© Strojni{ki vestnik 47(2001)2,94-105 © Journal of Mechanical Engineering 47(2001)2,94-105 ISSN 0039-2480 ISSN 0039-2480 UDK 621.983.3:004.94:519.61/.64 UDC 621.983.3:004.94:519.61/.64 Predhodna objava (1.03) Preliminary paper (1.03) Analize kakovosti pridr`evanja plo~evine pri globokem vleku Analysing the Quality of Sheet-Metal Holding during Deep Drawing Toma` Pepelnjak - Zlatko Kampu{ Preoblikovalni postopki postajajo zaradi zapletenosti izdelkov iz dneva v dan zahtevnejši. Pridrževanje pri globokem vleku se zaradi tega vedno bolj prilagaja poteku preoblikovalnega postopka, za kar se uporabljajo različni optimizacijski prijemi. V prispevku so predstavljeni sodobni načini optimizacije pridrzevanja s poudarkom na časovni optimizaciji sile držala, elastičnih in segmentnih pridrzevalih. © 2001 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: globoki vlek, pridrževanje pločevine, optimiranje, metode končnih elementov (MKE), simuliranje) Due to the increasing complexity of products, forming procedures are becoming ever more demanding. As a consequence, the holding procedure is becoming better adapted to the forming process through the use of various optimisation concepts. This paper presents the modern methods for the optimisation of holding, with an emphasis on the temporary optimisation of the blankholder force and the use of elastic and segmented blankholders. © 2001 Journal of Mechanical Engineering. All rights reserved. (Keywords: deep drawing, sheet metal holding, optimisation, final elements methods (FEM), simulations) 0 UVOD Pri globokem vleku se pojavlja natezno-tlačno napetostno stanje, ki ob neustreznih preoblikovalnih pogojih povzroča gubanje pločevine. V izogib gubanju pločevine se pri globokem vleku, pri katerem je relativni premer pestiča dp/s0 večji od 30, pločevina pridržuje z držalom. Slednje prepreči gubanje preoblikovanca v prirobnici. Sila, potrebna za pridrževanje pločevine, se običajno določa za sam začetek vleka, pri čemer se najpogosteje uporablja Sieblov obrazec [1]: Fd=A-pd , pd Enačba popisuje vplive vlečnega razmerja in geometrijske oblike orodja ter natezno trdnost materiala vlečenca. Sila držala se računa za sam pričetek vleka, vendar so raziskave pokazale, da je tako izračunana pridrževalna sila prevelika za celoten potek preoblikovalnega postopka. Silo pridrževala lahko zato med vlekom tudi zmanjšujemo. Sodobni načini preoblikovanja pločevine se nagibajo k optimiranju preoblikovalnega postopka ([2] do [5]). S tem se povečuje tehnološka varnost, zmanjšujejo 0 INTRODUCTION Deep drawing causes a stress-strain state in the workpiece that results in the wrinkling of the sheet metal if the forming conditions are not right. In order to avoid this wrinkling the sheet metal is held with a blankholder if the relative punch diameter dp/s0 is greater than 30 to prevent wrinkling in the flange. The required blankholder force is usually determined for the initial stage of deep drawing by the use of Siebel’s formula [1]: 400 (Ä-1 ) 3 + d 200 -s (1). The above equation describes the influences of the drawing ratio and the tool geometry as well as the tensile strength of the workpiece material. The blankholder force is calculated for the initial stage of deep drawing, however, research has shown that this results in forces which are too large for the later stages of the forming procedure. As a result, the blankholder force can be reduced during deep drawing. Modern concepts of sheet-metal forming include: optimisation of the forming procedure ([2] to [5]), which results in increased maimskixmmm VH^tTPsDDIK stran 94 T. Pepelnjak - Z. Kampu{: Analize kakovosti - Analysing the Quality preoblikovalne sile in povečujejo dosegljiva vlečna razmerja. Za boljši nadzor preoblikovalnega procesa so v zadnjih letih razvili različne nove pridrževalne sisteme stiskalnic, s katerimi lahko krajevno in časovno spreminjajo silo pridrževanja med samim globokim vlekom. Preskusi in numerična računalniška simuliranja so pokazali, da sile pridrževala ne smemo preveč zmanjšati, sicer se tudi pri najmanjši prirobnici lahko pojavijo gube [6]. V članku predstavljamo numerične simulacije optimizacije pridrževanja pločevine. Za preprečevanje prevelikih lokalnih tlakov pridrževala smo poudarek optimizacije usmerili na krajevno inčasovno prilagajanje pridrževanja s segmentiranimi pridrževali. 1 OPTMIRANJE PRIDRŽEVANJA PLOČEVINE Pri globokem vleku neokroglih preoblikovancev se natezno-tlačno napetostno stanje pojavlja samo na nekaterih odsekih vlečenca, drugje pa se lahko pojavlja npr. le upogibanje preko polmera matrice. Zaradi neenakomernega napetostnega stanja spreminjanje debeline preoblikovanca po obodu ni več nespremenljivo. Prav tako dobimo neenakomerne hitrosti gibanja materiala med samim preoblikovanjem. Posledica omenjenih nesimetričnosti so hitrejše gibanje pločevine na ravnih delih vlečenca ter počasnejše na vlečenih vogalih. Nadzor preoblikovalnega procesa z običajnim pridrževalom je v takem primeru zaradi neenakomerne debeline vlečene prirobnice preoblikovanca zelo zapleten. Raziskave so pokazale [4], da lahko dvojno delujoče mehanske stiskalnice uspešno zamenjujemo z enojno delujočimi sitskalnicami z ustreznim računalniško številsko krmiljenim (CNC) zadrževalnim sistemom. Sodobni zadrževalni sistemi, ki se običajno uporabljajo, delujejo v veliki večini po dveh načelih: - z elastičnimi pridrževali, - s segmentiranimi pridrževali. Zamenjava pridrževalne blazine s štiritočkovnim pridrževalnim sistemom za velika preoblikovalna orodja je bil prvi korak k izboljševanju nadzora pridrževanja zahtevnih vlekov v avtomobilski industriji. Rezultati kažejo pri pridrževanju z več medsebojno neodvisnimi hidravličnimi