Numerical simulation of ultra precision machining based on molecular dynamics and finite element simulation

Transcription

1 Rvsta d la Facultad d Ingnría U.C.V., Vol. 3, N 14, pp , 017 Numrcal smulaton of ultra prcson machnng basd on molcular dynamcs and fnt lmnt smulaton Wgang Guo 1,, Julong Yuan 1, Zhn Xang 1, Png Zhao 1, Bngha Lv 1 1 Ultra-Prcson Machnng Cntr, Zhjang Unvrsty of Tchnology, Hangzhou, Zhjang , Chna Hangzhou Vocatonal and Tchnology Collg, Hangzhou, Zhjang , Chna Abstract Wth th dvlopmnt of scnc and tchnology, th rsarch of ultra-prcson machnng tchnology has arousd mor and mor attnton. Exprmntal rsarch basd on ultra-prcson machnng machn or scannng prob mcroscopy s xpnsv and tm-consumng, so t s ncssary to adopt nw rsarch mthods to study th mcroscopc mchansm of ultra-prcson machnng tchnology. In ths work, th ffct of scal on msoscopc scal s studd basd on mso-mchancs thory, th ultra-prcson machnng procss s studd by usng molcular dynamcs and fnt lmnt smulaton. Molcular dynamcs s an mportant rsarch mthod of nano-procssng. In ths work, a molcular dynamcs smulaton modl s stablshd at th nanoscal, and th chp formaton and machnng surfac gnraton mchansm of slcon wafr undr nanomtr scal wr smulatd and analyzd undr dffrnt cuttng dpth and gomtrc angl. By usng th consttutv rlatonshp of th msoscopc sz matral, th fnt lmnt modl of ultra-prcson machnng procss was smulatd and th ultra-prcson machnng procss was smulatd. Th smulaton rsults provd th rlablty of th modl. Kywords: Numrcal smulaton, Ultra prcson machnng, Molcular dynamcs, Fnt lmnt. 1. INTRODUCTION Th rason why th modrn machnry ndustry s commttd to mprov th machnng accuracy s manly du to: mprov th stablty and rlablty of parts; promot th mnaturzaton of products; nhanc th ntrchangablty of parts.ultra-prcson machnng tchnology can not only mprov mchancal and lctrcal products prformanc, qualty, workng lf and rlablty.th us of ultra-prcson grndng and mcro-procssng tchnology whch dtrmns th lvl of procssng tchnology ntgratd crcuts on th ln wdth and th numbr of componnts, a drct mpact on th mcrolctroncs ndustry and computr tchnology. Th dvlopmnt and promoton of ultra-prcson machnng tchnology hav mprovd th machnng accuracy and tchncal lvl of th ntr machnry manufacturng ndustry, and hav gnrally mprovd th qualty, prformanc and rlablty of mchancal products and gratly nhancd th compttvnss of thr products(lu t al.,004; Km and L, 01). An atom or molcul on th surfac of a spcmn n th nanoscal machnng procss wll bcom a drct procssng objct. Thrfor, th physcal ssnc of nanoscal procssng s to cut off th combnaton of atomc bonds and achv th rmoval of atoms or molculs. Th tradtonal cuttng procss consums lss nrgy dnsty, and s actually procssd by th dfcts of th jonts btwn atoms, molculs or crystals. It's vry dffcult to cut off th bondng btwn atoms by nanoscal machnng wth convntonal machnng mthods.in modrn ultra-prcson manufacturng tchnology, th typcal mcro-cuttng procss s th us of damond sngl-pont tool, t has bn abl to achv dozns of nanomtr-scal cuttng (Brmann t al., 013). Howvr, thr s a lack of undrstandng of th matral dformaton and dbondng mchansm durng cuttng, th surfac and subsurfac matral proprts, and th ntracton btwn cuttng tools and workpcs. Rsarch on th mchansm of ultra-prcson machnng s on of th most mportant basc tchnologs n ultra-prcson machnng. It s an urgnt problm to dscuss th mcro mchansm of ultra prcson machnng tchnology,th ultra prcson machnng tchnology s a surfac formng procss at th atomc and molcular lvls.. At ths atomc scal, t s not th problm of "gomtrc rducton" n gomtry. Thr ar bound to b som nw laws that domnat th procss of matral rmoval and surfac craton(aly t al.,006). 315

