© Strojni{ki vestnik 48(2002)3,121-132 © Journal of Mechanical Engineering 48(2002)3,121-132 ISSN 0039-2480 ISSN 0039-2480 UDK 621.9.02:65.011.44 UDC 621.9.02:65.011.44 Pregledni znanstveni ~lanek (1.02) Preview scientific paper (1.02) Rezalne sile in njihov vpliv na gospodarnost obdelave Cutting Forces and Their Influence on the Economics of Machining Janez Kopa~ Rezalne in posebej specifične rezalne sile imajo značilen vpliv na stroške obdelave. Znanje in poznavanje prave tehnologije o obdelavi sta teoretična podlaga za prihranek energije v proizvodnji. Poznamo teoretične modele rezalnih in specifičnih rezalnih sil pri struženju, frezanju in vrtanju. Podane so kot vpliv obdelovanega materiala, postopka obdelave in tehnoloških parametrov. © 2002 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: obdelave z odrezavanjem, sile rezanja, prihranki energije, učinki ekonomski) Cutting forces, and especially specific cutting forces, have a significant influence on machining costs. Having the right knowledge and the right machining technology is a way of saving energy in the production process. There are theoretical models of cutting forces that specify the cutting forces during turning, milling, and drilling. In this paper we give an explanation of the influences of machining material, machining processes and technological parameters on cutting forces and economical machining. © 2002 Journal of Mechanical Engineering. All rights reserved. (Keywords: mechanical cutting, cutting forces, energy savings, economic effect) 0 UVOD Za obdelovalnost materiala so rezalne sile pri postopku pomemben kriterij. Zagotovljene informacije o pričakovanih komponentah rezalnih sil so pomembne zaradi spodaj naštetih razlogov. Od načrtovanih rezalnih sil med postopkom odrezovanja je odvisna potrebna moč stroja. Vrednost komponente rezalne sile povzroča, da se med postopkom odrezovanja deformirajo deli stroja, kar ima za posledico natančnost obdelave. Za razvoj sprotnega nadzora rezalnega postopka je pomembno poznavanje velikosti rezalnih sil v odvisnosti od materiala obdelovanca. Poleg tega pa rezalne sile določajo tudi meje pri optimiranju. Prava izbira rezalnega postopka in optimalnih tehnoloških parametrov znatno prihrani energijo pri obdelavi, kar neposredno vpliva na stroške. Vplivni dejavniki na velikost komponent rezalnih sil si sledijo po pomembnosti: a) način odrezovanja: neprekinjen oziroma prekinjen rez b) rezalni parametri: 0 PREFACE When it comes to the machinability of a material, the cutting forces used in the process are impor-tant criteria. Guaranteed information about the ex-pected cutting-force components is, moreover, par-ticularly significant for the following reasons. The forces occurring in the metal-cutting proc-ess provide information about the power require-ments of the machine and are therefore fundamental in the designing of the machine tool drive. Data on the cutting-force components are re-quired when designing the machine parts as the forces occurring during a cutting operation result in the deformation of certain machine elements, thus imparing the working accuracy of the machine. For developments in the field of adaptive control of the cutting process, knowledge of the material-depend-ent cutting force is also of major importance in defining the performance limit confining the range of optimization. Choosing the right cutting process and the optimum technological parameters results in signifi-cant savings of energy during machining. Of the factors influencing the cutting-force components, the following are very important: a) in the cutting methods: constant or varying cross-sectional area of the cut chip friction b) in the cutting conditions: gfin^OtJJlMlSCSD 02-3 stran 121 IVUgfTMECl Kopa~ J.: Rezalne sile in njihov vpliv - Cutting Forces and Their Influence podajanje (f) globina rezanja (ap) geometrijska oblika rezalnega roba rezalna hitrost (vc) hladilna tekočina c) material: kemijska sestava toplotna obdelava d) orodje: material orodja lomilec odrezkov prevleka obraba orodja 1 VPLIV REZALNIH PARAMETROV PRI IZRAČUNU KOMPONENT STATIČNIH REZALNIH SIL Rezultanta rezalnih sil sila F se pojavi med postopkom odrezovanja in je odvisna od smeri gibanja orodja in obdelovanca. Rezultanto rezalnih sil sestavljajo rezalna sila F, podajalna sila Ff in odrivna sila F (sl. 1). Obremenitev orodja pri struženju prikazuje slika 2. vrtenje obdelovanca rotation of workpiece gibanje orodja motion of tool Sl. 1. Rezalne sile pri struženju Fig. 1. Cutting force components during turning Rezalna sila Fc Potek rezalne sile lahko