Motion accuracy of NC machine tools

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1 otion accurac of NC machine tools ARIN DOINA, STANCIU IOAN, ARIN DAN IHAIL Dnamics Sstems Deartment Institute of Solid echanics-romanian Academ 15, Constantin ille Street, Bucharest, 1141 S.C. Turbomecanica S.A. 224, Iuliu aniu Street, Bucharest S.C. Aerofina S.A. 5, Fabrica de glucoza Street, Bucharest ROANIA Abstract: odern CNC machines have two rincial sstems: the cutting sstem and feeding sstem. Work iece accurac is the overall outcome of cutting and feeding sstems. This aer investigate the contour errors (circular and square corner ath) on the bases of a comlete CNC sstem, that includes all grou of functions in CNC machining. Traector lanning, traector tracking, the cutting rocess and the machine structure are established. The deendence of contour errors on traector rofile (ath), feed-rate, cutting deth and frequenc resonse of the table sstem are investigated as well. Ke-Words: High seed machining; Tracking control; otion accurac; Contour errors; Traector measurement; Structure. 1 Introduction In order to fulfill the requirements of modern industr, the accurac of multi-axes machines has been one of the rincial concerns in their design and imlementation. The qualit of workiece in terms of contour accurac is the outcome of cutting, feeding and machine structure dnamics. Surface finish have been studied from the ersective of cutting dnamics while contour accurac has been studied from the ersective of tracking control, but both need to be considered from the combined ersective of cutting, feeding and machine structure eseciall for milling rocess [2]. Scientific researchers examined cutting rocess dnamics with reference to the combined cutting force and machine tool sindle. Cutting force model for milling rocess develoed based uon tool geometrics, work materials and other factors, and these models hel to redict forces and determine otimal cutting arameters [1], [5]. One factor has remained unexamined the deviation due to feeding errors. The feed drive errors results from imerfection of machine control sstem. Control strategies used for NC machine tools are Feed Forward Control, Cross Couling Control and Otimal Control. Otimal Control is further broken down into Predictive Control (Generalized Predictive Control GPC), Adative Control and Learning Control. Feed forward control is oen loo comensation; it does not use ast or current ath error information in calculating command signals, nor does it address issues with coordinated motion. As a result, feed forward techniques resond oorl in the resence of disturbances or modeling inaccuracies. Cross-couled control (CCC) was develoed b Koren [4]. This method switched the focus of controllers from maintaining each axis at its target osition, to minimizing ath error. CCC estimates the oint on the target ath and uses this to determine the error for each axis. This error signal is than used in combination with an one of a number of controllers to control the coordinated osition. Otimal controllers create a command sequence that otimizes sstem erformance. Ticall, this is the minimization of the difference between target and redicted outut. GPC and its variations reresent advanced otimal control. GPC is comutationall intense for servo control. However, as comutational ower increases, these issues ma disaear [7]. Cutting dnamics, tracking control and contour accurac acquire new asects of investigation in the era of high-seed cutting. The aim of the aer is to examine accurac of contours (circular and linear ath - square corner analses) as an ensemble of cutting, feeding and machine structure dnamics. ISBN: ISSN

2 2 Dnamics of milling rocess Two structures imortantl contribute to the cutting dnamics: the sindle sstem (fig.1) and the feeding sstem (fig.2). The sindle and feeding table were modeled b a second order sstem in the X and Y directions. The equations for tool/sindle sstem are X & + C X& + K X F, (1) tx t tx t tx t Y & + C Y& + K Y F. (2) t t t t t t In milling rocess are imlicated two axes for realizing the workiece ath. These axis are structured identicall, one of them (X axis) is illustrated in fig. 2. The equations for feeding sstem are Fig.1. Dnamic model for sindle sstem. Fig. 2. Dnamic model for feed drive sstem. X & + C X& + K X F, (3) wx w wx w wx w Y & + C Y& + K Y F. (4) w w w w w where: t, C t and K t reresent tool mass, daming and stiffness, resectivel; X t and Y t are the dislacements of the tool in X - and Y - directions, resectivel, and F(t) is the cutting force. w, C w and K w are table mass, daming and stiffness, resectivel. x x The formation of cutting force and the excitation of the machine structure b the cutting force contribute to the cutting dnamics. The dnamic model of the milling cutter used in this aer is assumed to be a sstem with two modes of vibration in two erendicular directions, X and Y, and the feed direction is along the X-axis. The milling sstem under consideration shown in fig. 1, where the X and Y coordinate sstem is fixed with resect to the machine tool structure and its axes are aligned with the rincial modes of oscillation. This is a common characteristic of the sindle tool assembl, which is the most flexible art of a tical milling machine. The milling cutter has n teeth, which are assumed to be equall saced. The dnamics of the milling sstem can be given b equations (1) and (2). In order to exress cutting force F(t) the rotating coordinate sstem u v is used. Referring to the sstem, an tooth of the milling cutter can be view as a single oint cutting tool, thus the redictive machining theor established for turning can now be used. For tooth number () which is the instantaneous angular immersion φ measured clockwise from the negative Y-axis at a articular instant, the milling force comonents on it,, P P, which are in P1 2, 3 the tangential, radial and axial directions resectivel, can be calculated from the corresonding chi load, cutting conditions, and tool geometr b using the single-oint cutter mechanics as above mentioned. The total cutting forces of the cutter can be determined using the following equations Fx F F F x ( P 1 ( P 1 where the immersion angle cos φ sin φ + P 2 + P 2 sin φ ) cos φ ) (5) φ varies with time as φ Ωt ; Fx and F are the comonents of the cutting force alied on the th tooth. 3 Tracking control In order to imrove servo controller s erformances, various control techniques were alied to CNC machine tools in the ast ears. CCP is the structure of the cross-couled recomensation method in which a velocit recomensation gain K v is used to generate a feedback ISBN: ISSN

