Abrasive waterjet (AWJ) cutting is a widely-used materials processing technique, favorable for its ability to cut materials with a low machinability index. The process involves a multiphase slurry of high-speed water O(100m/s) mixed with abrasive particles and entrained air, which collide with a workpiece, inducing local deformation and failure. Often considered as an erosive procedure, AWJ is also favorable for cutting temperature-sensitive materials as low thermal damage is produced compared to conventional processes such as milling, or saw-cutting. AWJ also exhibits a high material removal rate (MRR) which facilitates fast manufacturing times. In contrast, the drawbacks of AWJ include a high manufacturing cost due to the purchase and disposal of abrasive grit, as well as grit embedment on the workpiece, which reduces its surface integrity. Pure waterjet (WJ) cutting does not feature these drawbacks, but suffers from a low MRR and is often limited to soft materials (e.g., plastic and food processing). It has been shown, however, that when WJ is pulsed, such that a spray of droplets is produced, material removal is enhanced [1] [2] [3] . This is attributed to the high impact pressures and stress waves generated when a droplet impinges a surface [4] [5] [6] . For pulsed-WJ, the intention is for droplets to repeatedly impinge the workpiece instead of a continuous stream. This is also the goal in water droplet (WD) impact machining, which is a process, similar to WJ, where the jet is immersed in a subatmospheric pressure environment [7] [8] . This environment mitigates aerodynamic drag and total atomization of the jet into a fine mist, allowing larger (compared to WJ), high-speed droplets to impinge the workpiece. Owing to the increased erosion rate of droplet-based methods and the economic and environmental benefits of an abrasive-less process, it is of commercial and scientific interest to investigate the effectiveness of WD. This is achieved, in this paper, by comparing the MRR of AWJ, WJ and WD on a high-strength
Abrasive waterjet (AWJ) cutting is a widely-used materials processing technique, favorable for its ability to cut materials with a low machinability index. The process involves a multiphase slurry of high-speed water O(100m/s) mixed with abrasive particles and entrained air, which collide with a workpiece, inducing local deformation and failure. Often considered as an erosive procedure, AWJ is also favorable for cutting temperature-sensitive materials as low thermal damage is produced compared to conventional processes such as milling, or saw-cutting. AWJ also exhibits a high material removal rate (MRR) which facilitates fast manufacturing times. In contrast, the drawbacks of AWJ include a high manufacturing cost due to the purchase and disposal of abrasive grit, as well as grit embedment on the workpiece, which reduces its surface integrity. Pure waterjet (WJ) cutting does not feature these drawbacks, but suffers from a low MRR and is often limited to soft materials (e.g., plastic and food processing). It has been shown, however, that when WJ is pulsed, such that a spray of droplets is produced, material removal is enhanced [1] [2] [3] . This is attributed to the high impact pressures and stress waves generated when a droplet impinges a surface [4] [5] [6] . For pulsed-WJ, the intention is for droplets to repeatedly impinge the workpiece instead of a continuous stream. This is also the goal in water droplet (WD) impact machining, which is a process, similar to WJ, where the jet is immersed in a subatmospheric pressure environment [7] [8] . This environment mitigates aerodynamic drag and total atomization of the jet into a fine mist, allowing larger (compared to WJ), high-speed droplets to impinge the workpiece. Owing to the increased erosion rate of droplet-based methods and the economic and environmental benefits of an abrasive-less process, it is of commercial and scientific interest to investigate the effectiveness of WD. This is achieved, in this paper, by comparing the MRR of AWJ, WJ and WD on a high-strength
Abrasive waterjet (AWJ) cutting is a widely-used materials processing technique, favorable for its ability to cut materials with a low machinability index. The process involves a multiphase slurry of high-speed water O(100m/s) mixed with abrasive particles and entrained air, which collide with a workpiece, inducing local deformation and failure. Often considered as an erosive procedure, AWJ is also favorable for cutting temperature-sensitive materials as low thermal damage is produced compared to conventional processes such as milling, or saw-cutting. AWJ also exhibits a high material removal rate (MRR) which facilitates fast manufacturing times. In contrast, the drawbacks of AWJ include a high manufacturing cost due to the purchase and disposal of abrasive grit, as well as grit embedment on the workpiece, which reduces its surface integrity. Pure waterjet (WJ) cutting does not feature these drawbacks, but suffers from a low MRR and is often limited to soft materials (e.g., plastic and food processing). It has been shown, however, that when WJ is pulsed, such that a spray of droplets is produced, material removal is enhanced [1] [2] [3] . This is attributed to the high impact pressures and stress waves generated when a droplet impinges a surface [4] [5] [6] . For pulsed-WJ, the intention is for droplets to repeatedly impinge the workpiece instead of a continuous stream. This is also the goal in water droplet (WD) impact machining, which is a process, similar to WJ, where the jet is immersed in a subatmospheric pressure environment [7] [8] . This environment mitigates aerodynamic drag and total atomization of the jet into a fine mist, allowing larger (compared to WJ), high-speed droplets to impinge the workpiece. Owing to the increased erosion rate of droplet-based methods and the economic and environmental benefits of an abrasive-less process, it is of commercial and scientific interest to investigate the effectiveness of WD. This is achieved, in this paper, by comparing the MRR of AWJ, WJ and WD on a high-strength 48th SME North American Manufacturing Research Conference, NAMRC 48 (Cancelled due to steel, DP 1180. Typically, this steel is about 70% martensite and the remainder ferrite [16] .
