Numerical Analysis in Ultrasonic Elliptical Vibration Cutting (UEVC) Combined With Electrical Discharge Cutting (EDC) For Ti6Al4V

This paper reports the numerical analysis results of ultrasonic elliptical vibration cutting (UEVC) combined with the electrical discharge cutting (EDC), called UEVC+EDC. UEVC delivers decreasing cutting forces, repressing side-burrs, and lowering tool wear. EDC is a cutting technique using a pulsed spark to remove material using thermal energy. Difficult-to-cut materials, such as Ti-6Al-4V, can be cut effectively by combining these two techniques. A numerical study was performed using ABAQUS finite element analysis (FEA) software by investigating the von Mises stress, cutting forces, and temperature. Numerical analysis was carried out by modifying the ultrasonic vibration frequency, distance of the discharge pulse, discharge voltage, and discharge pulse radius. UEVC+EDC was compared numerically and experimentally with regular cutting (NC) and UEVC in terms of cutting force and tool temperature. The results showed that the UEVC+EDC method could improve the cutting condition by reducing the cutting force and von Mises stress and increasing the tool temperature.

In the case of one-dimensional ultrasonic vibration-assisted cutting (1D-UVAC), this cutting method has been explored extensively, including experimental [18], FEA simulation [19], and theoretical models [20]. In 1D-UVAC, the tool modulates commonly in parallel, perpendicular, or even in the feed direction of the workpiece surface [10]. Recent investigations of 1D-UVAC since 2017 focused on surface texturing [21], microtextured surface [22], the influence of the tool material and geometry [23], development in the micro-milling device [24], and cutting force prediction using FEA [25]. 1D-UVAC accomplished revolutionary analyses, particularly in the cutting mechanism [19]. Therefore, the 1D-UVAC was not assessed in this study.
2D-UVAC involves two directions of tool motion along with the cutting speed and the thrust direction. In 2D-UVAC, the tool motion is elliptical/oval or even circular in stationary vibration. 2D-UVAC has also been explored extensively, and advances have been made in terms of experimental [1,4], FEA simulations [6,26,27], and mathematical models [28,29]. The recent publications since 2017 in 2D-UVAC involved surface roughness analysis [9], bone-cutting [30], atomistic investigation [31], nano-cutting [32], surface sculpturing [33], brittle-to-ductile transition [34], diffraction texturing effect [35], and tribology [36]. Accordingly, 2D-UVAC has become the best candidate to replace conventional techniques because of the simple implementation and apparatus. Therefore, this study examined this technique further by combining it with a thermal effect.
In the case of 3D-UVAC, the tool vibrates sequentially along in three directions to form a 3D elliptical locus in Cartesian coordinate space. Shamoto et al. [37] reported the first investigation of 3D-elliptical vibration cutting in 2008. Some studies on 3D-UVAC have been published since 2017, such as device development [38] [39], surface topography [40], carbon-fiber-reinforced plastic (CFRP) [41], surface integrity [42], wettability [43] and surface texturing [44]. Despite the research on 3D-UVAC in specific topics, the breakthrough of the cutting mechanism of 3D-UVAC could still be explored. In this study, however, 2D-UVAC combined with the electrical discharge cutting (EDC) technique is the focus; 3D-UVAC will be a future research topic.
Thermally Assisted Cutting (TAC) has been investigated extensively, and some reviews regarding this method are available [45][46][47][48]. TAC uses an external heat source, such as a laser [49] and plasma [50] device. The external heat source is used to localized preheat the workpiece surface, thereby decreasing the hardness and yield strength of the workpiece surface during machining. This decreases the cutting forces after localized preheating, minimizing tool wear and surface roughness [51]. On the other hand, the EDC technique can become an alternative external heat source. Jung et al. [52] used EDC in the assisted cutting of Ti6Al4V during micro-dimpling to decrease the cutting force. Few studies have examined the use of EDC in the TAC technique. Therefore, the EDC is proposed as the external heat source for this hybrid technique.
