© Strojni{ki vestnik 49(2003)6,298-312 © Journal of Mechanical Engineering 49(2003)6,298-312 ISSN 0039-2480 ISSN 0039-2480 UDK 621.778.2:62-426 UDC 621.778.2:62-426 Izvirni znanstveni ~lanek (1.01) Original scientific paper (1.01) Mo`nosti stabilizacije preoblikovalnih lastnosti `ice z ravnanjem med valji Stabilizing the Forming Properties of Wire by Using a Roller-Straightening Process Miha Nastran - Karl Kuzman Nestabilne preoblikovalne lastnosti vhodnih materialov predstavljajo v današnjem stanju avtomatizacije proizvodnje se vedno precejšen problem. Zlasti v velikoserijski proizvodnji, pri kateri vse več uporabljamo avtomatizirane montažne linije, je potreba po enakih polizdelkih praktično neizogibna. Dejstvo je, da so raztrosi geometrijskih značilnosti polizdelkov velikokrat posledica neenakomernih mehanskih lastnosti vhodnega materiala, na katerega proizvodni inženirji podjetij, ki se ukvarjajo s kovinsko predelavo, nimajo vpliva. Prispevek prikazuje možnosti stabilizacije preoblikovalnih lastnosti žice z uporabo ravnalnih naprav, ki so sestavni del vsakega proizvodnega procesa predelave žice. V začetku je najprej na kratko prikazana reologija jekel pri izmeničnih obremenitvah. Sledi modeliranje ravnalnega procesa in stabilizacijski algoritem. Na koncu preverimo model na konkretnem industrijskem primeru izdelave reber za mehanizme registratorjev. © 2003 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: preoblikovanje žice, ravnanježice, lastnosti preoblikovalne, stabilizacija lastnosti) The unstable forming properties of input material cause many problems in automated production processes. This is particularly so in mass production, where automated assembly lines are increasingly common, and product uniformity is a priority. It is a fact that the main reasons for the fluctuations in part geometries are the inconsistent mechanical properties of the input material, and production engineers are often unable to influence this. Here we investigate the possibility of stabilizing the mechanical properties of wire by using a roller straightener, which is used in every wire-processing production process. At the beginning a short outline of the steel’s response during cyclic straining is given. This is followed by the modeling of the wire-straightening process and by the stabilization algorithm. Finally, the model is tested on a real industrial process - the production of leverarch mechanisms for ringbinder files. © 2003 Journal of Mechanical Engineering. All rights reserved. (Keywords: wire forming, wire straightening, forming properties, stability properties) 0 UVOD Potreba po enakomernih mehansko preoblikovalnih lastnostih vhodnega materiala se zlasti kaže pri velikoserijski proizvodnji, pri kateri je potrebno zagotoviti ozka tolerančna polja geometrijskih značilnosti polizdelkov[1]. Dejstvo je, da dejansko jekla z absolutno enakomernimi mehanskimi lastnostmi ni. Vselej so v njem zaradi krajevno različne mikrostrukture, ki je posledica predhodnih tehnoloških postopkov obdelave jekla, opazne neenakomernosti, ki se preslikajo v geometrijska odstopanja izdelkov. Industrijski primer neenakomerne geometrijske oblike izdelka je prikazan na sliki 1. Širina izdelanega rebra se sčasom spreminja, kljub temu, da parametri procesa ostajajo ves čas nespremenjeni. 0 INTRODUCTION The need for wire with stable mechanical properties is especially important during mass production, where it is necessary to keep the geometrical features of products within narrow tolerance fields [1]. The problem is, however, that it is not possible to obtain steel that has absolutely homogenous mechanical properties. Due to local differences in the microstructure, which is a consequence of previous technological operations, there are always some inhomogenities in mechanical properties, which affect the final geometry. An industrial example of part-geometry fluctuation is presented in Figure 1. The width of the product is time dependent even though the process parameters remain constant. VH^tTPsDDIK stran 298 Nastran M., Kuzman K.: Mo`osti stabilizacije preoblikovalnih - Stabilizing the Forming 0 50 100 150 200 250 300 350 l [m] Sl. 1. Neenakomernost geometrijske oblike izdelka Fig. 1. Fluctuation of the product geometry Vzrok časovnemu spreminjanju geometrijske It is inevitable that the reason for the unstable oblike je potrebno iskati tudi v neenakomernih geometry is to be found in the non-stable mechanical mehanskih in geometrijskih lastnostih surove žice. properties of the incoming wire. Keeping the Zagotavljanje enakomernih lastnosti jekla že sega microstructure of the steel homogeneous is the na metalurško področje in se z njim v prispevku ne domain of the metallurgist and will not be considered bomo ukvarjali. Bolj kot definiranje vzroka nastanka in this paper. The solution of how to stabilize the prikazane neenakomernosti geometrijske oblike forming process, in spite of the fluctuation of in the izdelka je pomembna rešitev, s katero bi kljub material’s properties, is much more important than opaznim neenakomernim lastnostim žice stabilizirali finding the reason for the fluctuation of the krivilni postopek. Reševanje tega problema in mechanical properties. This paper discusses the smernice za stabilizacijo so tema nadaljnje razprave solution to the problem and gives directives for v prispevku. stabilising the process. 1 PREOBLIKOVALNE LASTNOSTIŽICE 1 FORMING PROPERTIES OF WIRE Pri raziskavi je bil najprej narejen preskus, s First, a test was made to confirm the major katerim smo potrdili prevladujoč vpliv preoblikovalnih influence of the mechanical properties on the značilnosti žice na končno geometrijsko obliko geometry of the product. The correlation between izdelka. Prav tako smo iskali odvisnost med the fluctuation in the wire’s geometry and the spreminjanjem geometrijskih parametrov žice ter geometry of the finished part were checked as well. končno geometrijsko obliko izdelka. A simulation of the straightening process was V ta namen je bila izdelana simulacija made, and a modification of Prager’s flow rule was ravnalnega postopka z uporabo spremenjenega used. It serves for the inverse approach to the Pragerjevega modela utrjevanja materiala, ki je bila identification of the wire’s flow stress. Parallel to this namenjena inverznemu načinu razpoznavanja meje an experimental