The paper begins with the state-of-the-art of WD in section II, followed by a description of the experimental setup in section III. Surface profile measurements and MRR results are discussed in section IV. Finally, the Conclusions, section V, summarizes the erosion characteristics and effectiveness of each of the processes.
Compared to a continuous jet, an array of droplet impacts produces improved erosion characteristics [2] . Experiments on low-speed jets show that the peak force induced by a train of droplet impacts is over three times greater than the continuous stream counterpart [9] . This is due to the discretization of jet momentum, which, when imparted normal to a surface, is exerted over a short time interval, generating large forces. For WD, it is imperative that a series of droplet impacts occur instead of a continuous jet. Accordingly, the distance between the nozzle and droplet formation zone is a parameter of significant importance. Poor MRRs are expected if the nozzleto-workpiece, or stand-off distance (SOD) is less than the droplet break-up length. Limited studies have investigated this length for extremely fast jets [10, 11] , such as the >500 m/s waterjet used in this study. Therefore, the MRRs at various SODs are probed in order to reveal the most effective distance between the nozzle and workpiece.
A generalized schematic of the process is shown in Figure  1 , where high pressure water is accelerated through an orifice producing a continuous jet, which, with downstream evolution, segments into droplets. The droplets then travel through an ambient gas (i.e., air) before colliding with the workpiece. For high-speed droplets, aerodynamic drag can play a significant role in speed-reduction and subsequent drop segmentation [12, 13] . Therefore, WD aims to mitigate these effects by allowing the jet/droplet stream to pass through a sub-atmospheric pressure environment (i.e., vacuum). In AWJ and WJ, the SOD is typically small (<5 mm), and it is expected that a continuous jet impinges the workpiece rather than a sequence of large droplets.
When the high-speed droplets impinge the surface, large pressures are generated due to the "water-hammer" effect. Upon impact, the liquid at the base of the droplet behaves in a compressible manner, where the impact pressure is given by:
where = 998 kg/m 3 is the water density, = 1450 m/s is the sound speed of water, and is the impact velocity [14] . This pressure gives rise to propagating shock waves, and a sudden redirection of momentum from the plate-normal to -parallel direction. This is called lateral liquid jetting, which can reach speeds faster than the speed of sound (i.e., supersonic) [15] . These high velocities and pressures induce shear and compressive stresses onto the workpiece resulting in deformation and ultimate material failure and removal. Repeated droplet strikes rapidly erode the surface resulting in a dwelled pocket. When the jet traverses linearly across the workpiece, a trench profile is created. For relatively slow traverse speeds or for thin materials, the droplet stream can penetrate through the material resulting in a complete cut. In this scenario, some of the droplet stream will pass through the material untouched, which can lead to ambiguous interpretation of MRR results. It is the goal of this study to form a trench which can be used to assess the MRR and material removal mechanisms. The trench dimensions and characteristics are investigated and compared to similar trench profiles of AWJ and WJ processes.
To study the WD process, a custom experimental apparatus was constructed which features a high-speed waterjet inside of a vacuum chamber. A schematic of the setup is shown in Figure  2 . A water-only Hypertherm AccuLine cutting head is mounted inside of a 1 m 3 stainless steel vacuum chamber. An Edwards E2M30 vacuum pump depressurizes the air inside the chamber, before each test, to 2.3 kPa. This pressure is chosen as it coincides with the vaporization pressure of water at 20°C. The pressure inside the chamber is monitored with a MKS 902 pressure transducer with a resolution of 13 Pa. For each test conducted, which lasts only a few seconds, the chamber pressure rises slightly to about 3 kPa. This is due to partial vaporization of the water stream. The jet is oriented horizontally and impacts normal to the plate target material. Gravitational effects are negligible at the high jet velocities used here. The jet and droplet velocity can be approximated through ideal flow as
where is the waterjet reservoir pressure. It is expected that the jet and droplet velocity remain relatively constant while traveling through the sub-atmospheric pressure environment. Upon impact, the jet/droplet stream strikes a 1 mm thick DP 1180 sheet metal sample which is mounted to a Velmex motorized traverse system. The plates are sanded prior to testing with 120-grit paper. This is done to remove the factory mill-scale. For the DP 1180 steel used in this study, the yield and tensile strength are 840 (0.2% offset), and 1176 MPa, respectively, and the density is 8,050 kg/m 3 [16, 17] . The high yield and tensile strength of this material renders its machinability index low, compared to mild steel or aluminum. This allows for evaluation of WD performance on a hard-tomachine material, highlighting its capability.
