Toolpath Planning for Manufacturing of Complex Parts Through Incremental Sheet Forming

Many manufacturing techniques have the capability to successfully form sheet metal parts. Common methods such as stamping, deep drawing, and die bending are well suited for large-volume manufacturing. However, the need for individual dies for any newly designed part is time-consuming and cost-inefficient for small batches. Current industry trends indicate an increasing demand for short lead times and customized products. This shift has led to the development of flexible sheet metal forming processes to move from mass production to mass customization [1].

Incremental sheet forming (ISF) was introduced in the late 1970s for the manufacture of small volume sheet metal parts [2]. The ISF process has gone through several changes since then to improve its geometric accuracy, formability, and product properties. However, the essentials of ISF have not changed—that is, the sheet metal is deformed into the desired shape in a stepwise manner as one or more generic tools move along a predefined toolpath and are mostly dieless without or with limited use of dies. Many variants of ISF have been developed. Single point incremental forming (SPIF) [3] is the simplest variant of ISF since it uses only one tool (forming tool) forming the geometry, while the back surface of the sheet is left unsupported. However, this lack of support at the back surface results in poor geometric accuracy due to undesirable global bending. The introduction of two-point incremental forming (TPIF) [4], which uses a supporting die on the back side of the sheet, improves geometric accuracy but degrades process flexibility. Double-sided incremental forming (DSIF) [5] is another variant of ISF, which exhibits advantages of providing back support while simultaneously maintaining the dieless nature of the process. In DSIF, a second tool is used on the opposite side of the forming tool as back support [6].

The development of ISF processes over the past several years has resulted in many applications. The demonstrated application fields of ISF products include automotive and aerospace industries, the biomedical field, architecture, and more. Some of these applications are summarized as follows.

In the automotive industry, forming dies are normally kept for 10–20 years before their disposal [7]. Once a product is discontinued, providing past model service parts is a major problem. However, the inherent dieless characteristic of the ISF process makes it particularly well suited for making replacement parts. In 2002, Amino et al. [8] collaborated and successfully applied ISF to produce a limited series of car hoods for the S800 sports car. Recently, Nissan has also investigated the use of ISF to make replacement parts for discontinued models [9]. Moreover, the use of ISF has shown great potential for adding features to existing stamped parts. Toyota has used the ISF process to add logo marks and styling details to door panels for special edition Toyota iQ-GRMN vehicles [10]. Another suitable area for ISF is in rapid prototyping; e.g., Jeswiet and Hagan [11] manufactured a limited series of headlights and heat/noise shields during the design phases. For sheet metal-based consumer products, such as might be found in a hardware store, design innovation-to-manufacturing process is cost and risk reduced by the ability to make limited runs of a functional product for limited customer testing.

Aerospace components typically have complex geometries and are made of lightweight materials, such as titanium, aluminum, and special steels that may be difficult to form. The high achievable formability and flexibility of the ISF process makes it very promising for aerospace applications. Some examples of attempts to illustrate its potential include scaled airfoils formed by Behera et al. [12] and C-channel fixtures designed for aircraft vibration testing by Gupta et al. [13]. The willingness to implement ISF techniques in the aerospace and automotive industries has accelerated the development of startup companies.

ISF is a very suitable technology for the biomedical field due to the need for highly customized unique parts. Special applications include ankle supports [14,15], dental prostheses [16], facial implants [17], cranial plates [18–21], knee prostheses [22,23], and clavicle implants [24]. The application methodology is based on computed tomography (CT) that is used to produce high accuracy patient-specific computer-aided design (CAD) models from which the shape of the implants can be established. The tailored geometry is then utilized in the ISF process to produce patient-specific medical devices.

The ability of ISF to generate large parts with complex and varying geometries provides new architectural opportunities. For example, a self-supporting lightweight roof structure was designed and manufactured by Bailly et al. [25]. All 140 individual pyramids that make up the roof structure were manufactured using ISF due to its ability to realize freeform designs with many nonidentical elements. Recently, ISF has raised a lot of interest in architectural design communities spurred by the increasing wish for individualized products. Customized interiors, ceilings, and doors made by ISF processes began appearing on social media [9].

