A High-Speed Machining Algorithm For Continuous Corners

Transcription

1 IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE) e-issn: ,p-ISSN: X, Volume 15, Issue 5 Ver. III (Sep. - Oc. 018), PP A High-Speed Machining Algorihm For Coninuous Corners Wang Yong 1,Zhangliqiang 1 1 (School of Mechanical Engineering, Shanghai Universiy of Engineering Science, China) Corresponding Auhor: Wang Yong Absrac: In order o mee he requiremens of high-speed machining of coninuous small line segmens, he mid-poin consrain algorihm is proposed based on he kinemaic smoohing algorihm based on jounce consrained acceleraion for he overlap of corner ransiion conours caused by he shor disance beween adjacen corners. By limiing he lengh of he corner ransiion secion o avoid he occurrence of conour overlap, he opimal corner ransfer speed is solved under he premise of fully uilizing he performance of he driver, and he corner smooh ransiion is realized. By comparing and analyzing he radiional poin-o-poin inerpolaion algorihm, he processing ime of he proposed algorihm is reduced by 6.8%, he processing efficiency is obviously improved, and he acceleraion curve saisfies G1 coninuous. Keyword: High-speed machining;jounce;corner smooh Dae of Submission: Dae of accepance: I. Inroducion In high-speed machining of complex surfaces, CAD/CAM is ofen used o discreize complex surfaces ino a series of consecuive iny segmens based on consrains such as olerances and machine dynamics. However, in his process, he smooh ransiion beween small and coninuous line segmens is no fully considered, resuling in frequen sar and sop of he sysem, which has a grea impac on he machine ool, and i is difficul o ensure he processing qualiy and processing efficiency [1]. In recen years, some research scholars have made improvemens o early linear inerpolaion and circular inerpolaion [][3][4]. Also well developed are various spline inerpolaion mehods ha use high-order spline inerpolaion o smooh sharp corners in he machining pah, allowing he machine o achieve coninuous uninerruped feed moion a he corners of he machining pah. Common splines include: PH, Bezier and NURBS curves [5-7].In addiion, some scholars have explored he global corner smoohing from he perspecive of kinemaics. The lieraure [8] and [9] proposed a corner smoohing mehod for high-speed machining based on he jump consrain. The lieraure [10] furher proposes a jump-based approach. Degree consrained kinemaic smoohing algorihm. Alhough he radiional poin-o-poin direc inerpolaion mehod can avoid his phenomenon, he feed moion mus be deceleraed o sop a he corner of he pah. Oherwise, he acceleraion value or he jump value of he drive may exceed he sysem limi, resuling in smooh surface of he machined par. Reference [9] uses he parameer consrain mehod o limi he feed rae, bu he acceleraion curve also has serious abrup and non-guide poins. The midpoin acceleraion value of he corner profile will cause abrup vibraion o cause he inerial vibraion of he feed moion, resuling in decline in qualiy. In his paper, he kinemaics smoohing algorihm proposed in [10] is used o realize he corner ransiion, and he midpoin consrain mehod is proposed. On he basis of he overlap of he corner conours, he midpoin of he sraigh line segmen beween he wo corners is se as he consrain poin., limi he lengh of he ransiion secion o avoid overlapping corner profiles. A he same ime, he speed and acceleraion of he feed moion a adjacen corners are smoohly ransferred. Finally, he proposed algorihm is analyzed experimenally, and he effeciveness of he proposed algorihm is verified by comparing he radiional poin-opoin inerpolaion algorihm. DOI: / Page

