Experimental study of water jet incremental micro-forming with supporting dies

Journal of Materials Processing Tech. 268 (2019) 117–131

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Journal of Materials Processing Tech. journal homepage: www.elsevier.com/locate/jmatprotec

Experimental study of water jet incremental micro-forming with supporting dies

T

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Yi Shi , Weizhao Zhang, Jian Cao, Kornel F. Ehmann Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA

A R T I C LE I N FO

A B S T R A C T

Associate Editor E. Tekkaya

Water Jet Incremental Micro-Forming (WJIMF) is a novel alternative to Single-Point Incremental Micro-Forming (SPIMF). Instead of using a rigid tool to form the sheet metal, a high-speed and high-pressure water jet is employed to induce plastic deformation. Dieless WJIMF has the capability to form a variety of shapes, but the total depth of the formed shape, which is affected by several process parameters, cannot be well controlled. To alleviate this problem, supporting dies can be used. This paper systematically studies the WJIMF process with several types of micro-machined supporting dies to produce micro-scale shell parts with designed geometries. It has been shown that the design of the toolpath has a profound impact on the final geometry of the part even with the same supporting die. The experimental results suggest that supporting dies with different geometries require unique toolpath strategies to achieve high geometric accuracy. Furthermore, it has been determined that water jet pressure plays an important role in the plastic deformation of the metal foil and that inappropriate combinations of toolpath and water jet pressure lead to buckling which is not found in macro-scale Water Jet Incremental Forming (WJIF). A numerical model in ABAQUS was developed to simulate the process and predict part geometry.

Keywords: Water jet incremental micro-forming Water jet technology Supporting dies

1. Introduction Single Point Incremental Forming (SPIF) is a dieless process in which a rigid tool with a round tip locally induces plastic deformation on the sheet metal in a consecutive manner. SPIF provides a great opportunity to produce complex customized parts for prototyping or small batch production. Although numerous studies have established that great formability and flexibility can be achieved by SPIF (Jeswiet et al., 2005), due to imitated geometric accuracy, the final parts very often do not meet their designed tolerances (Park and Kim, 2003). Toolpath compensation algorithms are a popular solution for improving the accuracy of the SPIF process (Park and Kim, 2003). Since the springback effect has significant impact on the geometric accuracy, annealing process can be employed right after SPIF process to reduce the springback and then improve the accuracy (Zhang et al., 2016). Nevertheless, additional processing times are typically involved in this kind of solution. Two-Point Incremental Forming (TPIF) was proposed to provide a partial or a full supporting die which is mounted beneath the sheet metal to support the part during the incremental forming process (Attanasio et al., 2008). By utilizing supporting dies, the geometric accuracy can be profoundly increased in comparison to SPIF. Nevertheless, the extra cost for fabricating the supporting dies is ⁎

involved. Double-Sided Incremental Forming (DSIF) (Malhotra et al., 2011), in which two forming tools are used, is another effective way which can greatly increase the geometric accuracy of the incremental forming process and save the cost for making the supporting dies at the same time (Moser et al., 2016). In all three of the above-mentioned incremental forming methods, tool wear is inevitable due to friction between the tool and the sheet metal, which requires that lubricants be constantly applied on the surface of the sheet metal during the entire process. Furthermore, as the demand for micro shell products keeps increasing, SPIF was first introduced at the micro level by Saotame and Okamoto (Saotome and Okamoto, 2001). To further reduce friction and improve the surface quality and geometric accuracy, high-speed rotational motion was added to the tool in the Single Point Incremental Micro-Forming (SPIMF) process to form miniature shapes on the aluminum foil (Obikawa et al., 2009). The speed of the spindle was reported to have had a noticeable impact on the forming limit in the incremental forming of conic and polygonal shapes (Sekine and Obikawa, 2010). The failure modes and scaling effects in SPIMF process with carbide tools were investigated by Beltran et al. (Beltran et al., 2013). Water Jet Incremental Forming (WJIF) combines the traditional SPIF process with water jetting technology to serve as an alternative

Corresponding author. E-mail address: [email protected] (Y. Shi).

https://doi.org/10.1016/j.jmatprotec.2019.01.012 Received 5 April 2018; Received in revised form 15 December 2018; Accepted 17 January 2019 Available online 18 January 2019 0924-0136/ © 2019 Elsevier B.V. All rights reserved.

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Fig. 1. Schematic depiction of WJIMF with different types of supporting dies. (a)Process representation; (b) Supporting die categories.

may be different as compared to the WJIF process at the macro-scale. The overarching objective of this paper is to introduce both half and full supporting dies into the WJIMF process to improve the geometric accuracy of the parts produced. To achieve this goal, three major aspects of WJIMF with supporting dies were systematically studied, i.e.: 1) the influence of toolpath strategy on geometric accuracy with different supporting dies, 2) the influence of water jet pressure on the final formed geometry and 3) numerical modeling for the prediction of the final geometry for a given supporting die, toolpath and process parameters. The detailed research work for each individual task are summarized as the followings. The rest of the paper is organized as follows. The description of the WJIMF process with supporting dies and of the corresponding toolpath designs will be first introduced in Section 2. Optimal toolpath strategies will be explored in terms of both total processing time and the final geometric accuracy of the parts. Section 3 offers a detailed account of the experimental setup used. Validation results obtained through a series of systematic experiments that consider the interrelation between the toolpath’s and the part feature’s geometric characteristics for both half and full supporting dies will be presented in Section 4. In addition to the toolpath design, the influence of the water jet pressure on the part’s plastic deformation behavior will also be highlighted. Finally, numerical simulation results, obtained by ABAQUS with a user-defined subroutine for WJIMF, of the final part geometry are given in Section 5. Experimental validation of these results for both the dieless and the process with supporting dies will also be presented. Section 6 summarizes the major conclusions of the work and identifies issues that remain to be addressed in the future.

