NUMERICAL MODELING AND EXPERIMENTAL EVALUATION OF MACHINING PARAMETERS FOR 2-DIMENSIONS ULTRASONIC-ASSISTED MICRO-MILLING AT LOW AND HIGH-SPEED MACHINING

Vibration assisted machining (VAM) is one of the hybrid machining processes for improving the machined surface quality. VAM performance is mainly influenced by the combination of machining and vibration control parameters, where surface rough ness value (Ra) became the benchmarking indicator. It is difficult to determine the optimum parameter combination to produce high precision products, especially for micro-milling, due to the interconnected correlation among parameters. The benefits of high-speed machining with VAM are high material removal rate and shorter machining time than low­speed machining. VAM operation at high­speed machining is still limited due to the high possibility of chatter occurrence. Therefore, this research aims to evaluate the 2D VAM resonant performance at low­speed and high­speed machining, operated at ultrasonic vibration and amplitude below one μm. The mathematical model and experimental evaluate the vibration effect based on machining mode, amplitude, and spindle speed variation. The mathematical modelling and experiment result complement each other, where the mathematical model can characterize the effect of resonant vibration, amplitude, and spindle speed increment on the tool path trajectory. The 2D resonant vibration at the feed direction causes interrupting cutting and transforms the tool path trajectory from linear to wavy. The mathe matical model and experiment result show the dominant influence of spindle speed and feed rate on the toolpath trajectory and Ra, where low spindle speed and feed rate result in better machine surface roughness. The low-speed machining with VAM results in Ra value between 0.1–0.155 μm, which is below the high­speed machining result, between 0.2–0.38 μm.


Introduction
Micro components are high commodity goods in manufacturing which consists of a micro slot and belongs to the characteristics of modular products [1][2][3]. Thus, a micro-component must have high precision machining quality to promote an ease assembly process [4]. The manufacture of micro components through machining must use a specific technology because of the high demand for quality and the final specifications of the produced components [5]. Moreover, with the high demands for the fulfillment of sustainable manufacture and energy saving, the entire pro duction process must be considered according to those aspects [6][7][8].

Engineering
The application of micro-milling can be used as one suitable machining method to produce high precision and highquality micro product [9]. To achieve the targeted quality of the end product, the utilization of Vibration Assisted Machining (VAM) onto the micromilling process is advantageous. The benefit of the utilization of VAM is mainly on the improvements of the end product quality where the surface roughness value (Ra) is relatively low in comparison with conventional machining mode. The Ra value for machining with VAM can achieve a high precision requirement for micro products [10][11][12]. The challenge to produce a low Ra value in the milling process is proper parameter combination between machining and vibration control parameters. The combinations between machining and vibration parameters are still in the development phase because each aspect will affect the machining process about the changes of the workpiece quality. It makes further development for micromilling still developing by adjusting the setting parameter under a different variation to obtain the appropriate combination according to the Ra value based on material and milling machine apparatus [13][14][15].
There are two classifications of VAM according to the position of induced vibration during the process that is 1dimension (1D) and 2dimensions (2D) VAM [16]. The main advantage of 1DVAM is more compatible to be implemented onto the micromilling machine since the vibration is induced only on the feed direction (xaxis). However, the reduction of Ra value through 1DVAM tend to be uneven since the machining process is conducted on the x-y plane and the vibration is only induced in the feed direction (xaxis) [17]. To overcome this limitation, the utilization of 2DVAM is highly reasonable for further development as it helps to provide a uniform effect on the product. In 2DVAM mode, vibration is induced at the feed direction (xaxis) and tangential to the feed direction (yaxis) [18]. Theoretically, inducing the vibration in both directions (x-y plane) can significantly decrease the Ra value of the finished product [19]. Unfortunately, the actual application of 2D-VAM demands applicable combinations between machining parameters (spindle speed, depth of cut, and feed rate) and vibration control parameters (frequency and amplitude) [20]. The combination must consider the material properties for the processed workpiece and the applied tool for the micromilling process. It makes the adjustment of parameter control on Vibration Assisted Micro-milling is complicated. Therefore, it has to be predicted before the machining to estimate the suitable parameter for the process to obtain the low Ra value of the processed product.
Every combination in the machining parameter provides a different result to the workpiece. For example, VAM is ideal for lowspeed machining combined with a low feed rate during machining [21]. The same approach is also recommended to reduce the Ra value for machining with VAM for low-speed machining and highlighted that the finished product's accuracy increased by 15 % [22]. The toolpath trajectory is highly influenced by the frequency of the induced vibration for the application of UltrasonicVAM and it can be observed through mathematical modeling and experimental [23]. The mathematical modeling can be used as a proper method to predict the toolpath trajectory, which helps to determine the chosen parameter is applicable for the machining process [24]. According to the previous studies, it can be said that the application of VAM improves the quality of the processed product and the importance of mathematical modeling to estimate the toolpath trajectory before the machining process.
Besides the machining mode based on VAM, machining parameters must be set accordingly, affecting the process of obtaining a low Ra value for the processed product. A comprehensive study through mathematical modeling can be conducted to predict the effect of machining parameters and machining mode (VAM) which each combination affects the Ra value of the product [25]. The effect of vibration in three levels (high, medium and low) varies the wear rate of the tool and workpiece where high vibration level allows to obtain low Ra value of the material [26]. Mathema tical modeling can done through finite element analysis and recommends that low-speed machining is more applicable for VAM operational compared to high-speed machining where a high-quality end product is achieved by lowspeed machining [27]. Depth of cut and feed rate in both machining mode (VAM and non-VAM) are considered important parameters aside from spindle speed, af fecting the tool lifetime where it can fulfill the sustainable manufacturing principle [28]. The increase in the tool lifetime is mainly affected by the chosen parameter where it produces suitable cutting force during the machining process [29].

