NGHIEN CLKU - TRAO DOI
/ NGHIEN Cl/U TINH ON DjNH CUA HE CAT OONG KHI CIA CONG TIEN
STUDY OF STABILITY OF DYNAMIC CUTTING SYSTEM IN TURNING
ThS. Nguyen Hai Nam
Bg mon Cong nghe Thiet bi va Hang Idiong Vii tru, Khoa Hang khong Vii tru, Hpc vien Ky thuat Quan sy
TOM TAT
Bai bdo phan tich ly thuyet su on dinh cua he dong luc hoc khi gia cong tien, xdc dinh cdc dieu kien mat on dinh cua he, phan tich dnh huong ciia che do cat vd dai luong tri cua luc cat so vdi su thay doi cua chuyen dich bien dgng dan hoi den tinh on dinh ciia qud trinh cat vd dua ra vi du cung nhu cdc ket qud nghien ciru.
Tir khoa: Qud trinh cat, tinh on dinh, tri, che do cat.
ABSTRACT
In this paper, the theoretical analysis of the stability of the dynamic cutting system in the turn- ing is made; the stability loss conditions are defined; influence of delay of cutting force in relation to change of elastic deformation displacement, and depths of cut on stability of system is analysed. The example and results are given.
Keywords: Cutting process, stability, delay, cutting conditions.
1. DAT VAN DE luc cSt la nguyen nhan chinh dan din su mit dnh on dinh ciia qua trinh cit. Vin Ah 6n dinh qua Bao dam su on dinh ciia qua trinh gia trinh cit da dugc nhan dugc su quan tam, nghien cong tren may cit got Itim loai luon la vin dS cip cuu cua nhiSu nha nghien ciiu [1-5], Trong phin thiet doi vcti nganh Co khi QM tao may vi no lien lom cac nghien ciiu, mo hinh v6 huong dong luc quan chat che den van de nang cao nang suit, chit hoc qua trinh cit thuong dugc sii dung dS nghien lugng va do tin cay ciia may Khi nghien ciiu su ciiu tinh 6n dinh va su tu dao dgng cac mo hinh on dinh dpng cua qua trinh cit, ta cin xem xet dpng luc hgc cua qua trinh cit. Trong nghien ciiu moi quan he giOa luc cSt va chuyin dgng tuong [5], tac gia da dua ra mo hinh trong khong gian.
doi giOa dao vao phoi vi chinh cac tinh chit ciia Tuy nhien, trong nghien ciiu do, cac tham s6 djc
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NGHIEN CUfU - TRAO D 6 I
tnmg cua qua trinh cat dirge xet nhu cac tham phucmg trinh dgng luc hpc qua trinh cat dirge md sd suy rong, vi vay co che anh hudng cua che do ta trong dang cac phuong trinh vi phan sau:cdng nghe cung nhir dai lugng tri cua lire cat din
tinh dn dinh cua qua trinh cat chua dugc lam rd. d'X Muc dich cua nghien cuu nay la lam ro su anh ^ ^ hudng ciia cac tham sd tren den tinh dn dinh cua
he. ^^°"^ ^°- dX
dt at
2. CAC NO! DUNG CHINH VA KET QUA NGHIEN CUtJ
Trong nghien ciiu nay, mot sd gian udc
va gia thiet co ban sau day dugc su dung de xay la vecto ham lire cat;
dung md hinh toan hpc dpng lire hgc qua trinh cat:
• X = {X^, X^y la vecto chuydn dich bien dang dan hoi cua dao;
at at at
"1 .^'^i '^=1, cJ^" -"I
1) Khi phan tich tinh dn dinh, phuongtrinh dgng luc hgc qua trinh cat cd the duoc xem nhu he dgng luc cau tao tu mot khdi lugng suy rong cua he con dao (bao gdm dd ga, ban dao va dao). He dgng lye nay tuong tac vdi qua trinh cat vdi lire cat phu thudc vao chuyen dich bien dang dan hdi eua he eon dao [5],
2) Dao thue hien di phdng ox I Xj nhu tren hinh 1;
Hinh 1: So dd md hinh hi ddng luc hoc qua trinh cat
3) Luc cat ti le vdi dien tich lap eSt va hudng cua lue khdng bi thay ddi trong khdng gian [5], ngoai ra sir thay ddi cua lire tre so vdi su thay ddi cua chuyen dich bidn dang dan hdi eiia dao.
