Design nd Testing of Coils for Pulsed Electromgnetic Forming. Golovshchenko, N. Bessonov, R. Dvies Ford Reserch & Advnced Engineering, Derborn, UA University of Michign-Derborn, Derborn, UA Pcific Northwest Ntionl Lbortory, Richlnd, Wshington, UA Abstrct Coil design influences the distribution of electromgnetic forces pplied to both the blnk nd the coil. The required energy of the process is usully defined by deformtion of the blnk. However, the dischrge lso results in significnt mount of het being generted nd ccumulting in the coil. Therefore, EMF process design involves working with three different problems: ) propgtion of n electromgnetic field through the coil-blnk system nd genertion of pulsed electromgnetic pressure in specified res, ) high-rte deformtion of the blnk, nd ) het ccumultion nd trnsfer through the coil with the cooling system. In the current work, propgtion of n electromgnetic field in the coil, blnk, die nd surrounding ir ws defined using consistent set of qusi sttionry Mwell equtions pplying corresponding set of prmeters for ech medi. Furthermore, deformtion of the blnk driven by electromgnetic forces distributed through the volume of the blnk ws modeled using solid mechnics eqution of motion nd the elstic plstic flow theory. During the dischrge of cpcitors the process ws considered to be dibtic due to the short durtion of the pulse, so het trnsfer during the dischrge time ws neglected. The distribution of electric current density integrted during the dischrge process defines the increse of temperture t every element of the coil. The distribution of temperture ws clculted s function of time using the energy conservtion lw. Keywords: heet metl forming, Electricl dischrge, Tool, Cooling Introduction Pulsed electromgnetic forming (EMF) uses coil s tooling, which is employed to generte electromgnetic pressure on the blnk during high-voltge electric dischrge of cpcitors. Typiclly, the coil is subjected to the sme pressure s the blnk. In the 4
nd Interntionl Conference on High peed Forming 006 cse of multi-turn coil, dditionl forces my be generted between the turns of the coil since the clernce between the turns is usully similr to the clernce between the coil nd the blnk. Typiclly, the mount of electric energy involved in n EMF process is lrgely defined by the required deformtion of the blnk. This electric energy pulse lso genertes significnt mount of het fter ech dischrge, which ccumultes in the coil over time. In order to implement the EMF technology in high-volume production, n efficient cooling system providing stble temperture of the coil needs to be developed. Therefore, we need to work with three different problems: ) propgtion of electromgnetic field through the coil-blnk system nd genertion of pulsed electromgnetic pressure in specified res, ) high-rte deformtion of the blnk, nd ) het ccumultion nd trnsfer through the coil tking into ccount the cooling system. These predictive tools re lso necessry element to design coil system tht would be fesible for high-volume production of utomotive pnels - specificlly of eterior pnels with clss A surfces. These predictive numericl models of electromgnetic elstic-plstic forming nd het trnsfer processes re ll importnt elements for model tht designs process tht works the first time nd tolertes high-volume production. Theoreticl pproch Propgtion of n electromgnetic field within coil-blnk-die-ir system cn be defined by qusi sttionry Mwell equtions: H = j, () H = E, () t j = σ ( E + v H), () Where H is mgnetic field intensity; j is current density; E is electric field intensity; σ is electric conductivity; v is velocity; is mgnetic permebility of the medium under 7 considertion. For short durtion processes we ssume = 4π 0, H/m. In EMF processes the coil nd die re lmost sttionry, while the blnk is quickly ccelerted; therefore, the eqution for mgnetic field intensity H cn be trnsformed in Lgrngin form. Bsed upon equtions ()-(), the eqution for vector H cn be written s: H = H v H, (4) t σ or trnsformed in integrl form d dt ( H) Hd vh ds = ds σ. (5) Dynmic elstic-plstic deformtion of solid cn be defined by the following eqution: 4