The EDC technique is categorized as a non-traditional cutting technique for high precision products and complex-shape cutting. In this study, EDC was combined with the 2D-UVAC method. The EDC technique is fundamentally electrical discharge machining (EDM). The EDC technique only operates with conducting materials. In the EDC technique, surface materials are removed by melting and vaporization from the discharged plasma spark, regardless of its hardness, where the discharged spark temperature is higher than the melting temperature of the workpiece. The materials properties in EDC, e.g., the thermal conductivity, melting temperature, and electrical conductivity, become important in the EDC technique [53]. In the EDC technique, dielectric fluids [54], such as deionized water and kerosene, are commonly used to occupy the dielectric medium between the tool and workpiece. In addition, the dry condition could also be employed [55].
The EDC technique has been investigated comprehensively, and research advances have been made [56]. Moreover, reviews regarding the EDC technique alone have been available broadly, e.g., surface modification [57], hybrid machining process [58], dielectric fluids [59], difficult-to-machine materials [60], metal matrix composites [61], and modelling/optimization [62]. Therefore, the EDC technique is not new in industry. On the other hand, the authors combined this EDC technique with the 2D-UVAC to determine the thermal effect on the material during vibration cutting using the FEA method.
This study used the dry-EDC technique. The dry-EDC is a variation of the EDC, which means the EDC technique is performed without dielectric fluids. Recent research since 2019 on dry-EDC has been performed. Macedo et al. [63] examined the anode power deposition in dry-EDC, focusing on the theoretical modeling of discharged plasma physics became their interest. The workpiece or the anode material absorbed approximately 80%-90% of the discharged plasma power, whereas the discharged plasma power loss by convection and radiation was considered. Jung et al. [52] studied the mechanism of micro-EDC drilling under dry conditions focusing on modeling the cutting forces. A decrease in cutting forces was observed due to the thermal softening effect. Dhakar et al. [64] conducted an experimental study comparing wet-EDC and neardry EDC. Toxicological emissions produced higher quantities in the wet-EDC. Therefore, the dry-EDC can be categorized as environment-friendly.
The EDC technique has been combined in recent times with several other cutting methods, such as ultrasonic motion [65], electro-chemical spark machining (ECM) [66], milling [67], and grinding [68]. Zhang et al. [69] examined ultrasonic-assisted micro-EDC, where a nitrogen plasma jet was also investigated. The ultrasonic vibration helps remove the debris easily from the discharged area. Thus, abnormal discharged sparks could be decreased and the cutting efficiency enhanced. Their results confirmed that the material removal rate (MMR) could be improved by adding an ultrasonic vibration effect. Li et al. [70] evaluated a hybrid method (EDC and Milling) for titanium alloy cutting. They proposed a special cutting tool to work sequentially between conventional milling and EDC. A decrease in cutting forces, reduced tool wear, removal of side-burrs, and improvement of surface roughness were achieved [70]. On the other hand, the hybrid technique regarding the combination between 2D-UVAC and EDC has not been accomplished and was the motivation for this research.
The FEA method is an extremely useful tool to analyze cutting parameters that cannot be measured during experiments, such as plastic strain, plastic strain rate, stress, and temperature in the primary shear deformation zone. Recent observations based on FEA and numerical in vibration-assisted cutting have been obtained. Zhenzhi et al. [71] studied the UVAC on bone material experimentally and numerically. The numerical FEA could predict the cutting forces and cutting temperature. In addition, the cutting forces in UVAC were lower than those in normal cutting. Chen et al. [19] examined vibrationassisted micro-milling numerically and experimentally. They concluded that the vibration frequency greatly affects the machining mechanism. More cracks were observed in the primary deformation zone in vibration-assisted milling than in conventional milling based on the numerical study. Gracia et al. [25] estimated the specific cutting energy for multi-directional ultrasonic vibration-assisted cutting using numerical analysis. A low average cutting force could be achieved when the tool was not permanently in contact with the deformed chip. In addition, the specific cutting energy was low when the vibration frequency was high. Xiang et al. [72] examined the FEA in ultrasonic-assisted milling in a specific case of SiCp-Al composites. In the case of a single particle of SiCp-Al composites, a high frequency could decrease particle breakage and low crack growth. The ultrasonic amplitude also affected the particle breakage, even though a proper amplitude must be selected to minimize particle breakage [72]. Lotfi et al. [73] assessed ultrasonic-assisted drilling experimentally and numerically. Their findings were similar to other studies in which ultrasonic vibrations affect the cutting mechanism, such as decreasing the cutting forces, reducing the cutting temperature, and lowering the built-up-edge. According to the literature above, ultrasonic vibration has a significant effect on metal cutting.
