NGHIEN Cflu-TRAOOdi XAY D V N G THUAT TOAN XU" LY SO LIEU DO DU'ONC KINH BE MAT TRU TREN MAY DO BA TOA DO BUILDING THE ALGORITHM FOR DATA PROCESSING OF DIAMETER OF CYLINDRICAL SURFACE MEASURED ON THREE COORDINATE MEASURING MACHINE PGS, TS Nguyen Tien Tho', TS Vu Toan Thang', ThS Vu Via Duy^ 'TrUdng Dai hoc Bach khoa Ha Noi ^TrUcJng Dai hgc Cong nghiep Ha NoL T6M TAT Khi be mat trii tren mdy toa do, dot vdi mat tru cd mat ddu vuong gdc vdi diidng tdm, trUdc tiin phdi xdc dinh vector phdp tuyen cua mat ddu roi chieu bo toa diem dUdc len tren mat ddu theo phiidng phdp tuyen, sau ditng gidi thuat xdc dinh dudng kinh trii; Con dot vdi be mat tru co mat ddu khong vuong gdc vdi dudng tdm tru phdi xdc dinh mot dudng tam khdi tao ban ddu roi quay dudng tdm dd ve trimg vdi dudng tdm tru, tii se xdc dinh dUdc dudng kinh tru Bdi bdo ndy trinh bay viec xay dung thuat todn xdc dinh dudng kinh cua chi tiet tru tii tap so lieu cdc diem tren mdy t(3a do, phuc vu cho viec thiet kephdn mem mdy tga dong thdi ndng cao kien thUc ludng nhdm khai thdc tot hdn mdy toa ttii Viet Nam ABSTRACT When measuring cylindrical surface on three coordinates measuring machine, if the top surface is perpendicular to the center line, it first determines the normal vector of the top surface and the set of coordinates of the measured points to the top surface under, then using the algorithm to determine the diameter of the shaft; if the top surface is not perpendicular to the center line, to define an initial centerline and then turning that center line coincides with the true centerline of the cylinder, then it be able to calculate the diameter This paper presents the development of algorithms to determine the diameter of the details of the cylinder from the data of measured points on three coordinates, it is applied to build the software for CMM and improve the understanding of coordinates measurements in order to better exploit CMM in Vietnam TAP C H l CO KHf V I £ T NAM V S6 +2 (Thang +2 nam 2013) NGHIEN CUfU-TRAO D | I.DATVANDE C= {x2-x,)(y,-y,)-{y2-y,){'c,-x,) Khi dat chi tiet trri can khong gian Trong : Cac x^, y_, z^ la tpa dp cac diem he tpa dp de cac cua may ba tpa dp (CMM), khong t h i d i m b i o true z cua may song song vdi 1, 2, dfldng tam tru, tdc li dfldng tam tru bi nghieng so vdi true z n i n theo cac tiit dien trin be mat tru ta khong dflpc tiet dien vuong gdc vdi dudng tam tru, vi vay, tiet dien thudng CO hinh elip Do do, de dung dudng kinh tru, phai chpn mpt mit phang ehuan vuong goe vdi tam tru de chieu bp sd h i u lin mat phing niy, nhu vay, hinh chieu cua bp so lieu se nam tren tiet dien vudng gdc vdi tim tru Mat phing ehuan thudng dflpc chpn la b i mat dau eua tru Trong cdng nghe gia cong cP khi, vi du phflong phap tien be mat