© Strojni{ki vestnik 47(2001)1,45-52 © Journal of Mechanical Engineering 47(2001)1,45-52 ISSN 0039-2480 ISSN 0039-2480 UDK 621.9:621.9.025.7:536.5 UDC 621.9:621.9.025.7:536.5 Predhodna objava (1.03) Preliminary paper (1.03) Analiza temperatur in toplotne energije pri odrezavanju An Analysis of Temperatures and Thermal Energy during Cutting Matja` Milfelner - Franci ^u{ V predstavljenem prispevku je opisana analiza temperatur in energij, ki se pojavijo med postopkom odrezavanja. Vpliv temperature na rezalno ploskev in rob rezalne ploščice je zelo pomemben, ker povzroči obrabo cepilne ploskve in rezalnega roba orodja, s tem pa se zmanjša obstojnost orodja. V zadnjem delu prispevka je prikazan primer simuliranja porazdelitve temperature na rezalnem robu orodja pri spremembi rezalne hitrosti in geometrije orodja. © 2001 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: temperature, energije toplotne, ploskve strižne, ploskve cepilne) This paper describes an analysis of the temperatures and energies which occur during the cutting process. The influence of the temperature on the cutting face and the cutting insert edge is very important since it causes wear of the tool face and of the tool cutting edge and thus the tool’s resistance to wear is reduced. The final part of the paper shows an example of a simulation of the isothermal lines on the tool cutting edge for the case of a change of cutting speed and a change of the tool geometry. © 2001 Journal of Mechanical Engineering. All rights reserved. (Keywords: temperature, thermal energy, shear plane, tool face) 0 UVOD Pri obdelavi materiala z odrezavanjem je pomembnih več temperatur. Med te temperature prištevamo temperaturo v strižni ravnini fl, ki vpliva na potek napetosti v strižni ravnini in temperaturi na cepilni ploskvi 9T in prosti ploskvi fl rezalne ploščice. Temperatura na cepilni ploskvi 9T povzroča obrabo na cepilni ploskvi v obliki kotanje, temperatura na prosti ploskvi fl pa obrabo proste ploskve. 1 TOPLOTNE RAZMERE PRI ODREZAVANJU Pri procesu odrezavanja oziroma tvorbi odrezka nastala mehanska energija se spreminja v toplotno energijo. Vir toplote pri odrezavanju z ostrim rezalnim robom rezalne ploščice razdelimo v dve področji: (slika 1a) - prvo z virom v strižni ravnini (1) in - drugo z virom na cepilni ploskvi (2). Po prvih ugotovitvah o spremembah energije pri procesu odrezavanja lahko predpostavimo da: [1] (slika 1b) 0 INTRODUCTION During machining several temperatures are important: the temperature in the shear plane qS, which influences the distribution of stresses in the shear plane; the temperature on the tool face qT; and the temperature on the free face qR of the cutting insert. The temperature on the tool face qT causes wear on the tool face in the form of a crater, whereas the temperature on the free face qR causes wear of the free face. 1 THERMAL CONDITIONS DURING CUTTING The mechanical energy produced during the cutting process and/or chip formation is transformed into thermal energy. The heat source during cutting with the sharp cutting edge of a cutting insert com-prises two areas: (Figure 1a) - the area with the source in the shear plane (1); - the area with the source on the tool face (2). On the basis of the first findings about the transformation of energy during the cutting process it is possible to assume that: [1] (Figure 1b) isfFIsJBJbJJIMlSiCšD I stran 45 glTMDDC M. Milfelner - F. ^u{: Analiza temperatur - An Analysis of Temperatures - se vsa energija, ki nastane v točki (1 - strižna ravnina) in (2 - cepilna ploskev) spremeni v toplotno energijo, energija iz točke 1 in 2 se usmeri na cepilno in prosto ploskev in energija je v točkah 1 in 2 enakomerno porazdeljena. Tudi z uporabo teh predpostavk je določitev glavnih temperatur, to je temperature na cepilni in prosti ploskvi rezalne ploščice, zelo zahtevna. To je predvsem zato, ker se del energije iz točke 1 odvede v odrezek vzdolž cepilne ploskve, drugi del pa v proces. Prav tako se en del energije iz točke 2 