wire straightener was designed in plastičnosti žice. Hkrati s tem je bilo treba konstruirati such a way that it was possible to measure the tudi preskusno ravnalno napravo, ki omogoča meritve transverse roller forces and to preset the rollers simple prečnih sil, ki delujejo na ravnalno kolo, ter preprosto way The experimental straightener also serves for nastavljanje položajev ravnalnih valjev. Prav tako je measuring the wire diameter. We also suspected that preskusna ravnalna priprava rabila sprotnemu the wire diameter has an influence on the final product merjenju ovalnostižice, za katero smo prav tako sumili, geometry. It was shown that the fluctuation in the da lahko vpliva na geometrijske značilnosti izdelka. wire’s diameter has no influence on the final geometry Izkazalo se je, da ovalnost žice nima bistvenega vpliva of the part. The scaled value of the measurements of na geometrijsko obliko. Na sliki 2 so prikazane wire’s diameter in the xz and yz planes are shown in povečane vrednosti meritve premera žice v ravnini x Figure 2, together with the scaled values of the part’s in y ter povečana vrednost širine izdelanega rebra. width. Korelacijski koeficient med meritvijo premera The correlation between the part geometry v ravnini x ter širino rebra je 0,65, med meritvijo širine and the wire diameter in the x direction is 0.65, while v ravnini y ter meritvijo geometrijske oblike pa 0,57. between the diameter in the y direction and the part’s Glede na to, da je korelacijski koeficient med geometry it is only 0.57. The correlation between the geometrijsko obliko in mejo plastičnosti 0,75 (sl. 3), flow stress and the part’s geometry is 0.75, which lahko sklepamo na glavni vpliv meje plastičnostižice implies a major influence of the flow stress. na končno geometrijsko obliko izdelka. A theoretical calculation shows that the Prav tako pokaže teoretičen izračun, da ima influence of the wire’s diameter on the transverse spreminjanje prečnega prereza žice v primerjavi s roller forces can be neglected. From which it can be | lgfinHi(s)bJ][M]lfi[j;?n 03-6_____ stran 299 I^BSSIfTMlGC Nastran M., Kuzman K.: Mo`osti stabilizacije preoblikovalnih - Stabilizing the Forming geometrija izdelka brel - product geometry brel 1 0,8 0,6 0,4 0,2 premer žice dx - wire diameter dx premer žice dy - wire diameter dy d= xrel dx (l) - dx min (dx max -dx min ) dy(l) - dymin yrel d =(d -d ) ymax ymin 200 l [m] 300 rel = b(l) - bmin (b max min Sl. 2. Odvisnost med geometrijsko obliko izdelka in premerom žice Fig. 2. Correlation between the product geometry and the wire’s diameter spremembo meje plastičnosti zanemarljiv vpliv na velikost prečnih sil na ravnalne valje. S tem lahko sklepamo, da je sprememba prečne sile povezana izključno s spremembo meje plastičnosti žice. Na sliki 3 je prikazana meja plastičnosti žice v odvisnosti od lege žice v kolutu [2], kjer je lepo razvidna soodvisnost med geometrijsko obliko izdelka ter mejo plastičnosti žice. Sklepamo lahko, da imajo preoblikovalne lastnosti žice bistven vpliv na nadaljnji krivilni postopek, vplivajo pa tudi na premer žice. Spreminjanje premera žice nima bistvenega vpliva na krivilni postopek, saj so odstopanja premajhna. 1.1 Osnovna zamisel stabilizacijskega algoritma Osnovna zamisel je v tem, da bi z ravnalnim postopkom, pri katerem se material obremenjuje izmenično v nateznem in tlačnem področju, vplivali na mejo plastičnosti na izstopu iz ravnalke. Osnova razmišljanju je eksperimentalno potrjeno dejstvo [2], da je meja plastičnosti žice odvisna od velikosti povečanja plastične deformacije, bodisi v nateznem ali tlačnem področju. Za dosego zastavljenega cilja je najprej treba imeti dober model ravnalnega postopka, zato si bomo najprej ogledali njegovo modeliranje. concluded that the variation in the transverse roller forces is only a consequence of the fluctuation in the flow stress. The time dependence of the wire’s flow stress [2] is presented in figure 3. The correlation between the wire’s flow stress and the product geometry is clear. It can be concluded that the forming properties of wire have a major impact on the subsequent bending process, as wel as having an influence on the wire’s diameter. The fluctuation in the wire’s diameter has no significant influence on the bending process, since it is too small. 1.1 The main idea of the stabilization algorithm The main idea is to use the straightening process, where the material is exposed to cyclical deformation in the tensile and compressive regions, to influence the wire’s yield stress at the end of the straightening process. The basis for this is an experimentally verified fact [2]: that the yield stress depends on the total amount of cyclical deformation in the tensile or compressive region. To achieve this we have first to have a good model of the straightening process, so the modeling will be presented first. meja plastičnosti žice Y - wire flow stress Y geometrijska oblika izdelka b - product geometry b 1 0.8 0.6 0.4 0.2 0 W> finr V A. m v*. a/ w Y rel b rel Y(l) - Ymin (Ymax -Ymin ) b(l) - bmin (bmax -bmin ) 0 100 200 l [m] 300 400 500 Sl. 3. Odvisnost med geometrijsko obliko izdelka in mejo plastičnosti žice Fig. 3. Correlation between the product geometry and wire’s yield stress VH^tTPsDDIK stran 300 — Nastran M., Kuzman K.: Mo`osti stabilizacije preoblikovalnih - Stabilizing the Forming 2 MODELIRANJE RAVNALNEGA POSTOPKA Pred nadaljnjo obdelavo žice na žično krivilnem avtomatu je le to treba izravnati v ravnalnih napravah ([3] in [4]). Glede na tip preoblikovalnega postopka, ki sledi, poznamo več vrst ravnalnih naprav, ki jih delimo predvsem po kontinuirnem ali prekinjanem načinu dela. V našem primeru se bomo omejili le na prekinjane ravnalne naprave, ki se uporabljajo pri izdelavi loka spenjanja prikazanega na sliki 1. Najprej je treba uspešno modelirati ravnalni postopek, ki bo dovolj hiter, da ga bomo kasneje lahko uporabili v algoritmu za stabilizacijo preoblikovalnih lastnosti žice. Prav zaradi tega smo se deloma umaknili iz povsem numeričnega postopka v analitično numerični popis dogajanja, ki omogoča hitrejše računanje. 