2 Rvsta d la Facultad d Ingnría U.C.V., Vol. 3, N 14, pp , 017 To sum up, ultra prcson tchnology not only drctly affcts th dvlopmnt of cuttng-dg tchnology and natonal dfns ndustry, but also xtnds to all aras of th natonal conomy, and th scal of applcaton s gradually xpandng. All countrs n th world attach grat mportanc to th dvlopmnt of ultra-prcson machnng tchnology as a prorty n th dvlopmnt of advancd manufacturng tchnology,t has bcom a ky tchnology for th succss of ntrnatonal comptton.. MOLECULAR DYNAMICS MODEL Th basc da of molcular dynamcs: th stablshmnt of a partcl (atom) systm to smulat th mult-body systm consstng of atomc nucl and lctron mcroscopc phnomna.by solvng th dynamc quatons, th moton and trajctory of atom n phas spac ar dtrmnd, th corrspondng macroscopc physcal proprts of th systm ar obtand. Thrfor, th cor problm of molcular dynamcs smulaton s to calculat th movmnt ruls and trajctors of all atoms.th molcular dynamcs smulatons only smulat a part of thm, and th smulaton lasts for only a fw pcosconds.th samplng thorm s drvd from statstcal mchancs, track dstrbuton statstcs and samplng statstcs(ln and Huang,004): S E ( X x ) (1) M Whr, E :Expct varanc; S :Statstcal varanc; M :Samplng pont; X x :Full orbt avrag; :Sngl sampl avrag; Molcular dynamcs s oftn usd to study th proprts of bulk matrals at gvn dnsts. For crystalln systms, th shap of th cll s nfluntal. In ordr to rduc th sz ffct causd by th smallr numbr of partcls n th molcular dynamcs smulaton systm than th numbr of partcls n th ral systm, th molcular dynamcs smulaton uss prodc boundary condtons. Th mathmatcal rprsntaton of prodc boundary condtons s(lu and Mlkot,007): A( X ) A( X nl), n ( n, n, n ) () 1 3 For a physcal systm wth N partcls, th Hamltonan form of th mchancs dscrpton can b wrttn as: H q 1,,..., N p (3) p H (4) q Hamlton functon H s: H p U (5) m Whr, q :Th gnralzd coordnats of th partcl; m :Th qualty of th partcl;u :Total systm potntal; Th Nwtonan form of th systm mchancs s(komandur and Raff,001): p :Th Gnralzd Momntum of th Partcl; r F( r ) / m 1,,..., N (6) 316

3 Rvsta d la Facultad d Ingnría U.C.V., Vol. 3, N 14, pp , 017 F U( r, r,... r ) (7) 1 n Whr, F :Th partcl's rsultant forc; 3. FINITE ELEMENT MODEL r :Th partcl's poston coordnats; Th fnt lmnt mthod s a numrcal mthod,ts basc da s that th contnuous dformd sold s dsprsd nto a structur composd of a fnt numbr of lmnts, and th physcal lmnts such as dsplacmnt and forc ar transmttd through ths nods. Th fnt lmnt mthod ncluds many dffrnt ways of dalng wth problms. In all of ths ways, n ordr to calculat forcs, strans and dsplacmnts, t s nvsagd to dvd th matral dally nto a fnt numbr of unts connctd to ach othr by nods.th ral structur s smplfd as a mchancal modl. Th lmnt mchancs charactrzaton ncluds th followng parts(luo t al.,005): Us th gomtrc quaton to drv th unt stran xprsson: Whr, :Stran vctor at any pont n th cll; pont n th cll; (8) :Elmnt stran matrx; () Th consttutv quaton s usd to drv th xprsson of unt strss: D :Th strss vctor at any (9) Whr, :Any pont n th unt of th strss vctor;d :Elmnt lastcty matrx; Usng varatonal prncpl, stablsh th rlatonshp btwn nod and dsplacmnt s as follows(ln t al., 003): Whr, F F k (10) :Cll load vctor;k s Elmnt stffnss matrx, th xprsson s: T k Ddxdydz (11) Th stffnss matrx of ach unt s assmbld nto th ovrall stffnss matrx of th whol structur,th nodal forc matrx of ach unt s aggrgatd nto th total load matrx,th common mthod s th drct stffnss mthod. Th prms of th st stffnss matrx s that th dsplacmnts of adjacnt clls at th common nods ar qual, and fnally th quaton of th whol structur s obtand as follows: F k (1) From th pont of vw of numrcal smulaton, th fnt lmnt smulaton algorthm has Lagrang mthod, Eulr mthod and ALE (arbtrary Lagrang and Eulr mthod) mthod. Most of th fnt lmnt smulatons adopt Lagrang mthod, Lagrang mthod s adoptd n th fnt lmnt smulaton n ths work. Th coupld quatons of thrmal lasto-plastc larg dformaton ar drvd(gang and Pan, 001): 317