valji kakovostnejše preoblikovanje kakor v primeru običajne uporabe dvojno delujoče stiskalnice [4]. S povečevanjem števila hidravličnih valjev se lahko predvsem pri orodjih z osnovno ploščo večjo od 1000x1000 mm poveČa nadzor nad potekom pridrževanja, pri čemer je število uporabljenih valjev odvisno od konstrukcije preoblikovalnega orodja in same stiskalnice [4]. Izkušnje na področju optimizacije pridrževanja srečamo tudi v slovenski industriji preoblikovalnih strojev, kjer podjetje Litostroj I.E. že nekaj časa vgrajuje za optimizacijo pridrževanja večtočkovne pridrževalne sisteme v svoje hidravlične stiskalnice [7]. Posebnost teh sistemov je pridrževalni technological safety, reduced forming forces; and increased attainable drawing ratios. For better control of the forming process various new holding systems for presses have been developed in recent years that enable the spatial and temporary variation of the blankholder force during deep drawing. Experiments and numerical computer simulations have shown that the blankholder force should not be reduced excessively, or wrinkles will appear even for a minimal flange [6]. This paper presents a numerical analysis of the holding optimisation where the emphasis was given to the spatial and time adaptation of the blank holding with segmented blankholders in order to prevent the holding pressures being to high on particular segments. 1 OPTIMISATION OF SHEET-METAL HOLDING When deep drawing noncircular workpieces, the stress-strain state only appears in certain workpiece parts, while others may only be bent over the die radius. Due to the nonuniform stress-strain state, the variation in workpiece thick-ness along its circumference is no longer constant. In addition, parts of the material move at a nonuniform speed during forming. These asymmetric condi-tions result in the faster movement of sheet metal in the straight parts of the workpiece and slower move-ment on the drawn edges. Due to the nonuniform thickness of the drawn workpiece flange, the control of the forming process with a conventional blankholder is very complex. Research has shown [4] that double-stroke mechanical presses can be successfully replaced with single-stroke presses by using an appropriate computer numerically controlled (CNC) holding system. The commonly used modern holding systems are mainly based on two principles: - with elastic blankholders, - with segmented blankholders. The replacement of the holding cushion with a four-point holding system for large forming tools was the first step towards improving the holding con-trol for demanding deep-drawing processes in the automotive industry. By using several independent holding cushions better quality forming than that obtained with conventional double-stroke presses has been obtained [4]. With an increase in the num-ber of hydraulic cylinders, control over the course of the holding can be improved, primarly in tools with a base plate greater than 1000 x 1000 mm where the number of cushions used depends on the design of the forming tool and the press [4]. Experience with the optimisation of holding can also be found in the Slovenian forming-machines industry. For some time now, Litostroj I.E. has been using multipoint blankholder systems in its hydrau-lic presses in order to optimise sheet-metal holding [7]. A special feature of these systems is that they | lgfinHi(s)bJ][M]lfi[j;?n 01-2_____ stran 95 I^BSSIfTMlGC T. Pepelnjak - Z. Kampu{: Analize kakovosti - Analysing the Quality sistem, ki je izveden v pehalu stiskalnice. Ker se are integrated in the press ram. Since these presses omenjene stiskalnice uporabljajo predvsem kot trans- are primarily used as transfer presses, the handling fer stiskalnice, je pomembna tudi izvedba strege of products between the presses is also important izdelkov med stiskalnicami [8]. [8]. Vsi našteti sistemi optimiranega pridrževanja All of the above-mentioned systems for temeljijo na osnutku elastičnega prilagajanja optimised holding are based on the concept of elas- pridrževala površini pločevine, ki je večje od elastičnih tic adjustment of the blankholder in relation to the deformacij običajnih pridrževalnih plošč (sl.1). surface of the sheet metal, which is greater than the Konstrukcijsko se problematika povečevanja elastic deformations of conventional holding plates elastičnosti pridrževala rešuje s posebnimi oblikami (Figure 1). In terms of design, the problem of increas- pridrževalnih plošč [4]. Za vse doslej naštete ing the elasticity of the holder is solved with the use pridrževalne sisteme uporabljamo specializirane of specially shaped holding plates [4]. All of the above prirejene stiskalnice z zahtevnim nadzorom holding systems require specialised presses with preoblikovalnega postopka. complex control of the forming process. V primeru preoblikovanja krojenih prirezov When forming tailored blanks of various različnih debelin žal tudi s povečano elastičnostjo thicknesses, however, even elastic blankholders pridrževala ne moremo kakovostno pridrževati cannot ensure high-quality holding of workpieces geometrijsko zapletenih preoblikovancev Za with complex geometry. In order to optimise the optimizacijo pridrževanja krojenih prirezov so se zaradi holding of tailored blanks, special segmented hold- tega razvila posebna segmentirana pridrževala, pri katerih ers have been developed with different thicknesses različne debeline krojenega prireza pridržujemo z of tailored blanks held with separate holder seg- medsebojno ločenimi segmenti [2]. Optimizacija ments [2]. In this case, the optimisation of holding pridrževanja v tem primeru ni izvedena v samem stroju is not performed in the machine with the use of