Overall, the hybrid cutting technique (2D-UVAC combined with the EDC (UEVC+EDC)) has not been implemented. This study proposed a novel FEA model that may be implemented in industry. The hybrid technique was proposed and carried out by numerical analysis in a two-dimensional manner. The cutting parameters, such as vibration frequency, discharge voltage, discharged radius, and discharge distance, were adjusted. The surface node temperature, cutting tool temperature, cutting forces, stress, and strain rate were analyzed accordingly. These findings are useful in metal cutting, especially in non-traditional cutting mechanisms.

NUMERICAL METHODOLOGY
Numerical analysis was carried out using commercial ABAQUS TM 2019 software. Dynamic explicit coupled temperature analysis was implemented. In this study, twodimensional (2D) analysis with deformable characteristics for both the workpiece and tool were considered. The titanium alloy (Ti6Al4V) and tungsten carbide were considered as a material for the workpiece and the tool, respectively. Table 1 lists their properties, where the workpiece Young's Modulus was considered to decrease with increasing temperature. The detailed descriptions regarding the boundary condition, meshing, contact interaction, J-C constitutive model, and Gaussian pulsed model are described in the next sub-chapter.
The following assumptions were made with the numerical model of UEVC+EDC:

FEA setup (boundary condition, meshing, and contact interaction)
where and are the amplitude in the x-and y-axis directions, as shown in Fig.  1, which was set to 10 μm for both directions. is the ultrasonic vibration frequency, which was set to be equal between 20 and 60 kHz. is the numerical time. is the phase shift difference between two sinusoidal motions, which were set to 90°. is the constant cutting velocity along the x-axis direction, which has a negative direction and was set to -2 m/s. This value was chosen considering that machining was carried out under a medium cutting speed in ordinary cutting, such as milling This numerical study used the VDISP subroutine algorithm for 'user defined' definition in ABAQUS while applying the boundary conditions for tool vibration. Fig. 2 presents the VDISP code to conduct the numerical simulation. All scales in this numerical study were in SI units [m, kg, Pa, and J]. The FORTRAN compiler should be installed on the computer because it is an essential add-in to run the VDISP subroutine function. In this case, the authors installed Microsoft @ Visual Studio Community 2019, Intel @ oneAPI Base Toolkit, and Intel @ oneAPI HPC Toolkit. The FORTRAN compiler must be linked with ABAQUS software inside the ABAQUS batch command 'abq2019.bat' by adding the call function (@call "…") opened using the Notepad++ program (see Fig. 2).
The meshing of the workpiece was quad-type (CPE4RT) for the Explicit library, and the coupled temperature-displacement was used. The geometric order was linear. The distortion control was set as a default, and the hourglass control was set as enhanced. The second-order accuracy was used, and plane strain type analysis was used. The element size was set to approximately 5 μm for the workpiece. For the cutting tool, the tri-type of mesh was used with the couple temperature-displacement. The element size was formed as dense as the cutting edge of approximately 2 μm, and the outer side edge that does not engage with the workpiece was set to approximately 10 μm. Moreover, the contact interaction was set for the explicit surface-to-surface contact. The surface of the tool was coupled together with the reference point. Table 1 lists the material properties of Ti6Al4V in the tool and workpiece.