Although, as stated earlier, ISF’s high flexibility and customization is of great potential for a wide variety of application areas, the commercial use of ISF has so far been limited. Some of the major issues are low geometric accuracy, excessive thinning associated with high wall angles, and the lack of multifeature toolpath generation solutions. Significant efforts have been devoted to resolving these challenges. Some of them are listed here.

The geometric accuracy achieved in DSIF is higher than in SPIF, as the unwanted bending reported in SPIF is significantly reduced due to the use of the supporting tool. However, producing parts with satisfactory accuracy is still challenging because geometric errors may arise from multiple sources, including machine compliance, motion inaccuracy, and in-process and post-process springback. Feedforward toolpath optimization [26,27], feedback toolpath compensation [28,29], in-process annealing [30], and post-process annealing [31] are some of the main strategies employed to solve this problem.

The deformation mechanisms in ISF stabilize necking and lead to higher formability than in conventional metal forming processes [32]. However, the inherently local nature of the process causes limited material flow, leading to nonuniform thickness distribution. As the sine law states, the wall thickness decreases as the wall angle increases [33]. Excessive thinning occurs at large forming angles, leading to fracture and hence failure of the formed part. Several factors, such as increasing the initial sheet thickness and applying a smaller incremental depth, can enhance formability [34], but in most cases, the maximum achievable wall angle without failure is less than 70 deg [35]. To have vertical wall angles, a multipass strategy has been developed [36,37] in which the final wall angle is achieved by a gradual increase of the forming angle in each pass. In multipass ISF, the material is redistributed from the other zones of the sheet to the inclined wall areas and, thus, postponing the onset of excessive thinning [38].

Strategies for single-feature toolpath planning have been the focus of many investigations. The research effort in this field falls into two categories: (1) development of new algorithms for toolpath planning and (2) exploration of the relationship between toolpath parameters and part quality. However, in real practice, the industry requires geometrically complex parts with multiple features. A common method to form complex geometries is to decompose the part’s CAD representation into separate features and generate separate toolpaths for each feature. The challenge with this method is determining the forming order. Features in parts may not be independent of each other. Therefore, individual features must be formed in the correct order to avoid unwanted deformation of already formed features.

Knowledge on feature recognition and forming sequence design is still limited. The available research is only focused on regular features, e.g., a flat or an inclined base with a conical or pyramidal feature on it. For example, Ndip-Agbor et al. [39] proposed to use Z-height-based slicing to recognize individual features. Their Z-height slicing strategy slices the component geometry via a series of XY-planes parallel to the initial plane of the sheet. Features are recognized by checking the relationship between intersection contours after projecting them onto the initial plane. The Z-height slicing strategy recognizes four features for the surface shown in Fig. 1 and suggests forming the inner features first followed by the outer features. However, the Z-height slicing strategy is only applicable to parts with all features formed from flat bases namely “plane-referenced” and cannot be applied to more complex geometries with features formed from curved bases namely “surface-referenced” (see the geometry in Fig. 2 as an example, which is generated by bending the geometry in Fig. 1). Horizontally slicing the surface in Fig. 2 results in discorded contours (see Fig. 3) that make it hard to fracture the surface into formable features. The aim of the present work is to extend the investigations on multifeature toolpath generation to very complex shapes with curved bases and features on it. The proposed concept is demonstrated through a case study by forming an air intake.

The part manufactured in this research is an air intake for a wood burning stove. Wood stoves are used by many people for heating or ambiance, and most modern woodstoves have either catalytic converters or air injection systems to reduce pollution, but they only work when the stove gets hot. It is upon startup that smoke gets into the room because a cold chimney and stove has a natural downflow of air as cold air is denser than the warm air inside a house. Attempts to hold burning paper up to the flue to start an updraft before kindling a starter fire often result in smoke or burned fingers. Placing a starter log in the firebox and letting it burn slowly with the stove door closed and the flue partially opened sometimes works on a mild winter day, but rarely on a well below freezing day; not enough heat can be generated to cause the reversal of air in the chimney. A mass of cold air in the chimney is too hard to push up by a small starter fire, so when the flue damper is opened, the mass of cold air starts flowing down and smoke from the startup fire, even if a starter brick, flows into the room. Most people just deal with the smoke by opening the windows when they start up the woodstove and then try to never let the fire die totally out. Some sources suggest opening up the stove and flue damper fully and letting the warm air in the room warm the stove and chimney until the warm air from the house starts flowing up the chimney. But this can take 30 min or more, and the downdraft through the chimney brings the smell of smokey chimney and/or stovepipe air (e.g., creosote) into the room which can chill and dampen the mood intended to be created by a nice warm fire. For people with lung health issues, even a little smoke or creosote smell is not acceptable, so they have to forgo woodfires. In the developing world where stoves may be the only source of thermal energy, persistent indoor smoke creates a serious health hazard.

