Evaluation of machine-tool motion accuracy using a CNC machining centre in micro-milling processes

The demand for micro holes, micro-moulds and micro forms continues to grow as high-tech industries demand miniaturized products. Sectors such as aerospace, microelectronics, medicine, and even the automotive sector, are just some examples of enterprises that are taking advantage of micro-manufacturing technologies. Within this framework, the need to adapt the knowledge of macro-scale manufacturing processes to micro-scale is evident. This paper evaluates, through theoretical principles and experimental work, the machine-tool motion accuracy of a medium machining centre specializing in the micro-milling of elliptical cavities on aluminium workpieces. Measurements were taken to evaluate: deviations and/or errors in geometric accuracy, and the geometric quality errors caused by motion control and control software. The results show that, due to the structure and inertia of the machine tool, acceleration and deceleration do indeed affect the accuracy and quality of the micro-part. Furthermore, errors from motion control and/or control software are present because differences in the moving carriages create instabilities.


Introduction
As many high-tech industries are now using miniaturized parts or products the demand for micro holes, micro-moulds and micro forms continues to increase. Aerospace, microelectronics, the medical sector together with the automotive sector, are but some examples of enterprises that are making the most of the micro-manufacturing technologies. Nowadays, the key success factor of these technologies comes from the ability to be flexible and manufacture a complete part in a single machining process. To meet the large scale production needs of mechanical components and micro products, the need to adapt the manufacturing process knowledge from macro-scale to micro-scale is evident.
One of the most significant research subjects in milling processes is in evaluating machine-tool motion accuracy, as this has a noticeable influence on the quality of the final machined part.
One of the first works in this field of research was developed by Weck and Schmidt [1], where they proposed a method using a laser beam and a four quadrant photodiode to evaluate the radial error-motion of a rotating table of a gear hobbing machine. Furthermore, they quantified the parallelism between the rotating axis and a linear guide-way. With the same approach, Zhang et al. [2] developed a displacement method to measure the 21 error components in the geometric error using a laser interferometer. Similar research work found that by measuring the positioning errors along the 15 lines in the machine work zone, a total of 21 geometric error components can be determined [3]. Iwasawa et al. [4] used a laser displacement interferometer and a rotary encoder to measure a much longer range of motion than ordinal circular test methods such as the double ball bar method can. Additionally, the proposed method allows positioning accuracy and other more complex test paths to be evaluated.
Measurement and evaluation of motion errors by the Double Ball Bar (DBB) test is a commonly used method, particularly in dynamic circle path tests. Bryan [5] and Kakino et al. [6] were pioneers in the use of this technique. Lai et al. [7] proposed a mathematical model that diagnoses the nonlinear error source in a guide-way system by measuring the contouring error using a double ball bar. A more robust system was developed by Qiu et al. [8,9], when they developed a device consisting of a double-bar linkage and two Canon K-1 laser rotary encoders. The experimental results demonstrated that the method and device developed are capable of evaluating most items of motion accuracy in NC machine tools. Similar work used three laser ball bars [10].
Die-manufacturing demands have allowed a measuring method to be developed that consists of a cross grid encoder. This method is widely used in two dimensions, i.e. in an XY, YZ or XZplane, because it has the ability to work with any chosen path. Rehsteiner and Weikert [11] used this method to evaluate motion accuracy in machine tools. Du et al. [12] developed a multi-step measuring method for motion accuracy in NC machine tools using a cross grid encoder and based on the kinematic error model of an NC machine tool. However, using these same macro-scale evaluation techniques to appraise machine-tool motion accuracy performance has disadvantages when applied to micro-scale. In the case of double ball bar, measuring range is greater than the scale of the interest. When this method is used, it is not possible to measure the servo induced error in machine tools in small-radius circular test paths. On the other hand, laser interferometer results are significantly dependent on environmental conditions as the laser wave length depends on temperature, humidity, air pressure and air circulation [12].
