A Look-ahead Control Algorithm with Arc Transition for High-speed Machining of Continuous Micro-segments

Transcription

1 Internatonal Journal o Engneerng and Techncal Research (IJETR) ISSN: 3-869, Volume-, Issue-8, August 4 A Loo-ahead Control Algorthm wth Arc Transton or Hgh-speed Machnng o Contnuous Mcro-segments Jun Zhang, Lqang Zhang Abstract To dmnsh the vbraton and shoc produced n NC machnng and realze the hgh-speed smooth transton, a corner transton model based on quadratc NURBS arc ttng or contnuous mcro-segments s establshed. The new nserted arc s everywhere curvature-contnuous, and can realze the corner path smooth transton. Based on the arc model, a loo-ahead control algorthm s proposed. The algorthm amed to obtan optmal transton speed on the condtons o the chord error and machne dynamcs, control acceleraton/deceleraton, avod the motor startng and stoppng requently, and acheve the hgh-speed transer smoothly. The smulaton results demonstrate that the proposed algorthm can attan hgher and more stable transton speed, mprove the machnng ecency, and satsy the requrements o hgh-speed machnng. Index Terms Hgh-speed machnng, smooth transton, arc transton, loo-ahead control algorthm I. INTRODUCTION Hgh-speed and hgh-precson machnng s manly used n machnng a seres o contnuous mcro lne segments whch are dscrete ormed by complex curve surace []. When processng mcro-segments, the tradtonal numercal control (NC) system oten tends to slow down to zero at the transer ponts. NC system requently starts and stops, accelerates and decelerates, so t s not conducve to hgh-speed machnng and s easy to have a great mpact and vbraton to the machne tool, then aects the machnng precson and machnng ecency []. Thereore, smooth transton speed at the corner o adjacent segments has become a ey technology or hgh-speed and hgh-precson NC machnng. In order to overcome ths problem, many scholars mae an ntensve study n recent years. Wang establshed a swtchng eedrate model or mcro-segments, whch based on the lnear acceleraton and deceleraton (Acc/Dec), and mplement the optmal transton eed by settng the pre-dsposal secton [3]. Zhang [4] proposed an assumptve arc transton method to deal wth the eedrate on the corner. Due to the nterpolaton o parametrc curve has the advantages o smooth speed, less data storage, easy to express, the parametrc curve, such as Bezer curve, B-splne and NURBS curve, s appled to Manuscrpt receved Aug 7, 4. Jun Zhang, College o Mechancal Engneerng, Shangha Unversty o Engneerng Scence, Shangha Chna, Lqang Zhang, College o Mechancal Engneerng, Shangha Unversty o Engneerng Scence, Shangha Chna, contnuous lne processng by scholars. Zhang et al. [5] establshed a quntc corner transton curve model, and proposed an nterpolaton algorthm based on the transton o the curve. Nng [6] proposed a quntc polynomal curve to obtan contnuous change o acceleraton and jer. Huang [7] constructed an adjustable orm o the cubc splne between the adjacent segments to realze the smooth speed transton. B [8] nserted a curvature-contnuous o cubc Bezer curve between the adjacent segments to realze the smooth corner transton. Zhao constructed a curvature-contnuous B-splne corner transton model, and proposed a real-tme loo-ahead nterpolaton algorthm [9]. Now most o the NC systems only support lne nterpolaton and arc nterpolaton. The above parametrc curves methods can provde a smooth transton speed, but cannot be wdely appled n the NC systems. Thereore, a corner transton model based on the quadratc NURBS arc ttng or contnuous mcro-segments s establshed n ths paper, whch support both arc nterpolaton and NURBS nterpolaton so that t can be wdely used. The nserted arc s everywhere curvature contnuous, so t can eectvely avod the machne