To prevent a cold-start wood burning stove from creating smoke that enters the room, Slocum created a patent pending device (the “NOSE”) to function as a directed forced air intake on the chimney’s shaft, as shown in Fig. 4. The intent was to reverse the draft using a hairdryer (or a bellows) blowing air into the air intake for 60 s when starting the stove (patent pending). The upward directed flow pulls air into the firebox below, fanning the startup flame and drawing smoke up the chimney. Once the flame is established, the hairdryer can be removed, and a flapper valve on the NOSE automatically closes.

The first prototype device was manufactured by welding pipe to a rolled-curved flange, which showed efficacy and established interest from friends and neighbors who also lamented that their stoves often smoked upon startup on a very cold morning. But the prototype was far too expensive for production especially given the closure method must be simple and failsafe and not depend on the user to place a cap over the end of the pipe. In addition, a groove for a sealing rope is desired over a fiber sheet gasket. Ideally formed sheet metal or casting would be used for production. But how to prototype the “production design”? Clearly, a rapid prototype plastic part cannot be used, and the price quoted for a direct metal sintered metal part from a local supplier was $3384. For production-scale quantities, ideally formed sheet metal could be used to most likely minimize cost, and hence to be able to prototype in sheet metal was most desirable. The target profile of the air intake, clearly a complex multifeature part, is depicted in Fig. 5. Critical features include an air duct, grooves for air sealing, and a cylindrical mount for connecting the air duct to the chimney. The methodology to form such a complex part will be introduced in Sec. 3, which includes the experimental setup, designed forming geometry and sheet materials. Then, an effort will be made to explore toolpath strategies for successfully forming each individual feature (air duct, seal groove, and cylindrical mount) in Sec. 4.1. Afterward, the optimal forming order will be investigated in Sec. 4.2.

ISF experiments were performed on the DSIF machine (Fig. 6) built at Northwestern University. The sheet was clamped at the edges onto the support frame, leaving an accessible forming area of 190 mm × 190 mm. Both the top and bottom tools were made from tungsten carbide with a 5-mm diameter hemispherical end unless otherwise specified. A six-axis strain gauge load cell (45E15A4, JR3 Inc., Woodland, CA) was mounted behind each tool for measuring forming forces and moments. The motions of the tools were controlled by predefined toolpaths sent to the motion controller (Turbo PMAC, Delta Tau Omron, Chatsworth, CA). Further details about the machine design can be found in Ref. [40] while the control system is described in Ref. [41]. A layer of Teflon-infused grease was applied to both sides of the sheet throughout the forming process to reduce friction in the tool-sheet contact area.

Figure 7 shows the dimensions of the target geometry. These dimensions were determined based on the effective forming area (190 mm × 190 mm) of the DSIF machine, and the maximum achievable wall angle (70 deg) [35] for commonly used alloys in ISF.

The forming of the air intake was investigated using deep drawing quality (DDQ) steel with a thickness of 0.8 mm. DDQ steel has been considered ideal for kitchen appliances for its high ductility. The main characteristic of DDQ steel is its high elongation (>50%).

As defined by Moser [42], a part is a single-feature part if intersecting the CAD surface model with any plane normal to the Z-direction produces only one closed curve. The intersection of the air intake surface with a XY-plane gives multiple closed-contours indicating that the air intake contains multiple features (Fig. 8). Since the intersection of a XY-plane and part surface results in multiple isolated contours, multifeature parts must be divided into separate features and formed in multiple steps.

The objective of this section is to find practical solutions to successfully form each individual feature. For the intended purpose, different toolpaths and materials were examined.