2.1 Reološki model Reološki model preoblikovanja materiala, ki ga bomo uporabili v računskem modelu, je bistven za natančno modeliranje. Bistveno pri ravnanju žice je, da material izmenoma obremenjujemo v plastičnem področju, s čimer dosežemo na koncu čim večjo ravnost žice. Obnašanje jekla pri takšni deformaciji je opisano z diagramom napetost -deformacija pri izmenični obremenitvi ([5] do [7]), ki jo je treba definirati s preizkusi. Maloogljična poprej hladno deformirana jekla, kakršna žica tudi je, izkazujejo pri tovrstni obremenitvi Bauschingerjev pojav [8], ki pomeni nižanje meje plastičnosti pri spremembi smeri obremenjevanja. Natančna simulacija ravnalnega postopka zaradi tega zahteva poznavanje obnašanja jekla pri izmenični obremenitvi. To pomeni poznavanje diagrama ct-e (sl. 4), ki pa ga je za primer žice z debelino 4 mm eksperimentalno težko definirati. Ena od možnosti je obrnjen postopek prek modeliranja upogibnega preizkusa, v našem primeru pa smo se odločili za poenostavitev in v Pragerjeve enačbe [9] za popis zveze med napetostjo in C 2 MODELING OF THE STRAIGHTENING PROCESS Prior to any further wire processing on the bending machinery it is necessary to straighten the wire in wire straighteners ([3] and [4]). Depending on the type of process that follows the straightening, many different types of straighteners can be applied. They can basically be divided into continuous and non-continuous types. We will confine ourselves to discontinuous wire straighteners, which are used in the production of the arch presented in Figure 1. First, it is necessary to develop a numerical model of the wire straightener that will be fast enough to calculate the required repositionings of the rollers mounted in the straightener. This was the reason for using an analytical numerical approach rather than a purely numerical simulation of the straightening process. 2.1 Constitutive model A constitutive model of the material that will be used in the model is essential for accurate modeling. The core of the straightening process is a cyclic, plastic deformation of the wire, which results in the final straightness of the wire. The material response for such deformations is characterized by the s-e diagram during cyclic deformation ([5] to [7]), which has to be defined during the experimental testing. Low-carbon cold-drawn steels exhibit the Bauschinger phenomena when they are cyclically deformed into the plastic region. This means lowering the yield stress when the material is deformed in the opposite direction. A reliable simulation of the straightening process, therefore, requires a knowledge of the material’s response during cyclical deformation. When presenting this in one dimension it is necessary to know the parameters of the diagram presented in Fig.4. In the case of wire with a diameter of 4 mm it is not a simple task to define this diagram. One possibility is an inverse approach, by modeling the bending test. In our case we chose a simplification, therefore an extended form of Prager’s [9] equation was used to describe the material’s L O N Aeb h C Aob Ls Sl. 4. Shematski prikaz Bauschingerjevega pojava [8] Fig. 4. Schematic representation of the Bauschinger phenomena gfin^OtJJlMlSCSD 03-6 stran 301 |^BSSITIMIGC Nastran M., Kuzman K.: Mo`osti stabilizacije preoblikovalnih - Stabilizing the Forming deformacijo vnesli še dodaten koeficient D , s katerim je dana možnost spreminjanja meje plastičnosti žice iz enega nihaja v drugega. Diferencialne enačbe Pragerjevega modela so: behavior during straightening. In order to capture the softening of the material, an additional term Dcyc was added to allow for it. The differential equations of Prager’s model are: ds = E Y2n-( 1 + K ) C = [(1 + K)-s-E-K-e\ ds = E-de C>0 ¦[( 1 + K )-s-E-K-e2 de C<0 Y=Y-D (1) (2) (3) (4). Pri tem so: E - modul elastičnosti (MPa) Y - meja plastičnosti v i-tem ciklu (MPa) s - napetost (MPa) e - deformacija n - faktor prehoda K - limita strmine v plastičnem področju (MPa) Vzrok, da smo se odločili prav za Pragerjev model zveze med napetostjo in deformacijo žice, je v tem, da ob pravilni izbiri parametrov n in K izredno dobro popiše obnašanje materiala med enoosnim nateznim preizkusom. Glede na to, da je plastična deformacija žice v ravnalni napravi za področje preoblikovanja izredno majhna (< 1%), je za pravilno modeliranje ravnalnega postopka pomemben prav prehod iz elastičnega v plastično področje. Navadno pri obravnavanju postopkov preoblikovanja upoštevamo Hookov zakon v elastičnem področju ter funkcijsko odvisnost meje plastičnosti od primerjalne plastične deformacije v plastičnem področju. Takšen popis pa predstavlja v področju prehoda iz elastičnega v plastično področje lomljeno krivuljo, ki ni primerna za popis zveze med napetostjo in deformacijo pri modeliranju preoblikovalnih postopkov, kakršen je ravnanje žice. Where: E - Young’s modulus (MPa) Y - yield stress in the i-th cycle (MPa) s - stress (MPa) e - deformation n - transition factor K - plastic slope limit (MPa) The reason why Prager’s model was used for the description of relationship between the stress and the deformation is that when appropriate values of the parameters n and K are chosen, a tensile-test experiment can be modeled very accurately. Since the material deformation during roller straightening is very low (< 1%), the transition region from the elastic to the plastic stress state is very important for accurate modeling. Normally, when forming processes are modeled we use Hooke’s law in the elastic region and a certain functional relationship between the equivalent plastic deformations and the yield stress in the plastic region. Such a description results in a transition field with a non-smooth curve that is not appropriate for modeling the stress-strain relationship for processes such as wire straightening in the roller straighteners. a) 600 500 — 400 300 200 -- 100 0 -n=2, K=0,005, Y=500 -n=1, K=0,005, Y=500 n=0.6, K=0,005, Y=500 n=2, K=0,01, Y=450 'n=2, K=0.005, Y=450 n=2, K=0.005, Y=400 800 700 ! 1 1 __+__ i Ltn— —---------1--------------------! —h" — ¦ — ! /J [ ] 600 .... —i—j i i PT \ 500 j 400 300 200 __ -f—\— L___1____ r i —i-------1—n —i-------1------- ____i____i____j _l____1___1____ 1 1 1 --- --- __ __ i mo — ti----i---- —1—1—X—1— --- 100 /: ~ eksperiment----------' - -------1-------j--------1-------1--------1-------1-------j--------1------- 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0,005 0,01 0,015 0,02 0,025 0,03 s b) 0,0 0,005 s 0,01 Sl. 5. Pragerjev reoloski model a) in primerjava s preizkusi b) Fig. 5. Prager s flow rule a) and a comparison with the experiments b) VH^tTPsDDIK stran 302 Nastran M., Kuzman K.: Mo`osti stabilizacije preoblikovalnih - Stabilizing the Forming Primerjava diagrama s-e, dobljenega z enoosnim nateznim preizkusom ter modeliranega diagrama s Pragerjevim modelom je prikazana na sliki 5. Prikazan je tudi vpliv parametrov n in K na obliko krivulje prehoda iz elastičnega v plastično področje. 