največjih zmogljivosti izbranih opravil na obdelovalnem stroju. 1 PREDSTAVITEV SISTEMA V zadnjem obdobju se je pojavila zahteva po vrhunski kakovosti izdelkov. Zaradi tega se inženirji srečujejo s težkimi nalogami - kako izboljšati produktivnost in ohraniti kakovost izdelkov. S povečevanjem rezalne hitrosti z namenom, da bi povečali produktivnost, se poslabša stabilnost sistema, kar vodi do preobremenitve stroja in zaradi tega do loma orodja. Pri tem je pomemben ustrezen nadzor obdelovalnega postopka s sistemom za spremljanje in optimiranje postopka odrezovanja. Z združitvijo obdelovalnih sistemov z veliko stopnjo avtomatizacije in prilagodljivosti v proizvodnji zagotovimo zanesljivost, natančnost in kakovost izdelka. Zahtevana velika prilagodljivost obdelovalnega postopka zahteva povečanje rezalnih parametrov. Rešitev tega problema je v razvoju sistemov za spremljanje in optimiranje postopka odrezovanja, ki temeljijo na metodah umetne inteligence. Cilj raziskave je razvoj prilagodljivega in zanesljivega sistema za spremljanje in optimiranje postopka odrezovanja (SOPO), ki je predstavljen na postopku frezanja z oblikovnim krogelnim frezalom (sl. 1). Sistem je razdeljen na naslednje dele: - tehnološki parametri, - sistem za spremljanje postopka frezanja, - model optimiranja rezalnih parametrov, - modul za posredovanje optimalnih rezalnih parametrov obdelovalnemu stroju. Sistem za spremljanje in optimiranje postopka odrezovanja je namenjen optimiranju postopka frezanja z genetskim algoritmom, s katerim optimiramo rezalne parametre ob vsaki spremembi rezalnih sil. S sistemom lahko prej napovemo vse pomembne veličine odrezovalnega postopka, ki se bodo kasneje dejansko pojavljale pri samem postopku obdelave. mated machine tools in industry, manufacturing requires reliable monitoring and optimization models and methods. The main objective of this paper is to de-velop an intelligent online monitoring and optimi-zation system for the ball-end milling process. By exploring the advantages of artificial intelligence methods, the optimization model is developed. The system for monitoring and optimizing the ball-end milling process is based on the measured cutting forces, the analytical cutting-force model, the tool-wear model and the optimization of cutting parameters with the genetic algorithm (GA). The devel-oped system will be applied to the manufacturing process for the determination of the optimum cut-ting parameters with the fewest number of experiments and the maximum cutting power on the tool machine. 1 PRESENTATION OF THE SYSTEM In recent years there has been an increase in the demand for high-quality products. Conse-quently, manufacturing engineers are faced with the difficult task of improving productivity without com-prising quality. The use of high machining speeds to increase productivity exacerbates the stability problems and might even lead to tool breakages in certain situations. This emphasizes the proper control of the machining process through an online monitoring and optimization system. The success of manufacturing systems with a high level of automation and flexibil-ity is the capability to strictly control the quality of the products, to guarantee working processes with a known reliability, and the availability of the whole system. The high flexibility required for the manufac-turing process also involves increasing the severity of the operating parameters. The solution to this problem is in the development of systems for monitoring and optimizing the cutting process based on artificial intelligence. The main objective of this research is to develop flexible and reliable system for monitoring and optimization (SOPO), which is shown on the ball-end milling process. (Fig. 1). The system is di-vided into: - technological parameters, - monitoring system, - optimization model, - response module. The system for monitoring and optimizing of the cutting process has been developed for the optimization with a genetic algorithm at various ob-tained cutting forces. The system can show all the important cutting process variables, which will later actually appear in the machining process itself. | lgfinHi(s)bJ][M]lfi[j;?n 0410 stran 447 I^BSSIfTMlGC Milfelner M., ^u{ F.: Sistem za spremljanje - A System for Monitoring Sl. 1. Sistem za spremljanje in optimiranje postopka odrezovanja Fig. 1. System for monitoring and optimizing the of machining process 2 REZALNE SILE PRI OBLIKOVNEM KROGELNEM FREZALU Frezanje z oblikovnim krogelnim frezalom je zelo pogost postopek obdelave, posebej v avtomobilski, letalski in preoblikovalni industriji [1]. Uporablja se za obdelavo prosto oblikovanih površin, kot so