The air duct was formed using a DDQ steel sheet by DSIF. Toolpaths were created using in-house developed toolpath generation software named ampl Toolpaths [42]. It is based on the volumetric adaptive slicing method reported by Malhotra et al. [43] and fully developed by Moser [42]. The tools traveled along spiral toolpaths (Fig. 9) with an incremental depth of 0.2 mm at a speed of 5 mm/s. The result of forming this sheet into the air duct is shown in Fig. 10. No fracture was detected until the part’s completion.

In most studies of the ISF processes, all four edges of the sheet are fully constrained by clamps, but in a recent paper, Leem et al. [44] manufactured a small-amplitude (5 mm) sinusoidal periodic structure using DSIF with only two side edges clamped. Based on this work, the first attempt was to manufacture the arch-shaped structure that resembles the cylindrical mount of the air intake (Fig. 11(a)) from a strip (160 mm × 300 mm) with two open sides (Fig. 11(b)), but with a larger forming depth (48 mm).

The top tool was programmed to move across the strip and downward (Fig. 12). A zigzag transversal toolpath strategy with an incremental depth of 0.2 mm was used. This symmetric toolpath was selected instead of continuous forming from one edge to the other side to avoid high forming forces, large global bending, and asymmetric shape. Forming was first carried out without the bottom supporting tool. Large springback was the major problem in this strategy leading to the failure of the process. Referring to Fig. 13(a), unwanted elastic bending occurred outside the forming region. The elastic recovery after unloading the top tool led to springback (Fig. 13(b)). Since the bending moment increases as the forming depth increases, a significant amount of springback occurred in the current case. The maximum geometric deviation was about 10 mm when the forming depth reached 30��mm.

To prevent the undesirable bending a bottom tool was used as a support in the second attempt. The bottom tool moved along the outer contour of the curved structure while remaining at the initial bottom plane of the sheet (Fig. 14(a)). Tearing failure (Fig. 14(b)) was observed at the sheet edge with this toolpath design. Such failure is possible either because of the sustained friction between the bottom tool and the DDQ strip as the bottom tool repeats its path or because the fillet radius at the transition between the part and the flat sheet is too sharp.

To overcome the problems encountered with the two aforementioned strategies, an attempt was made to form the cylindrical mount with all four edges of the sheet clamped. This forming strategy adds more support to the sheet to prevent it from undesirable global bending, but the sheet is subjected to an additional process; i.e., the manufactured part needs to be trimmed into the final arch-shaped structure after completing the forming process. The target geometry is depicted in Fig. 15 where the non-trimmed region has the same geometry as the desired cylindrical mount, while the trimmed flange region was designed according to the achievable forming area of the DSIF machine and the achievable wall angle of the material. This design can then be manufactured using the DSIF approach, in which the bottom tool moves inward and downward synchronously with the top tool. As shown in Fig. 16, the part has successfully been formed without fracture. Additionally, springback was significantly reduced by having the sheet’s edges fully constrained and not lifting the tools during the forming process. This forming strategy will be implemented to produce the air intake.

To generate the 12-mm-wide and 4-mm-deep grooves, required for a fiberglass sealing rope that is also commonly used on woodstove doors, two forming strategies were experimentally studied to investigate the feasibility of forming the groove. Each of the forming strategies was first examined individually on flat sheets. The better of the two will be implemented to form the seal groove on the curved sheet in the next section. In strategy “A” (Fig. 17), two tools with a 12-mm diameter, the same as the groove width, were used. The top tool moved straight down into the sheet to the controlled depth causing a hemispherical indentation. Simultaneously, it also moved along the surface, creating the groove around the air duct. The bottom tool stayed within the initial plane of the sheet and moved synchronously with the top tool along the inner contour acting as local support. In strategy “B” (Fig. 18), two tools with a 5-mm diameter were used. The groove was formed in two steps: the first step was the same as in forming strategy “A”, the top tool moved downward and along the groove while the bottom tool remained at the initial plane of the sheet and moved in-sync with the top tool along the inner contour. In the second step, the top tool remained at a Z-height of −4 mm (bottom of the groove) and continuously traveled along the previous toolpath trajectory while the bottom tool moved along the outer contour. The bottom tool started at a Z-height of −4 mm and gradually moved upward until it reached the initial plane of the sheet (Z-height of 0 mm).