2.2 Upogibni moment - ukrivljenost Naslednji korak pri modeliranju ravnalnega postopka je pravilen popis zveze med ukrivljenostjo žice vzdolž ravnalne naprave ter upogibnim momentom [10], ki deluje na žico. V praksi se lege ravnalnih valjev nastavijo tako, da začetni valji deformirajo žico približno na dvakratno vrednost ukrivljenosti v kolutu, toda v nasprotni smeri. Nato pa se ukrivljenost postopoma zmanjša do teoretične vrednosti nič na izhodu iz ravnalne naprave. Izhajamo torej iz diagrama, ki popisuje vrednosti ukrivljenosti žice na posameznem ravnalnem valju (sl. 6) in je dobljen na podlagi izkušenj. A uniaxial tensile test diagram is compared with the one modeled by Prager’s flow ruler in Fig.5. The influence of the parameters n and K on the form of the elastic-plastic transition curve is presented as well. 2.2 Bending moment – curvature The next step in the numerical simulation of the wire straightener is the definition of the connection between the wire curvatures and the bending moment acting on the wire along the straightener [10]. Initially the wire straightener is preseted to the know-how values so that the wire is initially deformed to double the initial curvature in the opposite direction. Normally, the curvature fades out towards the end of the straightener. The diagram describing the wire curvature (Fig.6) is therefore the basis for further calculations. It is based on the experiences of the company personnel. 0,006 0,004 0,002 0 -0,002 -0,004 -0,006 a) statično dinamično 0 25 50 75 100 125 150 l [mm] 8000 4000 0 -4000 -8000 b) ----------__T_--------------!---------------__--------------j----------------T--------------- / \ \ I /l \ I I __-X___l_i_____i______Z1-V_____¦_______j*t-_____ ._/____l__1____I_____/_±__\____I______j-i.__.^r__ -------------\-------L---1-----J------+-------\—I-----L-----4------------- -----------h--------\-l~"T-------+--------V1"/-------+---------- -------------1-----------\fj.----------+------------1L-----------¦!¦------------ 0 25 50 75 100 125 150 l [mm] Sl. 6. Ukrivljenost žice a) ter upogibni moment b) vzdolž ravnalke Fig. 6. Wire curvature a) and bending moment b) along the straightener Upogibni moment, s katerim je treba delovati na delček žice, če hočemo, da bo njegova ukrivljenost enaka k, je definiran z integralom zmnožka med napetostjo in ročico po prerezu žice (en. 5): In order to obtain curvature ki a certain bending moment has to be applied in the cross-section of the wire. It is defined by the numerical integration of the normal stress multiplied by the distance from the neutral plane over the cross-section of the wire (Eq.5). d0/2 0 kjer je k ukrivljenost žice v legi, ko se le ta dotika i-tega ravnalnega valja, s(k,y) pa je dobljena z uporabo diferencialnih enačb Pragerjevega modela. Upogibni moment na prvem ravnalnem valju je enak nič, saj se na njem deformacija žice še ne pojavi. Dejstvo je, da ravnalni valji delujejo na žico le v določenih singularnih točkah, zato je porazdelitev upogibnega momenta vzdolž ravnalne naprave lahko samo linearna. Izračunamo jo s pomočjo definiranih točk (en.5) na način: Mi =4- | s(kiy)Jd204-y2ydy (5), where ki represents the wire curvature when interacting with the i-th roller, s(ki,y) represents the material data obtained by Prager’s flow rule. The bending moment on the first roller is zero, since no deformation occurs there. Since the rollers are acting on the wire only at singular points the distribution of the bending moment from one roller to another is linear. This means that it is possible to calculate the bending moment distribution on the wire traveling through the roller straightener (Eq.5): M(x)=M(xi)+ M (xi +1 )-M (xi ) x < x < x +1 (6). Kljub temu, da je porazdelitev upogibnega momenta vzdolž ravnalne naprave linearna, pa porazdelitev ukrivljenosti ni odsekoma linearna As the moment is linearly distributed over the length of the roller straightener the wire curvature is not. Wire is locally subjected to a small amount of | IgfinHŽslbJlIMlIgiCšD I stran 303 glTMDDC Nastran M., Kuzman K.: Mo`osti stabilizacije preoblikovalnih - Stabilizing the Forming funkcija, čemur botruje dejstvo, da je žica deformirana v plastično področje. Ukrivljenost je določena z enačbo (7), le da ne iščemo upogibnega momenta, temveč ukrivljenost, katere rezultat je želen upogibni moment. plastic deformation, which causes a nonlinear distribution in the curvature along the wire straightener. It is defined by Eq.7, where the curvature at which the desired bending moments occur is looked for. d02 M(x) = 4 0 s(k(x)y)Jd02 4- 0 Poleg zveze med napetostjo in deformacijo je ukrivljenost žice odvisna še od tega, ali le ta v ravnalki miruje ali pa se giblje. Ker je ravnalni postopek dinamičen, bomo obravnavali le primer, pri katerem se žica vzdolž ravnalne naprave giblje. Primer upogibnega momenta in ukrivljenosti žice je za žico z debelino 4 mm podan na sliki 6. Številčne vrednosti ukrivljenosti in upogibnega momenta pa so prikazane v preglednici 1. ¦y2ydy k(x) = U(M(x)) (7). Apart from the stress–strain relationship, the wire curvature depends on whether it is traveling through the straightener or it is stopped within the straightener. Since the straightening process is dynamic, it will be focused only on the case where the wire is moving through the straightener. An example of the bending moment and the curvature for a wire with 4-mm diameter is represented in Fig.6. The values are listed in Table 1. Preglednica 1. Številčne vrednosti momenta in ukrivljenosti Table 1. Bending moment and wire curvature valj / roller ukrivljenost v mm-1 curvature [mm-1] upogibni moment v Nmm bending moment [Nmm] 1 2 3 4 5 6 7 -0,0025 0,0048 -0,0045 0,0034 -0,0031 0,0030 0,00 0 8397 -7950 7679 -6837 6311 0 Izračunane vrednosti upogibnega momenta in ukrivljenosti uporabljamo za izračun položaja ravnalnih valjev in s tem potižice skozi ravnalno napravo ter velikosti prečnih sil, ki delujejo na žico v ravnalki. Definicija lege žice v ravnalki temelji na numerični integraciji izraza za ukrivljenost vzdolž ravnalne naprave, definicija prečnih sil pa izhaja iz porazdelitev upogibnega momenta. 