The SOD is 686 mm for the results presented here. Other SODs were investigated from 10 mm to 1300 mm, with 686 mm providing the most favorable results of four SODs considered. For SODs less than 686 mm the results show limited MRRs. The SOD of 10 mm showed undetectable surface damage, while for larger SOD the MRR was increasingly higher. The poor MRR obtained from close SOD tests suggests that, at these lengths, the jet is still continuous and does not segment into droplets. For a SOD of 1300 mm, the MRR was lower than the SOD of 686 mm tests and with a significantly wider trench, indicating dispersion of the droplet stream. The 686 mm SOD provided the best results, and is therefore used to evaluate and compare the performance of WD with AWJ and WJ methods.
While WD tests utilize the setup shown in Figure 2 , AWJ and WJ tests are performed on a Wardjet X-1515. The cutting head on this system differs slightly from the cutting head used in WD. In AWJ and WJ, water flows through an orifice and into a 1.016 mm diameter nozzle where abrasive grit is added and mixed for AWJ (grit is not used in WJ). For AWJ the abrasive flow rate is 12.1 g/s. For all tests the pump pressure and orifice diameter are identical, 414 MPa and 0.406 mm, respectively. Therefore, the flow-rate and momentum discharged through the orifice are assumed to be identical, which allows for an impartial comparison between the three methods.
Test conditions of the three methods are shown in Table 1 . This matrix of test conditions categorizes each test method (e.g., AWJ, WJ, WD), SOD, and traverse speed as well as the calculated MRR results. Various traverse speeds are investigated to elucidate the traverse speed effect on MRR. It is apparent that AWJ tests exhibit significantly higher traverse speeds than WJ, owing to the rapid erosion characteristics of AWJ. The traverse speeds and MRR of WD fall in between AWJ and WJ, the reason for which is discussed in Section IV.
After the samples are processed, a Mitutoyo SJ-400 profilometer with a resolution of 0.1 m is used to record the surface profiles, which is performed for each sample at three random locations along the trench. The surface profiles are integrated to obtain the planar area of each trench. The product of the planar area and the sample's respective traverse speed is the MRR, which is the volume of material removed per unit time. The mass form of MRR is the product of MRR and the material density. The MRR is a useful parameter for evaluating the performance of each method since it is a quantitative measure of the erosion process. It can also be used to estimate cutting times by dividing the kerf volume by MRR. MRRs of various materials from the literature are shown in Table 2 . It is apparent that MRRs depend on the physical characteristics of the jet (i.e., pump pressure, orifice diameter, etc.) as well as the material being processed. High-strength materials typically have low MRRs, while softer materials exhibit high MRRs.
Typical surface profile measurements are shown in Figure 3 with the different colors representing three cross-section measurements along the trench length. Here, the three respective profile measurements of test conditions AWJ1, WJ4, and WD3 are shown in Figure (a), (b) , and (c), respectively. Figures 3(a-b) show that the average trench width of AWJ and WJ is approximately 1 mm, which coincides with the nozzle diameter used. This indicates that the liquid/slurry travels straight from the nozzle to the workpiece without significant radial dispersion. In contrast, the trench of the WD sample (Figure 3c ) is nearly 4 mm wide, which suggests that the jet has dispersed, presumably into an array of droplets. Figure 3 also reveals the consistency among successive profilometer measurements. It is apparent that each profile of the respective test condition exhibits a similar width, depth and overall shape. The consistency among test condition profiles can be further assessed by comparing their planar areas (or MRR). For example, the largest percent variation between planar areas is 4.9%, 27.0%, and 7.0% for AWJ1, WJ4, and WD3, respectively. These variations highlight the profile fluctuation along a single trench.
The shape of the profiles differs among each method. The profiles of AWJ feature a smooth transition from the unprocessed surface, down to the trench bottom, and back up again, with small deformed lips (i.e., buildup of material) on the edges, see Figure 3 (a). For WJ the transition is abrupt and without a lip. The trench surface also features a coarse, uneven structure, see Figure 3 (b). The WD surfaces exhibit an even rougher, crater-like structure as seen in Figure 3 (c). The Ushaped profiles of AWJ and WJ are absent in the WD samples, which feature a multitude of peaks and valleys. These characteristics are inspected further with high-resolution trench images (taken with a Nikon D3300 camera). Figure 4 shows images of the trenches for test conditions (a) AWJ1, (b) WJ4, and (c) WD3. It is apparent that the AWJ trench has a much smoother surface than WJ and WD. Figures 3(c) and 4(c) reveal the coarse structure of the WD technique, as many peaks and valleys are displayed.
