Investigation on cutting performance in ultrasonic assisted helical milling of Ti6Al4V alloy by various parameters and cooling strategies

Ti6Al4V alloy is one of the typical difficult-to-machine materials and often results in rapid tool wear, leading to poor machining quality in aircraft assembling. Compared to conventional helical milling, the ultrasonic assistant helical milling (UAHM) process has indicated its superior performance; however, it is still a great challenge to improve the hole surface quality and accuracy. In addition, few studies have been conducted on the effect of different variables and cooling strategies on the hole-making performance in longitudinal-torsional ultrasonic assisted helical milling (LT-UAHM). This paper, for the first time, reports effects of machining variables on geometric precision and surface roughness in LT-UAHM of Ti6Al4V. In addition, the lubrication/cooling mechanism on the simultaneous application of LT-UAHM and MQL is theoretically analyzed. The design approach of Taguchi experiment was employed to study how major variables such as the cutting speed, tangential feed, axial feed, and the workpiece hardness influence the dimensional and geometrical tolerances and surface roughness. This paper also discussed the effect of three cooling strategies, i.e., dry condition, air coolant, and minimum quantity lubrication (MQL) in LT-UAHM. Theoretical analysis demonstrated that the MQL coolant can be nebulized into hyper-fine droplets owing to the resonant cavitation phenomenon. Combined with the penetrating action caused by the separate-cutting principles of LT-UAHM, the cooling and lubrication performance of MQL was further enhanced. As a result, LT-UAHM with MQL had the most positive effect on circularity, cylindricity, nominal diameter, and surface roughness, contributing to 34%, 32%, 39%, and 40%, respectively. The second important machining factor was the cutting speed, contributing to 31%, 29%, 36%, and 22%, respectively. The tangential feed and workpiece hardness have the negative effect on geometrical accuracy, respectively.