4) Tat ca eac tham sd eua md hinh ddng luc hpc qua trinh cat la khdng ddi.
tucmg ung la ma tran khdi lugng, ma tran tieu tan va ma tran do cung cua he.
Trong he (1), khi tinh den eac gia thuyet (3), quy luat tao thanh luc cat cd dang sau:
ddng trong mat
F = X^ab^ia^-X^ + T^), 2 = 1,2 (2) dt
Trong do A. = {X^, Xj}\k he sd gdc dinh hudng lye, thda man dieu kien -^P^ + /^ = 1; cr ,N/
mm-] la he sd dugc xac dinh bang thyc nghiem;
r, [5] la dai lugng tre cua lye so vdi sy thay ddi cua biSn dang dan hdi;i3o =5f*sin^, [mm],
fep =—^—-, [mm] la chieu day va chieu rong cua sin^
lap cat; Sf' la lugng tien dao; /'"' la chieu sau eat;
^ la gdc nghieng chinh cua dao.
Nhu chung ta da biet, de nghien cuu sy dn dinh diem can bang cua he (1) X' ={Xl,X[Y, ta can phai phan tich phuang trinh tuyen tinh hoa trong lan can diem can bang [6]. Diem can bang ciia he (1) dugc xac dinh bdi he sau:
Vdi cac gian udc va gia thuyet tren, cJC' = aboi.^ — ^1 ) { - ^ ; •^^} (3)^^
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NGHIEN CUfU-TRAO D 6 |
Gia sii tu he (3) ta xac dinh dugc diem can bing X' = {X' ,Xiy .Khi dd, bang each thay X, = X* + X-, i = \,2 vao phuang trinh (1) va (2) va biln ddi so bd, ta thu dugc phuong trinh trong lan can diem can bang nhu sau:
de ^ dt "" (4)
Trong do:
' x=^{x^,X2 Y la vecto do chenh lech tga do tu vi , ^ "ii '^ 0 'iJ h^ ma tran tdng cac he sd
Trong cac bai toan ung dung thuc te, ta cSn phai xae dinh midn thay ddi cac tham so ciia he trong dd cd mi8n thay ddi eac tham sd cdng nghe (chd do eat) sao cho trong cac midn nay, h?
ddng luc hpc qua trinh cat la dn dinh. D§ phan tich tinh dn djnh ciia he vdi da thue dac trung (5) phy thupc vao cac tham sd ciia qua trinh cat, ta co thd su dung cac tieu chuan dn dinh khac nhau nhu tieu chudn Mikhailov, tieu chuan dai sd, phuong phap D-phan midn [7]. Trong nghien cuu nay, tac gia su dung tieu chuan dai sd Routh de nghien cuu sy anh hudng dai lugng tre va chieu sau cat ddn su dn dinh eua he. De lam dieu nay, trudc tien, ma tran Routh cau tao tu cac he sd cua da thiic dac trung (7) can duge xac dinh nhu sau:
la ma tran tdng cac he sd dp cung.
Cac ma tran/lEvac^ phu thupc vao ehe do edng nghe, co tinh eiia vat lieu phdi va dao, tham sd hinh hge cua dao (dupe xae dinh gian tiep qua he sd gdc dinh hudng lye) va thoi gian tre cua lye.
Da thiic dac trung cua he (4) cd dang:
(5)
h.{s) = d^s'^ +d^s^ +d-^s^ +d^s + d^ (6) Trong dd, cae he sd cua da thuc dupe xae dinh nhu sau:
rf,=)n„(c„+c^tA4)-h,i/[„-)i|,fc,+r(*5(^hi;-^y (7)
f'. =i^.i^!j*fr'fi-i^i:'':r'^A-'4(^'^:-A''i:l-ro&^lV-:-'^Ci;)
d.
d, 0 0
d, d.
d.
d, 0 do
di
d.
0 0 0 d.
