NGHIEN cuu-TRAODPI
Nghien ciiu cac thong so anh hudng den sU on djnh khi gia cong tren may phay CNC cao toe "DNIVI400"
(*) GS TSKH. BANH TIEN LONG (**) TS. HOANG VINH SINH (***) THS. PHAN VAN HIEU
TOM TAT
Bai bao trinh bay mot so ket qua nghien cmi anh hirotig cua so rang ciia dung cu cat, chieu sau cat, toe do cat den tinh on dinh trong qua trinh gia cong tren may phay CNC 3 true cao toe. Cae ket qua nay la tien de cho viec nang cao nang suat gia cong cat got, dong thoi van dam bao duo'c yeu to quyet djnh, do ia chat luotig be mat chi tiet.
Cic nghien ciru tir trudc [1], [2], [6] chu yeu giai thich hien tupng dao dpng do tic dung cua luc cat. Mo hinh luc cat dupc dua ra nhu hinh 2 cho thay cd the coi viec gia cong tren 1 mat phang 11 mo hinh 2 bac tu do.
Luc cat tiep tuyen vl lire elt hudng tam tinh cho rang cit thu j dupc tinh theo cdng thirc:
(1)
F,j^g[<^j(t)]K,.hi^).a^
F^=g[^j(t)]K^.h(^).a^
I. Dat van de
Gia cong cao toe (High Speed Machining - HSM) 11 mpt trong nhirng cdng nghe gia cong hien dai. Dd 11 mpt linh vuc chinh cua cdng nghe che tao miy. Cic ling dung chu yeu de thuc day cdng nghe theo hudng gia cong cao tdc la: gia cong nhom (cic bo phan 6 to, chi tiet may tinh nhd, thiet bi y te), cdng nghiep blng khdng (gia cdng chi tiet llm bang nhom cd thinh mdng), khuon man (gia cdng tinh vdi dp chinh xac cac chi tiet lam bang vat lieu cung nhu khuon dap, khuon ren, khuon nhua...). Gia cong cao tdc, ve co ban, la su ket hpp giira toe dp true chinh cao vl lupng an dao Idn.
Trong thuc te ciing gidng nhu khi gia cdng phay CNC (computer numerical control) trayen thdng, thi phay cao tdc ciing xuat hien nhirng hien tupng vet xude tren be mat cua chi tiet gia cong nhu hinh 1.
Hinh 1: V e t x u a c tren b e m a t sau khi gia cong (*) B p Giao duc-Dao tap
(**) Vien C P khi, Trucmg D H B a c h khoa, H a N p i
(***) K h o a Cong nghe, Trudng D H Cong nghiep TP. H C M ( C S N A )
Hinh XI Hrhchlgui»Hg H i n h 2: M o hinh lire cat trong m a t phang X Y
g (t) 11 mpt ham logic phu thupe vao vi tri cua rang thii j tai thdi diem t. Khi dung cu cat an vao phoi (gdc vi tri cila dung cu cat (p (t) nam trong khoing giiia gdc an dao cp^ vl gdc thoat dao cp^) g=l, cac trudng hpp khac thi g =0.
Kj vl K^ tuong ling 11 he so cat tiep tuyen va hudng tam, a 11 chieu sau cit, h (tp) 11 chieu dly cua phoi elt, trong dd bao gom chieu dly tmh (do dao chuyen dpng) vl dpng (do dao rung dpng) dupc xac dinh theo cong thiic:
(2) A[f.(/)] = A,,.,J*;(0] + /'.™™Ji(0] = /z.sin[^/r)] + M^-M,., •
So 0 7 - T h a n g 7 nam2010
NGHIEN ClfU-TRAO 001 uj va uj-1 la dp lech ciia rang thii j va j-1 nen ta
se co:
(3) M*,(0] = A,.Jt(0]+V.-c['^.(0]
= /z.sin[(().(/)] + [sin[(t)/0]cos[(t).(;)]]
T la chu ky chuyen dpng ciia rang :
x(t)-x{t-T) y{t)-y(t-T)_
60 ' a.N' (4)
O la van toe gdc quay cua true chinh, N la so rang ciia dung cu cat. Cong thirc (1) cho thay, khi chieu sau cat thay ddi se lam cho luc thay doi gia tri, llm cho rung dpng ciing thay ddi theo. Hien tupng mng dpng gay mat dn dinh trong qua trinh cat kim loai dupc gpi la Chatter. Viec nghien ciru hien tupng nay hien nay ciing dang 11 mpt hudng nghien ciiu ma nhieu phdng thi nghiem dang tien hinh v l da cd nhieu ket qua tdt