2 A High-Speed Machining Algorihm For Coninuous Corners Rs ACC/DEC ACC/DEC ACC/DEC Re Y Ve θ1 VS AS Am Ae As=0 Vc Vc Ae=0 Pm=[Xmid,Ymid] (ε) O Corner Pc=[Xc,Yc] θε θ X Fig1.Acceleraion consrained by JounceFig.Corner ransiion pah I. Adjacen corner midpoin consrain algorihm.1kinemaics smoohing algorihm based on Jounce The principle of jounce consrained acceleraion is shown in Fig.1. The jounce-limied acceleraion curve produces a smooh velociy and acceleraion ransiion profile ha limis he feed axis from a smooh ransiion from iniial velociy and acceleraion o final velociy and acceleraion, When he displacemen Rs, he velociy Vs and he acceleraion As, he jounce-limi, and he acceleraion-limi Am are known, he jerk j(), he acceleraion a(), and he velociy can be obained by inegraing he hopping curve s(). For he formula for calculaing he v() and displacemen r() curves, according equaion (-1). j( ) s( ) d 0 a( ) As j( ) d (-1) 0 v( ) Vs a( ) d 0 r( ) Rs v( ) d 0 The principle of jounce consrained acceleraion is shown in Fig.1. The jounce-limied acceleraion curve produces a smooh velociy and acceleraion ransiion profile ha limis he feed axis from a smooh ransiion from iniial velociy and acceleraion o final velociy and acceleraion, When he displacemen Rs, he velociy Vs and he acceleraion As, he jounce-limi, and he acceleraion-limi Am are known, he jerk j(), he acceleraion a(), and he velociy can be obained by inegraing he hopping curve s(). For he formula for calculaing he v() and displacemen r() curves, according p Eq. (-1).Calculaed according o Eq.(-). The ransiion lengh Rc can be derived: 7 4 V st1 AsT 1 S T 1 1 RC cos( 1) cos( 1 ) (-) Assuming he X axis is he limi axis, hen he acceleraion, velociy, and maximum conour error consrains of he limi axis can be calculaed: AC cos( 1 ) AC cos( 1) SxT1 3 VC cos( 1 ) VC cos( 1) AC cos( 1) T1 SxT1 cos( ) VC cos( 1) T1 (cos( 1 ) cos( 1)) AC cos( 1) T1 ( cos( 1 ) cos( 1)) SxT1 ( cos( 4 1 ) cos( 4 1)) cos( 1) cos( 1 ).Midpoin consrain algorihm Alhough he kinemaic smoohing algorihm enables smooh ransiions in feed axis speed and acceleraion during coninuous shor-segmen ool pah machining. However, he relaionship beween he lengh of he line segmen beween adjacen corners and he lengh of he corner ransiion secion canno be considered. There may be a phenomenon ha he corner ransiion conour overlaps during he machining process, as shown in Fig. 3. The disance beween he shor segmens of he wo corner conours is: k k 1 k k 1 R Pc P c ( Rc Rc ) (-4) DOI: / Page (-3)

3 The following parameers were se for easy calculaion: P P d, R l, R l k k 1 k k1 c c c 1 c A High-Speed Machining Algorihm For Coninuous Corners (-5) Where d is he lengh of he sraigh segmen beween he wo corners, is he lengh of he ransiion of he previous corner, is he lengh of he ransiion of he laer corner. If R>0, i means ha here is no overlap beween he kh and (k+1)h corner conours, and he fron and rear corners of he shor line segmen are independen corners, which do no affec each oher. If R<0, i means ha he kh and (k+1)h corner profiles overlap each oher, indicaing ha he fron and rear corners of he shor line segmen inerac wih each oher. Once his happens, he feed moion mus lower he ransfer speed a he corner, oherwise The feed moion of he overlap will exceed he limis of he drive sysem, causing he machine feed o remble. A he same ime, he acceleraion profile may also have a beaing or non-leading poin, which affecs he processing qualiy. Transii on pah Fig3.Overlapping corner ransiion pah If min{l 1,l }>0.5d means ha he wo corner ransiion linear segmens are more han half of he line segmen beween he inflecion poins, so se l 1 =l =0.5d hen he new ransfer speed a he wo corners is: V c =V c1 =V c If min{l 1,l }<0.5d means ha one side exceeds he midpoin and he oher side does no exceed he midpoin, hen se l 1 = 0.5d The new ransfer speed of he former corner and he second corner can boh be calculaed. V V c1 V c V c c (-6) Midpoin consrain algorihm is o selec he segmen midpoin as he consrain poin of he ransiion segmen, limi he segmen lengh of he ransiion segmen, and use i as a known parameer o re-solve he corner ransi speed. Vsx Vc cos( 1) Asx Ac cos( 1) Ac cos( 1 ) Ac cos( 1) SxT1 V cos( ) V cos( ) A cos( ) T S T 7 4 V sxt1 AsxT1 SxT1 R 1 c cos( ) cos( ) 3 c 1 c 1 c 1 1 x (-7) Assuming ha he limi axis is fed a he maximum hop limi of he drive, he opimum ransfer speed is deermined according o Eq.(-7) and Eq. (-8): DOI: / Page

