Machining, Measurement, and Control Laboratory. Research Summaries Department of Micro Engineering, Kyoto University

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1 Machining, Measurement, and Control Laboratory Research Summaries 27 Department of Micro Engineering, Kyoto University

2 Machining, Measurement, and Control Laboratory Department of Micro Engineering, Kyoto University Faculties and Staffs Professor Atsushi Matsubara, Dr. Associate Professor Soichi Ibaraki, Dr. Technician Iwao amaji, Dr. Secretary Hiromi Ishizuka 2

3 Table of Contents 1. High-Precision Positioning and Machining High-precision Machining by Measurement and Compensation of Motion Error 4 D. Kono On high-precision motion control by ball screw drives 5 T. Hatozaki Nanometer Positioning by using Hybrid Servo System 6 T. Fujita 2. Measurement for Machine Tools Prediction of Machining Accuracy of 5-Axis Machine Tools with Kinematic Errors 7 M. S. Uddin Measurement of Spindle Stiffness for the Development of Intelligent Spindle 8 M. Sugihara Laser Step Diagonal Measurement 9 for the Estimation of Three-dimensional Volumetric Errors T. Hata Measurement of Motion Accuracy Using a Laser Tracking System 1 A. Iizuka Self-calibration of the Cross Grid Encoder 11 S. Ibaraki 3. Machining Process Control and Tool Path Generation Development of a Cutting Force Monitoring System for Intelligent Machining 12 A. A. D. Sarhan Constant Engagement Tool Path Generation for the Improvement 13 of Machining Accuracy in 2D Milling with a Straight End Mill M. S. Uddin Control of Tool Life in End Milling Processes 14 T. Shimizu Issued: March 31, 27 3

4 High-precision Machining by Measurement and Compensation of Motion Error Daisuke Kono 2nd year master course student, Machining, Measurement, and Control Laboratory, Kyoto University Rectification machining process is often used to achieve sub-micron-order geometrical accuracy in cutting. To avoid machining errors due to loadings and unloadings of the workpiece, on-the-machine measurement is used. In on-the-machine measurement, motion errors of machine tools directly cause the measurement error. In order to solve these problems, motion errors in machining process are measured and compensated. Straightness error was measured, modeled, and compensated on a machine tool with ball screw system. In these days, demands for high-precision machining which aim to achieve sub-micron-order geometrical accuracy and surface roughness are increasing. Highprecision machining is defined as the machining between precision machining and ultra-precision machining, and flexibility and productivity as well as accuracy are required. The major sources of machining errors are motion errors of machine tools and tool deformations. In order to reduce machining errors, rectification machining process have been used. In this process, geometrical errors of workpiece are measured by using a coordinate measuring machine in semi-finishing and the errors are compensated in finishing To avoid machining errors due to loadings and unloadings of the workpiece, on-themachine measurement is used. In on-the-machine measurement, motion errors of machine tools directly causes the measurement error. In order to solve this problem, motion error compensation is effective. The compensation is often applied to coordinate measuring machines. However, it is generally difficult to apply the compensation to machine tools because of the fluctuation of motion errors that depends on operating conditions and thermal problems due to heating sources such as motors. The objective of this research is to develop a compensation method for high-precision machining. The final goals are to measure, model, and compensate the motion errors in machining process and to achieve.5 μm geometrical machining accuracy in the area of 1 mm 1 mm. For the first step of the reaserch, motion errors in Z direction on plane is measured and compensated on a machine tool with ball screw feed drive systems. 2 COMPENSATION METHOD Because a flat plane is required as the reference in machining, the flatness error is compensated in this research. Figure 1 shows a schematic view of the plane machining by using a non-rotational cutting tool such as a diamond bite. In this machining, motion errors in Z direction on plane are copied on the workpiece. The motion errors are estimated by using the motion error model and Z-axis is commanded to cancel the motion errors. The motion errors are modelled as the sum of straightness errors of and axis. Each straightness error is modelled by using Fourier series. Straightness errors are measured and the repeatable error components are modelled selectively. 4 The motion errors are measured by using a optical flat and a displacement sensor. 3 COMPENSATION EPERIMENT To investigate the effect of the compensation, a compensation experiment was carried out and the variation of the relative position of the tool to the table was measured. Figure 2 shows the experimental setup. The conditions were decided from cutting conditions for the plane machining. Figure 3 and 4 show the results without and with the compensation respectively. The variation of the relative position is smaller with the compensation. The variation is reduced from 1.7 μmp-v to.7 μmp-v. Z Pick feed Workpiece Tool Machined surface Fig.1 Plane machining Laser displacement sensor Fig.3 Relative position of the tool to the table without compensation Fig.4 Relative position of the tool to the table with compensation Z Optical flat Tool post table Fig.2 Experimental setup