odvede v - all energy occurring at points 1 (shear plane) and 2 (tool face) is transformed into thermal energy; - the energy from points 1 and 2 is directed onto the tool face and the free face; - the energy at points 1 and 2 is uniformly distrib-uted. Even with these assumptions the determination of the main temperatures, i. e. the temperatures on the tool face and on the free face of the cutting insert, is very demanding because some of the energy from point 1 moves to the chip along the tool face and the rest to the process. Also a part of the energy from (2) is conveyed to the chip and the other to the tool. Sl. 1. Toplotne razmere pri pravokotnem odrezavanju Fig. 1 Thermal conditions during orthogonal cutting Četrta predpostavka pri analizi postopka odrezavanja je, da se toplotna energija, ki nastane pri nastanku odrezka, ne izgublja v okolico. To pomeni, da je energija na enoto prostornine, ki preide v odrezek v strižni ravnini (1) enaka: The fourth assumption in the analysis of the cutting process is that the thermal energy generated during chip formation is not lost to the environment. This means that the energy per unit volume going to the chip in the shear plane (point 1) is equal to: UC1=R1-u u 1S (1) in energija na enoto prostornine, ki preide v odrezek na cepilni ploskvi (2) enaka: and that the energy per unit volume going to the chip on the tool face (point 2) is equal to: C2 pri čemer sta u in u specifični energiji pri strigu in trenju. 2 ANALIZA TEMPERATUR IN TOPLOTE Z uporabo dimenzijske analize lahko določimo temperature pri procesu odrezavanja za praktično uporabo. Prvi, ki je uporabil dimenzijsko analizo za rešitev problema temperature na cepilni UC2=R2-u u 2F (2), where uS and uF are specific energies in the shear and the friction. 2 AN ANALYSIS OF TEMPERATURE AND HEAT By means of dimensional analysis it is pos-sible to determine the temperatures in the cutting process for a practical application. Kronenberg [2] was the first to apply dimensional analysis to solve maimskixmmm VH^tTPsDDIK stran 46 M. Milfelner - F. ^u{: Analiza temperatur - An Analysis of Temperatures ploskvi rezalne ploščice, je bil Kronenberg [2]. Na podlagi svojega širokega znanja in izkušenj je utemeljil, da velikost povprečne temperature na cepilni ploskvi rezalne ploščice 9T lahko opišemo z enačbo, če vanjo vključimo spremenljivke, zapisane v preglednici 1. the problem of the temperature on the tool face of the cutting insert. On the basis of his knowledge and experience he postulated that the mean temperature on the tool face of the cutting insert qT can be de-scribed by an equation which use the quantities listed in table 1. Preglednica 1. Kronenbergove veličine za dimenzijsko analizo Table 1. Kronenberg’s quantities for dimensional analysis Veličina Quantity Simbol Symbol Enota Unit povprečna temperatura na cepilni ploskvi mean tool-face temperature q T K rezalna hitrost cutting speed V m/min nedeformirani prerez odrezka undeformed-chip area A mm2 specifična rezalna sila specific cutting energy kc MPa toplotna prevodnost thermal conductivity k W/mK specifična prostorninska toplota volume specific heat rC J/m3K V preglednici 1 imamo štiri dimenzijsko neodvisne veličine V, k, k in rC. Te štiri dimenzijsko neodvisne veličine lahko povežemo v enačbo v kombinaciji z eno od preostalih dveh nedimenzijskih veličin qT in A. Ti dve veličini sta dobljeni na podlagi načela o dimenzijski homogenosti. Iz te dimenzijske enačbe dobimo enačbo za povprečno temperaturo na cepilni ploskvi orodja: Table 1 lists four dimensionally independent quantities i. e. V, kc, k and rC. They can be combined in an equation with one of the other two non-dimen-sional quantities qT and A. These two quantities are obtained on the basis of the principle of dimensional homogeneity. From this dimensional equation the equation for the mean temperature on the tool face is obtained: T-(r-C)_lA-V2-(r-C)2 Vrednosti za vse te veličine dobimo pri Gottwein-u [3]. Razmerje med obema stranema enačbe je