[2]. Chatter tao ra rung dpng manh, am thanh Idn, chat lupng be mat xau. Cd 4 loai rung dpng: rang dpng tli sinh (regenerative), rung dpng ma sit (frictional), rung dpng ghep kieu (mode-coupling), rung dpng nhiet co (thermo-mechanical). Bii bao nay chi de cap den loai rang dpng tli sinh do nd xay ra pho bien nhat. Rung dpng tai sinh do nhiing nhap nhd be mat xep tang tao ra. Khi dung cu cat cat tiep xiic vdi phoi, do tac dpng cua luc cat lam dung cu cat rung dong v l tao nen cic be mat nhap nho. Ludi cat sau khi cat den be mat nay se llm cho chieu sau cat thay doi, lam cho dung cu cat dao dpng. Tuy theo cic nhan td tic dpng nhu be mat cat, dao dpng cua dung cu cat ma cd the lam cho rang dpng cua dung cu cat cang Idn len gay mat on dinJi hay trd nen on dinh. Cd nhieu phuong phap de loai bd rung dpng tli sinh. Pho bien nhat van la cich xlc dinh thong so cat tdi uu bang bieu do on dinh dupc xay dung tren CO sd thuc nghiem. Tlusty va Tobias da tao ra bieu do dn dinh (stability lobes diagram) nham xac dinh nhiing vimg lam viec on dinh khong cd rang dpng tai sinh.
Bieu do hinh 3 la mpt bieu do on dinh man. Bieu do niy xlc dinh qua trinh cat cd on dinh hay khong, dua vao toe dp cat v l chieu sau cat. Nhd bieu do on dinh niy ma ta cd the xac dinh che dp cat cho nang suit Idn nhat m l van dam bao tinh on dinh cua qua trinh cat. Trudc kia, khi van cdn phay d tdc dp thap thi viing on dinh qua hep nen khong the nang cao nang suit len dupc nira, cdn bay gid, nhd viec chpn che dp cat phu hpp, nang suat cd th8 tang len dang ke.
Kharq Sh dinh
BuBhg can ah djTh
T & (JB true chWi
Hinh 3: Hinh dang cp ban cua mot bieu do on dmh cua qua trinh phay [1], [6]
Cd the nhan thay, bieu do dn dinh phu thuoc vio dp cirng viing v l kha nang giam chan ciia he thdng miy-dao-phdi (gdm ca do gl). Do dd, vdi moi mpt may cdng cu cu the, khi chpn van tdc cat, chieu sau cat khac nhau thi se cho ra cic bieu do dn dinh khac nhau. May phay cao toe d Trang tam ky thuat Hong Hai dupc lay lam doi tupng xay dung bieu do on dinh. Phuong phip dupc sii dung la md phdng bang ly thuyet.
II. Xay dung bieu do on dinh bang phu-ong phap phan tich
Phuong phap phan tich su dimg cic phep bien doi.
Nd cho phep hieu rd hon ban chat ciia su on dinh va mat dn dinh.
•M/
L
I J«f-T)<0
y(/)>0
...J:
Hinh 4: Mo hinh 1 bac tu do giua dao va phoi khi cit
Neu coi lire theo phuong Z 11 khdng dang ke, cd dupc phuong trinh dao dong:
(5)Y(t) = G(rn).k.ap.Y.(l-e-J') Cd the bieu dien bang so do sau:
n
Gicd)
Ft
H(oji)
Hinh 5: So do ham truyen luc nit gpn
NGHIEN ClfU-TRAO DOI
Trong dd: (6) H(tn)=k.ap.Y.(l-e-J')
Theo tieu chuan dn dinh ciia Nyquist thi "he kin se dn dinh khi dudng quy dao G(co). H(co) khdng di qua va khong bao diem -1+Oj hay ndi cich khlc bien gidi on dinh cua he la, khi quy dao G(a)).H(co) di qua diem -1+Oj hay
(7) G.//(co) = G(<si).k.a^ .(1 - e"'') = -1 + Oj Suy ra
Trong do
{^)a -1
plim
G(co).A:.(l-e")
Tii^ .to
Giu))f-i'
True nuft:
«(«)
« ( < » ) ( l - < ' •"")
Hinh 6: Bieu dien ham truyen tren he tpa dp ao
Do a 11 mpt so thuc - nam tren true thuc nen vecto G(a) ).(1 - e~'"^) phai nam tren true thuc. Dua vao hinh ta cd gia tri gidi ban:
(9) a = ~1
"'•"' yt.2.Re[G(co)]
Tuy nhien, do dac diem ciia qui trinh phay 11 dao khdng cat lien tpc phoi va phuong cua dao cat thay doi lien tuc nen Tlusty dl dua them vao khai niem ve sd rang cat trang binh A',* vl ham trayen chieu phuong Go„«„(co)
(10) V .