nd Interntionl Conference on High peed Forming 006 ρ d dt d = σ ds + where v f d, (6) f j B = H j = H ( H), (7) = σ = pi + is stress tensor; ρ is density; p is pressure; is devitor prt of stress tensor, p = K, = GB D, (8) 0 nd 0 re ctul nd originl volumes respectively; B D is the devitor prt of the left T Cuchy-Green tensor B ; B = F F ; F = d / dx is deformtion grdient tensor; is the vector of ctul loction; X is the vector of originl loction; K nd G re bulk nd sher modulus respectively. The on Mises yield criterion is used to describe the elstic limit: σ y J ( ), (9) where σ y is current plstic flow stress (depends on strin nd strin rte). The energy conservtion lw is employed in the following form: d dt c Td = Pd + λ T ds, (0) j where T is temperture; P = is power generted in the form of het while n electric σ current is running through the coil nd blnk becuse of n ctive resistnce of their mterils. The ystem of equtions (5)-(0) represents full formultion of the problem. The electromgnetic forming mchine serving s genertor of pulsed currents cn be represented s R-L-C circuit. An electric current running into coil-blnk system s boundry condition cn be defined by the following equtions using n eplicit integrtion procedure. d(li) + RI = U, () dt du C dt = I, () At every time step we solved equtions () nd () nd, bsed upon the defined vlue of current I, clculted its density in the coil j = I / t the boundry cross-sections 4
nd Interntionl Conference on High peed Forming 006 where is squre of the cross-section of the coil. Boundry conditions for H were clculted bsed upon the electric current I employing the following eqution: l H dl = I. () where l is contour round the led cross-section. Assuming tht H is directed tngentil to the cross-sections of the incoming nd outcoming leds nd uniform long their contours, H cn be defined by () s H = I / L, (4) where L is the perimeter of the led of incoming or outcoming cross-sections. In this formultion the propgtion of n electromgnetic field in the coil, blnk, die, nd surrounding ir ws nlyzed using the sme set of equtions pplying corresponding set of prmeters for ech medi. ince there is number of metllic prts in close vicinity to the system (coil bndge, die, clmping system, etc.) we believed tht n eternl screen would be n pproprite boundry condition. According to this ssumption, the following boundry condition cn be pplied to the surfce of the screen: H = 0. (5) This system ws solved numericlly using the finite volume method, bsed on nonorthogonl regulr Lgrngin mesh which consists of 8 node cells, shown in Figure. Ech cell consists of 4 tetrhedrons. An emple of tetrhedron "bcd" is shown in Figure. erte "b" is in the center of the cell s fce, while verte "c" is in the center of the cell. A control volume is linked to every node of the mesh. According to the described discretiztion, ech cell contributes to the control volume [], s shown in Figure b. Figure : Numericl mesh in the control volume method b 44
nd Interntionl Conference on High peed Forming 006 Eqution (5) ws solved by integrting the first term in its left side by time: n+ ( H ) n+ n H H n+ = vh ds + ds, (6) t σ where is the volume restricted by the surfce ; ds = nd ; n is the eternl norml to. urfce integrls in other terms of (5) re being defined s sum of surfce integrls long the k surfces of the control volume surrounding this node, s shown in Figure. vh ds + ds σ n+ n+ n+ ( H ) = vh ds + ds ( H ) n+ ( k ) σ, (7) The vlues of ( H) nd vh re considered to be constnt for ech element of the mesh. The increments of H in ech node of the mesh depend on the vlues of H in the elements surrounding the node under considertion. In three-dimensionl formultions we hve 7 point pttern. The ctul position of the vertices of the tetrhedrl element t time t ws denoted by, b, c nd d. Let i ( i =,, ) be the right-hnd set of vectors directed long ny three different ribs of the tetrhedron (Fig. ). ector H ws ssumed to be liner function from rdius-vector in the element: H = A + b (8) A ws defined by the following system H H H = A = A = A (9) Then we obtined A ( ) = H i e i m e. (0) m Using the trnsformtion (0), we defined the pproimtion of H = where k ( A + b) = ek Hi ei ( mem ) = Hk k H in the element, () =, ( ) =, ( ) =. () ( ) A numericl procedure of integrtion (6)-(8) simulting the elstic-plstic deformtion of the blnk ws discussed in [,]. An eplicit integrtion procedure ws considered to be 45