npr. utopi, matrice, votlice, kalupi, turbine, propelerji in letalski sestavni deli. Zaradi različnih vzrokov, kakor so konstrukcijski (strukturni), optimirani ali estetski videz, postajajo geometrijske oblike izdelkov vedno bolj zahtevne. Z uporabo RPN/RPI sistemov in RNK obdelovalnih centrov lahko izdelamo zelo zahtevne oblike površin z oblikovnim krogelnim frezanjem. Napovedovanje rezalnih sil pri frezanju z oblikovnim krogelnim frezalom je zelo pomembno. V fazi načrtovanja rezalnega postopka znanje o rezalnih silah pomaga tehnologu pri določevanju rezalnih parametrov za obdelavo. Napovedovanje rezalnih sil je v podporo pri načrtovanju postopka, izbiri primernih rezalnih razmer za zmanjšanje obrabe, deformacije in loma orodja, ter pri konstruiranju boljših vpenjalnih priprav, kar izboljša kakovost izdelka. Model rezalnih sil pri frezanju z oblikovnim krogelnim frezalom [2] je del združenega sistema SOPO pri frezanju z oblikovnim krogelnim frezalom. 2.1. Geometrijska oblika oblikovnega krogelnega frezala Geometrijska oblika frezala ima pomemben vpliv na karakteristiko rezalne sile pri frezanju z oblikovnim krogelnim frezalom. Pri oblikovnem krogelnem frezalu poteka rezalni rob orodja po 2 CUTTING FORCES IN BALL-END MILLING Ball-end milling is a very common machining process, especially in the automobile, aerospace, die and mould industries [1]. It is used for machining freely shaped surfaces such as dies, moulds, turbines, propellers, and for aircraft structural elements. For various reasons, such as the structural, optimization or esthetic points of view, nowadays, most industrial part geometries are becoming more and more complicated. The recent advances in CAD/ CAM systems and CNC machining centers allows us to supply this demand for machining very complex sculp-ture surfaces by ball-end milling. The importance of predicting the cutting forces in ball-end milling is evident. In the process-planning stage, knowledge of the cutting forces helps the process engineers to select “appropriate values” for the process parameters. The prediction of cutting forces gives support in the planning of the process, in selecting suitable cutting parameters for the re-duction of excessive wear, the deformation and break-age of the tool, and helps to design better fixtures that increase the quality of the parts. The cutting force model for ball-end milling [2] can be utilized in an intelligent system for monitoring and optimization in the ball-end milling process. 2.1 Geometry of a ball-end milling cutter Cutting-edge geometry plays a very impor-tant role in the cutting force characteristics in the ballend milling process, whereas the straight-end mill, ballend mill cutting-edge geometry varies locally in the ball 0 BnnBjfokJ][p)l]Olf|ifrSO | | ^SSfiflMlGC | stran 448 Milfelner M., ^u{ F.: Sistem za spremljanje - A System for Monitoring površini krogle. Prav tako kakor se spreminja lokalni kot vijačnice, se spreminja tudi polmer frezala R, ki vpliva na rezalne sile in rezalno hitrost. Amplituda in potek rezalne sile pri frezanju z oblikovnim krogelnim frezalom sta odvisna od: vrste in geometrijske oblike frezala, rezalnih parametrov ter materiala obdelovanca. Geometrijska oblika in rezalne sile pri oblikovnem krogelnem frezalu so prikazane na sliki 2. Rezalni rob frezala leži na površini poloble in je določen z nespremenljivim kotom vijačnice. Rezalni robovi imajo kot vijačnice lb na prehodu iz polokroglega dela frezala na valjasti del. Glede na zmanjšanje polmera frezala v ravnini X-Y proti konici frezala v smeri Z se spreminja kot vijačnice - lokalni kot vijačnice. Enačba ovojnice na polkrožnem delu frezala se glasi: part. For example, as well as varying the local helix angle, varying the radius R directly affects the cutting forces through its effect on the cutting velocity. The selection of the proper cutter/cutting-edge geometry, as well as other process factors, is very important over the amplitude and waveform of the generated cutting forces during the machining. The geometry and the cutting forces on the ball-end milling cutter are shown in Figure 2. The cutting edge of the milling cutter lies on the hemisphere surface and is determined with the constant helix angle. The cutting edges have the helix angle lb at the transition from the hemispherical part of the milling cutter into the cylindrical part With respect to the reduction of the milling cutter radius in the X-Y plane towards the milling cutter tip in the Z direction the helix angle - the local helix angle changes. The expression for the envelope of the ball part is given by: x2+y2+(R0-z)2=R02 (1) koordinata točke z, ki leži na rezalnem robu