CIRCULAR PATH FOR CNC MACHINE TOOLS

Transcription

1 Proceedngs n Manufacturng Systems, Volume 8, Issue 1, 2013 ISSN CIRCULAR PATH FOR CNC MACHINE TOOLS Dona MARIN 1,*, Ncolae PREDINCEA 2 1) Scentfc researcher, PhD, Robotcs Department, Insttute of Sold Mechancs of the Romanan Academy, Bucharest, Romana 2) Prof., PhD, Machne and Manufacturng Systems Department, Polytechnc Unversty of Bucharest, Romana Abstract: Machne tools are bult from many components and each component contrbutes moton error to the fnal tool tp poston. There are multple error orgns ncludng geometrc, statc and dynamc loadng, thermal, msmatchng between servo-loop parameters, nterpolaton etc. In the same tme, the control of machne tools affects the accuracy of the work-pece. Therefore, n order to acheve hgh performances of feed drve system s requred to analyses smultaneously both mechancal and control systems. To acheve hgh qualty and productvty durng contnuous contourng, t s mportant to know how two axes work together. For ths reason, to nvestgate the nfluence of the nteractons on the system performance, crcular tests are conducted. Results of the process make t possble to understand accurate dynamc behavor of a feed drve system. Key words: feed drve system, contour errors, trajectory measurement, poston control loop. 1. INTRODUCTION Accuracy could be defned as the degree of agreement or conformance of a fnshed part wth the requred dmensonal and geometrcal accuracy. Error, on the other hand, can be understood as any devaton n the poston of the cuttng edge from the theoretcally requred value to produce a workpece of the specfed tolerance. The extent of error n a machne gves a measure of ts accuracy; that s the maxmum translaton error between any two ponts n the work volume of the machne. Ths, of course, depends on the resoluton of the system. Postonng can never be more accurate than ths as there wll be no further feedback to mprove the postonng wthn ths range (typcally of the order of 1 µm). However, more mportant then system resoluton, are the errors that occur between the measurement pont and the feedback pont [1]. Errors occur at the crcular contour and on all curved paths. These errors depend on the type of measurng system and they have dfferent effects. The machnng of a crcular contour nvolves two feed axes. Ther poston set ponts are computed by nterpolator of the CNC accordng to the selected type of nterpolaton, and appled to the feed drves. In addton to the nterpolaton, a great number of parameters and dsturbance varables are very mportant to the dmensonal accuracy of the actual contourng path, some of whch wll be analyzed n ths paper. Error measurement s not only made for error compensaton of a measurng (CMM) or machne tools, but also to dscover problems n the desgn, n the * Correspondng author: 15, Constantn Mlle Street, Bucharest, Tel.: ; Fax: E-mal addresses: marn_dona@yahoo.com (D. Marn), ncolaepredncea@yahoo.com (N. Predncea) development stage, for readjustment and reworkng n the manufacturng stage. The methods and the devces for measurng moton accuracy of NC machne tools are presented here. To acheve the hgh precson and super-fnshes, statc postonng accuracy or repeatablty s not enough. The acceptable contour wll depend on several factors ncludng cutter path complexty, machne statc and dynamc accuracy, the machne acceleraton and deceleraton rate, the machne control system and compensaton, data processng rate, etc. Any dynamc characterstcs n the machne tools wll lead to the generaton of vbratons, the effects of whch can lead to poor surface fnsh on the work pece ncreased machne tool wear, as well as tool fracture and damage to both the work pece and machne. Under contnuous machnng condtons, two types of vbratons occur because of movement between work pece and tool. These are externally excted and self-excted vbratons. All these errors n the machne tools nteract wth each other and make a complex stuaton for error compensaton research. 2. AN OVERVIEW OF MACHINE TOOLS ERRORS The moton error sources n NC machne tools are due to mechancal structures and due to servo control systems [2]. Moton errors due to mechancal structures: errors n postonng mechansm (unform expanson or contracton of the ball screw and lnear scale, cyclc error of the ball screw and lnear scale, nose n detectors, backlash); profle errors of gude way (squareness errors between two axes, straghtness errors, rotatonal moment, parallelsm error, frcton of the sldng cover);

