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1 Available online at ScienceDirect Procedia CIRP 14 ( 214 ) th CIRP International Conference on High Performance Cutting, HPC214 Influencee of Motion Error of Translational Rotary Axes onto Machined Surface Generated by Simultaneous Five-axis Motion Ryuta Sato a *, Kentaro Nishio b, Keiichii Shirase a, Gianni Campatelli c, Antonio Scippa c a Kobe University, 1-1, Rokko-dai, Nada, Kobe , Japan b Mitsubishi Heavy Industries, Ltd. d., 1-1, Wadasaki-cho 1, Hyogo, Kobe , Japan c University of Firenze, Via di Santa Marta 3, Firenze 5139, Italy * Corresponding author. Tel.: ; fax: address: sato@mech.kobe-u.ac.jp Abstract In machining process dynamic behaviorss of machine tools, such as tool vibration, vibration of mechanical structure, motion error of feed drive systems, influence machined surface. However, influencee of dynamic behaviors b onto machined surface generated by simultaneous five-axis axes onto machined surface generatedd by a simultaneous five-axis motion. The geometry used forr tests is e cone frustum, which motion has not been investigated up too now. This study focuses onn influence of motion error of translational rotary is typically used for evaluating machining accuracy of five-axis controlled machine tool. A method to simulate tool motion trajectory tool orientation for a five-axis machine has been b developedd based on modeling of t feed drive systems considering ir dynamic characteristic. The machined surface of cone frustum is predicted based on simulated results. In orderr to verify validity v of simulation result influence of motion error in each axis on finished surface, cutting tests have been carriedd out. The testss have proven that proposed simulation method can predict machined surface.. The influencee of motion error in each axis on finished surface is also discussed based on results of cutting tests simulations The Elsevier Authors..V. Published Open access by Elsevier under CC.V -NC-ND V. license. Sel Per Selection rformance ection Cutti peer peer-review r-review ing. under under responsibility responsibility of o of Internatio International onal Scientific Scientific Committee Committee of of 6th CIRP 6th Int CIRP ternational International Conference Conference on High on High Performance Cutting Key words: Five-axis machining center; Feed drive system; Motion error; Cone-frustum; Machined surface; Simulation 1. Introduction Five-axis machining processes are generally needed to machine sculptured surfaces in order to maintain optimal cutting parameters relative tool-surface machine tools can introduce geometrical errors on workpiece more than three-axis machine due to more complex geometry that introduces more error sources. In order to achieve higher quality for machined parts, it is orientation along surface. The five-axis required to evaluate errorr sources. all-bar measurement systems can be applied to identify geometrical errors such as offset orientation errors of rotational axes center [1], errors can be compensated based on identified results [2]. R-test systems [3]] can also be applied to identify geometrical errors [4]. In n addition, Dynamic synchronous accuracy between translational rotary axes strongly influences machined m accuracy with e simultaneouss five- method control method which can improve dynamic synchronous accuracy [5, 6, 7]. On or h, machined surfaces frequently have axis motions. One O of authors proposed an evaluation glitches due to various causes such as quality of NC program, geometrical accuracy of machine tools, characteristic off control systems, deflection of tools, so on. The glitches on machined surface deteriorate quality of machined parts. The authors proposed a general scheme of a simulation model based on e adaptive FE mesh of a machined component c that take care also a of tool Elsevier.V. Open access under CC -NC-ND license. Selection peer-review under responsibility of International Scientific Committee of 6th CIRP International Conference on High Performance Cutting doi: 1.116/j.procir