vbraton and shoc caused by the velocty and acceleraton mutaton. Then, a loo-ahead control algorthm s proposed to control Acc/Dec, and realze hgh-speed transton smoothly or contnuous mcro-segments. Fnally, the algorthm s analyzed and vered by the smulaton example. II. CORNER ARC TRANSITION MODEL A. Quadrc NURBS curve The arc can be represented by NURBS curve o Quadrc and hgher []. Hgher order NURBS curves are oten used to t the specal combnaton o curves and suraces, whch need more control vertces and weghts and lead to more computatonal complexty. In order to acltate calculaton, an arc corner model based on the quadratc NURBS ttng s used to realze the smooth transton at the adjacent corner. A pth-degree NURBS s dened by n N, p ( u) P C( u), a u b n N ( u) Where, p P are the control vertces (,,, m () ), s the weghts. The not vector s desgned as 6

2 A Loo-ahead Control Algorthm wth Arc Transton or Hgh-speed Machnng o Contnuous Mcro-segments U { a,, a, up,, um p,b,,b}, where a s set p p to zero and b s equal to one and s greater than zero or all. The N, ( u ) s the th B-splne bass uncton o p pth degree dened on the normalzed not vectoru. The bass unctons N, p( u ) s gven by the Cox-DeBoor recurson ormulas. Speccally,, u u u N, p( u), otherwse u u N, p ( u) N, p( u) u p u up u N, p( u ) u p u set = () B. Constructon o the transton arc ) Quadrc NURBS arc or As shown n gure, the arc Cu ( ) s tted by a quadrc NURBS curve, and used as the corner transton curve between two adjacent processng paths: QQ and QQ. The control ponts are P P and P. The lne PP and PP are respectvely tangent to the arc, and each pont o tangency s P and P. The postve weghts are and cos( / ). The not vector s U {,,,,,}. In ths way, arc s actually tted by the ratonal quadratc Bezer curve whch s the specal case o the quadratc NURBS curve. QO s the angle bsector o QQ Q. B s the mdpont o Cu ( ). ) Angle between adjacent segments In gure, the s the angle between adjacent segment where(, ), Q - Q θ Fg. Quadrc NURBS arc or as: Fg. Angle o adjacent segment Q + Accordng to the ormula o vectoral angle, s dened QQ- QQ+ arccos( ),,, N Q Q Q Q (3) The NURBS arc must satsy ve requrements n practcal applcatons, that s the least number o control ponts, the good parameter, the compact convex hull, and each central angle should not exceed 9. For, the arc should be dvded nto two stages and tted by the NURBS curves. For, arc can be tted by only a sngle NURBS curve. 3) Quadrc NURBS arc or As shown n Fg. 3, By usng the results o the ratonal quadratc Bezer curve, a new not u ( u.5 ) s nserted nto not vector U. Thus the new not vector s U {,,,.5,,,}.As a result, the arc Cu ( ) can be tted by two quadrc NURBS curves. The control ponts s P P P and P 3. The mdpont o arc s B, and the lne PP s tangent to the mdpont o arc. The postve weghts are 3, cos ( / 4). The lne PP and PP 3 respectvely belong to the adjacent machnng path QQ and QQ, and are respectvely tangent to the arc wth each tangent pont: P and P. The length o lne PP s equal to lne PP, 3 and both o them s PP P P P P. hal o PP, that s: 3 6

3 Internatonal Journal o Engneerng and Techncal Research (IJETR) ISSN: 3-869, Volume-, Issue-8, August 4 Q Start Read the data o transer pont Q Input processng parameters: v a T ε ε max,, P B P C(u) P O Q Q P 3 Fg.3 Quadrc NURBS arc or 4) Curvature contnuous Curvature contnuous, that s G contnuty, two contnuous curves at the endpont have the same coordnate, the same tangent vector, and the same center o curvature. Accordng to the ormer two sectons, the arc based on the quadratc NURBS ttng at the jont has the same tangent vector, and the curvature center s the crcle center. Thus, the arc transton curve s everywhere curvature-contnuous, so that t s bale to eectvely