5 On high-precision motion control by ball screw drives Takashi Hatozaki 2 nd year master course student, Machining, Measurement, and Control Laboratory, Kyoto University A ball screw drive is often used on machine tools. This research investigates various issues with the application of a ball screw drive to achieve sub-micrometer order motion accuracy. To isolate the issues with the ball screw drive, we built a test stand of one-axis drive which is driven by a high-accuracy ball screw and aerostatic guideway. The test stand achieved 1nm step positioning resolution, but its horizontal straightness error was about 4 micrometer. To reduce this error, we designed and developed a nut bracket which can improve horizontal straightness error from 4 micrometer to 1 micrometer. Recently, needs for high precision machining grow bigger and bigger. The high precision machining requires both geometric and surface accuracies under sub-micrometer order. In high precision machining tools, a linear motor is usually used. A linear motor has no friction, and thus it is easier to achieve higher precision motion accuracy. A critical issue with a linear motor as a drive for machine tools is its lower load capacity. On the other hand, a ball screw drive has advantages in higher stiffness and cost effectiveness. However, it is said that a ball screw drive is not suitable for high precision motion, since a ball screw drive can be a cause of vibration in itself, and is subject to larger friction. If we can achieve higher precision motion by a ball screw drive, it is more favorable as a machining tool. The objective of this research is to experimentally investigate the limitation in the motion accuracy of a ball screw drive. We also propose a scheme to improve its motion accuracy. 2 CONFIGURATION OF THE TEST STAND To isolate motion errors caused by a ball screw drive only, we made the test stand which consists of a ball screw and an aerostatic guideway. The test stand is shown in Fig1. The table and guideways are made of stone to minimize the thermal influence. The linear encoder s (by Heidenhain) resolution is 1nm. The CNC s (MELDAS MAGIC68 by MITSUBISHI) positioning resolution is also 1nm. The ball screw s (by NSK) diameter is 32mm and its lead is 1mm. 3 STEP POSITIONING ERROR MEASUREMENT First, we measured its step positioning accuracy. We put the gauge block to the front of test stand s table. Then, we set up a capacitance sensor (by Lion, with the resolution of 1nm) in front of the gauge block. We command the step-shaped reference trajectory of the step size 1 nm for 5 times in each of forward and backward directions. An example of measurement results is shown in Fig. 2. We can see the 1 nm step, and thus we concluded that this test stand has 1 nm positioning resolution. The first order delay observed in the response is caused by the friction between the ball screw and the nut. 5 4 STRAIGHTNESS ERROR MEASUREMENT We measured the horizontal straightness error when the table moves from =-6mm to =6mm. The federate was 3,6, and 12 mm/min. An example of measurement results is shown in Fig. 3. There is no difference due to the difference in the federate. We can see a periodic error whose cycle is 1mm and its maximum amplitude is about 4µm. Because the ball screw s lead is also 1mm, we concluded that this periodic error is caused by the ball screw s vibration. 5 IMPROVEMENT OF STRAIGHTNESS ERROR To improve the straightness, we designed and made the compliance nut bracket, as shown in Fig. 4. We measured the straightness error with the compliance nut bracket installed. An example of the results is shown in Fig 5. We can see that the maximum amplitude was reduced from 4µm to 1µm. horizontal displacement μm horizontal table displacemnt μm Z Fig1 test stand table position mm Fig3 horizontal straightness time s table position nm Fig2 step positioning Fig4 compliance nut bracket table position mm 4 6 Fig5 horizontal straightness with compliance nut bracket

6 Nanometer Positioning by using Hybrid Servo System Tomoya Fujita 4 th year undergraduate Student, Machining, Measurement, and Control Laboratory, Kyoto University Ever higher positioning performance is always required in the field of positioning. A one-axis positioning stage, driven by a servo motor and piezoelectric actuator, has been constructed.2 nanometer positioning resolution was achieved by using closed loop control. Precise positioning is a basic and important technology. Ever higher positioning performance is always required in the field of positioning. It is said that there will be more needs for the positioning system that can achieve 1nm positioning. As for the machine tools, ball screw drives are mainly used for positioning system. A ball screw drive has good characteristics to obtain long stroke and high load capacity. But positioning accuracy beyond 1nm is generally difficult to be achieved less than 1nm on conventional design. As a positioning method to realize high resolution and long stroke, hybrid servo system that consists of finemotion mechanism and course-motion mechanism is well known. In typical hybrid servo system, fine-motion mechanism table is always lifted on the course motion table; consequently there is offset between fine-motion table and course-motion table. Because of this offset, such a hybrid servo system is often subject to angular errors. To solve problem, the hybrid servo system has developed This paper reports positioning performance of the developed system. 3 POSITIONING EPERIMNET A fine motion step positioning experiment was carried out using a closed loop controller. In this experiment, the positioning error was measured at two points, the tool position and the table position. The value of tool position is measured by a capacitance displacement sensor, and that at the table is measured by a linear encoder. An example of experimental results, 2nm step response of the fine positioning, is shown in Figure2. (a) is the displacement of the tool position, (b) the displacement of the table. The position of (a) was recorded by passing through a low pass filter with 1Hz cut off frequency in order to cut off the noise. In the 2nm step both table and tool precisely followed reference. This means there is no influence of angular error and the system has 2nm positioning resolution. 2 CONFIGURATION OF THE SSTEM Developed positioning system, shown in Figure 1, consists of the following: (1)coarse motion mechanism comprised of a servomotor and a ball screw, (2)fine motion mechanism comprised of two support bearings, a preloaded unit and a piezoelectric actuator.(3)power amplifier (4)controlling and data processing computer. In this system, the piezoelectric actuator pushes the outer ring of the bearing. By this movement bearing balls push the inner ring. Then the inner ring and the screw move to axial direction. Though piezoelectric actuator has very short stroke, only few micro meter, it has good characteristics for precise positioning. Fig.2 2nm step response of the fine motion mechanism 4 SNCHRONIZATION TESTS Coarse and fine positiing experiment was carried out. In this experiment when the deviation between table position and reference(1mm) becomes 3 m fine motion mechanism starts to move. The result is shown in Figure3. in this experiment table position reached 1mm ±2nm in.8s since fine motion mechanism started to move. Fig. 1 configuration of the system Fig.3 1mm step response of the coarse and fine motion 6