2 27 Ryuta Sato et al. / Procedia CIRP 14 ( 214 ) machine deflection due to inertia cutting forces [8]. Authors also investigated influence of motion error of feed drive systems ontoo machined surface considering only of dynamic behavior of feed drive systems [9]. However,, influence of dynamic behaviors onto machined surface generated by simultaneous five-axis onto influence off motion error of motion is not investigated up to now. This study focuses translational rotary axes onto machined surface generated by a simultaneous five-axis motion. In order to identify relationships between motion error of each axis machined surface, machined surface of cone frustum, whichh is typically used for evaluating machining accuracy of five-axis controlled machine tool, is investigated. The cone frustum cutting test equivalent measurement tests are a typical tests for evaluating machining accuracy of five-axis of motion errors onto machined surface, simulation method forr machine tools [1, 11, 12, 13]. In this study, in order to clarify influence machined surface which can consider dynamic behaviors of axes is proposed. In order to clarify validity off simulation method, cutting tests have been also carried out. The influence of motion errors have also been discussed based on experiment simulation results. 2. Experimental method Cutting measurement tests have been carried out using a vertical type five-axis machining center as shown s in Figure 1. This machine tool has three translational (,, ) two rotational ( C) axes. All translational axess are located in spindle side, two rotational axess are located in table side. All translational axes are driven by AC servo motors ball screws. Especially, - d - axis are driven by two motors ball screws for each. All translational axes are controlled by semi-closed loop control systems with feed backed rotational angle of motor. Two rotary axes are drive by DD (Direct Drive) motors. Figure 2 showss cutting measurement tests method. Figure (a) shows cutting test method (b) showss measurement test method. In cutting test, a workpiece is slantingly attached on to table with a jig. The measurement test is carried out with a ball bar system (QC2,( Renishaw plc.).. Figure 3 showss schematic diagram of workpiece C Fig. 1.. Structural configuration of five-axis controlled machining center. Fig. 2.. Cutting measurement tests method. Workpiece d z Rotary table (b) - plane view (a) - plane view all bar End-milll D C Fig. 3.. Schematic diagram of workpiecee ball-bar settings. ball bar settings. In order to achieve simultaneous five-axis table with motion, workpiece is attached onto offsets along -axis d y, -axis d z, inclination angle around -axis. Since t motion off each axis for f cone frustum cutting depends onn offsets inclination angle [13], see parameters are set to achieve simultaneous five-axis sensitive direction of ball bar is set to parallel with bottom surface of workpiece. The referencee length of ball bar is set to 5 motion. In measurement test withh ball bar system, mm. The motion for measurement has e same toolpath of cutting test. Table 1 lists cutting setting conditions for experiments. The diameter d of bottom surfacee of cone frustum d y Jig

3 Ryuta Sato et al. / Procedia CIRP 14 ( 214 ) Table 1. Experimental condition for cone frustum cutting measurement. Tool type Square end mill Tool diameter 1 mmm Number of flutes 2 Workpiece Aluminum (A552) Diameter of bottom surface D 9 mmm Inclination angle Half apex angle Center offset d y, d z Feed rate Radial depth of cut Axial depth of cut Spindle speed 1 degg 15 degg 6 mm, 6 mm 6 mm/min.2 mm 2 mm 7 rpmr is set to 9 mm. As results that diameter of motion trajectory of tool center point (TCP) becomes 1 mm of square endmill with diameter of 1 mm is used for machining. The axial radial depths of cuts c are set to 2 mm.2 mm, respectively. The motion of axes are not influenced from cutting force because of cuttingg force is negligible in this cutting condition. The machined surface is observed with CCD microscope with 3,, pixels (TG3PC2, Shodensha inc.) as shown in Figure 4. The tool marks on machined surface are compared with simulated results as discussed below. For both cutting measurement tests, backlash compensation parameters are intentionally changed too yield motion errors at motion direction off each axis changing points, though re is no large motion error in machine with original setting. Fig. 4. Machined surface observation method. 3. Machined surface simulation 3.1. Simulation flow Figure 5 shows proposed flowchart for machined surface simulation. At first step, positional angular comms of each axis for cone frustum cutting are generated based on inverse kinematics. The generated positional angular comms are also feeded f to actual machine tool as an NC program. At second step of simulation, motion errors of each axis a are simulated Fig.. 5. Flow chart off machined surface simulation. with dynamic behaviors of each axis. The simulated position angle with dynamic behaviors indicates position angle of each axis in machine coordinate system. The tool posture; tool center point (TCP) t tool orientation in table coordinate systemm can be obtained by forward kinematics calculation as third step. Finally, machined surface including tool marks on surface s is predicted based on simulated trajectory