2 30 D. Marn and N. Predncea / Proceedngs n Manufacturng Systems, Vol. 8, Iss. 1, 2013 / errors that can be compensated by servo control system (lost moton, stck moton, stck slp, mstng of ptch error compensaton). Moton errors due to servo control systems: msmatchng of poston loop gans; radus reducton n crcular nterpolaton due to response lag; response lag or overshoot at junctons of two nterpolaton lnes. 2. CIRCULAR CONTOUR ERRORS BY THE INTERACTION OF FEED AXES A typcal example for errors dependent on acceleraton and velocty can be recorded n a crcular nterpolaton test on a vertcal-machnng center. Hedenhan Company, the producer of rotary and lnear encoders, made ths test. The results are: where poston control s by rotary encoder and ball screw, the crcles traversed at hgher velocty devate sgnfcantly from the deal path [3]. The same machnng center shows sgnfcantly better contour accuracy when s equpped wth lnear encoders (Fg. 1). There are two types of contourng errors: errors on the crcular contour, whch are dependng from the contourng rate and the crcle radus; dstortons of the crcular contour, whch result, when the partcpatng axes do not respondng equally. Dependng on the locaton at the machne tool where the measured data acquston takes place, we dfferentate between drect and ndrect poston measurements. Dependng on the locaton at the machne tool where the measurement acquston takes place, we dfferentate between drect and ndrect poston measurement [4]. Fgure 2 llustrates the ndrect and drect poston measurement n the poston control loop for a lead screw drve. Where: w x s the poston command varable; x the poston control devaton; v the actual velocty value; v s velocty set pont value; r x the poston feedback varable. For rotary as well as lnear drves, where the actual speed value s obtaned from the poston measurement, the actual value encoder must be nstalled free of backlash and tlt. At a crcular moton wth an angular frequency ω equal to the angular velocty v B / r, the actual poston values of the two feed drves have the followng tme characterstc: x = xˆ sn( ωt) ; y = yˆ cos( ωt + ϕ) (1) Fg. 2. Indrect and drect poston measurement n the poston control loop [5]. The actual radus of the crcle s r 0 = xˆ = yˆ, and the phase shft angle dfference between these axes s ϕ = 0. The result would be a dstorton-free crcular contour. If the axes X and Y have dfferent command responses, then xˆ yˆ ; ϕ ϕ, and we obtan X Y dfferent absolute values from the ampltude responses, and a phase shft angle dfference ϕ from the phase responses. Both dfferences result n a dstorton of the crcular contour Ampltude errors The resultng crcular contour s calculated from the geometrcal sum of the actual postons of both axes. If x ˆ yˆ, but ϕ = 0, the actual contour wll be staved n ellptcally, n the drecton of the axs wth the smaller ampltude rato. The nstantaneous radus value s the result of the followng correlaton: r = xˆ sn ( ωt) + yˆ cos ( ωt). (2) The largest crcular contour devaton occurs at the pont where one of the feed axes reaches ts maxmum value. Calculatng ths devaton caused by the dfferent command responses of the two-poston control loops of the X and Y axs from the dfference of the two actual values r = r F F. (3) FwL s wlx wly Fg. 1. Crcular test of machnng center a) poston control wth rotary encoder; b) poston control wth lnear encoder. Fgure 3 shows a contour where the Y axs have a smaller ampltude rato than the X axs. The crcle s staved n the drecton of Y. Not are drawn the errors caused by the contourng rate and a possbly exstng dstorton caused by the mechancal system, whch addtonally occurs n the case of the ndrect measurng system. In the case of the ndrect measurng system, we mght have the dstorton caused by the poston control loops and errors caused by dfferent mechancal transfer elements.