7 Prediction of Machining Accuracy of 5-Axis Machine Tools with Kinematic Errors M. Sharif Uddin Ph.D. Candidate, Machining, Measurement, and Control Laboratory, Kyoto University Kinematic errors due to geometric inaccuracies in 5-axis machine tools cause deviation in tool positions and orientation from commanded ones, which consequently affect accuracy on machined surface. This research work studies prediction of machining accuracy of a 5-axis machine tool with its kinematic errors. First, kinematic errors associated with linear and rotary axes of a 5-axis machine tool with tilting rotary table type, are identified by DBB method. By using an error model of the machine tool, erroneous tool position and orientations are computed. Then, machining error on a standard tilted taper cone (NAS979) specified by NAS is predicted and evaluated. A simple and easy procedure to compute machining error on the machined taper cone is presented. Using a straight end mill, cutting experiments are conducted to verify the prediction of machining accuracy. Because of having its versatile functionalities, 5-axis machine tools are extensively used in the manufacturing of dies and molds of complex geometry. However, kinematic errors due to geometric inaccuracies of structural components in a 5-axis machine tool often affect tool position and orientation with respect to workpiece, hence leading to an inaccuracy of machined surface in actual cutting operation. Therefore, in order to produce an accurate machined part, it is important to realize accurate tool position and orientation in 5-axis machining. Hence, kinematic errors in machine tools, which exist during machining, have to be identified and then, their influence on the machining accuracy must be predicted to improve accuracy of machine part. Motivated with this background, the objective of this research is to study prediction of machining accuracy on a 5-axis machine tool with it kinematic errors. Kinematic errors are practically identified on a 5-axis machine tool. With the aid of an error model of the machine tool, erroneous tool position and orientation are computed. Then, machining error on a tilted taper cone (NAS979) is predicted and evaluated. With a case study, predicted machining results are compared with experimental ones. 2 METHODOLOG Fig. 1 shows a 5-axis machine tool with tilting rotary table type, which is considered in this study as the target. Three squareness errors (γ xy, β zx, α yz) associated with linear axes (,,Z) and eight kinematic errors (α A, β A, γ A, β CA, δx A, δy A, δz A, δy CA) associated with rotary axes (A,C) are considered. The definitions with coordinate system of all these errors are illustrated in Fig. 2. By using DBB measuring device, these eleven kinematic errors for the target machine tool are identified. Then, using an error model, 5-axis machining simulation on a tilted taper cone (NAS979) is carried out. Machining error on bottom and top surface of taper cone is calculated. 3 RESULTS Cutting tests are carried on the tilted taper cone. After machining, surface measurements are taken on bottom and top face of taper cone. Fig. 3 shows simulated and measured machined surface trajectories. Results indicate that kinematic errors existing in a 5-axis machine tool have notable effects on machining errors. Further, simulated results well agree with measured ones, hence verifying the effectiveness of the prediction of machining accuracy in 5-axis machining. Fig. 1 5-axis machine tool with tilting rotary table type Fig. 2 Kinematic errors of a 5-axis machine tool in Fig. 1 y mm y mm Simulated and measured surface trajectory for bottom surface (error scale.5μm/mm) A Machine bed (a) 8 kinematic errors from rotary axes Z ref circle simulation measured measured (filtered) x mm Simulated and measured taper trajectory for top surface (error scale.5μm/mm) C ref circle simulation measured measured (filtered) Z Z γ Z Z Z β Z α Z (b) 3 squareness errors from linear axes (a) bottom surface (b) top surface x mm Fig. 3 Simulated and measured machining results

8 Measurement of Spindle Stiffness for the Development of Intelligent Spindle Motoyuki Sugihara 2 nd year master course student, Machining, Measurement, and Control Laboratory, Kyoto University In this research, we study a method to evaluate static and dynamic stiffness of a spindle on a machine tool by using a loading device, as a basis to develop the "intelligent spindle". The spindle displacement are calculated from several displacement signals and the tool load is measured with a tool dynamometer. The relationship between displacement and force is shown as stiffness-chart. The spindle stiffness is modeled from the obtained stiffness-chart. Recently, the rotational speed of a machine tool s spindle has been rapidly increased. The speed-up of the spindle causes various problems. We developed the Intelligent Spindle to address these problems. The function of the Intelligent Spindle includes the monitoring function of the spindle stiffness. It is important since the radial spindle stiffness affects the cutting performance. Furthermore, if the spindle stiffness can be quantified, the cutting force can be estimated from the spindle displacement. In this research, we measure the radial spindle stiffness when the spindle is rotating, in order to model the spindle stiffness. For that purpose, we attach a dummy tool and a measurement holder to the intelligent spindle that we developed. And we find a curve of the spindle displacement vs. force of the spindle system by applying a force when the spindle is rotating. The spindle stiffness is modeled from the obtained curve of the spindle displacement. 