dau thfldng dflpc tien tren cung mpt lan gi vdi be mat tru, dd, dam b i o dflpc dp vuong goc vdi dfldng tam cua tru Trong cac trfldng hpp mat dau khong vuong goc vdi tam tru, Hinh 1: Chi tiet cd mcit ddu vudng gdc vdi tdm tru mat dau se khong the dung Iam mat chuan de chieu bo so lieu dii'm Vay, phai xie dinh Cosin ch] phuong cua vec to phap ttla; dflpc dfldng tam tru mdi tinh dUpe dfldng kinh tru, ta cd the tiet diin song song trin mat (1) tru, mac du tiet diin la elip, ta van coi li hinh V/+B-+Ctron de xic dinh dflpc gan dung tam cua mdi tiet Trong : diin, vi coi tam lam nghiem khdi tao ban dau eho dfldng tam tru, sau xoay dfldng tam a Ii goe hpp bdi (?) va (Oyz) niy vi trung vdi dUdng tam dung eua tru bing cie /? la gdc hpp bdi (P) vi (Ozx) thuat toin va cie phep chiiu y la gde hpp bdi (?) vi (Oxy) XAC DINH DlTCfNG KfNH TRU KHI CHI TIET CO MAT DAU VUONG GOC VOL DU6NG TAM TRU Giai thuat dfldng kinh dupe thUe hien lan lupt theo cie bfldc sau: 1, Lay mat dau lam mat phang ehuan, trin xie dinh toa dp diem 1,2,3 (hinh 1) Viet phflpng trinh mat phing di qua diem do de xac dinh vector phap n (A,B,C) /! = (,.,-,.,)( ,-')-(-':-z,)(,.,-;0 S = ( : -)(>.-0-k,-.v,)(z,-z,) TAP CHf CO KHf VIET NAM Dflng he true toa dp mdi Ox'y'z', ed Oz' CO vector chi phflpng n (1^, m^, n^ True Oz' da cd, can xic dinh cie true Ox' va Oy' Vi mat phang Ox'y' vuong gdc vdi Oz' tai O n i n Ox'y' hoan toan xic dinh, nhiin hai true Ox' va Oy' co vi tri bat ky va chi can thoa man dieu kiin vuong gdc vdi De xay dflng cac thuat toin, can eo dinh hai true Theo d6, de don giin qua trinh tinh toin, xic dinh mpt hai true Ox' v i Oy' se la giao tuyen cua mat Ox'y' vdi mat phang Oxz hoae Oyz Vi du, Ifla ehpn trfldng hpp true Ox' U giao tuyen cua mat phang Ox'y' cd phflpng trinh: S6 1+2 (Thing 1+2 nam 2013) NGHIEN CUfU - TRAO D | cosa x + cos^ y + cosy z = (2) nay, b i n kinh dfldng tron ehinh la ban kinh tru Vdi mat phang Oxz cd phuong trinh: y=0 Tpa dp tam cua dfldng tron di qua diem niy dflpc tinh theo cong thflc: _ a(cc'+bb')b(dd'+aa') Nhfl viy, d i dang xic dinh dflpc vectP ehi phflpng cua Ox': 1,0, ^ ~ (3) 2(ce-be) " \ c[dd'+aa)-d{cc-\-bb") 2(ce-be) _ •" , , (10) Nhfl viy, eac cosin ehi hfldng cua Ox' se n cos/ (cosa^ , m, - , n, =—I l^cos;'J ' [ cosaV l^cos;'J O day X(j vi y^ lan Iflpt Ii hoanh dp va tung dp cua tim dfldng tron di qua diem hinh chieu (4^ eua 4, 5, len mat dau cua tru: Khi d i xie dinh dflpc cie true Oz' vi Ox' Vi true Oy' vuong gdc vdi ca hai true Ox' vi Oz' a = y'3 - yV b^ = y > y V e' = x', + x'ji d = x'j - x'^; d'= x'^ + x'|; e = y'3 - yV nin niu gpi J la vectP ehl hfldng eua Oy' thi: / cos^ cos/ T, cos/ cosa cos or cos/ cos/ cosa cosp [ cos a cos (5 sin^/? l^ cos;' cos/ Cosin ehi hfldng eua true Oy' Ii: , cos a cos y9 „ „ /j = ^ , m, =sinp, OT =-cotg/).cos/ (g) sin^ Do toa dp diem 4, 5, tren mpt tii't dien trin mat tru Chieu tpa dp cac diem lin mat dau chi tiet tru bing eieh chuyen toa dp diim tfl h? Oxyz sang he Ox'y'z' thdng qua mot ma tran sau: r i"l T/ /, h m^ rt, y ^ - ^^'3 - '^V Cie diem trin tiet diin cd the dflpc tang lin de nang eao dp chinh xac cua phep do, ta si xac dinh vector phap cua mat phing dau di qua n diim theo pbflOng phap binb phflong nho nhat LSC[1] vi xie dinh dfldng trdn di qua n diem theo pbflOng phip LSC, dfldng tron npi tiep nhd ldn nhat MIC [2], dfldng tron ngoai tiip nhd nhat MCC [2] hoac tim miin toi tbieuMZC[3] = n^i cosa ^ " il + y'l; b = y'^ - y',; c^'f^-x',; (9) '"3 "3 J Xie dinh dfldng trdn di qua ba diem XAC DINH DUdNG KINH TRU KHI M A T DAU KHONG VUONG G C V6I D U O N G TAM TRU Vdi binh tru dat bat ky khong gian, khong ed mat dau vuong gde vdi dfldng tim tru vi vay tiet dien se la mot dfldng Elip Neu ta dii'm trin tiet dien vi dflng dfldng tron thi tim cua dfldng tron se khong trung tim tru tai tiet dien Do viy, bin kinh cua dfldng tron niy khong phii la ban kinh cua tru Sau diy si trinh bay phflpng an de xie dinh dfldng kinh tru bat ky Gii sfl khong gian Oxyz, true cua hinh tru nghiing gdc a so vdi true Oz De xac dinh dfldng kinh tru, ta tien hanh theo cic ^ bfldc sau (hinh 2): TAP CHf CO KHf VIET NAM V S6 1+2 (Thing 1-2 nam2013) NGHIEN CUfU-TRAO D | l.Tren m a t p h a n g P j , d o d i e m A,,B,,Cj Qua A/, B^, C / x i c dinh dfldng trdn tam Xic dinh dfldng tron di qua diem cd tam I, Ij'Cx^', y^', z^') Dfldng thang di qua diem I/I^' co (x,,y,,z,) Trin mat phang P^, diem A^, B^, C^ Xie dinh dfldng tron di qua ba diem cd tam I^ (x,,y,,z,) 3.Xie dinh dfldng thing di qua tam I^ va I, cd vecto ehi hfldng Ii n[i,j,k) veetP chi hfldng la n{i', j\k'^ Lap lai cac bfldc 4, 5, cho d i n gde hop bdi hai dfldng thang I^I^ v i Ij'I^' nho thua mot gii tri eho trfldc thi ngflng, tde li: cos (n,rt'1 = i.i'+ j.j'+ k.k' ^ \ Dp ehinh xic eua phep yeu cau cang cao thi so lan lap cang nhieu Khi phep hpi tu dfldng thing I / ' I / ' dflpc eoi nhfl dfldng tryc ly tfldng cua tru Sau cd dflpc dfldng true ly tfldng, dfldng kinh eua tru chinh la gii tri trung binh cua dfldng kinh hai dfldng tron di qua diem flng vdi lan lap cudi cung Hinh 2: Xdc dinh dUdng kinh tru mat ddu khong vuong goc dUdng tdm Dflng he toa dp mdi Ox'y'z', gdc tao dp O, ed true Oz' (i, j , k) Cac true mdi Ox' va Oy' dflpc xic dinh tflPng tfl d mue II Chuyen so toa dp eua cac die'm tfl toa dp eu Oxyz ve he toa dp mdi Ox'y'z' Cie diim A|,Bj, C, chieu lin mat phing (Pj') diqual^va vudng gde vdi y ^ ta dflpc A,', B,', C,' Vi (P/) song song vdi Ox'y' nen eic die'm A^', B,', C,' eo cung cao dp Tflong tfl cic diem A,, B^, C^ chieu lin mat phang (P,') di