The experimental outcome of strategy “A” is shown in Fig. 19(a). Due to sheet bending that occurs between the top tool and the fixture (Fig. 19(b)), the attempt to form the groove was unsuccessful. On the other hand, in strategy “B” (Fig. 20), the groove was successfully formed by pushing the material from the unconstrained bending region back to the initial plane of the sheet in the second step (refer to the sketches in Fig. 18). Strategy “B” will be implemented to produce the air intake.

Upon completion of the investigation into the optimal toolpaths for each individual feature, individual feature toolpaths were combined into the final toolpath. The inner features were formed first; i.e., the forming sequence is: (step1) seal groove, and then (step 2) cylindrical mount was tested first. As can be observed in Fig. 21, this sequence resulted in the deformation of the already formed features; i.e., the groove is overwritten by the cylindrical mount. It is evident that the cylindrical mount must be formed first. In the current example of the air intake, a suitable forming sequence should be: (step 1) cylindrical mount, (step 2) air duct, and then (step 3) seal groove. With this sequence, the final product (Fig. 22) was successfully produced using the toolpaths developed in Sec. 4.1.

In step 3, the groove was formed on the cylindrical mount after the first two steps. The toolpath strategy “B” designed in Sec. 4.1.3 needs to follow the curved cylindrical mount surface rather than just stay on a flat plane. In addition, the as-formed cylindrical mount surface may also deviate from the designed shape as a result of springback and unintended deformation caused by the subsequent formation of the air duct. Because of the deviation between the as-formed shape and the designed shape, if one forms the groove simply based on the designed shape, an irregular groove depth may be obtained or may even cause the tools to puncture the sheet. Therefore, in this case, it is necessary to know the shape contour of the cylindrical mount at the end of step 2 to properly position the tools. To accomplish this, direct shape measurements at a few discrete positions along the groove were carried out by slowly moving both the top and bottom tools to approach the cylindrical mount surface, detecting contact by the force sensor, and reading the contact coordinates from the machine’s controller as shown in Fig. 23. The measurement points were located along the forming contours. The toolpaths were determined through interpolations between the measurement points.

As it can be observed, the feature forming sequence suggested by Ndip-Agbor et al. [39] is not applicable to the air intake geometry. As discussed earlier, all features that Ndip-Agbor et al. investigated have flat bases or “plane-referenced”, which is why features can be identified by slicing the part’s surface using XY-planes. All features in their cases can be formed by tools moving along a contour on a horizontal plane and then making a step downward/upward to the next contour. For “plane-referenced” cases, forming the inner features first is beneficial to the geometric accuracy, as this method ensures that every feature is formed from the initial plane of the sheet, thereby guaranteeing contact between the tools and the sheet at the beginning of every feature. However, in the case of the air intake, the groove was formed from a curved base or “surface-referenced.” The groove cannot be distinguished from the cylindrical mount as an independent feature using a series of XY-planes. When forming this kind of feature, toolpath contours are no longer on the same horizontal plane but move up and down according to the curved base. In the current case, since the groove is based on the cylindrical mount, if the groove is formed first, the subsequent cylindrical mount formation will deform the already formed groove.

By calculating the gradient of the “plane-referenced” surface in Fig. 1, it can be observed that the interfaces between features are contour loops that are made up of points that have a gradient of zero (Fig. 24). However, for the “surface-referenced” surfaces shown in Figs. 2 and 5, no such contour loops can be observed. To overcome this impediment, a new strategy for this class of surfaces can be proposed that is based on an analysis of the gradients of the surface. The criterion for determining the type of geometry and its feature forming sequence can be stated as: If each interface between features is a contour loop on which all the points have a gradient of zero, then the geometry satisfies “plane-referenced” condition. For this type of geometry, the innermost feature should be formed first followed by the outer features in the later forming steps. Otherwise, the geometry follows “surface-referenced” rules, in which the outermost feature must be formed first and then designing the inner feature toolpaths based on the outer feature.