4 Rvsta d la Facultad d Ingnría U.C.V., Vol. 3, N 14, pp , 017 T p l T 0 (13) ( Kp KG ) d D dv RT dv F V Whr,d :Nod spd; K p :Elastoplastc stffnss matrx;k G :Gomtrc stffnss matrx;f 0 :Th rat of chang of workpc nodal forc; 4. SIMULATION AND VERIFICATION Th nos radus has a grat nflunc on th surfac qualty, and th varaton of workpc jont dsplacmnt dcrass wth th dcras of nos radus. Ths s bcaus th blunt cuttng dg of th machnd surfac s squzd and rubbd to a dgr corrspondng to th sharpnss of th cuttng dg. Th mor blunt th cuttng dg s, th gratr th dformaton of th machnd surfac s.thrfor, to achv ultra-prcson cuttng, must b carrd out a vry small amount of rmoval, th cuttng dg of th tool must b xtrmly sharp or tool nos radus s xtrmly small, so as to rmoval of th cuttng thcknss s small nough. Rsarch shows that to achv a 1 μm, th tool tp radus should b lss than 1 μm.whn th tool nos radus, th workpc dsplacmnt curv s shown n Fgur 1: V (a) ρ=4 μm (b) ρ= μm (c) ρ=0.6 μm Fgur 1. Workpc dsplacmnt curv wth dffrnt tool nos radus 318

5 Rvsta d la Facultad d Ingnría U.C.V., Vol. 3, N 14, pp , 017 Th cuttng dpth manly affcts th machnng ffcncy, but has no obvous nflunc on th surfac qualty,,whn th cuttng dpth s vry small, th normal cuttng can not b carrd out.. Fgur s th nod dsplacmnt curvs of dffrnt cuttng dpth, t can b sn from Fgur that th nod dsplacmnt ncrass wth th cuttng dpth ncrass slghtly, and at th ap=0.3ρ tm pont,dsplacmnt s obvously ncrasd, ths s du to th xtruson of th machnd surfac and th addtonal plastc dformaton on th machnd surfac. Incrasng th cuttng dpth can mprov th cuttng ffcncy, but th xcssv cuttng dpth wll affct th machnng accuracy and surfac qualty du to th cuttng forc and cuttng hat ncras. Gnrally, th cuttng dpth and th tool dg radus ar qut qual. (a) ap=0.6ρ 5. CONCLUSIONS (b) ap=0.3ρ Fgur. Varaton curvs of dsplacmnt at dffrnt cuttng dpths In ths work, th mchansm of ultra prcson machnng s rvald from a mcroscopc pont of vw, and a msoscopc consttutv rlaton of matrals s stablshd. Th machnng procss was smulatd by molcular dynamcs smulaton, and th chp formaton and machnng surfac gnraton mchansm wr smulatd undr dffrnt cuttng dpth and tool gomtry angl,, stablshd th ultra prcson machnng procss modl, and th procss s smulatd,th smulaton rsults show th fasblty of th modl. ACKNOWLEDGEMENTS Ths topc of rsarch s supportd by Natural Scnc Foundaton of Chna (No ), Scnc and Tchnology Dpartmnt of Zhjang (No. 017C31113), Tachng rform projct of hghr ducaton n Zhjang (No. jg016098) and Rsarch projct of Zhjang socty of Socal Scnc (No. 016N07Y). REFERENCES Aly M.F., Ng E., Vldhus S.C.,Elbstaw M.A.(006). Prdcton of cuttng forcs n th mcro-machnng of slcon usng a hybrd molcular dynamc-fnt lmnt analyss forc modl, Intrnatonal Journal of Machn Tools and Manufactur, 46(14), Brmann D., Stnr M., Krbs E. (013). Invstgaton of Dffrnt Hard Coatngs for Mcromllng of 319

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