IMPROVING CNC MACHINE TOOLS ACCURACY BY MEANS OF THE CIRCULAR TEST AND SIMULATION

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1 Proceeding in Manufacturing Sytem, Vol. 5 (00), No. 3 ISSN IMPROVING CNC MACHINE TOOLS ACCURACY BY MEANS OF THE CIRCULAR TEST AND SIMULATION Radu-Eugen BREAZ, Octavian BOLOGA, Gabriel RACZ 3, Valentin OLEKSIK 4 Abtract: Thi paper preent a method for improving the accuracy of CNC machine tool by mean of a joint approach: experimental tet and imulation. In the firt tage, a circular tet wa performed, by mean of a pecial meauring device. The error hown by the meaurement were evaluated and poible caue were aeed. After running a imulation proce, which took into conideration the phenomena which may caue the error, poible olution for reducing the error were propoed. Finally, new meaurement validated ome of the olution. The propoed approach i indented to be ue at the hop floor level, o it wa kept a traightforward and fat a poible. Key word: accuracy, circular tet, ballbar tranducer, CNC machine tool, imulation.. INTRODUCTION Computer numerically controlled (CNC) machine tool have played an important role in preciion machining. In recent year, machine tool builder have been under increaing preure from the manufacturing indutry to provide a higher contouring accuracy for a multiaxi CNC machine tool. The increaing demand for higher dimenional accuracie and the trong trend toward hop floor automation induce the need to develop cot-effective method to improve the performance of CNC machine tool. The dimenional accuracy of machined part i one of the mot important factor in determining thi performance. In multi-axi machine uch a machine tool, coordinate meauring machine and robot, it i often difficult to achieve the deired accuracy due to the complexity and the interaction of the variou error ource.. CIRCULAR TEST To achieve high-preciion machining, CNC machining centre mut have contouring accuracy. Therefore, a meaurement method to ae the contouring accuracy of CNC machine centre ha to be etablihed. In recent year, a circular tet ha been developed to meaure and diagnoe contouring error of CNC machine tool [ 6]. The circular tet i a widely ued method to meaure motion error of CNC machining centre. During the tet, a circular path i generated by a CNC controller and a tranducer bar i mounted between the machine pindle and table. A the machine travel around the circular path, the bar meaure the deviation relative to a tandard circle. The deviation can then be ued to indicate the motion error of CNC machining centre. For thi reearch, a Renihaw QC0 ballbar ytem wa ued (Fig. ). The ytem and it oftware i ued to meaure geometric error preent in a CNC machine tool and detect inaccuracie induced by it controller and ervo drive ytem. Error are meaured by intructing the machine tool to 'Perform a Ballbar Tet' which will make it cribe a circular arc or circle. Small deviation in the radiu of thi movement are meaured by a tranducer and captured by the oftware. The reultant data i then plotted on the creen or to a printer or plotter, to reveal how well the machine performed the tet. If the machine had no error, the plotted data would how a perfect circle. The preence of any error will ditort thi circle, for example, by adding peak along it circumference and poibly making it more elliptical. Thee deviation from a perfect circle reveal problem and inaccuracie in the numerical control, drive ervo and the machine' axe. During the data capture eion, the Ballbar move in a clockwie and counter-clockwie direction through 360 data capture arc with 80 angular overhoot arc. PhD, Aoc. Prof.,. radu.breaz@ulbibiu.ro PhD, Prof., Head of Department of Machine and Equipment, octavian.bologa@ulbibiu.ro 3 PhD, Aoc. Prof.,. gabriel.racz@ulbibiu.ro 4 PhD, Lecturer, valentine.olekik@ulbibiu.ro Univerity Lucian Blaga of Sibiu, Department of Machine and Equipment, Emil Cioran 4, Sibiu, Tel./Fax , ext / Fig.. The ballbar ytem.