Kim et al. [13], Monreal and Rodriguez [14] and Schmitz et al. [15], conducted investigations into the contribution of acceleration and deceleration in macro-scale part dimensional errors, while Philip et al. [16], who studied a micro-scale case, proposed a new acceleration-based methodology for micro/meso-scale machine tool performance evaluation. The authors developed two micro/meso-scale machine tool (mMT) prototypes at the University of Illinois in Urbana-Champaign. These were then used as test vehicles for new performance evaluation methodology. This novel research presents a technique for measuring radial and tilt error motions of ultra-high-speed miniature spindles. The technique was based on measurements of radial motions in two mutually orthogonal directions of a precision artefact using (noncontact) laser Doppler vibrometers [17].
According to Schwenke [18], the main error sources affecting accuracy are kinematic errors, thermo-mechanical errors, loads, dynamic forces and motion control and control software. In the case of thermal-mechanical errors, these are present due to modifications of heat/cold sources in machine tools and therefore to thermal expansion coefficients. Several studies have focussed on this issue [19][20][21]. The finite stiffness of the structural loop can be a significant i flue e o the a hi e's a ura ; hi h a o ur due to the eight and position of, for example, the workpiece or moving carriages of the machine. Schwenke [18] Schellekens et al. and Spaan, reported that these kinds of errors are more important in comparison with kinematic errors. In the case of dynamic forces, the machining forces, measuring forces or forces caused by accelerations or decelerations contribute to location errors relative to the workpiece. In order to measure the geometrical error caused by motion control and control software and to distinguish from errors explained by other error origins, different feed speeds are applied for the same motion path [18].
Another approach, in order to reduce errors, is to compensate the error based on a previously developed model. Eskandari et al. [22] used a tool path modification in order to compensate for the position error, geometric error and thermal error through different techniques such as regression, neural networks, and fuzzy logic. On the other hand, Fan et al. [23] investigated an error model determined by orthogonal polynomials in an attempt to obtain higher accuracy.
After reviewing the literature, there are several works pertaining to evaluating the performance of machine-tool motion accuracy on a macro-scale but there is no research at all into the characterization of the radial error using a CNC machine in micro-milling processes. This paper provides the insight needed to improve milling as a micro-manufacturing process, by considering the geometrical error caused by motion control and control software error sources when a CNC machining centre or an in-house micro machine centre is used instead of a specialized machine. It is highly useful to characterize machine-tool motion accuracy and evaluate their influence on the desired dimensions and geometrical features of the final piece. Additionally, this will help identify those process parametersaxial depth of cut per pass (ap) and feed per tooth (fz),-which have a greater effect on the ensuing feature quality and to what degree changing these process parameters will affect feature quality. Therefore, this work based on the principles of kinematics, will contribute to understanding the relationship between machine dynamics, process parameters and the quality of the geometrical features on the final micro features. This study is performed without the support of an extra controller, e.g. Aerotech, thus allowing the dynamics of the system to be able to be adjusted online in order to improve the performance of the machine tool. In contrast, an experimental methodology, as an alternative to expensive commercial solutions, is proposed to identify the motion error.
The paper is set out as follows. In Section 2, a brief study of the theoretical principles applied to the milling centre machine used in this work is presented. According to these results, an experimental work is proposed to prove that the contour error in microcavities is mainly affected by the structure and inertia of the machine tool, and that these also produce additional errors as a result of instabilities in the motion control and control software. Section 3 shows the experimental set-up carried out in this work. Furthermore, the process parameters tested allow us to analyze which of them significantly affect accuracy and final shape. The main findings, presented in Section 4, are found through practical methodology and not an expensive commercial solution. Finally, conclusions are presented in Section 5.