incremental forming technique (Jurisevic et al., 2006). The major difference between conventional SPIF and WJIF is that a high-pressure and -speed water jet is implemented as the forming tool instead of a rigid tool. The significant advantage of WJIF is that no rigid tool-workpiece contact occurs obviating the need for a lubricant. WJIF was first introduced by Iseki in forming a 0.3 mm aluminum sheet with an accompanying simplified prediction model (Iseki, 2001). Jurisevic et al. identified the technological window for the WJIF process by introducing a parameter called the “relative water jet diameter” which was defined as the ratio of the water jet diameter to the blank thickness (Jurisevic et al., 2006). Unlike the SPIF process that forming force depends on the toolpath, displacement of the workpiece, tool position and the mechanical properties of the sheet metal. The forming force in WJIF only depends on water jet pressure and its corresponding diameter. As a result, it is usually constant during the entire WJIF process and is independent of water jet position. The geometry of the shape is no longer managed by the rigid tool’s position that is controlled by an XYZ motion stage in SPIF. This poses a considerable, as of yet not explored, challenge related to the ability to maintain part accuracy. Several key processes parameters, such as pressure, jet diameter, blank thickness, feed rate of the motion stage, toolpath, and the incremental step, exert a profound influence on the final geometry. Analytical and numerical analyses were proposed by Lu et al. to understand the influence of the process parameters on the minimum forming pressure (Lu et al., 2011). To overcome the limitation of low geometric accuracy of WJIF, supporting dies are used in a manner similar to the TPIF process. Beverage cans were incrementally formed by a rotating water jet nozzle from 0.23-0.27 mm thick steel sheet with a full supporting die (Emmens, 2006, 2007). Various shapes of laminated supporting tools were fabricated for WJIF of 0.23 mm thick aluminum sheet by Jurisevic to study the best forming toolpath strategy (Jurisevic et al., 2008). However, all the aforementioned studies of WJIF in the literature were performed at the macro-scale with sheet metal thicker than 0.1 mm. To achieve the best geometric accuracy of formed parts at the micro-scale by WJIF, a supporting die might be necessary. Currently, there are no studies specifically focusing on the understanding of the WJIF process at the micro-scale with supporting dies. Thus, it is necessary to perform a systematic study on Water Jet Incremental Micro-Forming (WJIMF) with supporting dies to understand the fundamental phenomena which

2. Process and toolpath description The WJIMF process utilizes a high-speed and -pressure micro water jet as a forming tool to induce local plastic deformation on the metal foil instead of the rigid tool used in the traditional SPIF or TPIF processes (as shown in Fig. 1). Although the ultimate goal in the sheet metal incremental forming process is to form the sheet metal without a die with small tolerances, the geometric accuracy of the process decreases when no supporting dies are used, particularly in the WJIMF process. Our previous studies (Shi et al., 2018) have shown that the 118

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way to the center of the die. On the opposite, the one-step full spiral toolpath 1-e begins from the center to the edge. The last toolpath, 1-f, is a two-step spiral pattern that starts from the edge of the cylinder and ends at a specific diameter d just like toolpath 1-a. The second step of toolpath 1-f is intended to form the center area of the sheet metal by spiraling outward from the center to the specific diameter d. The second full die includes five micro channels that are machined close to each other with a width of 1.3 mm, length of 14 mm, spacing of 1.2 mm, and depth of 0.25 mm. The reason for choosing this geometry is that the features with such close spacing and aspect ratio (ratio of width to depth of the channel) are particularly challenging for dieless WJIMF in regarding the ability to maintain the desired geometric accuracy. Furthermore, this kind of sheet metal product with a micro channel pattern has applications in fuel cell fabrication which is currently in high demand in the electric vehicle industry. Similar to Die #1, a scanning, square spiral and normal spiral toolpaths were selected as illustrated in Fig. 4. Since micro channels are asymmetric patterns, the zigzag scanning direction will affect the WJIMF process. Toolpaths 2-a and 2-b are two scanning toolpaths which scan along the channel direction and perpendicular to the channel direction, respectively. The whole scanning area is 14 mm in width (W) by 16 mm in length (L). The square spiral toolpath, which has the same overall scanning area as toolpaths 2-a and 2-b, is depicted in Fig. 4 (2-c). Toolpath 2-d and 2-e are regular spiral patterns in different directions with a diameter D of 16 mm that cover all five micro channels on the supporting die. The last toolpath, 2-f, includes local square spiral toolpath with a width w of 1.3 mm that starts form the edge to the center of every single channel as shown in Fig. 4 (2-f). By implementing toolpath 2-f, the water jet will only be applied to areas with channel features and not the areas between two channels where the metal foil should be kept flat. Consequently, the toolpath will be separated into five disconnected subtoolpaths. During the forming process, these five individual sub-toolpaths will be formed one by one in sequence. Die #3 has a uniform step that is 0.25 mm deep to make sure that the overall shape will not exceed the depth of 0.25 mm. As for the shape itself, it can be programmed to have all different kinds of toolpath patterns. Toolpath 3-a in Fig. 5, as an example, is the same as toolpath 2-f in Fig. 4. Similar micro channels can be formed by using Die #3 with toolpath 3-a. To demonstrate that the partial supporting die as the flexibility of generating complex and customized shapes on the sheet metal, toolpath 3-b is designed to create the letters “N” and “U” with a flat bottom surface.