3 re-comensation loo. One feature of CCP is that it imlements secific traector strateg for each target traector. For linear feeding along the ath OB, the contour error ε is the shortest distance between the actual tool osition P and the target ath (fig.3). The velocit comensation V k ( V k K v ε ) tries to ush the tool back into the target ath. After the velocit is modified, the tool takes on a velocit vector, which is a vector combination of the required tangential velocit V t and the modifing velocit V k triggered b the contour error. The comonents of the re-comensated velocit are V V + V V cos α K ε sin α (6) x tx kx t V V + V V sin α + K ε cos α (7) t k t where α is the angle between the tangent of the instantaneous traector and the X axis. The comonents of the osition error are the differences between the comonents of the monitored actual osition (X, Y ) and those of the desired osition (X f, Y f ). ε X sin α Y cos α (8) v v 2 ε R R R X + Y (9) After the re-comensation, the tool adots a velocit vector, which is the vector combination of 2 Fig.4. Circular tracking using CCP. the original tangential velocit V t along the traector and the modifing velocitv k, which tries to ush the tool back into the right traector. b ( Y / R) + K vε( X R) ( X / R) + K ε( Y R) Vx Vbx + Vkx V / (1) V Vb + Vk Vb v / (11) 4 Exeriments 4.1 Exerimental set u ikromat 9A is the machine tool used for the exeriments. The exerimental sstem used in this stud: comuter with acquisition laque DAQ 5, amlifier model 48B21 and three accelerometers te PCB 353B33 mounted on the table (fig. 5). The samling frequenc is 12 Hz er channel. Fig.3. Linear tracking using CCP. Recentl, it has been reorted that the accurac of a linear motion around a square corner can be regarded as an imortant index to evaluate the erformance of NC machine tools. Thus, as an alication, the linear motion traectories containing a square corner will be resented in section 4. A circular traector (fig. 4) along the arc ABC is the target contour of machining; P is the actual tool osition and R is the distance between P and the origin of coordinates. The contour error ε is calculated from Fig. 5. Exerimental set-u. ISBN: ISSN

4 Fig. 6. Test iece ath. Workieces are made of aluminum allo; the cutter is a three-edge-high-seed steel milling tool with a diameter of 5 mm. The traectories are circular and linear with continuous ath. Cutting conditions were set as follows: sindle seed 14 rm; different feed rates for finish milling; axial deth of cut,5 mm and radial width of cut 1 mm. Test iece for erformance tests of continuous ath controlled milling machines is the well-known work iece NAS 913 reresented a circular contour and a square (fig. 6). 4.2 Sstem analsis An imact hammer excited the table and the signals from accelerometers were collected and analzed. This te of measurement is used to make a modal model of the structure, which can than be used to redict the behavior of the structure under given circumstances. The resonse of the sstem measured in the same oint on the three directions (X, Y, Z) of the machine tool are resented in fig. 7. Fig. 8. Amlitude-frequenc characteristics. Using FFT analses, the frequenc resonse of the table sstem were illustrate in fig.8. The eak of the frequenc is to 52 Hz. Higher harmonic comes to 156 Hz. Beside eigenvalue frequenc can be seen another two frequencies at 22 Hz and 33 Hz. Fig. 7. Shock resonse at imact hammer. 4.3 Square corner error In order to examine the effects of feed rates, the linear motion traectories containing a square corner were machined with different feed rates and measured with a control machine, Zeiss. The error around the measured corner is defined with three arameters, a, b and δ, as illustrated in fig. 9. The relationshi between the federate and the values of a, b and δ is resented in fig. 1. Obviousl, the values of these arameters are well roortional to the feed rate. Fig. 11 shows the measurement results and in this figure it can be ISBN: ISSN