prikazano v diagramu na sliki 2. Os X predstavlja desni del enačbe, os Y pa levi del enačbe. Če je dimenzijska analiza pravilna, potem je krivulja v diagramu premica. Enačbo (3) izboljšamo tako, da veličino A=b-t - nedeformiran prerez odrezka nadomestimo s t - nedeformirano debelino odrezka, ker ima b - nedeformirana širina odrezka zanemarljiv vpliv na qT, medtem ko ima t zelo velik vpliv. Naslednja izboljšava je v tem, da upoštevamo količnik k/rC kot eno spremenljivko namesto dveh posameznih spremenljivk k in rC. Vse ostale Kronenbergove spremenljivke so bile dobro izbrane. V preglednici 2 so prikazane izboljšane veličine, ki vodijo do enojne nedimenzijske veličine in iz tega izhaja, da je povprečna temperatura na cepilni ploskvi rezalne ploščice: (3). The data on all these quantities are available from Gottwein [3]. The relation between both sides of the equation is shown in the diagram in figure 2. The X-axis represents the right-hand side of the equation and the Y-axis represents the left-hand side of the equation. If the dimensional analysis is correct, the curve in the diagram is a straight line. Equation 3 is improved by replacing A=b-t of the undeformed chip area, by t, the undeformed chip thickness, because the undeformed chip width b has a negligible influence on qT, whereas t has an appreciable influence. The situation is further improved by considering the quotient k/rC rather than the individual quantities k and rC. All the other Kronenberg variables were correctly selected. Table 2 shows the improved quantities leading to a single non-dimensional quantity and using this we can calculate that the mean temperature on the tool face of the cutting insert: 1 V-t k/r-C (4). gfTTMBfeflMISCSD stran 47 M. Milfelner - F. ^u{: Analiza temperatur - An Analysis of Temperatures 2 ( C ) 2 k2 Sl. 2. Gottweinov diagram Fig. 2. Gottwein’s diagram Preglednica 2. Izboljšane Kronenbergove veličine za dimenzijsko analizo Table 2. Improved Kronenberg quantities for the dimensional analysis Veličina Quantity Simbol Symbol Enota Unit povprečna temperatura na cepilni ploskvi mean tool-face temperature q T K rezalna hitrost cutting speed V m/min nedeformirana debelina odrezka undeformed chip area t mm specifična rezalna hitrost specific cutting energy u J temperaturna difuzivnost temperature diffusivity k/rC m2/s Na prvi pogled enačba (4) prikazuje, da sta V in t enako pomembna glede na 6T. To lahko prikažemo z drugo enačbo, v kateri določimo temperaturo v odvisnosti od rezalne hitrosti V in nedeformirane debeline odrezka t iz eksperimentalnih vrednosti: At first glance equation 4 suggests that V and t are equally important with respect to qT. How-ever, qT can be represented by another equation in which the temperature is determined in terms of the cutting speed V and the undeformed chip thickness t from experimental values: 0*V0,5-t0,3 (5). Povprečno temperaturo v strižni ravnini določimo na temelju privzetega modela, ki sloni na Piispanenovem modelu nastanka odrezka. Pri procesu nastanka odrezka se lastnosti v strižni ravnini spreminjajo, zato lahko strižno ravnino opišemo kot gibljivi toplotni vir. Povprečno temperaturo v strižni ravnini določimo z enačbo [4]: 6S =0,754-R1uS pri čemer so: V - rezalna hitrost, t - nedeformirana debelina odrezka, g - strižna deformacija, pC - The mean temperature in the shear plane is determined on the basis of the adopted model based on Piispanen’s model of chip formation. During the process of chip formation the properties in the shear plane change, so the shear plane can be described as a mobile heat source. The mean temperature in the shear plane is determined by equation [4]: V-tg n, ^+00 (6), (k/p ¦ C) where V is the cutting speed, t is the undeformed chip thickness, g is the shear deformation, pC is the grin^SfcflMISDSD VH^tTPsDDIK stran 48 M. Milfelner - F. ^u{: Analiza temperatur - An Analysis of Temperatures specifična prostorninska toplota in k - toplotna prevodnost. Koeficient R1 določimo iz enačbe: specific volume