delimo z širino odrezka b in ga prikažemo v odvisnosti od debeline odrezka h v dvojnem logaritemskem diagramu. Dobimo linearno odvisnost: feed (f) back engagement (ap) cutting-edge geometry cutting speed (vc) cutting fluid c) the material: chemical composition heat treatment d) in the tool: tool material chip breaker coating tool wear 1 RELATIONSHIPS FOR THE CALCULATION OF THE STATIC CUTTING-FORCE COMPONENTS The cutting force F acting on the tool during the machining operation can be divided in terms of the directions of motion of the tool and the workpiece into the cutting force F, the feed force Ff and the passive force F (Figure 1). The conditions of the tool’s engagement are described in Figure 2 for the turning process. [1] vrtenje obdelovanca rotation of workpiece S------ gibanje orodja motion of tool Sl. 2. Razmere pri struženju Fig. 2. Conditions of engagement during turning Cutting force Fc The course of the cutting force F related to the width of the cut b is a function of the thickness of the cut h in the system of log-log coordinates as a straight line that is described by the equation: Fc=b-kc1.1-h b = ap sin^ h = f-sin% (1) (2) (3). VH^tTPsDDIK stran 122 Kopa~ J.: Rezalne sile in njihov vpliv - Cutting Forces and Their Influence Zgornjo enačbo je izkustveno razvil Kienzle in popisuje odvisnost rezalne sile F od prereza odrezka, kar prikazuje slika 3. Standardna specifična rezalna sila je odvisna od širne odrezka b in debeline odrezka h, kjer je b x h=1mm2, ter vplivnega koeficienta rezalne sile 1-m , kar je razvidno iz enačbe. Standardna specifična rezalna sila k 11 je v veliki meri odvisna od materiala, rezalnih parametrov, orodja in vpliva tehnološkega postopka. Povečanje rezalne sile je odvisno od vplivnega koeficienta rezalne sile 1-m karakteristik materiala obdelovanca in materiala orodja ter različne globine rezanja. Predstavitev izkustvene vrednosti rezalne sile F je odvisna od prereza odrezka b*h oziroma globine rezanja a kot funkcija debeline odrezka h. Rezultat je premica v dvojnem logaritemskem diagramu, ki je podana z enčbo: This equation was established by Kienzle according to the empirically determined dependence of the cutting force F on the cross-sectional area of the cut a x f or b * h, subject to the turning data shown in Figure 3. The specific cutting force k l.l related to the cross-sectional area of the cut b x h = 1 mm2 and the rise in the cutting force related to the nominal width of the cut 1-m are entered into the equation as characteristic datoc [2] The specific cutting force kll is, in this case, largely dependent on the material, the cutting conditions, the tool and the procedural influences. The increase in the cutting force related to the nominal width of the cut 1-m characterises the cutting-force behaviour of a workpiece-material-tool-material combination for different thicknesses of cut. The representation of the experimentally determined cutting-force values F related to the cross-sectional area of the cut b * h or a * f as c a function of the thickness of the cut h also results, under log-log coordinates, in a staight line, which can be described by the equation: kc=k1.1-h1 Fc b-h (4). en 5= U 2000 ~ A. ¦= mm Š 1000 I 800 600 ^ is m 200 kcU ¦ 1740N Imtrr / / A / i / iL / / > 1-m s 0,7265 ,__i_ 4- 1 r 1 r 1 u 4- "Url 1. h l-«»e - KIENZLE enačba / equation a 1 0,1 mm 0,2 0,4 0,6 0,8 1,0 debelina odrezka h / nominal thickness of cut h Sl. 3. Grafična predstavitev poteka rezalne sile in specifične rezalne sile Fig. 3. Graphic determination of the cutting force and the specific cutting force 2,0 V tej zvezi je specifična rezalna sila k podana kot funkcija debeline odrezka h. Te povezave nas pripeljejo do enačbe za rezalno silo F : Through this relation, the specific cutting forces kc are given as a function of the thickness of the cut h. These connections lead to a further equa-tion for the calculation of the cutting force Fc: F=b-h-k (5). ^vmskmsmm 02-3 stran 123 frflaBnTTMirel Kopa~ J.: Rezalne sile in njihov vpliv - Cutting Forces and Their Influence Podajalna sila Ff Za izračun podajalne sile F , vpeljemo enako zvezo kakor pri rezalni sili F, ta je definirana kot linearna funkcija podajalne sile, ki je funkcija širine odrezka b kot funkcija debeline odrezka h, kar je predstavljeno v dvojnem logaritemskem diagramu: Ff=b- Značilen podatek: standardna specifična rezalna sila je odvisna od prereza odrezka, ki je b x h = 1mm2. Povečanje podajalne sile je odvisno od vplivnega parametra podajalne sile, kar je upoštevano v enačbi. Nasprotno kakor pri enačbi rezalne sile, moramo v enačbi za izračun podajalne sile upoštevati, da je raztros pri podajalni sili F/b=f(h) večji kakor pri rezalni sili. Odrivna sila F V skladu s pravili za izračun podajalne sile F , lahko odrivno silo F izrazimo z enačbo: Fp=b- V preglednici 1 so zbrane vse enačbe za izračun rezalnih sil in torzijskih momentov za nekaj najbolj pogosto zastopanih postopkov obdelave. 