Five-axis NURBS Path Real-time Generation Method in CNC System
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1 Five-ais URBS Path Real-time Geeratio Metho i CC Sstem Che Liagji, Gao Chagi, Feg Xiazhag Five-ais URBS Path Real-time Geeratio Metho i CC Sstem Che Liagji, Gao Chagi, Feg Xiazhag Zhegzho Istitte of Aeroatical Istr Maagemet chejiaiclj@63.com, chagigao@zzia.e.c, phfz@zzia.e.c oi:.456/ijact.vol2.isse3.6 Abstract A real-time path geeratio metho with o Uiform Ratioal B Splie(URBS techolog i the Compter Aie Desig(CAD fiel is presete a realize i a five-ais Compter mericall Cotrolle(CC sstem. I this metho, the tool path was represete ito two URBS crves, tooltip a tool-orietatio splie crve, base o the same ot vector. The Ctter Locatio(CL ata was firstl calclate a the trasforme to five motio commas of five aes of machie tool throgh the real-time post-processio algorithm. The acceleratio/eceleratio cotrollig metho was also presete to avoi the impact of machie tool. The propose five-ais splie iterpolatio metho is realize i or evelopig five-ais CC machie tool a the reslt of machiig shows that the metho is feasible.. Itroctio Kewors: CC,Five-ais machiig, URBS, Path geeratio Comple parts sch as aeroatical trbie blaes, impellors, ies, mols are machie o five-ais Compter merical Cotrolle (CC machies. The core of the machies is the cotor cotrollig sstem which ecies machiig efficiec a accrac of a part. However, the crret five-ais CC sstem mostl provie ol lie iterpolators, that is, tool motio alog straight lies is spporte. To machie a srface, the tool paths, which are also ow as the ctter locatio (CL paths, are tpicall approimate with piecewise liear segmets b CAD/CAM sstems. The approimatel machiig metho has its ow rawbacs i avacig efficiec a accrac of a machie part. To overcome the isavatages, it mst be tae ito accot that the five-ais cotrol sstem has itelliget abilit to geerate the tool paths of the machie srfaces. o-uiform Ratioal B-Splie (URBS, as the ol staar of ata-echage of proct sactioe b ISO, has bee mostl se i almost all CAD/CAM sstems to escribe wor-piece s srface. Base o the realit, the CC sstem shol be provie with the abilit to irectl geerate five-ais URBS crves or srfaces i real-time. Some URBS iterpolatio methos ha bee propose b several ivestigators[-6]. Cheg et al.[2] ha propose a real-time URBS crve motio comma geerator for CC machies. Zhimig et al.[5] evelope a URBS crve iterpolator for CC machiig base o the geometric properties of the tool path. However, most of them ha cocetrate their attetios o 3-ais ball-e machiig, bt for five-ais URBS srface iterpolator, little has bee oe. Whe evelopig a realizig a five-ais CC sstem with fctio of URBS iterpolatio, relate st mst be carrie ot. I this paper, a real-time five-ais URBS crve geeratio metho is give. 2. URBS Crve Represetatio A p-egree URBS crve with parameter ca be efie as follows: C ( [ ( ( ( ] T i z i ( W P i i ( W i ( 64
2 Iteratioal joral of Avacemets i Comptig Techolog Volme 2, mber 3, Agst, 2 where P i is the i th 3-D cotrol poit; W i is the correspoig weight factor of P i ; (+ is the mber of cotrol poits; i,p (, B-splie basis fctio with egree of p, ca be calclate b the followig formla: ( i < i+ i, ( otherwise i i+ p+ (2 ( ( + i+, p ( i+ p i i+ p+ i+ (prescribe [,..., + + ] is the ot vector. More iformatio abot URBS ca be fo i [7]. where i i p 3. URBS Path Real-time Geeratio Metho The tas of real-time URBS splie iterpolatio is to calclate et iterpolatio perio s CL ata that iclig tool-tip locatio cooriatio a tool-ais orietatio a the trasfer the CL ata ito machie tool s motio commas sch as X,Y,Z,A,C throgh post-processio. 3.. Real-time Calclatio of CL Data As show i Figre, C ( a C ( is the ctter ceter poit splie a the orietatio splie, respectivel. The two splies are costrcte i the same ot vector. Assme that parameter is fctio of time t, that is, (t. B sig Talor s epasio of the parameter with respect to time t to obtai the first orer approimatio iterpolatio algorithm, the first orer approimatio p to the first erivatives is + + T s t t (3 t z C ( C ( C ( T + - e + T + C ( Figre. Priciple of five-ais URBS Iterpolatio + C ( + C ( + where T s is iterpolatio perio, a + are correspoig parameters of crret a et time t a t +. The feerate of tool-tip poit alog C ( is efie b Sice the crve spee V ( C( t C( t (4 65