3 D. Marn and N. Predncea / Proceedngs n Manufacturng Systems, Vol. 8, Iss. 1, 2013 / Fg. 3. Crcular contour dstortons due to ampltude errors. Fg. 4. Crcular contour dstortons due to phase error. r = r F F. (4) Fmech s mechx mechy For the poston control loops and the mechancal transfer elements together we obtan a dstorton error r = r F F F F. (5) F s wlx mechx wly mechy The absolute value of the radal error s ndcated, snce the actual contour can be larger or smaller than the dstorton free contour. The error components of the poston control loops and the mechancal system can compensate each other. For the ndrect poston measurng system, the approxmate total dstorton error s r r r. (6) F Fmech For the drect measurng system a breakdown nto a poston control loop component and a mechancal component s not possble. The generated dstorton error caused by unequal K V factors, unequal delay tmes FwL T σ x and/or unequal mechancal natural frequences ω s d mn calculated wth equaton (3) Phase error In order to determne the dstortons caused by dfferent phase responses, we can set x ˆ = yˆ = r 0, and we have 2 2 r = r sn ( ωt) + cos ( ωt + ϕ). (7) 0 The actual radus at the angles ωt = (1/ 8) 2π and ωt = (3 / 8) 2π,.e. the 45 0 ponts between the feed axes, we have 1 Mnmum at ωt = 2π; r = r sn(2 ϕ), 8 3 Maxmum at ωt = 2π; r = r sn(2 ϕ). 8 We obtan an expanson or a contracton of the crcular contour at the 45 0 ponts, dependng on the dfference between the two-phase shft angles. Fgure 4 shows a schematc vew of the contour dstorton caused by phase error. The phase shft angle of the two axes for the poston control loops and for the drect measurng system s: ϕ = ϕ. (8) wlx ϕ wly The phase shft angles of the two axes for the mechancal transfer elements s ϕ = ϕ. (9) mechx ϕ mechy The phase shft angles of the two axes for the poston control loops ncludng mechancal transfer elements and the ndrect measurng system ϕ = ϕ + ϕ ) ( ϕ + ϕ ). (10) ( wlx mechx wly mechy The dstorton error caused by dfferent phase shft angles n the poston control loops and/or the mechancal transfer elements are calculated wth relaton ϕ ( 1± 0.5sn(2 ϕ) 1) r = r. (11) 0 Snce the deal actual radus n conventonal machnng s approxmately equal to the set pont radus, we set r 0 r s and obtan: ϕ ( 1± 0.5sn(2 ϕ) 1) r. (12) r s The radus dstorton at the crcle s ndcated as an absolute value. The phase error results due to the two sgns under the root n a ± value. The crcle wll expand and contract. The K V factor and the lowest mechancal natural angular frequency ω also affect any errors at d mn the crcle caused by the dstorton of the deal contour due to dfferences n the two axes partcpatng to the nterpolaton. Both values must be as hgh as possble n order to keep the errors small [6]. In concluson, we can say that: Errors and dstortons occur at the crcular contour and on all curved paths dependng on the type of measurng system they have dfferent effects; In addton to the contourng rate dependent errors, unequal parameters and varables n the axes nvolved n the moton also generate dstortons of the contour path. These are separated nto ampltude and phase errors. Ampltude errors cause a contracton of the crcle n the drecton of the axes wth the smaller ampltude rato.

4 32 D. Marn and N. Predncea / Proceedngs n Manufacturng Systems, Vol. 8, Iss. 1, 2013 / Phase errors cause an expanson and a constrcton n the 45 0 dagonals between the feed axes drectons. The phase error s a ± value; Both errors usually occur combned, so that the cause for the dstorton cannot be clearly determned wth a crcular contour test. 3. CONTOURING ERRORS MEASUREMENT Crcular tests provde a quck and effcent way to measure the machne s contourng accuracy and then to dagnose ts error sources. Crcular tests are accepted n ISO [7]. The dagnoss methodology to dentfy moton error source n NC machne tools based on the double ball bar (DBB) method s now wdely accepted n today s ndustry. Typcal DBB devces consst of two hghprecson balls connected by a telescopng bar, and the dstance between two balls s measured by a lnear scale nstalled on the telescopng bar. The DBB devce s used to measure a contourng error profle as the machne s traversng along a crcular trajectory (Fg. 5). Today s market requres a moton accuracy test under the condton where the DBB test cannot be performed. For example, most DBB systems work wth rad of 50 ~ 300 mm, although some applcatons requre the machne to perform a crcular nterpolaton of smaller radus. Furthermore, the measurement accuracy of the DBB method s mpared at the feed rate hgher than 10 m/mn, due to the frcton between the ball and the magnetc socket. Another crtcal dsadvantage of the DBB method s that t s restrcted only to crcular tests due to ts nature [8 and 9]. Cross grd encoder method, or the KGM method development by Hedenhan s used for the measurement of two-dmensonal contourng error. Most mportantly, there are no restrctons on the moton to be measured due to a mechancal lnkage, as n the DBB method. Snce the KGM method s non-contact optcal measurement, t s more sutable for hgh-speed and hghaccuracy measurement [3]. The KGM method observes the relatve error between a spndle (tool tp) and a table (work-pece). Its contourng error profles contan not only moton errors due to CNC servo