qua I^ va vuong goc vdi IJ^ ta dflpc A „ B ; , C ; Qua A^', B|', C,' xic dinh dfldng trdn tam I|'(X|', y^', 2,') TAP CHI CO KHf V I £ T NAM V De xie dinh dp tru cung nhfl ting dp ehlnh xac cua phep do, ta ed the xac dinh nhieu hPn diem Diem thfl trd di h o i n toan nam tren tiet dien bat ky eua mat tru Nhd phep chuyen he toa dp nhfl trin, ta thu dflpc toa dp cac diem he toa dp euoi cung Oxiyizi Chieu tat ca cie diem len mat phang OxiyL Bing pbflOng phap binh phflpng nho nhat, dflng dfldng tron xap xi qua tap cie diem niy eho ta dfldng kinh tru vdi dp ehinh xic eao hon Sai lech gifla cie ban kinh cho ta tru =R -R KET LUAN Khi thflc hiin cic be mat tru tren may ba tpa dp (CMM), viec xic dinh tam tru la dii'm quan trpng de xic dinh dung dUdng kinh mat tru Vdi bp so lieu tpa dp eic diem do, thuat toin n i u trin d i dUa hai giii p h i p xie dinh tam tru trUdng hpp tru cd mat dau vuong gdc vdi S6 1+2 (Thing 1+2 nam 2013) NGHIEN CUfU-TRAO edl dfl6ng tam vi tru khong ed mat dau vuong gde vdi dUdng tam Cic thuat toan niy li ed the ip dung de thiet ki cac menu dp trii cho miy CMM, mac du so lUpng phep tinh phai thUc hiin nhieu, nhUng vdi trinh dp tin hpe phat trien nhU ngiy hoan toin cd the thu dflpc kit qua mpt each nhanh ehdng • Ngay n h ^ bii: 01/2/2013 Ngay phan biin: 23/02/2013 Ngfldi phan biin: PGS, TS Vii Quy Dac; TS Pham VAn Bong, Trfldng Dai bpc Cong nghiep Hi Npi Tai lieu tham khao: [ ] Vu Toan Thang, "Nghien cflu phUOng phap toa dp kieu tay quay" Luan van Thac sy Khoa hoc Ky thuat TrUdng Dai hoc Bach khoa Ha Npi, 1999 [2] Jyunping Huang - Department of Industrial Engineering, National Huwei Institute of Technology, 64 Wun-Hwa Road, Huwei, Yun-Lin, Taiwan, 63208, ROC "An exact solution for the roundness evaluation problems" Precision Engineering 23 (1999) 2-8 , Journal of Elsevier Science, 1999 [3] P.B Dhanish' Calicut Regional Engineering College, Mechanical Engineering Department, 673 601 Cahcut, India " A simple algorithm for evaluation of minimum zone circularity error from coordinate data" International Journal of Machine Tools & Manufacture 42 (2002) 1589-1594, 2002 TAPCHf CO KHf VIETNAM V S6 1+2 (Thing 1+2 nam201 ... tiet dien Do viy, bin kinh cua dfldng tron niy khong phii la ban kinh cua tru Sau diy si trinh bay phflpng an de xie dinh dfldng kinh tru bat ky Gii sfl khong gian Oxyz, true cua hinh tru nghiing... c^''f^-x'',; (9) ''"3 "3 J Xie dinh dfldng trdn di qua ba diem XAC DINH DUdNG KINH TRU KHI M A T DAU KHONG VUONG G C V6I D U O N G TAM TRU Vdi binh tru dat bat ky khong gian, khong ed mat dau vuong gde... dfldng kinh tru vdi dp ehinh xic eao hon Sai lech gifla cie ban kinh cho ta tru =R -R KET LUAN Khi thflc hiin cic be mat tru tren may ba tpa dp (CMM), viec xic dinh tam tru la dii''m quan trpng