Johnson-Cook Constitutive Model
The plastic deformation of the material is generally justified according to three factors (strain hardening term, thermal softening, and strain rate hardening [74]). In this study, the plastic deformation of Ti6Al4V was justified using the Johnson-Cook constitutive model, as shown in Eq. 3 [74], which was set in the ABAQUS material properties.
where is the plastic stress flow; is the equivalent plastic strain; ̅ is the plastic strain rate; ̅̇ is the reference or absolute strain rate (1 s -1 ). is the yield strength of the workpiece; is the hardening modulus; is the strain rate coefficient. is the cutting temperature on the primary deformation zone; = 25°C; is the melting temperature of the workpiece. Table 2 lists the material constant for the Johnson-Cook model with n and m coefficients set to 0.34 and 0.8, respectively.

Johnson-Cook Damage Model
The Johnson-Cook damage model can model a deformed chip during the numerical analysis of metal cutting. The element will generally be eroded or separated when the damage initiation parameter exceeds one [76]. The common value can be described using Eq. 4 [75], which is the summation ratio between the accumulation of changing of the equivalent strain in each numerical increment and the initial equivalent plastic strain at the start of a fracture , as expressed in Eq. 5, where D1 -D5 are the Johnson-Cook damage parameters for Ti6Al4V, as listed in Table. 3. In this study, however, the Johnson-Cook damage model for the ductile fracture criterion based on fracture energy was adopted. The fracture energy was set to 10,000 J/m 2 for damage evolution, where the multiplicative degradation was used. According to Zhang et al. [76], the formulation for the damage initiation parameter based on the damage energy can be described using Eq. 6, where Gf is the Hillerborg's fracture energy; u p is the equivalent plastic displacement; is the equivalent plastic stress. In this case, the deformation of the chip will not show a serrated surface.

Pulsed Gaussian Heat Flux
The plasma spark of the EDC process was assumed to be a pulsed Gaussian heat flux, as shown in the schematic diagram in Fig. 1. On the other hand, the plasma spark can be modeled as a uniform heat flux based on previous studies, such as micro-drilling with discharge cutting [52] or EDC [77]. In addition, the uniform heat flux can explain the thermal physics, but the Gaussian heat flux [78,79] is preferable because it is more realistic in physics and for accuracy in numerical analysis. Eq. 7 expresses the pulsed Gaussian heat flux, where the center of pulsed Gaussian heat flux is located from the zero reference of the workpiece with a distance (see Fig. 1). The distance of the cutting tool tip nose from the zero reference of the workpiece, ∆ = 10 μm. The position of Gaussian heat flux is set in fixed as well as the cutting tool since the workpiece moves along x-axis.
In Eq. 7, is the heat flux distribution as a function of the x-axis (X) variable. was 50 μm to 200 μm (see the numerical model assumption point 7). is the radius of the pulsed Gaussian heat flux. The Gaussian shape coefficient equals 2. and are the discharge voltage and current, respectively.
is the heat fraction number that determines how many percentages of heat energy penetrate the workpiece. was set to 18% (0.18) according to Liu and Gao's paper [79]. is the pulse frequency during the discharged simulation. The pulse frequency determines the number of cycles of the plasma spark formed across the discharged gap [57]. In this study, the pulse frequency was set constant at 100 kHz.
For numerical analysis, the heat flux was set on the workpiece surface, as shown in Fig. 1, and the DFLUX subroutine was written in notepad++ and saved as a FORTRAN function (".for"). Fig. 3 shows the DFLUX subroutine used in this study.

EXPERIMENTAL SETUP
The experimental UEVC and UEVC+EDC were conducted in the CNC lathe turning to validate numerical results, as shown in Fig. 4. Although the numerical models were conducted in a 2D platform, the numerical models still can be validated, particularly using a 3D platform, such as turning. Table 4 lists the detailed experimental setup for numerical and experimental trials. Experiments are difficult to perform precisely using similar numerical parameters because, in the numerical trials, the vibration frequencies were set at a high range of values: 20, 30, 40, 50, and 60 kHz. It was fundamentally considered for high-performance machining and in high cutting speeds, such as ultrasonic vibrationassisted milling.