4 A High-Speed Machining Algorihm For Coninuous Corners 1(cos( 1) cos( 1 )) Rc T1 4 7Sx (-8) 1(cos( 1) cos( 1 )) Rc Sx 7Sx Ac cos( 1) cos( 1 ) 1(cos( 1) cos( 1 )) Rc 3 Sx ( 4 ) 7Sx VCS max cos( 1) cos( 1 ) Assuming ha A=Amax, hen he opimum ransfer speed can be calculaed. 1Rc T1 7Ac (-9) 7 Ac (cos( 1 ) cos( 1)) Sx 1Rc 1AR c c VCAmax 7 In summary, he new ransfer speed can be calculaed. V min{ V, V }(-10) C CS max CAmax II. Simulaion and experimen In order o verify he effeciveness of he proposed algorihm, he coninuous shor-segmen processing pah is compared wih he radiional poin-o-poin direc inerpolaion algorihm. Fig4.Experimenal pahfig5.simulaion pah The experimenal equipmen is shown in Fig 4. The planar XY moion is driven by wo linear moors o ensure good posiion synchronizaion and pah racking. The linear encoder feedback resoluion is 0.8um. The closed-loop sampling ime of he servo sysem is 0.1ms, and he posiion feedback bandwidh of he X and Y axes is w n =5Hz. The experimenal processing pah is a snowflake pah as shown in Fig 5, wih a oal lengh of 96.5 cm and 77 corners. In order o show ha he mehod can play he performance of he driver, i is compared wih he radiional poin-o-poin direc difference compensaion algorihm. The poin-o-poin inerpolaion algorihm requires he ool o sar deceleraing before each corner poin unil he corner sops compleely, and hen he seering feed is fully synchronized wih he pah specified by he G01 code; he experimenally se maximum allowable conour error is 0.1 mm. Real-ime sampling and commanding of differen algorihms using a servo conroller. Se he maximum feed speed of each axis of he drive o 100mm/s, he maximum acceleraion is 1000cm/s, he maximum jump is mm/s4, and he maximum jump is 10 7 mm/s4. DOI: / Page

5 A High-Speed Machining Algorihm For Coninuous Corners X axis Y axis Fig6. Comparison of speed curves of wo algorihms Fig 6 shows he velociy profile of he wo algorihms moving on he machining pah. I can be seen ha he velociy curve of he poin-o-poin inerpolaion algorihm has large flucuaions, and he algorihm needs o sop compleely a each corner, he acceleraion jumps, and he drive The load is large. I can also be seen from he figure ha he midpoin consrain algorihm akes 10.8s, he poin-o-poin algorihm coss 11.08s, and he processing efficiency increases by 6.8%. A he same ime, he acceleraion curve of he proposed algorihm reaches G1 coninuously as shown in Fig 7. X 轴 Y 轴 Fig7. Acceleraion curve based on midpoin consrain algorihm III. Conclusions In his paper, we use he mehod of hopping o consrain he acceleraion curve, and propose a midpoin consrain mehod for he special case in he processing pah, ha is, he overlapping of adjacen corner conours, limi he lengh of he ransiion segmen o preven he corner ransiion conour from overlapping, and achieve smooh speed and acceleraion. Transfer, he acceleraion curve reaches G1 coninuously. Finally, he algorihm is compared wih he radiional poin-o-poin direc inerpolaion algorihm. I is found ha he processing ime DOI: / Page

6 A High-Speed Machining Algorihm For Coninuous Corners of he midpoin consrain algorihm is reduced by 6.8% compared wih he poin-o-poin inerpolaion algorihm, and he processing efficiency is improved. References [1]. Choi Y K, Banerjee A. Tool pah generaion and olerance analysis for free-form surfaces[j]. Inernaional Journal of machine Tools and manufacure, 007, 47(3): []. Lei W T, Sung M P, Lin L Y, e al. Fas real-ime NURBS pah inerpolaion for CNC machine ools[j]. Inernaional Journal of Machine Tools & Manufacure, 007, 47(10): [3]. Heng M, Erkorkmaz K. Design of a NURBS inerpolaor wih minimal feed flucuaion and coninuous feed modulaion capabiliy[j]. Inernaional Journal of Machine Tools & Manufacure, 010, 50(3): [4]. Nozawa R, Kawamura H, Sasaki T. Acceleraion/deceleraion circui: U.S. Paen 4,554,497[P] [5]. Tulsyan S, Alinas Y. Local oolpah smoohing for five-axis machine ools[j]. Inernaional Journal of Machine Tools and Manufacure, 015, 96: [6]. Bi Q, Wang Y, Zhu L, e al. A pracical coninuous-curvaure Bezier ransiion algorihm for high-speed machining of linear ool pah[j]. Inelligen roboics and applicaions, 011: [7]. Beudaer X, Lavernhe S, Tournier C. 5-axis local corner rounding of linear ool pah disconinuiies[j]. Inernaional Journal of Machine Tools and Manufacure, 013, 73: [8]. Shingo Tajima.Kinemaic corner smoohing for high speed machine ools[j].inernaional Journal ofmachine Tools & Manufacure,016,108:7-43. [9]. Fan W,Gao X S.Inerpolaion of parameric CNC machining pah under confined jounce[j].the Inernaional Journal of Advanced Manufacuring Technology,01,6(5): [10]. Tajima S, Sencer B. Global Tool-pah oohing for CNC Machine Tools wih Uninerruped Acceleraion[J]. Inernaional Journal of Machine Tools & Manufacure, 017. Wang Yong. A High-Speed Machining Algorihm For Coninuous Corners. IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE), vol. 15, no. 5, 018, pp DOI: / Page