nd Interntionl Conference on High peed Forming 006 suitble to simulte high-rte deformtion process. The electromgnetic prt of the problem ws solved using n implicit integrtion procedure. In order to reduce computtionl time for prcticl three-dimensionl problems, the integrtion step in the EM problem ws n times lrger thn in the elstic-plstic problem. The prmeter n ws defined for ech prcticl cse in order to represent the chnges in the distribution of the electromgnetic field ppropritely. The clernce between the coil nd the blnk ws epnding due to the ccelertion of the blnk driven by repelling electromgnetic forces. Therefore, the mentioned clernce ws re-meshed periodiclly. Results of the numericl simultion The objective of numericl simultion ws to ssist the development of the efficient coil for the restrike opertion of preformed luminum blnk. Preliminry eperimentl results indicted tht sometimes electromgnetic pressure is pplied in the re where plstic deformtion ws not epected. Therefore, specific ttention ws pid to the distribution of electromgnetic pressure nd the formtion of the blnk. Prmeters of the dischrge were tken from the eperimentl results produced using commercil EMF mchine nd single turn coil mde of luminum lloy 606-T6. The mimum energy of the mchine ws.5 kj with mimum chrging voltge of 5 k. Two cses were simulted: C=0.000F nd C=0.0005F. Results of the numericl simultion re shown in Figure. blnk coil b c Figure : Results of the numericl simultion of EMF restrike of preformed luminum blnk mm thick mde of AA6-T4: ) initil position of the blnk nd coil; b) position of the blnk nd distribution of plstic strins in it fter the EMF process with the following prmeters C=0.000 F, U=5 k; c) similr results for the bnk of cpcitors C=0.0005 F 46
nd Interntionl Conference on High peed Forming 006 0.005 m 0.004 0.0005F 0.000F 0.00 0.00 0.00 0 0.E+00.E-05.E-05.E-05 sec 4.E-05 Figure : Rdil displcements of the point vs time for C=0.000F nd C=0.0005F Anlyzing the strin distribution for two cses, we cn conclude tht for the cse of C=0.0005F mimum plstic strins were t the formbility limit. A displcement of the point of the blnk, locted on the eternl surfce of the blnk, fcing the die nd belonging to the bisecting line of the ngle being formed, is shown in Figure. As it ws mentioned before, specil ttention ws pid to the distribution of density of electric currents nd pressure pplied to the blnk. For the single turn coil described bove these distributions re shown in Figure 4. 5 MP 0 6sec 5 0 5 0 5 α 0 50 50 50 50 Figure 4: The coordinte system of cross-section of the coil (left) nd the distribution of EMF pressure t the time moment t=6 sec fter the beginning of the process (right) An ttempt ws mde to simulte composite coil which consists of two prts copper lyer fcing the blnk nd steel lyer reinforcing the coil ginst electromgnetic pressure. As result (Figure 5), the density of electric currents in the re of the crosssection fcing the blnk cn be significntly incresed. Even though composite coil is epected to 47
nd Interntionl Conference on High peed Forming 006 Composite coil Bsic (homogeneous) coil 7.E+09 A/m 6.E+09 5.E+09 R/R=0 bsic 4.E+09.E+09.E+09 steel copper.e+09 0.E+00 α 0 90 80 70 60 Figure 5: Results of the numericl nlysis of the composite (copper-steel) coil compred to the bsic coil fbricted from steel be more epensive due to the necessity of the lyers joining, it my provide better efficiency, higher strength, nd less het ccumultion compred to the coils mde of homogeneous mteril. pecil ttention should lso be pid to the ccumultion of het in the coil in high-volume EMF processes. As in well-known induction heting processes, electric currents in EMF processes tend to run within reltively thin lyer due to the skin effect. Lter, the