XJSIJ A N H HU'dNG C O A LIJC CAT DEN CAC TINH C H A T
C O A H E DAN DONG TRUC CHINH MAY TIEN CNC
INFLUENCE OF CUTTING FORCES ON THE PROPERTIES OF THE DRIVE SPINDLE OF CNC TURNING MACHINE
TSKH. Pham Dinh Timg', KS. Nguyin Ngpc Nam^
'Hpc viln Ky thuat Quan sU
^TrUdng Dai hpe Himg VUdng
T O M TAT
Bdi bdo nghien cdu sU dnh hUdng cua lUc cat din cdc tinh chdt cua ddng cd ddn ddng true chinh. Cdc kit qud nghien cdu dd chi ra rdng quan he gida cong sudt cua dgng ed vd cong sudt cdt dnh hudng mgt cdch nguyen tdc din cdc tinh chdt dgng cua dgng ed. Ngodi ra, do hiiu dng tdphia qud trinh cdt diem cdn bdng cua hi co mien hut gidi han.
TH khda: He ddn dgng, lUc cdt, diem cdn bang, on dinh, mien hut.
ABSTRACT
The paper studied the influence of cutting forces on the properties of the motor spindle drive.
It is shown that the ratio of the power of the servo motor and the power cutting have an principle influence on the change of the dynamic properties of the motor. In addition, the equilibrium point is of limited region of attraction on account of reaction from the cutting process.
Keywords: Dynamic cutting system, equilibrium point, stability, attraction region.
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I.DATVANDE
HI dan ddng cac ed cau edng tac la mdt trong nhiing bd phan quan trpng eua may CNC, nd thUe hien chuyen ddng tao hinh cua chi tiet tUdng Ung vdi chUdng trinh dieu khien eho trUdc. Dp chinh xac chuyen dich cac cd cau cdng tac la mdt trong cac yeu td chinh anh hudng den dp ehinh xac gia cdng chi tilt.
Dam bao va nang dp dp chinh xac ehuyen dpng cua cac ca cau cdng tac dupe thUc hiln bang nhieu phUdng phap khac nhau: PhUdng phap cau true, nhU cai tien phan cd khi tU ddng cd den cd cau cdng tac sao eho giam thieu tdi da cac khau biln ddi, sU dung ddng cd tuyin tinh trong vai trd he dan ddng;... PhUdng phap dieu khiln, nhu xay dUng cae he he dieu khien so, dieu khien thich nghi, Ung dung tri tue nhan tao, nhu mang ndron, logic md d l dilu khien he dan ddng [1-3].
Cho dd da dat dUpc nhilu thanh tUu trong van de dilu khien dp chlnh xac he dan ddng ed cau cdng tac. Sdng trong hau hit cae nghien eUu, klii phan tich va tong hpp dieu khiln he dSn ddng may CNC, lUe cat dUdc eoi la ngoai lUe tac dung lln ddng cd, ma khdng tinh den quy luat eua lUe cat, nhU ham npi lUc.
Trong bai bao nay trinh bay cac ket qua nghiin cUu v l sil anh hUdng ciia lUc cat den eac tinh chat ddng cua he d i n ddng true chinh.
2. MO HINH TOAN HOC CUA HE DAN D O N G TRUC CHfNH
Khdng mat tinh tdng quat, chung ta gidi han xet trUdng hdp he dan ddng true chinh sif dung ddng cd dien mpt ehieu kieh tii dde lap, dieu khien bang diln ap phan Ung. Phan ifng eua ddng cd dUdc ndi cdng vdi true chinh (hinh 1). Khi dd phUdng trinh ddng lilc hpc eua he dan ddng.
