IM!MJ!hi<C6NG NGHE
t i > - r z - ?" .'>'-i-5NGHIEN cufu ANH Hl/dNG CUA LI/C CAT DEN DO CHINH XAC GIA CONG TREN MAY CNC 3 TRUC
STUDYING THE EFFECT OF CUTTING FORCE ON MACHINING ACCURACY OF A 3-AXIS CNC
Bui Thanh L3m,TranQuyCM
T d m t ^ t
Bai bao cho thay anh hu'dng cOa ldc Ccit trong c)ua trinh gia cong tren may CNC ddoc do bSng thife nghiem trfn thi^t bl do life c3t KISLER, Bai bao dua ra do tiij danh gia sai so gia eong tren may phay CNC 3 true va mo hlnh to^n hoe mang no ron md ph5ng sai so gia cong trong moi che do cat. Ttf viec si^ dung md hlnh toin hpc dd, ta cd th^' dif doin va danh gia sai sd gia eong. Ket qua thu ddpc md ra m6t hu'dng nghidn cdu kh^ quan va khci nang ap dung vao thdc te nham lam giam sai sd gia cdng bang each bii trifc tiep vao chifong trinh NC.
Tiy khda: Mang no-ron/ may CNC/ NC/gi3i thuat back propagation/ Matlab/ Sai sff life e5t
Abstract
Thispaperindicatestheeffectofthecuttingfbrcein machining processesonCNCmachines experimentally measured by KISLER, a cutting force measuring device. Indeed, it introduces the graph used to evaluate the machining errors on a 3-axis CNC milling madiine, and the mathematical model of neural network that demonstrates the machining errors in each cutting mode. By using this mathematical model, we can predict and evaluate the machining errors. The findings open upapromising research trendand the ability to apply to pradice to reduce the machining errors by compensating for them directly in NC programs.
ThS. Bill Thanh tam -Tnitmg Oai hoc Cong nghiep ifa Noi KS. Iran Quy Cao-InfffligSHOLPhmmg Dong Email: [email protected]
1.GldlTHI$U
Ngay nay, vdi sQ phat trien nhanh chdng cQa khoa hoe va cdng nghe tren t i t c l cac linh vUe thi san pham co khi ngiy cang p h l i cd yeu cau cao hon ve chat iQpng sin pham, mQc dp tQ ddng hda sin xult va d i e biet la dp chinh xic hinh d i n g hinh hoe cua sin pham.
Vi vay cic cdng nghe gia cdng truyen thdng tren eic may van nang khd d i p Qng tdt nhu cau ngay cang cao nay v l do dd SLf canh tranh eua sin pham tren thj trudng bi han che. ThQc te dd ddi hdi phai phat trien va .ighien cQu
Ngay nhin bai: 6/12/2012 Ngay diap nhan dang: 28/5/2013
cle cdng nghe mdi nham n i n g cao dp chi'nh xac hinh dang hlnh hpc ndi rieng va nang eao chat luong san pham che tao ndi chung.
Viec nghien cQu cae chi tiet hinh dang hinh hoc phQc tap vdi dp chinh xac eao thudng dapc ap dung nhieu tren cle trung t i m gia cdng. Tuy nhien trong qua trinh gia cdng ludn ludn khdng ^i''J''^' hoan hao va g l y sai sd F^OJ-k) gia cdng. Co rat nhieu F]i,j,k) nguyen nhan gay sai sd trong do anh hQdng cua iQc cat den dp
chinh xae gia cdng la mdt van de djnj duoc quan tam. Vi^c han che Idn nhil sai sd gay ra do lUc e l t se Ilm tangdt chinh xac gia cdng. Do do, vi&c g ^ sai sd gia cdng do I n h hQdng cilalvi cat —* nang cao dp chinh xac gia cSng I I mdt trong nhQng nhifm vu quan trong eua n g i n h co dien tQ.