preko posebnih pridrževalnih sistemov, temveč kar v special holding systems, but in the tool itself (Fig- samem orodju (sl. 1). Posamezne segmente krmilimo s ure 1). Individual segments are controlled with the plinskimi vzmetmi. Tako lahko segmente obremenjujemo use of gas springs, which load each individual medsebojno popolnoma neodvisno. Takšen način workpiece segment independently of the others. pridrževanja omogoča tudi pridrževanje z lokalno This method also enables holding with locally dif- popolnoma različnimi silami pridrževanja, kar je najbolj ferent blankholder forces, which is most useful in uporabno predvsem pri preoblikovanju krojenih prirezov the forming of tailored blanks. Segmented S segmentiranimi pridrževali je mogoče zelo učinkovito blankholders very effectively solve the problem of Sl. 1. Pridrževalna plošča s povečano elastičnostjo [4] (levo) in orodje s segmentiranim pridrževalom [2] (desno) Fig. 1. Holding plate of increased elasticity [4] (left) and tool with a segmented blankholder [2] (right) ^BSfiTTMlliC | stran 96 i T. Pepelnjak - Z. Kampu{: Analize kakovosti - Analysing the Quality reševati tudi problematiko naleganja pridrževala na različno debele dele pridrževane prirobnice preoblikovanca, ki nastanejo zaradi preoblikovalnega postopka ali uporabljane platine (npr. krojenega prireza). Pomanjkljivost orodij s segmentiranimi pridrževali je njihova zelo visoka cena, ki je odvisna od vgrajenih plinskih vzmeti in tlačnih sistemov za zagotavljanje pridrževalnih sil. S tega vidika je zamisel izvedbe povečane elastičnosti pridrževanja že v sami stiskalnici boljša, saj omogoča prilagodljivost pridrževanj za vsa uporabljana orodja brez dodatnih osnutkov optimizacije pridrževanja v samem orodju. 2 OPTMIRANJE PRIDRŽEVANJA GLOBOKEGA VLEKA KORITA Iz pregleda raziskav optimizacij pridrževanja v svetu smo prišli do sklepov, da je smiselno analizirati kombinacijo sistema elastičnih in segmentiranih pridrževal. Za primerjavo rezultatov optimizacijskih strategij z ostalimi avtorji ([2] do [6]) smo analizirali sile pridrževanja za konvencionalno in segmentirano pridrževalo. Glavni cilj pri tem je bil določitev sistema za časovno in krajevno optimizacijo pridrževanja s segmentiranim pridrževalom. Analizirali smo tri različne zasnove pridrževalnih konceptov na primeru globokega vleka korita: - običajno pridrževanje z nespremenljivo pridrževalno silo, - običajno pridrževanje s spreminjanjem pridrževalne sile, - pridrževanje s segmentiranim pridrževalom. Izdelek je bil izbran v sodelovanju s podjetjem Litostroj E.I., ki je tehnologijo preoblikovanja podobnega izdelka s transfer stiskalnicami že uporabilo za naročnika v tujini [7]. Za testni izdelek smo izbrali pločevinastemu koritu podoben izdelek (sl. 2) z izmerami 400x400 mm, s polmeri zaokrožitve 80 mm na vogalih in 45 mm na dnu korita. Material testnega izdelka je nerjavno jeklo, katerega materialne lastnosti, potrebne za simuliranje z MKE, so zbrane v preglednici 1. Uporabljani program za simuliranje preoblikovanja pločevine računa s togimi lupinskimi elementi orodja ([9] do [12]), zaradi česar smo za izračune elastičnega pridrževanja najprej analizirali segmentirano pridrževanje. Izračuni potrebnih pridrževalnih sil segmentiranega pridrževala in Preglednica 1. Materialne lastnosti analizirane nerjavne pločevine Table 1. Material characteristics of the analysed stainless- steel sheet metal fitting the blankholder to the held workpiece flange parts of various thicknesses resulting from the forming procedure or the used blank (e.g. tailored blank). The disadvantage of tools with segmented blankholders is that they are very expensive because they contain gas springs and a pressure system which provides the blankholder forces. For this reason, the idea of increasing the elasticity of holding in the press is better, since it enables holding to be adapted for all the used tools without additional optimisation of holding in the tool. 2 OPTIMISATION OF HOLDING IN THE DEEP DRAWING OF SINKS After reviewing the present situation with regard to blankholder optimisation, we can conclude that it is reasonable to analyse a holding system con-sisting of a combination of elastic and segmented blankholders. To compare the results of the optimisation strategies for holding force to the research work from other authors ([2] to [6]), the variable blankholder forces have been analysed for conven-tional and segmented blankholders. The main objec-tive was to determine the system for the spatial and time optimisation of the segmented holding of the blank. Three different holding concepts used for deep drawing a metal sink were analysed: - conventional holding with constant blankholder force, - conventional holding with varying blankholder force, - holding with segmented blankholder. The product was selected in cooperation with Litostroj E.I., which has used this technology for forming a similar product with transfer presses for a foreign client [7]. A product similar to a sheet-metal sink was chosen for testing (Figure 2) with dimen-sions 400 x 400 mm, rounding radius 80 mm on edges and 45 mm at sink bottom. The material chosen for the test product was stainless steel. Its characteris-tics, which were used in the FEM simulations, are presented in Table 1. The program used for the simulation of the sheet-metal forming involves rigid-shell tool elements ([9] to [12]), and so the segmented holding was analysed first for the calculations of elastic holding. The calcula-tion of the required blankholder forces for a segmented blankholder and the thicknesses of the held flange in C MPa 1345 E MPa 210000 r0 1 0,9 n 1 0,376 n [1] 0,3 r45 1 1,41 Rp MPa 300 r kg/m3 7800 r90 1 1,005 Rm MPa 640 s0 mm 0,7 ^vmskmsmm stran 97 T. Pepelnjak - Z. Kampu{: Analize kakovosti - Analysing the Quality platina / blank :" 700 izdelek / product R80 /^,R45 U t pestič/ punch pridrževalo / blankholder platina / blank * matrica / l&ssullilll Predprocesor / ! CAD: I-Deas Preprocessor Simulacija / Simulation Pam-Stamp Pregledovalnik / Postprocessor Pam-View ________ ŠTEVILO ELEMENTOV / NUMBER OF ELEMENTS: Pestič / Punch: j 836 Pridrževalo / Blankholder:............ Matrica / Die: Platina / Blank: 925 ...1292.. 3568 ROBNI POGOJI / BOUNDARY CONDITIONS: ________.................................................... symmetry X-axis simetrija v Y osi / symmetry Y-axis____________ TRENJE / FRICTION: COULOMBOV ZAKON / COULOMB LAW Petsič- platina / Punch-Blank m = 0,1....... Pridrževalo - platina / Blankholder-Blank m = 0,1....... Matrica - platina / Die-Blank: m = 0,1 HITROST PESTIČA / PUNCH SPEED: ________............................. Sl. 2. Geometrijska oblika testnega izdelka in plošče (levo) in model za simuliranje z MKE (desno) Fig. 2. Geometry of the test product and blank (left) and FEM simulation model (right) debeline pridrževane prirobnice v analiziranih časovnih korakih so pomenili vhodne podatke za analize elastičnega obnašanja pridrževala in preračune izmer elastične pridrževalne plošče ([7] in [13]). 2.1 Model globokega vleka na osnovi MKE z običajnim držalom Simuliranja globokega vleka smo izvajali s programom Pam-Stamp® [9]. Program je prirejen za preoblikovanje pločevine in računa po eksplicitni numerični metodi z lupinskimi elementi. RPK (CAD) model plošče in orodja ter mrežo MKE (vozlišča in elemente) smo pripravili v programu I-DEAS, pri čemer smo upoštevali osno simetričnost modela in analizirali le 1/4 celotnega modela. V predprocesorju Pam-Stamp-a smo modelu po MKE dodali podatke o materialu, robnih pogojih, pogojih trenja med orodjem in ploščo in preostale za simuliranje potrebne podatke (sl. 2). Pločevina je bila popisana z the analysed time intervals were used as the input data for the analyses of the elastic behaviour of the blankholder and the calculations of the dimensions of the elastic holding plate ([7] and [13]). 2.1 FEM model of deep drawing with a conventional blankholder is a specialised program for sheet-metal forming which uses an explicit numerical method and shell elements. A CAD model of the blank, the tool and the FEM mesh (nodes and elements) were prepared in the I-DEAS program. Since the model is axisymmetric, only one quarter of the model was analysed. Data on the material, the boundary conditions and the friction conditions between the tool and the blank, as well as other data required for the simulations were added to the FEM model using the Pam-Stamp pre-processor (see _^(SMM]__ V@_?irW]D[K stran 98 T. Pepelnjak - Z. Kampu{: Analize kakovosti - Analysing the Quality Preglednica 2. Analizirani načini pridr zevanja in pojavi okvar preoblikovanca Table 2. Analysed holding methods and defects on the workpiece Način pridrževanja Holding Spreminjanje sile Variation of the force Kakovost preoblikovanja in izbrani odločitveni kriterij Quality of forming and the selected criterion Fd= Fd,sie (po Sieblu /due to Siebel) nespremenjeno v redu (KMD, gube, Fp, tanjšanje) unchanged good (FLC, wrinkles, F, thinning) Fd =1,5 Fd,sie nespremenjeno unchanged v redu (KMD, gube) slabše (Fp, tanjšanje) good (FLC, wrinkles) worse (Fp, thinning) Fd =2 Fd,sie nespremenjeno unchanged slabo - trganje (KMD) bad - tearing (FLC) Fd =0,75 Fd,sie nespremenjeno unchanged boljše (KMD, gube, Fp, tanjšanje) better (FLC, wrinkles, Fp, thinning) Fd =0,5 Fd,sie nespremenjeno unchanged slabo - gubanje (pomiki prirobnice) v redu (Fp, tanjšanje) bad - wrinkles (flange displacements) good (Fp, thinning) Fd =1,5 Fd,sie* Fd,sie*1,5 Fd,sie pada - raste decreases-increases v redu (KMD, gube, Fp) boljše (tanjšanje) good (FLC wrinkles, Fp) better (thinning) Fd = Fd,sie* 0 N pada decreases boljše (KMD, gube, Fp, tanjšanje) better (FLC, wrinkles Fp, thinning) Opomba: Fd,sie je pridrževalna sila, izračunana po Sieblovem obrazcu. Kakovost preoblikovalnega postopka smo vrednotili glede na referenčen vlek s silo pridrževanja Fd = Fd,sie. Note: F d sie is the blankholder force calculated according to Siebel’s formula. The quality of forming has been evaluated according to the reference blankholder force of Fd = Fd,ie. elasto-plastičnim zakonom, orodje pa je bilo togo. V elastičnem področju velja Hookov zakon (popis z E, n) ter Holomonov zakon utrjevanja v plastičnem področju. V prvi fazi raziskav smo analize preoblikovanja najprej naredili z običajnim pridrževalom z različnimi velikostmi pridrževalnih sil. Nespremenljiva sila pridrževala F d sie , izračunana po Sieblovem obrazcu, pomeni referenčno vrednost, s katero smo primerjali različne načine pridrževanja -preglednica 2. Rezultate simuliranj po MKE preoblikovanja korita smo vrednotili s kriteriji: -- - - velikost preoblikovalne sile; tanjšanje materiala, ki ne sme preseči 20 % debeline pločevine; diagram krivulj mejnih deformacij (KMD) iz katerega preberemo pojave lokalnih tanjšanj in trganja materiala; pomiki vozlišč v smeri z’, s katerimi vrednotimo gubanje ravne površine (prirobnice). Za najuspešnejše vrednotenje gubanja prirobnice preoblikovanca se je izkazalo določevanje pomikov pridrževane prirobnice v smeri z’. Za kriterij smo vzeli Dz=0,05 mm, znotraj katerega smo lahko zelo dobro določili mejo velikosti sile pridrževanja, Figure 2). Sheet metal is described using the law of elasto-plasticity and the tool is rigid. Hook’s law ap-plies in the elastic zone (description with E and n) and Holomon’s law of hardening in the plastic zone. In the first phase of the