After forming, the surfaces of the unclamped and clamped part were scanned using a Romer Absolute Arm with an integrated laser scanner to evaluate the geometric accuracy and springback. Figure 25(b) compares the measured section profile of the unclamped part against the designed geometry along section A–A (Fig. 25(a)). Due to springback, machine compliance, and global bending, geometric deviation of the formed part was as high as 6 mm. Figure 25(c) shows the deviation of the unclamped part from the clamped part. As it can be observed, springback caused by unclamping was about 1 mm. Our previous work of in-situ springback compensation using active displacement control on the forming tool and active force control on the supporting tool [28] reduced the maximum shape deviation amount for various single feature forming cases (cone, fish fin, and pyramid) to 1.2–2.0 mm from the original 4.8–5.7 mm. In this work, springback compensation was not the focus, and hence not applied. Nevertheless, the amount of geometric deviation is similar to those observed in single-feature forming. In our future work, in-situ springback compensation will be investigated for multifeature incremental forming. Figure 25(d) compares the measured thickness distribution against the Sine law prediction based on the measured wall angle. The results are in reasonable agreement. The mismatch in some regions is attributed to material redistribution during multipass forming, the influence of the paint coating thickness, and mismatch between the internal and external surfaces.

The formed part underwent stress-relief annealing before trimming. Annealing was carried out at 600 °C for 1 h and slowly cooled to room temperature. The annealing parameters were selected according to the ASM Handbook [45]. The periphery of the part was constrained by mechanical clamps to prevent shrinkage during annealing. The resulting air intake was cut free from the sheet from which it was formed and placed over a 2-in.-diameter hole in a section of 6-in. sheet metal pipe characteristic of that used with woodstoves whose stovepipe diameters used include 6 in., 7 in., and 8 in. (Fig. 26). The NOSE is attached at least one diameter away from the end of the pipe, so having to deform the pipe by about one-tenth of its diameter to match the radius of curvature of the nose is readily accomplished by the use of steel band clamps. In fact, even though the NOSE had a groove for a fiberglass seal rope, no rope was even needed for this test as the seal was quite good and no leakage detected (e.g., with a thin strip of paper or soap bubbles). This could be due to the fact that the pressure is so low and the dead space in the region between the NOSE cavity and the sheet metal pipe so flow even from any cracks in the attachment interface is into the device and up the stovepipe. As shown in Fig. 26, when a hairdryer is applied to the NOSE opening, which is the intended consumer use case, the paper strips used to detect flow at the stovepipe outlet fluttered strongly.

The manufacture and testing of the functional sheet metal production prototype was very successful and thus demonstrates the capability and suitability of the incremental sheet forming process to produce complex-shaped parts in a small lot production. An air intake with three features has been used as a vehicle to study the toolpath design and toolpath sequence to form multifeature parts. Experimental testing of various toolpath strategies leads to the following conclusions:

1. A proper forming sequence must be considered in ISF for the manufacture of multifeature components. The features in the “plane-referenced” type of geometry should be formed in the order where the inner most features that do not enclose any other features are formed first followed by the outer features that enclose them, while features in the “surface-referenced” type of geometry should be formed in reverse order as compared with the “plane-referenced” type of geometry.

2. The type of geometry can be determined based on the criterion stated in Sec. 4.2 by examining the interfaces between features. If the interface is a closed-loop contour on which every point has a gradient of zero, then the geometry is “plane-referenced”; otherwise, it is “surface-referenced”.

3. When forming the inner feature in the “surface-referenced” type of geometry, toolpaths must be based on the actual surface profile of the outer feature to accommodate for the difference between the as-formed shape and the designed shape.

4. An integrated process of the product design and manufacturing method is needed for innovation; currently, the most approach is experience-based. While this work provides a guideline for rapid forming sheet metal parts with complex geometry, more work needs to be performed to make process planning seamlessly such that a novice in manufacturing processes can navigate the complex manufacturing world with ease to achieve the desired functionality. Future work will also integrate in-situ springback compensation to improve part geometric accuracy.

The authors would like to gratefully acknowledge the support from the U.S. Department of Energy under Award No. 8J-30009-0021C and U.S. Department of Commerce, National Institute of Standards and Technology as part of the Center for Hierarchical Materials Design (CHiMaD) 70NANB19H005.

Conflicts of interest have been declared to the Editor and will be included in a Conflict of Interest Declaration section of the final paper. This article does not include research in which human participants were involved. Informed consent is not applicable. This article does not include any research in which animal participants were involved.

The data sets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.