shape of the part made by dieless WJIMF can be easily affected by several processes parameters, i.e., water jet pressure, relative jet diameter which is defined as the ratio of the water jet diameter dWJ and of the blank thickness t (as shown in Fig. 1 (a)), incremental step Δ, and motion feed rate Vst. Therefore, with the objective to precisely control the shape formed by WJIMF, it is necessary to explore the possibility of improving the geometric accuracy by introducing supporting dies into the WJIMF process. For WJIMF with supporting dies, the metal foil/ workpiece is clamped with pre-tension to make sure no slip occurs during the forming process. Pre-tension also ensures that the bottom surface of the metal foil stays in close contact with the die surface for full support dies (Fig. 1 (b)), which keeps the areas that are not designed to be formed as flat as possible. The XY motion stage moves the metal foil together with the clamping system along predefined toolpaths to generate the incrementally formed shapes. The supporting die in the WJIMF process can be divided into two main categories – partial supporting dies for unspecific support and full supporting dies for specific support. Partial supporting dies are used with the intention to impose geometric limitations, and at the same time, still allow the flexibility to form complex shapes defined by the users. On the other hand, full supporting dies only allow the exact shape of the die be formed with high precision. This greatly lessens the flexibility of the process. Three supporting dies were manufactured by CNC milling from a 304 stainless-steel rod with all dimensions illustrated in Fig. 2, including two full supporting dies (Die #1 and #2) and a partial supporting die (Die #3). Full supporting dies are usually designed for forming only one single geometry with high geometric accuracy (as indicated in Fig. 1 (b)). Partial supporting dies offer a compromise between the dieless WJIMF and the WJIMF process with full supporting dies and provide the flexibility of the traditional incremental forming process. However, the overall depth of the geometry is limited as indicated in Fig. 1 (b). For all the supporting dies, several toolpaths were designed to explore the influence of the toolpath geometry on the accuracy of the generated shapes. A description and rationale for the chosen toolpaths for each of the supporting dies is given below. The first full supporting die (Die #1) was chosen to have a simple cylindrical cutout with a diameter of 10.16 mm and a depth of 0.5 mm because this is the simplest symmetric shape that can easily be compared to dieless WJIMF parts. The six different toolpaths used with Die #1 are shown in Fig. 3. The critical dimension D was set to 12 mm that is slightly larger than the diameter of the cylindrical part feature to ensure that all the toolpaths will cover the entire supporting die feature. The incremental step Δ = 0.1 mm is the distance between each iteration of the toolpath and is the same for all toolpaths in this paper. Toolpath 1-a is a zigzag scanning pattern which covers the entire area of the feature on Die #1. Toolpath 1-b is a square spiral that starts from the outside to the inside until the center point of the die is reached. Toolpath 1-c is a partial spiral in pattern that starts from the edge of the cylinder and ends at a specific diameter d. In this way, only the wall of the shape is formed, and the center area is free of deformation. Toolpath 1-d is a one-step full spiral pattern that starts from the edge all the

3. Experimental setup High-speed water jets are most commonly used for cutting all types of materials with abrasive particles. Pure water jets without abrasive particles have applications in peening process, cutting soft materials, cleaning, and cooling purposes. As for sheet metal forming processes, pure water jets are adopted, in lieu of abrasive water jets, to only induce necessary plastic deformation on the workpiece instead of erosion. As explained in Fig. 1, the impact of a micro high-speed water jets on the

Fig. 2. Dimensions of the three dies machined for this study. (unit: mm). 119

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Fig. 3. Toolpath strategies for Die #1.

time, to collect the water during the process with drainage pipes mounted underneath. Since the alignment of the supporting die position to the water jet is critical for the process, a kinematic mounting stage that holds the clamping system for the supporting die and workpiece was fabricated to ensure that the relative position of the supporting dies to the water jet will not change after changing the workpiece. The clamping system for adding pre-tension to the metal foil is illustrated in Fig. 6 (a). The top and the bottom clamps are made from aluminum to hold the metal foil in position. An O-ring placed in between the top and bottom clamps pushes the metal foil into the O-ring groove to create the pre-tension in the workpiece. All the supporting dies are mounted at the center of the bottom clamp. The right photo in Fig. 6 (b) shows the clamping system and the three supporting dies used in this study.

metal foil causes plastic deformation that is similar to the plastic deformation induced by a rigid tool in SPIF. The stagnation water pressure that provides the forming force can be calculated by (Obara et al., 1995):

Pst =

1 2 ρV 2

(1)

where ρ is the density of the water and V is the water jet impact velocity. Fig. 6 shows the schematic drawing and photograph of the entire experimental setup for WJIMF with supporting dies. The high-pressure water jet system consists of a customized air-driven pump from MAXPRO technologies, stainless-steel pipes, and a self-designed manifold with an orifice inside. The high-speed micro jet is generated by pumping high-pressure water through a sapphire/diamond orifice with a 152.4 μm (0.006 inch) in diameter. The air-driven pump, which transfers air pressure to water pressure with an amplification factor of 796, was designed to have a maximum 450 MPa water output. An air bearing stage from PI (type A311) was chosen to provide the XY motion of the workpiece with an accuracy, repeatability, and encoder resolution of 5 μm, 0.5 μm, and 5 nm, respectively. To protect the motion stage from water, a two-level acrylic enclosure system was designed to keep the motion stage in a dry working environment, and at the same

4. Experimental results The workpiece utilized in this study is annealed 316 stainless-steel foil with a thickness of 50.8 μm. The stand-off distance, i.e., the distance between the nozzle exit and the surface of the workpiece, was maintained at the same value (15 mm) in all the experiments that is shorter than the breakup length of the water jet which is around 25 mm in the setup used. Although the stand-off distance changes as the metal foil is 120

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Fig. 4. Toolpath strategies for Die #2.

pressure was also studied to ascertain its influence on WJIMF with supporting dies. For each individual experiment, the water jet pressure was kept constant during the entire process. Due to the nature of the air-driven pump, water pressure fluctuations that do not exceed 5% are inevitable. For Die #1, based on the geometry of the supporting die, the key process parameters applied are listed in Table 1. Fig. 7 shows the photos

being formed, in the author’s previous experiments and results reported by Jurisevic et al. (Jurisevic et al., 2008) reveal that the stand-off distance does not have a large impact on the final results as long as the water jet is stable. This section presents the experimental results for WJIMF for the three supporting dies for all types of toolpaths described in the last section. The other very important process parameter – water jet

Fig. 5. Toolpath strategies for Die #3. 121

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Fig. 6. Schematic drawing and photos of the experimental setup for WJIMF with supporting die.