(13) N. =- 360 dac trang cho sd dao tham gia vao qua trinh cat
(14) G„„„,(co) = p^G^((o)+p^G/co) dac trung cho anh hudng cua luc cat cic phuong den dao dpng ciia dao. Cic gii tri p^, |J._^ 11 ty so giiia luc elt theo phuang tuong iing x va y chieu len phan giac gdc cit so vdi luc cat tong va duoc tinh bdi cong thiic:
Hinh 7: So d6 tinh |i^, \i
.i-<^.
(15) ^^ =cos(P +<^,,^ -90'')cos((l)„^ -90°) p, =cos(p +(!),„, -180°)cos((t)„„, -180°) Nhu vay ta se xay dung dupc bieu do on dinh bang each ve cich dudng d bien gidi on dinh. Bieu do on dinh dudi day duoc xay dung bang 5 dudng bien on dinh tir bac 0 den bac 4 iing vdi gia tri N = 0...
2.^-<.Re„,„,[G(co)]
(11) ^ - ^ - i N = 0...k (12) e = 2?: - 2 tan Re[G.,.„,(co)]
Im[G„„,„,(co)]
Hinh 8: D6 thi on dinh ly thuyet dupc xay dung tir cac duong bien on djnh
TAP CHI c a KHI VIET NAM V So 07-Thang 7 nam 2010
NGHIEN CI^U-TRAO DOI
III. Mo phong va danh gia ket qua
Dua tren mo hinh dupc trinh biy d muc II, phan mem tinh on dinh theo phuong phip phan tich dupc xay dung theo so do:
Nhap thong s5
dau vao Tinh ham truy en Tinh gioi han on dinh Hinh 9: Cac buac xay dung phan mem tinh on dinh theo phuong
phap phan tich
CIc thdng so dau vao bao gom cac thong so ve che dp cat, he sd vat lieu v l thong so dpng hpc ciia dao.
Thong so Hjj chieu rong cat a chieu sau cat
p
Phay thuan n
N fz m
Gia tri 0.1 0-0.010
5000-30000 2 0.0002
0.04
Don vi
mm
rpm - m/rang
kg
Staliiily Lobss Diagnvn
®0^.M'
Kt Kn
1000*271 0.02 6.10*
2.10^
rad/s - N/m2 N/m^
Being thong so dau vao
Hinh 10: Bieu do on dinh may phay cao toe "DNM400" khi dimg dao CP 1,2 va 4 rang cat
Theo cdng thiic (10) v l cac bieu do hinh 10 thi, khi tang so rang len hai lan thi gidi ban on dinh gilm di mpt mia v l sd dinh ciing se giam di mpt mia. Khi elt nhieu rang cat thi lire cat se deu hon so vdi khi cat it rang, nhd vay chat lupng be mat cua san pham tdt hon.
10 3'
a
7 6 E
f '
3 2 1 0 0
•
J
V
1
Slabi
1 '
/
ty Lobes Diagram
\ \ / V WF W ^ - ^ ^
1 1 .
5 1 1.5 2 Spindle Speed(rpm)
,
2.5
- -
• ' • -
- '
• • - -
-
3 ik'tfl"
Slahtty Lnt»a Diagram
Spindls Spaed(T|}m)
Spindla Speed (rpm)
Hinh 11: Bieu dp 6n djnh cua may phay cap tPC "DNM400" khi chiSu sau cat la 0,1; 03 va 0,5mm
NGHIEN cuu-TRAODOI
Khi tang chieu sau elt thi luc cat ting, dan den he thong kem dn dinh, viing on dinh nhd di, ddng thdi tdc dp cat cing ting thi he thdng cang dn dinh (hinh 11 cho thay rd dieu niy).
III. Ket luan va hu-ong phat trien
Bieu do dn dinh ciia he thdng cdng nghe phu thuoc vao cic yeu td cong nghe nhu: so rang cua dung cu cat, chieu sau cat, tdc dp cat. Vdi mdi mpt yen td thay doi se cd mot bieu do on dinh khac nhau. Ket qua nghien ciiu tren cho thay, hoan toan cd the tinh toin dupc bieu do on dinh cua mpt he thong cdng nghe (miy phay CNC cao toe - Dung cu cat - phdi) bat ky bang ly thuyet.