Xult p h i t tQ yeu eau thifc t l flOi chung tdi d l manh dan chpn hifdng nghien cQu khio s i t sai sd gia cong do luc e l t tren m i y CNC de nhim dilau g i l i phap bu sai sd dd. De tai"KhSosii I n h hudng cua luc e l t den dp chinh xac gia edng tren may CNC" cd y nghiavi cd tinh thac tien kha eao. Ngoai yngh'a khoa hpc tren, de tai cdn mang tinli Qng dung phuc vu trQc ti^p eho dao tao, chuyen giao cdng nghe dac bietii Qng dung v i o thuc te sin xuat gia cong tren may CNC.
2. MO HlNH T O A N H O C COA LI/(
cATVASAISdMAY[2].
2.1.Tinh toan lUc e l t Yun [10] da phat trien mdt mdhW iQe elt. Cd 3 thanh phan luc tri/cgiat tren true x, y, z cd the suy ra tif li*
thdng thudng (dF„{(|))) Va liic masJ (dF, ((]))) m l chling ti le vdi chieu d^
Idp phdi chua e l t nhu sau:
<"
A„
A„
A„
A„
A3,
A„"
A„
A„
X
• K.(i,j,k) K,(IJ,k)K„(l,j,k)C, K,(i,J,k)K„(l,j,k)Cj
Trong 66:
1
4 8 TapdiiKHOAHOC&CONGNGHE. S o 1 7 . 2 0 1 3
SClENCETECHNOLOGYl
A,,=C,cos{(|>-a,)t^(i,j,k);
A„=COS((t.)t,(i,j,k);
A,3=-sin((ti-a,)t,(i,j,k);
Aj, =C,sin((}»-a,)t^{i,j,k);
A^j =sin((t)-a,)t^(i,j,k);
A „ - c o s ( 4 . - a , } t , ( i , j , k ) ; A3,=C,t,(i,j,k);
A,; =eostehtJi,j,k); A33 = 0 ;
cose^.
' sine,/
Cj =sineh{sinec -cosGcCOtG^);
cos9^ o / ^ ^ » C, -^; B, - cosa, ( — ) ;
sin9,^ cos9^
cos0,^ =sina,.sineh; cf): la vj tri gdc ua dung ey elt; a^ la gdc nghieng phia au cua dyng cu cat; 9^ I I gdc xoln; K^, J la luc cat xac djnh; t^{i,j,k) la chieu d i y hoi chaa elt tQc thdi; 9^ la gde t h o l t hoi; Ao I I chieu cao eCia phan tQ dia ucz.
Cle t h i n h phan iQc eat tae dung len lot dudng ranh tai mot gdc cat quay jyed the dupe tfnh t o i n nhusau:
theo phuong z cua iQc t i c dung, v l z la vj trf vong. NhQ tren hinh 2, mdt dao phay phang bao gdm 2 phan; phan ranh va phan chudi ed the dupe don g i l n hda thanh dam cat hang. Do vdng udn dung cu cat:
5 , - 6 , + 5 , + f ( L f - z ) =
4[-(L-L,)%3(L-L,nL-z,)].
^ [ ( z , - z ) ' - ( L , - 2 ) ' + 3 ( L , - z ) = (L,-z,)]
U - { L - L , ) % 2 ( L - L , ) ( L - z , ) ( L , - z ) ] ( 5 )
vao den tQ mdt syanpse. Dae trQng cua neuron la mdt ham kich hoat phi tuyen ehuyen ddi mdt t d hop tuyen tinh eua tat ea eae tin hieu dau vao thanh tin hieu dau ra.
IVldt no-ron nhan tao I I mdt don vj tfnh t o i n hay dOn Vj xQ ly thdng tin co sd cho hoat dgng cua mdt mang no-ron. So do khdi cua hinh 2 chi ra md hinh cQa mdt no- ron nhan tao.
=Jij,k)
=,(i.i.k)
=Jij,k)
=Bii:
^
All A „ Ai, A „ LAJI A „
A , , ' A„
A „ j
X
K„(l,J,k) K,(i,j,k)K„(i,j,k)C, _K,(i,J,k)K.(i,J,k)C, Q c thanh phan lac cat theo chieu y v^ z tai mot goc e l t quay tCiy y co le CO duoc bSng each lay tong cac I Jc ic dung len moi ranh d goc elt quay Jth^:
=,(i,j,k)
=|i.i,k) .