research work, the analyses of forming were performed with a conven-tional blankholder using different magnitudes of the blankholder force. A constant blankholder force F calculated according to Siebel’s formula was d,sie used as a reference value for the comparison of the different holding methods (Table 2). The results of the FEM simulations of forming the sink were evalu-ated using the following criteria: - magnitude of the forming force; - thinning of the material, which must not exceed 20% of the sheet-metal thickness; - diagrams of the forming limit curves (FLC), in which localisation and tearing of the material can be seen; - displacements in the ‘z’ axis, which are used to evaluate the wrinkling of the flat surfaces (flange). The determination of the displacements of the held flange in the ‘z’ axis proved to be the most successful method for the evaluation of the wrin-kling of the workpiece flange. Dz=0.05 mm was taken as a criterion, and within this interval it was possible isfFIsJBJbJJIMlSlCšD I stran 99 glTMDDC T. Pepelnjak - Z. Kampu{: Analize kakovosti - Analysing the Quality 'z'pomik / 'z'displacement [mm] -o. i -0.075 -0.05 -0.025 I— 0 0. 025 0.05 0.075 0.1 F = 0,50 F d,sie F = 0,75 F d,sie Sl. 3. Napoved gubanja prirobnice Fig. 3. Prediction of flange wrinkling pri kateri se je material pričel gubati. Slika 3 prikazuje analizo gubanja prirobnice pri dveh različnih silah pridrževanja. Primerjave simuliranj običajnega pridrževanja s togim držalom so pokazale, da dajejo spreminjajoče (padajoče - naraščajoče) sile pridrževanja boljše rezultate kakor pridrževanje z enako veliko nespremenljivo silo. Tudi vlečna sila na pestiču je zaradi tega manjša, s čimer se zmanjša tudi potrebna energija za globoki vlek. To je pomembno predvsem pri izdelkih z velikimi površinami, pri katerih pridrževalna sila pomeni pomemben delež celotne preoblikovalne sile. Kljub zelo velikim tlakom na pridrževani preoblikovanec proti koncu globokega vleka se izkaže, da sile ne smemo preveč zmanjšati (npr. na vrednost F d = 10 % F d sie ali celo F d = 0 N), saj se v teh primerih pričnejo proti koncu vleka pojavljati gube v prirobnici. 2.2 Model globokega vleka na osnovi MKE s segmentiranim pridrževalom Iz osnov preoblikovanja je znano, da je pri globokem vleku izdelkov z ravnimi deli na teh mestih potrebna večja pridrževalna sila, ki zavira prehiter tok materiala preko vlečnega polmera. V primeru običajnega pridrževala v ta namen uporabljamo zadrževalne letve, preko katerih mora drseti pločevina, preden vstopi v vlečni del matrice. V analizah z MKE smo namesto pridrževalnih letev uporabili segmentirano pridrževalo. Z njim dosegamo boljšo in enakomernejšo porazdelitev tlakov po prirobnici preoblikovanca ter se s tem približamo željenemu stanju pridrževanja z elastičnim pridrževalom. Pri pritisku p d =3,6 MPa (F d =0,75 F d sie ) na ravne dele prirobnice smo že v prejšnjih raziskavah ugotovili, da se material na prirobnici ne guba, vendar smo pregled z enakim tlakom izvedli tudi za segmentirano pridrževanje. to accurately determine the upper blankholder force limit at which the material began to wrinkle. Figure 3 shows the analysis of the flange wrinkling for two different blankholder forces. Comparisons of simulations of conventional holding using a rigid holder showed that varying the blankholder forces yielded better results than holding with a constant force. As a result, the drawing force on the punch is also smaller, which reduces the energy required for deep drawing. This is important mainly in products with a large surface area, where the blankholder force represents a significant percentage of the total forming force. In spite of very large pres-sures on the held workpiece which occur towards the end of the deep drawing, it turns out that the forces must not be reduced excessively (e.g. to F = 10% d F or even to F = 0 N), because this causes wrin-d,sie d kling of the flange towards the end of the drawing. 2.2 FEM model of deep drawing with a segmented blankholder It is well known from the theory of forming that when deep drawing products with flat sections a greater holding force is required in such sections to prevent a too rapid flow of material over the drawing radius. In the case of conventional blankholders, draw-beads are used for this purpose, over which the sheet metal slides before entering the drawing zone of the tool. In the FEM analy-ses, a segmented blankholder was used instead of draw beads. Such a blankholder gave a better, more uniform, distribution of pressures along the workpiece flange and thus enabled to approximate the desired state of holding with an elastic blankholder. It was already observed dur-ing previous research that at a pressure of pd=3.6 N/mm2 (Fd = 0.75 Fd,sie) on flat sections of the flange, the flange material did not wrinkle. A reference simulation was also performed for segmented holding, using the same pres-sure. The selected blankholder segment size was 100 x grin^SfcflMISDSD ^BSfiTTMlliC | stran 100 T. Pepelnjak - Z. Kampu{: Analize kakovosti - Analysing the Quality Gib pestica / Punch travel: hp = 47 mm hp = 108 mm hp = 150 mm a) tlak držala / blankholder pressure [MPa] 2 . 5 ¦I . ', 10 12. 5 15 17. 