2 REZALNI PARAMETRI Podatki o obdelavi, kot sta globina rezanja a in podajanje f, so namenjeni izračunu povprečnega prereza odrezka a *f = b*h in nakazujejo prek znanih enačb na velikost rezalne sile. Rezalna geometrija Rezalna geometrija ima precejšen vpliv na velikost komponent rezalnih sil. Po eni strani deformacija v strižni coni vpliva na geometrijsko obliko odrezka, po drugi strani pa je geometrijska oblika odrezka definirana z geometrijsko obliko orodja. Na velikost komponent rezalnih sil tako vplivajo razmere v strižni coni in geometrijska oblika orodja. Če se spremeni cepilni kot g (zmanjša ali poveča), se spremenijo omenjene sile (povečajo ali pomanjšajo) za naslednje vrednosti: rezalna sila F za približno 1,5 % podajalna sila Ff za približno 5,0 % odrivna sila F za približno 4,0 % za vsako stopinjo (1°) spremembe cepilnega kota. Če je velikost prostega kota a 3° = a = 12°, ta nima značilnega vpliva na komponente rezalnih sil. Feed force Ff For the calculation of the feed force Ff, a rela-tionship can be established that is similar to that used for the cutting force Fc, which is based on the linear behaviour of the feed forces related to the width of cut b as a function of the thickness of cut h as shown under log-log coordinates: k f11-h1 (6). As characteristic data, the specific feed force kf11 related to a cross-sectional area of cut of b x h = 1 mm2 and the increase in the feed force related to the nominal width of the cut 1 - m are included in the equation. Unlike to the cutting-force equation, this equation to calculate the feed force must be regarded as an approximate solution as the scatter of the test values in the representation F f / b = f (h) is larger than with the cutting force [3]. Passive force Fp In accordance with the rules of calculating the feed force F the passive force Fp can be expressed as: k p1.1-h1 (7). Table 1 shows some of the equations for computing the cutting forces and torques that occur during machining, such as turning, drilling, milling, etc. 2 CUTTING CONDITIONS The machining parameters as data back engagement a and feed f pass over by way of the cross-sectional area of cut a*f = b*h immediately into the cutting-force equations indicated. Cutting-edge geometry The cutting-edge geometry has a major influence on the quantity of the cutting-force components. On the one hand, the deformation processes in the zone of shear are affected by it and, as a result, so is the geometry of the chip formation, on the other hand, the tool angles determine, for geometrical reasons, the relative quantities of the various force components. As the rake angle g decreases (increases), there is an increase (decrease) of the: cutting force F by about 1.5 % feed force Ff by about 5.0 %. passive force F by about 4.0 % for every degree of rake angle change compared to the test value. Within the usual range of clearance angles a 3° = a = 12° no influence can be determined on the cutting-force components. VBgfFMK stran 124 Kopa~ J.: Rezalne sile in njihov vpliv - Cutting Forces and Their Influence Preglednica 1. Enačbe rezalne sile in torzijskega momenta Table 1. Cutting-force and torque equations Obdelovalni postopek Machining process Enačbe za izračun Equation for the determination of Rezalna sila Fc Torzijski moment Md Cutting force Fc Torque Md Struženje Turning Fc=b-h-kc Fc=b.kc11.h1-mc h = f-sinX a p D-d Md = b-h-kc-D + d Md = b-kc11-h 1-mcD + d Skobljanje Planing Podobno kakor struženje Like turning Vrtanje Drilling Posamezen rezalni rob: Each cutting edge: Fc=b-h-kc Fc=b.kc11.h1-mc b= 2 DZ;*=a2 Md = 2b-h-kc--Md = 2b-kc11-h1- D Md = f-kc~ Povrtavanje Boring Posamezen rezalni rob: Each cutting edge: Fc=b-h-kc Fc=b.kc11.h1-mc b= 2 DX;X=a2 Md = 2b-h-kc-D + d Md = 2b-kc11-h 1-mcD + d Md = f-kc D2-d2 Frezanje Milling Posamezen rezalni rob: Each cutting edge: Fc=b-h-kc Fc=b-kc11-h1-mc h = fzsin 1000m/min, kar vpliva na velikost rezalne sile c Hladilna tekočina Vpliv hladilne tekočine je bistvenega pomena pri velikih rezalnih hitrostih. Pri majhnih rezalnih hitrostih, se rezalne sile zmanjšajo zaradi prodora hladilno-mazalne tekočine v dotikalno območje, kar povzroči zmanjšanje trenja med odrezkom in orodjem. Pri večjih rezalnih hitrostih ima hladilno-mazalna tekočina v strižni coni samo hladilni učinek. Pri sodobnih rezalnih materialih ni nujno potrebna uporaba hladilno-mazalne tekočine, ker imajo nove prevleke rezalnih orodij dobre značilnosti. Sodobne in naravi prijazne metode obdelave s hladilno-mazalno tekočino so metode minimalnega hlajenja, pri tem za mazanje uporabljajo sistem razprševanja naravnega olja s stisnjenim zrakom. 