avod the machne vbraton and mpact whch s caused by the velocty and acceleraton mutaton, and realze a smooth transton. III. A LOOK-AHEAD CONTROL ALGORITHM FOR ARC TRANSITION When the machne processes the contnuous mcro -segments, eedrate wll mutate at the corner o adjacent mcro-segments. I not to control the speed or advance plannng, t wll lead to the overcut due to beyond the machne lmts o acceleraton/ deceleraton, and then t has a bad eect on the processng qualty. Thereore, n order to adjust the processng speed and mae the acceleraton/deceleraton o processng speed satsy the changes o transton path, so a loo-ahead control uncton need to be added. In ths paper, the loo-ahead control processng manly acheves three unctons: to establsh a corner arc transton model based on the quadratc NURBS ttng, to obtan optmal transton speed under the condtons o the chord error and machne dynamcs, to realze the acceleraton/deceleraton n the processng o the lne and arc. The low chart o loo-ahead control uncton s shown n Fgure 4. A. Machnng error As shown n Fg. 5, ater nsertng transton arc at the adjacent segment, due to the nconsstency o machnng path t leads to machnng error. So t requres the machnng error does not exceed the systematc error. The machnng error manly comes rom two aspects. One s the contour Calculate the adjacent segment angle θ Calculate the mcro-segments length Q Q + I <θ π/ Calculate the control ponts P P P P 3 Judge the angle ranges Quadrc NURBS arc ttng I π/ <θ<π Calculate the control ponts P P P Calculate the transton Speed accordng to Eq. (8), (9), () Judge acceleraton/deceleraton regon o each mcro-segment Acceleraton and deceleraton control uncton End Fg.4 Flow chart o the loo-ahead control uncton error, between the nserted arc and adjacent lnes, another s the chord error, that generated by arc nterpolaton. The contour error, s dened as: L [ sn( / )],, (4) cos( / ) Where L, s the dstance o arc transton, that s, the dstance rom corner pont to transton pont. The dstance o arc transton can be calculated rom the Eq. (4) as: L cos( / ),, (5) sn( / ) The chord error, s gven as ollows: r r ( v T/ ) (6),, Where v, s the machnng velocty under constrant o the chord error. T s the nterpolaton perod. r s the radus o quadrc NURBS arc, and t s derved rom the Eq. (6) as: r sn( / ), (7) sn( / ) (For the convenence o calculaton, n ths paper the contour error and chord error s set to the maxmum error o the machne tool.) 63

4 A Loo-ahead Control Algorthm wth Arc Transton or Hgh-speed Machnng o Contnuous Mcro-segments B. Turnng speed transton speed When the transton arc s processed, the transton speed v s calculated under the lmtaton o chord error and machne dynamcs. Under the lmtaton o contour error, the transton speed s derved rom the Eq. (6) as: v r ( r ) (8),, T Under the constrant o machne dynamc, a constant speed o the arc transton method s proposed, so only the normal acceleraton has an eect on the transton speed. Thus, the transton speed s dened as: v a r (9), max Where a max s the maxmum acceleraton o machne tool. The transton speed v can not only satsy the prescrbed tolerance o chord error and machne dynamcs, but also can t exceed the machne program speed v. Thereore, the transton speed must be the mnmum among the three veloctes, whch s dened as: v mn( v, v, v ) (),, Q L, θ ε, L, L 3, O ε, L,+ L,+ r Q + Q L,+ Transton arco, Transton dstance L,, Deceleraton dstance L,, Acceleraton dstance L,, Unorm dstance L 3, error,, Chord error, Fg.5 The arc transton path C. Arc transton speed smoothng, Arc radus r, Contour Due to the nconsstency o programmng speed and arc transton speed durng processng segment, t s necessary to adjust the machnng velocty or Acc/Dec. v, v, Accordng to the arc transton speed programmng