using the partial spiral toolpath which allows the bottom surface to be freely formed by the water jet, the part does not show noticeable buckling. However, just like in normal dieless WJIMF, the bottom surface of the truncated cone will bulge up and does not perfectly follow the supporting die geometry. Therefore, to generate a truncate cone shape with a flat bottom surface, toolpath 1-f shown in Fig. 3 is the most appropriate. The normal spiral inward toolpath ensures that the wall of the cone shape reaches the bottom surface of the die, while the spiral outward toolpath flattens the bottom surface and prevents the occurrence of buckling at the center of the part. Nevertheless, slight buckling occurs on the boundary where the two spiral toolpaths with different directions meet each other (Fig. 7 (f)). The measured geometry data is plotted in Fig. 8 for the parts shown in Fig. 7 from (c) to (f). The average standard deviation of the geometry is obtained be evaluating:

Table 1 Values of process parameters used for Die #1. Parameter

Value

Water jet pressure from the pump (PWJ) Motion stage feed rate (Vst) Incremental step (Δ) Nozzle diameter (dN) Toolpath ending diameter (d) Stand-off distance (Dst)

75 MPa 20 mm/s 0.1 mm 152.4 μm 6 mm 15 mm

for each individual part made by toolpaths 1-a to 1-f in Fig. 3. The profound influence of the toolpath on the final geometry of the part with Die #1 can be clearly observed in Fig. 7. The different toolpath strategies lead to different directions of the plastic flow. Buckling in some scenarios (marked by red dashed lines) in Fig. 7 (a), (b) and (d) is caused by the limited plastic deformation in the thickness direction induced by the use of supporting dies. The scanning toolpath in Fig. 7 (a) fails to form a full circular shape which is defined by the supporting die. Buckling starts to happen on the edge of the supporting die as the scanning toolpath reaches the half of its total scanning area. The square spiral inward toolpath creates a diagonal buckling pattern. The height of the buckling on the part increases in the radial direction and reaches its maximum at the center of the toolpath (end of the toolpath). A circular buckling pattern occurs with the normal spiral inward toolpath (Fig. 7 (d)). In this case, as in the previous, the height of the bucking reaches its maximum at the center. Buckling does not appear for the normal spiral outward toolpath, but the geometry of the formed parts made by the same toolpath but in the inward directions is significantly different. Toolpaths that are responsible for buckling on the part are not reported in the literature for water jet incremental forming with supporting dies for thick aluminum sheet (0.23 mm thick) (Jurisevic et al., 2008). This type of phenomenon is the first of its kind observed particularly for WJIMF on thin stainless-steel foil. It can be seen that by

σ¯ =

1 n

n

∑ |σi| i=1

(2)

where σi is the deviation from the supporting die geometry at each measurement point from the Alicona measurement results after the part was released from the clamp. It is quite obvious that toolpath 1-f yields the best result for Die #1 (Fig. 8) as supported by the standard deviation data listed in Table 2. The wall angles for the three normal spiral inward toolpaths, 1-c, 1-d, and 1-f, are basically identical because all other process parameters used are the same in forming the truncated cone shape. The spiral outward toolpath creates a sphere like shape, in lieu of the truncated cone shape. At this particular parameter setting, the plastic deformation is not large enough to reach the bottom of the supporting die for the spiral outward toolpath. For toolpaths 1-c and 1d, the metal foil actually touched the surface of the die during the forming process. However, after the water jet pressure was turned off and the clamp released, because of springback, the overall depth of the part was less than the depth of the die (< 0.5 mm). On the other hand, toolpath 1-e has a different toolpath direction. In addition to 122

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Fig. 7. Photos the parts formed by using the corresponding toolpaths in Fig. 3.

springback, the plastic deformation flows outward as the part is being gradually formed from inside to outside leading to smaller amounts of accumulated deformations at the center. Therefore, the part formed by toolpath 1-e is the shallowest among all four toolpaths examined, as seen in Fig. 8. Toolpath 1-f minimizes the springback and buckling effects and ensures that the total depth of the part to coincide with the depth of the die with an acceptable tolerance (˜ 10 μm).

Table 2 Average standard deviations of different toolpaths. Toolpath #

1-c

1-d

1-e

1-f

Average Standard Deviation σ¯ (mm)

0.1698

0.1291

0.1587

0.1050

Fig. 8. Geometry measurements of parts made by using toolpaths 1-c, 1-d, 1-e and 1-f. 123

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Fig. 9. Comparison between WJIMF with supporting dies and dieless WJIMF for toolpaths 1-c, 1-d, 1-e and 1-f.

obtain WJIMF parts that fit Die #1 geometry the best, toolpath 1-f is preferred. A trade-off needs to be made between the wall angle and buckling for different pressure settings. Lower jet pressures generate better surface quality without buckling for small wall angles. On the other hand, although larger jet pressures can create steeper walls, they jeopardize the wall surface quality and induce possible buckling due to the large plastic deformations. Fig. 10 shows that the side wall of the formed cone shape is controlled by the water jet pressure instead by the supporting die. The cylindrical cutout on Die #1 constrains the total forming depth of the shape but allows the wall angle to vary. To constrain the wall angle, a supporting die (Die #1 A) with a 15 ° cone wall was fabricated as shown in Fig. 11 (a). The toolpath evaluation for Die #1 shows that toolpath 1f yields the best result. Therefore, toolpath 1-f with an inner diameter, d, of 6 mm and an outer diameter, D, of 10 mm was adopted for Die #1 A to be used with different water jet pressures. Fig. 11 (b) compares the measured geometries at three different pressures. For a jet pressure of 75 MPa, due to its low value, the wall angle cannot reach 15 ° since, under these conditions, contact does not occur between the metal foil and the supporting die wall. As the pressure increases the wall angle also increases, but unlike the results shown in Fig. 10, the maximum wall angle will be limited to 15 ° by the supporting die. An excessive water jet pressure, however, causes buckling just like the part formed by the 90 MPa jet pressure in Fig. 10. These results imply that process parameter control is essential in preventing undesired buckling during the forming process even for a fully constrained supporting die. A water jet pressure of 82.5 MPa yields the closest cone geometry to the Die #1 A geometry. The corresponding averaged deviation is only 0.0215 mm. In conclusion, once the process parameters are properly selected, WJIMF can be easily applied to produce desired geometries at the micro-scale level with high accuracy. Forming channels that are very close to each other, as shown for Die #2, imposes huge challenges for dieless WJIMF. The forming of two close neighboring features will affect each other during the process and reduces the geometric accuracy of the shape. Therefore, WJIMF with supporting dies is necessary for this type of feature. Based on the preliminary tests with Die #2 given its shallow features, the parameter settings given in Table 3 were employed. A water pressure of 60 MPa and motion stage feed rate of 10 mm/s were verified to guarantee a smooth surface finish after WJIMF. As for the experiments with Die #2, six different toolpaths shown in Fig. 4 were used. The obtained parts are shown in Fig. 12. Among the six toolpaths, only the scanning toolpath along the channel Fig. 4 (2-a) and square spiral inward toolpath for each individual channel Fig. 4 (2-f) produce satisfactory shapes. The scanning toolpath perpendicular to the channel is able to form the channel shapes at the beginning, whereas the channel shapes on the supporting die cannot be followed as the plastic flow affects the forming process in a way similar to Fig. 7 (a). Diagonal buckling and circular