3 OBDELOVANI MATERIAL Kemična sestava Če poznamo kemično sestavo obdelovalnega materiala, lahko le ocenimo velikost rezalne sile pri obdelavi. Vendar pri tem ni pravila in so zato potrebne meritve sil. wrong results. For cutting-edge angles smaller than those on which the test value is based the feed force can be determined by calculation in such a way that the mathematical value of the feed force for the smaller cutting-edge angle is subtracted from the double test result (Ff = f a=70°) - f (<70f). Within the range of the usual values for the corner radius, no appreciable influence on the cutting-force components can be determined as long as the term 2 r = ap is fulfilled. Cutting speed The influence of the cutting speed on the cutting-force components must be differently assessed for the various workpiece materials and the tool materials with their specific ranges of application. The application range for high-speed-steel tools is, in general, for cutting speeds of about 25 m/ min; so that for this material the cutting behaviour is described with sufficient accuracy by the indication of the specific cutting-force value at v = 25 m/min. To prevent built-up-edge formation, no cutting speeds of v < 30 m/min are normally used for carbide cutting tools . As regards the cutting-speed-dependent behaviour of the cutting forces in turning operations in the range of v < 1000 m/min, fundamental examinations are available. c Cutting fluid The influence of cutting fluids varies depending on the cutting speed. At low cutting speeds, the cutting forces are reduced owing to the penetration of the lubricant into the contact zones and the diminished friction between chip and tool. At higher cutting speeds within the range of the formation of continuous chips, the cutting fluid only has a cooling effect. Modern and ecological methods use near-dry cutting with a minimum amount of natural oil dispersed with pressurised air. 3 WORKPIECE MATERIAL Chemical composition According to the present state of knowledge, the chemical composition of the workpiece materials is only suggestive of the size of cutting-force com-ponents in exceptional cases, because definite laws relating to this influence are quite rare. VBgfFMK stran 126 Kopa~ J.: Rezalne sile in njihov vpliv - Cutting Forces and Their Influence Toplotna obdelava Raziskava vpliva toplotne obdelave na rezalne sile je pokazala, da vpliv toplotne obdelave ni natančno definiran glede na rezalne sile. Pri običajnih rezalnih orodjih, kakor sta hitrorezno jeklo in karbidna trdina, je treba vpliv toplotne obdelave na podatek k 11 in 1-m izmeriti za vsak primer posebej. Pri preskusih odrezovanja toplotno obdelanih materialov s hitroreznimi jekli so izmerjene rezalne sile manjše kakor pri mehko žarjenih obdelovancih. Ta ugotovitev velja tudi za potek rezalne sile v povezavi z 1-m . Meritve rezalnih sil pri odrezovanju z orodji iz karbidne trdine so pokazale, da primerjava toplotno obdelanih proti mehko žarjenim vzorcem kaže večje vrednosti za k1 in1-m . Medtem ko primerjava med normalizacijo c1 in žarjenjem na mehko ni pokazala značilnih sprememb rezalnih sil. Odvisnost specifične rezalne sile k 11 in povečanj rezalne sile glede na širino odrezka preko vplivnega eksponenta 1-m je povezana z napetostmi in deformacijskimi karakteristikami obdelovanega materiala. Zato ni natančno definirana povezava in lahko pričakujemo večje raztrose rezultatov. 4 ORODJE Dogodki v rezalni coni, kjer potekata strig in nastanek lamel odrezka, prvinsko vplivajo na podajalno in odrivno silo. Tudi tu je značilen raztros glede na zvezo sila / debelina odrezka. Linearni popis komponent rezalne sile, kot funkcije debeline odrezka je izveden kot približna rešitev. Materiali za rezalna orodja Če uporabimo rezalno keramiko (Al2O3), so rezalne sile proti karbidni trdini za okoli 10% manjše. Vzrok so boljše torne razmere pri drsenju odrezka po cepilni ploskvi rezalne ploščice. Lomilnik odrezkov, ki je v moderni obliki že integriran na rezalni ploščici je dimenzioniran tako, da je polmer za iztek odrezka čim večji. S tem lomilnik nima bistvenega vpliva na rezalne sile; zmanjšana pa je tudi obraba segmenta lomilnika. Na