Positioning errors due to axis motion
In the following an attempt to establish the theoretical principles that characterize the CNC machining centre used in this research is made, all the time emphasizing that it is not a specialized machine for micro-milling. In the first part of this section, the structure of the machine is introduced in order to determine the possible kinematic and load errors it may cause. Then a simple model for a circular contouring system is presented with the aim of calculating the error generated by the control motion and control software.
The first consideration to take into account is the difference in the motor type on each axis. In this case, the CNC milling centre used is a Deckel Maho 64V in which the X-axis has a linear motor, whereas the Y-axis has a servomotor which, according with the machine manufacturer, has a positioning precision of 8 and 20 µm, respectively. The configuration of these actuators used on the feed axes is different and crucial to obtaining accuracy in the final pieces. A linear motor has as its base element a moving coil, with 3-phase winding, and a stationary magnet track. Mounted side by side of these is the reactive part of the motor consisting of a steel base with permanently attached magnets ( Figure 1a). On the other hand, the rotary servomotor has two principal parts; the stationary stator and the inside rotor ( Figure 1b). Some advantages of the linear motor over the servomotor include the elimination of the mechanical actuation assembly. This allows the linear motor to reach higher maximum traverse speeds than the servomotor as the servomotor is limited by its components (ballscrew, leadscrews, ballnuts, gearboxes, etc). In this case, the linear motor has a maximum traverse speed of 70 m/min, while the servomotor drives up to 40 m/min. As for acceleration, significant inertia of each rotating element in the servomotor is not available in a lineal motor type. Although the linear motor can provide a linear motion system with distinct advantages, thanks to the direct coupling, it is considerably more sensitive to differences in load application. The following equations compare the total inertia of both systems: The inertia of a rotary system is given as: The ball screw inertia is calculated as a cylindrical object, according to the following equation: (2) where, γ b is the weight of the shaft per unit volume, D b is the shaft diameter and L b is the shaft length.
For a load moving along a straight line the inertia is: where, M carriage includes all traversing mass and l is the travelling distance along a straight line per revolution of the motor.
The assumed specifications of the ball screw, mass of carriage (table and other components) and travelling distance are: According to manufacturer specifications, motor inertia is 0.0068 Kgm 2 , therefore from equation.1; J total is 0.01535 [kg·m 2 ] In both cases, the servomotor and linear motor, M carriage includes all traversing mass, such as workpiece, bearings, coil slider, encoders, etc. However, according to Equation 3, the M carriage is reduced by the second term squared, related to the pitch of the actuator.
In comparison, the load in a linear motor system is the sum of all weights directly connected to the moving coil slider according to Equation 4: (4) Figure 2 shows both carriages on the X and Y-axis. In order to approximate the weight of the carriage on the X-axis the following elements are taken into account: X-axis carriage structure asse l , spi dle otor, heat e ha ger u it, the tool's ooli g s ste , the spi dle tra erse carriage (headstock and headstock support, lineal guides) and others (cable hangers, spacers, fixing attachments, etc). As a result, the translating mass on the X-axis carriage is greater than that on the Y-axis carriage, and consequently, control loop sensitivity to load mass in the X-axis is also greater. This means an additional demand on the controller, in order to maintain performance and stability due to the difference of loads. The contour error for the microcavities is also affected by the servo feedback delay. According to Aun-Neow Poo et al. [24], the simple system model for circular contouring system is given by: The closed-loop transfer function for this system is: Where, X i , X 0, Y i , and Y 0 are the Laplace transform of x i, x 0, y i and y 0 , respectively, K x and K y are the X-axis and Y-axis velocity gain, respectively. The system inputs for the circular contour are: Where, R is the radius of the circle and: The radial error e r (t) is given as: The amount of mismatching in the system velocity gains K x and K y is calculated by: In order to demonstrate the contour error captured when axes have different dynamic characteristics, the ideal case is shown first. When the system obtains matched gain, the dynamic contour error obtained is very small and in macro machining it is negligible.
Evaluated range for this function is 0-360 degrees but error is defined in Equation 11 as time function. Based on this analysis, it is more useful to depict results in degrees and not in time; hence the maximum value of time is calculated based on the angular velocity in order to e aluate the fu tio fro to π radia s. Figure sho s that he the gai is at h increases in response the radial error also increases.
A useful accuracy indicator of a given function or process is the sum of the predictive quadratic error, which is defined as: (14) Figure 4 shows the sum of square errors and it is evident the growing trend means that when the speed gains are different then one of the axes is moving faster than the other.
However, Figure 5 shows the position of x 0 (t) and y 0 (t) for all cases and because errors in the cutter path of the circle are small but do exist (in the order of 10 -3 of R) they cannot be observed by mere sight. In order to obtain a representation of the experimental results, the systems were modelled with a 20 to 1 proportion in the velocity gains (Y axis gain is 20 times greater than X axis gain, hence the X axis is slower in time response than the Y axis). Figure 6 shows that when the difference in the velocity gains is magnified, the contour error for circle generation is significant. Note that the drive element friction effects have not been considered and that the model was simplified; although these can be taken into account in future work.