' "" dt" " dt "
Trong dd: k^ = 1/C^: H I so truyin cua ddng cd thed tin h i l u dilu khiln, [1/ (V.s)j;
k ' = R/{C^,C^):HI sd truyin cua ddng cd theo tai trpng tif phia qua trinh eat, [1/ (s.N.m)];
U^(t)^[T^ ^ ^ ^ + M(t)], thanh phan dUpc ' dt
tad thanh bdi md men can chuyen ddng quay . rotor, [Nlm];T„ J-R
-,tUdng Ung la cac hang sd diln-cd, hang s6 diln cua ddng ed, chiing cd ddn vi la [s];J: Md men quan tinh eua ddng cd, [kg.m^];R, L diln trd va dp tu cam eua mach phan ufng, [ H ], [H];
C^,C^: Cac tham sd cua ddng cd, cd ddn vi lan lupt la, [ F - s ] , [ ] ;£y: Toe dp quay eua
A
true chinh [ s"' ]; U : D i l n ap dilu khiln, [V].
De lam rd toan bd phUdng trinh (1) trUde tiln can lam rd md men can ehuyen dpng quay ciia ddng caM(t). Md men nay cd the tach thanh hai thanh phan: Thanh phan can chuyen ddng quay khi khdng eat M , (t) va thanh phan dUdc tao thanh do lUc cat M^ (t), nghia la M{t) = M , (?) + M^ (t). Quy luat thay doi cua M , (t) dUdc xae dinh bdi eae dac diem cau triic ciia cum true chinh va cac tinh chat cua bp phan 6 bi. Cac quy luat nay chiing ta da bilt, cd the lam quen trdng [4]. Trong nghien eiiu nay chiing ta gia sif M , (t) = M , „ = const.
Cd nghia la cau true cua true ehinh va cac bp phan cua nd la ly tUdng. Ddi vdi thanh phan
M j {t), ed hai yeu td e h i n h tao t h a n h t h a n h
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phan md menM^{t): Md men cat, md men dupe tad bdi sU thay ddi cua lUc ma sat trdng cae bd phan 6 bi do sil thay ddi cua lUc cat.
Tnidng hdp gia cdng vdi dUdng kinh phdi i?*^* =constva he sd hiln d d i ^ , m d dun lilc cat vao lUc ma sat (tUdng tU he sd ma sat) la hang sd (phin tich sil bien doi nay dUpc trinh bay ky trong [4]). Khi dd,
M,{t) = R""F,+k,4{F,f +{F,f +{F,f (2)
dUdc mpt vdng, \s\ ,V ^ - tdc dp tiln dao, [mm/s];
b=t^l sin (p - chieu rdng ldp cat; a = f^- sin <p - ehieu day ldp cat; (p: Gde nghiing ehinh. 2.
Hudng cua lUe trong khdng gian khdng hi thay daiF = Fa{x^,X2,X3Y' trong d d j , : HI sd dinh hudng lue trong khdng gian.
Vdi muc dich Iam rd sU anh hUdng ciia lUc eat den tinh chat ciia he dan ddng. Vi vay, chiing ta gia sit ed t h i b d qua bien dang dan hdi cua dao va phdi. Khi do, md dun lUc cat dUde xac dinh:
(3) 0}
BChi dd, md men can chuyen dpng quay cua rotor cd dang:
M{t) = M,„+M,i,l) = M,^ + (f!,Z,+k,)>Tl,-V, (4) Hinh 1: Sd do tao thdnh md men cdn chuyen ddng
quay cua true ehinh
Trong dd, F, - thanh phan lilc cat theo hudng van tdc cat; F ^ : Thanh phan lUc eat theo hudng vudng gde vdi true quay phdi; F^: Thanh phan lUe cat theo hudng tiep tuyin (song song) vdi true quay phdi.
De lam rd quy luat cua lUe eat, chiing ta sif dung cac gia thilt sau [5]. 1. Md dun lilc cat ti 11 vdi d i l n tieh ldp cat, nghia la:
F^=a-S, trong d d c r : he sd dac trUng cho ap life eua phoi l l n mat trUdc cua dao,N/mm^
,S = a-b=t • f^- d i l n tich ldp eat,[mm^],?^
- chieu sau cat,[mm],/e = \Kd^^- lifdng tien i-r
, „ 2;r , , , k . . dao, [mm/vong], 1 = thdi gian phoi quay — +6) = U^
PhUdng trinh (1) ed tinh den (4), cd dang:
TT'^^T : t + * f i - i ^ V « = t , [ / - * > , . (5) df dt {<a of dt )
Trong dd:
Phddng trinh (5) khac phUdng trinh chuyin ddng cua ddng ca diln mdt chilu [6-71, tnidc tiln, bdi sU xuat hiln hai thanh phan phi tuyin.