2 EPERIMENTAL SETUP AND PROCEDURE Fig.1 shows the schematic of the experimental setup. Eddy current displacement sensors are installed in and directions near a front bearing of the spindle. The radial spindle displacement at the nose part of the spindle is measured by dividing the difference of the signal of the opposed sensors by two. A thermocouple is installed near the displacement sensor to estimate the change of the spindle temperature indirectly. The temperature measured by this thermocouple is referred as to the spindle temperature hereafter. A tool holder that we designed and made is attached to the spindle. A dummy tool is clamped to the holder, and a bearing and a housing are attached at end of the dummy tool. The housing is connected to a shaft by a universal joint and the edge of the shaft comes in contact with a tool dynamometer. In this experiment, we apply the force by moving the spindle by the hand. The following is the experimental procedure. Procedure 1(Cold start): After the machine is started up, the load test is carried out at rotational speeds of, 15, 3, 45min -1. Procedure 2(Warm up): The spindle is warmed up by rotating. After the spindle temperature becomes stable, the load test is carried out. Procedure 3(Cool down): The spindle is stopped. After the spindle temperature is reduced and stable, the load test is carried out. 3 RESULTS The relationships between the spindle displacement and force at warm up condition are shown in Fig. 2. When the rotational speed was min -1, the shift of the spindle displacement was observed. Even when this shift was not observed, the hysteresis loops were observed in the curves of the spindle displacement vs. force. The hysteresis loop at the warm up condition was the smallest. Therefore, to evaluate the spindle stiffness in rotation, it is necessary to rotate the spindle and carry out the ex- 8 periment when the spindle temperature is stable. When the hysteresis loop is small, the slope of the curve tends to decrease as the force grows. We approximate the slope of the curves of the spindle displacement vs. force in rotation by using the logistic function. The estimated curve of the spindle displacement vs. force is obtained by integrating the approximated slope. Fig. 3 shows the comparison between measured and stimated curves of the spindle displacement vs. force. The standard deviation of their difference was 2.3 N at maximum. Force N Force N Sensor target Displacement sensor Force N Measurement Ball bush holder Bearing Universal joint First Second Measured Estimated Displcement μm Fig. 3 Comparison between measured and estimated curves Force N Force N First 2 First Second Second Displacement μm Displacement μm (a) min -1 (b) 15min Front bearing system Displacement μm Displacement μm (c) 3min -1 (d) 45min -1 Thermal sensor Shaft Recorder Amp. Dynamometer Fig. 1 Schematic of the experimental setup First Second Fig. 2 Relationships between the spindle displacement and force(warm up)

9 Laser Step Diagonal Measurement for the Estimation of Three-dimensional Volumetric Errors Takafumi Hata 4 th year undergraduate student, Machining, Measurement, and Control Laboratory, Kyoto University The laser step diagonal measurement is a method for the identification of all the volumetric error components including linear errors, straightness and squareness errors, by using only a laser interferometer and a flat mirror. This research first discusses inherent and critical issue with the conventional formulation of the laser step diagonal measurement. Then, we propose a new formulation of the laser step diagonal measurement to accurately estimate the machine's volumetric errors even under the existence of setup errors. Recently, high-precision and ultra-precision machine tools have been rapidly introduced into the market. To ensure the motion accuracy over the 3D workspace of these machine tools, it is important to evaluate all the volumetric error components including linear displacement errors, straightness errors and squareness errors. As a method of measuring linear displacement errors, it is now general to use a laser interferometer whose resolution is high enough. To measure straightness errors and squareness errors, we often use a displacement sensor and artefacts whose geometrical accuracy is higher than the motion accuracy of the machine. For the measurement of high-precision machines and ultra-precision machines, this measurement costs more. Moreover, because it is only one dimensional measurement, an operator needs to change the setup every time to measure motion errors in different direction. Thus, it is very time-consuming. The laser step diagonal measurement is the method to estimate all the volumetric errors by using a laser interferometer only. Since it does not require high-accuracy artefacts, it does not cost much. Furthermore, because all the volumetric errors can be estimated by only three diagonal measurements plus three linear measurements, it may significantly reduce measurement time. In this research, we propose the new formulation for the estimation of volumetric errors by using results of step diagonal measurement even under the existence of setup errors. Its validity was verified both analytically and experimentally. 2 LASER STEP DIAGONAL MEASUREMENT The typical setup of the step diagonal measurement is shown in Fig. 2. At first, an operator needs to set the laser direction along a diagonal of the cubic measurement range. Then, the flat mirror is set at the spindle of the machine, such that its surface becomes perpendicular to the laser direction. Finally, the machine is moved along the zig-zag path as shown in Fig. 1, and its displacement along the diagonal direction is measured. This measurement is repeated for three different diagonals of the measurement volume. Using all results of these measurements, all the volumetric errors over this space can be estimated. In this research, we showed that a critical issue of the conventional formulation of the step diagonal measurement is that alignment errors of the laser direction and the mirror potentially cause significant estimation errors. No matter how careful the operator sets up the laser head and the mirror, it may not be possible to satisfy the perpendicularity of laser optical axis and the mirror. In the new formulation that we proposed, an operator measures linear displacement errors beforehand directly with a laser interferometer. By using the proposed formulation, the influence of misalignments can be removed, and thus the machine s volumetric errors even under the existence of setup errors. 