The parts formed by dieless WJIMF with the four toolpaths (Fig. 3 (c)-(f)) were also measured and then compared in Fig. 9. Without the constraint enforced by Die #1, the final shapes are much deeper by dieless WJIMF with toolpaths 1-d and 1-f, as shown in Fig. 9. Nevertheless, for all normal spiral inward toolpaths, all the parts made by both WJIMF with supporting dies and dieless WJIMF have the same wall angle due to the identical process parameter settings. To achieve the same depth as with the die (0.5 mm) by dieless WJIMF with toolpath 1-c, the ending diameter of the toolpath 1-c needs to be specified. Since the overall depth h of the truncated cone is given by:

h = 0.5(D − d) tan (θ)

(3)

where θ is the wall angle defined in Fig. 1 (a), D is the toolpath starting diameter as defined in the previous section, and d is the toolpath ending diameter. Experiments were conducted to measure the wall angle, θ, with the given experimental parameters. For dieless process, the toolpath starting diameter should be the same as the diameter (10.16 mm) of the cylindrical cutout on Die #1. The appropriate toolpath ending diameter was determined to be d = 6 mm, as calculated based on Eq. (3). Therefore, although the final geometries obtained by both the dieless WJIMF and WJIMF process with Die #1 are close for toolpath 1-c (as shown in Fig. 9), additional trial experiments are actually required for the dieless WJIMF process to reach a similar depth as with the WJIMF process with Die #1. In addition to that, the maximum depth of the truncated cone from dieless WJIMF is larger than 0.5 mm. It is still extremely hard to well control the geometry of the shape, especially the depth of the shape, by purely adjusting the process parameters in dieless WJIMF. A bulged-up bottom surface is also inevitable for the truncated cone shape formed by the dieless WJIMF process. From another perspective, not every single toolpath strategy can create the desired shape with supporting dies. The outcome for WJIMF with supporting dies is quite sensitive to toolpath selection. For the dieless WJIMF process, the wall angle of the truncated shape can be controlled by processes parameters, such as water jet pressure, feed rate, and incremental step. It was also found that for the two-step toolpath 1-f, buckling on the boundary can also be affected by these process parameters. Here, the influence of water jet pressure on the final part geometry is analyzed. Three different water jet pressures, i.e., 60, 75 and 90 MPa, were chosen with the same motion stage feed rate, incremental step and nozzle diameter as listed in Table 1 to investigate the influence of the water jet pressure. Fig. 10 illustrates measured geometries for three parts produced under the different pressures. The water pressure mainly affects the wall angle of the cone shape and the buckling on the boundary (as marked in Fig. 10). The wall angle ascends as the water jet pressure increases, while buckling increases as jet pressure increases. Buckling can hardly be seen with a pressure of 60 MPa, but is fairly obvious for a pressure of 90 MPa. In conclusion, to 124

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Fig. 10. Measured geometry of parts made by using toolpath 1-f at three different water jet pressures – Die #1.

observed causing the entire forming area to become curved, especially at the center. Considering that the total processing time, with toolpath 2-f saves more than half of the scanning toolpath’s time as listed in Table 4, makes it very time efficient as compared to the other five toolpaths. Given the current process parameters, however, the best of all formed channels is less than half of the depth of the supporting die (0.25 mm). To realize deeper channels, two possible solutions are proposed – increase of the water jet pressure and application of multiple repetitions of the same toolpath. Toolpath 2-f was selected to explore these two possible solutions. Three different water jet pressures, 60 MPa, 75 MPa and 90 MPa, were planned to investigate the impact of water jet pressure on the final depth of the formed channels. All other process parameters remained the same as in Table 3. Ten measurements of the depth on different channels and different locations (two measurements on each channel’s center and edge positions) are taken to get the average value and standard deviation for each pressure. Fig. 14 contains both the plot of the relationship between water jet pressure and channel depth and the microscopic pictures of channels for every water jet pressure. The depth of the formed channels almost linear increases as the water jet pressure ascends. The depth of the channel reached the depth of supporting die with a water jet pressure of 90 MPa. From the microscopic pictures, it is not hard to notice that the overall surface quality decreases as the pressure increases. The excessive water jet pressure also affects the surrounding areas, especially for a water jet pressure of 90 MPa. Therefore, even though a high water jet pressure greatly improves the depth of the channels, the entire shape and surface quality of the channels gets much worse than the shapes formed with low water jet pressures. The other alternative is by using multiple repetitions of the exact same toolpath contributing to additional process time. Experiments were conducted for both 60 MPa and 75 MPa water jet pressure with a total of four repetitions. The depth of the channels grows from 0.1 mm all the way to 0.15 mm after three repetitions by a water jet with pressure of 60 MPa. The same depth is achieved by a single run at a 75 MPa water jet pressure (Fig. 15). The advantage of employing multiple repetitions is that the initial surface quality will be retained even after several runs. As a result, the surface quality of the channels after three runs with a 60 MPa water pressure is better than that with a single run at 75 MPa A similar trend is observed at a 75 MPa water pressure, i.e., the depth of the channels increases from 0.15 mm to 0.2 mm after three repetitions. As the number of repetitions further increases, the growth of the depth of the channels slows down and finally reaches the maximum after four runs. This is mainly due to the working hardening effect of the materials. The measured geometry of parts after four repetitions is illustrated in Fig. 15 (b). From all the above unsatisfactory channel feature results, it can be concluded that the high aspect ratio of the channel is another challenge for the WJIMF process. Due to the fact that fabricating a full supporting die is expensive and time-consuming, a partial supporting die was designed to achieve higher flexibility with relatively lower geometric accuracy. In this study, two toolpaths, shown in Fig. 5, were programmed to demonstrate