= B i I I
2Ell
Trong dd, 5^ la do vdng cua chudi, 6, II do vdng cua ranh, cj)^ la gdc vdng cua chudi, L, I I chieu dai ranh, v l l^la md men quan tinh eCia ranh.Trong sudt qua trinh dao phay phang e l t vat lieu theo true x hoac y, dp vdng udn dung cu elt thu dapc anh hadng den dp chinh xac hinh dang cQa phdi.
Nha vay, chung ta thay dupe mdi quan he cua luc cat vdi cic thdng sd chieu
^ ^ day phoi (t) va van tdc cat (v). TQ mdi quan he nay, chung ta tien h l n h nghien cQu Inh hUdng cua cac che dp eat den sai sd ehi tiet thay vi di tien hlnh nghien cQu anh hudng cua luc cat den sai sd. Viee xay dQng md hinh danh gia sai sd se dQa vao mdi quan '^' henay{hinh1).
2.2. Tinh t o i n do vong cat Mpt trong nhQng nguyen n h i n ii'nh cQa sai sd gia cdng la do vdng cat D lae e l t gay ra. Bang elch g i n dyng 1 elt nhQmdt dam due hang, dp vdng it cd the daoc suy ra:
= ^ [ ( z , - z ) - - ( L ^ z ) % 3 ( L - z y ( L - Trong dd F I I iQc elt, 1 la md men j l n tinh mat e l t cQa dyng cu elt, E la d dun Young, L I I phan nhd ra, z^ vi tri
Minh 1. Moi quan he cOa life cat va sai so gia eong 3. X A Y D I / N G M d HiNH OANH .1 GlA SAI S6 B A N G MANG NCr-
^^^J***' RON TRUViN NGl/pC (BACK PROPAGATION) TRONG M d i TRl/dNG MATLAB
No-ron la mdt don vi tinh toan cd nhieu dau vao v l mdt dau ra, mdi d i u
Hlnh 2. Mo hlnh phi tuyen cDa mot no-ron d day, chung ta xac djnh ba thanh phan CO b i n cua mdt md hlnh nP-ron ; - Mgt tap hdp cic weights hay cle ket ndi, ma mdi mdt trong chung daoc d i e trung bdi mdt trpng sd cQa rieng nd. TQc la mdt tin hieu x tai dau vao cCia w/eightsjndivdi neuron kse dupe nhan vdi trpng sd w/eights w . d do k la chi sd cua neuron tai dau ra cua w^eights dang xet, cdn j chi diem dau vao cua weights, Cac trgng sd weights c u l mdt neuron n h i n tao cd the nhan c l cic g i l tri I m v a c l c g i l trjdQPng.
- Mpt bd cdng de tinh tdng cle tin hieu dau vao cua neuron, da dupe n h i n vdi cae trpng sd weights tUOng Qng;
phep t o i n daoc md ta d d i y tao nen mdt bd td hpp tuyen tinh.
- IWdt ham kich hoat (activation function) de gidi han bien dp dau ra cua neuron H i m kich hoat cung dapc xem xet nhu la mdt ham nen; nd nen (gidi han) pham vi bien dp cho phep cua tfn hieu dau ra trong mdt khoing g i l tri hOu han. Md hinh neuron trong hinh 4 cdn bao gdm mdt he sd hieu chinh t i e ddng tQ ben n g o i i , b^. He sd hieu chinh b|_ ed t i e dyng tang len hoac
^ n 1 7 . 3 0 1 ^ .TanrhiifHnflwnfJimMr,wr,ne .ao
•aSSEESaCONGJIG H E
Bang 1. Cac che do gia cong trong 20 lan gia cong
Hlnh 3. Mo hlnh phi tuyen thi^ hai cua mot neuron
t«»,i*.™ih«„v= / ^ - " " " - ? ^ - ' " - V " ' ' — ^ ' ^ » = ' * ^
Hlnh 4. Mo hinh mang no-ron 3 Idp mo phong sai so g i l m di dau vao thue cda h i m kfch hoat, tuy theo nd daong hay am. Cd nhieu loai ham kfch hoat.