frezala, je: z = R0 - polmer polkrožnega dela frezala, y - kot med konico rezalnega roba pri z=0 in vzdolžno lego z, lb - kot vijačnice rezalnega roba frezala. Za frezala z nespremenljivo dolžino se lokalni kot vijačnice spreminja glede na polmer frezala in ga izračunamo po enačbi: The z - coordinate of the point located on the cutting edge of the milling cutter is: tan lb (2), R0 - radius of the hemispherical part of the milling cutter y - angle between the cutting edge tip in case of z=0 and the axial position z. lb - helix angle of the cutting edge of the milling cutter For the milling cutters of constant length the local helix angle changes with respect to the milling cutter radius and it is calculated according to the equation: tan lb (y) = • tan l R0 (3), R(y) - polmer orodja v ravnini X-Y glede na kot k. Kotna lega k v smeri osi Z od središča polkrožnega dela do točke na rezalnem robu je: k = arcsin Polmer rezalnega roba v ravnini X-Y, ki se dotika točke na spiralnem in krogelnem rezalnem robu pri kotu y, določimo: R(y) - tool radius in X-Y plane with respect to angle k The angular position k in the direction of the Z axis from the center of the hemispherical part to the point on the cutting edge: R(y) R0 (4). 0 The radius of the cutting edge in the X-Y plane, which touches the point on the helical and spherical cutting edge with angle y, is determined as follows: R(y) = 1-(ycotlb-1)2-R0 (5). Kotni razmik med rezalnimi robovi na frezalu: fP = Angular spacing between the cutting edge on the milling cutter: 360° Nf Nf - število rezalnih robov. Kotna lega rezalnega roba: Nf - number of cutting edges Angular position of the cutting edge: (j) yNq j = 1,2,...,Nq (6), (7), gfin^OtJJlMlSCSD 04-10 stran 449 |^BSSITIMIGC y -i~ dFR j \ lA i \ \dFT ni <9.: |C(z) dFR fz-sinq dFA Sl. 2. Rezalne sile in geometrijska oblika pri oblikovnem krogelnem frezalu Fig. 2. Cutting forces and geometry in the case of ball-end milling cutter Nq - število kotnih leg, q(j) - kotna lega rezalnega roba, fP - kotni razmik med rezalnimi robovi. Debelina vzdolžnih delov na rezalnem robu frezala: Nq - number of angular positions q(j) - angular position of cutting edges fP - angular spacing between cutting edges Thickness of axial differential elements on the cutting edge of the milling cutter: dz(i) = i\D AD - vzdolžna globina reza, N - število vzdolžnih delov na rezalnem robu frezala. Kotna lega rezalnega roba pri odrezovanju i = 1,2,...,Nz (8), AD - axial depth of cut N - number of axial differential elements on the cutting edge of the milling cutter Angular position of the cutting edge during cutting Y(ij,k): Y ( i,j,k ) = e( j ) + j>P ( k-1 ) - — -tanlb (9). Nedeformirano debelino odrezka lahko zapišemo z enačbo: The undeformed chip thickness is deter-mined as follows: hb=fz-sinY (10), fz - podajanje na zob. Debelina odrezka h b je funkcija prečnega in vzdolžnega kota: fz - feeding per tooth The chip thickness hb in the function of the radial and axial angle : 04-10 gfin^SfcflMISDSD | ^BSfiTTMlliC | stran 450 x z z C x A Milfelner M., ^u{ F.: Sistem za spremljanje - A System for Monitoring fz • sin Y • sin k (11), Y - kotna lega rezalnega roba pri odrezovanju v smeri vrtenja frezala, k - kotna lega v smeri osi z od središča polkrožnega dela do točke na rezalnem robu. Generalizirana enačba za debelino odrezka se glasi: Y - angular position of cutting edge during cutting in the direction of rotation of the milling cutter k - angular position in the direction of Z a x i s f r o m t h e c e n t e r of the hemispherical part to the point on the cutting edge The generalized equation for the chip thick-ness is as follows: hb(i,j,k) = fz-sin[_Y(i,j,k)}sin[k(i)] (12). Napaka v enačbi (12) za debelino odrezka se pojavi le v območju konice frezala [3]. Geometrijsko obliko oblikovnega krogelnega frezala in usmeritev rezalnega roba uporabimo v enačbah za določitev rezalnih sil. 2.2 Določitev rezalnih sil za oblikovno krogelno frezalo Enačbe za delno obodno dFT, prečno dFR in vzdolžno dFA rezalno silo so: The error in Equation (12) for chip thickness is significant only in areas around the ball tip [3]. The geometry of the ball-end milling cutter and the orientation of the cutting edge are used in the equation for the determination of the cutting forces. 