2.3 Numerična integracija ukrivljenosti Ukrivljenost žice je dobljena z enačbami (5) do (7) in je osnova za nadaljnji preračun. Ker je odvisnost ukrivljenosti le odsekoma gladka krivulja, analitičen postopek integracije praktično ni mogoč. Zato je potrebno uporabiti numerično intergacijo izraza za ukrivljenost žice vzdolž ravnalne naprave. V splošnem je matematični izraz za ukrivljenost definiran z enačbo: k(x) t2y dx2 Based on the calculated values for the bending moment and the wire curvature, it is possible to define the roller position of the wire straightener and the roller force acting on each roller. The definition of the position is based on the numerical integration of the wire curvature term along the straightener axis. Roller forces are based on the bending moment distribution. 2.3 Numerical integration of the curvature The presented equations (5-7) describe the technique for obtaining wire curvature, which is the basis for the calculation of the roller positions within the wire straightener. The function describing the wire’s curvature is smooth only in the interval between two adjacent rollers. This is the reason why it is not possible to integrate the wire’s curvature analytically. Thus it is necessary to use numerical integration of the curvature term along the straightener. In general the curvature of a mathematical function is expressed by the following term: 1 + dx (x) (8), kjer sta: k(x) - ukrivljenostžice r(x) - polmer ukrivljenosti Izraz (8) je nelinerana diferencialna enačba drugega reda, ki jo je mogoče na podlagi dejanskih where: k(x) - wire curvature r(x) - bending radius This is a second-order nonlinear differential equation, which can be simplified based on special VH^tTPsDDIK stran 304 Nastran M., Kuzman K.: Mo`osti stabilizacije preoblikovalnih - Stabilizing the Forming geometrijskih značilnosti še nekoliko poenostaviti. Ker je prvi odvod funkcije (poti žice skozi ravnalko) praktično enak nič, ga lahko zanemarimo, s čimer se izraz za ukrivljenost poenostavi v: k(x) Napaka, ki jo naredimo pri neupoštevanju prvega odvoda funkcije, je za primer izravnavanja žice z debelino 4 mm manjša od 1 odstotka, kar je zanemarljivo in torej lahko za nadaljnji preračun uporabimo kar enačbo (9). Dvojna integracija vzdolž ravnalke da iskano lego, ob tem pa moramo upoštevati dve konstanti, ki se pojavita ob vsakokratnem integriranju in določata lego žice na prvem in zadnjem ravnalnem valju. Dejansko se v praksi nastavlja lega ravnalnih valjev in ne ukrivljenost. Ta je le posledica lege, poleg tega pa so ravnalke navadno nastavljene tako, da so valji, nameščeni na eni strani, pritrjeni, na drugi pa jih je mogoče premikati. Pravilna rešitev integracije je torej tista, ki da pot žice takšno, da se le ta dotika ravnalnih koles. Zato je na tem mestu potreben iterativen postopek točnega določanja začetne ukrivljenosti žice na posameznih ravnalnih valjih. Nekaj možnosti poti žice skozi ravnalko je prikazanih na sliki 7. 2.4 Prečne sile na ravnalne valje Prečne sile na ravnalne valje uporabljamo za inverzen izračun trenutne meje plastičnosti žice, kar je temelj za stabilizacijski algoritem. Njihov izračun sloni na momentnem ravnotežju sil, ki delujejo v sistemu žica - ravnalni valji. Postopek izračuna je shematično prikazana na sliki.8. 2.5 Eksperimentalno testiranje simulacije Predstavljen numerični model ravnalnega postopka je bil testiran na žici, na kateri smo poznali napetost tečenja. Izmerjene in izračunane vrednosti geometrical characteristics. Since the first derivative of the function is small, it can be neglected, which means that the mathematical curvature term can be simplified: cfy dx2 (9). A numerical error that originates from the neglecting of first derivative is calculated for the wire of 4 mm, and represents less than 1%, which can be neglected. For the further calculation, Eq.9 can be used instead. Double integration along the straightener axis gives the results, but it is necessary to consider both constants from the integration. They define the position of the wire on the first and last roller. In pratice the position of the rollers is changed. The wire’s curvature change is only a consequence of changing the roller positions. Apart from this, the position of the four upper rollers normally stays constant, but it is possible to change the positions of the rollers on the opposite side. A correct solution of the numerical integration is the one where the wire exactly touches the rollers. Therefore, an iterative approach is necessary to define accurate initial curvatures of the wire on each roller. Some possibilities are presented in Fig.7. 2.4 Transverse roller forces The transverse roller forces are needed for the inverse calculation of the current yield stress of the wire, which is the basis for the stabilization algorithm. The calculation is based on the moment equilibrium in the system of wire and straightening rollers. The procedure is schematically represented in Fig.8. 2.5 Experimental testing of the simulation The numerical model of the wire straightener was tested on a wire with known yield stress. The measured and calculated values for the roller forces were practically the same (Fig.9). This means that the 0,2 0,0 ^sr---------------j------------ -0,2 -0,4 -0,6 -0,8 25 50 100 75 l [mm] Sl. 7. Različne izračunane poti žice skozi ravnalko Fig. 8. Different calculated wire paths through the straightener 125 150 ^vmskmsmm 03-6 stran 305 |^BSSITIMIGC Nastran M., Kuzman K.: Mo`osti stabilizacije preoblikovalnih - Stabilizing the Forming M1 M2 M3 M4 M5 M6 M7 1 F1 1 F2 1 F3 x > M(x) ZFi'xi M (x)=0 => Fi Sl. 8. Izračun prečnih sil na ravnalne valje Fig. 8. Calculation of the transverse roller forces 900 800 700 600 500 400 300 200 100 0 izračunano - calculated izmerjeno - measured 3. kolo - 3rd roller 2. kolo - 2 nd roller 1. kolo - 1st roller 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 lega ravnalnega kolesa - roller position [mm] Sl. 9. Eksperimentalno testiranje simulacije ravnanja [11] Fig. 9. Experimental verification of the straightening simulation [11] Preglednica 2. Simulacija ravnalnega postopka Table 2. Simulation of the straightening process številka ravnalnega valja / roller no. 1 2 3 4 5 6 7 položaj / roller setting [mm] 0 -0,69 -0,05 -0,25 -0,02 -0,17 0 prečna sila na valj / transverse roller force [N] 325 940 1230 1200 1130 805 255 sil, ki delujejo na ravnalno kolo so bile praktično enake (sl. 9). To pomeni, da je model dovolj natančen in da ga lahko uporabimo v obrnjeni metodi določanja trenutne meje plastičnosti žice. Rezultati simulacije so lege ravnalnih koles ter prečne sile na ravnalne valje in so za primer žice s premerom 4 mm prikazani v preglednici 2. 