Xác định vận tốc thích hợp khi đo hay dò nhanh trên máy đo toạ độ dạng cầu trục

NGHIEN ClJfU-TRA0D6l XAC DINH VAN TOC THICH HOP KHI DO HAY DO NHANH TREN MAY DO TOA D O DANG CAU TRUC PGS.TS.. Bdi bdo ndy trinh bdy cdeh xdc dinh van tdc do hay dd thich hdp dUa tren c

NGHIEN ClJfU-TRA0D6l

XAC DINH VAN TOC THICH HOP KHI DO HAY DO NHANH TREN MAY DO TOA D O DANG CAU TRUC

PGS.TS Thai Thi Thu Hd', ThS Pham Hong Thanh'

'TrUcfng Dai hpe Bdch khoa Tp Ho Chl Minh -TrUcfng Dai hpc Tran Dai Nghia

To increase CMMs productivity, higher probing speeds ofCMMs are chosen Performing at higher probing speed results in increasing the dynamic errors and the vibration of CMMs and affects their ac-curacy For this reason we should specify reasonable CMMs velocity when probing at high speed

This article presents the method specifying the reasonable speed of CMMs to eliminate the plastic deformation phenomenon ofworkpiece

De tdng ndng sud't do cua mdy do tga do, gidi phdp dUdc lUa chgn Id do d cdc van tdc cao hdn Khi tdng tdc do do ddn den sai sd dpng lUc hgc cua mdy cung se tdng theo vd dnh hUdng khdng nhd den

dp chinh xdc cua kit qud do, vi vdy khi do hay dd nhanh cdn phdi xdc dinh tdc dp do thich hdp Bdi bdo ndy trinh bdy cdeh xdc dinh van tdc do hay dd thich hdp dUa tren cd sd hqn chi hien tUdng bien dang deo ciia be mat vat do

1 BO TRI VA P H A N T I C H Q U A TRINH DO,

DO NHANH

De thUe hien qud trinh do ta ehon phuong

va eham ciia dau do vdi b l mat vat the theo

phuong thing dUng (phuong song song v6i true

Z) vd CO hu6ng tU tren xu6ng dUcfi Khi chpn nhU

the, he thong do se ciing viing hon, dong th6i ban

chl hien tUpng nay vd biln dang cong cua kim do

la rat nho nen co t h i bo qua

v^V^VV^SSSSSSS

Hinh 1: Vi tri cua dau do va vat do t^i thOi diem X<\

N G H | £ N C U U - TRAO DPi

C6 ihi m6 ta qua trinh d6 xSy ra nhil sau:

T?i thdi dilm t, vi tri t t o dau d6 d6i vdi

m4y do tga d0 c6 gid tri Zj Khi t < t, mdy do

chuyen d^ng vdi vgm t6c khfing d6i v^ Bdi vi dSu

dd chua ch?m v4o v^t thi, vj tri Z^ cia dSu dd ddi

vdi mdy do coi nhU blng vdi vj tri nghi Z^ = 0 Liic

ndy Ididng cd liJc tdc dvng gifla ddu dd vd v|it do

(F^ = 0), mdy do tpa dd dang dich chuyin dSu dd

vdi v4n tdc khdng ddi, vi v$y Z^ tdng tuyin tinh

T^ thdi dilm t = \, ddu dd va ch^m vdi bl mjt

vjt the Ddu dd vd cdc khdi lilijng gdn cflng vdi

nd (nhu khdi lUpng eda bd ph^n treo) se gdy ra

lUc va d4p F^ Vi dau dd dflng trong thvic nghidm

id lo^ dau dd cd bd phgjl chuyin ddi vi cdm biln

Ivlc nin gid thilt rdng ngay thdi dilm va ch?m t

= t„, h | thdng ddu dd dd tim biln djng vd gili tin

hi|u ddng din mdy do tpa dd vd mdy bdt dSu ch?y

ch|m vd dflng I?i (hinh 2)

Hinh 2: Vi tri ciia dau dd vd v^t do tai thdi dilm t=tg

Mdy do tpa dp nh^in dilm do tai thdi gian

t = t^ bang cdeh cpng them khodng dich chuyin

ddu dd (so vdi vj tri nghi eda nd) vdi vj tri cfla

thudc do, trong Idii bu bdn Idnh dau dd Khi ddu

dd ch^m vdo bl m^t vat thi, cd v$t thi vd ddu dd

biln dang ddn hdi mdt khodng Z(t) (hinh 3)

