Vu Via Duy^ 'TrUdng Dai hoc Bach khoa Ha Noi ^TrUcJng Dai hgc Cong nghiep Ha NoL T6M TAT Khi do be mat trii tren mdy do ha toa do, dot vdi mat tru cd mat ddu vuong gdc vdi diidng tdm, t
Trang 1XAY 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 do be mat trii tren mdy do ha 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 do diem do dUdc len tren mat ddu theo phiidng phdp tuyen, sau do 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 do 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 do tren mdy do 3 t(3a do, phuc vu cho viec thiet kephdn mem mdy do 3 tga do dong thdi ndng cao kien thUc do ludng nhdm khai thdc tot hdn mdy do 3 toa do 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 center-line and then turning that center center-line coincides with the true centercenter-line 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
Trang 2NGHIEN CUfU-TRAO D 6 |
I D A T V A N D E
Khi dat chi tiet trri can do trong khong gian
he tpa dp de cac cua may do ba tpa dp (CMM), do
khong t h i d i m b i o true z cua may song song vdi
dfldng tam tru, tdc li dfldng tam tru bi nghieng
so vdi true z n i n khi do theo cac tiit dien t r i n
be mat tru ta khong do dflpc tiet dien vuong gdc
vdi dudng tam tru, vi vay, tiet dien do thudng
CO hinh elip Do do, de do dung dudng kinh tru,
phai chpn mpt mit phang ehuan vuong goe vdi
tam tru de chieu bp sd h i u do lin mat phing niy,
nhu vay, hinh chieu cua bp so lieu do nay se nam
tren tiet dien vudng gdc vdi t i m 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, do 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,
khi do mat dau se khong the dung Iam mat chuan
de chieu bo so lieu dii'm do Vay, phai xie dinh
dflpc dfldng tam tru mdi tinh dUpe dfldng kinh
tru, ta cd the do 2 tiet diin song song t r i n mat
tru, mac du 2 tiet diin do la elip, ta van coi l i hinh
tron de xic dinh dflpc gan dung tam cua mdi tiet
diin, vi coi 2 tam nay lam nghiem khdi tao ban
dau eho dfldng tam tru, sau do xoay dfldng tam
niy vi trung vdi dUdng tam dung eua tru b i n g cie
thuat toin va cie phep chiiu
2 XAC DINH DlTCfNG KfNH TRU KHI
CHI TIET CO MAT DAU VUONG GOC VOL
DU6NG TAM TRU
Giai thuat do dfldng kinh dupe thUe hien
lan lupt theo cie bfldc sau:
1, Lay mat dau lam mat phang ehuan, t r i n
do xie dinh toa dp 3 diem 1,2,3 (hinh 1)
2 Viet phflpng trinh mat phing di qua 3
diem do do de xac dinh vector phap n (A,B,C)
/! = (,.,-,.,)( ,-')-(-':-z,)(,.,-;0
S = ( : -)(>.-0-k,-.v,)(z,-z,)
C = {x2-x,)(y,-y,)-{y2-y,){'c,-x,)
Trong do : Cac x^, y_, z^ la tpa dp cac diem
do 1, 2, 3
Hinh 1: Chi tiet do cd mcit ddu vudng gdc vdi tdm tru
Cosin ch] phuong cua vec to phap ttla;
(1) V/+B-+C-Trong do :
a Ii goe hpp bdi (?) va (Oyz)
/? la gdc hpp bdi (P) v i (Ozx)
y la gde hpp bdi (?) v i (Oxy)
3 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 x i c dinh, tuy nhiin hai true Ox' va Oy' co vi tri bat ky va chi can thoa man dieu kiin vuong gdc vdi nhau De xay dflng cac thuat toin, can eo dinh hai true nay Theo d6,
de don giin trong qua trinh tinh toin, xic dinh mpt trong 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:
Trang 3cosa x + cos^ y + cosy z = 0 (2)
Vdi mat phang Oxz cd phuong trinh: y=0
Nhfl viy, d i dang xic dinh dflpc vectP ehi
phflpng cua Ox':
1,0, (3)
Nhfl viy, eac cosin ehi hfldng cua Ox' se
nay, b i n kinh dfldng tron ehinh la ban kinh tru
Tpa dp tam cua dfldng tron di qua 3 diem niy dflpc tinh theo cong thflc:
_ a(cc'+bb')- b(dd'+aa')
^ ~ 2(ce-be) " , ,
\ (10)
_ c[dd'+aa)-d{cc-\-bb")
•" 2(ce-be)
(cosa^
l^cos;'J
n c o s /
, m, - 0 , n, =—I ' (4^
[ cosaV l^cos;'J
Khi d i xie dinh dflpc cie true Oz' v i Ox'
Vi true Oy' vuong gdc vdi ca hai true Ox' vi Oz'
nin n i u gpi J la vectP ehl hfldng eua Oy' thi:
/
c o s ^ cos/
cosa
cos/
= n^i
cos/ cosa
cos or
cos/
cosa cosp
1 0
T, [ cos a cos (5 sin^/?
