Compuer nd Informion Siene The Forming Theory nd Compuer Simulion of he Rory Cuing Tools wih Helil Teeh nd Comple Surfes Hurn Liu Deprmen of Mehnil Engineering Zhejing Universiy of Siene nd Tehnology Hngzhou 310023, Chin sr This pper reserhed he forming heory of he uing ools wih helil eeh nd omple surfes. Dedued he nonliner equions of he movemen of NC sysem o genere suh ools, presened he wy o find he soluion of he equions, luled he ross seion grphis of he eeh profile nd ompuer simulion of NC mhining. Keywords: rory uing ools, Helil eeh, Compuer simulion 1. The uing edges of he rory ools wih helil eeh Fig.1 showed rory ool wih omple surfes. The oordine of ny poin on he uing edge:, y os( + ϕ), z sin( + ϕ) r r Where r p : he rory rdius of ny poin P : The posiion ngle of he rdius line rele o he oy pln. From derivive geomery, we know h should e sisfied y he following equion Where β : he helil ngle of uing edge. The ngen veor of uing edge: z 158 1 y dz dr d sin 2 d gβ dr 1 + (2) r dy dr d os ( + ϕ ) + r os( + ϕ ) ( + ϕ ) r sin( + ϕ ) If p, r p, re susiued y p, rp, + 2π / z, equion will e he oordines of he wo uing edged nd, whih re in he neighorhood wih eh oher, respeively. nd so re he Eqs (3), fer roe n ngle φ ou is, should e susiued y + 2π z. z represens he nuer of eeh. 2. he eslishmen of he oordine sysem / In he Fig.2, grinder is genering rory uing ool. Two oordine sysem need o e eslished. 1) The fied oordine sysem Oyz The - is of his sysem is he roion is of he work; he originl poin O of his sysem is he roion ener of he lrger end of he work. 2) Grinder oordine sysem Oyz The originl poin Os is he ener of grinder wheel, he y s is is prllel o y -is, he ngle eween s nd equl (3)
Compuer nd Informion Siene Noveer, 2008 o π / 2 Σ. The oordines of poin Os in fied sysem re, y, z. The oordine rnsformion of wo sysems n e se s sin Σ 0 osσs + y 0 1 0 ys y (4) z osσ 0 sin Σ z s z 3. The surfe equion nd norml veor of grinder The surfe of grinder is irulr one, le M represen ny poin on he one, he oordines in lol sysem of M n e epressed s following ( see Fig.2) M ( R rm, ym rm, zm rm (5) Where r : The rdius of poin M θ : The ngle posiion prmeer α : The oom ngle of he grinder The oordines in he fied sysem re M ( R rm sin ε + rm os ε + M y r + y M ( R rm osε + rm sin z z ε + M The norml veor in he lol sysem is: nm ( osα, sinα,sinα ) (7) The norml veor in he fied sysem is: nm ( osα sin Σ + sinα osσ, sinα,osα osσ + sinα sin Σ) (8) Le M represen ny poin he lrges irle of he grinder, he oordine of poin M in lol sysem n e epressed s following: M 0, ym R, zm R (9) Where R: he rdius of he lrges irle of he grinder θ : The ngle posiion prmeer The oordines of he sme poin in he fied sysem re R osε + M 4. The moving equions of NC sysem y R + y z R sinε + z, M, M The prolem o e solved y his hesis is: when use grinder wih urin shp o genere he eeh of he uer, he wo neighorhood uing edges nd should e mde ou y he wo sides of he grinder in he sme ime, so h, he relive movemen of he work nd grinder should sisfy speil mhemil nd geomeril relionship. Suppose h, he on poins on -side of grinder nd uing edge of work re M nd P respeively. The oordines in he fied sysem should e he sme Following relion n e derived from Esq. nd Esq. (6) p ( R rm sin Σ rm Σ + os ( R rm osσ rm sin Σ z z M p p p (6) (10), y y, z z (11) y + r os θ y (12) 159
Compuer nd Informion Siene The norml veor of he grinder M should e veril o he ngen veor of he uing edge P, so h 160 n 0 (13) p From Esq.(3) nd Esq.(8), we oin: ( sin Σ + osσ) gα gα (sin Σ osσ) (14) pz Suppose h he oning poins of he lrges irle nd uing edge re M nd P respeively, he oordines of suh wo poins in he fied sysem should e he sme: From Esq. nd Esq.(9), we oin: m py p m, y y, z z (15) p R osσ, y rp os( + φ) R, z rp sin( + φ) R sin Σ (16) he sme ime, on he sme grinder, he posiion of he ener poin C should e single. From Esq.(12) nd Esq.