Engineering
The above studies show the effect of machining mode and parameter process according to the end product quality. Unfortunately, no comprehensive study focuses on the mathematical modeling implementation based on the variation of machining mode and parameter process. Furthermore, a limited study compared the VAM application according to machining speed (low and highspeed machining) based on the toolpath trajectory and inhibited the recommended parameters for the machining process. The present study focuses on comparing machining mode (VAM and nonVAM) through mathematical modeling and experimental test to obtain the relation between toolpath trajectory and the quality of the milling process according to the Ra value. To provide more reliable results, the mathematical modeling is also done by varying the spindle speed and amplitude for VAM operational. More specific evaluation for the micromilling process is expected to enhance the prediction of toolpath trajectory and its relation to the quality of the processed product. It can be used as a quick reference to determine the suitable combination of machining parameters.

Materials and methods
The cutting mechanism during the milling process can be predicted using numerical modeling to estimate the toolpath trajectory. Spindle speed, machining mode, the amplitude of piezoelectric transducer for Vibration Assisted Machining (VAM), feed rate and frequency influence the cutting process. In this study, the toolpath trajectory for the microendmilling process is set as the baseline for modeling the interaction between tooltip and workpiece. The toolpath trajectory for endmilling is formed as a trochoidal curve and can be predicted through (1), (2) for the xaxis and yaxis of nonVAM mode: Where v f is feed rate, mm/second; t is machining time, second; z is the number of flutes; ω is the angular velocity of the spindle, rad/second; r is the tool radius, mm; n is spindle speed, rpm; i is the sequence number of the tooltip, for two-flue type, i = 0 and 1. The application of (1), (2) for four-flute type, i = 0, 1, 2, 3. The tooltip position in ordinate x and y are x i and y i , respectively, within the time frame; 1 second equals 360° rotation.
The use of VAM for the milling process makes the workpiece oscillates in two directions. Therefore, (1), (2) transforms to (3), (4) in order to plots the trajectory of the tooltip relative to the workpiece. The (3), (4) is needed since the vibration is induced in a sinusoidal wave with the same phase but having opposite direction at each axis. The modeling is taken by setting the changes in frequency and amplitude within the timeframe.
So the toolpath trajectory with sinusoidal wave addson to the xaxis and yaxis, has amplitude displacement based on the tooltip rotation within specific timeframe. Where A x and A y are the amplitude at each axis; j 0 is the phase angle; λ is the wavelength. The wavelength is the ratio of vibrational and spindle frequency.
The experiment method is taken by using a specimen (3.3×18×18 mm) for each test. The setting parameters ( Table 1) were used for the micro milling process. The specification of the machine was already reported in another study [30]. A piezoelectric transducer (PZT4) was used to produce vibration to induce a sinusoidal curve for the workpiece. The generator ultraso nic (USG110 hybrid precision) was coupled to the piezoelectric at frequency 24 kHz with phase angle 90° oppositely. The VAM mechanism was assembled from BoltClamped Langevin Transducer.  Fig. 1 presents the VAM mechanism attached to the motor stage. The tool for the milling process was used end-milling tool with two-flute type made of carbide coated with TiA1N. The quality of the milling process was estimated according to the surface roughness value (Ra). The Ra was measured by Surfcom 2800SD312 with a cutoff value of 0.08 mm, length of measurement 4 mm and measuring the speed of 0.3 mm/s. The measurement was taken along the feed direction. The detailed parameters for the experiment test are shown in Table 1. Since spindle speed, feed rate, and depth of cut are affecting the milling process performance. Thus each combination was set under two different machining modes, are VAM and non-VAM. The milling process was conducted to the workpiece according to the parameters combination in Table 1. Each parameter combination was tested three times to the workpiece.