Bieu do on dinh la yeu to quyet dinh chat lupng cua be mat chi tiet sau khi gia cdng. Neu cd the xay dung dupc mpt bp ho so cac bieu do on dinh thi cd the ho trp rat tot cho ky su thiet ke quy trinh cong nghe trong viec tu chu lua chpn cic thong so cong nghe de dim bio chat lupng sin pham sau khi gia cong.
Cong viec nay trade day phai diing cac bang tra hay so tay cong nghe, rat phiic tap, dp tin cay khong cao vi nd khdng xay dung cho he thong cong nghe dang su dung.
Mpt viec can phai lam sap tdi la tien hanh thuc nghiem de cd dupc:
- Cac thdng so co ban cua co he may-dao-phoi (do ga) nhu he so gilm chan, he so dp ciing. Cac thong so niy rat quan trpng de tinh toan bieu do on dinh cua tirng he thdng cdng nghe cu the.
- Thuc nghiem kiem tra ket qua ly thuyet.
Cac nghien cmi nay dycrc thirc hien trong khuon kho luan an "Toi uai hoa qua trinh gia cong tren may phay CNC 3 true cao t6c DNM400"
Ky hieu:
aj^ chieu rpng cat
c^ he so gilm chan theo phuong x v l y (Ns/m) F^: luc hudng tam (N)
F,: luc tiep tuyen (N)
Fx,y: luc cat theo phuong x va y (N) fz: tdc dp chay dao mdi rang (m/tooth) g((pj): him tac dpng giiia dao v l phoi h((pj): chieu day cua pboi cat (m) hxx: he so cat (N/m-)
j : rang cat thii j
K^ he sd luc cat hudng tam (N/m-) Kj he so lire cat tuyen tinh (N/m^)
'^x.y ^^ so dp Cling theo phuong x va y (N/m)
™xy- ' ^ o i lupng ciia dung cu elt theo phuang x va y(kg) '
n: tdc dp vdng quay (rpm) N: so ring cua dung cu elt t: thdi gian (s)
T: chu ky chuyen dpng rang (s) a chieu sau cat (mm)
p: ^ '
x: dich chuyen ciia dung cu cat theo phuong chay dao X (m)
y: dich chuyen ciia dung cu cat vudng gdc phuong chay dao y (m)
(p vi tri gdc cua rang thir j (deg) (p^ vi tri gdc ket thiic cat (deg) (p_, vi tri gdc bit dau cat (deg)
x: thdi gian lap lai vi tri cua rang ke tiep (s)
^ he sd gilm chan tuong ddi (o^ tan so tu nhien (rad/s)
<1): ma tran chuyen doi. •
Tai lieu tham khao:
1. Banh Tien Lpng; Tran The Luc; Tran Sy Tuy, Nguyen ly gia cong vat heu; NXB Khpa hpc va Ky thuat. Ha Npi, 2001.
2. Nguyen Van Khang, Dao dpng ky thuat, NXB Khoa hpc va Ky thuat, 2005.
3. Nguyen Doan Phupc; Ly thuyet dieu khien tuyen tinh; NXB Khoa hpc va Ky thuat, 2005.
4. Nguyen Hpai Son, ITng dung Matlab, Khoa Xay dung va Co hpc img dung, 2006.
5.X. K. Luo;A simulated investigation on the machining instability and dynamic surface generation; International Joumal of Advanced Manufacturing Technology. -2005. - Vol. 26. - pp. 457-465.
6. Ronald Faassen; Chatter Prediction and Control for High-Speed Milling; Umversity
Press Facilities, Eindhpven, the Netherlands, 2007.
7. Kai I. Cheng; Machining Dynamics - Fundamentals, Apphcations and Practices; Springer, 2008.
8. Janez Gradis; On stability prediction for millmg; International Joumal of Machine TPPIS & Manufacture 45.-, Elsevier Ltd, 2005.
9. Tpny L. Schmitz, Stabihty in High-Speed Machining; Natipnal Institute ef Standards and Technplogy Gaithersburg, 2001.
10. Tamas Insperger, Gabpr Stepan; Updated semi-discretization method for periodic delay-differential equations with discrete delay;
International Joumal for Numerical Method in Engineering, 2004.
11. http://www.mcmastercom 12. http://www.makeitfrom.com
TAP CHI c a KHI VIET NAM V So 07-Thang 7 nam2010
