XAY D U N C T H U A T T O A N SQ D U N G K E T HdP DONG
THdlBDAUDODELOAIBO
Dp LECH TAM, NANG CAO DO CHINH XAC PHEP DO SAI LECH DO TRON TRONG HE TOA DO CUC
Ta Thj Thuy Htittng, Biii Van Bien'
Tdm tdt
Do trdn la mdt chi tieu de ddnh gid sai sd hinh ddng hinh hgc eua cdc chi tiit cd khi diing trong ede lap ^ep co do ehinh xdc cao nhU 6 ldn, piston-xilanh, be mat tru trdn lap vdi 8 ldn, o trUdt, song ddn hUdng tru,... Tuy thuoc vdo cdp do ehinh xdc cua lap ghep md dung sai do trdn yiu edu tii mgt vdi micron den vdi chue micron, do do cdc thiit bi do sai lech dd trdn cdng phdi dat do chinh xdc cao. Bdi bdo ndy trinh bdy phUdng phdp xdy dUng thuat todn sd dung kit hdp 3 ddu do de loai bd sai sS do do lech giUa tdm chi tiit vd tdm bdn quay, ndng cao do ehinh xdc ciia phep do do trdn.
Tii khod: do do trdn, do lech tdm.
1. Ctf sd \i thuyet do do trdn trong he toa do cifc
Chi tiet tru dfldc hinh thdnh khi mdt dfldng sinh quay xung quanh mpt true song song vdi nd, do vdy mdi dilm tdm trln tiet dien cat ngang dfldc bieu diln bang mdt ban kinh quay R va gde quay 6.
* ThS., Khoa Dien - Co.
Hinh 1: Nguyen ly do 36 iron trong he tpa 36 ct/c Tren Hmh 1 khi quay chi tilt quanh tim (tam ehi tilt trimg vdi tdm quay), sfl dung 1 dau do dich chuyen thang dat hfldng kinh se cho biet thdng tin vl bien thien bdn kinh R tai tiing vi tri gde quay Oi trln tilt diln do la m(e). Sau mdt vdng quay si cho hinh anh bien dang thi^c cua chi tiet do, sfl chinh lech Idn nhat gifla cdc gid tri Ri chinh Id sai lieh dp trdn.
Trln Hinh 2 bieu dien sa dd do dd troD, sfl dung 1 dau do dat ed dinh trong kh6ng gian de quit chi tiet hinh tru trong khi ehi tiet quay. Tin hieu cua ddu do dflpc xdc dinh bdng ham m(6), gpi p Id mdt diem do trln biln dang 50 TRddNG 0A.\ HOC HAI PHONG
trong h i toa at ciic
chi tiet, 6 la gde gifla diem P va dau do, sai lech dp trdn dflde ki hieu ham r(9). Neu khdng cd do lech tam O = O' (Hinh 2), biln thiln cua dau do se la sai lech dd trdn:
m(9)=r(0) (1) Tuy nhiln, neu cd dp lech tam O ?i O'
(hinh 2b) thi dau do se do dflde mdt lfldng:
m(e) = r(e) + Ain(e) = r (o) + e^(9jsina + e fejcosa
Vdi ex(6) va ey (6) la sai lech gifla tam quay va tdm chi tiet do (gdm ca sai lech tam va dao ddng tam quay) ehieu Iln true x va true y.
a)Kh6ngc6l&JitamO= 0' b)Cd lech tdm quay O^ O' Hinb 2: SO do do 3d trdn sit dung mgt
ddu do dieb chuyen Nhdn thdy nlu do sai lich dp trdn bang 1 dau do, trong qua trinh thu nhdn vd xfl U so heu van tdn tai 2 van de: Tam eua ehi tilt ddt trln bdn do khdng trung vdi tam quay eua ban - ton tai sai lech tam. Mat khac trong qua trinh lam viec ludn tdn tai mpt Ifldng sai sd do khe hd khdp ddng cua 6 quay gay ra dao ddng tdm. Dp lech tam cua phep do chinh la tdng hdp cua 2 thanh phdn sai lech tdm vd dao dpng tdm, anh hfldng trfle tiep den dp chinh xac cua phep do.
