Aville online t www.sienediret.om Proedi CIRP 8 (2013 ) 265 270 14 th CIRP Conferene on Modeling of Mhining Opertions (CIRP CMMO) Modeling nd Simultion of the Eletrohemil Mhining (ECM) Mteril Removl Proess for the Mnufture of Aero Engine Components Astrt F. Kloke, M. Zeis, *, S. Hrst, A. Klink, D. Veselov, M. Bumgärtner Lortory formhine Tools nd Prodution Engineering, Steinhstrße 19, Ahen 52074, Germny Leistritz Turomshinen Tehnik GmH, Mrkgrfenstrsse 29-39, Nuremerg 90459, Germny * Corresponding uthor. Tel.: +49-241-80-27467; fx: +49-241-80-22293; E-mil ddress: m.zeis@wzl.rwth-hen.de. In order to inrese the effiieny of jet engines hrd to mhine nikel-sed nd titnium-sed lloys re in ommon use for ero engine omponents suh s ldes nd lisks (lde integrted disks). Here Eletrohemil Mhining (ECM) is promising lterntive to milling opertions. Due to lk of pproprite proess modeling pilities eforehnd still knowledge sed nd ost intensive thode design proess is pssed through. Therefore this pper presents multi-physil pproh for modeling the ECM mteril removl proess y oupling ll relevnt onservtion equtions. The resulting simultion model is vlidted y the exmple of ompressor lde. Finlly new pproh for n inverted thode design proess is introdued nd disussed. 2013 The Authors. Pulished y y Elsevier Elsevier B.V. B.V. Open ess under CC BY-NC-ND liense. Seletion nd nd/or peer-review peer-review under responsiility under responsiility of The Interntionl of The Interntionl Sientifi Committee Sientifi of Committee the 14th CIRP of Conferene the 14th CIRP on Modeling Conferene of Mhining on Opertions Modeling of in Mhining the person of Opertions" the Conferene in the Chir person Prof. of Lu the Conferene Settineri Chir Prof. Lu Settineri Keywords: Eletrohemil Mhining (ECM); simultion; ero engine omponents; inverse prolem 1. Introdution To hieve weight redution nd inresed therml effiieny of jet engines, hrd to mhine lloys suh s Ti-6Al-4V nd Inonel 718 re in ommon use for the mnufture of ero engine omponents. Espeilly the milling proess of lisks mde of Ni-sed lloys rehes its tehnologil nd eonomil limit. Here Eletrohemil Mhining (ECM) is ost-effetive lterntive. In ECM high mteril removl rtes n e relized without developing ny white lyer or het ffeted zone. Additionlly vi ECM it is possile to hieve finished surfes qulities during rough mhining opertions, whih elimintes the need for further tretment like ost-intensive finish milling steps or polishing opertions [1, 2, 3]. But due to ost intensive tool developing proesses nd rther high investment osts for the mhine tools, ECM is mostly used in produtions with lrge th sizes. Min reson for high tool osts is n only knowledge-sed, itertive thode designing proess. After test run the produed workpiee hs to e mesured nd the differene etween trget nd tul geometry due to lolly hnged onditions of eletrolysis is sutrted from the thode nd so forth. On the other hnd the theoreti kground of the eletrohemil mteril removl proess with ll its different physil spets is very well known, ut up to now it hs never een sueeded to omine ll different spets together into one suffiiently preise model to simulte the proess for the mnufture of ero engine omponents. This pper presents new pproh for modeling the ECM mteril removl proess y oupling the onservtion equtions for fluid flow, eletri fields, eletrohemil surfe retions, ioni trnsport nd het trnsfer. Bsed on initilly introdued governing equtions, possile oupling strtegies re presented nd disussed. Afterwrds, the erodynmi ross-setion of ompressor lde is lulted in two different wys. 2212-8271 2013 The Authors. Pulished y Elsevier B.V. Open ess under CC BY-NC-ND liense. Seletion nd peer-review under responsiility of The Interntionl Sientifi Committee of the 14th CIRP Conferene on Modeling of Mhining Opertions in the person of the Conferene Chir Prof. Lu Settineri doi:10.1016/j.proir.2013.06.100