3 RESULTS An example of experimental results is shown in Table 2. In order to experimentally investigate the estimation accuracy of volumetric errors, in this experiment, we gave an error to reference trajectories, which is sufficiently large compared with the actual motion accuracy of the machine, and compared estimated volumetric errors with given values. In straightness and squareness errors, the estimates obtained by using the new formulation of step diagonal measurements is significantly closer to the given values than those obtained by the conventional formulation. machine's spindle Z flat mirror laser head laser beam Fig. 1 Typical setup in laser step diagonal measurement Table 1. Reference errors and their estimates based on the proposed and the conventional formulations Linear displacement error Straightness Error in toward Straightness error in Z Ref. value given to the machine Estimated by proposed formulation Estimated by Conventional formulation 7.μm 5.96μm -7.28μm 12.66μm 12.7μm 12.4μm 12.μm 16.21μm 29.83μm 9

10 Measurement of Motion Accuracy Using a Laser Tracking System Atsushi Iizuka 4 th year undergraduate student, Machining, Measurement, and Control Laboratory, Kyoto University Laser tracking system (LTS) is composed of four laser interferometers which track a target automatically. LTS can measure 3-dimensional coordinates theoretically with the accuracy of sub-micron order. To apply the LTS to the evaluation of volumetric errors of a machine tool, we carried out experiments to evaluate static measurement accuracy of LTS. In the accuracy inspection of machine tools, linear positioning accuracies are often regarded as the most important part of the machine s motion accuracy. However, in order to secure the machine s motion accuracy over the entire workspace, it is important to accurately evaluate 3- dimensional volumetric errors, which contains linear positioning errors, straightness and squareness errors. To realize the improvement of 3-diensional motion accuracy of machining tools, we need a precise method to measure the machine s motion in 3-dimensinal space. To measure straightness or squareness errors, conventionally we use a displacement sensor with straight or square edge. Since it is only one degree of freedom measurement, we have to do complicated set-up again and again to measure 3-dimensinal motion accuracy with them. In this research, we apply the Laser tracking system (LTS) for the measurement of motion errors of machining tools. The LTS can measure a 3-dimensional location of any point in the measurement area and potentially have measurement accuracy up to sub-micron order. 2 PRINCIPLE AND DEVICE The LTS is based on the trilateration principle to estimate target s coordinate from measured laser displacement. Since the each tracker s location cannot be measured precisely, the LTS also uses a self-calibration method to estimate the target s and trackers locations at the same time. Figure 1 shows the optical system of a laser tracking interferometer (tracker). A moving mirror and a quadrant photo diode (QPD) are added to a usual interferometer. Moving mirror is driven by the feedback signal from QPD, which can observe the displacement between the center of a target and the end of laser. 3 EPERIMENT Figure 2 shows a measurement experiment of LTS on a machining center (MC). Throughout this study, we used the LTS developed by the National Institute of of Advanced Industrial Science and Technology (AIST) in Japan. The target is a corner-cube mirror attached to the spindle. Instead of using four trackers in one time, we measured the MC s motion with one tracker, and repeated the same measurement with total four different locations of the tracker, under the assumption that the MC s repeatability errors are small enough. In this experiment we evaluated static measurement accuracy of LTS. The locations of trackers, as well as the measurement range, are shown in Fig. 3. The measurement range was 1mm 1mm 1mm and 5mm 5mm 5mm. 4 RESULTS The estimation error of the target position by using the LTS was several hundred microns at maximum. This estimation error is too large, and at this time we did not completely find out its causes. This estimation error was twice or third times larger in the measurement than the case. One possible cause of the difference between and measurements is thought to be due to the location of trackers. Particularly in the measurement, relative positions of measurement points with respect to trackers are not so different to each other, and thus it is hard to estimate parameters effectively. This is confirmed by mathematical analysis. By optimally setting trackers with respect to the measurement range, it is expected that the estimation error will be significantly reduced. More research efforts will be required to further improve the estimation accuracy of the LTS. Laser Head Photo Detector Plane mirror Quadrant photo diode Moving mirror Fig. 1 Optical system of the tracker Target Fig. 2 Test of LTS on machining center 1mm 1mm 1mm 5mm 5mm 5mm Fig. 3 Trackers (A,B,C,D) and measurement range 1