2.2 Determination of the cutting forcess during ballend milling The equations for the differential tangential dFT, radial dFR and axial dFA cutting forces are: dFT = KT-hb-db = KT -fz ¦ sin Y¦ sin k¦db dFR dFA KR ¦ hb ¦ db = KR ¦ fz • sin Y • sin k ¦ db KA ¦ hb ¦ db = KA ¦ fz • sin Y • sin k ¦ db (13), KT - obodni koeficient materiala K - prečni koeficient materiala KA - vzdolžni koeficient materiala db - delna dolžina rezalnega roba, če namesto db vstavimo: dobimo: db = KT - tangential coefficient of material KR - radial coefficient of material KA - axial coefficient of material db - differential length of cutting edge if instead of db we enter: dz sin k we obtain: dFT=KT-fz-sinY-dz dFR=KR-fz-sinY-dz dFA=KA-fz-sinY-dz (14), (15). Posplošena enačba za obodno, prečno in vzdolžno rezalno silo se glasi: The generalized equation for the tangential, radial and axial cutting force is: in velja,če je kot Y(i,j,k): jEX < Y(i,j,k) < jENza protismerno frezanje, če je dFT (i, j, k) = KT-fz- sin \Y(i,j,k)\-dz dFR (i, j, k) = KR-fz- sin [Y (i, j, k)] ¦ dz dFA (i, j, k) = KA-fz- sin [Y (i, j, k)] ¦ dz if the angle Y(i,j,k) is: (16) jEX populacije / Generation S. of initial population J 1 1 Selekcija / Selection Križanje/ Crossover r < pc Mutacija / Mutation r < pm Ne No Optimalni rezalni parametri / Optimal cutting conditions fz, vc, AD, RD Sl. 4. Optimiranje rezalnih parametrov z genetskim algoritmom Fig. 4. Optimization of cutting parameters with the genetic algorithm 0 BnnBjfokJl[M]|f|ifrSfl | | ^SsFÜWEIK | 0,000 0,005 0,01 0 0,015 0,020 0,025 0,030 0,035 Cas t [ s] Milfelner M., ^u{ F.: Sistem za spremljanje - A System for Monitoring učinkovite rezalne parametre z uporabo hevrističnih metod. Zelo težko je razložiti logično povezavo med rezalnimi veličinami, ker so te odvisne od rezalnih parametrov (rezalne hitrosti Vc, podajanja fz, globine frezanja AD in širine frezanja RD). Iz tega razloga za določevanje in optimiranje rezalnih parametrov uporabimo genetske algoritme. Pri optimiranju rezalnih parametrov upoštevamo vse vplivne dejavnike, ki se pojavljajo pri postopku frezanja. Ob upoštevanju vseh naštetih predpostavk smo razvili model optimiranja na temelju genetskih algoritmov, ki je namenjen določevanju optimalnih rezalnih parametrov pri postopku frezanja z oblikovnim krogelnim frezalom. Model temelji na sprotnem optimiranju rezalnih parametrov, na podlagi rezalnih sil, zajetih s sistemom za spremljanje postopka frezanja. Optimiranje rezalnih parametrov (rezalne hitrosti V, podajanja fz, globine frezanja A in širine frezanja RD ) z genetskim algoritmom temelji na vrednostih rezalnih sil F, FY in FZ izmerjenih s sistemom za spremljanje postopka frezanja, analitičnemu modelu rezalnih sil in izkustvenem modelu obstojnosti orodja (sl. 4). 5 ANALIZA REZULTATOV Za potrditev sistema za spremljanje postopka frezanja in modela optimiranja smo opravili obsežno število preizkusov na NK frezalnem stroju, pri različnih parametrih frezanja. V tem poglavju so predstavljeni rezultati preizkusov ter primerjava in analiza rezalnih sil, v odvisnosti od rezalnih parametrov. 5.1 Uporabljena preizkusna oprema Razviti analitični model rezalnih sil za oblikovno krogelno frezalo uporabimo za napovedovanje rezalnih sil in optimiranje rezalnih parametrov. Za preizkuse smo uporabili: - RNK frezalni stroj MORI SEIKI FRONTIER - M, - merilno ploščo KISTLER 9259A, - material obdelovanca Ck45, - oblikovno krogelno frezalo tip R216.44-10030-040-AL10G - GC 1010 s premerom 10 mm, kotom vijačnice 30° inštirimi rezalnimi robovi. 5.2 Povezava med rezalno silo in rezalnimi parametri Rezalna sila F in rezalna hitrost V sta glavni vplivni veličini ma obdelovalnega postopka. Zmnožek rezalne sile in hitrosti je sorazmeren rezalni moči obdelovalnega stroja. Količina odvzetega materiala je glavno kazalo produktivnosti postopka odrezovanja. Velikost rezalne sile med odrezovanjem je odvisna od rezalnih parametrov (rezalne hitrosti V, podajanja fz, globine frezanja AD in širine frezanja R D). Povečanje rezalne hitrosti je prednost, ker povečuje logues, were optimized by heuristic methods. The formulation of the relations between the cutting quantities is very difficult because they depend on the cutting parameters (cutting speed Vc, feeding fz, axial depth AD, radial depth RD). For this reason the genetic algorithm was used for the op-timization of the cutting parameters. All the influ-encing factors that appear in the ball-end milling process were considered. By taking into account all the influenc-ing factors the genetic algorithm optimization model for ball-end milling was developed. The online optimization of the cutting parameters is based on the cutting forces collected by the monitoring system. The optimization of the cutting parameters (cutting speed Vc, feeding fz, axial depth AD, radial depth RD) is based on the meas-ured cutting forces FX, FY and FZ, the analytical cutting-force model and the empirical tool-wear model. (Fig. 4). 