systems, but also those due to errors n mechancal structures of the machne. On the other hand, contourng error profles of poston feedback sgnal do not contan moton errors due to mechancal errors. Therefore, by comparng these two profles, one can dstngush moton errors due to servo control systems from those due to mechancal structures. Many latest NC machne tools have a fast CPU and hgh-capacty memory, whch makes t easy to sample poston feedback sgnal n a fast rate. The samplng of poston feedback sgnal requres no addtonal physcal devce f the NC machne tool has an addtonal memory to store sampled data. The resoluton of the grd encoder s 4 nm n ts two drectons; the resoluton of the three lnear dsplacement transducers s 20 nm. The resoluton for the rotatons depends on the dstances between the optcal heads and the lnear dsplacement transducers. The dagnoss methodology based on the DBB measurement manly focuses on moton errors due to mechancal structures. The dagnoss method based on KGM focuses more on moton errors due to CNC servo control systems. Compared to moton errors due to mechancal structures, those due to CNC servo control systems are easer to compensate by properly re-tunng parameters n servo controllers. After the measurement and dagnoss of contourng errors, ths method automatcally tunes servo parameters n order to reduce contourng errors. 4. EXPERIMENTAL SET UP Three axes mllng machne s used for the experments. The expermental system (Fg. 6) used n ths study: computer wth acquston plaque DAQ 500, amplfer model 480B21 and three accelerometers type PCB 353B33. The samplng rate s 1/1200 per channel. Work-peces are made of alumnum alloy; the cutter s a three-edge-hgh-speed steel mllng tool wth a dameter of 25 mm. The trajectores are crcular wth contnuous path. Cuttng condtons were set as follows: spndle speed 1400 rpm for fnsh mllng wth axal depth of cut 0.5 mm per contour; spndle speed 710 rpm for rough mllng; the cuttng depth 10 mm. 5. EXPERIMENTAL RESULTS The crcular test provdes a rapd and effcent way of measurng a machne tool s contourng accuracy. The crcular tests show how the two axes work together to move the machne n a crcular path. As the machne s traversng wth multple a xes along a crcular trajectory, Fg. 5. Photograph of the prototype measurement devce. Fg. 6. Expermental set-up.

5 D. Marn and N. Predncea / Proceedngs n Manufacturng Systems, Vol. 8, Iss. 1, 2013 / each axs goes through snusodal acceleraton, velocty and poston changes. The measured crcular path data wll show any devaton the machne makes from a perfect crcle. The shapes are dagnosed and correlated to servo msmatch, backlash, squareness error, cyclc error, stck slp, machne vbratons, etc [10]. In order to nvestgate the nfluence of the nteractons on the system performance crcular moton trajectores are machned. Results of these processes make t possble to understand accurate dynamc behavor of a feed drve system. The roughng, sem-fnsh and fnsh stages have very dfferent requrements. In the roughng stage the goal s to remove materal as rapdly as possble; large forces and tool deflectons are permtted as long as the allowable tooth stress and the avalable spndle power are not exceeded. Durng the sem-fnshng stage, tool deflectons are mportant snce the goal of ths stage s to create a unform thckness for fnshng. In the fnshng stage tool deflectons should be carefully controlled. Ideally, the cuttng force should be held at a low constant value to acheve close tolerances and good surface fnsh [11]. For exemplfcaton, two work-peces wth the same radus was machned, wth dfferent operatng condtons, and can be observed that the ampltude of vbratons are bgger durng roughng mllng (Fg. 7) than fnshng mllng (Fg. 8). Cuttng condtons were set as follows: for roughng mllng spndle speed s 710 rpm and the feed rate 120 mm/mn; for fnshng mllng spndle speed rpm, feed rate 250 mm/mn wth axal depth of cut 0.5 mm per contour, cuttng depth 10 mm. Operatng condtons Roughng mllng Fnshng mllng Table 1 r.m.s. values for dfferent operatng condtons Feed rate [mm/mn] r.m.s. on X axs [m/s 2 ] r.m.s. on Y axs [m/s 2 ] Machnng crcular path and comparng the roughng operaton wth fnshng operaton, the dagrams shows that the vbratons are two tmes hgher for roughng than fnshng process. Ths s noted n Table 1 where r.m.s. values were calculated for both cases. From spectral analyss performed for the roughng and fnshng operatons was found that the domnant frequency values are the same for the X and Y axes nvolved n nterpolaton, only ampltudes are dfferent owng to dfferent cuttng efforts. An example s presented n Fg. 9,a and b, for X axs, n both cases (roughng and fnshng mllng). The same phenomenon happens on the other axs nterpolaton attend (Y axs n ths case). Vbratons durng fnshng mllng process, when axs partcpatng to the nterpolaton changes the drecton of movement, are llustrated n Fg. 10 and 11. Acceleraton ampltudes ncrease or decrease when the drecton of feedng s change because the stffness of the mechancal components of feed drve system s varyng caused by pre-loaded and the values and drecton of cuttng forces are changed [12]. a Fg. 7. Vbratons durng roughng mllng b Fg. 8. Vbratons durng fnshng mllng. Fg. 9. Spectral analyses on X drecton for: a) roughng mllng; b) fnshng mllng.