l^ cos;' c o s /
Cosin ehi hfldng eua true Oy' Ii:
, cos a cos y9 „ „
/j = ^ , m, =sinp, OT =-cotg/).cos/ (g)
sin^
4 Do toa dp 3 diem 4, 5, 6 tren mpt tii't
dien trin mat tru
5 Chieu tpa dp cac diem do lin mat dau
chi tiet tru bing eieh chuyen toa dp 3 diim do tfl
h? Oxyz sang he Ox'y'z' thdng qua mot ma tran
sau: r i"l T/ 1
/, m^ rt, y (9)
h '"3 "3 J
6 Xie dinh dfldng trdn di qua ba diem
O day X(j v i y^ lan Iflpt Ii hoanh dp va tung
dp cua t i m dfldng tron di qua 3 diem hinh chieu eua 4, 5, 6 len mat dau cua tru:
a = y'3 - yV ^ " il + y'l; b = y'^ - y',;
b^ = y > y V c ^ ' f ^ - x ' , ; e' = x', + x'ji d = x'j - x'^; d'= x'^ + x'|;
e = y'3 - yV ^ - ^^'3 - '^V Cie diem trin tiet diin do cd the dflpc tang lin de nang eao dp chinh xac cua phep do, khi do ta si xac dinh vector phap cua mat phing dau di qua n diim do theo pbflOng phap binb phflong nho nhat LSC[1] vi xie dinh dfldng trdn
di qua n diem do 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]
3 XAC DINH DUdNG KINH TRU KHI M A T DAU KHONG VUONG G 6 C V6I D U O N G TAM TRU
Vdi binh tru dat bat ky trong khong gian, khong ed mat dau vuong gde vdi dfldng tim tru
vi vay tiet dien do se la mot dfldng Elip Neu ta do
3 dii'm trin tiet dien do vi dflng dfldng tron thi tim cua dfldng tron se khong trung tim tru tai tiet dien do Do viy, b i n 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 trong khong gian Oxyz, true cua hinh tru nghiing gdc a so vdi true Oz De xac dinh dfldng kinh tru, ta tien hanh do theo cic bfldc sau (hinh 2): ^
Trang 4NGHIEN CUfU-TRAO D 6 |
l.Tren m a t p h a n g P j , d o 3 d i e m A,,B,,Cj Qua A/, B^, C / x i c dinh dfldng trdn tam Xic dinh dfldng tron di qua 3 diem do cd tam I, Ij'Cx^', y^', z^')
(x,,y,,z,)
2 Trin mat phang P^, do 3 diem Â, B^, C^
Xie dinh dfldng tron di qua ba diem do 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)
Hinh 2: Xdc dinh dUdng kinh tru khi mat đu
khong vuong goc dUdng tdm
4 Dflng he toa dp mdi Ox'ýz', gdc tao dp
O, ed true Oz' (i, j , k) Cac true mdi Ox' va Oý
dflpc xic dinh tflPng tfl d mue IỊ
5 Chuyen so do toa dp eua cac diém tfl
toa dp eu Oxyz ve he toa dp mdi Ox'ýz' Cie d i i m
do A|,Bj, C, chieu lin mat p h i n g (Pj') d i q u a l ^ v a
vudng gde vdi y ^ ta dflpc A,', B,', C,' Vi ( P / ) song
song vdi Ox'ý nen eic diém Ấ, B,', C,' eo cung 4 KET LUAN
cao dp Tflong tfl cic diem do A,, B^, C^ chieu lin
mat phang (P,') di qua I^ va vuong goc vdi IJ^ ta
dflpc A „ B ; , C ;
7 Dfldng thang di qua 2 diem I/I^' co
veetP chi hfldng la n{í, j\k'^
Lap lai cac bfldc 4, 5, 6 cho d i n khi 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 = ịí+ j.j'+ k.k' ^ \
Dp ehinh x i c eua phep do yeu cau cang cao thi so lan lap cang nhieụ Khi phep do hpi
tu dfldng t h i n g I / ' I / ' dflpc eoi nhfl dfldng tryc
ly tfldng cua trụ Sau khi cd dflpc dfldng true ly tfldng, dfldng kinh eua tru chinh la gii tri trung binh cua dfldng kinh hai dfldng tron di qua 3 diem flng vdi lan lap cudi cung
De xie dinh dp tru cung nhfl t i n g dp ehlnh xac cua phep do, ta ed the xac dinh nhieu hPn 6 diem Diem do thfl 7 trd di h o i n toan nam tren tiet dien bat ky eua mat trụ Nhd phep chuyen he toa dp nhfl trin, ta thu dflpc toa dp cac diem nay trong he toa dp euoi cung Oxiyizị Chieu tat ca cie diem nay len mat phang OxiyL Bing pbflOng phap binh phflpng nho nhat, dflng dfldng tron xap xi qua tap cie diem n i y eho ta dfldng kinh tru vdi dp ehinh xic eao hon Sai lech gifla cie ban kinh cho ta do trụ
=R -R
6 Qua Ấ, B|', C,' xic dinh dfldng trdn
tam I|'(X|', y^', 2,')
Khi thflc h i i n do cic be mat tru tren may
do ba tpa dp (CMM), viec xic dinh tam tru la diím quan trpng de xic dinh dung dUdng kinh mat trụ Vdi bp so lieu tpa dp eic diem do, thuat
t o i n n i u t r i n d i dUa ra hai giii p h i p xie dinh tam tru trong trUdng hpp tru cd mat dau vuong gdc vdi
Trang 5dfl6ng 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 do 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 nay 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: 1 PGS, TS Vii Quy Dac; 2 TS Pham VAn Bong,
Trfldng Dai bpc Cong nghiep Hi Npi
Tai lieu tham khao:
[ 1 ] Vu Toan Thang, "Nghien cflu phUOng phap do 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