3 Five-ais URBS Path Real-time Geeratio Metho i CC Sstem Che Liagji, Gao Chagi, Feg Xiazhag V ( The first erivative of with t is obtaie as t t t C ( t V ( C ( Therefore, the first-orer iterpolatio algorithm is obtaie b sbstittig Eq.(4 ito (5, (5 ca be processe as follows: + + The first a seco erivative of C ( with C( i i TV s ( C ( is obtaie as ( W ip i ( W i ( W ip i i i 2 ( W where the geeral algorithm for st orer erivative of i,p ( is C ( a ( + + ( i i i+, p p i+ p i i+ p i+ ( W i ( ( + ito C ( a ( C are obtaie b sbstittig the calclate Sppose the tool-ais it vector is + T +, so 3.2. Real-time Post-processio of CL Data C ( C ( C ( C ( T (5 (6 (7 (8 (9 C. B ow, we have the followig CL ata: C ( + (o, o,o z T + (t, t,t z For five-ais machie of table tiltig/rotatig tpe (Figre 2., the followig post-processio metho is presete to trasfer the CL ata ito the machie s motio commas i real-time. (a if t t, t, the (b else if (c else if ( else t, t t, t z,the,the A,C A arcsi( t, C A arcsi( t, C π /2 ( 66
4 Iteratioal joral of Avacemets i Comptig Techolog Volme 2, mber 3, Agst, 2 A arccos( t z arccos( t / si A t > C 2π arccos( t / si A t < Z C A X Y Figre 2. A Tpe of five-ais Machie with Tiltig/rotatig Table For the calclatios of the three traslatio cooriatio, the Cramer rle is se here. b c a b c X 2 b2 c2 a2 b2 c2 3 b3 c3 a3 b3 c3 a c a b c Y a2 2 c2 a2 b2 c2 a3 3 c3 a3 b3 c3 a b a b c Z a2 b2 2 a2 b2 c2 a3 b3 3 a3 b3 c3 where a cosc b cos A si C c t o ( l+ l2 t ( a2 si C b2 cos A cos C c2 t 2 o ( l+ l2 t a3 b3 si A c3 tz 3 oz + l2 ( l+ l2 tz I Eq.(, l a l 2 represet vertical istaces of tool-tip poit a itersectio poit of A a C ais to rotatio table. 4. Acceleraio /Deceleratio Cotrollig Metho Assme that the acceleratio a eceleratio is a a the estiatio feerate is v as show i Figre 3. V v a -a t Figre 3. Moel of liear acceleratio/eceleratio S D 67
5 Five-ais URBS Path Real-time Geeratio Metho i CC Sstem Che Liagji, Gao Chagi, Feg Xiazhag For the acceleratio process, the followig metho ca be se V ( at For the acceleratio process, the e problem to be solve is evalatio of eceleratio poit. I Figre 3, S D, istace of eceleratio, ca be calclate as follows S D v 2 ( 2a The istace of eceleratio, which is also the legth betwee eceleratio poit a estiatio poit alog the splie crve, ca be calclate as follows C ( S D (2 D where D is correspoig parameter of the eceleratio poit. The followig ewto-rapso metho is se to calclate D. If f( C( S (3 D The we have the followig reslt: f( D f( Assme that the iitial vale of D is, that is, -S D,the we have the followig eqatio i+ i f( i/ f ( i i (4 where i is a iteger. Eq.(4 ca be eqivalet to the followig formla f( i i + i C( i i (5 f( i i Eqs.(4 a (5 ca be obtaie sig Simpso itegral metho. 5. Realizatio i Five-ais CC Sstem The propose five-ais URBS iterpolatio metho has bee realize i the evelopig five-ais CC sstem. The tpe of the five-ais machie is table tiltig/rotatig. Figre 4 shows that the CC sstem is cotrollig cttig tool alog a URBS crve path to machie a impeller. a machiig process 68
6 Iteratioal joral of Avacemets i Comptig Techolog Volme 2, mber 3, Agst, 2 6. Coclsios b machiig reslt Figre 4. Five-ais URBS Path Geeratio O the basis of aalzig the efects of the eistig five-ais liear iterpolatio metho se i the machiig of sclptre srface, five-ais URBS iterpolatio metho with ACC/DEC cotrollig is presete a realize i a CC sstem. Differece from iscretizatio machiig metho of the fiveais liear iterpolatio, the propose metho irectl iterpolates a crve o a free-form srface. Coseqetl, the mber of the C coe for the same machiig path ca be greatl ecrease a machiig efficiec a accrac is also avace. 7. Acowlegmets This research is wholl spporte b the atioal atral Sciece Foatio of Chia (o throgh Zhegzho Istitte of Aeroatical Istr Maagemet. The athors tha for their spport for this research. 8. Refereces [] M. Tiho, et al, URBS iterpolator for costat material removal rate i ope C machie tools, Iteratioal Joral of Machie Tools & Mafactre, vol.44, pp , 24. [2] M. Cheg, M. Tsai, a J. Ko, Real-time URBS comma geerators for CC servo cotrollers, Iteratioal Joral of Machie Tools & Mafactre, vol. 42, pp. 8-83, 22. [3] G. Qii, R. Zhag, a B.Greewa, Developmet a implemetatio of a URBS crve motio iterpolator, Robotics a Compter-Itegrate Mafactrig, vol.4, pp.27-36, 998. [4] M. Tsai, C. Cheg, a M. Cheg, A real-time URBS srface iterpolator for precisio threeais CC machiig, Iteratioal Joral of Machie Tools & Mafactre, vol.43, pp ,23. [5] X. Zhimig, C. Jicheg, a F. Zhegji, Performace evalatio of a real-time iterpolatio algorithm for URBS crves, Iteratioal Joral of Avace Mafactrig Techolog, vol.2, pp , 22. [6] B. Bahr, X. Xiao, a K. Krisha, A real-time scheme of cbic parametric crve iterpolatios for CC sstems, Compters i Istr, vol. 45, pp , 2. [7] L. Piegl, O URBS: a srve, IEEE Compter Graphics & Applicatio, vol., o., pp. 55-7,
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