Fig. 11. Measured geometries made by using toolpath 1-f at three different water jet pressures on Die #1 A.

Table 3 Values of process parameters used for Die #2 and Die #3. Parameter

Value

Water jet pressure from the pump (PWJ) Motion stage feed rate (Vst) Incremental step (Δ) Nozzle diameter (dN) Stand-off distance (Dst)

60 MPa 10 mm/s 0.1 mm 152.4 μm 15 mm

buckling patterns (marked by read dashed lines) occur when the square spiral inward (Fig. 12 (c)) and normal spiral inward (Fig. 12 (d)) toolpaths are utilized, respectively. For the square spiral inward toolpath 2-c, interestingly, the buckling pattern follows the diagonal direction of the toolpath. The normal spiral outward toolpath has the capability to form every single channel, but their depths are shallow compared to other toolpaths. Furthermore, the circular toolpath is visible on the final shape which makes toolpath 2-e unsuitable for forming channels. Fig. 13 compares the geometries of the parts formed by toolpaths 2a and 2-f. The two geometries are very close, however, the square spiral inward toolpath designed for every channel performs better especially in terms of the gaps between the channels. The major reason is that the water jet that follows scanning toolpath 2-a, exerts pressure in the regions between the channels where the designed geometry is flat. As a result, more deformation is accumulated during the process. After the part is released from the clamp system, additional springback is

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Fig. 12. Photos of each individual part formed by using the toolpaths in Fig. 4.

has the same depth as Die #2. The photos of the parts formed by the WJIMF process with Die #3 are shown in Fig. 16. The part formed by toolpath 3-a that generates similar channel pattern is compared with the part in Fig. 12 (f). The only difference between these two parts is the supporting die. Geometry measurements were compared at two different locations, i.e., at the center and near edge part of the channel (as shown in Fig. 17). The comparison in Fig. 17 indicates that the geometry of the formed channels with the partial supporting die is close to the one with the full supporting die at the near edge of the part. Nevertheless, at the center of the part, the channel shape becomes considerably worse with the partial supporting die. The reason for this is that there is no support between the channels anymore. The plastic deformation prorogates as each channel is being formed leading to slightly deeper features at the center. The partial supporting die cannot handle the features that are close to each other as well as the full supporting die, but it provides better flexibility as demonstrated with the second toolpath. Toolpath 3-b designed for the letters N and U can be successfully applied to form the desired geometry on the stainlesssteel foil (Fig. 16 (b)).

Fig. 13. Geometric measurement of parts made by using toolpaths 2-a and 2-f. Table 4 Processing time of by WJIMF with Die #2 for six different toolpaths. Toolpath #

2-a

2-b

2-c

2-d

2-e

2-f

Processing Time (s)

113

113

113

101

101

49

the properties of the partial supporting die. The standard deviation of the geometry is no longer presented because there is no specific reference geometry on the partial supporting die to compare to. Die #3 126

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Fig. 14. The influence of water jet pressure on the depth of formed channels.

Similar to the letters formed by WJIMF with the partial supporting die, other complicated shapes can also be easily generated by utilizing various commercial CAM software to generate toolpaths with a spacing that is on the same order or less than the water jet diameter to avoid rough surface generation.

5. FEM simulation An ABAQUS FEM model of the WJIMF process was developed for simulation with a user-defined subroutine, VDLOAD. The major goal of this model is to accurately predict the geometry, including the wall angle and the depth, of the formed features, so that it can replace high cost physical experiments for process parameter optimization. Given that WJIMF is a fast metal forming process, the ABAQUS dynamic explicit solver was selected. It should be noted here that in the experiments, the diameter of the O-ring clamp is around 90 mm, which is much larger than the formed region. Directly simulating the whole sheet metal would significantly increase the computation time. In the experiments, the water jet pressure is large enough to introduce large strain rates when it hits the sheet metal. The radius of the water jet, on the other hand, is at the micro level, so that the total forming force is very small (< 1 N). As a result, at any time during the process, the deformation is localized at the point of the water jet impingent implying that the deformation outside the water jet region is negligible. Therefore, the effects imposed by the clamped boundaries that are outside the forming region onto the shape of the formed geometry are insignificant. For validation, cross-section geometries from two simulations with different workpiece sizes (squares with a 28 mm and a 14 mm side length) but the same forming area and parameters are compared. The comparison result in Fig. 18 indicates that the boundary condition’s effect on the geometries produced is negligible. As a result, in the subsequent simulations, a smaller area of the sheet metal is modeled instead of the complete region defined by the real clamped boundary. A square shape was selected to ensure a uniform mesh for smoother simulation results. The outer perimeter of the die and of the clamp are circular in the experiment while in the simulation they are of the same square shape as the sheet metal. The side lengths of the square workpiece and the die are selected

Fig. 16. Photos of each individual part formed by using the toolpaths in Fig. 5.