2 58 R.E. Breaz et al. / Proceeding in Manufacturing Sytem, Vol. 5 (00), No. 3 / 57 6 Fig.. The initial meaurement. Fig. 4. The third meaurement after backlah compenation. Fig. 3. The econd meaurement after a mechanical adjutment of the encoder mounting. Figure how an initial meaurement reult on a Realmeca C vertical machining center. After running the oftware analyi, three main group of error were reported: Cyclic error, of about 40 µm on each axi; Backlah error of about 60 µm on X-axi and 40 µm on Y-axi: Reveral pike on X axi of about 00 µm. The poible caue for the cyclic error could be: the axi ballcrew thread i defective cauing the axi to move in a inuoidal manner rather than at a uniform rate, or the encoder mounting may be eccentric, or the ballcrew mounting may be eccentric or badly adjuted reolver or inductoyn. After a mechanical adjutment of the encoder mounting, a econd meaurement wa performed. The reult are preented in Fig. 3. A ignificant improvement in the reult i noticeable, further compenation tep are neceary. A backlah compenation algorithm i included in CNC equipment oftware. The algorithm allow the uer to introduce the maximum value of the backlah on each axi and the CNC controller will compenate it. After thi compenation tep, a ne w meaurement wa performed (Fig. 4). The remaining ignificant error i the reveral pike on X axi. In order to find a compenation method, the poible caue have to be analyzed. Reveral pike appear when an axi i being driven in one direction and then ha to revere and move in the oppoite direction, intead of revering moothly it may paue momentarily at the turnaround point. There are everal poible caue of thi problem: An inadequate amount of torque ha been applied by the axi drive motor at the axi reveral point cauing it to tick momentarily at the reveral point, a the frictional force change direction. The ervo repone time of the machine i inadequate on backlah compenation. Thi mean that the machine i unable to compenate for the backlah in time; cauing the axi to top while the lack caued by the backlah i being taken up. Servo repone at the croover point i poor, cauing a hort delay between the axi topping movement in one direction and tarting movement in the other. 3. THE MODEL OF THE SYSTEM In order to find a olution to compenate the reveral pike, a tudy of the feed chain of the X-axi, aimilated a a cloed loop poition by mean of a imulation proce wa propoed. The firt approach in tudying the ytem behaviour i to build a reliable model of it, baed upon tranfer function. One of the tep involve the decription of each axi of movement a a poition control ervo ytem. Generally, uch kind of ytem, no matter which actuation ytem i ued, ha a chematic tructure a depicted in Fig. 5. The relation between the angular peed of the DC ervomotor ω and the input voltage U, with regard of the complex variable, can be expreed a [7 and 8]:

3 R.E. Breaz et al. / Proceeding in Manufacturing Sytem, Vol. 5 (00), No. 3 / K H 0 P( = =. (8) M ( + τ Conidering the voltage input and the tatic moment a tep input and applying the Laplace tranform to thee input: U( = U. (9) Fig. 5. Schematic tructure of a poition control ervo ytem. α K a K t = [ U( + τ RB + K t K v, () R M ( ] RB + K t K v R motor armature winding reitance [ Ω]; J r rotor inertia [kgm ]; B vicou friction contant [Nm/rad]; K t motor torque contant [Nm/A]; K v velocity contant [V/rad]; K a the amplifier gain; K th tachometer gain [V/rad]; τ m mechanical time contant [] which can be expreed a: RJ τ =, () m RB + K K t v τe= ατm. (3) τ e electrical time contant of the motor; α the attenuation factor. Then the motor peed can be expreed in the following form: KU ( K M ( = + τ αk a K t K = RB + K t K αr K = RB + K t K v v. (4) [rad/v]. (5) [rad/nm]. (6) Equation (4) how the component of the tranfer function of the cloed velocity loop: one tranfer function between the input voltage and the motor peed and one between the tatic torque (diturbance) and the motor peed, leading to the following: and H 0 K ( = =. (7) U( + τ M ( = M. (0) then the motor peed t) i given by the following expreion: αk K K R t a t α t - ω ( t) = ( U M ( e τ). () RB + K t K v RB + K t K v The unknown factor in equation () are the amplifier gain K a and the tachometer feedback K p which i included in α. Impoing that for the maximum voltage U m and for the maximum tatic load M m, the motor peed ha to reach the maximum value ω m, thee two factor can be determined. The condition tated above characterize the tationary regime of the ytem, when t : t τ lim e = 0. () t In thi condition, equation () become: α K a K t α K t R ω m = U m M m. (3) RB + K t K v RB + K t K v Now we have to determine the analogical to digital converter gain K c, the encoder gain K e, and gear reducer gain K g. The encoder i characterized by the encoder gain K e, defined a the number of pule emitted for one rotation of the lead crew: N imp K e = π [pule/rad]. (4) N imp number of the pule emitted by the encoder at a full rotation. The gear reducer gain K g can then be expreed a: = K g ip π [m]. (5) U DAC the digital to analogical converter input voltage [V]; n number of bit of the converter. The block diagram of the poition control ytem i preented in Fig. 6. Starting from the control voltage of the velocity loop U c (, obtained at the output of the analogical to digital converter:

4 60 R.E. Breaz et al. / Proceeding in Manufacturing Sytem, Vol. 5 (00), No. 3 / 57 6 Fig. 6. The block diagram of the poition control ytem. U c ( = K p K e xr ( K e K c( ). (6) K g K p poition controller proportional gain; x r poition reference (BLU). It i now poible to determine the Laplace tranform of the angular peed of the motor with regard of the poition reference x r ( and the tatic load M (. Replacing relation (6) in (4), we obtain: Fig. 7. The imulation diagram. ( K 0 xr ( K M ( ) ω ( =. (7) τ + + K KK p K c K K = K g e 0 and K = K K p K c K e. (8) The relation (7) indicate the fact that the cloed poition loop can be conidered a a econd order ytem with the characteritic equation: Voltage Amplifer gain Ka Torque /R Kt Motor torque contant Angular peed J.+B Dynamic + ξωn + ωn = 0. (9) where the damping ratio and natural frequency are: ξ ; Kτ = n ω = K. (0) τ Kv Motor velocity contant Kth The relation between natural frequency and the damping ratio i: ωn = ξk. () Taking into conideration equation 0, the poition controller gain Kp may be expreed a: 4. COMPUTER SIMULATION K p = 4ξ τk K K. () Baed upon the model of the ytem, a imulation diagram wa built for the poition control ytem, uing Matlab & Simulink oftware, a hown in Fig. 7. The velocity loop ubytem i preented in Fig. 8. The CNC feed drive act a a poition control ytem, but with a numerical character. c e Tachometer gain Fig. 8. The velocity loop ubytem. In order to take that into conideration, two zeroorder hold block were introduced in the model. One of thee block wa included in the digital to analogical converter (DAC) block and the other one on the poition feedback loop, after the encoder, within the ample and hold block. The zero-order hold ha the following tranfer function: T e H 0 =. () where T i the ampling period of the numerical ytem.

5 R.E. Breaz et al. / Proceeding in Manufacturing Sytem, Vol. 5 (00), No. 3 / Input data The input data the imulation wa gathered taking into conideration the experimental ytem, a feed drive of a CNC milling machine. The poition control ytem, on all feed dive a actuation device on feed drive Sanyo T730-0 dc ervomotor. The experimental parameter are yntheized in Table. According to paragraph 3, the following parameter may be calculated: α = 0.344, K a = , K = 9.88 rad/v. With a U DAC = 8 V and n = 4, we obtain for the digital to analogical converter gain the value K c = V/bit. Finally, impoing a damping ratio ξ = and according to (5), a value K p = 0.08 i obtained for the poition controller gain. Experimental parameter Table Parameter Unit Value Motor rated power P [W] 300 Motor rated armature voltage [V] 75 Ub Motor rated torque M [Nm].8 Motor rated rotating peed n [min-] 500 Motor intantaneou maximum [A] 40 armature current i Motor armature winding [ Ω]. reitance R Motor torque contant Kt [Nm/A] 0.73 Motor velocity contant Kv [V/rad] 0.73 Motor intantaneou maximum [rad/] angular acceleration ε Motor rotor inertia Jm [ kgm] Mechanical time contant τm [m] Electrical time contant τe [m] Load inertia Jl [ kgm] Motor vicou braking contant [Nm/rad] Bm Tachometer gain Kth [V/rad] Lead crew tep [mm] 5 Gear ratio ig - Incremental encoder gain Ke [imp/rad] 500/π Ma of the lide [kg] 30 Cutting force [N] 000 Sampling period T [] 0.0 Figure 9 preent the imulated poition output compared with the reference poition input for the uncompenated ytem for a pecific movement cycle. The ytem accelerate, then the machine lide travel with contant velocity, then it decelerate and the velocity change it ign, following another accelerationdeceleration cycle but with revered direction. From Fig. 9 one may notice that a hort delay between the axi topping movement in one direction and tarting movement in the other occur, which caue the reveral pike of the X-axi. A fit approach in compenating thi delay would be the increaing of the poition controller gain K p. However, a greater value of K p will introduce a ignificant amount of ocillation in the ytem, o it ha to be accompanied by another compenation method. In order to reduce the ocillation, a derivative component D wa introduced in the poition controller, a component which i alo allowed by the CNC controller. Initially, the derivative gain K d of the poition controller wa kept to zero. According to the documentation of the CNC controller, the derivative component D of the numerical poition controller i defined by the following equation: K ( z ) d D =, (3) T z -T where z = e i the dicrete variable Finding a proper value for the derivative gain K p uing an analytical proce may be poible, but it i rather complicated. A trial an error iterative imulation wa ued in order to find a et of appropriate value for both the increaed proportional gain K p and the derivative gain K d of the numeric poition controller. After running the above mentioned proce, an acceptable et of value were find a K p = 5 and K d = 0.. The imulated poition output compared with the reference poition input for the compenated ytem i preented in Fig. 0. It i here noticeable the fact that the delay between the axi topping movement in one direction and tarting movement in the other i ignificantly reduced compared with the ituation of the uncompenated ytem output reference output reference Diplacement X [m] Diplacement [m] Time [] Fig. 9. Poition output uncompenated ytem Time [] Fig. 0. Poition output uncompenated ytem.