Diudd

Hinh 3: Biln d^ng ciia vdt do vd dau dd klii va ch^m

Vi tri cua vjt do Z^ dupc xde dinh:

Z = Z „ ( ' O ) + Z ( ' ) T ( « - 2 ( ' « ) ) (1)

Trong dd:

+ R Id bdn kinh ddu dd + Z (t) vi tri cua ddu dd vdi vdt do tai thdi dilm t j

+ Zj(tj) vi tri eda ddu dd ddi vdi may do tpa dd t?i thdi dilm t„

+ Z vj tri xdc dinh cua vdt do ddi vdi may

do tpa dd t?i thdi dilm t„

Gid tri R chi ylu dupc xde dinh bdi viSc hi|u ehinh h | thdng ddu dd Phdn mem ed sOa dung cdc biln dang ndy hay khdng phu thudc vjo tflng trfldng hpp cu thi Chlng hgn, ddi vdi vat mau bdng nhdm, ddu dd ldm bdng dd hdng ngoc

cd dudng kinh 0.3mm, lUe dd tinh 4.9.10' N thi vit ldm Id Inm L\Ie tdc dung trong qua trinh dd nhd, tuy nhiin nd thfldng khdng d i nhd de tranh phd hiy bl m?t vdt do, d|e bi|t ddi vdi cdc vat die dupe ldm bdng cdc lo^ v^t H|u cd dd cflng tUUng ddi thap nhU: nhdm, ddng thanh, ddng thau Sau day ta se tim hilu llje tde ddng cflc d?i bdng bao nhieu dl vgt do cd thi chiu dflpc md khdng bi

biln d?ng dio Ta tinh \\fc va eham, sau dd so sdnh

vdi li^c cho phip Gid thilt rdng ddu dd khdng nSy khi mdy do tpa dd tiln din va va ehgm vdi be mat v|Lt do d ldn va ehgm ddu tiln va nhfl v§y, toan lig nang Iflpng cia ddu dd se truyin vao bl mgt do va ldm bl m$t v|it do b| biln dgng

2 XAC D(NH L y c DO THf CH HOP Vi|c xdc djnh v^n tdc dd thieh hpp dila vdo lUe dd thich hpp Dl xdc djnh lUc dd diiA hpp F^i thi trfldc hit cdn phdi xde djnh lUe dd cho phip Lvtc dd cho phip Id lUc dd md gdy ra flng suat trUpt tgi mdt dilm ndo dd trln bl mat tiep xue vflpt qud gid tri gidi hgn vd bdt dSu xdy ra qui trinh biln dgng dio Gid thilt miln biln dgng khi ddu dd va eham vdi bl mgt vjt do cd di|n tich vung tilp xue Id hinh trdn (hay hinh ehilu cua ban cau tilp xue len mgt phlng vudng gdc vdi uyc kim dd Id hinh trdn) thi flng suat trong miln bien dgng dupe tinh:

fW

3 F

" 2 ;r.r^

(2)

(3)

Tfl dd, lUe dd thieh hpp dUa tren dilu kien bat ddu xiy ra bien dgng dio dupe xdc djnh:

Trong dd:

+ (Tfl la flng sudt tgi t t o cia di?n tich tilp xuc

+ r ban kinh cia bdn cdu biln dgng

+ z(t) tung dd cia bdn cau tilp xue

+ F lUc tac dung

Gid tri flng suat gidi hgn dupe xdc dinh

bang gidi ban dan hdi cua v^t do Khi tinh todn,

trong thfle te gia tri gidi han ddn hdi dupe thay

thi bang gid tri eua ing suat chdy o^, vi hai gid tri

nay chi chech lech nhau vdi phdn tram nin ching

cd thi thay thi nhau dl md td lUe dd eho phep

Dl tranh hien tUpng bien dang deo thi lUc F^, nen

ludn ludn nhd hon hoac bang lUc F Thudng

thi sfl bien dgng deo bat dau rd ret d dau dd dudi

ldp be mat nen sU hU hgi be mat rat khd dd tim

Trong cdc trudng hpp va chgm gifla ddu dd vd vdt

do se lam xuat hien ing suat tilp xuc 0ng suat

tiep xuc ldn nhat la ing suat khi xuat hien biln

dang deo dupe xac dinh tfl cdng thflc (3) nhu sau:

r=0,908d.3

5,99&F, E '