266 F. Kloke et l. / Proedi CIRP 8 ( 2013 ) 265 270 Besides the simultion of the lssil ECM proess with the im to lulte the lde ontour y using predetermined thode geometries new inverted simultion strtegy is presented. This new pproh uses the lde trget geometry in order to lulte thode shpe y inverting the eletri field. 2. Theoretil Bkround ECM is mnufturing tehnology where mny different physil disiplines nd spets need to e onsidered (p. figure 1). In order to simulte this mteril removl tehnology esides the modeling of the eletromgneti field the eletrolyte flow hs to e nd the ioni trnsport. So in this hpter the governing equtions for omplete desription of the eletrohemil mteril removl proess re nmed nd possile physil ouplings re disussed. Eletri Field urrent density equls zero euse only n externl voltge is pplying. The eletri displement field is defined s:. (4) Herein is the eletril field onstnt nd the mteril dependent reltive permittivity. Altogether urrent density n e written s: 2.2. Eletrolyte. (5) Flow fields of Newtonin fluids n ompletely e desried y the Nvier-Stokes equtions [6]. Equivlent to the ontinuity eqution of hrge the onservtion of mss n e written s:. (6) Here the veloity vetor. ed to ontinuum the onservtion of momentum results to:. (7) Surfe Retions Fluid mehnis Fig. 1. Physil Couplings in ECM [4] 2.1. Eletri Field Het Trnsfer Geometry Struture The eletri field forms the sis for eletrohemil equtions [5] nd the ontinuity eqution of hrge whih sttes tht lol eletri hrge density hnges y the divergene of the vetor of urrent density :. (1) If mgneti fields re negleted, the eletril field is defined y the negtive grdient of eletri voltge :. (2) With the speifi eletri ondutne, the eletri displement field nd the externl vetor of urrent density the vetor of urrent density results to:. (3) In se of eletrohemil mhining the externl Within eqution (7) is n elertion vetor, the pressure nd the tensor of sher stresses. In ECM used y the eletrolysis of wter hydrogen gs is produed fluid hd to e desried s two phse flow whih in generl n e solved y the Nvier-Stokes equtions s well. Cused y high flow veloities nd shrp inlet ngles of the thodes, flow fields in ECM proesses for ero engine omponents re mostly turulent. In order to hieve dequte simultion times the Nvier-Stokes equtions re not omputed diretly. Hene turulene hs to e modeled seprtely e. g. y the k- -model [7]. 2.3. Eletrode Surfe Retion To model the ECM proess the mthemtil desription of surfe retions is of entrl importne. Bsilly urrent density n e written s the differene of node (index A) nd thode (index C) retions:. (8) Herein is Frd represent the retion veloities. These retion veloities n e desried with the help of the trnsition stte theory nd re defined s [8]:. (9)
F. Kloke et l. / Proedi CIRP 8 ( 2013 ) 265 270 267 dependent frequeny ftor is proportionl to the rtio ) onstnt [9]:. (10) Differene of free enthlpy (Gis free energy) is expressed y the sum of the enthlpy differene in the energeti ground stte nd the Glvni potentil.. (11) Eqution (11) here denotes the mximum potentil differene whih does not our in relity so tht pssge ftor with is pplied. If the nodi urrent density equls the thodi urrent density, potentil differene equls the equilirium rest potentil. This interreltionship leds to the exhnge urrent density :, (12). (13) If n externl potentil is pplied to the eletrohemil ell, the potentil within the ell hnges from equilirium rest potentil to nd the over-voltge :. (14) Hene the new potentil differene is:. (15) Summrized nd with the sustitution the lol urrent density n e lulted y the so-lled Butler-Volmer eqution: 2.4. Het Trnsfer. (16) In order to model n ECM-proess the het trnsfer is divided into het trnsfer in solids nd het trnsfer in fluids under negleted therml rdition. Bsed on the first trnsfer