5 ANALYSIS OF THE RESULTS An extensive number of tests were made on the milling machine to confirm the monitoring system and the optimization model with different cutting parameters. This chapter presents the results of the experiments and the comparison and analysis of cutting forces depending on the cutting parameters. 5.1 Experimental setup The developed analytical cutting-force model for ball-end milling is applied for the cutting-force estimation and the optimization of the cutting parameters. The experimental model consists of: - CNC milling machine MORI SEIKI FRONTIER -M, - piezoelectric dynamometer KISTLER 9259A, -workpiece material Ck45, - solid ball-end milling cutter type R216.44-10030-040-AL10G - GC 1010 with four cutting edges, of 10 mm diameter and 30° helix angle, 5.2 Relationship between the cutting force and the cutting parameters The cutting force, F and the cutting speed, V, are the two main quantities for an efficient machining operation. Their product is proportional to the cutting power of the milling machine. The metal removal rate is the main indicator of the productivity of the cutting process. The cutting force developed during the machining can be controlled by varying the cutting parameters (cutting speed V, feeding fz, axial depth AD, radial depth RD). An increase of the cutting speed | lgfinHi(s)bJ][M]lfi[j;?n 0410 stran 455 I^BSSIfTMlGC Milfelner M., ^u{ F.: Sistem za spremljanje - A System for Monitoring Sl. 5. Največje rezalne sile v odvisnosti od rezalne hitrosti in podajanja Fig. 5. Relationship between the maximum cutting force, the cutting speed and the feeding količino odvzetega materiala. Rezalno hitrost je smiselno povečati do vrednosti, pri kateri največja rezalna sila ne preseže kritične vrednosti, ker to vodi do deformacije orodja, obdelovalnega stroja in obdelovanca. Na sliki 5 je prikazana vrednost največje rezalne sile F za frezalo R216.44-10030-040-AL10G v odvisnosti rezalne hitrosti V, podajanja fz, globine frezanja AD. 5.3 Določitev obstojnosti orodja z genetskim algoritmom Za določitev obstojnosti orodja v odvisnosti od največje rezalne sile F smo razvili izkustveni model obstojnosti. Izkustveni model je predstavljen v naslednji obliki: is an advantage; however, an the increase in cutting force is a disadvantage because no increase in the metal removal rate results from it, but rather larger deformations of the machine and workpiece occur. Figure 5 presents the maximum cutting force, Fmax, for the cutter R216.44-10030-040-AL10G, ac-cording to cutting speed Vc, feeding fz, and axial depth AD. 5.3 Estimation of tool wear using the genetic algorithm Based on the tool wear and the maximum cutting force, Fmax, a relationship for the empirical tool wear model is developed. It is proposed in the following format: Fmax=K1 + (K2-T)K (23), F - največja rezalna sila, T - obstojnost orodja v mm, K1, K, K - koeficienti obstojnosti. V izkustvenem modelu za določitev obstojnosti orodja imajo največji vpliv koeficienti obstojnosti. K1 je stopnja rezalne sile in je odvisen od rezalnih parametrov pri frezanju z oblikovnim krogelnim frezalom. K je gradient obstojnosti orodja, ki je odvisen od rezalnih parametrov, rezalnega orodja in materiala obdelovanca. Če je vrednost K majhna, potem se obraba orodja počasi zvečuje in nasprotno. Koeficient K pove, kako hitro se bo pojavil lom orodja, ko se rezalna sila poveča čez kritično vrednost. Vrednost koeficienta K3 je tem večja, čim trši je material obdelovanca oz. pri neprimernih rezalnih parametrih. Iz preizkusnih vrednosti največje rezalne sile F , zajete s sistemom za spremljanje postopka frezanja, lahko z uporabo genetskega algoritma določimo koeficiente obstojnosti. Program za določitev koeficientov obstojnosti je napravljen v programskem paketu MATLAB. Z genetskim Fmax - maximum cutting force T - tool life [mm] K1, K2, K3 - tool-wear coefficients. In the empirical tool-wear model, the tool-wear coefficients have their physical meaning. K1 is the cutting-force level, which depends on the cutting parameters of the ball-end milling opera-tions. K2 is the tool-wear gradient, which depends on the cutting parameters, the tool and the workpiece materials. A small K2 indicates slow progress of the wear. K3 represents how fast the tool is broken when the cutting force is above a critical level. The harder the workpiece material is or the more uncomfortable cutting parameters the tool has, the larger K3 is. From the experimental data of the maximum cutting force, Fmax, the coefficients of the proposed tool-wear model can be found by using the genetic algorithm. The program for the determination of the tool-wear coefficients was made with the program package MATLAB. The genetic algorithm is used to 0 BnnBjfokJ][p)l]Olf|ifrSO | | ^SSfiflMlGC | stran 456 Milfelner M., ^u{ F.: Sistem za spremljanje - A System for Monitoring algoritmom poiščemo optimalne koeficiente obstojnosti, ki jih uporabimo v modelu. Vsoto razlik rezalnih sil, dobljenih iz sistema za spremljanje postopka frezanja in rezalnih sil iz izkustvenega modela smo uporabili kot funkcijo uspešnosti. Funkcijo uspešnosti zapišemo kot: 1 N E - povprečna absolutna napaka Fmmaoxd ( e li) - največja rezalna sila, določena z modelom, Fmeakxsp ei riment - največja rezalna sila, dobljena s preizkusom. search for the optimum tool-wear coefficients, which will be used in the model. The sum of the difference between the experimental cutting-force data and the cutting force obtained from the developed model is used as the optimum objective function. The objec-tive function is: model (i) F eksperiment max(i) (24), E – average absolute error Fmmaoxd(ei)l - estimated maximum cutting force Fmeakxsp(ei)riment - experimental maximum cutting force Preglednica 1. Primerjava eksperimentalnih z izkustvenimi vrednostmi rezalne sile Fmax Table 1. The comparison of the experimental and empirical cutting forces Fmax Obstojnost orodja Tool life mm 19250 260,7 260,7 38500 280,0 280,2 57750 290,8 3 Povprečna napaka Average error Preizkus Experiment Fmax [N] 256,9 77000 326,3 327,1 96250 355,3 3 Izkustveni model Empirical model 246,7 302,6 353,3 115500 392,4 380,8 3,03 134750 429,3 409,6 4,81 173250 467,6 470,4 0,60 231000 536,4 568,3 5,62 Napaka Error % 4,14 0,01 0,10 3,92 0,24 0,58 2,30 Preglednica 2. Optimalni koeficienti obstojnosti Table 2. Optimum tool-wear coefficients Koeficienti obstojnosti Tool-wear coefficients R216.44-10030-040-AL10G K1 246,70577 K2 0,0004 K3 1,26198 Za določitev koeficientov obstojnosti pri frezanju s frezalom R216.44-10030-040-AL10G in rezalnimi parametri (širina frezanja RD = 0,4 mm, globina frezanja A = 0,4 mm, podajanje fz = 0,1 mm/zob, rezalna hitrost Vc = 188,5 m/min) smo izbrali naslednje vhodne parametre za delovanje genetskega algoritma. Velikost populacije 500 organizmov. Največje število generacij 30. Velikost posameznega kromosoma 10 bitov. Uporabili smo genetski operaciji križanje in mutacijo. Verjetnost križanja pc = 0,55 in mutacije pc = 0,1. Optimalne koeficiente obstojnosti je genetski algoritem našel v tretji generaciji s povprečno napako modela 2,30%. Izkustveni model obstojnosti orodja je prikazan v diagramu (sl. 6). For the determination of the tool-wear coeffi-cients in ball-end milling the R216.44-10030-040-AL10G milling cutter and cutting parameters (radial depth RD = 0.4 mm, axial depth A D = 0.4 mm, feeding fz = 0.1 mm/tooth, cutting speed Vc = 188.5 m/min) were used. The evolutionary parameters for the genetic al-gorithm were as follows: population size, 500; number of generations, 30; and number of genes for each chro-mosome, 10. The genetic operations known as crosso-ver and mutation were used. The probability of crosso-ver was pc = 0.55 and the probability of mutation was pc = 0.1. The optimum tool-wear coefficients were found in the 3rd generation with an average error of 2.30%. The empirical tool-wear model is presented in the diagram (Fig. 6). stran 457 bcšd04 Milfelner M., ^u{ F.: Sistem za spremljanje - A System for Monitoring Sl. 6. Izkustveni model obstojnosti orodja Fig. 6. Empirical tool-wear model 5.4 Optimiranje postopka frezanja z oblikovnim krogelnim frezalom Za optimiranje rezalnih parametrov pri frezanju z oblikovnim krogelnim frezalom smo razvili model optimiranja na podlagi genetskega algoritma. Algoritem smo napravili v programskem okolju MATLAB. Z algoritmom smo dokazali, da informacijo, ki jo dobimo iz izmerjenih rezalnih sil, lahko prepoznamo s predlagano metodo. Rezalne sile, obstojnost orodja in rezalne parametre pri frezanju z oblikovnim krogelnim frezalom lahko napovemo z majhnim številom generacij in z zadovoljivo napako. Algoritem daje hitre in natančne rezultate, ki jih lahko vključimo v postopek sprotnega spremljanja postopka frezanja. Pri frezanju z oblikovnim krogelnim frezalom je zelo pomembna določitev optimalnih rezalnih parametrov. Zaradi velikih rezalnih hitrosti, trdih materialov in majhnih premerov orodja lahko zelo hitro pride do loma orodja. Z neprimerno izbranimi rezalnimi parametri podaljšamo čas obdelave in zmanjšamo obstojnost orodja. Za tehnologa je zelo težko izbrati optimalne rezalne parametre pri zelo velikem številu različnih orodij, materialih obdelovanca in načinih obdelave. Rezalni parametri so optimirani glede na najmanjši obdelovalni čas, tako da poiščemo največje rezalne parametre, ki jih določimo glede na dobo trajanja orodja. Vsoto razlik največjih rezalnih