Sai lech tam la sai sd he thdng, bang cac gidi phap vl thilt hi nhfl: lfla chon d quay cd do chinh xac dinh tdm cao, dilu ehinh tdm ehi tiet vl gdn nhat vdi tam ban quay bang bdn
chinh tam,.. ed thi han chi phdn ldn dflde sai sd nay. Tuy nhiln, dao ddng tdm Id sai sd ngau nhiln, vi vdy de loai bd het thdnh phdn lieh tdm bao gdm cd dp dao dpng tdm phdi sfl dung phfldng phap ket hdp 3 dau do.
2. Xay dUng thuat toan do do trdn bang phi/tfng phap sOrdung 3 dau do (2)
Hinb 3: Stf do do do trdn sCrdung ba ddu do dich cbuyen Trln hinh 3 sfl dimg 3 dau do dich chuyen dat cd dinh vdi nhau edc gdc ^, x quanh chi tiet do. Gia sfl O Id dilm giao cfla 3 ddu do va gan tam quay cua ehi tilt. Cac toa dp X, y CO dinh dfldc ehi ra d trln hinh ve.
Tin hieu cua cae dau do dich chuyen dfldc xac dinh bang cac ham mA(0), mB(9), mc(0) tfldng flng vdi cac tin hieu do dfldc xde dinh nhfl sau:
' (3) (4) (5) i n ^ ( q ) = r(q) + ej((q)
nig (q) = r(q - f) + e^ (q).sinf + e^^ (q).cosf mj,(q) = r ( q - t ) + e^(q).sint + e^(q).cost CJ ddy, ex(e), CYCG) la thdnh phdn tfldng flng theo phfldng x va y cua sai sd do lech tam vd dao ddng tdm quay.
Khi tam Oi cua chi tiet lech so vdi tam quay O2 mdt Ifldng Id e nhfl hinh 4, thdnh phan ey ldm ddu do B se tang Iln mdt Ifldng tfldng flng vdi gdc ^ va lam dau do C giam di
m p t Iflpng tfldng flng v d i gdc -c, do d o k i t h d p 2 d a u d o nay eo die khfl dfldc ey.
V d i c d n g thfle (8) t h d n h p h a n Ileh tam h d a n toan b i Idai b d . T i l p t u e x a c dinh bien d a n g chi t i l t , tfl d o t i n h sai lech d p trdn.
T h e o [3] b i e n d a n g e h i t i l t d o tai tflng vi tri gdc 9 dflde k h a i t r i e n t h e o Fourier nhii sau:
Hinh 4. Khi tdm chi tiet lieh so vA' tdm quay Thanh p h a n ex se ldm dau do B va C gidm mpt Iflpng tfldng flng gdc (|i va t , trong khi dau d o A tang len 1 Iflpng dflng bang ex, do dd k i t h d p 3 dau do nay se khfl dflpe cdc thdnh p h a n ex.
N h a n 2 ve c u a phfldng t r i n h (4) v d i - sinT/sin(T-i}i) vd 2 v l eua phfldng t r i n h (5) v d i sinij»/sin(T-(ti) ta ed:
sinx / . \ sinx sm(^x-(pj
sin (p sinx sin(^x-(pj sin(p /
M
-•p) s i n f x -
\ sin(psinx
n{x-(p) sinx n ( x - ( p )
\ smfa sm(T-(pj cosTsiiim
r ( e ) = R + i ; c i C O s ( i e - a i ) 1=1
r(e) = R + S (a; t^os ie + bj sin if i=l
Trong do:
(10)
(11)
1
~Im,(e)
(l + T , + T 2 ) N j , i
Ci la bien do meo; ai, b, la cac tan so meo;
ai la gde lieh pha.