splošno se priporoča, da je odmik lomilnika od rezalnega robu v vrednosti okoli 10 x f (torej desetkratnega pomika orodja). Obraba orodja Obraba orodja je zanesljivo v povezavi z velikostjo rezalnih sil. Deli se na dve značilni, in sicer na obrabo proste ploskve, ki jo povzroča Heat treatment Investigations aimed at defining the influence of heat treatment on the cutting forces have led to the result that there is no definite dependence of the main cutting force on heat treatment. However, as regards high-speed-steel tools and carbide cutting tools, the qualitative effects of heat treatment on the data kcl.l and 1-mc can be determined separately. Under the experimental conditions, heat-treated materials for the high-speed-steel tool material gener-ally show much lower cutting-force values than for soft-annealed steels. This statement also applies to the increase in the cutting force related to the nominal width of the cut 1 –mc. The cutting-force measurements conducted with carbide cutting tools showed that heat-treated materials, as compared to soft-annealed materials, frequently reveal higher values for kcl.l and 1-mc. A com-parison of the cutting forces for normalised and soft-an-nealed materials, however, does not result in any appreci-able differences. While the dependence of the specific cutting force kc1.1 and of the increase in the cutting force related to the nominal width of the cut 1-mc on the strength and deformation characteristics within the entire range of materials examined may be shown, no definite relationship can be attributed to this influ-ence owing to the wide range of scatter. 4 TOOL The deformation conditions in the shear zone of the tool – some of which varied for different thicknesses of the cut and made themselves felt in the position and size of the shear-ing plane and in the amount of chip crowding – had an effect on the feed forces and the passive forces. In view of the range of scatter of the various test results, a linear description of these force components as a function of the thickness of the cut must therefore be regarded as an approximate solution. Tool material When aluminium-oxide tools (cutting ceramics) are employed as a tool material, the resulting cutting forces are about 10 % lower than with carbide metal because with a ceramic cutting material there are more favourable frictional conditions on the true rake or chip face. The size of the chipbreaker bsp should be dimensioned so that the radius of chip curvature is as large as possible. This is to ensure that on the one hand the size of the chip breaker will not have any major influence on the cutting-force components, and on the other hand, the wear action on the true rake is as low as possible. The rule-of-thumb value ‘chip former = 10 times the feed’ can generally be regarded as favourable. Tool wear Numerous results are available concerning the in-fluence of tool wear on the cutting-force components. As a consequence of the increasing friction areas between the |gnnäS)^o^"02-3 stran 127 IvBgfTMlGC Kopa~ J.: Rezalne sile in njihov vpliv - Cutting Forces and Their Influence drsenje rezila po že obdelani površini obdelovanca, in na obrabo cepilne ploskve orodja, prek katere drsi odrezek. Značilen vpliv na večanje obrabe pa ima seveda čas uporabe orodja. Tudi tu ocene povečanja obrabe niso mogoče v zadostni natančnosti, zato so potrebne meritve. Le približne ocene povedo, kakšna sta vpliv in povezava med obrabo orodja in povečanjem rezalne sile: rezalna sila F se poveča za 10% za vsak 0,1 mm obrabe W podajalna silaFf se poveča za 25% za vsak 0,1 mm obrabe W odrivna sila F se poveča za 30% za vsak 0,1 mm obrabe W p Kot definicija kriterija izločilne obrabe rezalnega orodja pa seveda ne more biti pravkar omenjena povezava med rezalno silo in obrabo proste ploskve orodja W. 5 DINAMIČNA REZALNA SILA Temeljita raziskava dinamičnih rezalnih sil pri struženju je pokazala, da ima poleg statične komponente rezalne sile tudi nastanek odrezka velik vpliv na komponente rezalnih sil. V strižni coni in v področju nastanka nalepka na rezalnem robu, se lahko dinamična komponenta rezalne sile F poveča za 20%, podajalna sila F in odrivna sila F pa se lahko povečata za 50% f V področju zveznega nastanka odrezka se lahko dinamična komponenta rezalne sile zmanjša za 5 do 10 odstotkov (sl. 4). Znaten vpliv na dinamično rezalno silo ima tudi lega lomilne stopničke b , ki je lahko odvisna že od oblike sintrane ploščice. Majhna oddaljenost lomilne stopničke poveča gostoto odrezkov v taki meri, da je dinamična sila v strižni coni v smeri podajalne