*3.9. Measured Width of Flexure Elements*

The widths of the flexure elements were measured from the micrographs to compare the cutting accuracy of the μAWJ on the MicroMAX and the CNC milling on the Zund. Figure 15 shows the micrographs of the top and bottom views of flexure elements machined on the MicroMAX and Zund, respectively. Comparing Figure 15a,b shows that the bottom elements are slightly wider than their top counterparts. This is the result of the presence of edge taper as the TAJ was deactivated for cutting thin materials. There are two options to reduce or minimize the magnitude of the edge taper. One remedy is to reduce the cutting speed and the other is to conduct stack cutting. The OMAX MAKE software incorporates an optimal stack height calculator.

(**d**) Bottom – Zund with I0.76 mm end mill

**Figure 15.** Width of flexure elements measured from micrographs.

The average widths of the top and bottom flexure elements were measured from the micrographs and are presented in Figure 16. Also shown in the figure are their trendlines and the designed width of the flexure elements. The maximum deviations between the trendlines and the designed width are 0.004 mm and −0.0003 mm for the μAWJ- and Zund-cut flexures. The measured width of the flexure machined with both tools displays a consistent pattern with the even segments wider than the odd counterparts. The difference in the width between the odd and even elements is considerably larger for the μAWJ-cut flexure than for the Zund-cut one. Careful examination of the tool path shown in Figure 1b indicates that, for waterjet machining, the nature of the machining differs for the odd and even segments of the flexure elements. Specifically, the odd and even elements were cut in the constrained and unconstrained modes, respectively.

**Figure 16.** Average element widths of full-scale flexure (C-C and U-U) machining mode).

Unconstrained or constrained cuttings referred to the conditions that the edges of the adjacent elements had already or yet to be cut. Note that the tool offset for the 7/15 nozzle is one half of the mixing tube diameter, or 0.38 mm whereas the gap between elements are 0.76 mm. While cutting the odd segments, the AWJ is constrained by the materials on both edges (C-C). The AWJ cut nearly straight downward. On the other hand, for the even segments with the edges of the adjacent segments already cut, the AWJ is unconstrained on both edges (U-U). This is referred to as the constrained-constrained and unconstrained-unconstrained (C-C/U-U) cutting mode. Under the U-U cutting mode, the AWJ tends to be deflected slightly toward the adjacent segments where the material beyond those edges have been removed. As such, the even segments are slightly wider than their odd counterparts. Refer to Figure 17 for a graphical interpretation of the two modes of cutting.

**Figure 17.** Tool path for the C-C and U-U cutting mode.

The remedy to mitigate the difference in the element width is to revise the tool path such that the machining must be carried out consistently in the unconstrained-unconstrained (U-U) or alternating constrained-unconstrained (C-U) modes for all the elements. For the unconstrained mode, a slotting in the middle of the gap between elements, as illustrated in Figure 18, is added to the tool path (magenta dotted lines). As such, all the edges are carried out in the unconstrained mode. The second remedy is to split the tool path of the flexure element into two sub-segments at the left turn-around points as shown in Figure 19. Cutting are conducted by cutting all the top edges in the constrained mode followed by cutting the bottom edges in the unconstrained mode. As such, the edges will be cut in the C-U mode.

**Figure 18.** Tool path for U-U cutting mode.

**Figure 19.** Tooth path for C-U cutting mode.

Cutting tests using both modes were conducted on 0.51-mm thick aluminum. The difference in the width of the odd and even flexure elements reduced significantly and were about the same as that cut with the Zund, as shown in Figure 20. However, the pre-slitting along the middle of the gaps significantly weakened the stiffness of the workpiece, particularly toward the mid-span. During the passage of the AWJ, the force exerted onto the workpiece tended to push the flexure elements sideway and downward, particularly at mid-span where the support was the minimum. As a result, the element width became nonuniform along the length of the flexure element. In particular, the width

increased from one end, reached the maximum at the mid-span, and then reduced toward the opposite end, as shown in Figure 21. The same trend with less severity was observed for the C-U cutting mode.

**Figure 20.** Comparison of average element widths of flexures cut with μAWJ (U-U mode) and Zund.

**Figure 21.** Nonuniform element width resulted from the C-U cutting mode.

The above anomalies of the observed nonuniformity of the element width along its major axis is attributed to the weak stiffness of the flexure element due to its peculiar geometry.