of TCP tool orientation Feed drive system s model Figure 6 shows dynamics models of feed drive mechanisms for each axis. Table 2 (a) (b)( shows list of parameters of models for translational a rotary axes. Table 2. Parameter list of dynamics model of feed drive mechanisms. J m, J m1, J m2 K a, K a1, K a2 l c b, c b1, c b2 f b, f b1, f b2 c t, c t1, c t2 f t, f t1, f t2 c i, c i1, c i2 d t1 d t2 J t M t, 1, 2 m, m1, m2 t y n1, y n2, z n1, z n2 y g1, y g2, z g1, z g2 x t, y t,z t J c f M l g, C Generatepositionalcomms Simulatemotionerrorofeachaxis Calculatetoolcenterpoint (TCP)toolorientation Predictmachinedsurfaceprofile (a) Translational axes kgm 2 Inertia of motor ball screw N/m Equivalent axial stiffness m Lead of ball screw Viscous damping of bearings, ball screw s/rad d nut Coulomb's friction torque of bearings, balll screw nut Ns/m Viscous damping at linear ball guides Coulomb's friction force of linear ball N guides Ns/m Internal damping coefficient Distance from centerr of driven part to m linear guide way m Distance from centerr of driven part to nut kgm 2 Inertia of driven partt around yaw axis kg Mass of table Motor torque rad Rotational angle of motor rad aww angle of drivenn part m Axial displacement of o nut m Axial displacement of o guide carriage m Axial displacement of o table kgm 2 s/rad rad Start End (b) Rotary axes Total inertia of rotary axis Viscous damping of bearings Coulomb's friction torque Maximum gravity disturbance torque Motor torque Rotational angle of tablet

4 272 Ryuta Sato et al. / Procedia CIRP 14 ( 214 ) m1 1 m2 2 l 2 m1 J m1 l 2 m2 J m2 m f b1, c b1 f b 2, c b2 K a1 c i1 K a2 c i2 J m f b, c b d t1 d t 2 t l m 2 y K a c i y g 1 y n1 t J t, M t y n 2 y g 2 x t M t f t, c t (a) -axis model (b) - -axis model f g1 c g1 f g2 c g2 calculated from designed drawing specification data. However, parameters on friction dumping cannot be calculated. These parameters are identified through by matching measured simulated motor torque curves during motion [14]. Figure 7 shows block diagram of servo control system of each axis drives. The system has typical P PI controllers for position velocity controllers, respectively. The output signal from velocity controller is inputted to dynamics model shown in Figure 6 as motor torques. The simulated rotational angles of motors are feed backed into servo controller model from dynamics model. K pp is proportional gain of position loop, K vp is proportional gain of velocity control loop, T i is integral time of velocity control loop. These parameters are determined based on set values in NC controller. The backlash compensator is also introduced into servo control system model. All simulations are carried out using MATLA Simulink. Positional (or angular) comms acklash compensator Velocity Position (or angle) controller controller Motor torque 1 K pp K vp 1 T i s s Feed backed position (or angle) f, c Fig. 7. lock diagram of servo control system. Center of gravity of -axis C J M g (d) C-axis model f, c M g Fig. 6. Proposed models for feed drive mechanism of each axis. sin -axis feed drive mechanism is modeled as a 2 DOF system with axial stiffness as shown in Figure 6 (a). It had already been confirmed that model can accurately simulate motion errors [14]. - -axis are modeled as a 4 DOF model as shown in figure (b) since axes are driven by a couple of motors ball screws. This model considers rotational angles of both motors translational yaw motion of driven part. Two rotary axes, - C-axis are modeled as 1 DOF model shown in figures (c) (d), because of rotary axes are drive by DD motors. Since -axis is influenced from gravity, moment due to gravity force is considered into -axis model. The parameters such as inertia, mass stiffness can be l (c) -axis model 2 J ( M l ) 3.3. Machined surface simulation The tool posture; tool center point (TCP) tool orientation in table coordinate system can be obtained by forward kinematics calculation from simulated positions angles of each axis. The obtained trajectory of TCP orientation indicates trajectory orientation of tool center line. Figure 8 shows schematic drawing of proposed machined surface simulation method. In proposed method, interval of TCP data is determined as same with feed per flutes on machined surface. The trajectories of cutting edges can approximately be defined as circle with center of TCP data as shown in Figure 8. The intersection points of circle arcs which represent cutting edge trajectories can be obtained from TCP data tool diameter. This result represents machined surface Work piece Tool Feed direction Intersectional points Tool marks TCPs Cutting edge trajectories Fig. 8. Schematic drawing of machined surface simulation.