het is redistributed due to the mteril therml conductivity. After every new dischrge of the mchine dditionl het is being generted in the skin lyer. This het genertion process cn be considered to be dibtic. To define the mount of het, electric current density ws integrted over the durtion of the process nd produced the distribution of het due to the ctive resistnce of the coil mteril (Figure 6). Further het flow nd temperture redistribution hppens within much longer period of time between pulses of the EMF mchine. In production conditions unloding of the stmped blnk nd loding of the net blnk would tke plce between two dischrges. 48
nd Interntionl Conference on High peed Forming 006 50 o C 40 0 0 0,0E+00,0E-05,0E-05,0E-05 sec 4,0E-05 t=0 microseconds Figure 6: Distribution of mimum temperture vs time (upper grph) nd distribution of temperture in the coil cross-section (lower grph) during one dischrge of the EMF mchine In order to develop n efficient cooling system of the coil, numericl model of the het trnsfer through the coil ws developed. This model took into ccount the ir-cooling system which provided the ir flow long the coil surfce. The prmeter which ws epected to drive the cooling process ws the velocity of ir flow. According to the results of numericl simultion shown in Figure 7, the ir flow with the speed of 0 m/sec could ccomplish stisfctory result since it provides stbiliztion of the temperture of the coil. lower ir flows of 5 nd 0 m/sec provide stbiliztion t higher tempertures, which my not be pproprite for the insultion mteril nd my reduce thedurbility of the coil. 49
nd Interntionl Conference on High peed Forming 006 60 o C 40 0m/s 0 00 5m/s 80 60 0m/s 40 0 0 0 0 40 60 80 00 sec 0 Figure 7: Mimum (thin lines) nd verge (thick lines) tempertures of the coil vs. time for production rte of 60 prts/hour with velocity of ir flow of 0, 5, nd 0 m/sec An eperimentl study of the cooling process ws conducted using the flt coil mde of steel nd micrt insultion pltes, illustrted in Figure 8. Air flow ws delivered through the slots between the micrt pltes in the corners of the coil. The spirl surfce ws insulted from the blnk by thin plte of insultion mteril. The ir flow ws directed between the spirl surfce nd insultion plte so it would provide cooling of the working surfce of the coil where mimum mount of het is generted. In this eperimentl study the energy of the process ws specified bsed upon the energy llowing to form cones mde of mm thick luminum sheet into the die with open round windows 76 mm in dimeter, shown in Figure 8. In durbility study the luminum blnk ws replced by n luminum plte which ws clmped to the coil with four bolts, s indicted in Figure 8. An eperimentl study showed tht fter 5000 dischrges the coil did not hve ny signs of dmge nd, therefore, hs the potentil to be used in high volume production conditions. 50
nd Interntionl Conference on High peed Forming 006 Air flow evcution Air flow delivery Aluminum blnk simultor b c d Figure 8: Eperimentl fiture employed for n eperimentl study of coil durbility nd het ccumultion: flt coil with ir cooling system; b ssembled fiture for testing coil durbility; c - eperimentl die for estimting the energy of the coil testing procedure; d formed blnk 4 Conclusions This work developed numericl models tht describe three criticl elements of the EMF process: ) propgtion of n electromgnetic field through the coil-blnk system nd genertion of pulsed electromgnetic pressure in specified res, ) high-rte deformtion of the blnk, nd ) het ccumultion nd trnsfer through the coil with n ir-cooling system. The process models provide the cpbility to nlyze EMF restrike processes from the perspective of coil design, blnk deformtion, nd cooling systems for the coil. References [] Bessonov, N.; Golovshchenko.: Numericl imultion of Pulsed Electromgnetic tmping Processes. Proceedings of the st Interntionl Conference on High peed Forming, Dortmund, Germny, 004, p.8-9. [] Bessonov, N.; ong, D.: Appliction of vector clculus to numericl simultion of continuum mechnics problems. Journl of Computtionl Physics.67/,999, p.-8. 5