11 Self-calibration of the Cross Grid Encoder Soichi Ibaraki Associate Professor, Machining, Measurement, and Control Laboratory, Kyoto University The cross grid encoder is an optical diffraction grating type encoder to measure two-dimensional position of a optical head by using a grid plate where grids are aligned orthogonal to each other. As a basis to establish a methodology to measure evaluate motion accuracy of high- and ultra-precision machine tools by using the cross grid encoder, this research presents a self-calibration scheme of a measurement error of the cross grid encoder caused mainly by the misalignment of grids. The cross grid encoder (KGM by Heidenhain), shown in Fig. 1. is an optical diffraction grating type encoder to measure two-dimensional position of a optical head by using a grid plate where grids are aligned orthogonal to each other. Its big advantage is that it can measure the contouring error in the 2D plane for an arbitrary reference trajectory. By a single setup, one can measure various errors such as straightness errors, squareness errors, or contouring errors in circular interpolation, which potentially reduces the measurement time significantly compared to conventional measurements. To apply the KGM to the evaluation of motion errors of high-precision or ultra-precision machine tools, it is important to evaluate the measurement accuracy of the KGM itself. Just as commercial linear encoders, the KGM is likely subject to measurement errors caused mainly by the misalignment of grids. When compared to motion accuracy of high-precision or ultra-precision machines, this measurement error may not be negligibly small. Generally, the measurement error can be calibrated by comparing with the reference measurement device whose measurement accuracy is known. In the case of the KGM, it is very difficult, or practically not possible, to calibrate the two-dimensional measurement accuracy at every point over the entire measurement range. The objective of this research is to propose a selfcalibration scheme of the KGM to calibrate the measurement accuracy over the entire region by only using the KGM and the machine to be measured, without using any reference. The KGM typically has about ±1 μm measurement error over the measurement range 23 mm due to the misalignment of grids. The goal of this research is to reduce it to about its 1/1 by applying the compensation based on the calibration. 2 METHODOLOG For the measurement of straightness error by using a straight edge, the reversal and multi-probe selfcalibration approaches are well-known. The basic idea of the approach employed in this research is an extension of these conventional self-calibration schemes into the two-dimensional measurement. The self-calibration procedure is illustrated in Fig. 2. First, under the setup (a), the machine s motion error is measured for some given reference trajectory. Secondly, the KGM plate is rotated by 9 deg, and then the same measurement is conducted by using exactly the same reference trajectory. Finally, the KGM plate is shifted and the same measurement is repeated. If there is no measurement error, under the assumption that the machine s repeatability error is negligibly small, three measured error trajectories must coincide with each other. The difference in three measured trajectories is attributable to the measurement error that depends on the location of the measurement point on the KGM grid 11 plate. The objective of the self-calibration is to identify measurement errors, and the machine s motion errors, from the difference in three measured trajectories. 3 RESULTS An example of experimental results is shown in Fig. 3. To investigate the calibration accuracy by the proposed selfcalibration approach, one-dimensional measurement error of the KGM over a segment of the length 9 mm was directly measured by using a linear encoder comparator. Fig. 3 shows the comparison of measured and calibrated measurement error profiles. The estimation error was about.3 μm at maximum. Fig. 1 Cross grid encoder (KGM by Heidenhain) Machine s motion (example) (a) View : standard setup (b) View 1: rotated by 9 deg (c) View 2: shifted to direction Fig. 2 Setups of the KGM plate for self-calibration (a) measured KGM trajectories (b) measured and calibrated measurement error Fig.3 Experimental validation of calibration accuracy of the self-calibration scheme

12 Development of a Cutting Force Monitoring System for Intelligent Machining Ahmed A. D. Sarhan Ph.D. Candidate, Machining, Measurement, and Control Laboratory, Kyoto University In this research work, the authors use displacement sensors in the spindle structure to monitor cutting forces. However, the monitoring quality in the long term is a problem because sensor signals involve offset drift which, mainly attributable to the thermal displacement of the spindle. To cope with this problem, we develop a sensor fused monitoring system, which has not only displacement sensors but also thermal sensors in the spindle and machine structure. The estimation and compensation of the spindle thermal displacement based on temperature data from these thermal sensors can provide more accurate monitoring of cutting forces. In the researches on cutting force monitoring, there are two main approaches: an internal sensor approach and an external sensor approach. Some researchers have succeeded in the cutting force monitoring by utilizing motor currents in CNC-Servo systems. However, it is often difficult to estimate cutting forces in an accurate and stable manner by motor currents in an end-milling process, since the magnitude and the direction of cutting forces change frequently and the friction change on guideways influences the monitoring accuracy. For such applications, external sensor approach is promising, and there are many researches on cutting force monitoring by using several types of sensors such as strain gauges, displacement sensors, force sensors, acceleration sensors and so on. The authors used spindle displacement sensors to measure the spindle displacement due to cutting forces, as they are satisfying the following criteria: No restriction of working space and cutting parameters; Wear and maintenance free, easy to replace, and cost effective; Function is independent of workpiece mass, size, and geometry; And, reliable signal transmission. The objective of this research work is to develop a method to effectively monitor the cutting conditions by using various spindle integrated sensors including force and thermal sensors (i.e., displacement and temperature sensors) to fuse the data to accurately predict cutting forces at high speed cutting. To this end, we develop an intelligent spindle with various integrated sensors from which we can obtain the most concrete signal in the machining process. As the drift of the displacement due to the thermal deformation of the spindle was found to be important for the more accurate monitoring of cutting forces, its compensation scheme is proposed, and then the compensation performance is evaluated. 