Introduction
In aviation industry, hole-making is the last but also an important manufacturing stage for assembling products, and tiny errors during hole-making process make the assembly sets fail to achieve conformity. As to traditional drilling, the major problems is that the cutting speed of the drilling center is zero, which may lead to adverse situations like dimensional deviation and tool deflection of holes drilled through larger thrust cutting force [1]. As an emerging hole-making technology, helical milling can achieve high accuracy and quality which has been extensively used to manufacture parts in aerospace industry. Helical milling is a process of producing holes through rotation of mill tools along the helical path. Benefited from its kinematic mechanism, helical milling is able to produce holes with diversified diameters without changing tools with corresponding tool diameters, thereby realizing great multi-functionality of the cutting tools and reducing machining time and costs [2]. Iyer et al. [3] comparatively studied traditional drilling and helical milling by using these two methods to produce precise holes on AISI D2 hardened steel, respectively. The result was that the roundness of holes produced through helical milling using a solid carbide tool was superior to that of holes produced by an indexable tool, and the surface roughness of holes was approximately 0.3 μm. This indicates that helical milling can eliminate the procedure of reaming used to machine precision holes. Amini et al. [4] studied the effect of machining parameters on the machined hole quality by helical milling of CFRP and make the comparison of thrust forces and surface damage between helical milling and conventional drilling. Thrust force reduction and no hole cracks were observed in helical milling due to the convenient chip escape. Denkena et al. [5] helically milled compounds of the titanium layer and CFRP, finding a sinusoidal behavior of undeformed chip thickness in the milling process. That produced small and separated chips through helical milling, which made a contrast with the large and continuous chips produced through the traditional method. The study also found that the cutting tool performed three orientation movements during helical milling, and this incurred extremely high demand for stiffness and rigidity as well as feeding drive acceleration. Shan et al. [6] studied the influence of the helical pitch (i.e., the axial feed) and they found a much longer cutter path during helical milling when compared with traditional drilling. Besides, they also found a negative correlation between the length of the cutter path and the magnitude of the variables, and a positive correlation between the helical pitch and the cutting force followed by tool vibrations during orbital milling. Yet the axial force applied during orbital milling was around 8-10 times smaller compared with traditional drilling. Olvera et al. [7] pointed out that the application of traditional drilling and helical milling to titanium alloy assisted by a ball-nose end mill could lead to a smaller error of circularity and dimension in helical milling and drilling, respectively.
It is worth mentioning that the various advantages of this method compared with conventional drilling are mainly due to intermittent cutting by periphery edges for smaller chips and better heat dissipation. However, the cutting mechanism on frontal cutting edges is still continuous. As reported by Li et al. [8], hole quality of helical milling Ti6Al4V alloy with TiAlN tool is evaluated and the results indicated that the wear rate of the end cutting edge and side cutting edge is different, which leads to the variation trend of cutting force in axial and horizontal direction during the process of hole-making. The tremendous wear of front edges induces the more severe thermal damage and this kind of serious wear pattern will eventually bring the breakdown to the manufacturing tool. Moreover, microsmearing was observed on the hole surface which caused by the end cutting edge. As a result, the potential surface damage can be covered by the smearing.