5 Ryuta Sato et al. / Procedia CIRP 14 ( 214 ) profile. The machined surface can be expressed from two profiles on bottom surface upper surface of workpice, approximately. The tool marks on surface can be represented by connecting pairs of intersectional points. 4. Experiment simulation results 4.1. Motion trajectory Figure 9 shows velocity of each axis during e cone frustum cutting motion under conditions of Table 1. All five axes move during motion motion direction of axes changed except C-axis. It is expected that motion error exists around motion direction changing points. Figure 1 shows measured simulated motion trajectories of TCP. It can be seen that stepwise errors can be observed around motion direction changing points, proposed model can well simulate motion trajectory Machined surface Figure 11 shows experiment simulation results of machined surface around motion direction changing points of each axis. Velocity mm/s Velocity deg/s Angle deg (a) Translational axes C Angle deg (b) Rotary axes Fig. 9. Velocity of each axis during cone frustum cutting c motion. 9 Experiment Simulation 18 1 div. : 5 m 27 Feed rate: 6 mm/min Radius: 5mm Feed direction: CW Fig. 1. Comparison of measured simulated motion trajectories. Fig Influence off motion error of each axis onto machined surface.

6 274 Ryuta Sato et al. / Procedia CIRP 14 ( 214 ) Workpiece L 2 2) The -axis motion error does not affect machined surface in case of peripheral milling with square end mills using table tilt type machine tools. The authors will try to develop a simulation method which can simulate or factors, such as tool deformations structural vibrations of machine tools. Fig. 12. Schematic drawing of influence of -axis motion error. In figure, upper graphs represent enlarged motion error around each changing point, lower figures represent machined surfaces. In pictures of machined surface, solid lines are appended onto tool marks in order to make clear marks. It is clear from figures that interval of tool marks are changed around stepwise motion errors, except motion direction of -axis is changed. These disturbed tool marks can be observed as glitches on machined surface. It also can be seen that proposed simulation method for machined surface can adequately predict influence of motion error onto machined surface. Figure 12 describes influence of -axis motion error onto ball bar length machined surface. Since sensitive direction of ball bar is set to parallel with bottom surface of workpiece, ball bar length is influenced from -axis motion error as shown in figure. On or h, since side line of end mill is parallel to both of -axis machined surface, motion error along -axis cannot be copied onto machined surface in case of peripheral milling by square end mills. This fact is reason why disturbed tool marks cannot be observed around point of motion direction of -axis change, as shown in Figure 11 (c). It is expected, of course, that -axis motion errors influences machined surface if tool is tilted in universal head type machine tools. It can be said from results that proposed simulation method for machined surface can adequately predict influence of motion error onto machined surface, -axis motion error does not affect machined surface in case of peripheral milling with square end mills using table tilt type machine tools. 5. Conclusions In this study, a simulation method for machined surface which can consider dynamic behaviors of axes is proposed, cutting test has been also carried out. The conclusions can be summarized as follows: 1) The proposed simulation method for machined surface can adequately predict influence of motion error onto machined surface L 1 all bar Acknowledgements This work was supported by JSPS KAKENHI Grant-in-Aid for oung Scientists () No , Machine Tool Engineering Foundation, Die Mold Technology Promotion Foundation. The authors also would like to sincerely acknowledge all support from MTTRF ( Machine Tool Technology Research Foundation). References [1] Tsutsumi M, Saito A. 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Analysis of circular trajectory equivalent to cone-frustum milling in five-axis machining centers using motion simulator. In: International journal of machine tools & manufacture; 64, 213. P [14]Sato R, Tsutsumi M. Modeling, controller tuning techniques for feed drive systems. In: Proceedings of ASME dynamic systems control division; Part A, DSC-74-1, 25. p [15]Kato N, Tsutsumi M, Tsuchihashi, Sato R, Ihara. Sensitivity analysis in ball bar measurement of three-dimensional circular movement equivelent to cone-frustum cutting in five-axis machining centers. In: Journal of advanced mechanical design, systems, manufacturing; 7-3, 213. p