2 METHODOLOG Four eddy-current displacement sensors S 1~S 4 are installed on the housing in front of the bearings to detect the radial motion of the rotating spindle. In order to measure spindle temperature, several thermocouples T 1, T 2 and T 3 are attached to the spindle and machine structure. The thermocouple T 1 is installed in the same hole where the displacement sensor S 4 is installed, T 2 is installed at returned oil inlet, and T 3 is installed in the machine bed. To estimate the spindle thermal displacement in radial direction, the spindle displacements and temperatures are measured during the spindle rotation without cutting. The spindle is started at 3 min -1 and kept rotating for 3 minutes. After that the spindle speed is increased to Displacement μm 12 RMS of the estimation errors N 6, 9 and 12 min -1 for every 3 minutes. This test is repeated for four times. The sampling frequency used is 1 Hz. 3 RESULTS The monitoring results show that all the displacement sensor signals involve two components of fluctuations: the transient component and the periodic component. The estimated thermal displacement in direction can be obtained as follows. Δ x [ T1 ( n) T3 ( n) ] α x + [ T2 ( n) T ( n) ] β x t ( n) = 3 Where, α and x Measured Estimated Time min Displacement μm Measured Estimated Time min (a) -axis (b) -axis Fig. 1. The comparison of estimated and measured thermal displacement 22 First test 2 Second test Third test 18 Forth test Spindle speed min -1 β are regression factors obtained by x applying Least-squares method to the spindle displacement and spindle temperature. The first part of the equation represents the transient thermal displacement while; the second part represents the periodic thermal displacement. Similarly, the estimated thermal displacement in direction can be obtained. The thermal displacement is estimated from the temperature signals and compared with the measured one. Then the estimated errors (measured minus estimated spindle thermal displacement) are calculated. Figure 1 shows the comparison of estimated and measured thermal displacement at spindle speed 6 min -1. The root mean square R.M.S. of the estimated errors after the compensation in the and directions are shown in Fig. 2. It is found that the maximum R.M.S of the estimated errors is less than 7 N in direction and 12 N in direction. RMS of the estimation errors N First test Second test Third test Forth test Spindle speed min -1 (a) -axis (b) -axis Fig. 2. The R.M.S. of the estimated errors interpreted into force

13 Constant Engagement Tool Path Generation for the Improvement of Machining Accuracy in 2D Milling with a Straight End Mill M. Sharif Uddin Ph.D. Candidate, Machining, Measurement, and Control Laboratory, Kyoto University In 2D contour end milling, conventional contour parallel paths offer varying cutting engagement with workpiece, which inevitably causes the variation in cutting loads on the tool, and consequently, results in geometric inaccuracy on machined surface. This research work presents an algorithm to generate a new offset tool path, which is able to regulate cutting engagement with workpiece at a desired value. The key idea of the proposed algorithm is to modify the previous tool path trajectory to regulate the pre-cut surface trajectory for the finishing path such that the finishing path is subject to the desired engagement angle. Using a straight end mill, cutting experiments on a 2D core workpiece of hardened steel are carried out to verify the effectiveness of the proposed approach. Conventional contour parallel offset (CPO) paths generated by commercial CAM software are mostly used to machining of dies and molds. However, when the mechanics of cutting is considered, CPO paths possess inherent cutting problems. The critical cutting problems are significant variation in cutting engagement, that causes change in cutting load/force, and tool deflection, amplifies tool wear, and consequently affects geometric accuracy on machined surface. Also the variations in cutting engagement are a great concern from the process stability and efficiency perspective. In order to tackle varying cutting engagement in contour machining, major methods reported in literature are feedrate scheduling. In this case, federates are scheduled based on several regimes of engagement or continuously varied to regulate constant material removal rate. However, performance of feedrate scheduling strongly depends on the feedrate control performance of servo controller of NC machine tools. On the other hand, in order to regulate cutting force for improving machining accuracy, the modification of tool path is more promising. Motivated with the idea, the main objective of this research is to propose an algorithm to generate a new offset tool path trajectory, which will regulate cutting engagement at a desired value on the finishing path. The inherent idea of the proposed algorithm is to modify the semi-finishing path with an aim that a desired cutting engagement angle is regulated on the machining with the final path (i.e. finishing path) while the geometry of the final path itself is preserved. 2 METHODOLOG An algorithm for tool path modification to regulate cutting engagement angle is presented. Referring to Fig. 1, the detailed algorithm of computation of modified semifinishing tool path can be summarized as follows: Step1: For the given tool center location, o k (i) (i=1,,n k), of the finishing path, compute the intersection point of the tool circumference with the newly generated offset surface, q k(i) R 2 (i=1,,n k), by offsetting o k(i) to the workpiece s side by the tool radius, r. This operation can be written by: q k (i) = offset (o k (i), +r), where (i=1,,n k ) Step2: Compute the desired intersection point of the tool circumference with the previously cut surface, p * k (i) R 2 (i=1,,n k) such that the engagement angle, α en(i), can be maintained at the desired cutting engagement angle, α * en (i). In other words, find p * k (i) such that: p * k (i) o k (i) q k (i) =α * en (i), and p * k (i) - o k (i) = r, where (i=1,,n k ). Notice that p * k (i) R 2 (i=1,,n k) defines the trajectory of modified pre-cut surface (see also Fig. 1). Step3: Set i=i+1 and repeat the steps (1) and (2) till i=n k. Step4: Then, by offsetting modified pre-cut surface trajectory, p k * (i), by the tool radius r, compute the modified tool center trajectory of the semi-finishing path, o k-1(i) R 2 (i=1,,n k-1) as follows: o k-1 (i) = offset (p k * (i), -r), where (i=1,,n k ) Fig. 1 Concept of the proposed algorithm 3 RESULTS Cutting experiments are carried out on a 2D core contour (Fig. 2) on the machining under CPO tool path and the modified constant engagement (CE) tool path generated by the proposed algorithm. Compared to CPO path, variations in cutting force along finishing are significantly reduced by the modified CE tool path (Fig. 3). A uniform and improved geometric accuracy on machined surface is also achieved by the proposed modified CE tool path (Fig. 4). mm Reference surface (=) for CMM measurement 2 1 Machined surface error (mm) Workpiece surface End mill Boundary of raw stock Feed p k(i) α en(i) o k-1(i) o k(i) q k(i) Finishing path Original semi-finishing path R2 3 3 R5 R7 4 R12 B R8 R mm Fig. 2 Core contour R8 R6 A 7 Core boundary after machining Path modification o k-1(i) o k(i) Reference surface (=) for CMM measurement Cutting force (N) End mill Strategy 2 (Modified CE tool path) Strategy 1 (Contour parallel path) Machining time in finishing (sec) Fig. 3 Cutting force profiles Strategy 1.6 (Contour parallel path) Strategy 2 (Modified CE tool path) Distance along reference surface (mm) Fig. 4 Machined surface error profiles Workpiece surface Modified semi-finish surface Feed p k(i) α en(i) s q k(i) Finishing path Modified semi-finishing path p k * (i) α en * (i) 13

14 Control of Tool Life in Endmilling Takuya Shimizu 4 th year undergraduate student, Machining, Measurement, and Control Laboratory, Kyoto University In the machining of hardened steep for die/mold manufacturing, it is crucial, but quite difficult even for an expert operator, to determine machining conditions such that the entire machining process can be finished safely and efficiently, without reaching the end of tool life by the end of the entire process. This research proposes a long-term control strategy of cutting forces such that the desired tool life can be obtained. The cutting force is monitored only time-by-time at each "check point" discretly set on the tool path, and the feedrate profile is modified such that the increase of cutting force is regulated along the desired curve. The setting of machining conditions is difficult in the die machining. It is necessary to develop the machining support system that can autonomously decide optimum machining conditions such that anyone, even a nonexpert operator, can perform safe, accurate, and efficient machining. The technique for optimizing machining conditions from the viewpoint of cutting force control has been proposed in the Intelligent Machine Tool Project that our group has researched for this purpose. The cutting force is one of important parameters that reflects the severeness of the machining process. The purpose of cutting force control is to prevent the tool failure when cutting forces are larger than the desired level, and to raise the machining efficiency when cutting forces are smaller than the desired level. Numerous researches have been reported in the literature on the cutting force control in end milling processes. There have been, however, very few practical applications employed in commercial products. A critical issue is the cost of installing a sensor to monitor cutting forces; reliable, high-accurate sensors to measure cutting forces, such as a dynamometer, is expensive. Furthermore, past researches almost never considers a long-term change of machining process, such as the increase of cutting force due to the tool wear. In this research, we propose a long-term cutting force control strategy in order to regulate the tool life. The feed rate is regulated based on the cutting force measured only time-to-time at each check point set on tool paths. Therefore, no expensive, high-accurate sensor for fulltime monitoring of cutting force is needed. 2 METHODOLOG The initial feed rate profile is scheduled based on a simple prediction model of cutting force such that the cutting force is regulated at the desired constant level. Because the rise of the cutting force by the progress of the tool wear is not considered in the initial feed rate profile. It is necessary to update the model during the process. Fig.1 shows the overview of the proposed technique. First, the index of tool wear progress that we proposed is computed from the cutting force monitored at each check point. Next, the target value of the cutting force till the next check point is set. The target level is determined such that the cutting force will keep raising and reach the end of tool life beyond the desired cutting distance. The feedrate profile till the next check point is then recomputed based on the updated process model. 3 RESULTS To validate the effectiveness of the proposed long-term cutting force control scheme, simple cutting experiments are conducted, where a straight side cutting is repeated until the end of tool life by using a φ6mm straight end mill. The work piece is hardened steel, SKD61 (HRC53). When the initial feed rate (1152mm/min) is never changed, the cutting force kept increasing as shown in black circles in Fig. 2. In this case, the end of tool life was reached at the cutting distance 64m. Setting the control objective to extend this to 8m, we applied the proposed long-term cutting force control scheme. The blue line in Fig. 2 shows the target level of cutting force control. The red circles show cutting forces measured at each check point. The end of tool life was reached at 876m in this case. The maximum error in the cutting force control was about 18N, and the cutting length was increased by a factor of about 1.4. Cutting force N Optimization of cutting feed rate based on model Endmilling Monitor of limited cutting force Estimation of progress level of tool wear Control of tool life by change at cutting feed rate Fig.1 Overview of a proposal technique Keeping initial feed rate Target level of cutting force Control of cutting force Cutting length m Fig.2 Measured cutting forces 14