heat and k is the heat conductivity. The coefficient R1 is determined from the equation: 1 1+1,328 (7). V-t Specifično strižno energijo uS izračunamo po enačbi [5]: uS= The specific shear energy uS is calculated according to equation [5]: FS-VS V -t -b-csc( je: Dq (k/p-C) The shear plane length lS = t/sin (0). The difference in the temperature in the shear plane D6>is: (10). Povprečno zvišanje temperature na površini odrezka zaradi trenja določimo po enačbi: (k/p-C) The mean temperature increase on the chip surface due to friction is determined according to the equation: Dq kjer je a dolžina stika med orodjem in odrezkom. Specifično energijo trenja uF odrezka ob cepilno ploskev izračunamo po enačbi (6): VC-a (11), (k/p-C) where a is the length of the contact between the tool and the chip. The specific energy of friction uF of the chip against the tool face is calculated according to equation (6): FC-VC V-t-b (12), pri čemer sta FC - strižna sila in VC - hitrost odrezka. Povprečno zvišanje temperature na cepilni ploskvi je vsota temperature v strižni ravnini in temperature zaradi trenja: Where FC is the shear force and VC is the chip speed. The mean temperature increase on the tool face is the sum of temperature in the shear plane and the temperature due to friction: DqT @qS + DqF (13). Prav tako je specifična rezalna energija vsota specifične strižne energije in specifične energije trenja: In addition, the specific cutting energy is the sum of the specific shear energy and specific energy of friction: u@u +u (14). Na koncu lahko iz rezultata dimenzijske analize definiramo, da je povprečna temperatura na cepilni ploskvi: In the end it is possible to define, on the basis of the result of the dimensional analysis, the mean temperature on the tool face to be: V-T k/ p C (15). Sin^ObJJPsflDslJSD I stran 49 glTMDDC M. Milfelner - F. ^u{: Analiza temperatur - An Analysis of Temperatures 3 PRIKAZ TEMPERATURE NA REZALNEM ROBU V prikazanem primeru je predstavljen potek temperature na konici rezalne ploščice [7]. Simuliranje je izvedeno na podlagi metode končnih elementov in prikazuje izotermo porazdelitev temperature na rezalnem robu, odrezku in obdelovancu. Prvi primer prikazuje porazdelitev temperature pri spremembi rezalne hitrosti. Parametri odrezavanja so prikazani v naslednji preglednici: 3 REPRESENTATION OF TEMPERATURE ON THE CUTTING EDGE The example shows the areas of temperature on the cutting insert tip [7]. The simulation is made on the basis of the finite element method (FEM) and shows the isothermal lines of temperature on the cutting edge, chip and workpiece. The first example shows the isothermal lines of temperature for the case of a change of cutting speed. The cutting parameters are shown in the fol-lowing table: rezalna hitrost cutting speed rezalna sila cutting force podajanje feed globina reza depth of cut cepilni kot rake angle radij rezalnega roba cutting-edge radius material orodja tool-insert material material obdelovanca workpiece material 914, 1220 935, 956 0,254 mm/vrt 6,35 mm 20 karbidna trdina tungsten carbide m/min N o 0,025 mm AL6061-T6 2.5 2 1.5 ' 0.5 I 450 419 3S-8 358 3?7 296 2RR 2:-5 204 174 143 Obdelovanec Workpiece 4.5 5.5 6.5 7 7.5 Sl. 3. Sprememba temperature pri različnih rezalnih hitrostih Fig. 3 Change of temperature for the case of different cutting speeds 0,12 0.08 Temperatura (F) TerrperatL :•=¦" o.ce 0.04 0.12 0.1 h o.oe 0.06 0.04 Temperatura (F) Temperature (F) 1250 lies 1081 Vr>~ 913 829 /!'