speed v, and the length o each mcro-segment QQ, there are seven acceleraton/deceleraton modes to consder, that s: only the acceleraton perod, only deceleraton perod, both acceleraton perod and deceleraton perod, all the acceleraton perod and unorm perod and deceleraton perod, both the acceleraton perod and unorm perod, both the unorm perod and deceleraton perod, only the unorm perod. As shown n Fg. 5, Only the acceleraton perod, v v v, the machnng path s gven as ollows: L L L Q Q L3, L,,,, Only deceleraton perod, v v v, the machnng path s gven as ollows: L L L Q Q L, L3,,,, 3 Both acceleraton perod and deceleraton perod, max( v, v ) v,the machnng path s gven as ollows : L L L L Q Q L3,,,,, 4 All the acceleraton perod and unorm perod and deceleraton perod, max( v, v ) v, the machnng path s gven as ollows: L, L, L, L, QQ 5 Both the acceleraton perod and unorm perod, v v v, the machnng path s gven as ollows: L L L Q Q L,,,, 6 Both the unorm perod and deceleraton perod, v v v, the machnng path s gven as ollows: L, L3, L, L, QQ L, v v v, the 7 Only the unorm perod, machnng path s gven as ollows: L L Q Q L, L,,, Thus, the machnng acceleraton/deceleraton perod or every mcro-segment s judged through the transton speed and the length o each mcro-segment. Then, the acceleraton/deceleraton methods provded by reerences [3, 4] can be used to realze the smooth speed. 64

5 Y-axs (mm) Feedrate (mm/s) Machnng error (mm) IV. SIMULATION AND VALIDATION In order to very the correctness and easblty o the proposed algorthm, a path segment s establshed or machnng comparson, as shown n Fg.6. The NC machnng parameters are: The maxmal machnng speed s v mm/s, the maxmal acceleraton s amax 3 mm/s, and the nterpolaton perod s T=ms, the maxmal contour error s,, =.mm, =.5mm, the maxmal chord error s In ths paper, the smulaton s perormed by usng MATLAB sotware. Based on the lnear Acc/Dec method, the comparson o machnng error chart s shown n Fg. 7 and the speed curve contrast gure Fg.8 can be obtaned on account o the quadrc NURBS arc transton algorthm and drectly transton method respectvely. As shown n Fg.6, the nserted arc maes the transton corner path smoother, avods processng corner drectly, can greatly lessen the machne tool vbraton and mpact rom machnng corner, and mproves product qualty o the parts and tool le. Internatonal Journal o Engneerng and Techncal Research (IJETR) ISSN: 3-869, Volume-, Issue-8, August 4 The orgnal lnear path The quadrc NURBS arc transton path acceleraton/deceleraton eectvely, and acheve more stable transton and hgher machnng productvty. Machnng error o proposed algorthm Machnng error o lnear method Machnng path (mm) Fg.7 Machnng error comparson Velocty curve o drectly transton method Speed curve o the proposed transton algorthm X-axs (mm) Fg.6 The transton path comparson It must produce the contour error between the nserted arc and the orgnal lnear toolpath. However, accordng to Fg. 7, the results analyss show that: The machnng error o the proposed algorthm can be controlled under the lmt range o the maxmal programmng error, so the algorthm does well n valdty and can meet the precson requrements o processng worpeces. From Fg. 8, t s seen that the tme used or machnng the transton arc paths are.34s, whle those or the orgnal lnear paths are o.39s. Thus, the loo-ahead control algorthm proposed n ths paper can mprove the machnng ecency sgncantly. Furthermore, the arc transton speed and the average velocty or usng the proposed scheme are aster and smoother. Thereore, the proposed loo-ahead control scheme can meet the requrements o hgh speed and hgh accuracy. Especally, when9 8, the larger the angle s, the aster transton speed s. For example, the transton velocty s the maxmal machnng speed wth mm/s