(16), following equion n e derived. M ( R r sinε r osε + M M p R osσ (17) y M + r M r p p m os( + φ) R (18) While, during he generion, he oordine Z remin unhnged, so h: z r sin( + φ) R sin Σ (19) p p pz ( R rm ) g osσ rm sin Σ z z α (20) Esq. (14)(17)(18)(19), nd (20) form nonliner equion sysem wih five equions, In hese equions here re 6 unknown prmeers: θ, θ, p, p, r, φ. One of he prmeers n e given efore hnd, so he equions re solvle. 5. Emple There is rory ool wih he ouside surfe of rnseed one, s showed in Fig.4. The min prmeers of he ool res following: The mimum dimeer: d10mm The lengh of he uer: l24.5mm The nuer of eeh: z20 The pe ngle: ξ 7 The helil ngle: β 20 The prmeers of he grinder re s following: The dimeer of he grinder: D80mm The oom ngle of he grinder: α 60 The prmeers of insllion re lised elow: Z0 Insllion ngle: Σ 20 Through ompuer lulion, he oordines of he grinder ener during generion n e solved ou nd lised ellow. (Deleed) 6. The ompuer modeling nd simulion of he generion of he rory ools In generion, he relive displemen of he grinder nd he work is very omplie. Only y numeril onrol operor n relize suh moion requiremen. For esifying he heoreil deduion nd numeril lulion, we used he impored I-DES sofwre o simule he uing movemen of he work nd he grinder he SUN-CD worksion. This is he firs ime o use ompuer solid modeling in reserh of he rory ools wih omple surfes, nd we mde he es use of he new hievemen in ompuer grphis, nd ompuer id Design home nd rod. The I-des sof wre sysem onins 5 fmilies:1)solid modeling, 2)sysem ssely,3)engineering nlysis,4)sysem
Compuer nd Informion Siene Noveer, 2008 dynmis nd 5)drfing. The reserh of his hesis used wo of hem: solid modeling (Geomod) nd engineering drfing( Geodrw) Firs, ree he oje of he work nd grinder, ording o heir shpes, nd sored hem wih Geomod; seondly, mde grinder nd work o move rele o eh oher; hn do he oolen operion, every posiion. The generion of he work orresponds o u oje operor, one of he oolen lulion. Finlly, fer he grinder goes hrough ll move posiions he eeh profile of he work ws formed. In he eginning, we hoose hnd operion, y sele menu wih mouse, le he grinder nd work go severl seps ording o he required replemen, nd reorded our operion ino progrm file. pssge of he I-des progrm orresponds o one uing sep is s follows: Reurn o min menu---ge he sored work----orien i his ime----roe ou is es---give he vlue of roe ngle---sore i he seond ime---ge he sored grinder---rnsle i long nd y direion respeively ---give he vlue of he rnsle moun ---sore he grinder one more ---reurn o min menu gin--- sele oolen operion ---sele uing operion ---define he uer, he grinder---define he oje o e u, he work---sore he new uer work he hird ime In running his shor pssge of progrm, we n see from he seen of he ompuer series of piures in onsequene: The originl shpe of he work; The originl posiion of he grinder; The roion of he work; The rnslion of he grinder rele o he work; The grinder in uing wih he work; The shpe nd he size of he hip formed from uing, i is growing lrger nd lrger every momen; The work u is wiing for furher uing; Thn, le he Forrn progrm, wih whih he oordines of grinder ener were luled, o oupu uomilly pssge of progrm s menioned ove, whenever displemen is luled. Every movemen is orresponding o one pssge of I-des form ely. In his wy, he whole genere progress n e simuled. The shpe of he work wih one groove showed in Fig.3. The seionl urvure of he ooh profile showed in Fig.4. 7. Conlusions From he nlysis nd reserh menioned ove, following onlusions n e rrived : 1) The forming heory of he rory ools wih helil eeh nd omple surfes is orre. To genere suh kind of ools, hree oordines numeril onrol mnufuring sysem is needed. 3) From ompuer simulion, we n esify he formuls of heorei deduion nd resul of numeril lulion presened in his pper. We n emine if he inerferene nd oher prolem. Whih re ofen used y inorre prmeer seleion, would ke ple nd he wy o preven i efore hnd. Referenes o Qingshn, sudy on virul mnufuring model of revolving milling uer in 2-is numeril onrol proessing. J Mer Proess Teh, 2000,120(1-3):68-75. Chen hogung, mnufuring model of ride-ipped spheril milling uer. Pro.Insu. Meh. Engrs., 1999,213()713-724. 161
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