Experimental set-up
The CNC milling machine used to perform the experiment was a Deckel-Maho © 64V Linear (3axis, vertical spindle) with a positioning accuracy of 20 and 10 µm in Y and Z directions, respectively and 8 µm in X direction. The machine centre has a speed ranging from 1 to 12,000 rpm and is driven by a 19KW spindle drive motor. The FANUC 180i controller offers control of up to three independent part program paths with up to eight servo-controlled axes per path at increments as low as 0.1 µm. To minimize errors, heat-shrink tool holders and an EROWA clamping system were used in all the experiments. Figure 7 provides a close-up view of the machining set-up. Furthermore, a warm-up was performed in order to preserve the thermal conditions and avoid producing any thermo-mechanical errors. The workpiece material tested in this study was aluminum alloy (Al 7075-T6) with a hardness of 90 HRB due to its high machinability. Test blocks of dimensions 12x25x25 mm were prepared as a raw material. A Mitsubishi MS2SBR0010S04 ball nose end mill tool of 200 µm in diameter was used. Figure 8 and Table 1 show the geometric characteristics of the tools. Before performing the milling operations, the micro-tool was measured with a Non-contact Laser System supplied by Mida repeata ilit of σ . μ i order to o pe sate for tool errors (Figure 7 right). A conventional mineral-oil coolant was used (CUTTINSOL 5 by COLGESA©). Experiments were carried out by machining micro-elliptical cavities of 525 µm on the major axis, 500 diameter µm on the minor axis and 250 µm in depth, as Figure 9 shows. This geometry was selected in order to enhance the effect of the differences between the Xaxis motion and Y-axis motion.  Table 1. Geometric characteristics of the ball nose end mill cutter.

Length of Cut (ap) [mm]
0.3 Table 2 shows the factors analyzed. Experimental design was defined by three factors: axial depth of cut per pass (ap), feed per tooth (fz), and axis machining direction. The X-Axis machining direction is defined when all micro-cavities are aligned along the X direction, as shown in Figure 9, while the Y-Axis machining direction is when cavities are aligned through the Y axis machine direction. Response variables related to accuracy were divided into two desired dimensions: (major axis (M) and minor axis (m), (see Figure 9). Micro-cavity shape was also evaluated.

Number of flutes 2
Dimensional measurements on the XY plane were performed with a Microscope Discovery 12 from Zeiss© and Quartz PCI© Software was used to collect the digital images (150x magnification). Table 2. Variable factors and factor levels performed.

Results and discussion
525µm Major axis 500µm Minor axis 250µm Depth X-axis machining direction Y-axis machining direction Table 3 shows three different inputs, such as axial depth of cut per pass, feed per tooth and axis machining direction for experimental sets and two measured outputs on the shape machined i.e. major axis and minor axis. In addition, relative errors were calculated using desired measures and those measures obtained. The maximum error obtained when X-axis direction machining is used is 12%, while in the Y-axis direction the maximum error is of 3.65%. Minimum error results are 1.4 and 0.6, respectively. According to these results, it may be possible to develop a compensation model in simple geometries, such as microcavities, and a practical solution could be used to compensate the desired profile in the CAD program and then generate the part machining program. An in-depth analysis of the major axis (M) measure was conducted. Table 4 summarizes the results of the ANOVA analysis. Table 4 reveals that feed per tooth and the machining axis are the most significant factors in the major axis (M) measure. This confirms that the geometrical error sources are motion control and control software and can be identified by, as mentioned in Section 1, applying different feeds for the same motion path [18].  Figure 10 shows the main effects plots on the major axis (M) measure. When feed per tooth increases, the major axis (M) also increases. On the other hand, when x-axis machining is used the major axis (M) measure is greater than when y-axis machining is used.