To separate the frontal cutting edges from the cutting area, a feasible strategy is to exert low amplitude (2-20 μm) and high frequency (> 20 kHz) vibration to helical milling process which proposes the novel holemaking process as ultrasonic assisted helical milling. Paktinat and Amini [9] studied longitudinal vibration (L-UAD) and longitudinal-torsional vibration (LT-UAD) during AISI 1045 drilling through numerical methods and experiments. The results were that the surface quality of workpieces drilled could be improved by about 50-60%, respectively, in L-UAD and LT-UAD. Amini et al. [10] carried out the parametric investigation of rotary ultrasonic drilling of CFRP with comparison to conventional drilling. The thrust force reduced by up to 30%, and the roundness and cylindricity decreased by up to 80% and 72% in rotary ultrasonic drilling. Noma et al. [11] performed a study on how ultrasonic vibration affected the micro-scale by helical milling of through holes in chemically strengthened glass. They concluded that helical milling could acquire a higher machining accuracy and cutting efficiency and prolong the life of tools. Ishida et al. [12] performed helical milling CFRP using cryogenic cooling and ultrasonic vibration, and they found that the new method of hybrid helical milling could reduce delamination at machined surfaces and reduce thrust force. Zou et al. [13] analyzed the relationship between microscopic motion trajectory and phase difference from the perspective of kinematics. They found that the axial cutting force and burr heights of Ti6Al4V alloy in LT-UAHM are lower than those in HM.
Another critical part to produce high-quality holes is eliminating cutting heat caused in hole-making [14]. When the traditional lubrication method is used, not enough coolant fluids penetrate into the cutting region, leading to overuse the cutting fluids and largely increasing the machining cost. With the intermittent cutting mechanism in ultrasonic assisted helical milling, the effectiveness of lubrication will be further improved by the tool-workpiece separation. Besides, industry owners are reducing use of mineral-based oils under the pressure of more consideration of environment problems, law implementation, and increased restrictions [15]. Thus, a plenty of investigations have been conducted, focusing on replacement of mineral-based coolant for lubrication with ecological and sustainable coolant with higher efficiency and smaller cost. Methods proposed in these former investigations include cryogenic method, compressed air, and MQL [16][17][18]. Sasahara et al. [19] verified that application of one nozzle to the cooling system could draw hole circularity to one side. When two nozzles were used, the results were better. Moreover, they witnessed nearly the same surface roughness when MQL and the traditional method were used. Yet MQL could significantly reduce the surface roughness in comparison with the dry condition. Tasdelen et al. [20] drilled hardened steel in different conditions of cooling. They found that the 1 3 condition of compressed air generated the largest surface roughness. However, the methods of emulsion lubrication and MQL generated nearly the same surface roughness. Qin et al. [21] performed a comparative study on the influence of MQL and the traditional dry condition and the wet (flood coolant) condition on helical milling of Ti6Al4V alloy in high rang of cutting speed. The flood condition and MQL had nearly the same performance in the aspects of hole surface roughness and cutting force, and MQL was superior to the flood condition in terms of the tool life. Ge et al. [22] carried out the experimental work for helical milling (HM) of the CFRP/TiAl4V stacks in dry, MQL, and cryogenic conditions. The cutting temperature in cryogenic condition is much lower than that those at dry and MQL conditions and MQL is benefit to cylindricity of machined hole. The previous researches show that the dimensional and geometrical tolerances and the surface roughness are significantly affected by the cutting parameters and the cooling/ lubrication conditions in helical milling. However, less research has been focus on the effects of cooling strategies and cutting variables applying in LT-UAHM. Also, the combined effect of LT-UAHM and MQL on lubrication and cooling performance in hole-making of Ti6Al4V alloy is limited. Thus, this work mainly aims to investigate the surface finish and accuracy of the holes machined in LT-UAHM of Ti6Al4V alloy. The present work utilizes Taguchi experimental design to investigate the influence of cutting variables on tolerances and surface roughness in LT-UAHM of Ti6Al4V alloy with three cooling conditions (the dry condition, compressed air, and MQL) through experiments, and the effect of variables and cooling condition refer to the machined hole quality in LT-UAHM of Ti6Al4V alloy have been discussed.