6 6 R.E. Breaz et al. / Proceeding in Manufacturing Sytem, Vol. 5 (00), No. 3 / 57 6 Fig.. The meaurement after compenating the reveral pike on X-axi. After completing the imulation proce, the compenation parameter were introduced in the experimental ytem and the circular tet wa run again. The meaurement reult i preented in Fig.. One may notice the fact that the reveral pike on X axi were reduced ignificantly, a fact which confirmed the propoed approach. Thu, by a combined imulation and experimental proce, the overall accuracy of the CNC machine wa ignificantly improved. The proce wa performed entirely at the hop floor level, with low-cot involved and in a very hort period of time. 5. CONCLUSIONS Thi paper preent an approach for improving the contouring accuracy of a CNC machining centre. The reearcher in the field of CNC machine tool accuracy may find in the literature numerou uch method, but mot of them have to be implemented in the deigning phae of the machine, or require intervention in the CNC controller tructure. Both of the above-mentioned approache are time conuming and cannot be applied at the hop floor level, which wa the main goal of thi reearch. The propoed method i uitable to be implemented at hop floor level, which i very important in today demanding production environment, where the manufacturer have to adjut rapidly the accuracy of their product, according to the cutomer pecification. The firt tage of thi approach involved a circular tet, which revealed the mot ignificant error of the machine during a circular movement. Some of the error were compenated either by mechanical adjutment of the feed axe or by uing internal compenation algorithm implemented within the CNC controller. However, a large amount of reveral pike appeared on the X axi could not be compenated by thee mean. In order to compenate the remaining error, a logical approach would be to alter the control parameter of within the CNC controller. It i well known that indutrial CNC controller offer a wide range of option regarding the control ytem parameter, which may be altered in order to obtain a better dynamic behaviour, and contouring accuracy of the machine. However, the ignificance of thee parameter and alo the determination of ome analytical relation to calculate an optimal value of them are hard to be found. Moreover, complex mathematical model of the poition control ytem on each axi are hard to be implemented, due to the difficulty to meaure and/or calculate the parameter of uch model. The author propoed a traight-forward mathematical model of a feed axi, baed upon continuou tranfer function and preented a method for calculation of the model parameter. Alo, the numerical character of the control ytem wa taken into conideration by introducing pecific tranfer function. Baed upon the propoed model, a trial and error imulation proce wa performed and a et of appropriate parameter were found. A new circular tet validated the reult of the imulation, howing that the remaining error were reduced ignificantly. REFERENCES [] J.B. Bryan, A imple method for teting meauring machine and machine tool, Part : Principle and application, Preciion Engineering, 4(), 98, pp [] W. Knapp, Circular tet on NC machine tool in indutrial application, Indutrial and Production Engineering, 0(3), 986, pp [3] Y. Kakino, Y. Ihara and Y. Nakatu, A tudy on the motion accuracy of NC machine tool, Part : Diagnoi of motion error origin by uing double ball bar tet, Bulletin of JSPE, 5(0), 986, pp [4] M. Burdekin and J. Park, Contiure A computer aided ytem for aeing the contouring accuracy of NC machine tool, 7th International MATADOR Conference Proceeding, 988, pp [5] Y. Kakino, Y. Ihara and Y. Nakatu, The meaurement of motion error of NC machine tool and diagnoi of their origin byuing telecoping magnetic ball bar method, Annal of CRP, 36(), 987, pp [6] Y.S. Tarng, J.Y. Kao and Y.S. Lin, Identification of and Compenation for Backlah on the Contouring Accuracy of CNC Machining Centre, International Journal of Advanced Manufacturing Technology, 3, 997, pp [7] A. Buxbaum, K. Schierau and A. Straughen, Deign of Control Sytem for DC Drive, Springer Verlag, Berlin, 990. [8] R.E. Breaz, O. Bologa,V. Olekik and G. Racz, Computer Simulation for the Study of CNC Feed Drive Dynamic Behaviour and Accuracy, Proceeding of the IEEE Region 8 EUROCON 007, International Conference on Computer a a tool, pp. 9 33, Waraw, Poland, September 007.