Major axis M, (µm)
Axis machining 0=X, 1=Y Figure 11 shows that the values of major (M) and minor axis (m) exceed the desired value of 525µm and 500 µm, respectively. When both graphics are compared, it is evident that the values of the major and minor axes on the X-axis machining direction are larger than the values obtained on the Y-axis machining direction. Figure 12 shows a micro-cavity in the XY plane. It is also worth mentioning that when the axis of machining is the X-axis, the value of the major axis is greater than the value obtained using the Y-axis machining direction. So, and according to the results, it can be concluded that the difference between the X-axis motion and Y-axis motion is what is affecting the accuracy of the final shape. These results can be explained by machine kinematics. Figure 13 shows a schematic explanation for the tendency of the ellipses long axes. A spindle motor starts with an initial speed to go from point A to point B, using the path in double line. When the micro-tool arrives at point B, the spindle motor decelerates in order to end at zero speed, however, when working with micro distances another trajectory is machined (triple line) because of the inertia of the spindle and consequently this fails to stop as desired. On a macro-scale, these accelerations and decelerations are not as noticeable because these variations, compared with the dimensional size of the pieces are negligible, but on a micro-scale they are proportionally important. The explanation for this behaviour is that, as distances are short the programmed feed rate is never reached. The results obtained by the calculated relative errors infer that the influence of acceleration and deceleration is not the only element that affects the accuracy of the final feature. Figure  14 shows that the errors obtained are not equal when an X-axis direction is used or when a Yaxis machining direction movement is used.  According to experimental data by Andolfatto et al. [25], the repartition of the mean value of the error sources along the experimental trajectory, on a macro-scale, are shown in Table 5.

Figure 10 Main effects plot for major axis (M) measure
The major source of error is the link errors at 86.9%. Table 5 also shows the percentages applied to the mean values of the experimental data in this work. The comparison is made in order to emphasize that while on a macro-scale the errors may be negligible, on a micro-scale it means that the manufactured final product does not comply with the desired dimensions. In addition, the most influential factor on the geometrical error are the link errors and on average these errors affect the end product with 86.9% of the total error. In comparison with some previous research by Chen et al. [3], these authors used a three-axis CNC horizontal machining centre and developed a displacement measurement approach. They found that one of the maximum translational errors is 29 microns. This is evidence that, although on a macroscale this is insignificant, on a micro-scale this has an enormous affect because the characteristics of the final piece contain details of the same size. Moreover, the Andolfatto et al. [25] study quantifies the dynamic errors as 0.6%, but on a micro-scale this error increases as a result of micro tool deflections and vibrations. Thus, further research should be performed in order to analyze this error source.

Conclusions
This work investigates the machine-tool motion accuracy of a medium CNC machine in the micro-milling of elliptical cavities. Furthermore, it studies the influence of the process parameters and the quality of the geometrical features on the final micro shape features. The methodology of this study includes an analysis of the structure of the machine which used in the tests, as well as a model to test the control motion and control software. Then, an experimental study was performed with a geometry selected to evaluate the error which is produced according to the theoretical principles studied. Furthermore, a brief comparison of the results with previous studies on a macro-scale has been incorporated.
Some specific conclusions can be drawn as follows:  The present work developed an experimental approach in order to characterize the radial error using a CNC machine instead of specialized machine or in-house micro machine centre in the micro-milling process. Furthermore, this methodology is a practical solution replacing expensive commercial solutions such as laser interferometer, double ball bar, laser Doppler vibrometers, etc.
 Results suggest that CNC standard machine tools are capable of performing micromilling to produce micro-cavities, but inertial and kinematic values are highly significant when it comes to affecting motion control.
 The dimensions of the cavities obtained were close to the desired values; achieving a percentage of error below 5%.
 It could be seen that, by performing an inspection of the machine tool, the mass moved by the X-axis is greater than the mass moved by the Y-axis. Mass has a direct effect on inertial force thus, the greater the mass, the slower the time response of the system, because X-axis mass is greater than Y-axis mass and this results in a greater error in the X-a is. E peri e tal results o fir that the differe e i a es' otio produces errors in the final micro part. Using a medium milling centre with similar characteristics for micro-milling could be proposed a compensation model.
 Accuracy and final shape are affected by the dynamics of machine tool. At a microscale, accelerations and decelerations are significant and cannot be assumed to be negligible, as they would be in the case of macro-scale. Results suggest that accuracy and final shape are mainly influenced by feed per tooth.