in odrivne sile lahko večja za 100 odstotkov od statične. F [N] statična sila - povprečje average of static force cut surface and the flank of the tool or between the chip and the chip face, on the one hand and the changing conditions of engagement of the tool on the other, a substantial in-crease in the cutting-force components with increasing cut-ting time is registered. In view of the number of factors, a quantitative statement on the increasing force in relation to the increasing tool wear can only be an approximation. Nu-merous experimental results have shown that for an increase of the cutting-force components as the tool wear increases the following corrective values should be introduced: cutting force Fc: increase of about 10% per 0.1-mm width of land wear W feed force Ff: increase of about 25% per 0.1-mm width of land wear W passive force Fp: increase of about 30% per 0.1-mm width of land wear W As a definition of the total wear is impossible, the increase in the cutting force was related to the width of the land wear W. 5 DYNAMIC CUTTING FORCE Fundamental examinations of the dynamics of cutting forces during turning have shown that in addition to the factors influencing the static cuttingforce components the chip formation has a major in-fluence on the cutting-force components. In the range of shear-chip formation, built-up-edge formation and the rigidity of the process, a high dynamic cutting-force component occurs in machin-ing, which may acount for a cutting force Fc of up to 20%, and for the feed force Ff and the passive force Fp up to 50% of the static components. In the range of continuous chip formation, the dynamic cutting forces drop to 5–10 % of the static share, see Figure 4. A considerable influence on the dynamic cutting forces is exercised by the chip-breaker distance bsp , which can be made directly by shape-sintering of the cutting insert. With a short distance and thus heavy crowding of the chip flow, the share of the dynamic force in the direc-tion of the feed force and the passive force can amount to as much as 100 % of the static share. F [N] A dinamična komponenta m P0-50Z dynamic component t [s] t [s] VBgfFMK Kopa~ J.: Rezalne sile in njihov vpliv - Cutting Forces and Their Influence 6 PRAKTIČNA PREDSTAVITEV Praktična uporaba eksperimentalno dobljenih rezultatov je prikazana na sliki 5. Specifična rezalna sila vpliva na energijo, potrebno za obdelavo. Za prihranek energije in stroškov je ekonomična izbira največjega možnega podajanja. Največje tehnološko mogoče podajanje je izbrano glede na postopek in zahtevano hrapavost (Ra). Kratka primerjava pokaže, kako lahko s pravilnim načrtovanjem tehnoloških parametrov dosežemo 2-kratni prihranek energije in časa obdelave ter tako Fc/b [N/mm] 2000 1000 6 PRACTICAL DEMONSTRATION The practical use of the experimental results is shown in Fig. 5. The specific cutting force has an influence on the energy needed for machining. With regard to saving energy and costs it is best to choose the maximum possible feed rate. The maximum technologically justifiable feed rate is chosen based on the limits of the process or the specimen roughness (Ra). The short comparision shows that using the right technological parameters can save more than 2x the equivalent of energy: short- kc [MPa] 0,1 0,5 h[mm] Sl. 5. Eksperimentalni rezultati rezalnih in specifičnih rezalnih sil Fig. 5. Experimental results of cutting and specific cutting forces 2 10 8 6 ^^T ^"struženje - turning 10"1 1 10 log h [mm ] Sl. 6. Specifične rezalne sile, odvisne od postopka obdelave Fig. 6. Specific cutting forces during the process gfin^OtJJlMlSCSD 02-3 stran 129 IVUgfTMECl Kopa~ J.: Rezalne sile in njihov vpliv - Cutting Forces and Their Influence Podatki, zbrani v diagramu na sliki 6, kažejo razliko med postopki obdelave v odvisnosti od debeline odrezka h. Nasproten postopek pokaže, kako je specifična rezalna sila manjša pri večjem podajanju [4]. Da predstavimo in primerjamo teoretične rezultate s praktičnimi vplivi, je treba pogledati sliko 7. Razvidna sta vpliv obdelovalnega materiala in vrsta obdelave na stroške obdelave. Če primerjamo obdelavo mehkega materiala, npr. aluminij ali jeklo, s trdimi materiali, na primer nikljeve zlitine, opazimo, da je razlika v stroških obdelave kar 4-kratna. Pri tem je seveda opazen tudi vpliv rezalne sile, ki v povezavi s hitrostjo narekuje moč stroja, kar pa je tudi eden od stroškov.Razvidna je tudi razlika glede na vrsto postopka; struženje povzroča znatno večje stroške kakor frezanje, če gledamo glede na odvzem enake prostornine materiala. MATERIAL