3 STABILIZACIJSKI ALGORITEM Prikazan numerični model ravnalnega postopka je jedro algoritma za stabilizacijo meje plastičnosti žice. Poleg tega pa je pred samo vpeljavo sistema treba izpolniti še nekatere robne pogoje. Obnašanje žice pri izmenični deformaciji je najbolj pomemben parameter, ki dejansko pove, ali je z ravnalnim postopkom mogoče stabilizirati mejo developed numerical model is accurate enough and can therefore be used as an inverse method for the characterization of the flow properties of the wire passing through the roller straightener. The result of the simulation is the roller position and the roller forces. For the wire with a diameter of 4 mm they are presented in Table 2. 3 STABILIZATION ALGORITHM The above-presented numerical model of the wire-straightening process serves as the basis for the stabilization of the yield stress of the wire. Certainly, there are some preconditions, which have to be fulfilled in order that the flow stress stabilization can be carried out. The wire’s behavior under cyclic deformation is the most important parameter, which tells whether it will be possible to stabilize the yield stress or not. VH^tTPsDDIK stran 306 Nastran M., Kuzman K.: Mo`osti stabilizacije preoblikovalnih - Stabilizing the Forming plastičnosti ali ne. Obnašanje dveh različnih vrst žice je prikazano na sliki 9. Diagram prikazuje mejo plastičnosti žice po ravnanju v odvisnosti od celotne plastične deformacije [11], ki smo jo za potrebe stabilizacijskega algoritma definirali z izrazom: Izraz pomeni vsoto absolutnih vrednosti ukrivljenosti žice na posameznem ravnalnem valju in je mera za velikost izmenične plastične deformacije. Maloogljična jekla navadno izkazujejo izmenično mehčanje (krivulja B na sl. 10). To pa je odvisno od velikosti prirasta plastične deformacije. Če je le ta večji, se material lahko zopet utrjuje (krivulja A na sl.10). Sprememba meje plastičnosti je torej odvisna od materiala in prirasta plastične deformacije. Za primer jekla B na sl.10 je mogoče z nadzorom velikosti prirasta plastične deformacije (nastavitve ravnalnih koles) uspešno izvesti stabilizacijo meje plastičnosti. Glavna zamisel stabilizacije je v tem, da z numeričnim modelom ravnanja, predstavljenega v prejšnjem razdelku, definiramo mejo plastičnosti žice, ki je trenutno v ravnalki. Na podlagi eksperimentalnih podatkov s slike 10 se nato izračunajo potrebne popravke nastavitev ravnalnih koles. Posledica tega je izpostavitev žice drugačnim izmeničnim deformacijam, kar povzroči tudi drugačno vrednost meje plastičnosti po ravnanju. Dejstvo je, da se meja plastičnosti žice ne spreminja v dolžini, manjši od dolžine ravnalne naprave. Z meritvami je bilo ugotovljeno, da je frekvenca spreminjanja meje plastičnosti približno 8 do 10 min, kar pomeni približno 180 m žice (sl. 11). 3.1 Postopek Ravnal kolesa. Z num kolesa izrazili parametrov po lege koles itn samo meja pla The behavior for two different wire types is presented in Fig.10. It presents the yield stress of the wire after being straightened with respect to the total amount of wire curvature [11], which has been for the purpose of the stabilization algorithm defined as: ZW (10). It represents the sum of the absolute values of the wire’s curvature on a single straightener roller and it is a measure of the total cyclic plastic deformation. Low-carbon cold-drawn wire materials normally exhibit cyclic softening (curve B in Figure 10). This depends on the plastic increment. If the plastic increment is higher, it is possible that the material will harden again (curve A in Figure 10). The change of the flow stress depends on the material and on the increment of the plastic deformation. In the case of material B from Fig.9 it is possible that the mechanical properties of the wire are stabilised by controlling the plastic increment, which comes from controlling the positions of the straightening rollers in the roller straightener. The basic idea of the stabilization is that by using a numerical model of the wire straightener, described in the previous paragraph, the wire’s yield stress passing the roller straightener is calculated. By combining the data from Figure 10, the necessary adjustments of the wire’s curvature are calculated afterwards. This means that the wire is exposed to different amounts of cyclic deformation, which means a different yield stress of the wire after straightening. The yield stress of wire does not fluctuate over short time periods. It was confirmed from measurements that the cycle time of the flow-stress fluctuation is 8–10 min, which means approximately 180 m, as shown in Fig. 11. asured by the tion the roller dependent on stress, wire e yield stress as: tot S|ki| [mm-1 ] žica A - wire A 610 590 570 550- 530 510 0.015 0.016 0.017 0.018 0.019 0.02 0.021 Sl. 10. Meja plastičnosti za žici dveh različnih proizvajalcev v odvisnosti od kTOT Fig. 10. Yield stress of the wire, from two different suppliers, depending on kTOT Nastran M., Kuzman K.: Mo`osti stabilizacije preoblikovalnih - Stabilizing the Forming 600 590 580 570 560 0 Yj l Yj+1" Yj+2 l točka reagiranja sistema - system reaction point l0 interval j interval j+1 lf [m] Sl. 11. Spreminjanje meje plastičnosti ter prikaz točk, kjer ukrepamo [11] Fig. 11. Fluctuation of the flow stress of the wire and the reaction points [11] Fi = f (Y(l)) Enačba inverznega postopka pa je na podlagi en. (11) naslednja: Based on Eq.11, the inverse is: Y (l) = f -1(Fi (l)) (11). (12). Razlika med trenutno mejo plastičnosti in povprečno vrednostjo v določeni količini žice se izračuna kot: The difference between the current yield stress and the average yield stress of the wire is calculated as: DYj =YjDl -YAVG 1lf Dl JY(l)dl----j Y(l)dl f0 (13), pri čemer sta: A - opazovani korak (sl.11) lf lj - celotna dolžina žice od začetka