Gia sii rang, hieu diln the phan iSng la dai lupng khdng ddi, va cho trUdc, nghia la U = const, nd tUdng iing vdi gia tri xac lap tan sd quay cua ddng cd. Trang thai xac lap ciia (5) dupe xac dinh bdi phUdng trinh:
(6)q
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Trong dd, U^ = kJJ - k'^M^^.
Nghiim eiia (6) xac dinh eac gia tri xae lap tin sd quay cda ddng cd:
(7) 2
TU (7) ehiing ta thay rang, dUdi dieu kien {C/„,) < 4k^_ trong he (5) khdng tdn tai dieu khien, bdi vi dieu khien tupng Ung vdi gia tri thUe tde dp quay cua ddng cd. Dudi dieu kiln (t/^,) > 4k^, thi mdt gia tri hieu dien t h l phan Ung tUdng ilng vdi hai diem cin bang (hai gia tri tan sd quay ciia ddng cd), edn dUdi dil'u kien(f/^) = 4k^, thi he (5) cd duy nhat mdt diem cin bang. NhU viy, neu ta thay ddi diln ap dieu khien U thi ehung ta se n h i n dUde sd do chuyen dich vi tri can bang cua he nhU trin hinh 2. Khdng khd khan de chUng minh, nhanh tren tUdng Ung vdi cae diem can bang on dinh (vi du, tan sd o;^'' tren hinh 2). Nhanh dudi tUdng Ung vdi cae diem can bang khdng dn dinh (vi du, tan sdc;^*' t r i n hinh 2).
De phan tich tmh dn dinh eua he, theo Lyapunov [8] can phai nghien ciiu phUdng trinh tuyen tinh hda trdng lan can diem cin bang. Chiing ta xem xlt he (5) trong lin can d i l m c i n bang. Sau khi thay a){t) = 0)^+ Cl(t), va tuyin tinh hda, chung ta n h i n dupci
(8) Tinh dn dinh cua he (8) phu thude vao
dau eua bilu thde: | 1 ^ | . Ta ed
Trong (9) mau so ludn dUPng. Vi vay, dau (9) dupc xac dinh bang dau eiia tif sd. Trong bilu thUe tU sd d hai nhanh quy dao chuyen dich diem can bang, thanh phan(C^^)^ ~^^m ^^
Hinh 2: Sd do chuyin dich diem cdn bdng he ddn dgng true chinh tiiy thudc vdo hieu dim the phdn dng dudi cdc gid tri khdc nhau cua hisd k .
ludn dUdng. Vi vay: 1 ^ > 0 , vdi r- . L i<^0) J dilu ]den4{UJ^-4k^+U^, tUdng dng vdi nhanh tren ciia quy dao (hinh 2). Neu
rang tUdng ifng vdi V(^J'-4^™-C^™>
nhanh dudi ciia quy dao, dli 1 =i— < 0 NhU viy, nhanh dUdi tUdng ifng vdi sU e i n bang khdng on dinh.
3. THAO L U A N CAC KET QUA MO PHONG s 6 Chiing ta xem xet vi du cu the ddi vdi he dan dpng true chinh sif dung ddng ca d i l n mdt
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chilu kich thich dde lap va dUdc dieu khiln bang hieu dien the phan Ung. Cac tham sd cua ddng cp:r^ ^ 0 . 3 6 4 , 5 , r „ = 0 . 0 4 8 2 , 5 ,
, N-m M,,
^0.68,- - 0 ,
>C, = 0 . 6 8 , F - 5 . ^ . - 2 0 0 0 0
De nghien cUu he (5) chung ta hien thilc nd trong mdi trUdng matlab-simulink.
Vi du, chin dung pha cua he dUdc dUa ra trin hinh 3. Chung ta thay rang, he cd hai diem can bang O^ va O^ diem c i n bang thU nhat khdng on dinh, cdn diem thd hai la dn dinh. Ngoai ra, mdt nhanh cua dUdng phan each dac tnfng cho attractor (mien hiit).