Kinematic analysis of conventional helical milling
For helical milling, the nominal diameter of the ultimate hole is the combined value of the diameter of the helical path and the cutting tool. The cutting tool does three movements simultaneously, i.e., axial feed motion, spindle rotation, and tool revolution around machined hole axis, as depicted in Fig. 1. Therefore, the feed rate includes the axial feed rate and tangential feed rate during helical milling, as calculated in Eqs. (1) and (2), respectively.
The helix angle and tangential and axial feed can also be obtained through Eqs. where f t and f a are tangential and axial feed rate, respectively; n rot and n rev are spindle rotation speed and orbital revolution speed, respectively; a p is axial feed per orbital Helical milling kinematics revolution; ft t and ft a is tangential and axial feed per tooth respectively; z is tooth number. As a result, the cutting tool has two kinds of machining path. In case of axial feeding of the cutting tool, workpieces are machined by the front cutting edge. In case of tangential feeding of cutting tool, workpieces are machined by the periphery cutting edges which used to construct walls of cylindrical holes of the machined workpieces. Correspondingly, the process of helical milling simultaneously comprises two types of cutting, i.e., axial cutting and peripheral cutting. Axial cutting is continuous and is carried out by the axial cutting edge, similar to essential drilling. Peripheral cutting is discontinuous and is carried out by the peripheral cutting edge, similar to face milling. This is the reason why the geometry of undeformed chips produced by the front cutting edge is continuous whereas that produced by the peripheral cutting edge is discontinuous [23].

Kinematic analysis of LT-UAHM
In LT-UAHM, longitudinal and torsional ultrasonic vibration imposed on the cutting tool simultaneously. As presented in our previous study by Zou et al. [13], the trajectory equation of the particular point P on cutting tool can be calculated: where A is longitudinal vibration amplitude, θ is torsional vibration amplitude, and φ is phase shift between longitude and torsion vibration. ft is the frequency of the longitude vibration and f θ is frequency of the torsional vibration.
The microscopic cutting trajectory at one point on the cutting edge by longitudinal-torsional vibration can generate an elliptical trajectory, as shown in Fig. 2. Compared to the conventional helical milling, the cutting mechanism at the frontal cutting edge changes to intermittent cutting. In addition, the intermittent cutting characters of the elliptical vibration will improve the quality of machining [24].

Materials and equipment
Test materials adopted Ti6Al4V alloy plates (diameter: 258 × 125 × 5 mm). The experimental device adopted a five-axis high-speed vertical machining center of DMC75V model with a high-speed linear controller. This study also used 6-mm four-fluted cemented carbides milling tools without coating. Figure 3 shows the images of tools used in this study.  This study adopted a MQL system equipped with two nozzles forming 45° angles with the tool axis. Three conditions, i.e., the dry condition, compressed air, and vegetable-based oil MQL, were applied to the experiments. The pressure of the compressed air was 5 bar, and the flow rate of the oil in the MQL system was 10 ml/h. The compressed air is also supplied by MQL unit. By turning off the oil mist switch, the compressed air is ejected at the outlet of the nozzles. Experimental configuration and setup are shown in Fig. 4. A Hexagon CMM machine (model GLOBAL S) equipped with PC-DMIS software and a Renishaw probe (model PH10T) was used, for the purpose of measuring the dimensional and geometrical tolerances. Three sections that were 1 mm, 2.5 mm, and 4 mm away from the workpiece surfaces were measured. Moreover, a Mitutoyo SJ-500 surface roughness meter device was used to determine the hole surface roughness. The measurement range is 4 mm evaluation length and 0.8 mm sampling length in four different areas. Finally, the average of measured values was reported to serve as the mean surface roughness (Ra) of holes machined.