merjenja Potrebno popravo parametra kTOT za bolj enakomerno mejo plastičnosti žice po ravnanju dobimo z uporabo diagrama na sliki 10. Potrebna poprava izhaja iz velikosti odstopanja trenutne vrednosti meje plastičnosti DYj od povprečne vrednost YAVG.V obliki funkcije: where: Dlj - measured interval (Fig.11) lf - cumulative length of the wire In order to stabilize the yield stress in the next step, j+1, it is necessary to correct the value kTOT according to the findings presented in Fig.10. The necessary correction is defined by the difference between the current value of the yield stress, DYj, and the average value of the yield stress YAV G . The function is: Dk Novo izračunano vrednost kTOT je nato treba enakomerno porazdeliti na vse ravnalne valje hkrati, in sicer tako, da izpolnimo robne pogoje (žica se mora dotikati ravnalnih valjev, pri tem pa lahko spreminjamo le lege drugega, četrtega in šestega ravnalnega valja). Prav tako ni mogoče spreminjati ukrivljenosti na vseh ravnalnih kolesih. Prvo je namreč določeno z ukrivljenostjo žice v kolutu, zadnje pa je odvisno od ravnosti žice na izstopu. Prav tako je ukrivljenost na predzadnjem ravnalnem valju odvisna od ravnosti žice na izstopu. Torej je v ravnalni napravi s sedmimi ravnalnimi kolesi (n=7) v eni ravnini mogoče poljubno spreminjati ukrivljenost na štirih ravnalnih valjih. u-1(YAVG - DYj ) TOT TOT TOT kT j+1 j (14) (15). The new calculated value of kTOT is necessary to distribute uniformly on every roller in such a way as to fulfill all the boundary conditions (the wire should touch the roller, but only the second, fourth and sixth rollers can be changed). Furthermore, it is not possible to change the curvature on all rollers. The first one, k1, is defined by the coil curvature, and the last one should be zero. The one before the last is defined by the zero condition on the last roller as well. A seven-roller wire straightener (n=7) allows for curvature adjustments on four of the rollers. The correlations between the adjacent curvatures VBgfFMK stran 308 Nastran M., Kuzman K.: Mo`osti stabilizacije preoblikovalnih - Stabilizing the Forming Razmerja med posameznimi nastavitvami morajo ostati should remain constant. The second roller is taken enaka. Referenčno vrednost predstavlja drugo ravnalno for reference and the curvature on the others is kolo, ukrivljenosti na preostalih treh pa izrazimo kot: expressed as: i = 3..(n-2) j-ti korak / j-th step i = 3..(n - 2) j+1-korak / j+1-step (16) (17). Koeficienti q2i so v ravnalnem postopku The coefficients q2i are constants in a certain nespremenjeni in pomenijo razmerja med nastavitvijo roller-straightening process and represent the ratios na drugem ravnalnem kolesu in preostalimi (tremi - v between the curvature on the second roller and the primeru ravnalke s sedmimi ravnalnimi kolesi). En. other three (in the case of the seven-roller (15) lahko sedaj izrazimo kot: straightener). Eq.15 can be expressed as: DkT 2 j+1 1 + Zq2i 1 + Žq2i (18). Nova ukrivljenost na drugem ravnalnem kolesu je: The new, wire curvature on the second roller is: DkTOT n-2 A (19). k =k + 2 j+1 2j Preostale tri ukrivljenosti k 1, k4 1 in k5j 1 Curvatures k j 1, k 1 and k5j 1 are defined by določimo z enačbo (17). Nove lege ravnalnih koles so Eq.17. The new positions of the straightening rollers določene s postopkom, opisanim v prejšnjem poglavju are calculated using the numerical model of the o numerični simulaciji ravnalnega postopka. straightener presented in the previous section. The Odvisnost lege od ukrivljenosti lahko zapišemo z position of the rollers can be expressed by the uporabo odvisnosti: function: x =V(k ) ij+1 ij+1 ij+1 (20). Zveza med lego ravnalnega kolesa in skupno The connection between the roller position and ukrivljenostjo žice kTOT ni linearna in je za primer jekla total wire curvature, kTOT, is not linear and is presented B s slike 10 prikazana na sliki 12. Stabilizacijski in Fig.12 (steel B from Fig.10) The stabilization algoritem za to jeklo pa lahko zaradi nižanja meje algorithm for the steel B can be, due to the softening plastičnosti pri izmenični obremenitvi opišemo of the material during the total cyclic deformation, preprosto z naslednjimi enačbami: schematically presented by the equations: če/if YjD+l1^YjD če/if Y Dl < Y Dl TOT > TOT k +1 ^k k TOT , k TOT (21) (22). Če je meja plastičnosti v ciklu j+1 večja kakor v ciklu j, potem je treba vrednost kTOT povečati, če hočemo, da bomo dosegli nižjo mejo plastičnosti materiala. 0.8 0.6 0.4- 0.2 If the yield stress in the cycle j+1 is higher than in cycle j, then the value kTOT should be increased to soften the material. 0 0.014 0.016 0.018 kTOT [1/ mm] 0.02 0.022 Sl. 12. Zveza med lego ravnalnih koles in celotno ukrivljenostjo kTOT Fig. 12. The connection between the roller settings and the total curvature, kTOT | IgfinHŽslbJIMlIgiCšD I stran 309 glTMDDC Nastran M., Kuzman K.: Mo`osti stabilizacije preoblikovalnih - Stabilizing the Forming Začetek - Start merjene sile na ravnalno kolo measured roller forces (Fi,j) nastavitev ravnalke po izkušnjah roller setting by experience (xi, 0 ki 0) I matematični model žično ravnalnega postopka _> mathematical model of the wire straightening process Y(l) = f-1(Fi(l)) en. - Eq. (12) Z DY =Y -Y aklj 1j 1AVG 1lf Dl, | Y(l)dl- \Y(l)dl en. - Eq. (13) f0 Z ne - no če - if AYj > 0 zmanjšaj - decrease kTOT en. - Eq. (14) da - yes t TOT . -1 u1(YAVG-DYj) povečaj - increase kTOT en. - Eq. (14) Tj +O1T = u-1(YAVG - DYj) izračun - calculation ki,j+1 en. - Eq. (16 do 19) T izračun - calculation xi,j+1 en. - eq. (20) Sl. 13. Shematičen prikaz stabilizacijskega algoritma [11] Fig. 13. Schematic representation of the stabilisation procedure [11] Sl. 14. Preizkusna ravnalna naprava Fig. 14. Experimental wire straightener Celoten postopek stabilizacije je shematsko The whole stabilization procedure is prikazan na sl.13. schematically presented in Fig.13. 