(4)

Tl'R'

Sfl dung kit qud cia (Johnson 1985) vd

(Tabor 1951) kit hpp cdng thic (4) ta cd:

3F

[cr„l =2,6cr, =2,6x—%•

r = 0,9086.'-^^

Y E

=*F„ = 9 0 , 8 5 8 ^ 5

-(5)

F„ < F„ «

90,858-£•" (6)

(7)

Trong d6:

+ E^, //, Id m6 dun ddn h6i vd he so Poatxon cua ddu d6 vd vdt do

+ R Id bdn kinh cua dau dd + E* Id m6 dun ddn hoi tUOng duong Mat ciia vdt do gid thilt Id mat phdng

3 XAC DJNH VAN T 6 C D 6 T H I C H H<?P

Va eham cua dau d6 v6i vat do co thi dUpe

mo hinh h6a nhu va chgim cua mat cau c6 khoi lupng m* v6i mat phang m* Id khoi lUpng tUOng duong cua ddu do vd nhiing phdn dUpc noi cUng vdi no Tinh toan lUc va eham dUa trln 1^ thuyet Hec (milu ta tong biln dang ciia hai kh6i cdu dupe ep 1^ v6i nhau bdng mpt lUc ndo do) Khi dau do ep vdo mat phang thi dp dich gan dUpc hieu nhu Id tdng biln dang A cua dau dd co bdn kinh R vd vdt do (mat cdu eo ban kinh co) dUpc xae dinh tai mot thdi diem:

1 [9~

A = - 3 -

2^4 ;W-I*-^« (8)

Trong cong thic tren:

• "^k la tdng dp eong chinh cia cde mat Trong

trudng hpp cu thi nay gpi la ban kinh eong tUPng dUdng cia ddu dd vd mat phang X ^ ~ ~ + F^, lflc dd thich hpp * Tfl do tong biln dgng Z(t) cd thi dflpc bieu diln nhu h t o cia lflc do F., (t):

- ( 0 - J ^ (9)

NGHIEN CUU - TRAO OPi

Trong do: , -J^

^ _ 1 5 7 H ' V - V (13)

+ R la bdn kinh eiia dau do [ S.^fR.E' )

+ bdn kinh cua vat do Id vo cung

+ F|^|lUc do thieh hpp Tbi vdo phUOng trinh (10) ta tim dUpclUc

Sif dung phuong trinh trln ta e6 thi tinh

d6 thich hpp:

dupe lUc ciia dau d6 va eham vdi mat phang bdng |125 ^, ,3 g

vile giai phUPng trinh vi phan: ^hl "" \| 1 4 4 (14)

Fy{t) = -yfRE*z''=m'Z (10)

3 LUc va eham F^^ (dupc coi nhU gia tri cUc

Phuong trinh vi phdn trln dUpc vilt lai dai eiia lUe thich hpp F^|'"" )

nhu sau:

:-IRE'Z'- ^d-z j„j "^ '^ V i 4 4 "

3 m dV Trong do v,j Id vdn toe eua may do tpa do

tai thdi diem dd Toe dp va ch?im thieh hpp v^

Phuong trinh vi phan (II) Id phUong dupe xde djnh nhU toe dp dd khi lUe va eham F^

trinh vi phdn cap 2 cua Z(t) khuyet t De giai bdngvdilUcFo^tUphUongtrinh (6) vd(14)taxac

u ,^ * • u • u- ^ i A-^ ^^ • dinh vdn toe dd thich hop nhU sau:

phuong trinh vi phan nay ta d^t v = — , ta eo ' '^ d'Z dv dv dZ dv dt

U V ; Mt^fjf

dt' , dt dZ' dt ' dZ • Chon vi tri nghi -^ < 43^874 £_ =>y^ = 43.874 L - i ; - (15)

cua dau do Id vj tri ban dau vdi cdc dieu kiln ban \E' m \E m

dau nhu sau:

t = 0 4 THI/C NGHlfilVI XAC DINH VAN TOC D 6

V = 0 THiCH HOP

- z = o

Thi vdo phuong trinh (11):

a Doi vdi mdu thep:

+ Vdt do dupc lam tii thep C45 cd

dv 2-lRtZ'- , ^ 3m\dx' E^ = 20QG?a; a, =3\0MPa; ^2=^^^

^'~dZ^^ *— Z~dZ = —^=—- +DduddcdE, =435Gpa

'" 2- ^ ^ ^ + Bdn kinh dau dd R = 1,5 mm

T-• • I u • " i i_ ^ + Khoi lupng dau dd m* = 22s; u, =0,2

Lay tieh phan hai ve ta dUpc nghi|m tong ^ &> ^'i '

qudt:

^ ^ , Gid tri van toe thich hop khi do Id:

Z'-J-^^ + C (12) „ = 41.98mmA

Di xic dinh hdng sd C, sfl dung eac dieu ''• ^ ° ' ''*' •"*" • * " " =

kienbandau(t = 0,v = 0,z = 0 ) t a c d C = O.Tfldd , , , ,

biiu thic xac dinh Z cd dang: + ^ " ^° '''"="= '^"^ " ''"P ' ^ ' * ° ' " "

Ej = 72GPa;(7, =&kGlmm^; ii^ = 0,32

+ Dau dd cd Ej = 435 Gpa + Ban kinh dau dd R = 1,5 mm

NGHIEN ClJfU - TRAO e 6 l

+ Khdi lupng dau dd m* = 22g; f^^ = 0,2

Van toe thich hpp khi do la: v^^, = 6,697mm/s

c D6i vol mau dong:

+ Vat do dupc lam tir ddng thau cd

E^ = UOGPa; CT - 18 kG/nmr: //, = 0,33

+ Ddu dd cd E, = 435 Gpa

+ Ban kinh dau dd R = 1,5 mm

+ Khdi tupng dau dd m* ^ 22g; fj^ =^ 0,2

Van tdc thich hpp khi do Id:

,-^^.= 25.09Snim s

d V^t va eham tren mgt so mau khi van toe

dd lon hon van toe thich hpp

Hinh 4a: \ et iren be mat mau hop kim nhom khi van

toe do kVn hem van toe thich hpp

Hinh 4b: \'et tren be mat nKui llicp khi \mi luc do Ion

hon \an toe thicii hop

Hinh 4c: Vit trln bl mat mdu hpp kim dong khi van

tdc do ldn hon van tdc tliich hpp

5 KET LUAN

Van tdc va eham ldn nhdt phu thupc vao

thupc tinh vat lieu (E,v,cr^) ciia vat do va dau

dd, ban kinh dau dd va khdi lupng tuong duong dau dd, vi vdy van toe thich hpp dupc chpn bang gia tri van ldc va ch^m Idn nhat Khi thuc hien do hay dd tai van tdc thich hpp se han che hien tupng bicn dang deo be mdt vat do, tuy nhien van toe nay se ldm cac khau va cac khdp ciia mdy do bien dang va gay ra sai sd dpng lire hpc ciia may do tpa dp.*:*

Nguoi phan bien: PGS.TS Pham Ngpc Tuan

Tai lieu tham khao:

[I] W van Vliet, Development of a Fast Mechan-ical Probe for Coordinate Measuring Machine, ISBN 90-386-01689, PhD thesis, Eindhoven Uni-versity of Technology, 1996

[2] W Onno Pril, Development of High Preci-sion Mechanical Probes for Coordinate Measur-ing Machine, PhD thesis, Eindhoven University

of Technology, 2002

[3] W.C.Young, Roark's Formulas for Stress and Strains, ISBN 0 -07-100373-8, McGraw-Hill,

1989

[4], Butler C, An investigation into the perfor-mance of probes on coordinate measuring ma-chine, Industrial Mefrology 2, 1991

[5] Tyler Estler W et al Practical aspect of touch-trigger probe error compensation Precision Engi-neering 21, 1997

[61 Woz'niak A., Dobosz M., Research on hys-teresis of triggering probes applied m coordinate measuring machines Metrology and Measure-ment Systerms, vol XII, no 4,2005

[7] Remshaw, Probing systerms for coordinate measuring machines, United Kingdom, 1996 [81 X.M.Targ, Giao trinh gian ylu co hpc ly thuyit, 1979

[9] Le Quang Mmh, Nguyin Van Vupng, Sure bin vat lieu tap 3, 1997