to be 14 mm, which is larger than the 10 mm inner diameter of the die. The element type for the sheet metal is the uniform square S4R for fast simulation speed and ease of element size control. The water jet that introduces the pressure to the sheet metal for forming is 0.152 mm in diameter. To determine element size for the mesh of the workpiece, different element sizes, i.e., 0.05 mm, 0.08 mm, 0.1 mm, 0.13 mm, and 0.15 mm, which are smaller than the diameter of the pressure application region were used. The forming depths at the center are compared in Fig. 19. It can be seen that when the element size is larger than 0.1 mm, there are variations in the predicted forming depth at the center. When the element size is smaller than 0.1 mm, the predicted depth converges to a stable value. To reduce computation time, the side length of the S4R elements was set to 0.1 mm. As for the supporting die, since it contains a circular cavity, C3D4 tetrahedral elements were utilized to facilitate auto mesh generation. A coarse mesh is applied to the die because its only function is to provide support and undergoes negligible deformation, as it will be shown in the following paragraph. The mesh for both the sheet metal and the supporting die is illustrated in Fig. 20. As for the material properties of the stainless steel dies a Young’s modulus of 210 GPa and a Poisson ratio of 0.3 was assumed. Since the die has a thickness of 1.5 mm, which is much larger than the 0.0508 mm thickness of the sheet metal, it was assumed that it undergoes only very small linear elastic deformation during the simulation and is simulated with the ABAQUS built-in linear isotropic elastic material model. The simulations show that the maximum principal strain

Fig. 15. (a) The influence of the number of repetitions on the depth of formed channels. (b) Measured cross-section profile of the part after four repetitions. 127

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Fig. 17. Comparison between the parts made by the partial and full supporting dies with toolpath 2-f.

Fig. 18. Cross-section geometries from water jet incremental forming simulations with different workpiece sizes but the same toolpath and parameters.

Fig. 20. Mesh of the (a) stainless-steel sheet and (b) Die #1 used in the simulation.

standard for sub-size specimen. According to the ASTM E8/E8M-09 standard, the width and gauge length of this sub-size uniaxial tensile specimen were 6 mm and 25 mm, respectively. A Young’s modulus of 173.8 GPa was measured in the elastic region. This elastic region is simulated with the ABAQUS built-in linear isotropic elastic material model. A uniaxial yield strength of 230 MPa at the uniaxial equivalent plastic strain of 0.2% was obtained from the plastic region. This plastic region is simulated with the ABAQUS built-in isotropic hardening plasticity material model using the stress-strain data from the tensile test. The boundary conditions and the pressure load in the FEM model are illustrated in Fig. 21. The boundary conditions are applied to the edges of the sheet metal and the side surfaces of the die to constrain all the degrees of freedom. The pressure load is applied on the top surface of the sheet metal. The user-defined load field subroutine VDLOAD is utilized in order to simulate the moving pressure introduced by the water jet. At a certain time, the area that is impacted by the water jet is calculated via the toolpath and the water jet radius. The pressure in this region is calculated by:

Fig. 19. Relation between the workpiece element size and the forming depth at the workpiece center.

in the die is less than 7 × 10−6, justifying the application of a coarse mesh and of pure elastic material properties for the die with negligible deformation. To determine the elastoplastic properties of the thin stainless steel sheet metal with a thickness of 50.8 μm, uniaxial tensile tests were performed on a Sintech 20 G tensile machine with a VIC-3D digital image correlation (DIC) system based on the ASTM E8/E8M-09 128

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Fig. 21. Illustration of the boundary conditions and pressure load in the WJIMF FEM model.

P = cos2 αPst

(4)

Fig. 23. Comparison between experimental results (solid lines) and numerical simulations (dashed lines) for both dieless WJIMF and WJIMF with supporting die - Die #1.

where Pst is the water jet stagnation pressure from the experiment, and α is the change in the angle of the surface normal direction before and after forming obtained directly from ABAQUS (Lu et al., 2011). The pressure applied to the other area that is free from the water jet is zero. Since the WJIMF forming result is very sensitive to the feed rate, the simulation step time is 1:1 to the real experiment, which is around 40 s when Die #1 and toolpath (1-d) are utilized. This setup leads to a long simulation time combined with the very fine sheet metal mesh. For the FEM explicit algorithm, the minimum stable time increment is given by:

Δt = Le

ρ E

region of the part for a longer time and causes larger deformations than predicted by the simulation results. The other possible reason may be related to the mass scaling method used in the FEM simulation. The discrepancy at the bottom is still in an acceptable range. In conclusion, the numerical model has the capability to successfully simulate the WJIMF process and is in close agreement with the part geometry obtained in the experiments. In Fig. 24, a simulation result of WJIMF with Die #1 and toolpath 1d is presented. The color contours depict the displacement distribution in the z-direction (units: mm) of the WJIMF process corresponding to the process parameters listed in Table 1. To investigate the effects of the supporting dies on the plastic deformation of the workpiece, simulations were performed without a die and with Die #1 using toolpaths 1-c and 1-e. As an indicator of the material’s plastic deformation, the principal plastic strain at the bottom surface of the sheet metal and along the x–z cross-section of the workpiece was extracted and plotted in Fig. 25. It can be seen from Fig. 25 that processing with a supporting die tends to lead to more uniform and symmetric plastic strains in the forming areas. However, fluctuations in the plastic deformation can occur at the outer edges of the die. In the dieless process, the sheet metal fluctuates as the water jet follows the trajectory since there is nothing underneath to constrain the motion in the z direction. The support provided by the die limits the fluctuations of the workpiece during high pressure forming. Therefore, compared to the dieless process, the WJIMF process with a supporting die can form geometries closer to the forming target with better symmetry and surface quality. As a summary, the introduction of a supporting die into WJIMF can produce high-quality geometries but can also result in fluctuating plastic deformations at supporting edges. This plastic deformation may lead to buckling and fracture that needs to be avoided by using appropriate process parameters and toolpaths.