sil, dobljenih iz analitičnega modela 5.4 Optimization of the ball-end milling process For the optimization of the cutting parameters in ball-end milling the genetic algorithm optimization model was developed. The optimization algorithm was made in MATLAB. The present model has been proven to provide a reliable optimization of the cutting process for ball-end milling. The cutting forces, the tool life and the cutting parameters in ball-end milling can be esti-mated in a few evolution generations with an accept-able error. The algorithm has a fast reaction and accu-rate results that can be applied to the online monitoring of the milling process. In ball-end-milling operations it is important to select the tool’s optimum cutting condi-tions. Because of the high cutting speeds and the hard materials the small tools are very easily broken. A con-servative selection of cutting parameters would result in a longer machining time, and other unsuitable selec-tions of cutting parameters would mean frequent tool changes, which also wastes machining time. It is very difficult for operators to select the optimum cutting parameters for so many different types of tools, workpieces and different machining tasks. The cutting parameters were optimized based on the minimum machining time to find the maximum cutting parameters that are able to meet the tool-life requirements for a specific machining task. The genetic algorithm was used to optimize the tool cutting parameters with the analytical cutting-force model. The sum of the difference of the maximum 0 BnnBjfokJ][p)l]Olf|ifrSO | | ^SSfiflMlGC | stran 458 Milfelner M., ^u{ F.: Sistem za spremljanje - A System for Monitoring rezalnih sil in rezalnih sil iz empiričnega modela, cutting forces, which were obtained from the analyti- smo uporabili kot funkcijo uspešnosti. Zapišemo cal force model and the empirical model, were used jo kot: for the objective function. The objective function is: oz. 13( X max Xmax Ymax Ymax Zmax Zmax Min(E)= F model -F dovoljena + F model -F dovoljena + F model -F dovoljena or Min(E) = Fmmaoxdel - Fm model dovoljena max )(25) (26) ob upoštevanju pogojev: Conditions: Fmodel ^ Fdovoljena Fmodel ^ Fdovoljena Fmodel ^ Fdovoljena Xmax Xmax , Y max Y max , Z max Z max , Fmodel ^ Fdovoljena Fmodel ^ Ypdovoljena Fmodel ^ Fdovoljena Xmax Xmax , Y max 7 max , Z max Z max , Fmodel ^ F max max dovoljena F model ^ F max max dovoljena E - absolutna napaka FXmodel , FYmodel , FZmodel, Fmmodel - največja rezalna sila, določena z analitičnim modelom, FXdovoljena FYdovoljena FZdovoljena Fmdovoljena dopustna največja rezalna sila glede , na obstojnost Za določitev optimalnih rezalnih parametrov smo izbrali optimiranje po dveh spremenljivkah (podajanju fz in rezalni hitrosti V). Izbrali smo naslednje vhodne parametre: velikost populacije 500 organizmov, število generacij 15 in velikost posameznega kromosoma 10 bitov. Uporabili smo genetski opravil križanje in mutacijo. Verjetnost križanja pc = 0,65 in mutacije pc = 0,1. Optimalne rezalne parametre je genetski algoritem našel v trinajsti generaciji z napako 0,28%. Evolucijski potek genetskega algoritma za določitev E - absolute error model model model model FXmmodaexl , FY mmoadxel , FZmmoadxel , Fmmaoxdel - maximum cutting forces calculated by the analytical cutting-force model FXd omvaoxljena , FYdmo vaoxljena , FZdmovaoxljena , Fmdaoxvoljena - maximum cut-ting forces determined by the tool-life estimation For the determination of the optimum cutting parameters the optimization of two variables (feeding fz and cutting speed Vc) was used. The evolutionary parameters for the genetic algorithm were as follows: population size, 500; number of generations, 15; and number of genes of each chromosome, 10. The genetic operations crossover and mutation were used. Probability of crossover was pc = 0.65 and the probability of mutation was pc = 0.1. The optimum cutting parameters were found in the 13th generation with an average error of 0.28%. The evolution of the genetic algorithm for the deter- - 2.0 1.5 1.0 0.5 0.0 Velikost populacije / Population size: M=500 Število generacij / No. of generations: G=30 Verjetnost križanja / Probability of crossover: p =0,65 Verjetnost mutacije / Probability of mutation: p =0,1 Napaka / Error : E-------- Rezalna sila / Cutting force F *100:-------- Podajanje / Feeding f : Rezalna hitrost / Cutting speed V *100: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Generacija / Generation Sl. 7. Evolucijski potek genetskega algoritma Fig. 7. Evolution of the genetic algorithm grin^OtJjiMiscsD 04-10 stran 459 |^BSSITIMIGC Milfelner M., ^u{ F.: Sistem za spremljanje - A System for Monitoring Preglednica 3. Optimalni rezalni parametri Table 3. Optimum cutting parameters Rezalni parametri Cutting parameters Vhodni parametri Initial parameters Optimalni parametri Optimum parameters Fmax 247,60 N 247,61 N RD 0,4 mm 0,4 mm AD 0,4 mm 0,4 mm fz 0,1 mm/zob (mm/tooth) 0,11 mm/zob (mm/tooth) Vc 188,5 m/min 199,5 m/min lm 100 mm 100 mm Tc 2,5 s 2,1 s Časovna razlika obdelave Cutting time difference 16,4 % optimalnih rezalnih parametrov je prikazan v diagramu (sl. 7). Iz dobljenih vrednosti vidimo, da se čas obdelave pri optimalnih rezalnih parametrih zmanjša za 16,4%. 