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

The demand for micro holes, micro-molds, 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 provides the insight needed to improve milling as a micro-manufacturing process. The goal is to characterize motion system to reduce error and improve accuracy with different process parameters on final shape for micro-parts while standard milling machine with linear motor and servomotor is used. Geometrical error and accuracy caused by motion control and control software error sources is evaluated and analyzed. Results will help decision on process parameters and it verifies that standard milling machine is useful to produce micro-parts. The work is carried out by theoretical principles and experimental work, the machine-tool motion accuracy of a medium machining center specializing in the micro-milling of elliptical cavities on aluminum 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-molds, and micro forms continues to increase. Aerospace, microelectronics, the medical sector, together with the automotive sector, are 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 the 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 guideway. 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 (DBB) 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 guideway 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 numerical control (NC) machine tools. A 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 XZ-plane, because it has the ability to work with any chosen path. Rehsteiner et al. [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 the micro-scale. In the case of double ball bar, the 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. [10], conducted investigations into the contribution of acceleration and deceleration in macro-scale part dimensional errors, while Philip et al. [15], 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-highspeed miniature spindles. The technique was based on measurements of radial motions in two mutually orthogonal directions of a precision artifact using (non-contact) laser Doppler vibrometers [16].
According to Schwenke et al. [17], 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 thermo-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 [18][19][20]. The finite stiffness of the structural loop can be a significant influence on the machine's accuracy; which can occur due to the weight and position of, for example, the workpiece or moving carriages of the machine. Schwenke et al. [17] reported that these kinds of errors are more important in comparison with kinematic 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 [17].
Another approach, in order to reduce errors, is to compensate the error based on a previously developed model. Eskandari et al. [21] 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. [22] 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 center or an in-house micro machine center 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 parameters-axial 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 center machine used in this work is presented. According to these results, an experimental work is proposed to prove that the contour error in micro-cavities 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 section, an attempt to establish the theoretical principles that characterize the CNC machining center 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 center used is a Deckel Maho 64 V 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 (Fig. 1a). On the other hand, the rotary servomotor has two principal parts; the stationary stator and the inside rotor (Fig. 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 (ball screw, lead screws, ball nuts, 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: 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 traveling 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 traveling distance are: According to manufacturer specifications, motor inertia is 0.0068 Kg m 2 ; therefore, from Eq. 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 Eq. 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 Eq. 4: Figure 2 shows both carriages on the Xand 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 assembly, spindle motor, heat exchanger unit, the tool's cooling system, the spindle traverse 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 micro-cavities is also affected by the servo feedback delay. According to Poo et al. [23], 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°but error is defined in Eq. 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 evaluate the function from 0 to 2π radians. Figure 3 shows that when the gain mismatch 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: Figure 4 shows the sum of square errors and it is evident that the growing trend means that when the speed gains are different then one of the axes is moving faster than the other.
However, Fig. 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 modeled 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 © 64 V Linear (3-axis, 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 center has a speed ranging from 1 to 12,000 rpm and is driven by a 19-KW spindle drive motor. The Fanuc 180i controller offers control of up to three independent part program paths   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 12×25×25 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 shows the geometric characteristics of the tools. Before performing the milling operations, the microtool was measured with a non-contact laser system supplied by Mida © (repeatability of 2σ≤0.2 μm) in order to compensate for tool errors (Fig. 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 micron on the minor axis and 250 μm in depth, as Fig. 9 shows. This geometry was selected in order to enhance the effect of the differences between the Xand Y-axis motions. 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 Fig. 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 Fig. 9). Micro-cavity shape was also evaluated.
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 (×150 magnification). 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 and minor axes. 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 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 micro-cavities, and a practical solution could be used to compensate the desired profile in the CAD program and then generate the part machining program.

Results and discussion
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 [17].    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. Figure 11 shows that the values of major (M) and minor axis (m) exceed the desired value of 525 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 points A to 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 behavior 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 Y-axis machining direction movement is used. The graphics demonstrate that the percentage errors on both axes of the ellipse (major and minor axes) are lowest when it is machined in the Y-axis direction. The previous idea that linear motor is better than servomotor is not clear while mass seems to have more effect on axes movement. The results show that the geometrical error is caused mainly by three sources; all of which are related to each other. The kinematic errors are caused by the machine's  Fig. 11 Effect of feed per tooth using Xand Y-axes machining directions on major and minor axes Fig. 12 Measure of the major axis (M) a Micro-cavity performed using X-axis machining (left) and performed using Y-axis machining (right) structure and because there are not the same loads in the moving carriages, produce motion control, and control software errors.
According to experimental data by Andolfatto et al. [24], the repartition of the mean value of the error sources along the experimental trajectory, on a macro-scale, are shown in Table 5. 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 macroscale, 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 is 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 center and developed a displacement measurement approach. They found that one of the maximum translational errors is 29 μm. This is evidence that, although on a macro-scale, 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. [24] 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 for two different motion systems. 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 center 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 micro-milling 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 x B y A y B x X-axis machining direction Y-axis machining direction  axis. Experimental results confirm that the difference in axes' motion produces errors in the final micro-part. Using a medium-milling center with similar characteristics for micro-milling could be proposed as a compensation model. & Accuracy and final shape are affected by the dynamics of the machine tool. At a micro-scale, 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. & According to the results, the difference between the X-axis motion and Y-axis motion is what is affecting the accuracy of the final shape, but this difference is due to mass displacement for each axis than motion solution either it is linear motor or servo motor