¦ CCCi 576 +9' 4-117 323 239 154 70 Obdelovanec Workpiece 0.2 0.25 Sl. 4. Sprememba temperature pri različni obliki rezalnega roba Fig. 4. Change of temperature for the case of a different cutting-edge shape grüT^dfcflMieKn VBgfFMK stran 50 Orodje Tool M. Milfelner - F. ^u{: Analiza temperatur - An Analysis of Temperatures V drugem primeru je prikazana porazdelitev temperature pri spremembi oblike rezalnega roba in cepilnega kota [8]. Parametri so: rezalna hitrost cutting speed podajanje feed globina reza depth of cut cepilni kot rake angle radij rezalnega roba cutting-edge radius material orodja tool-insert material material obdelovanca workpiece material 4 SKLEP V današnjem času se je z uvajanjem novih obdelovalnih sistemov povečala potreba po vse boljšem rezalnem materialu in natančnih informacijah o postopkih obdelave in parametrih, ki vplivajo na proces odrezavanja [9]. Za določitev parametrov, ki vplivajo na proces pri odrezavanju, uporabimo programe za analizo in simuliranje. Glede na opravljeno simuliranje in raziskave smo ugotovili in priporočamo za obdelavo materiala AL6061-T6 orodje iz karbidne trdine in delo z naslednjimi tehnološkimi parametri: rezalna hitrost Vc = 1220 m/min, podajanje f = 0,254 mm/vrt in globina rezanja a = 6,35 mm. Razlika temperature je pri povečanju hitrosti od 914 do 1220 m/min približno 20°C. Za struženje jekla X5CrNiMo17122 pa priporočamo rezalno orodje iz karbidne trdine (M20-M30 GC2025) in geometrijo rezalne ploščice g = 15° in r = 0,025 mm ter naslednje tehnološke parametre odrezavanja: rezalna hitrost Vc = 144 m/min, podajanje f = 0,12 mm/vrt in globina rezanja a = 2 mm. S takim prijemom bomo dosegli najboljše rezultate odrezavanja. The second example shows the isothermal lines of temperature for the case of a change of shape of the cutting edge and rake angle [8]. The parameters are: 144 m/min 0,12 mm 2 mm/vrt 15, 20 tungsten carbide X5CrNiMo17122 ° 0,025 mm 4 CONCLUSION The introduction of new manufacturing systems means there is a need for better cutting materials as well as accurate information on the machining process and the parameters influencing the cutting process [9]. Programs for the analyses and for the simulation were used to determine of the parameters which influence the cutting process. The results of the simulation and experiments reported here support the following conclusions. For machining of the material AL6061-T6 we recommend a tungsten-carbide cutting insert with the following cutting conditions: cutting speed Vc = 1220 m/min, feed f = 0,254 mm/rev and depth of cut a = 6,35 mm. The example shows that in the case of an increase in speed from 914 to 1220 m/min the temperature increases by about 20°C. The recommended cutting conditions and geometry of the cutting insert for machining the material X5CrNiMo17122 with a tungsten-carbide cutting insert (M20-M30 GC2025) are: rake angle g =15°, cutting-edge radius r = 0,025 mm, cutting speed Vc = 144 m/min, feed f = 0,12 mm/rev and depth of cut a = 2 mm. Using this approach the best cutting results can be obtained. 5 LITERATURA 5 REFERENCES [1] Shaw, M. C. (1984) Metal cutting principles. Oxford Univerity Press, New York. [2] Kronenberg, M. (1954) Grundzüge der Zerspanungslehre. Springer Verlag Berlin. [3] Gottwein, K. (1925) Maschinenbau 4, 1129. [4] Loewen, E. G, M.C. Shaw (1954) Trans. Am. Soc. Mech Engrs 76, 217. [5] Leone, W. C.(1954) Trans. Am. Soc. Mech Engrs 76, 121. [6] Hahn, R. S.(1951) Proc. First U.S. Nat. Cong. Appl. Mech., 661. [7] Kopač, J. (1998) Influence of cutting material and coating on tool quality and tool life. Journal of Materials Processing Technology, Vol.78 No.1-3, 95-103. gfin^OtJJlMISCSD stran 51 M. Milfelner - F. ^u{: Analiza temperatur - An Analysis of Temperatures [8] Čuš, F. (2000) The inclusion of the geometrical shape of the cutter into the optimization of the milling process. Int. j. adv. manuf. technol., vol. 16, no. 6, 392-403. [9] Čuš, F.(1997) Analiza suhega rezanja pri postopku čelnega frezanja - Analysis of dry cutting in the process of face milling. Strojniški vestnik, let. 43, št. 3/4, 153-159. Naslov avtorjev: Matjaž Milfelner profdr. Franci Čuš Inštitut za proizvodno strojništvo Fakulteta za strojništvo Univerza v Mariboru Smetanova 17 2000 Maribor Authors’ Address: Matjaž Milfelner Prof. Dr. Franci Čuš Production Engineering Institute Faculty of Mechanical Eng. University of Maribor Smetanova 17 2000 Maribor, Slovenia Prejeto: Received: 15.9.2000 Sprejeto: Accepted: 12.4.2001 grin^SfcflMISDSD VH^tTPsDDIK stran 52