(8)
Tiep theo, cae dinh thiie cua eac ma tran gdc con dugc tinh toan:
\di d, 1
A, = d 3 , A j = , . ^ 3 = r 4 " 2
d, d, 0 d, d^ d„
0 d, d,
•
f^,''d„^, (9)
Dieu kien on dinh duoc ki§m tra theo tieu chuan Routh:
A, > 0 , ; = 1, 2, 3, 4 Da thiic dac tnmg (5) co the biSu diln
duoi dang:
(10) Sau day la mpt vi du cu thd: Cac dii lieu ban dau: (J = 2000, [TV/mm^], lugng tidn dao
5*"' = 0.2, mm/vdng, gdc nghieng chinh 9 = 60", chieu day Idp catag = S'p sin^ = 0.173, mm, cac tham sd cau true he dugc the hien trong bang 1.
Bdng 1. Cdc tham sd cua he ddng luc hoc qud trinh cat
m. [Na^/mm]
L 0 10 =J
h. [N.s/mm]
["1.0 0.2]
[02 1.2 J
c[N/mmJ r 10' 3-10' 1 [310^ 1.2-10'J
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NGHIEN CUrU-TRAOeCl
Trong nghien cuu nay, tac gia xay dung mpt ehuong trinh cho phep xae dinh mien dn tham sd theo tieu ehuan Routh. Hinh 2 dua ra vi du mien dn dinh ciia he trong mat phang tham sd (?*'", r ). Ta thay rang, ddi vdi mdi gia tri cua dai lugng tri ^ tdn tai mot gia tri gidi ban ehidu sau cat dam bao tinh dn dinh ciia he. Dai lugng tri r eiia luc e5t phu thude vao nhi6u y6u td va dupe xac dinh bdi the tich bien dang deo trong midn cat thii cap va sa cap. Ddi vdi mdi truong hpp cu thS, dai lupng tr8 dugc xac dinh bang thyc nghiem.
St 1 0
Hinh 2: Mien dn dinh he trong mat phang tham sd (t). ,T)
3. KET LUAN
Ket qua phan tich cac Aihx kien mat dn dinh eua he ddng lye hpc qua trinh cat da chi ra rang, dai lugng tre ciia lye so vdi su thay ddi cua chuyen dich bien dang dan hdi va chieu sau eat anh hudng Idn dSn tinh dn dinh ciia qua trinh cat. Nghien cuu da xac dinh mien dn dinh tham sd, trong do cd tham s6 cdng nghe, cho phep lya chpn chd do cat phii hgp theo tieu chuan dn dinh qua trinh cat trong giai doan thiet cac qua trinh cdng nghe. •
Ngay nhan bai: 28/4/2014 Ngay phan bien: 18/5/2014 Tai lieu tham khao:
[1]. Ky^iHHOB B . A . flnnaMMKa cxaHKOB. M, MarnHHOcxpoeHHe, 1967.
[21 3iifcflc6epr, M . E. ABTOKOJiedaHHS MeTajiJiopeacyiuHx cxaHKOB. C.-IId: HaaaHne OKEC, 1993.
[3]. Beiiu B.JI., BacHJibKoe JX-B, S y d a p e s lO.M. flnnaMHRa xexHOJiorHHecKHx CHCXCM, 2 0 0 2 .
[4]. BacHH C A . noBbimeHHe BwdpoycxoHHHBocxn HHcxpyMenxa n p n xoieHHii n 4'pe3epoBaHHn - M.:
MarnHHOcxpoeHHe, 2 0 0 6 .
[51 SaKOBOpoxHbiH B.JI., OJICK M.E. ^HnaMHKa n p o u e c c a pe3aHHfl. CHHeprexHHecKHH noaxoji. POCXOB wjji;.
Teppa, 2 0 0 6 .
[6. JIanyHOB A . M . OdmaH s a i j a i a o 6 ycxoHiHBOcxH ,aBHHceHHa M.: FocTexHSflax, 1950.
171 EeceKcpcKHH B.A., TTonoB E . n . T e o p n a CHCTCM aBXCMaxHiecKoro ynpaBJieHna CII.: Hsflax. npoi^eccHa, 2 0 0 4
T A P C H i C O K H I V I E T N A M , S d 5 n a m 2 0 1 4 www.cokhivietnam.vn