Meanwhile, in the current setup, the ultrasonic tool holder was only working in a fixed natural frequency of approximately 16.9 kHz. Therefore, the S.R (Speed Ratio) was set to be similar between the numerical and experimental trials. S.R is the speed ratio between the cutting velocity and maximum vibration speed ( 2 ⁄ ). S.R in the numerical trials is equal to 0.628, 0.942, 1.256, 1.570, and 1.884 with between 20 and 60 kHz, amplitude of 10 μm, and cutting velocity of 2 m/s. Thus, the rotational speeds of the workpiece in experimental trials were set to 120, 80, 60, 48, and 40 rpm with a fixed vibration frequency of 16.9 kHz and a vibrational amplitude of 1 μm to maintain an equal S.R with the numerical study (see Table. 4). In addition, the phase shift vibration for the experiment was set to be similar at 90° (120° -30° = 90°). An elliptical vibration was generated using an ultrasonic hybrid precision generator of three channels where channels 2 and 3 were activated, and channel 1 was off (see Fig. 4). The bending-bending vibration mode was activated using activated channels 2 and 3 only. The detailed design of the ultrasonic tool holder is reported elsewhere [44].
The cutting depth Dh was set equal to 100 μm, which is similar to the numerical trials. On the other hand, the numerical trials did not have a feed rate of 100 μm/rev. Thus, the numerical cutting forces must be multiplied by 0.01 mm 2 (0.10 x 0.10 mm 2 ). The mini dynamometer KISTLER type of 9256C was used to measure the cutting force signal. The mini dynamometer can measure the signal maximum at a frequency of approximately 5 kHz; thus, a signal with a frequency > 5 kHz is probably eliminated. The DAQ (Data Acquisition) device of NI (National Instruments) PCI-E 6034E installed on the PC (Personal Computer) was used.
The NI PCI-E 6034E has a data speed of approximately 200 k Sample/s with an analog input of 16 channels. The sampling frequency of 40 kHz and data sampling of 20 k was set in LabVIEW 2011. No low pass filter was used to capture the force signal and thermocouple signal. The tool temperature was measured using thermocouple type K and recorded with the same DAQ NI PCI-E 6034E. The thermocouple was placed under the cutting tool, as shown in Fig. 4. The conventional tungsten carbide tool with a triangular shape was used. A FLIR camera type T540 IR camera with the setting of the emissivity of titanium material (≈ 0.75) was used to record cutting temperature, especially around the chip deformation zone.
An adjustable copper electrode was used to perform the EDC technique, as shown in Fig. 4. The adjustable copper electrode had a circular shape similar to the workpiece shape. A manual one-axis micro-stage MMT-M1-338-C1 was used to adjust the discharged gap. The distance between the tool and Gaussian pulse in the numerical study was set to a maximum of approximately 200 μm. On the other hand, the distance between tool and copper electrode was set to 5 mm in the experimental setup because it is difficult to set it very close to the cutting tool, and it will disturb the chip flow. Accordingly, the distance was set to approximately 5 mm to allow space for escaping the deformed chip. The EDC was performed under dry conditions without a dielectric. The RC power generator was used to perform EDC, as shown in Fig. 4. The discharged voltage was set to a maximum of approximately 220 V with a discharge capacitance Cp of 1.5 μF. The Numerical Analysis in Ultrasonic Elliptical Vibration Assisted Cutting (UEVC) Combined with Electrical Discharge Cutting (EDC) for Ti6Al4V 13 discharged radius was measured using a 3D optical surface profiler. The most common diameter of the micro-crater was approximately 40 -110 μm, as shown in Fig. 5. Generally, the plasma spark dimensions are related to the micro-crater diameter. Therefore, the plasma spark radius in the numerical trials was approximately 40, 60, and 80 μm.  Fig. 6. The maximum stress in NC was concentrated in the main shear deformation with a red color, and the maximum stress was approximately 1,325 MPa (260), 1,317 MPa (290), and 1,296 MPa (300), respectively. It is relatively constant stress in the case of the NC method. In the case of UEVC, the von Mises stress concentrated in the main shear zone decreased when the tool started to leave the main shear zone, as shown in Fig. 6. In addition, by adding EDC in the UEVC, the contour showed a decrease in stress on the main shear zone in the blue region during tool retraction. EDC indicated a decrease in von Mises stress. Fig. 7 compares the temperature contour of NC, UEVC, and UEVC+EDC, showing frames 260, 290, and 300. In the case of NC, the temperature in the shear deformation zone was constant at approximately 230-240 °C, as shown in Fig. 7. In the case of UEVC, the temperature in the shear deformation zone was higher than that in NC. During tool retraction, as shown in frame 300, the temperature in the shear deformation zone in UEVC was still higher than that in NC. The temperature ranged from 240 to 270 °C, which indicates that the UEVC has a better material removal rate because of the enhanced relative cutting and increased nominal cutting depth, which correlated with the elevated temperature in the shear deformation zone [80]. In the case of UEVC+EDC, the temperature in the shear deformation zone was higher than that in both NC and UEVC because of the EDC Gaussian plasma spark. The temperature was approximately 500 -630 °C. The Gaussian plasma spark involves the cutting process in the UEVC, and the von Mises in UEVC+EDC (Fig. 6) decreases because of the increasing cutting temperature in the shear deformation zone.