5 found that the error shaes near the corner are ver similar to one another following the feed direction. Fig. 9. Parameters a, b, δ of corner error. Fig. 1. Relationshi between the feed rate and the arameters of corner error. Fig. 11 easurement results of a square corner. The cause of corner errors while aroaching a corner was examined in this aer. The feed rate (acceleration) data with resect to different ositions in the traector were recorded using accelerometers for each axis that articiate to interolation (X and Y-axes of the machine tool). From figure 12 the increasing and reducing rocesses in feed seed near the corner are clearl observed. Fig. 12. Vibrations on X and Y axis during the cutting rocess with feed rate 2 mm/min. While aroaching the corner, the seed is reduced along the first linear motion. With a little dela, the second linear motion starts. Because of the inertia of the driving sstem, increasing the seed to a secified value for the second motion and reducing the seed to zero for the first motion instantaneousl are imossible. Therefore, if no dwell between both linear movements has been secified, there is a overla between the seed reducing rocess of the first motion and the seed increasing rocess of the second motion around the corner. As a result, the overla effect caused the corner error. In other words, in order to obtain a shar shae, it is necessar to secif a dwell action at the corner in NC contour manufacturing with a high feed rate. The new generation of machine tools has in NC rograms secials functions (for examle G 61 and G 62) for correcting error corner. ISBN: ISSN

In the same time, it can be observe that acceleration amlitudes increase or decrease when the direction of feeding is change because the values and directions of cutting forces are changed and

Tracking error were evaluated along a square corner test ath (scale is 1:1) for finish milling with 2 mm/min feed rate and illustrated in fig. 13. Fig. 13. Tracking error for square corner 4.

The vibrations, which aear during the milling rocess, are reresented in fig. 14. Fig. 14. Vibro-record for feed rate 15

6 In the same time, it can be observe that acceleration amlitudes increase or decrease when the direction of feeding is change because the values and directions of cutting forces are changed and rigidit of the mechanical comonents of feed drive sstem are varing caused b re-loaded. Tracking error were evaluated along a square corner test ath (scale is 1:1) for finish milling with 2 mm/min feed rate and illustrated in fig. 13. Fig. 13. Tracking error for square corner 4.4 Contour error for circular ath In order to examine the contour error for the circular traector (fig. 6) four workieces was machined with different feed rates. The vibrations, which aear during the milling rocess, are reresented in fig. 14. Fig. 14. Vibro-record for feed rate 15 mm/min during the cutting rocess. Fig. 15. Profilograms for circular traectories; a) feed rate 15 mm/min; b) feed rate 3 mm/min. In fig. 15 are illustrated roundness and radial errors motion measurement under different feed rates. In the first case the circularit is 9 µm, in the second case the circularit is 12 µm. We can observe that the errors are bigger when feed rate increase. 5 Conclusion The aer investigated the contour errors on the bases of a comlete CNC sstem. The feed drive errors results from imerfection of machine tools control sstem. Tracking errors is equivalent to assuming erfect feeding, hence leaving the variation of cutting forces and its consequences due to this cause unchecked. It was determined that contour errors increased with feed rate, at a rate that escalates with curvature. Feed drive errors were evaluated along a square corner ath. The exerimental results verif that the cause of corner errors in contour manufacturing is due to the increase and reduction in feed seed near the connection osition between two linear motions to form the corner. The aroach roosed in this aer reresents a new wa of understanding CNC machining. References: [1] Altintas, Y., Engin, S., Generalized odelling of echanics and Dnamics of illing Cutters, Annals of CIRP, 5(1) (21), [2] Cheng, Y.., Chin, J. H., achining contour errors as ensembles of cutting, feeding and machine structure effects, International Journal of achine Tools & anufacture,43 (23), [3] Kim,.S., Chung, S.C., A sstematic aroach to design high-erformance feed drive sstems, International Journal of achine Tools & anufacture,45 (25), [4] Koren,Y., Variable gain cross-couling controller for contouring, Annals of CIRP, 4 (1) (1991), [5] Li, H., Li, X., odelling and simulation of chatter in milling using a redictive force model, International Journal of achine Tools & anufacture,4 (2), [6] arin, D., Errors of three-axis machining center, Toics in Alied echanics, vol III, Editura Academiei Române, 26, [7] Renton, D., Elbestawi,.A., High seed servo control of multi-axis machine tools, International Journal of achine Tools & anufacture,4 (2), ISBN: ISSN

CALCULATION METHOD OF MILLING CONTACT AREA FOR BALL-END MILLING TOOL WITH TOOL INCLINATION ANGLE

U.P.B. Sci. Bull., Series D, Vol. 76, Iss. 3, 214 ISSN 1454-2358 CALCULATION METHOD OF MILLING CONTACT AREA FOR BALL-END MILLING TOOL WITH TOOL INCLINATION ANGLE Yishu HAO 1, Guoqing TANG 2, Meng ZHANG