Alumnium lumnuim *¦ <•, ¦ 7075 - TB lain tirbori ttfttl «W 1020, 111 Bhn Ultra high sL-ength *t**l DGic, 212 Bhn Stilni*« «Hi, mirtonvbc 410. Ann. 163 Bhn Law «toy «Ml 4340. O. & T, 33(2 Bhn 310. Iflft Bhn P H ttaintau «•«¦ 1 7 - 7 PH Titimumilläy Ti-e*J-JV Th7AI-2CbM Ta, 2L5 6hn Low * :ioy IU«I 4H0,0 I T, 52 Rc Malybdarrum «Hoy Mc-5Ti Tidnium i c > TV3AMJV'11Cr. 2» &hn lrC bi« high t»mp ahpf A-2W Afl*d 320 Bhn Uitr* h^h ttrtnnth wi*t DCK.47RC Cü bi 11 bit« hinh timp ¦ c-y HS 25 Nickst 6s» high temp »lksy ¦ inecnel 'X TmUJum »ii 3 y ¦ 90 Ti-10 W NiC h*l b«H h*oh Itmp tfloy ¦ RHW41 A(*d. ICO Bhn Nicfctl bit* nigh i»mp alloy ¦ Ineonal 700, *D*d. 400 Bhn' 1 S results collected in the diagram in Fig.6 show diferences between processes, such as turning, HSC, grinding soft material and hard steels, depend on h (thickness). The reverse observation shows how the specific cut-ting force is lower with a higher feed rate [4]. Comparing the theoretical and measured re-sults with the practical effect shows, in Fig. 7, how great is the influence of the type of machined materials, reflected in the cutting forces and the machining costs. The product of the cutting force and the cutting speed provides the power needed for the process: this is the energy costs. As first, the relative costs be-tween soft (Al, steel) material and hard (nikel-based alloys) materials are a factor of four different for ma-chining. Another influence is the chosen type of ma-chining: the turning process is much more expensive than milling, which means the technologist has to be very careful when preparing the offer for the customer. V I I i I I I I I I ¦= struženje, turning H frezanje, milling m 1« XO m ]«0 IK V 1K» '000 ... stroški obdelave (s) machining costs (s) Sl. 7. Relativni stroški obdelave mehkih in trdih materialov Fig. 7. Relative costs of machining soft and hard materials 7 VHO - OBDELAVA Z VELIKIMI HITROSTMI Uporabno območje debeline odrezka (h) pri obdelavi z velikimi hitrostmi je omejeno. Za primerjavo rezultatov (poglavje 6 - običajna obdelava) z rezultati sodobne obdelave v trdo je mogoče videti, da je odvisnost enaka. To pomeni, da sta rezalni postopek in rezalna geometrija (a,p,y,r,x) teoretično še vedno enaki. Klasična in sodobna obdelava VHO imata skupno to, da je njun izid odrezek in da se za oba postopka uporablja isti matematični model. S slike je razvidno, da je pogosto odrivna sila pri odrezovanju v trdo celo večja od glavne rezalne 7 HSC – MACHINING CONDITION The usable (h) thickness by HSC machining is explicitly limited in this process. By comparing the result shown before (section 6: classical machining) with the results of modern HM (hard machining) we can see that the relationship is the same. It means that cutting processes with an exact cutting geom-etry (a,b,g,r,c) are still in the same theoretical area. The classical cutting and modern HSC machining both have as a “product”, therefore the same models and equations are used for both processes. Figure 8 shows that the passive force can be larger than the cutting force. In prac- VBgfirWEBS stran 130 Kopa~ J.: Rezalne sile in njihov vpliv - Cutting Forces and Their Influence 100.000 10.000 1.000 ------ -^ >. A'cTj/ yf ^L_^cn rezalna sila * cutting force ...» normalna rezalna sila normal cutting force obdelovani material: 100CR6 machining material: rezalno orodje: PKB cutting tool: frezanje dry up milling Rezalni pogoji: Cutting conditions: ap = 5 mm ae = 0,1 mm fz = 0,1 mm vc = 50 m/min d = 40 mm, z = 1 a = 10° g = 0° re = 1,2 mm 0,001 imenska debelina odrezka h nominal thicknes of cut h [mm] Sl. 8. Sile pri frezanju v trdo [5] Fig. 8.Hard machining (HM) and forces [5] 0,01 sile. To v praksi pomeni odmik orodja od načrtovanega obrisa obdelovanca in s tem napake na izdelku. Zato v praksi zmanjšamo debelino odrezka. 8 SKLEP Nepoznavanje področja rezalnih sil ima lahko za posledico slabo obdelavo, lome orodja, in večje obdelovalne stroške. Običajni obdelovalni postopki še vedno ponujajo banko tehnoloških podatkov, v kateri so podatki o rezalnih silah glede na obdelovalni material, postopek, rezalno orodje itn. S tehnološko pripravo lahko inženir izbere in določi najboljši postopek in s tem debelino odrezka (h). Le ta mora biti vedno največja po vsem obrisu obdelovanca, glede na zahtevano hrapavost površine. To je prvi korak, ko lahko tehnolog prihrani energijo in zmanjša izdelovalne stroške. Sodoben način napovedi velikosti rezalnih sil je model analitičnega simuliranja. Program je pomoč, ki omogoča napovedati potek dogodkov med obdelavo na osnovi nastavitev tehnoloških