The surface roughness discrepancies are justified by each processes material removal mechanism. For ductile materials machined by AWJ, the primary mode of material removal is particle-impact plasticity [20] . Evidence of plastic flow can be seen on the trench edges in Figure 3(a) , where formation of built up lip material occurs on the edges. Upon impingement, the abrasive grit, with its sharp edges, ploughs the surface. This locally strains the material to failure, forming cracks and voids which coalesce and lead to ultimate surface failure and material removal. Several empirical and analytical models have been proposed to capture this erosion mechanism of AWJ [21, 22] . However, these are of course material dependent.
In contrast, neither WJ nor WD tests show this degree of plastic behavior. Studies on WJ show that the largest von Mises stress occurs below the surface, directly beneath the impinging jet, suggesting intergranular fracture [23] . Studies on droplet impacts reveal the formation of surface micro-pits due to shock-wave-induced loading, while other studies suggest that shear failure is responsible due to lateral liquid jetting [24, 25] . These erosion mechanisms evidently result in little plastic flow as indicated by the surface profiles in Figures 3(b-c) and in Figure 4(b-c) .
The general characteristics, such as surface roughness, edge material buildup, and trench width, of the AWJ, WJ, and WD trench profiles, shown in Figures 3 and 4 , are typical of each In Figures 5 and 6 , it is apparent that there is a weak dependence of MRR on traverse speed. This has been found in other MRR studies [18, 20] . It can therefore be asserted that MRR is independent of traverse speed. For decreasing traverse speeds, the trench depth will increase; however, the MRR will remain fixed.
This traverse speed independence on MRR is not observed in WD. Figure 7 shows a linearly decreasing relationship between MRR and traverse speed. A line of best fit is plotted to elucidate this finding. It is noted that test condition WD1 created a cut and was therefore too deep for the profilometer to measure. At this low traverse speed, it is expected that the MRR would fall close to the line of best fit prediction. This unusual finding demands further investigation into the material removal mechanism(s) of WD. According to Eqs. (1-2), the impact pressure induced by the WD droplets is 1.32 GPa, which exceeds the material tensile strength. (This calculation was performed with parameters of pump pressure P=414 MPa (60 ksi), water density ρ=998 kg/m^3, and speed of sound in water c=1450 m/s.) The maximum impact force of low speed droplets is approximately 0.84 2 2 [26] , where is the droplet diameter. One possible explanation for the increased MRR at low traverse speeds is that a significant liquid pool develops over the micro-pits which can accelerate erosion. It has been shown that droplets impacting shallow pools induce greater peak forces than drops impacting dry surfaces [27] .
The average MRR of AWJ and WJ are 36.4 and 0.164, respectively, while for WD the MRR confers to the following relationship
where is the traverse speed. In Figure 8 (a) the MRR is plotted with respect to traverse speed. The MRR of each process are approximately an order of magnitude different from one another, with WJ being the lowest, AWJ the highest, and WD in between. From these results it can be asserted that the WD technique out-performs WJ, but does not exhibit the high MRR of AWJ. Another aspect of WD is its large trench width (see Figure 8 (b)). The reason for this is the radial dispersion of droplets from the jet axis. This affects the accuracy of the cutting process, which is not the focus of this research, but will need to be addressed to reduce this kerf width for industrial implementation. On the other hand, the resulting residue of WJ and WD is simply the material removed, instead of a material + abrasive particle slurry as in AWJ, which has an alternative goal for better metal cutting.
A novel materials processing technique, WD, is presented, which features a high-speed stream of droplets that impact and erode solid materials. The stream of droplets travels through a sub-atmospheric pressure environment in order to mitigate airresistance and subsequent droplet break-up. This process is compared to similar conventional processes, i.e., AWJ and WJ cutting. The metric used to evaluate the erosion characteristics of each process is the MRR, which is the volume of removed material per unit time. This is performed on a difficult-tomachine steel, DP 1180. Trench profiles are created by traversing for each of the jets across the sample. The trench area and traverse speed are used to calculate the MRR. The abrasive waterjet exhibits the highest MRR of 36 mm 3 /s (average of all tests), followed by WD with 6.58 mm 3 /s, and finally WJ with 0.164 mm 3 /s. Future work is required to identify the relationship between MRR and traverse speed and to reduce the kerf width and improve the general quality of the cut. 