1. Results of the Effect of Vibration-Assisted Micro-milling
The application of Vibration Assisted Machining (VAM) during the micro-milling process shifts the toolpath trajectory. The model of the trajectory can be estimated by using numerical modeling where (1), (2) for nonVAM trajectory and (3), (4) for VAM. Fig. 2 presents the result of mathematical modeling for machining mode with and without VAM according to feed direction (xaxis) and tangential direction from feed direction (yaxis).

Fig. 2. Toolpath trajectory model for machining: a -without VAM; b -with VAM
As shown in Fig. 2, the changes in toolpath trajectory can be observed clearly. The trajectory for nonVAM displays a model curve pattern that indicates the tool and workpiece are always in contact along with the cutting process where there is an interval between 1 st and 2 nd cutting. The interval value is 0.11 mm, where during machining with VAM, the interval between 1 st and 2 nd cutting is not observed. As seen in Fig. 2, b, the trajectory for VAM shows a repeated circle pathlike pattern with an intersection path between 1 st and 2 nd cutting. It demonstrates a repeated cutting process at the same surface on the workpiece.

2. Results for amplitude variation on tooltip trajectory
The variation of amplitude is affecting the toolpath trajectory for VAM. The modeling is done by varying the amplitude between 0.5-7.5 μm with interval 1 μm. The amplitude is set for the xaxis, where the amplitude of the yaxis is half of the xaxis amplitude. Fig. 3 presents the trajectory model for each amplitude variation. As the amplitude increase, the interval between 1 st and 2 nd cutting becomes narrow. The repeated cutting process (circle pathlike pattern) is started from an amplitude of 2.5 μm. The increment of amplitude after 2.5 μm affects the size of the peak and valley of the wave from the cutting trajectory. It is observed that there is an intersection between toolpath trajectories by using amplitudes of 6.5 and 7.5 μm. It indicates that increasing the amplitude for VAM can improve the quality of the machining process for micromilling.

Spindle speed variation on tooltip trajectory
The spindle speed during the machining process has a critical influence on the machining duration. The machining duration is associated with the material removal rate from the workpiece.

4. Resonant Vibration Assisted Micro-Milling Performance
The surface roughness value (Ra) from the workpiece after the milling process is the critical parameter that should be addressed carefully, particularly for a micro-component that requires high accuracy. According to the parameter, micro-milling performance can be determined by measuring the surface roughness of the end product. The micro-milling process with and without VAM is compared according to the surface roughness. Since the milling speed also affects the surface roughness, let's compare the surface roughness of the tested specimen with and without VAM under different milling speeds. Fig. 5 presents the surface roughness (Ra) at the different slot of the specimen under low and high-speed milling process with and without VAM (Ra VAM and Ra NON-VAM , respectively). Engineering All specimens processed by VAM have a relatively lower surface roughness than those processed without VAM during low-speed machining. For high-speed machining, the specimens processed with VAM tend to have a higher surface roughness than those without VAM. However, for machining with spindle speed 80,000 RPM, a specimen processed without VAM has a higher surface roughness value, contrary to VAM, where the surface roughness is lower.