A set of flexure elements with large aspect ratios of length/width and length-/thickness.

The stiffness of the serpentine flexure supported only on two end points connected to its frame is the weakest at the mid-span.

For cutting very thin materials, the cutting speed is too fast for the TAJ to respond with taper compensation. Therefore, the TAJ is usually deactivated resulting in measurable edge taper. Figure 22 shows the measured element width at the mid-span of a 0.51 mm thick stainless-steel flexure under the C-C/U-U cutting mode. In addition to the nonuniform element width of the even and odd flexure segments, the presence of the edge taper resulted in a difference of about 0.1 mm between the element widths measured on the top and bottom surfaces.

Subsequently, we decided on adopting the AWJ stack cutting process as the final remedy to minimize the nonuniformity of the width of the even and odd flexure elements and the edge taper. The stack was formed by using 3M double-adhesive tapes with a thickness of about 60 μm. A 10 mm thick aramid honeycomb with fiberglass faceplates was used to support the metal stack for further enhancing the stiffness. The cutting model is equipped with a stack calculator to estimate the optimum number of layers based on the cutting parameters. The optimum number of sheets is defined as the total stack height at which the average cutting time per sheet has reached the minimum. Figure 23 illustrates the results of stack calculation for two aluminum (0.51 and 0.64 mm thick) and one stainless steel (0.51 mm thick), respectively. The estimated numbers of layers for the three metals cut at the quality level of five are 13, 10, and 7, respectively. The cutting times for single sheets reduce from 3.90

to 0.90, 4.13 to 1.12, and 4.95 to 1.80 min, respectively. The reductions in the cutting time are 4.4, 3.7, and 2.8 times for the three metals.

**Figure 22.** Edge taper resulted from deactivation of the TAJ.

**Figure 23.** Typical optimum stack heights for two metals.

Figure 24 show the side view of a stack of flexure consisting of one 0.41 mm thick aluminum sheet and five 0.51 mm thick stainless-steel sheet. The top aluminum sheet served as the sacrificial cover where the edge rounding, and frosting took place. Several iterations of cutting with the TAJ activated to minimize the edge tape were conducted. Figure 25 illustrates the element widths of one of the interior flexures (#5) of the stack shown in Figure 24. The significant reduction in the edge taper of the μAWJ-cut flexure was evident when compared the data shown in Figures 24 and 25. Although the edge taper was still slightly higher than that of the Zund-cut counterpart it can further reduce with additional iterations. Most important, the stack cutting eliminated the difference in the width of the even and odd elements, even below the level achievable with the Zund.

**Figure 24.** μAWJ-cut stack of stainless-steel flexure supported by aramid honeycomb.

**Figure 25.** Comparison of element width of flexures cut with Zund and μAWJ under stack cutting at mid-span.

With the increase in the stiffness of the stack together with the support of the honeycomb, the sideway and downward displacements of the flexure element in response to the μAWJ loading also reduced considerably. As a result, the nonuniformity of element width reduced accordingly, as shown in Figure 26. In fact, comparing Figures 26 and 27 shows that the total variation in the element width was less for the μAWJ-cut flexure than the Zund-cut counterpart.

**Figure 26.** Element width measured at mid-span and one end of flexure cut with μAWJ under stack cutting.

**Figure 27.** Element width measured at mid-span and right end of single-sheet flexure cut with Zund.

Yet another advantage of stack cutting is to use the top sheet as the sacrificial cover to reduce frosting on the top surface and the burr on the bottom edge of the interior sheets.

#### *3.10. Further Downsizing of* μ*AWJ Nozzle*

As discussed in Section 3.2, machining a 0.33 scale flexure was unsuccessful using the 4/8 μAWJ nozzle. One of the reasons was that the kerf width of the nozzle was nearly the same as the width of the gap of the flexure. During machining the μAWJ traversed twice (back and forth) through the gap. In the presence of edge rounding on entry side, the strength or stiffness of high-aspect-ratio flexure element might be weakened to the degree that it could no longer maintain its shape without distortion. Further downsizing the μAWJ nozzle might be needed to machine the 0.33 scale flexure successfully.