(5)

where Le is the element dimension, ρ is the material density, and E is the Young’s modulus. As a result, to accelerate the WJIMF simulation, the material densities are increased by 1000 times. In this way the time to complete one simulation can be reduced from about 20 days with real material densities to about one and a half days with a mass scaling factor of 1000 on a 96 computational core (Intel Xeon processor) cluster. For the entire cross-section profile, illustrated in Fig. 22, the adopted mass scaling yields a similar geometry as the one obtained in simulations with real material densities, validating the negligible effects of mass scaling on the prediction results. To demonstrate the prediction capability of the WJIMF FEM model, typical simulation cases with different spiral toolpaths are presented for both the dieless and the Die #1 supporting die configurations. The final part results are plotted in Fig. 23 to compare to the experimental results with the four toolpaths shown in Fig. 9. It can be seen that in all scenarios the simulations agree well with the experiments especially with respect to the wall angle. The simulation results show slightly shallower features for the cases with the outward toolpaths especially in the center region. The major reason that is responsible for this phenomenon is that the motion stage speed cannot reach a steady 20 mm/s due to the acceleration and deceleration as a result of the extremely small diameter of the toolpath. For outward toolpaths, the motion starts with a circular path of zero diameter. During the first few circles with small diameters the motion stage needs time to accelerate from zero velocity to a steady 20 mm/s. Therefore, water jet pressure remains at the center

6. Conclusion & future work This paper provides a systematic experimental and numerical study of WJIMF with three supporting dies. The influence of process parameters and toolpath on the geometry of the formed part is significant for WJIMF with supporting dies. Compared to the dieless WJIMF, this study proves that the geometric accuracy of the part is improved by using supporting dies. However, toolpath selection is critical to achieve a high accuracy part with excellent surface quality. The major findings for toolpath selection can be summarized as follows:

• For full supporting dies, all the single step scanning and spiral

toolpaths do not follow well the die geometry. Buckling may occur when the whole area scanning and the spiral toolpaths are used. The best toolpath strategy should follow the shape of the features on the supporting die to achieve the best performance without unnecessary

Fig. 22. Part shapes from the original and large density dieless WJIMF simulation. 129

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Fig. 24. Results of ABAQUS FEM simulation in terms of the sheet displacement in the thickness direction after WJIMF with Die #1. (Toolpath 1-d, PWJ = 75 MPa, Vst = 20 mm/s, Δ = 0.1 mm).

•

due to uneven plastic deformation and induce unwanted plastic deformation to the surrounding areas. Instead of using high water jet pressure, multiple repetition of the same toolpath is suggested to reach the same goal, i.e., to increase the depth and to follow the feature’s high aspect ratio on the supporting die. Apart from the experiments, a WJIMF FEM simulation model was also developed with a user-defined load field subroutine VDLOAD. This model can be utilized for the better understanding of the sheet metal deformation mechanism during the forming process such as the evolution of the plastic strain. The plastic strain information from the simulation also helps to: (1) explain why a better geometry can be obtained by using supporting dies; and (2) the possible reason for buckling at the edges of the supporting dies when inappropriate parameters are used. Simulation cases with different toolpaths and dieless or supporting die configurations were performed and the results agree well with the experiments especially in terms of the wall angle. There are some discrepancies, however, in the bottom shape of the final parts, which might be caused by the mass-scaling for the sake of simulation speed. This issue will be addressed in the future work to refine the predication capability of this model. Overall, with the introduction of supporting dies and the selection of appropriate process parameters and toolpaths, the geometric accuracy of the WJIMF process has been significantly improved in comparison to its dieless counterpart. Numerous experimental trials, however, are required to achieve optimized forming results, such as the one shown in Fig. 11 with a water jet pressure of 82.5 MPa. In addition, the current setup cannot produce parts with large wall angles (> 25 °). In addition, the large plastic deformation in this process can easily cause buckling. Therefore, there are still challenges to be addressed before this technique is ready for applications in practice. Future research work on the WJIMF process needs to focus on developing methods to increase the formability of the process with larger wall angles. A plausible approach is to add multi-axis motions to the water jet nozzle to trace the part surface during the forming process to keep the pressure constant on the sheet metal surface. In addition, a better control of the water jet pressure is also essential to produce parts with improved accuracy and surface quality. More complex die geometries should be

buckling. When multiple separated features are designed on full supporting dies, like the separated channels on Die #2, only the features on the supporting die should be formed by water jet pressure. The best forming accuracy can be achieved by using supporting dies with wall angles within the water jet’s forming capability (< 20 ° in the present case), but such supporting dies add to the cost of the parts produced. For partial supporting dies, since their purpose is to only control the overall depth of the shape, geometric accuracy is reduced due to the absence of supports between the features. However, partial supporting dies allow for higher flexibility and the ability to form complex shapes. The overall depth is restricted by the depth of the supporting die. The fabrication time and cost are lower than in the case of the full supporting dies. Extra alignment time for the full supporting dies is also saved.

It can be further concluded that toolpath design is extremely important for the WJIMF process with supporting dies. The toolpath cannot be a simple scan pattern to cover all the features on the supporting die. Inappropriate scan toolpaths lead to large springback or even sever buckling. To prevent and reduce springback after the forming process, the toolpath should always follow the contour of each individual feature on the supporting die one at a time from outside to inside. Region without designed features on the supporting die should not be loaded with water pressure. Consequently, the alignment of each individual feature is necessary before the incremental forming process begins. Buckling is another issue that needs to be avoided during the process. Buckling appears to be a unique phenomenon for water jet incremental forming on thin stainless-steel sheet. Process parameters also affect the WJIMF process with supporting dies. Water jet pressure was confirmed to have a significant influence on the depth of geometry, which is similar to the dieless WJIMF. Adjusting the water jet pressure can therefore change the depth of the shape when supporting dies with high aspect ratios are used, like supporting dies with channels in the present case. Excessive water jet pressure is not recommended because it will jeopardize surfaces quality

Fig. 25. The principal plastic strain at the bottom surface and along the x–z cross-section from simulations without and with die support using toolpaths (a) 1-c and (b) 1-e. 130

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tested to demonstrate the forming capability of the WJIMF process. For FE simulations, a better material model should be developed to predict damage, fracture and buckling of the workpiece during the WJIMF process.

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