Tfldng tfl khai triln tai vi tri gdc (Q-if) va V} tri gde ( 6 - T )
r(e-i}.)=R+ X(aiCoa(e-*)+bisini(e-(ti)) i=l
(6)
(7)
r(e-(p)=R+|(^
, . '^fia cosi(p
^ ' 1^[-Ka,sini(
Kp+SUlW +bj (aniecosi(p-cosi9aniip)J
i(p-b|Sini(p)cosi9 ] i(p+b,cosiq))ani9j (12)
r { e - T ) = R + X { a i C o s i ( e - T ) + b i s i n i ( e - x ) ) i=l
sinfx-p]
C d n g 2 ve c u a cac phflPng t r i n b (3)+(6)+(7) ta dfldc tin h i i u k i t h d p e u a 3 d a u d o mt(9) nhfl sau:
m , (9) = mA(e)+Ti.mB(e)+T2.mc(9)
= r(e)+T,. r(e-<t))+T2.r(9-x) (8) Trong do:
Ti=sinT/sin(T-(t.) (9) Ti=sin(|i/sin(x-(t))
5 2 I TRddNGDAI HOC HAI PHdNG
-b^sinix)cosi0 1 x-t-b cosix)sini6l
(13) / \ • ^ [ ( a cosix-t
r(e-x) = R + y r ' ti'l,-Ka,sinix-(- Thay (11),(12),(13) vao (8) ta ed:
q (e) =(1+Tl+T2) R+JJCa +TJ(a. ccsi(p-h anicp) +'^(a ccsix-b siiiiT))ccsi8+
+(b^ +T|(aj sini(p + bj cosicp) , +Tj(a^sinix + b, cosix))sinie)
Dat E; = (1 + Tl cos i^ + T2 cos ix) va F; = (Tl sin ii|i + Tj sin ix)
trong n? toa ao cue
Thflc hiin bien ddi toan hpc xac dinh:
|^|;in,(G)a«(ie).E,+i;m,(e)sm(ie)j-j (15) -i;n\(e)(cos(ie)£^+sin(ie)j;)
^[i:n\(e)^(ie).E-i;n^(e)cos(ie)FJ
' ~ ^ + ^ (16)
||;n^(6)(sin(i9)£.-cos.(i9)j;)
O ddy tai mdi vi tri do khdc nhau se tfldng flng cac gdc 9 khae nhau, j la vi tri cua gde 9 thfl j, c6 N dilm do, moi diem do tfldng flng vdi mdt gdc 9, nhfl vdy j chay tfl I^N; i Id chi s6 tai tdn so meo thfl i.
Bien dp tai tan sd meo thfl i dfldc tinh theo cdng thflc [3]:
= ' = v / ^ (17) Gdc lieh pha:
ai=arctan(bi/ai) ^gj Ap dung edng thflc (15), (16), (17) vd
(18) xac dinh dfldc bien dp meo c, vd gdc lech pha tti tai tflng tdn sd meo thfl i, ta hodn toan xac dinh ddcfc biln dang chi tilt do r(9) theo cdng thflc (ll).Sai lich dp trdn dfldc tinh theo cdng thflc:
A„=r(9)™,-r(9).,„ (19) 3. Ket luan
phep do dd trdn sfl dung ket hdp 3 dau dd da loai bd dflde dd lech tam ra khdi kit qud do.
Dieu ndy ed y nghia ldn trong viec nang cao dp chinh xdc cua phIp do, dac biet khi chat Ifldng d quay cua thilt bi do khdng dam bdo, tdn tai dp dao ddng tdm trong qua trinh do. Xay dflng thuat toan trln ldm ed sd de thiet ke thiet bi va la giai phap hieu qud ndng cao dp ehinh xae cho phep do.
T A I LifiU THAM K H A O [1] Nguyin Tien Thp, Nguyen Thi Xuan Bay,
Nguyen Thi Cam Tu (2006) Do lUdng kiim tra trong chi too Cd ldn, NXB Khoa hpe vd Ki thudt [2] BMuralikrishnan, S.Venkateehalam (2005) A
note on the three- point method for roundness measurement. Precision Engineering 29, pp 257 •- 260.
[3] David Whitehouse (2002) Surfaces and their AfeasuremeMt.Taylor & Francis PubUshers.
[4] CX.Zhang, R.K.Wang (1992) Pour Point Method of Roundness and Spindle Error Measurements. Annals of the CIRP Vol 42, pp 593-596.
TAP CHl KHOA HOC Vol 04. No 1 6 - 5/2016 I
XAY DUNG THUAT TO AN SU DUNG KET HOP DONG THCJI3 DAU DO DE LOAI BO D p LECH TAM, N A N G CAO DO CHfNH XAC PHEP DO SAI LECH
DO T R O N T R O N G H $ TOA DO CVC
Abstract: Roundness is a form error to assess the geometric tolerance of the mechanical parts used in the high precision assembly of roll bearings, piston-cylinder, slider hearings, guiding shaft etc.. Depending on the level of precision assembly that roundness tolerances required from a few microns to about dozen microns, so the roundness measuring device must respectively high accuracy. This paper presents methods of improving the accuracy of roundness measurements using three probes combine to eliminate error of the eccentric between instantaneous rotary table and measuring part.
Keywords: roundness, spindle error.
5 4 I THUONG DAI HOC H A I P H O N G