Dudi dang edng thQc t o i n hpc, chdng ta cd the md t l mdt neuron k b i n g cap edng thQc sau:
1 1 2 3 4 S 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Toe do quay true chinh 5 (vong/phtjt)
2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000
Chieu sau cat t (mm)
1,5 1,5 1,5 1,5 2 2 2 2 25 25 25 25 3 3 3 3 3.5 35 35 3.5
Tocdo tien dao theo true X,Y
(mm/phiit) 200 300 400 500 200 300 400 500 200 300 400 500 200 300 400 500 200 300 400 500
Tjc do tien dao theotnjcZ (mm/phiit) 20
(6)
v l y ^ = f ( u ^ + b j (7) Trong dd x,, x^,..., x_^ I I cac tfn hieu
d i u v i o ; wJ,W|^,...,w^^ la eac trong sd weights cQa neuron k; u^ la dau ra bd td hpp tuyen tinh tuong Qng; b^ la he sd
hieu chinh. vay|^-f(V|_) (9) He so hieu chinh b^ la mot tham sd Trong cdng thQc (8), chung ta da
ngoai cua neuron nhan tao k. Chung them mot weights men. Dau vao cua ta ed the thay dapc su co mat cua nd nd la:
trong cdng thQc (7). Mdt each tUOng x^^ -Hi (10) duong, chiing ta cd the t d hop cac va trong sd cua nd la
cdng thQc (6) va (7) nhu sau: % o ^ ^ k ' " '
e^=Z%'<, (8)
f
U... a
-1
'1
-
Hinh 5. Mao gia cong th«c nghilm Hinh 6. Ga thiet bi .a gia cing tren m j y CNC 3 true
0 TapdiiKHOAHOCSiCONGNGHE. S d 1 7 . 2 0 1 3
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.mam L _
1 ^ 1 • "
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•huSSSP'T^^-^'-
Hinh 7, Bien thien luc cat trong lan gia cong thifS
fT
I r
Bvia _____
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x - t ^ ^ ^
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II
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Hlnh 8.8ien thien luc c^t trong lan gia cong this 4
OriihiluccJtFx, F\ w F/
Hlnh 9. Bien thien lye eat trong lu'ot gia eong thit 20 Hinh 10. Thong so lUc eat trung binh thu duac trong 20 lan thyc nghiem gia cong
Hlnh 11. Mo phong sai so kfch thudc thu tfiftfc theo phi/ong X Hinh 12, Mo phong sai so kich thudc thu duoc theo phuong Y
Sai so trong qua trinh mo ph6ng
Hlnh 13 Mo phong sai so kich thudc thu dugc theo phuong Z Kinh 14. Sai so trong qua trinh md phdng
S o 1 7 . 2 0 1 3 • T a D d i i K H O A H O f & f n N f i N f l H f ' i l
BEaffitCQNG NGHE
Bang 2.5d luot gia cong vdi cac ehe do cat
Gia tri trung binh ciia sai so va gia tn mo phong (mm)
Sai so thirc te do Sai so mo phong
M I 0.27715 0.27657
My 0.2911 0.320365
Aflz 0.0662 0.05686 N h U v a y c h u n g t a v e lai m d h l n h c u a
n e u r o n k n h u t r o n g h l n h 3 . T r o n g h l n h nay, n h i e m v u c u a h e s d h i e u c h i n h la t h Q c h i e n h a i vi&c: (1) t h e m m o t t i n h i e u d a u v a o c d d j n h la 1 , (2) t h e m m g t t r p n g s d w e i g h t s m d i b a n g g i l t r j cQa h e s d b^. M a c d i i cac m d h i n h t r o n g h i n h 3 v l 4 I I k h a c n h a u v e h i n h t h Q c n h u n g t a o n g t Q v e b i n c h a t t o a n h g c .
M d h i n h m a n g n o - r o n m d p h d n g sai s d g i a c d n g ( H i n h 4 ) m a t a e g i l sQ d u n g la m o t m d h l n h m a n g ncJ-ron 3 i d p , t r o n g d o c d 4 I d p d a u v a o ( I I e i c t h d n g s d : c h i e u s a u c a t t , lUc c a t t h e o p h u o n g X, iQc c a t t h e o p h u a n g y, iQc e l t t h e o p h a o n g z) v a 3 I d p d i u ra (la t h d n g s d sai s d t h e o 3 t r u e x, y, z).