in solids n e lulted y [6]:. (17) Herein is the speifi het pity, the isotropi therml ondutivity nd speifi het soure. In omintion with the onservtion of mss nd momentum the onservtion of energy for fluid n e written s [6]: 2.5. Ioni Trnsport Mehnisms In generl it is distinguished etween the three types of ioni trnsport mehnisms diffusion, migrtion nd onvetion [8]. Diffusion sys tht moleulr prtile flux is proportionl to the grdient of molr onentrtion :. (19) the onservtion of mss for eh element:. (20) With the help of the Stokes-Einstein eqution in whih is the dynmi visosity of the fluid nd n e lulted y:. (21) Migrtion Ioni migrtion desries the movement of ions in n eletri field. Positive hrged ions move through the eletri field in the diretion of the negtive pole. Assumed tht the ions reh sttionry vlue of migrtion veloity, ioni moility n e lulted y the Nernst-Einstein eqution. Therein denotes the universl gs onstnt:. (22) Convetion Finlly dissolved prtiles n e moved y onvetion. This veloity is severl orders of mgnitude higher thn diffusion or migrtion nd n e desried y the Nvier-Stokes equtions (p. hpter 2.2). But the wll ner oundry lyer is n exeption used y the no-slip ondition. In summry, ll ioni trnsport mehnisms n e expressed for one speies (index ) to eqution (23). Therein denotes hemil retion term: 2.6. Frdy s Lw (23) where denotes the inner energy., (18) Besides the omplete desription sed on onservtion equtions the eletrohemil mhining lw [4]. For multiphse mterils nd due to the ft tht
268 F. Kloke et l. / Proedi CIRP 8 ( 2013 ) 265 270 not eh individul retion is removl effetive,. (24) In eqution (24) represents the effetive mteril removl rte, the dissolving veloity, the speifi mteril removl rte, the urrent effiieny, the speifi weight of the lloying ddition, the molr mss nd the eletrohemil vlene. Due to the ft tht eh element n e ionized differently strong, eletrohemil vlenes in eqution (24) re hrd to forest so tht the djustment ftor indites the proility for eh individul retion tking ple. But these proilities re not known extly euse they re on their prt funtion of temperture, ph-vlue nd so forth. For this reson nd due to the ft, tht the effetive mteril removl rte n e determined very extly in nlogil experiments, vlues of re often used s sis for further simultions [10]. 2.7. Physil Coupling First of ll the lol urrent densities out of the Butler-Volmer eqution (16) hve to e oupled with eh elementry retion re known, the lol, nlytil dissolving veloities n e lulted y:. (25) Here denotes the stoihiometri oeffiient of the redued speies. Up to now no generl nlytil expression for the ondutne of strong eletrolytes s they re used in ECM exists [11]. For this reson nd due to the ft tht this interreltionship is experimentlly well proven, here liner pproh (slope ftor ) is used to model s funtion of temperture:. (26) Similr to eqution (26) the eletril ondutivity of two-phse flows n e lulted y semiphenomenologil pprohes, e. g. of Bruggemnn et l. [12]. Generlly in ECM het is generted y Joule heting nd eletrohemil retions. Provided tht nerly ll eletril energy is onverted into het [13], Joule heting of the eletrolyte n e lulted in. (27) Therein is the differene in potentil etween node nd thode nd the lol gp width. Due to their low speifi resistnes, Joule heting of used solids is negleted. Het generted y surfe retions n e expressed y the produt of lol urrent density generted y Butler-Volmer retion nd over-voltge : Simultion step 1 Simultion step 3 Simultion step 3. (28) Finlly ll equtions of this hpter re introdued into one multi-physil model 3. Modeling nd Simultion 3.1. Simultion Softwre For modeling nd simultion the ommeril FEsoftwre COMSOL Multiphysis hs een used. Due to the modulr design of this softwre tool it is possile to omine different physil phenomen together into one simultion model. COMSOL hs lredy proven to e suessful in severl different eletrohemil mhining opertions like jet-ecm [14] or in the mnufture of shver ps [15]. 