4.1 Effect of Feed Rate on Milling Forces
In UAVM, the high-frequency vibration of the milling cutter in the vertical direction can be taken as the forced simple harmonic vibration in the Z-axis, while the constant rotating movement of the cutting edge can be regarded as uniform linear motion along the Y-axis within a relatively short time and distance. As a result, in UAVM, the relative motions of the cutting edge to the workpiece in the Z- and Y-axes are respectively expressed as follows:
$$z\left( t \right) = a\sin \left( {2\pi ft} \right),$$
(1)
$$y\left( t \right) = vt,$$
(2)
where a and f are the vibration amplitude and vibration frequency of the cutting edge in the Z-axis, respectively. v is the instant linear speed of the cutting edge in the Y-axis. The relative motion speed of the cutting edge to the workpiece is expressed as follows:
$$v_{z} = 2\pi fa\cos \left( {2\pi ft} \right),$$
(3)
In such a manner, the actual motion of the cutting edge in the Y-Z plane is a combined motion of the simple harmonic vibration and uniform linear motion in two perpendicular directions, which demonstrates a sinusoidal cutting locus.
In UAVM, it is commonly believed that lower milling forces over CM are obtained mainly due to the reduced tool-workpiece friction induced by the vibration of the milling cutter [20]. In this study, Fx, Fy, and Fz in both UAVM and CM increased with feed rate. It is worth noting that the milling forces for UAVM in three directions, i.e., Fx, Fy, and Fz, all showed lower amplitudes than those in CM, which could be explained from two perspectives. On one hand, milling forces were substantially influenced by the sinusoidal cutting motion of the cutting edges in UAVM. When the cutting edges vibrated in the vertical direction in UAVM, the end face of the milling cutter intermittently contacted with the workpiece in the high-frequency vibration mode, which could be divided into the cutting stage and the separation stage. Moreover, the dynamic uncut chip thickness in the UAVM method was significantly more complex than the nominal chip thickness in the CM method, which was caused by the complex tool motion trajectories and the separation-stage cutting in UAVM. In consequence, the resultant milling forces were reduced due to the intermittent contact between the end mill and workpiece. On the other hand, the separation space produced between the milling cutter and the workpiece in UAVM could enhance the lubrication with reduced friction, which further facilitated the reduction in milling forces [21]. In addition, for UAVM, the continuous change of relative velocity, relative acceleration and reversed frictional force between a milling cutter and workpiece promoted material removal as well [22].
4.2 Effect of Feed Rate on Surface Topography and Roughness
Surface topography substantially affected the bulk properties and service life of material and was hence characterized by surface texture and surface roughness in this study. For CM, it could be found that the tool feed trajectories with uniform spacing of ridges along the feed direction had a spacing distance equal to feed. The width of the adjacent ridges increased with the feed rate, which was considered as the principal factor influencing the machined surface topography in CM. In contrast, because the feed direction was perpendicular to the vibration direction of the end mill in UAVM, the surface texture of the UAVM workpiece was a combined result of the uniform feed trajectories in the feed direction and the sinusoidal texture in the end plane of the cutting tool because of the vertical ultrasonic vibration in UAVM. Moreover, the extension direction of the sinusoidal texture was along the tangential direction of the end mill. As for the distance between the adjacent ridges in the fine sinusoidal vibration textures along the feed direction, it could be determined by the rotational speed and ultrasonic vibration frequency of the milling cutter, which however were set as constant values in this study. Thus, the distance between the adjacent ridges along the feed direction was found identical on the machined surfaces. In terms of the fine vibration textures existing between the feed trajectories, their occurrence was attributed to the periodic contact and separation between the end mill and workpiece, which therefore manifested the vital evidence of intermittent machining in UAVM.
In addition, apart from the cutter edge trajectories on the machined surfaces, additional chatter marks appeared along the tangential direction of the end mill, which was caused by the regeneration of waviness of the workpiece surface due to overlapping cuts in CM [23, 24]. As a result of the self-excited vibration, the chatter marks were identified when the feed rate increased from 60 to 72 mm/min in CM, which indicated that regenerative chatter was induced due to the increased feed rate. In consequence, the pronounced chatter marks introduced extra unevenness to the machined surfaces as revealed by the increased surface roughness values. In contrast, the surfaces produced by UAVM were covered with the ridged textures and fine sinusoidal vibration textures between feed trajectories rather than chatter marks, which suggested that the vertical ultrasonic vibration was beneficial to suppress the cutter chatter in UAVM.
Surface roughness greatly affects the surface accuracy and quality of a machined workpiece, hence, it was highly essential to consider the surface roughness for assessing the machined surface integrity of the workpiece. In UAVM, an intersection usually formed between two adjacent cutter trajectories due to the cutter feed, while the surface roughness was just determined by the residual height of the intersections. In this study, the steady roughness values indicated that the variation of feed rate from 36 mm/min to 72 mm/min does not cause significant fluctuation on the height of the trajectories in CM and UAVM although the corresponding machined surfaces exhibited varied cutting trajectories and textures. However, the deteriorated surface quality with higher surface roughness values was indeed revealed in UAVM compared to CM. Similar results were also reported by Suárez et al. [25] that the surface of Ni-alloy 718 produced by rotary ultrasonic elliptical machining demonstrated Ra roughness value of 25.63% higher than that machined by CM. In general, the increased Ra roughness values were ascribed to an extra high-frequency vertical vibration introduced to the end mill by UAVM in addition to the horizontal cutting movement in CM, which suggested that another additional material removal mode in the vertical direction was imposed by UAVM. Moreover, Zhang et al. [16] also observed larger surface roughness in rotary ultrasonic elliptical end milling (REUM) of Ti6Al4V compared with CM, which was ascribed to the uniform microtextures mapped on the finished surface of REUM rather than the mechanical surface defect in CM.