Discussion
The application of Vibration Assisted Machining (VAM) affects the cutting mechanism for the workpiece in the micromilling process. According to the mathematical modeling as shown in Fig. 4, it can be observed significantly that the superimpose vibration to the toolpath trajectory. The trajectory model shows the effect that occurs on the workpiece where machining with VAM can improve the quality of machining because of the separation period between the tooltip and workpiece. It is advantageous for machining with VAM because the interval between 1 st and 2 nd cutting can be narrowed down. Thus the tooltip conduct repeated cutting on the same surface from the workpiece. Therefore, the repeated circle pathlike pattern within one machining cycle proves that the machining with VAM can reduce the surface roughness of the workpiece.
The superimpose vibration on VAM is dependent on the produced amplitude by a piezoelectric transducer which significantly affects the toolpath trajectory between the tooltip and workpiece. The amplitude directly increases the peak and valley of the toolpath trajectory, where a higher amplitude causes the interval between 1 st and 2 nd cutting to decrease. It can be noticed distinctly according to the trajectory model in Fig. 5, where the intersection between 1 st and 2 nd cutting appears at amplitude 5.5 μm. The amplitude 6.5 and 7.5 μm cause the intersection area between 1 st and 2 nd cutting to become wider, making the separation period during cutting more extended, which help to increase the cooling time for the product before the subsequent cutting. An extended cooling time is highly recommended where the lifetime of the tool can be prolonged. Unfortunately, producing high amplitude requires high energy consumption for the piezoelectric transducer where it is undesirable for sustainable manufacturing.
In order to improve the quality of the end product for the micromilling process with VAM under a lower amplitude, it should be combined with the spindle speed of the machining. It can be seen in Fig. 5 where the effect of spindle speed at amplitude 0.5 μm at xaxis and 0.25 μm at yaxis shifts the toolpath trajectory. At highspeed machining, the effect of spindle speed in VAM micro milling is not observed, which means a cutting mechanism similar to without VAM. The effect of spindle speed during lowspeed machining is observed where the interrupting cutting occurs. The interval between 1 st and 2 nd cutting becomes narrower when the workpiece oscillates under a certain spindle speed. Therefore, it emphasizes that the application of VAM for the micromilling process should be accompanied by compatible spindle speed, especially when the VAM is using low amplitude. The feed rate also has to be considered to maintain the quality of the end product for VAM with low amplitude.
The combination of spindle speed, feed rate, and machining mode has significantly affected the quality of the micro-milling process, which can be measured through the surface roughness value (Ra) of the end product. The increment of feed rate at specific spindle speed for lowspeed machining with VAM escalated the surface roughness value where the Ra for feed rate 0.2 mm/s and 1 mm/s range between 0.1-0.155 μm and 0.136-0.379 μm, respectively. The same result is also shown for machining without VAM, where the increment of feed rate at a specific spindle speed increases the Ra value. The main difference between the twomode is that the Ra value for VAM is lower than without VAM, which has a Ra value at feed rate 0.2 mm/s and 1 mm/s are ranging from 0.139-0.156 μm and 0.2-0.38 μm, respectively. The result proves that machining with VAM under the same parameter with nonVAM for lowspeed machining reduces the surface rouges value of the end product, which indicates a better-quality product can be obtained.
High-speed micro-milling has no clear-cut trend or pattern where each parameter independently affects the result. It can be observed according to the Ra value for VAM and nonVAM without significant differences. Further, the mathematical modeling as shown in Fig. 2 emphasizes the pattern of surface roughness value in Fig. 5 where changes one parameter milling process Engineering will transform the Ra value fluctuate. The mathematical model can predict the cutting mechanism according to each parameter process. Thus the effect of each parameter can be estimated before the milling process and help determine the quality of the process. The experiment result presents the effect of each milling process where one single parameter will significantly affect the quality of the end product, particularly for high-speed micro-milling. During low-speed machining, the effect of machining mode by using Vibration Assisted Machining (VAM) results in a better milling process quality where the workpiece's low surface roughness value can be achieved compared to non-VAM machining.
The limit of this study is that the evaluation of VAM performance is reviewed from only the tool path trajectory and its influences on the surface roughness value achievement. Therefore this numerical model in this study can be developed into the surface generation modelling. Also, the experimental results can be used as a baseline for further investigation in the influence of VAM application at highspeed milling on the accuracy dimension achievement and tool wear rate.

Conclusions
Vibration Assisted Machining (VAM) micromilling changes the toolpath trajectory so the interrupting cutting can be obtained, which is desirable to decrease the surface roughness value of the workpiece. The interrupting cutting starts at amplitude 5.5 μm at feed direction and 2.75 μm tangential to the feed direction. Machining with VAM under spindle speed more than 30,000 RPM causes the toolpath trajectory similar to nonVAM machining. Feed rate 0.2 mm/s has a better surface roughness value compared to feed rate with 1 mm/s for lowspeed machining. The effect of VAM is not observed for highspeed machining since the surface roughness value of the end product cannot be predicted precisely and tends to have a higher surface roughness value than low speed machining.