3.2. Coupling Strtegies In order to solve the Butler-Volmer eqution for eh elementry retion the exhnge urrent density nd the pssge ftor hs to e known. While in most ses tkes the vlue 0.5, vlues for unfortuntely only exist for smll numer of individul retions [16]. Thus, urrently it is not possile to set up omplete nlytil model euse mny prmeters re not existing nd hve to e found in future experimentl studies. experimentl dt of the effetive mteril removl rte [10]. In figure 2 simultion steps nd possile oupling strtegies re summrized y their nmes within COMSOL Multiphysis nd prtiulr physil effets they tke into ount. Fluid Flow Turulent Flow Het Trnsfer Het Trnsfer in Fluids AC/DC Eletri Currents AC/DC Eletri Currents Mthemtis Moving Mesh Fig. 2. Simultion steps nd possile oupling strtegies
F. Kloke et l. / Proedi CIRP 8 ( 2013 ) 265 270 269 3.3. Initil nd Boundry Conditions Tle 1 summrizes typil initil nd oundry onditions of ECM proesses for the mnufture of ero engine omponents. Finl simultion exmples re sed on these vlues. Aero engine omponents suh s ldes nd lisks re mnuftured in severl steps so tht feed rte nd voltge re vried in predefined rnge. Tle 1. Typil initil nd oundry onditions Initil nd oundry ondition Symol nd physil unit Vlue Inflow temperture T i / K 308.15 Inflow ondutivity of the eletrolyte 0 / (ms/m) 55 Slope of the ondutivity 2.8 Feed rte v f / (mm/min) 0.3-1 Effetive mteril removl rte V eff 1.51 Voltge U / V 7-20 Surrounding temperture T 0 / K 298.15 4. Results nd Disussion Bsed on rel ompressor lde geometry finlly simultion with the three simultion steps nd ouplings desried ove ws mde. Besides the trget geometry thode geometry whih hs proven itself in prtie ws given in order to vlidte the simultion model. Figure 4 shows the results of the simultion. It is mpped exellent y the simultion in omprison to trget geometry. Geometril devitions of less thn 150 μm in triling nd leding edge n primrily e explined y inuries of the predetermined inflow ondutivity of the eletrolyte. Another reson whih is reognizle generted y COMSOL. So shrp triling edge is uilt whih does not orrespond with the trget geometry in this re. Cthode geometry Simulted geometry Mximum devition < 10 μm In this hpter the results of simultion using the model with the initil nd oundry onditions desried ove re presented for rel ompressor lde pplition. Bsed on the lde trget geometry itself nd thode geometry whih hs proven to e suessful in prtie the simultion model is vlidted. In seond step new inverted pproh is presented where thode geometry is omputed. 4.1. Clssi Simultion Fig. 4. Clssi ECM proess simultion 4.2. Alterntive Cthode Clultion 1 mm Figure 4 shows shemtilly the ECM proess of the mnufture of ompressor or turine lde. Tool thodes re moved with onstnt feed rte towrds the lde (node) nd due to lol onditions of eletrolysis the lde is formed. Cthode Inlet Feed diretion Leding edge Outlet Due to the ft tht even with the help of working simultion model the thode design proess would still e itertive now new pproh is presented. By inverting the eletri field it is virtully possile to ompute thode geometry y using the trget lde geometry s node. ECM proess is inverted so tht lter tool geometry forms itself due to lol onditions of eletrolysis nd lde trget geometry. Figure 5 shows the results of this inverted pproh for thode design y ompring lulted geometry (lk line) with the one lredy proven itself in prtie (lue line). For the flow surfes nd the triling edge good results n e stted nd onerning the leding Triling edge Feed diretion Fig. 3. Priniple of ECM lde mnufture Cthode Anode slight differene etween trget nd lulted ontour. is of essentil