Numerical von Mises Stress and Cutting Temperature Element
Figs. 9, 10, 11, and 12 present the numerical result of the von Mises and the temperature at surface element 39. Element 39 was selected because it is located at the top of the workpiece surface, as shown in Fig. 8. Fig. 9 compares the stress and temperature of the three different cutting methods (NC, UEVC, and UEVC+EDC). In the NC method ( Fig. 9(a)), the stress and temperature increase as the main cutting zone is approached. The maximum stress and temperature indicate that element 39 is close to the main cutting zone. The stress and temperature then decrease as element 39 leaves the main cutting zone. Hence, element 39 becomes a deformed chip. This trend of the stress and temperature at a specific element location for the NC process shows a similar trend to Ayed et al. [81].
The UEVC driven at 40 kHz ( Fig. 9 (b)) produced a fluctuated stress and temperature pattern due to the presence of the tool vibration. Therefore, during the retraction mode, the stress was relieved and decreased considerably [82]. In addition, in the UEVC+EDC method (Fig. 9 (c)), due to the presence of the pulsed Gaussian discharged plasma, element 39 experiences considerable thermal load before entering vibrationassisted cutting mode; thus, the temperature increases considerably to 1200°C, and the stress element decreases. This thermal loading effect also increases the temperature element to 600°C. Thus, the stress element decreases significantly. Fig. 9 (d) summarizes the average stress and temperature element; the UEVC+EDC increases the temperature element and decreases the stress element compared to the UEVC and NC methods.  Fig. 10(b). On the other hand, the maximum temperature was lowest compared to other distance pulses because the Gaussian heat flux was close to the deformed chip. Therefore, the temperature was distributed uniformly around the deformed chip during cutting. The average stress was lowest compared to other distance pulses. By increasing the distance pulses, the maximum temperature pattern showed a Node 39 th shift to the left because of the relative position of the element to the Gaussian heat flux. Bringing the Gaussian heat flux to as close to the main shear deformation as possible could be more effective in minimizing the average stress, as shown in Fig. 10(f). As shown in Fig. 10(f), the UEVC+EDC effectively decreased the average von Mises stress compared to the UEVC. Based on Eq. 7 of the pulsed Gaussian heat flux, the heat energy increased with increasing discharged voltage because the maximum peak temperature will increase for pulsed Gaussian heat flux. As shown in Fig. 11, the maximum peak temperature will increase from 300 °C to nearly 1500 °C when the discharge voltage is increased from 50 V to 250 V. The von Mises stress decreased with increasing peak temperature. As shown in Fig.  11(f), the average value for stress and temperature was taken; the stress decreased with increasing average temperature. On the other hand, the stress increased slightly at V = Fig. 12 shows the von Mises stress and temperature of element 39 by the effect of different discharged radii of the pulsed Gaussian heat flux from 40 µm to 80 µm. Based on Eq. 7, the heat flux decreased with increasing the discharged plasma radius R because the discharged voltage and current were constant at V = 200 V and I = 1 A. As shown in Fig. 12, when the discharged radius was increased, the maximum temperature discharge plasma at element 39 became weaker, as observed in Figs. 12(a), 12(b), and 12(c). The maximum temperature of element 39 decreased from approximately 1200 °C to 400 °C. Thus, it yielded higher von Mises stress. Fig. 12 (d) presents the average value; R = 40 µm produced a more effective decrease in the average von Mises stress because of the higher average temperature. In the case of the NC method, the cutting forces increased gradually and achieved a steady-state at 0.8 s then it dropped to zero after 1.6 s, as shown in Fig. 12(a). A fracture developed at the end of the cutting process because the deformed chip in numerical analysis was left out of the main cutting zone, as shown in Fig 13(d). The deformed chip remained at the end of the cutting process in the UEVC and UEVC+EDC method. Although no fracture propagation occurred in UEVC+EDC (Fig. 13(d)), fracture propagation in UEVC began to grow at the end of cutting in frame 1000. Therefore, the cutting forces trend decreases but does not achieve a zero level in both UEVC and UEVC+EDC because the deformed chip remains at the end of the cutting process due to tool vibration motion.