6 34 D. Marn and N. Predncea / Proceedngs n Manufacturng Systems, Vol. 8, Iss. 1, 2013 / Fg. 10. Vbratons durng mllng process, when X and Y axs movng n one drecton. rate. The standard verfcaton of machne contourng accuracy s the use of crcular tests. The double ball bar method s wdely accepted as a tool to measure the moton accuracy of NC machne tools and to dagnose ther error sources. The DBB method can only perform crcular tests due to ts nature. Moton errors due to mstakng of CNC servo control systems are, however, often easer to observe on non-crcular paths. For measurng the moton accuracy n arbtrary shape contourng, we have presented the KGM method and ts advantages related to DBB method. From expermental part of the paper, durng the cuttng process, we can observe that the contour errors depend on feed rate. The feed drve errors result from mperfecton of machne control system. In order to realze hgh-performance of feed drve systems s requred to analyze both mechancal and control system smultaneously. Therefore, machne feed drve s an ntegral part of a machne control system. REFERENCES Fg. 11. Vbratons durng mllng process, when X and Y axs movng n the other drecton. a Fg. 12. Proflograms for crcular trajectores; a feed rate 150 mm/mn; b) feed rate 300 mm/mn. To analyze the crcular trajectory dependng on the feed rate were processed two peces wth dfferent feed rates: 150 mm/mn and 300 mm/mn. In Fg. 11 are llustrated roundness and radal errors moton measurement under dfferent feed rates. In the frst case the crcularty s 9 µm, n the second case the crcularty s 12 µm. It can bee observe that errors are bgger when feed rate ncrease. 6. CONCLUSIONS For hgh speed machnng operatons, machne tool contourng accuracy s very mportant. To acheve hgh qualty and productvty, t s mportant to know for meetng the requred accuracy whch s the optmal feed b [1] Y. Kakno, Y. Ihara, A. Shnohara, Accuracy Inspecton of NC Machne Tools by Double Ball Bar Method, Hanser Publshers, Munchen, [2] Y. M., Cheng, J. H., Chn, Machnng contour errors as ensembles of cuttng, feedng and machne structure effects, Internatonal Journal of Machne Tools and Manufacture, vol. 43, 2003, pp [3] Hedenhan GmbH, Measurng Systems for Machne Tool Inspecton and Acceptance Testng, sept [4] D. Marn, N. Predncea, Crcular Contour Errors and Dstorsons n Hgh Speed Machnng, Proceedngs of the Internatonal Conference on Manufacturng Systems ICMaS 2004, Romanan Journal of Tehncal Scences Appled Mechancs, Tome 49, Specal number 2004, Edtura Academe Române, pp [5] H., Gross, J., Hamann, G., Wegartner, Electrcal Feed Drves n Automaton, Bascs, Computaton, Dmensonng, Publcs MCD Corporate Publshng, Munchen, 2001 [6] D. Marn, Errors of three-axs machnng center, chapter 8, Topcs n Appled Mechancs, vol. 3, edted by Romanan Academy, 2006, pp [7] ISO 230-4, Acceptance Code for Machne Tools Part 4, Crcular Tests for Numercally Controlled Machne Tools, [8] M. Weck, Handbook of Machne Tools, vol. 3, Publsher: John Wley & Son Ltd, Chchester, [9] M. Weck, Werkzeugmaschnen Fertgungssysteme 5 Messtechnsche Undersuchung und Beurtelung, 6, Auflage, Sprnger, [10] D. Marn, Feed drve systems optmzaton of NC machne tools, chapter 5, Research Trends n Mechancs, vol. 4, edted by Romanan Academy, 2010, pp [11] D. Marn, Dynamcal systems performance of Numercally Controlled machne tools, Proceedngs of the Amercan Conference on Appled Mathematcs, Harvard Unversty, Cambrdge, USA, January 27 29, 2010, pp [12] D. Marn, Improvement of the machne tools performance, WSEAS Transactons on Systems and Control, vol. 5, Issue 3, march 2010, pp