In this study, the fine sinusoidal vibration textures between the tool feed trajectories were evidence of the high-frequency material removal mode introduced by UAVM. In this regard, compared with CM, the increased surface roughness values in UAVM were consequences of the extra sinusoidal vibration textures induced by the high-frequency vibration of the end mill.
4.3 Effect of Feed Rate on Subsurface Microstructure
The subsurface microstructure of the workpieces subjected to CM and UAVM consisted of two zones: plastic deformation zone and bulk material zone, as similar to that revealed by Zhang et al. in the rotary ultrasonic elliptical end milling of Ti6Al4V alloy [16]. The plastic deformation zone closely located below the machined surface was commonly characterized by rotated grains and deflected grain boundaries along the cutting direction, which generally resulted from intensive plastic deformation induced during the milling process [26]. In contrast, the bulk material zone located beneath the plastic deformation zone remained undisturbed as it was far away from the intensive plastic deformation zone. In this study, the cross-sectional views of the subsurface microstructures machined by CM and UAVM under different feed rates showed no obvious thermally-affected microstructures, such as recasting and white layers, which indicated that the temperature rise in the milling zone should be not higher enough to melt the Ti6Al4V alloy, thus inducing no phase transformations under the various milling conditions.
In terms of the subsurface plastic deformation zone of workpieces machined with CM and UAVM, it displayed the opposite trends with an increasing feed rate. In CM, the increased thickness of the subsurface deformation zone was caused by more intensive plastic deformation induced by the increased feed rate; while the descending thickness of the deformation layer in UAVM indicated that the subsurface plastic deformation was significantly enhanced at a relatively low feed rate, and was however mitigated with an increased feed rate. The thickness variation of the subsurface deformation layer in UAVM can be interpreted in this way: as feed rate increases, the contact time between the end mill and the machining surface in the unit area decreases, which thus undermines the high-frequency impact effect of the ultrasonic vibration on the surface [27]. In this regard, the thickness of the subsurface deformation zone of the UAVM workpieces gradually decreases as a result. In addition, Sun et al. [28] also reported analogous results with an increasing feed rate in end milling of Ti6Al4V alloy.
It was generally recognized that a mitigated plastic deformation zone in machining signified improved machining quality. In this study, the thickness of the plastic deformation zone on the surfaces machined by CM and UAVM took on two opposite trends with feed rate, and the surface machined by UAVM displayed a thinner subsurface plastic deformation layer than by CM. Thus, it was concluded that an increased feed rate was beneficial to reducing the thickness of the subsurface plastic deformation layer, thus enhancing the machining quality of SLM alloy by using UAVM.
4.4 Effect of Feed Rate on Surface Microhardness
The mechanical properties and service life of a machined part were substantially influenced by the work-hardening effect that resulted from a combination of the uneven stress fields in the machined surfaces. In order to evaluate the effect of surface hardening on the machined surfaces, surface microhardness was usually taken as a crucial indicator. In this study, the surface produced by UAVM generally showed greater microhardness values than by CM due to high-frequency impact of the end mill similar to the findings revealed in the rotary ultrasonic elliptical end milling of Ti6Al4V alloy [16].
As for the effect of cutting heat induced by the end mill, it should be positively correlated with the degree of plastic deformation, which meant that the thicker plastic deformation zone below the milling surface was correlated with server thermal effect. Following this line of reasoning, the workpiece induced with the thicker plastic deformation zone should present lower surface microhardness due to the thermal softening effect, thus representing a negative correlation between them. How, as revealed in Figures 8 and 9, plastic deformation zone thickness and surface microhardness were positively correlated, indicating that thermal impact was insignificant in the process of UAVM and CM in this study. Moreover, as shown in Figure 8, the cross-sectional views of the subsurface microstructures machined by CM and UAVM under different feed rates showed no obvious thermally-affected microstructures as well, which further verified the unimportant effect of cutting heat in this study.
In terms of the causes of enhanced surface microhardness in UAVM, the high-frequency vibration of the milling cutter introduced a great impact to the cutting zone similar to the effect of shot peening which was a surface modification process commonly adopted to improve the surface hardness and residual compressive stress by shooting micro media onto a workpiece surface at a high speed [29, 30]. The enhanced surface hardness in shot peening was mainly attributed to the severe plastic deformation in a surface [31]. Similarly, it was concluded that the improved surface microhardness in UAVM was ascribed to the intensive plastic deformation resulting from the high-frequency impact effect of the end mill in UAVM.
Under normal conditions, the microhardness variation and thickness variation of a plastic deformation layer shared a similar trend with an increased feed rate, therefore, the hardened surface should be closely associated with the degree of the subsurface plastic deformation in machining [17]. In this study, it was not difficult to find that feed rate had a marked impact on the surface microhardness of the Ti6Al4V alloy. However, the underlying mechanism between them varied in CM and UAVM. As for CM, the increased surface microhardness value was mainly attributed to the strain hardening resulted from intensive plastic deformation as feed rate increased; while in terms of UAVM, the significant reduction in surface microhardness was directly caused by the decreased contact time between the end mill and the machining surface in a unit area with an increased feed rate. In spite of different mechanisms regarding the origin of surface microhardness in CM and UAVM with an increasing feed rate, the thickness variation of the subsurface plastic deformation layer and the corresponding surface microhardness shared the same trend with an increase in feed rate. Therefore, it was concluded that the thickness of the subsurface plastic deformation layer and the corresponding surface microhardness were positively correlated regardless of the machining methods of CM or UAVM whatsoever.