6 SKLEP V prispevku je predstavljen razvoj sistema za spremljanje in optimiranje postopka frezanja z oblikovnim krogelnim frezalom. Sistem je namenjen spremljanju postopka frezanja in je preizkušen z velikim številom preizkusov, z različnimi rezalnimi orodji, materiali obdelovancev in rezalnimi parametri. Za optimiranje rezalnih parametrov smo razvili računalniški program z metodo optimiranja genetskih algoritmov. Sistem je namenjen spremljanju in napovedovanju rezalnih sil, obstojnosti orodja in optimiranju rezalnih parametrov. Osnovna zamisel, ki je opisana, je prikaz odnosov med orodjem in obdelovancem, določenim z analitičnim modelom rezalnih sil. Rezultati prikazujejo, da lahko razvite metode, predstavljene v prispevku, uporabimo za napovedovanje obstojnosti orodja, rezalnih sil, optimiranje rezalnih parametrov, povečanje natančnosti, zanesljivosti, produktivnosti ter zmanjšanje stroškov in časa obdelave. mination of the optimal cutting parameters is pre-sented in Fig. 7. With the optimum cutting parameters the machining time was reduced by 16.4 %. 6 CONCLUSION This paper presents a system for monitoring and optimizing the ball-end milling process. An extensive number of tests with different cutting tools, workpieces and cutting parameters, were performed to confirm the monitoring system. For the optimiza-tion of the cutting parameters in ball-end milling the genetic algorithm optimization program was devel-oped. The system is intended for cutting-force monitoring and the prediction of cutting forces, tool wear and the optimization of the cutting parameters. The basic concept included in the paper is the repre-sentation of the relations between the tool and the workpiece, determined by the analytical cutting-force model. Experimental results show that the proposed model presented in the paper can be used for tool-wear and cutting-force estimations, optimization of the cutting parameters, improvements to product ac-curacy, reliability, productivity and a reduction in pro-duction costs and production time. 7 LITERATURA 7 REFERENCES [1] Lee, P., Y. Altintas (1996) Prediction of ball end milling forces from orthogonal cutting data, International Journal of Machine Tools and Manufacturing, Vol. 36, 1059-1072, 1996. [2] Milfelner, M., F. Čuš (2003) Simulation of cutting forces in ball-end milling. Robotics and Computer Integrated Manufacturing, Vol. 19 (1/2), 99-106. [3] Ramaraj, T C. (1994) Analysis of the mechanics of machining with tapered end milling cutters, Transactions American Society for Mechanical Engineers, Vol. 116, 398-604. [4] Liao, T W., L.J. Chen (1998) Manufacturing process modeling and optimization based on multi-layer perceptron network, ASME, Journal of Manufacturing Science and Engineering, Vol. 120, 109-119. 0 S3"in3(aül[M]! ma stran 460 Milfelner M., ^u{ F.: Sistem za spremljanje - A System for Monitoring [5] Čuš, F., J. Balič (2003) Optimization of cutting process by GA approach, Robotics and Computer Integrated Manufacturing, Vol. 19, (1/2), 113-121. [6] Goldberg, E. E. (1989) Genetic algorithm in searching, optimization and machine learning, Addison-Wesley. [7] Hui, W. J., Y.G. Xi (1996) Operation mechanism analysis of genetic algorithm, Control Theory and Applica- tion, Vol. 13(3), 297-303. [8] Brezočnik, M. (2000) Uporaba genetskega programiranja v inteligentnih proizvodnih sistemih, Fakulteta za strojništvo, Maribor. [9] Kopač, J., S. Šali (2001) Tool wear monitoring during the turning process, Journal of Materials Processing Technology, Vol. 113, (1/3), special issue “5th APCMP, Seoul, Korea”, 312-316. Naslov avtorjev: dr. Matjaž Milfelner prof. dr. Franci Čuš Fakulteta za strojništvo Univerza v Mariboru Smetanova 17 2000 Maribor matjaz.milfelner@uni-mb.si franc.cus@uni-mb.si Authors’ Address: Dr. Matjaž Milfelner Prof. Dr. Franci Čuš Faculty of Mechanical Eng. University of Maribor Smetanova 17 SI-2000 Maribor, Slovenia matjaz.milfelner@uni-mb.si franc.cus@uni-mb.si Prejeto: Received: 21.4.2004 Sprejeto: Accepted: 30.9.2004 Odprto za diskusijo: 1 leto Open for discussion: 1 year stran 461 bcšd04