Attempts were made to assemble a 2/6 μAWJ nozzle to machine the flexure. The length of the φ0.15 mm mixing tube was reduced to 12.7 mm. Specially processed 320 mesh garnet with a flow rate of 30 mg/min was used. The vacuum assist option was activated to boost the low Venturi vacuum induced by the small waterjet. Figure 28 shows the comparison of three stainless steel flexures, with scale of 0.5 (a1–a3), 0.4 (b1–b3), and 0.33 (c1–c2), machined on the MicroMAX with the 5/10, 4/8, and 2/6 nozzle, respectively. As discussed in Section 3.2 (Figures 2 and 5) and Section 3.7 (Figure 13a,b), the matches between the tool paths and the full-and 0.5-scale parts were slightly better for the μAWJ–cut flexures than for the Zund-cut counterparts. Figure 28c3 shows that the overall match between the 0.33-scale flexure and the tool path displayed a slight localized degradation when compared with the matches with its larger counterparts.

Considerable R&D is being conducted to continue downsizing μAWJ nozzles toward micromachining. The material independent waterjet is capable of machining a wide range of part size and thickness [1,2]. One of the main concerns is the lack of proper fixturing devices to hold extremely thin stocks for micromachining. The success in applying AWJ stack cutting to stiffen the workpiece while enhancing the cutting efficiency has eased the above concern and paved the way for precision AWJ micromachining of very thin stocks provided further development of μAWJ technology would meet the stringent requirements. A wide range of materials from metal, nonmetal, to anything in between can be used to form the stack [2].

**Figure 28.** Downsized stainless steel flexures cut with μAWJ nozzlles on MicroMAX: flexure with frames (**a1**, **b1**, and **c1**); tool paths superimposed onto flexure elements (**a2**, **b2**, and **c2**); and tool paths superimposed onto flexure elements—zoomed in (**a3**, **b3**, and **c3**).

## **4. Discussion and Summary**

Cutting tests were conducted to investigate the performance comparison of μAWJ, lasers, wire EDM and CNC milling. These tests were investigated through the collaboration of MIT and OMAX Corporation [4]. The results demonstrated that μAWJ using the MicroMAX had the best overall performance for this test part, with the fastest cutting speed without inducing heat damage to the parts. The CO2 laser performed the worst causing significant heat damage (i.e., the presence of the HAZ) in terms of discoloring, warping, and the presence of excess slag. The solid-state laser pulsed at 50 kHz with a spot size of around 50 μm and the wire EDM with a 0.15 mm wire were able to cut the parts at significantly slower speed to minimize the heat damage. The cutting speeds were one to two orders of magnitude slower than that of the MicroMAX. The cutting accuracy of the solid-state laser and the wire EDM are however higher than that of the μAWJ that had jet diameters of 0.25 and 0.3 mm for the 5/10 and 7/15 nozzles, respectively.

Under the MicroCutting Project, one of the flexures used as the prototype microsplines for the NASA asteroid gripper was selected as the reference part for all the machine tools investigated. It must be clarified that such a selection may not necessarily take advantage of the best features of some of the machine tools. Specifically, the rating of the performance of individual tools was based narrowly on the inspection of the as machined/built flexures. In other words, the machine tool with a poor rating in this report does not represent its overall performance for other machining applications.

Micrographs or photographs of most finished flexures machined with individual tools were taken for inspection. The graphs were inspected and compared to determine the performance of individual tools for machining and building of the flexures. The performance was rated based on several criteria such as the cutting accuracy and speed, degree of part deformation (mechanical and thermally induced), edge quality, setup time and effort, and others. One of the inspection methods used frequently was to superimpose the part tool path onto the graph of the flexures as the means to determine whether there was any mismatch of the two. A mismatch could be caused by 3D part distortion induced by the cutting tools, inaccurate machining and building, and other factors. Another inspection method was to measure various dimensions of the flexure such as the width and the length of the flexure element and the spacing between elements.

3D printing using nonmetals, such as the GR and HTL from BMF and polymer with solid filler from Formlabs, although precisely fabricated, do not have the strength and stiffness to maintain the shape of the flexure without distortion in terms of warping, bending, and deflection. Furthermore, the printing processes usually took hours to complete. AlSi10Mg and 17-4PH stainless steel flexures built with LPBF using metal powders and finished the flexures with wire EDM by Moog Inc. appear to maintain their shape well. They also took several hours to build. Due to the presence of defects and voids in LPBF-built materials as compared with the wrought and a relatively rough surface of the finish parts, their fatigue performance is likely to be negatively impacted. The performance of the LPBF-built parts is expected to improve progressively as the process continues to refine.