3.2 Testiranje stabilizacijskega algoritma Prikazan stabilizacijski algoritem je bil eksperimentalno preverjen na industrijskem primeru izdelave reber, sestavnih delov mehanizmov za registratorje in mape v podjetju NIKO Železniki. V skladu s predstavljenim algoritmom smo spremenili 3.2 Testing of the stabilization algorithm The presented numerical model of the stabilization algorithm was finally evaluated in the production of arches for leverarch mechanisms at a company called NIKO Železniki. According to the presented algorithm the roller positions were changed to grin^SfcflMISDSD ^BSfiTTMlliC | stran 310 Nastran M., Kuzman K.: Mo`osti stabilizacije preoblikovalnih - Stabilizing the Forming Preglednica 3. Nastavitve ravnalnih koles Table 3. Roller presetting valj št. i roller no. i x i,1 kTOT = 0,0174 mm-1 x i,2 kTOT = 0,0193 mm-1 Axi 1,3,5,7 2 4 6 0 mm 0,19 mm 0,17 mm 0,53 mm 0 mm 0,17 mm 0,22 mm 0,61 mm 0 mm -0,02 mm 0,05 mm 0,08 mm 0,2 I__________i______ 0,0 [^.„"j.___ -0,2 -0,4 -0,6 -0,8 150 l [mm] 0 100 200 300 400 500 razdalja v kolutu - distance along coil [m] Sl. 15. Preizkusno vrednotenje predlaganega modela: a) pot žice, b) širina izdelka (slika1) pred spremembo (nastavitev j) in po (nastavitev j+1) spremembi lege ravnalnih koles Fig. 15. Experimental verification of the proposed model: a) wire path, b) product width (Figure 1) before (setting j) and after (setting j+1) presettings of the rollers lego ravnalnih valjev za izračunane vrednosti. Posledica tega je bila spremenjena pot žice skozi ravnalko in s tem tudi spremenjena meja plastičnosti žice. V končni fazi se je spremenila geometrijska oblika rebra, kot posledica spremembe meje plastičnosti žice. Na sliki14 je prikazana preizkusna merilna oprema, nameščena na žično krivilni avtomat. S spremembo poti žice skozi ravnalko, ob čemer je bila žica še vedno ravna, se je spremenila širina izdelka, kot glavni geometrijski parameter izdelka (sl. 15b). Spremembe lege ravnalnih koles so prikazane v preglednici 3, pot žice skozi ravnalko pred spremembmo in po njej lege valjev pa na sliki 15a). 4 SKLEP V prispevku je bil najprej prikazan numerični model ravnanja žice v ravnalni napravi, ki v nadaljevanju rabi kot jedro stabilizacijskega algoritma. Zamisel je bila preizkusno ovrednotena, s čimer smo potrdili, da je takšen način stabilizacije geometrijskih parametrov izdelkov iz žice mogoč, kljub temu, da so the calculated values. This means that the wire path through the straightener was changed as well, which means a certain difference in the flow stress of the wire that is coming out of the wire straightener. Because of this difference there is a clear change in the geometrical parameters of the finished arch. The experimental set-up mounted onto the bending machine is presented in F ig.14. By changing the wire path through the straightener (wire remains straight), the width ,as the major geometrical parameter, changed as well (Fig.14.b). Table 3 presents the corrections performed on the straightening rollers. Figure 15 a) presents the wire path through the straightener before and after the roller presetting. 4 CONCLUSION A numerical model of the wire-straightening process has been presented, which serves as the core for the stabilization algorithm. The idea was experimentally verified, which confirmed that the stabilization of the geometrical parameters of the product made out of wire is possible, even though | IgfinHŽslbJlIMlIgiCšD I stran 311 glTMDDC Nastran M., Kuzman K.: Mo`osti stabilizacije preoblikovalnih - Stabilizing the Forming v njej prisotne spreminjajoče se materialne lastnosti. Pri tem nas ne zanimajo vzroki za te neenakomerne lastnosti materiala, temveč se osredotočimo na samo stabilizacijo. Nadaljnje možnosti uporabe se odpirajo predvsem v smeri izdelave pločevinastih izdelkov. Kakršenkoli drug način poprave geometrijske oblike je zaradi večje zapletenosti izdelkov otežen. Postopek s stabilizacijo meje plastičnosti jekla pa ponuja tudi v tem primeru odlične možnosti. 5 ZAHVALA Zahvala gre sodelavcem podjetja NIKO Železniki, kjer so bili opravljeni vsi preskusi, nenazadnje pa tudi Ministrstvu za gospodarstvo, ki je delo financiralo v okviru EUREKA projekta E!2382. the input material had an inhomogeneous yield stress. The reasons for the material inhomogenities are not a part of the discussion. We have only focused on the stabilization principle. Further applications are also possible in the field of sheet-metal forming. Any other way of correcting the geometry of sheet-metal parts is more difficult because of the complex geometry. The material’s yield-stress stabilization algorithm also promises good results in this field of production. 5 ACKNOWLEDGEMENT The authors would like to thank the personnel of NIKO Železniki, where all the experiments were done, as well as to the Slovenian Ministry of the Economy, which supported the project financially in the frame of EUREKA E!2328 found. 6 LITERATURA 6 REFERENCES [I] Kuzman, K (2001) Problems of accuracy control in cold forming, J.Mat.Proc.Tech., Vol.113, No.1/3, 10-15. [2] Nastran, M., K. Kuzman, B. Kavčič (2002) Problems of process control in leverarch mechanism production, Report on the Eureka E!2382 INNOFORM Project, May 2002, Delft. [3] Glomb, R. (1994) Straightening round material, Wireworld, vol.2, 62-69. [4] Schneidereit, H., M. Schilling, M. Paech (1999) Innovative Richttechnik, Draht, vol.2, 46-51. [5] Huml, P. (1987) The Influence of strain path on wire properties, Advanced Technology Of Plastiticity, Springer-Verlag, Vol.2. [6] Stüve, H.P (1983) Einfluss von Wechseln der Beanspruchungsrichtung auf die Fliesspannung von Metallen, Berichte aus dem Inst.f.Umformtechnik, Nr.74.,Universität Stuttgart. [7] Huml, P (1984) Utilization of flow stress in metal forming calculations, Annals of the CIRP, 33, 147-149. [8] Chakrabarty, J. (2000) Applied Plasticity, Springer-Verlag, New York. [9] Yanagi, S., Y. Maeda, S. Hattori (1993) Residual stress of thin strip after leveling process, Adv.Tech.of Plast., vol.2. [10] Guericke, W., M. Paech, A. Eckehard (1996) Simulation des Richtens von Draht, 1996, Draht, vol. 1/2, 23-29. [II] Nastran, M. (2003) Prispevek k stabilizaciji procesa hladnega preoblikovanja žice, Disertacija, Fakulteta za strojnwtvo, Ljubljana. Naslov avtorjev: dr. Miha Nastran profdr. Karl Kuzman Fakulteta za strojništvo Univerza v Ljubljani Aškerčeva 6 1000 Ljubljana miha.nastran@domel.com karl.kuzma@fs.uni-lj.si Authors’ Address:Dr. Miha Nastran ProfDr. Karl Kuzman Faculty of Mechanical Eng. University of Ljubljana Aškerčeva 6 1000 Ljubljana, Slovenia miha.nastran@domel.com karl.kuzma@fs.uni-lj.si Prejeto: Received: 13.3.2003 Sprejeto: Accepted: 12.9.2003 Odprto za diskusijo: 1 leto Open for discussion: 1 year grin^SfcflMISDSD ^BSfiTTMlliC | stran 312