Numerical Cutting Forces and Comparison
The cutting forces in UEVC and UEVC+EDC typically fluctuate due to the vibration mechanism of the tool with periodically tool engaging and the tool disengaging into the main shear deformation zone. Moreover, the maximum peak of the cutting force Fc in the UEVC+EDC decreased slightly compared to the maximum cutting force Fc in the UEVC. Evidently, the cutting force Fc can be reduced by adding EDC to UEVC. On the other hand, EDC does not decrease the thrust force, and Ft shows a similar pattern with UEVC alone.  (Fig. 14(a)) and 30 kHz (Fig. 14(b)), there were no significant fluctuations of the cutting force pattern. This indicates that the tool still contacts the main cutting zone continuously with less fluctuating vibrations. Furthermore, S.R > 1 at higher frequencies, such as 40 kHz (Fig. 14(c)), 50 kHz (Fig. 14(d)), and 60 kHz (Fig. 14(e)). Therefore, the cutting forces begin to fluctuate, which indicates the tool leaving the main cutting zone, and UEVC+EDC is more effective in decreasing the average cutting force by the higher frequency if S.R > 1 is considered. Fig. 15 summarizes the average cutting force for UEVC+EDC with different distance plasma pulses Xo = 50-200 µm ( Fig. 15(a)), different discharge voltages Vd = 150-250 V ( Fig. 15(b)), and different plasma radii R = 40-80 µm (Fig. 15(c)). The average cutting forces for NC and UEVC are also included for comparison. According to the results, the average cutting forces decreased in UEVC compared to NC due to active tool vibration. By adding the EDC method to UEVC, the cutting forces were improved slightly, as indicated by marginally lower cutting forces at various vibration frequencies, as shown in Fig. 15(a) and Fig. 15(b). Lowering plasma spark distance Xo and increasing discharge voltage Vd will help decrease cutting force, especially the principal force Fc. Fig. 15(c) presents a contradictory result; the cutting forces increased at a high plasma radius. As mentioned in Chapter 4.2, the heat flux becomes weaker by increasing the plasma radius.   16 shows the validation between the numerical and experimental cutting forces of both UEVC and UEVC+EDC methods. The principal force Fc was considered along the tangential direction of cutting in turning, and the thrust force Ft was considered along the feed direction in turning. According to numerical results, adding the EDC method to the UEVC could decrease the cutting forces slightly in the low S.R. On the other hand, there was no significant effect at a higher S.R, especially for Fc in the numerical study. The experimental results showed that a force reduction can still be observed at higher S.R. In this validation result, there was disagreement between the numerical and experimental results for both Fc and Ft. Fig. 16 shows that the numerical value was higher than the experimental value. In the case of Fc, in numerical results, the cutting force ranged from 40 to 25 N. By contrast, the cutting force Fc in the experimental results was less than 20 N. The nominal cutting speed in experimental validation was lower than in the numerical for a similar S.R. The nominal cutting speed was influenced directly by the validation results. The decreasing pattern was similar when the S.R was increased. When S.R = 1.884, Fc in the experimental case increased due to the very low cutting speed, possibly because higher friction occurs at the lowest cutting speed. A similar pattern with principal force in the thrust force was noted for the numerical result when S.R increased; a decreasing thrust force was observed with a low S.R. Fig. 17 compares the numerical and experimental tool temperatures for the NC, UEVC, and UEVC+EDC method. Fig. 17 presents at low-speed ratio when S.R = 0.628. Fig.  17(a) shows the node temperature of pattern 79, which is located on the rake face of the cutting tool. The node temperature in both UEVC and UEVC+EDC has a fluctuated graph compared to that in the NC. In NC, the numerical tool temperature constantly increased and reached a steady state with a mean value of 160.59 °C. The numerical tool temperature in the UEVC fluctuates or even increases compared to NC. Similar evidence suggests that the tool temperature in UEVC is higher than NC during micro-grooving [74]. The average tool temperature in UEVC was higher than NC. Furthermore, in the case of UEVC+EDC, the effect of the Gaussian plasma spark induced heat into the rake face. The average tool temperature was 471.32 °C. Hence, the material removal process in UEVC+EDC could be more effective than others because of the higher temperatures. Fig. 17 (b) compares the numerical results with the experimental tool temperature measured using a type-K thermocouple. The type-K thermocouple was located under the cutting tool. The tool temperature was 60-80 °C because it was not located close to the rake face. Despite the different values from the numerical results, Fig. 17 (b) provides similar evidence that the average temperature in UEVC+EDC was the highest. Generally, the tool temperature increases from ambient temperature 25-30 °C to increase to a steady-state. The experimental temperature result for UEVC and UEVC+EDC must be examined using a median filter because of electrical signal disturbances from the ultrasonic generator and RC EDM generator. Fig. 17(c) presents the experimental tool temperature at near shear deformation. The IR camera results provided similar evidence that the tool temperature in the UEVC+EDC was highest at approximately 215 °C. Fig. 18 shows the results for the case of a higher S.R (S.R = 1.884). At a high S.R, a similar pattern can also be found. In the case of numerical tool temperature, compared to the low S.R, the tool temperature decreased for both UEVC and UEVC+EDC methods. The periodical cutting engagement with the workpiece decreased due to the more fluctuated pattern of the tool temperature. The tool vibrates more frequently at high S.R. As shown in Fig. 18 (b), the experimental tool temperature also showed similar evidence, with UEVC+EDC being the highest. On the other hand, the average value tool temperature in the UEVC+EDC was similar within the UEVC of an approximate 1 °C or 2 °C difference. The UEVC+EDC graph pattern shows where there is a significant increase in the peak intensity. This might be due to the high plasma discharge with a sudden effective discharge gap. The IR camera results provided similar evidence that the tool temperature in UEVC+EDC was the highest, even with a high S.R, suggesting a better material removal process using the UEVC+EDC method.

CONCLUSION
Numerical and experimental studies were performed on UEVC+EDC compared with the NC and UEVC methods in terms of the von Mises stress, cutting forces, and temperature. The following conclusions were drawn: 1. According to numerical results, the stress concentration on the shear zone in the UEVC+EDC decreased because of the vibrational tool effect (engage and disengage sequences) and Gaussian heat flux during the cutting process. The heat from the pulsed Gaussian heat flux induced the main shear zone, resulting in a decrease in von Mises stress. 2. According to the numerical results, the cutting forces in the UEVC+EDC decreased with increasing distance, Gaussian heat flux, and discharge voltage, but the cutting forces were not decreased by the high radius of Gaussian heat flux with a constant discharge voltage and current. In addition, the numerical results were verified by the experimental results. Although there were significant differences due to the different cutting speeds used, a similar trend was found in which the UEVC+EDC decreased the cutting forces. 3. The cutting forces decreased with increasing S.R in the numerical results. On the other hand, the cutting forces were high when the S.R was high experimentally because of the very low cutting speed and high friction. 4. According to the numerical and experimental results, the tool temperature in UEVC+EDC was highest. The discharge plasma spark increases the shear deformation zone and the tool temperature. These results suggest that a higher material removal state can be achieved using UEVC+EDC.