270 F. Kloke et l. / Proedi CIRP 8 ( 2013 ) 265 270 importne for suessful model of the eletrohemil removl proess. At the moment is only impreisely determined t the inflow oundry nd hs to e improved in order to reh higher simultion ury. It is impossile tht thodes ut themselves like in of this lultion is to prove how ner the simultion n mp relity. Furthermore the inverse prolem nnot e solved unique so tht severl solutions re possile. Existing thode geometry Workpiee geometry Simulted geometry Mximum devition < 80 μm Fig. 5. Alterntive thode design simultion 5. Summry nd Outlook All neessry equtions to desrie the ECM proess nlytilly nd how they re onneted to eh other hve een presented nd disussed. With experimentl results for the effetive mteril removl rte ording een uilt up tking into ount fluid flow, eletri field nd het trnsfer. In order to vlidte the simultion model rel ompressor lde hs een simulted in one erodynmi ross-setion in two different wys. Besides the simultion of the lssil ECM proess with the im to lulte the lde ontour y using predetermined thode geometries new inverted simultion strtegy ws presented. This new pproh uses the lde trget geometry in order to lulte the thode shpe y inverting the eletri field. Both simultions showed good results ompred to relity. To hieve even etter results, the effets of the hydrogen evolution t the thode hve to e inorported in the existing model. It is neessry to model the eletrolyte either s two-phse flow or to use semi phenomenologil pproh whih onsiders the gs phse influene to the ondutivity of the eletrolyte, e. g. of Bruggemnn et l. In next step 3D-model is going to e uilt nd y the here presented inverted pproh thode is eing lulted nd 1 mm mnuftured. Afterwrds lde is going to e mhined with this tool nd mesured s well s ompred to trget geometry. Aknowledgements This work hs prtilly een funded y the Germn Federl Lnd NRW within the projet EF 2037 von Nikelsis-Turinenshufeln für 700 Grd Referenes [1] Rjurkr K.P., Levy G., Mlshe A., Sundrm M.M., MGeough A., Hu X., Resnik R., De Silv A., 2006, Miro nd Nno Mhining y Eletro-Physil nd Chemil Proesses, CIRP Annls - Mnufturing Tehnology, 55:643 666. [2] Kloke F., Zeis M., Klink A., Veselov D., 2012, Tehnologil nd Eonomil Comprison of Roughing Strtegies vi Milling, EDM nd ECM for Titnium- nd Nikel-sed Blisks, Pro. CIRP, 2:98-101. [3] MGeough J.A., 1974, Priniples of Eletrohemil Mhining, Chpmn nd Hll. [4] Kloke F., Zeis M., Klink A., 2012, Tehnologil nd eonomil pilities of mnufturing titnium- nd nikel-sed lloys vi Eletrohemil Mhining (ECM), Key Engineering Mterils, 504-506:1237-1242. [5] Tipler P., Mos G., 2004, Physik für Wissenshftler und Ingenieure, Spektrum Akdemisher Verlg. [6] Shröder W., 2004, Fluidmehnik, Ahener Beiträge zur Strömungsmehnik, Wissenshftsverlg Minz in Ahen. [7] Wilox D., 1994, Turulene Modeling for CFD, DCW Industries, In. [8] Forker W., 1989, Elektrohemishe Kinetik, Akd. Berlin Verlg. [9] Steinfeld J., Frniso J., Hse W., 1998, Chemil Kinetis nd Dynmis - Seond Edition, Prentie Hll. [10] Kloke F., Zeis M., Klink A., Veselov D., 2013, Experimentl Reserh on the Eletrohemil Mhining of Modern Titnium- nd Nikel-sed Alloys for Aero Engine Components, ISEM 2013, in press. [11] Atkins P.W., de Pul J., 2006, Physiklishe Chemie, Wiley-VCH. [12] Kozk J., 1998, Mthemtil models for omputer simultion of eletrohemil mhining proesses, Journl of Mterils Proessing Tehnology, 76/1-3:170-175. [13] Kueth H., 1965, Der Aildungsvorgng zwishen Werkzeugelektrode und Werkstük eim Elektrohemishen Senken, Disserttion RWTH Ahen. [14] Hkert M., 2009, Entwiklung und Simultion eines Verfhrens zum elektrohemishen Atrgen von Mikrogeometrien mit geshlossenem elektrolytishen Freistrhl, Disserttion TU Chmnitz. [15] Vn Tijum R., Pjk P.T., 2008, Simultion of Prodution Proess using the Multiphysis pproh: The Eletrohemil mhining Proess, COMSOL Conferene. [16] Holze R., 2007, Eletrohemistry, Springer.