Experimental methods
To evaluate how the major variables affect the hole machining process on the premise of reducing the experiment number, this study considered five factors on the basis of Taguchi design: axial feed per orbital revolution (a p ), tangential feed per tooth (f t ), spindle speed (n), workpiece hardness (HV), and the type of the cooling condition. A total of 18 experiments were performed under assistance of Taguchi L18 orthogonal arrays. The experiment variables and variation degrees of the experiments are shown in Table 1. It is worth noting that 243 (3 5 = 243) experiments were needed if all experiment conditions were considered, but this was actually impossible due to costs and time limit. For the purpose of eliminating experimental errors,

Results and discussion
This study performed 18 experiments and measured the tolerances and nominal diameters of formed holes with assistance of the CMM device. The design array of the 18 experiments followed the surface roughness and the measured tolerance in each experiment are depicted in Table 2; the experiment results will be analyzed by Minitab software and discussed in the following section.

Surface roughness
As a key characteristic that can determine the surface quality, surface roughness has a great influence on the application of components in the case of dynamic loads [25]. According to Table 2, Ra value in extreme adverse cutting condition was 1.04 μm and other experiment results were all below that, which indicating the superior performance of LT-UAHM. It has been stated that helical milling includes two cutting mechanisms which are at the periphery cutting edges and the frontal cutting edge, respectively. For the frontal cutting edge, the LT-UAHM can change the cutting mechanism from continuous to discontinuous cutting which can reduce the axial cutting force, benefit heat dissipation and chip removal, reduce the tool weal, and improve the surface quality. In order to understanding the cutting mechanism, the cutting force in the experiment number 4 was measured by a Kistler 9527B dynamometer, as shown in Fig. 6. The axial component of the cutting force (≤ 80 N) was smaller than that of the traditional helical milling due to the elliptical vibration kinematic and intermittent cutting of the frontal edge during LT-UAHM process.
For the purpose of identifying the importance of process parameters in affecting surface roughness, this paper conducted ANOVA (analysis of variance) test. ANOVA can test the importance of all major elements and their interactions  because it realizes comparison between the mean squares and the estimated experiment errors at the special confidence levels. Firstly, the main elements and the interactions between every two elements were considered. Next, the elements with less importance were considered as the model error. The final ANOVA of the surface roughness is shown in Table 3.
The P value (P < 0.05) corresponds to a 95% confidence level, indicating the crucial factors, as shown in Table 4. The conclusion is that all of the main parameters are important. In regression analysis, cooling condition is defined as a categorical variable and as a result of that, for each cooling condition (dry, air, and MQL), independent correlation is introduced, as shown in Table 4. In the final model for estimating surface roughness, the R 2 value was 98.6%, and this indicates that the fitted model has high accuracy.  The main influence of the parameters on average values of surface roughness is shown in Fig. 7. Figure 7a shows the comparison of the cooling methods which illustrates the acquisition of the maximum and minimum surface roughness by using the dry machining and the MQL condition, respectively. The Ra value of MQL was reduced by 46.19% and 27.23% compared with dry cutting and air cooling condition, respectively.
MQL condition is more efficient at lubricating and cooling in LT-UAHM process owing to two following respects. One reason is the ultrasonic nebulization effect which is induced by the cavitation phenomenon. Cavitation is the process that causes bubbles to grow, shrink, and finally collapse into tiny bubbles due to the ultrasonic acoustic energy. In traditional MQL method, the coolant is ejected by compressed air at high pressure, and relatively uniform and fine droplet sprayed into cutting region. Comparably, in LT-UAHM process, the cutting fluids will further break into ultra-fine droplets under the acoustic cavitation effect. These ultra-uniform droplets will eventually nebulized by the ultrasonic acoustics energy which is propagated from tool to coolant liquids, as shown in Fig. 8a and b. With the generated hyper-uniform and hyper-fine coolant drips, excellent cooling and lubrication can be achieved in LT-UAHM. Similar nebulized phenomena were also reported in grinding of Ti6Al4V due to the effect of cavitation bubbles in ultrasonic assistant MQL proposed by Madarkar et al. [26]. The other critical reason is the tool-workpiece intermittent separation characteristic during LT-UAHM. Note that the HM operations involve constant contact between cutting edges and workpiece material, as shown in Fig. 8c. The cutting fluids are not efficiently entering into the cutting zone. As a result, the cutting heat  Fig. 7 The main influence of processing parameters on surface roughness: a cooling condition, b spindle speed, c tangential feed, d axial feed and e hardness 1 3 will accumulate rapidly. Also, insufficient lubrication leads to the increase of friction between cutting edges and workpiece, resulting in worse surface roughness. On the contrary, the nebulization oil mist and compressed air can effectively approach the interface of cutting edges and materials due to the intermittent separation in LT-UAHM. Consequently, it can be concluded that the MQL with LT-UAHM can essentially enhance the lubrication and cooling performance, and that will improve the surface roughness as well as the hole dimensional and geometrical accuracy which is discussed in "Sects. 5.2-5.4." Figure 7b shows that surface roughness increases with the increase of cutting speed. Actually, when the cutting speed increases, yield stress of workpiece materials is reduced; subsequently, the cutting force and friction are reduced and plastic deformation at the higher temperature is facilitated. Thus, both the process stability and the surface quality are improved [27]. Figure 7c shows surface roughness increase when tangential feed increases. Actually, the undeformed chip thickness at the periphery cutting edge increases when the tangential feed increases, which further increases the cutting force and the surface roughness.
When the axial feed reaches its maximum value, surface roughness increases slightly under the effect of eliminated plowing force. Smaller feed rate and cutting depth facilitates the appearance of plowing force as a result of the small undeformed chip thickness. Table 2 shows that the small axial feed appears in the range of 0.000636943 to 0.005732484 mm/tooth. As a result, a nonuniform plastic flow can form in the materials and the surface will deteriorate [28], as shown in Fig. 7d. This indicates that axial feed is negligible in the overall trend of the surface roughness. Figure 7e indicates that the surface roughness increases with the increase of workpiece hardness. The reason is that reduction of the built-up edge can lead to surface with higher uniformity.
To obtain the contribution percent of each process parameter, this study divided the sum of squares of each factor by all the number and then multiplied the sum by 100. Figure 9 shows the contribution percent of the parameters on surface roughness. According to the result of statistical analysis, the top three factors that have the largest influence on the surface roughness are tangential feed, cutting speed, and lubrication method, with the influence being 20%, 22%, and 40%, respectively.