4 . T I ^ N H A N H THU'C N G H I D M D O LLTCCAT
Be da bao va danh gia sal sd thdng qua md hinh da bao de tai tien hanh thac nghidm gia cdng chi tiet vdi v i t lieu hop kim nhdm 6061, dung cu la dao phay ngdn, tdc do true chfnh I I 2000 (vdng/
ph), khdng dung dung dieh tron ngudi va kiem nghiem daoc ket qua (bing 1).
Thiet ke mau the hien tren hinh 5, 6. Ket q u i thu dugc qua thiet bi do luc e l t KISLER
Vi du d mdt so luot gia cdng vdi cac che do e l t nhu bang 2
Ket q u i sai sd sau khi gia cdng do duoc va md phdng sai so lUe e l t b i n g mang no-ron trong mdi trudng matlab.
Thdng ke sd lieu ve sai so iQc e l t theo phuang X, Y, Z do dugc sau khi gia cdng thue te mau thu dQoc nhQ (Hinh 9,10,11).
Oanh gia sai sd thac va sai sd qua md phdng bang mang no-ron trong mdi trudng Matlab
Gia trj trung binh eua do lech trong
20 lan gia edng thu dugc la tUdng ddi nhd, ket q u i md phdng sai sd bang mang nd-ron cd t h ^ c h i p n h i n 6iiac.
NhQ vay md hinh danh gia sai sd bang mang no-ron da x i y dQng ed the Qng dung vao thQc te s i n xuat dUOc.
5. KET L U A N
Di t l i da neu len dQOc I n h hQdng cua iQc cat trong q u i tr'mh gia cdng va dQa ra dUdc moi quan he giQa che do gia cdng - iQc cat v l sai sd gia cdng de tQ do dua ra md hinh dQ b i o sai sd gia cdng de tien h l n h thQc nghiem.
Sau qua trinh nghien cQu va thac nghiem cho thay ket qua t h u dugc thong qua md phdng va ket qua thQc the trong qua trinh thUe nghiem lech nhau rat nhd v l ed the chap nhan dUde. Md hinh mang no-ron md phdng sai sd trong qua trinh gia cdng thdng qua viec n h i p cle thdng sd dau vao cd san cd ket q u i tQOng ddi k h i quan va cd the Qng dung vao thuc te s i n xuat nham g i l m sai sd trong gia edng tren may CNC 3 true.
Phan bien khoa hot: TS. Phiinq Xuan Smi
TAI LI|U THAM KHAO
[ I j . Banh Tien Long, Nghien ziSis bu sai so v; tri bang phan mem dieu khien khi gia cong phay CNC, Tap chiCokhiViet nam, 2007;
[2]. Chana Raksiri, Manukid Paniehkun
"Geomatric and force errors compensation in a 3-axis CNC milling machine", MACHINE TOOLS &
MANUFACTURE
[?;. t.LJ. ?ohez,"Five-Qxis nulling tool kinedaft chain design ..nd analy^i^'! - MACHINE TOO[i|
MANUFACTURE
14]. [ LJ. Bohez, "Compensating for s y s t S errors in 5-axis NC machining", COMPUTER-AlHi DESIGN, w w w elsevier.com _
[5]. Ninh fide Tdn, "Dung sai va lip gliip.'-ll Giao Due.
[6]. Nguyen Tien Tho - Nguyen Tlij Mn Bly- Nguyen Thj Cam Tu, Ky thuat do lucfng kiem tra traiij che tao eO khi -NXB Khoa hgc ky thuat.
[7]. Nguyen ThUdng Han, 8o ludng cic dai lum^
vat ly.-NXB Khoa hpc kythuat.
[8]. Trln Van Oich, Cong nghe gia cdng tren mi) CNC NXB KHvaKT, 2000;
(91. Ta Duy Liem, He thong dieu khien sochomi) cong eu, NXB KHvaKT;
[10] W,S, Yun, D.W. Cho, An improved force model considering the size effect in end ASM£ Intemational Mechanical Engineering Coni and Exposition, Orlando, PL, 510 November [21)011 223-229