5 20 b) Sl. 4. Porazdelitve tlakov po prirobnici za različne začetne tlake pridrževanja: a) pd =3,6 MPa na vseh segmentih ter b) pd = 3,6 MPa na ravnih delih in pd = 2,4 MPa v vogalih Fig. 4. Distribution of pressures on the flange for different initial holding pressures: a) pd =3.6 MPa on all segments and b) pd = 3.6 MPa on the straight parts and pd = 2.4 MPa on the edges Izbrana velikost segmentov držala je 100x100 mm. V naslednji fazi smo na ravnih delih prirobnice ohranili tlak p =3,6 MPa, na vogalih pa smo znižali pritisk na p d = 2,4 MPa (F d =0,5 F d sie ). Kljub zmanjšanju pridrževalne sile v vogalih vlečenca z vrednotenjem pomikov vozlišč mreže MKE nismo zaznali gubanja prirobnice. Kriterij ugotavljanja gubanja je pomik vozlišč, večji od Dz=0,05 mm. Slika 4 prikazuje tlake na prirobnici med vlekom preoblikovanca v treh fazah vleka. Zmanjšanje pritiska držala vpliva tudi na zmanjšanje pridrževalne sile in s tem tudi silo merjeno na matrici (sl. 5). Kot je razvidno iz slike 5, se z zmanjševanjem pridrževalne sile na posameznih segmentih na F = 0,5 Fdi občutno zmanjša celotna sila preoblikovalnega postopka. Energijski izračun preoblikovanja ob pridrževanju z nespremenljivo silo Fd = 0,75Fd i in krajevno optimirano silo kaže na 35,8 odstotno zmanjšanje porabe energije v slednjem primeru. Rezultati globokega vleka z uporabo segmentiranega držala so namenjeni za analize elastičnega pridrževanja [13]. Zaradi različnih debelin pločevine, ki so posledica različnih napetostno deformacijskih stanj po prerezu neokroglega vlečenca ter anizotropije materiala, se 100 mm. In the next phase, the pressure of p =3.6 MPa d was maintained on the straight parts of the flange of the sink circumference, while on the edges it was reduced to p = 2.4 MPa (F =0.5 F ). In spite of a reduced d d d,sie blankholder force on the workpiece edges, the evaluation of the FEM mesh-node displacements did not reveal any wrinkling of the flange. A node displacement in ex-cess of Dz=0.05 mm was used as the criterion for estab-lishing the wrinkling. Figure 4 shows the pressures on the flange during three phases of deep drawing the workpiece. A reduction of the blankholder pressure also reduces the holding forces and the force measured on the die (see Figure 5). As Figure 5 shows, with decrease of blankholder force on particular segments down to F d =0.5 F , significant decrease in total force used for d,sie forming procedure can be achieved. The calculated energy for particular forming process performed with unique holding force of F = 0.75 F and with the spatial d d,sie optimised one reveals 35.8 % reduction in energy con-sumption. The results of deep drawing with the seg-mented blankholder served for the analyses of the elas-tic holding [13]. Different sheet-metal thicknesses, which resulted from different stress-strain states across the cross-section of a noncircular workpiece and material anisotropy, caused the appearance of locally different | IgfinHŽslbJlIMlIgiCšD I stran 101 glTMDDC T. Pepelnjak - Z. Kampu{: Analize kakovosti - Analysing the Quality 9> S s 120 160 mm gib pestiča / punch travel h 240 sila pestiča / punch force (Fd=0,75FdÄJ sila na matrici / die force (Fd=0,75Fdsle) sila pestiča /punch force (Fd=0,75Fdste - straight part; Fd=0,5FdiSie in the corner) sila na matrici / die force (Fd=0,75Fdste - straight part; Fd=0,5Fd]Sle in the corner) Sl. 5. Sila na orodju pri enako veliki nespremenljivi sili pridr zevanja vseh segmentov ter zmanjšani sili pridrzevanja v vogalih izdelka Fig. 5. Force on the tool at equal and constant holding forces for all segments and a reduced blankholder force on the product edges pojavljajo različni lokalni tlaki pridrzevanja. Velikosti teh tlakov v različnih fazah vlečenja ter pripadajoče porazdelitve debelin po značilnih prerezih prirobnice vlečenca pomenijo vhodne podatke za analize elastične pridrževalne plošče. Z njimi lahko optimiramo prilagajanje pridrževala porazdelitvi debelin prirobnice vlečenca in lokalno uravnavamo tlake pridrzevanja med samim vlekom. V zadnji fazi analiz smo pridrževalne sile posameznih segmentov časovno spreminjali glede na večanje tlaka na posameznem segmentu. Takšna optimizacija predstavlja nov koncept prilagajanja pridrževalne sile zahtevam preoblikovalnega postopka, ki do sedaj še ni bila izvedena. Zasnova časovne optimizacije pridrževalne sile posameznega segmenta temelji na prilagajanju tlaka pridrzevanja glede na vnaprej predpisano največjo vrednost pd (sl.6). Ob prekoračitvi največjega tlaka ,max držala na posameznem segmentu smo zmanjšali pridrževalno silo tega segmenta. S tem pridrževalni tlak ponovno pade pod dopustno vrednost. Simulacije z MKE s prilagajanim tlakom pridrzevanja smo analizirali glede na opazovane tehnološke parametre kot so gubanje, trganje, holding pressures. The magnitudes of these pressures in different phases of the deep drawing and the corre-sponding distributions of thicknesses across the char-acteristic cross-sections of the workpiece flange were used as the input data for the analyses of the elastic holding plate. Such analyses can be used to optimise the adjustment of the blankholder to the distribution of the workpiece flange thicknesses and locally control the holding pressures during deep drawing. In the last phase of the presented analyses the blankholder forces of individual segments were varied with time, with respect to pressure increases on an indi-vidual segment. This is a new concept in the adjustment of holding to the requirements of the forming process, which has not been analysed yet. The optimisation con-cept of the blankholder pressure on each segment was based on the adaptation of the applied pressure accord-ing to the pre-defined value of maximum blankholder pres-sure pd,max - Figure 6. Once the maximum blankholder pressure on a particular segment was exceeded its blankholder force was decreased to decrease the pres-sure to less then the critical value. The FEM simulations with adopted blankholder pressures were analysed ac-cording to demanding technological parameters such as wrinkling criteria, tearing, thinning and FLD curve as well. VBgfFMK stran 102 T. Pepelnjak - Z. Kampu{: Analize kakovosti - Analysing the Quality tanjšanje in diagram KMD. Analiza poteka preoblikovanja s tlaki pridrževanja 3,6 MPa na vseh segmentih držala pokaže, v katerih časovnih korakih vleka se tlak na posameznem segmentu zveča preko opredeljene dopustne vrednosti. Iz izkušenj smo določili, da sme biti zvečanje tlaka na segmentu do največ 10-kratne vrednosti tlaka na začetku vleka. Silo pridrževanja na posamezni segment smo nato zmanjšali na njeno polovično vrednost in jo tako obdržali, dokler tlak pridrževala ponovno ne prekorači mejne vrednosti. Optimizacija sil pridrževanja je pokazala pričakovano dodatno zmanjšanje potrebnih vlečnih sil, kar ugodno vpliva tako na potek vleka kakor tudi na porazdelitev debelin vlečenca. Vrednotenje za preoblikovanje porabljene energije je pokazalo 43,6 odstotno zmanjšanje glede na referenčen preoblikovalni proces z nespremenljivo silo Fd = 0,75Fd i na vseh segmentih držala. The analysis of the forming process with an initial holding pressure of 3.6 MPa on all blankholder segments shows those time intervals during deep drawing during which the pressure on an individual segment exceeds the predefined allowable value. On the expert basis, it was determined that the pressure increase on an individual segment may be up to 10 times the initial value. The blankholder force on each individual segment was then reduced to half its value and maintained at this level until the pressure on the particular blankholder segment reached the maximum level again. The optimisation of the blankholder forces showed the expected additional decrease in the required drawing forces, which has a favourable effect both on the deep-drawing process and on the distribution of workpiece thicknesses. The evaluation of the energy needed for the forming operation showed a decrease of 43.6 % in comparison with the reference forming process with a unique holding force of Fd =0.75 Fd,sie on all segments of the blankholder. Proces preoblikovanja pločevine Sheet metal forming process Tehnološke omejitve/ Technological limitations: - KMD / FLD - gubanje / wrinkling - trganje / tearing - tanjšanje / thinning Simulacija z MKE preoblikovanja s segmentiranim pridržalom FEM of forming with the segmented blankholder Krmiljenje tlaka (filter) Pressure control (filter) brez krmiljenja tlaka without pressure A control -pd d,max ~~~s krmiljenjem laka with pressure control Prilagajanje tlaka pridrževala posameznega segmenta / Adaptation of blankholder pressure for particular segment: - zmanjšanje pridrževalne sile / decreas e of blankholde r force - funkcijski filter (koračna funkcija, strmina) / functional filte r (step function , ramp) Optimiziran preoblikovalni proces (nižje preoblikovalne sile, manj porabljene energije, večja tehnološka varnost) Optimised forming process (lower forming forces, less work needed, bigger technological safety) Sl. 6. Zasnova krajevne in časovne optimizacije tlaka pridrževala pločevine Fig. 6. Optimisation concept for spatial and time adaptation of blankholder pressure ^vmskmsmm 01-2 stran 103 | ^BSSITTMIGC p T. Pepelnjak - Z. Kampu{: Analize kakovosti - Analysing the Quality 3 SKLEPI Analize preoblikovanja neokroglega izdelka so pokazale, da se s spreminjanjem in optimiranjem pridrževalne sile lahko zmanjšajo sile globokega vleka. Optimizacijo pridrževanja smo vrednotili s kriteriji zmanjševanja preoblikovalnih sil, tanjšanja preoblikovanca in vrednotenjem procesne varnosti. S tem prihranimo del potrebne energije preoblikovanja. S simulacijami po MKE se lahko napovejo izboljšave poteka sil pridrževanja, pri katerih se izdelek kakovostno preoblikuje. Razvili smo zasnovo krajevne in časovne optimizacije segmentiranega pridrževanja, s katero lahko s simulacijami po MKE dodatno izboljšamo preoblikovalni proces že v navideznem okolju. Pri globokem vleku velikih preoblikovancev pogosto pomeni energija, porabljena za pridrževanje pločevine med preoblikovanjem, pomemben delež celotne porabljene energije. Sile pridrževanja so pri tem lahko celo večje od samih vlečnih sil. Vrednotenje rezultatov pridrževanja s segmentnim pridrževalom ob zmanjševanju sile pridrževanja na vogalu izdelka je pokazalo, da je potrebna celotna energija za vlek za 35 odstotkov manjša, kakor v primeru enakomernega pridrževanja vseh segmentov z enako silo. Pri vrednotenju časovno in krajevno optimirane pridrževalne sile smo ugotovili celo 43,6 odstotno zmanjšanje energije potrebne za preoblikovalni proces. Nov način prilagajanja pridrževalnih sil posameznih segmentov je oprt na časovno analizo stičnega tlaka med orodjem in prirobnico preoblikovanca. Z njim se dodatno povečuje prilagodljivost pridrževalnega sistema. Z zmanjševanjem pridrževalne sile posameznega segmenta ob prekoračitvi kritične vrednosti stičnega tlaka se dodatno zmanjšuje za preoblikovalni proces porabljena energija. Hkrati se povečuje tehnološka varnost in izboljšuje porazdelitev debelin preoblikovanca. Zahvala Avtorja se zahvaljujeta Ministrstvu za znanost in tehnologijo in podjetju Litostroj E.I., ki sta v okviru projekta L2-1689-0782 delno financirala predstavljene raziskave. Zahvaljujeva se tudi TECOS-u, razvojnemu centru orodjarstva Slovenije za brezplačno uporabo programskega paketa Pam-Stamp®. ^BSfiTTMlliC | stran 104 3 CONCLUSIONS The presented analyses of forming noncircular workpieces showed that it is possible to improve the forming process with the optimisation of the blankholder force. The optimisation has been evaluated according to the reduction of the forces in deep drawing by varying and optimising the blankholder force, decreasing the local material thinning and evaluating the process safety. This can help reduce the energy required for forming. Using