Hole sizes
The hole diameter is another important influence factor of hole quality on which the cutting parameters can have a large impact. ANOVA of the hole diameter is shown in Table 5,  Fig. 9 The contribution of processing parameters on surface roughness with the assumed ideal diameter of formed holes being 10 mm. Likewise, each main parameter plays an important role in hole diameter. By using regression analysis, the linear regression correlations between input parameters and hole diameter presented in the different cooling conditions ( Table 6).
The influence of each main parameter on the nominal size of holes is shown in Fig. 10, and it implies that the range of variation of the hole diameter is 10.01-10.05 mm, regardless of the cutting condition. Figure 10a shows the influence of different cooling/lubrication conditions on the nominal size of holes. The result implies that the best tolerance can be realized by the MQL system owing to the durable oil  Fig. 10 The main influence of processing parameters on hole sizes: a cooling condition, b spindle speed, c tangential feed, d axial feed and e hardness tribofilm which is formed between the cutting tool and the machining surface. Besides the mentioned before, the vibration motion of tool not only separates the contact between tool and workpiece during cutting process which is beneficial to the oil mist penetration into but also generates high pressure during high frequency vibration. Due to the high pressure, a durable tribofilm will develop [29]. The stability of the tribofilm results in a low adhesion between cutter and chips which can efficiently facilitate the cutting process by reducing heat and friction. As a result, a significant improvement of hole diameter is obtained by MQL system in the LT-UAHM process. In the case of the compressed air condition and the dry condition, insufficient lubricating and cooling of the cutting region despite elliptical vibration leads to deterioration of the hole quality. Figure 10b shows that the deviation of hole diameter reduces with the increase of the cutting speed which is the only positive impact factor to hole quality. Actually, since larger cutting speed can reduce the cutting force and promote more heat to be generated in the cutting area, the diameter deviation can be reduced. Figure 10c and d manifest that on the premise of kinematics of the helical milling, larger axial and tangential feed can increase the undeformed chip thickness and further increase the tool deflection and cutting force. This furthermore leads to the divergence of the diameter of the formed holes from the nominal size.
According to Fig. 10e, deviations of the hole diameter from the nominal size are kind of more in harder materials because these materials have larger cutting force and strength [30]. Moreover, dimensional deviation is more and tool deflection is higher in harder workpieces. Figure 11 shows the contribution of parameters on hole size accuracy of machined holes. A clear fact is that the cooling/lubrication condition and cutting speed are the top two influence factors of variations of dimensional tolerances. In contrast, the axial feed, tangential feed, and material hardness have the smallest impact on variations of dimensional tolerances. Compared with dry milling, MQL has a great potential in the LT-UAHM process so that the lubricating method has a higher influence.

Hole circularity
As a geometric error, circularity is used to evaluation of the radial error between the lowest point and the highest point for a single circular element. ANOVA of circularity variance for the making-hole is shown in Table 7, indicating that important factors correspond to the P value smaller than 0.05. The result shows that all the main factors have an important effect. Additionally, a linear correlation between hole circularity and machining parameters is introduced in Table 8.
The influence of different cooling/lubrication conditions on hole circularity is demonstrated in Fig. 12a. The result also shows that vegetable-based oil is apparently superior to the dry condition and compressed air. Figure 12b illustrates the influence of variations in cutting speed on hole circularity. It is noting that larger cutting speed can affect the tolerance positively because of increase in process stability, just like the influence of the cutting speed on the dimensional tolerances.
The influence of tangential feed on circularity of holes is also manifested in Fig. 12c. It is noticed that the trend of circularity variation is like that of dimensional tolerances. However, deviations of hole circularity are reduced when axial feed, i.e., the axial cut depth per tooth is increased, as shown in Fig. 12d. Actually, the contact surface between workpiece and the tool in the cross section of each hole can be enhanced when the axial cut depth per tooth is higher. Thus, the deviation of each section of formed holes is smaller. Moreover, when the axial cut depth per tooth is higher, the tool path is shortened and the quantity of helical loops is reduced, so that errors of cutter and some other factors that influence machining process can be reduced and process stability can be increased [31]. The influence of hardness of the workpiece on circularity of holes (Fig. 12e) resembles the result illustrated in the above section.
In addition, Fig. 13 presents the significance of the process parameters on hole circularity. It shows that the lubrication system has the largest impact on hole circularity, followed by the cutting speed, the tangential feed, the axial feed, and the hardness of workpiece. Fig. 11 The contribution of processing parameters on hole sizes  Figure 14 presents circular profiles of the maximum and minimum values for specimen of 350 hardness under the MQL lubrication. From Fig. 14a, it can be seen that the factors such as high tangential feed and errors of the tool path (test no. 12) can increase circularity deviations. In contrast, Fig. 14b (test no. 16) shows that lager cutting speed and low tangential feed in the MQL system help reach the minimum deviation when the acceptable tolerance level is considered.