Chung ta phan tich cac kit qua nhan dupc:
1) Cac tinh chat ddng cua ddng ca d i l n mdt ehieu cd the bi thay doi Idn do phan iing tif phia qua trinh cat.
2) Su anh hUdng cua qua trinh cat d i n cac tinh chat ddng cua he d i n ddng true ehinh phu thudc vao cac tham sd eiia qua trinh cat, eiing nhU eae tham sd eiia ddng ca. Dac trUng la, sU xuat h i l n tinh phi tuyen eua he tang l l n theo mdc dd giam cdng suat eua ddng ca so vdi edng suat ciia qua trinh cat. Ngoai ra, ddi vdi diem can bang dn dinh t i l m can tdn tai mien hut gidi han.
3) Su tdn tai dilm cin bang khdng dn dinh se mau t h u i n vdi cac khai niem thUc ve eac tinh chat dpng cd dien. Song, can phai tmh den yen td: Diln tieh ldp cat tang nhanh theo mUc dp giam van tdc cat khi khdng thay ddi tdc dp tien dao. Kit qua la, md men can chuyin dpng quay ciia dpng ca tang nhanh va khdng ti II. Khi edng suit eua ddng cd khdng dam bao, gia tri cdng suit can cd the vUpt qua gia tri cdng suat ddng cd. D i y la mpt trong eae ca che giy ra hien tUdng ket dao.
4. KET LUAN
Cac tinh chat dpng cua ddng ed ciia cac cd eau chap hanh ciia may cat gpt bi thay ddi do anh hUdng ciia qua trinh cat (lUc eat). Trong trUdng hdp nay, lUc cat dUdc bilu dien trong tpa dp trang thai he. Quan he giUa edng suit dpng ca va cdng suat qua trinh cat anh hUdng mpt each nguyin tac den cac tinh chat ddng ciia dpng ca. N i u cdng suat cua ddng cd ldn hdn nhilu cdng suat qua trinh eat, thi sU anh hudng ciia lilc cat cd the bd qua. Trong trUdng hpp ngUdc lai, he dpng lUe hpc, vi du, eua he dan dpng true chinh la phi tuyen manh. Dudi cac c h i dp cat xac dinh, tiiy thupc vao diln ap phan ifng ciia ddng cd ed the tdn tai hai diem can bang, mdt trong sd do la khdng on dinh.
Ngoai ra, diem can bang dn dinh ed mien hut gidi ban.•>
Hinh 3: Chan dungpha cua he
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Ngay n h i n bai: 25/8/2014 Ng^y phan biln: 17/9/2014
Tid lilu tham khao:
[1]. Ren Tong, Using Genetic Algorithms and Fuzzy Control for Spindle of CNC Machine Tool. Pro- ceedling of the 2004 International Conference on Intellgent Mechtronics and Automation Chengdu, China August (2004).
[21. Faa-Jeng Lin, Rong-Jong Wai, Adaptive Fuzzy-Neural-Network Control for Induction Spindle Motor Drive, IEEE Transaction on Energy Conversion, Vol.17, No.4, December (2002).
[3]. M. Liang, T. Yeap, S. Rahmati, A. Hermansyah, Fuzzy control of spindle torque for industrial CNC machining. International Journal of Machine Tool & Manufacture 43 (2003) 1497-1508.
[4]. Zakovorotny V.L. Dynamics tribosystems. Self-organization, evolution. Rostov on Don 2003 (in ru- sian).
[51. Zakovorotoy V.L, Lukyanov A.D, Nguyen Dong Anh, Pham Dinh Tung. Synergistic system synthesis of controlled dynamics of machine tools, taking into account the evolution of coupling Rostov on Don (2008).
[61. Klyuchev V.L The theory of the drive. M. Energoatomizdat,1985.(in russian).
[7]. Ivanov - Smolensky V.A. Electrical machines. M. Edition of "Energy". 1980 (in russian).
[8]. Kim D.P. Theory of automatic control. Lmear systems. M. Fizmatlit, 2007 (in russian).
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