FEM simulations it is possible to predict improvements in the variation of blankholder forces which will result in high-quality forming. A concept for spatial and time optimisation of the blankholder force for a segmented holder has been developed for additional optimisation improvements of the forming process with FEM simulations in the virtual environment. When deep drawing large workpieces the energy required to hold the sheet metal during forming frequently represents a significant portion of the total energy, and the blankholder forces may even exceed the drawing forces. An evaluation of the results of holding using segmented blankholders and reduced holding forces on product edges showed that the total energy required for deep drawing is reduced by 35 percent in comparison with the situation where all the segments are held uniformly, i.e. with equal force. The evaluation of spatial and time optimisation of the blankholder pressure has shown a reduction in the energy used by 43.6 percent in comparison with the reference forming process. The described new approach to the adjustment of blankholder forces on individual segments is based on temporary analyses of the contact pressure between the tool and the workpiece flange. This also increases the adaptability of the holding system. By reducing the blankholder force on an individual segment at the time the critical limit for contact pressure is exceeded the energy required for forming can be further reduced. At the same time, the technological safety is increased and the distribution of thicknesses in the workpiece improved. Acknowledgement The authors gratefully acknowledge the assistance of the Ministry of Science and Technology, and Litostroj E.I., which partially financed the research as part of the L2-1689-0782 project. We would also like to thank TECOS, the Toolmaking Centre of Slovenia, for free use of the Pam-StampS program package. T. Pepelnjak - Z. Kampu{: Analize kakovosti - Analysing the Quality 4 OZNAKE SIMBOLOV pridrževalna sila sila držala izračunana po Sieblovem obrazcu pridrževana površina tlak pridrževala mejni tlak pridrževala natezna trdnost meja plastičnosti vlečno razmerje premer pestiča začetna debelina pločevine konstanta materiala eksponent utrjevanja modul elastičnosti Poissonovo razmerje gostota materiala Lankfordovi koeficient normalne plastične anizotropije v smereh 0°, 45° in 90° glede na smer valjanja d,mej 4 SYMBOLS Fd F d,sie Ad pd p Rm Rp b0 dp s0 C n E n r r, r 0 45 90 5, r9 blankholder force the blank holder force calculated by Siebel’s formula holded surface blankholder pressure limit blankholder pressure tensile strength yield strength drawing ratio punch diameter initial sheet thickness material constant hardening coefficient elasticity modulus Poisson’s coefficient material density Lankford’s coefficients of anisotropy in directions 0°, 45° and 90° according to the rolling direction [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] 5 LITERATURA 5 REFERENCES Lange, K. (1990) Umformtechnik, Handbuch für Industrie und Wissenschaft, Band 3: Blechbearbeitung, Springer Verlag, Berlin. Siegert, K., M. Ziegler, S. Wagner (1997) Closed loop control of the friction force. Deep drawing process, Journal of materials processing technology, Vol. 71, 126-133. Cherrill, A.P., S. Zhang, K.B. Ousterhout (1998) A variable force binder for a draw press. Journal of materials processing technology, Vol. 73, Nr. 1-3, 7-17. Siegert, K., M. Ziegler, S. Wagner (1998) Advanced forming technologies. Sheet Metal Forming Beyond 2000. Genval, Brussels. Gunnarsson, L., N. Asnafi, E. Schedin (1998) In-process control of blank holder force in axi-symmetric deep drawing with degressive gas springs. Journal of materials processing technology, Vol. 73, Nr. 1-3, 89-96. Kergen, R. (1998) A Comparison of different blank-holder force control principles based on the cup test. Sheet Metal Forming Beyond 2000. Genval, Brussels. Kampuš, Z., K. Kuzman, D. Noe, J. Kramar, T. Perme, A. Bergant, T. Pepelnjak, B. Jerman, P. Vogrič (2000) Globoki vlek pločevine z logistično usklajeno avtomatizacijo: letno in zaključno poročilo aplikativnega raziskovalnega projekta v letu 1999. Fakulteta za strojništvo Ljubljana. Perme T, D. Noe (2000) Computer aided planning of manufacturing systems using the LASIMCO simulation package. 2000 Int. CIRP Design Seminar on Design with Manufacturing: intelligent design concepts methods and algorithms, Haifa, Israel, May 16.-18. 2000. Haifa, Israel: CMSR, 487-492. Pam-stamp, Ver. 98, Users manual, ESI Coorp., France, 1998 Gantar, G., K. Kuzman (2000) FEM prediction of deep drawing process with optimised conventional holding of blank. Proc. of MicroCAD’2000, Int. Computer Science Conference, Miskolc, Hungary, 15-20. Kuzman, K. (1999) Prispevek k hitremu razvoju in izdelavi orodij za globoki vlek pločevine (Contribution to the fast sheet metal deep drawing tool development and production). Strojniški vestnik, 45, 6, 238-249. Pepelnjak T, G. Gantar, K. Kuzman (2001) Numerical simulations in optimisation of product and forming process, Journal of materials processing technology, Vol 115, Nr. 1, 122-126. Jerman, B., R. Hodnik, J. Kramar (2001) Analiza raznosa tlaka pri uporabi prilagodljivega pridrževala z možnostjo nadzora pridrževalne sile med globokim vlekom. Strojniški vestnik, Vol 47, 2, str. 83-93. Naslov avtorjev: dr. Tomaž Pepelnjak doc.dr. Zlatko Kampuš Fakulteta za strojništvo Univerza v Ljubljani Aškerčeva 6 1000 Ljubljana Athors’ Adress: Dr. Tomaž Pepelnjak Doc.Dr. Zlatko Kampuš Faculty of Mechanical Eng. University of Ljubljana Aškerčeva 6 1000 Ljubljana, Slovenia Prejeto: Received: 22.12.2000 Sprejeto: Accepted: 27.6.2001