Hole cylindricity
Comparison of the response dates shows that tolerance of hole cylindricity has correlation with the magnitude of hole circularity. The increase indicates the influence of process parameters on straightness of the hole axis. Table 9 is ANOVA of hole cylindricity, with P < 0.05 (reliability > 95%) representing important factors. The  Fig. 12 The main influence of processing parameters on circularity: a cooling condition, b spindle speed, c tangential feed, d axial feed and e hardness Fig. 13 The contribution of processing parameters on circularity 1 3 result indicates that each main parameter is important. By the linear regression, the correlation between input variables and cylindricity is conducted and presented in Table 10. Figure 15a manifests the influence of different cooling/ lubrication conditions on hole cylindricity. It is clear that MQL milling is superior to other methods as well. Additionally, the compressed air reduced this tolerance compared to dry condition. Actually, compressed air merely penetrates into the cutting area with the increment of hole depth during traditional helical milling. Thus, the cutting heat accumulate gradually with the cut depth and eventually deteriorate the hole cylindricity tolerance.
However, owing to the excellent characteristic of elliptical cutting mechanism, the heat dissipation will be enhanced by the better permeation of the air coolant into hole depth when applied the LT-UAHM technology.
The influence of cutting speed on hole cylindricity is shown in Fig. 15b. The result is that cutting speed plays an important role in positively affecting this tolerance. Figure 15c-e presents that the influences of the axial feed, the tangential feed, and the workpiece hardness show a similar trend in terms of circularity. It is clear that the influence of the axial feed on hole cylindricity is improved, see Fig. 15d. It has been discussed in the previous section that this is attributed to reduction in undesired movement errors of the machine tool, shorter tool path, and other influencing factors. Figure 16 shows the contribution percent of each main parameter on hole cylindricity. It can be seen that various lubrication conditions have remarkable impact on this tolerance, and the impact of axial feed increases even twofold. In fact, hole cylindricity is a combined factor of straightness tolerance and circularity tolerance. Therefore, the comparison result of the nominal size and circularity of holes shows that the influence of the manner with amount of axial feed and the cooling/lubrication condition on the hole straightness is a criterion for affecting hole cylindricity.

Conclusion
In this study, LT-UAHM for hole-making of Ti6Al4V alloy with dry condition, compressive air, and MQL method were carried out to investigate the cutting variables and cooling strategies on the hole-making performance. The surface finish, dimensional, and geometrical accuracy at various cutting parameters and conditions were measured. The impact factors, including the cutting speed, the axial feed, the tangential feed, and workpiece hardness, on the quality of machined holes by Taguchi design are discussed. This work also demonstrates the nebulized effect due to the combination of MQL and ultrasonic acoustic vibration in LT-UAHM. With the theoretical analysis and experimental research, the following conclusions can be drawn.
(1). The combination effect of MQL and LT-UAHM is theoretically analyzed. The MQL liquids can be further nebulized into uniform-fine droplets due to the ultrasonic acoustic cavitation occurred on the rake face of tool. The nebulized droplets can greatly promote the cooling and lubrication effect. Also, the separate-type cutting of LT-UAHM enables coolant to penetrate into the cutting area and ensures better heat dissipation including air condition and MQL condition. (2). Considering the feature of LT-UAHM with intermitted cutting in the elliptical cutting trajectory, the lubricating condition has the most important influence on hole Fig. 15 The main influence of processing parameters on cylindricity Fig. 16 The contribution of processing parameters on cylindricity cylindricity, circularity, nominal diameter, and surface roughness, contributing to 32%, 34%, 39%, and 40%, respectively. The cutting speed is the second most important factor, contributing to 29%, 31%, 36%, and 22%, respectively. (3). Although higher axial feed affects the nominal size of holes negatively, it can reduce the geometrical tolerance of machined holes. The reason is that the undesired movement errors of the machine tool reduced and the tool moving path shortened. Moreover, the effect of axial feed on the hole cylindricity is almost twice that of circularity. (4). Affected by tool deflection, the effect of workpiece hardness on the geometric dimensional tolerances is negative. (5). According to the statistical analysis and research results, ideal holes can be machined by optimizing the cutting parameters, such as increasing axial feed, cutting speed, and reducing feed rate, respectively. In this work, the most ideal hole can be obtained by simultaneously applying UAHM and MQL strategy at n = 4000 rpm, f t = 0.02 mm/tooth, and a p = 0.3 mm/tooth.

Competing interests
The authors declare no competing interests.