parametrov, orodja, obdelovanca in stroja. Sodobni obdelovalni stroji imajo močno računalniško podporo s programom za “visoko podajanje”, kar omogoča obdelavo s konstantno rezalno silo in nespremenljiv prostorninski odvzem [6]. V tem primeru so dinamični učinki manjši, odrezovalni postopek pa je stabilnejši. Če upoštevamo vse povzetke o rezalnih silah, so rezultati naslednji: manjša obraba rezalnega robu, boljša hrapavost obdelane površine, večja natančnost in gospodarnejša proizvodnja. tice, it causes failure on a dimension of the product, as a result, we have to reduce the feed rate. 8 CONCLUSION With a little knowledge of the cutting forces we can expect worse machining with tool breakages and higher production costs. Conventional machining is stil based on a technological data bank, where cutting forces are provided for various machining materials, machin-ing proceses, cutting tools, etc. By tehnological prepa-ration the enginer has to choose and find the best proc-ess with regards to the thickness of the cut (h). H has to be a maximum value with regard to the all-over contour of the workpiece to the required surface roughness. In this way we make the first step in reducing the energy and the machining costs. The modern concept is a model of analytical simulation for the prediction of the cutting forces[6]. The program is an aid enabling us to forecast the course of events during the machining process with given initial conditions such as the technological parameters, the tool, the workpiece and the machine. Modern machine tools (HSM) with strong software and programs such as “high feed” are work-ing on a concept of constant cutting forces regard-ing the constant machining volume rate [6]. In this case the dynamic effect is lower and the cutting proc-ess much more stable. To consider all the summarized effects on the cutting forces the results are: reduced wear on the cutting edge, better workpiece-surface roughness, greater accuracy and economic productivity. stran 131 Kopa~ J.: Rezalne sile in njihov vpliv - Cutting Forces and Their Influence 9 SIMBOLI 9 SYMBOLS globina rezanja širina odrezka lega lomilne stopnične notranji premer rezanja zunanje premer rezanja rezultanta rezalnih sil rezalna sila podajalna sila odrivna sila debelina odrezka specifična rezalna sila standardna specifična rezalna sila standardna specifična podajalna sila standardna specifična odrivna sila vplivni eksponent rezalne sile vplivni eksponent podajalne sile vplivni eksponent odrivne sile torzijski moment polmer ploščice podajanje podajanje na zob rezalna hitrost prosti kot strmina cepilni kot nastavni kot kot konice kot oprijema (frezanje) natezna trdnost meja elastičnosti podaljševanje redukcija površine trdota po Vickersu (število) ap b b sp d D F Fc Ff Fp h k c k c1.1 k f1.1 k p1.1 1-mc c 1-mf 1-mp Md r f fz vc a l g c e js Rm Re A5 Z HV10 mm mm mm mm mm N N N N mm MPa MPa MPa MPa Nm mm mm mm m/min ° 0 0 0 0 0 MPa MPa % % back engagement nominal width of cut chip breaker distance inner diameter of cut outer diameter of cut resultant cutting force cutting force feed force passive force nominal thickness of cut specific cutting force specific cutting force unit specific feed force unit specific passive force unit coeficient of cutting force coeficient of feed force coeficient of passive force torque corner radius feed feed per tooth cutting speed clearance angle cutting-edge inclination rake angle tool cutting-edge angle tool included angle cutting motion angle (milling) tensile strength yield point elongation reduction of area Vickers hardness (number) 10 LITERATURA 10 REFERENCES [1] [2] [3] [4] [5] [6] König, W., K. Essel, L. Witte: Specific cutting force data for metal - cutting, Verlag Stahleisen MBH, Düseldorf. Dolinšek, S., J. Kopač (1992) Odrezavanje, dopolnitveno gradivo za predavanja in vaje, Fakulteta za strojništvo, Ljubljana. Milfener, M., F. Čuš(2001) Analitical model of cutting forces simulation in end milling. ICIT 2001, Slovenija. Muren, H. (1976) Odrezavanje, Tehniška založba Slovenije. Schultz, H. (1996) Hochgeschwindigkeitsbearbeitung, Carl Hanser Verlag. Kopač, J., G. .Peterlin (2001) Novi pristopi pri visokohitrostnih obdelavah na osnovi CAM, Orodjarstvo 2001. Avtorjev naslov: profdr. Janez Kopač Fakulteta za strojništvo Univerza v Ljubljani Aškerčeva 6 1000 Ljubljana janez.kopac@fs.uni-lj.si Author’s Address: ProfDr. Janez Kopač Faculty of Mechanical Eng. University of Ljubljana Aškerčeva 6 1000 Ljubljana, Slovenia janez.kopac@fs.uni-lj.si Prejeto: Received: 26.2.2002 Sprejeto: Accepted: 23.5.2002 VBgfFMK stran 132