Thermally based manufacturing processes such as lasers and wire EDM can potentially induce heat damage resulting from the induction of the HAZ. The remedy is to reduce the cutting power by pulsing the lasers at high rates or cutting the part with EDM at multiple passes, at the expense of the cutting time [4].

The test results show that the width of the flexure element is sensitive the mode of cutting for waterjet. The original tool path consisted "constrained" and "unconstrained" cutting modes for the odd and even flexure segments, respectively. As a result, the width of the odd segments is slightly but consistently narrower than that of their even counterpart. One of the remedies was successfully implemented by modifying the tool path such that the two edges of each element were cut under the constrained (C) and unconstrained (U) modes, respectively. The large-aspect ratios of the flexure element in both length-to-width and length-to-thickness had very low stiffness. The flexure elements were displaced sideway and downward in response to the forced exerted by the μAWJ. The stiffness was the weakest at the mid-span and increases toward the two ends. Test results showed that the element was wider at the mid-span than at the two ends, indicating that the material removal was inversely proportional to the amplitude of the displacement.

Subsequently, AWJ stack cutting was applied to improve the performance of the μAWJ. A stack of several pieces of aluminum and/or stainless steel was assembled by using a 3M double-sided adhesive tape. The total thickness of the stack was about 4 mm that was thinner than the optimum thickness estimated by the optimum stack height calculator resided in MAKE. Test results demonstrated that AWJ stack cutting has achieved the following improvements:


In conclusion, several sets of subtractive and additive machine tools were applied to fabricate a reference part, a prototype flexure developed at NASA/JPL as components of microsplines on asteroid grippers for the Asteroid Redirection Mission. Aluminum and stainless-steel flexures with scales from full, 0.5, 0.4, to 0.33, were fabricated. Only the AWJ using experimental micro nozzles was able to fabricate flexures with 0.5 scale and smaller. The performances of the selected tools were evaluated qualitatively and quantitatively, as summarized in Table A1 in the Appendix A. It should be pointed out that these tools may not be optimized for fabricating the reference part. Based on the test results, the performances of the μAWJ on the MicroMAX platform and the CNC micro milling conducted

on the Zund G-3 L2500 stood out among all the tools investigated in the MicroCutting Project. For machining a single piece of flexure, the Zund performed slightly better than the MicroMAX in terms of part accuracy (element width and the uniformity along its axis) and edge quality (roughness and taper). When stacking together with taper compensation using the TAJ was adopted for the μAWJ, the above advantages disappeared or the trend even reversed. The combined stack machining and taper compensation not only improved the part accuracy and edge quality but also enhanced the productivity of the μAWJ. Comparing to single-sheet machining, optimum stacking reduced the cutting times to about 4 and 3 folds for aluminum and stainless-steel sheets, respectively. As mAWJ is further downsized toward micromachining of very thin and delicate materials, stack machining would be an enabling process for fixturing such materials. On the other hand, stack machining would not be an option for most CNC micromachining as the miniature spindles and end mills would not be able to handle the increased load resulted from stacking.

**Author Contributions:** Conceptualization, H.-T.L. and N.G.; methodology, H.-T.L.; validation, H.-T.L.; formal analysis, H.-T.L.; investigation, H.-T.L.; resources, N.G.; data curation, H.-T.L.; writing—original draft preparation, H.-T.L.; writing—review and editing, N.G.; visualization, H.-T.L.; supervision, N.G.; project administration, N.G.; funding acquisition, N.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded partially by an OMAX IR&D project, an NSF SBIR Phase II grant number 1058278.

**Acknowledgments:** This work was supported by an independent research and development (IR&D) fund from OMAX Corporation. The research and development of the micro abrasive waterjet technology was supported by NSF SBIR Phase 1 and 2 Grants (No. 0944239 and 1058278). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF. Special thanks are to the participating technical personnel at CBA and industrial laboratories and manufacturers including Formlabs, Datron Moog Inc., and BMF Precision Technology Co, Ltd for machining/building the reference parts made from various materials and providing them for the evaluation and comparison of their performances. The authors would also like to thank Axel Henning for reviewing the paper.

**Conflicts of Interest:** The authors declare no conflict of interest.