at Q (Fg.6), thus t can avod the requent Tme (s) Fg.8 Machnng speed comparson V. CONCLUSION In ths paper, a corner transton model based on the quadratc NURBS arc ttng or contnuous mcro-segments s establshed. The model s everywhere curvature contnuous, can decrease the speed luctuaton and the machne tool sgncantly, and realze the smooth transton. Meanwhle, t can be nterpolated by the arc nterpolaton, whch can be wdely used n NC manuacturng. Then, accordng to the arc corner transton model, a loo-ahead control algorthm s proposed to acheve acceleraton/deceleraton control. Under the restrcton o the machnng error and machne dynamcs, the algorthm can obtan optmal transton speed, and attan the acceleraton/deceleraton control. Furthermore, t can avod startng/stoppng motor requently, realze hgh-speed smooth machnng o contnuous mcro-segments, and mprove the qualty and ecency o machnng sgncantly. The smulaton results demonstrate that, compared wth 65

6 A Loo-ahead Control Algorthm wth Arc Transton or Hgh-speed Machnng o Contnuous Mcro-segments tradtonal algorthms, the proposed algorthm s smple and practcal, can acheve the transton speed hgher and more stable at adjacent segment, can mprove the machnng speed greatly, and satsy the demands o hgh speed machnng. ACKNOWLEDGMENT The authors wsh to than the helpul comments and suggestons rom my teachers and colleagues n College o Mechancal Engneerng. The research s sponsored by the project supported by hgh level cultvaton project o shangha unversty o engneerng scence (No. gp). REFERENCES [] Q.L.Zhong, J.LI, S.H.Huang, Interpolaton o the mcro-lne at hgh contnuum speed wth hgh accuracy n RP system, J Huazhong Unv o Sc & Tech,, 8(3): [] J.Hu, L.J.Xao, Y.H.Wang, et al, An optmal eedrate model and soluton algorthm or hgh speed machne o small lne blocs wth loo-ahead, Internatonal Journal o Advanced Manuacturng Technology, 6, 8(9): [3] Y.H.Wang, L.J.Xao, Sh.Sh.Zeng, Z.Y.Wu, Sh.B.Zhong,et, An optonal eedrate model and soluton or hgh-speed machnng o small lne blocs wth loo-ahead, Journal o Shangha Jaotong Unversty, 4, 38(6): [4] D.L.Zhang, L.S.Zhou, Adaptve algorthm or eedrate smoothng o hgh speed machnng, Acta Aeronautca et Astronautca Snca, 6,7(): 5-3. [5] X.H.Zhang, D.Yu, D.Sh.Yang, Y.Hu, W.Y.Han, Corner curve transton nterpolaton algorthm or hgh speed machnng o mcro-lne segment, Journal o mechancal engneerng,, 46(9): [6] P.Z.Nng, Q.Z.B, Y.H.Wang, J.Sh, A hgh-lexble acc/dec loo-ahead algorthm based on quntc polynomal ederate curve, Modular machne tool & Automatc manuacturng technque, 4, 4(4): 5-8. [7] J.Huang, A.P.Song, J.M.Tao, W.ZH.Yn, Smoothng transer or the corner o adjacent NC processng segment, Journal o Shangha Jaotong Unversty, 3, 47(5): [8] Q.Z.B, Y.Q.Jn, Y.H.Wang, An analytcal curvature-contnuous Bézer transton algorthm or a lnear tool path, Internatonal Journal o Machne Tools & Manuacture, 57(): [9] H.Zhao, L.M.Zhu, H.Dng, A real-tme loo-ahead nterpolaton methodology wth curvature-contnuous B-splne transton scheme or CNC machnng o shortlne segments, Internatonal Journal o Machne Tools & Manuacture, 65(3): [] F.Zh.Sh, Computer-Aded Geometrc Desgn and NURBS, Bejng: Hgher Educaton Press, 3(n Chnese). Jun Zhang receved hs BS degree rom Changchun Insttute o Technology n, Chna. He s currently a master student o mechancal engneerng n Shangha Unversty o Engneerng Scence. Hs research nterests nclude CAD/CAM/CNC, manuacturng automaton and control. Lqang Zhang receved hs PhD rom Shangha Jaotong Unversty n 8, MS degree rom Qngdao Technologcal Unversty and BS degree rom Shandong Unversty, Chna. He s currently an assocate proessor o mechancal engneerng n Shangha Unversty o Engneerng Scence. Hs research nterests nclude CAD/CAM/CNC, manuacturng automaton and control. 66