Incremental Metal Forming Processes in Manufacturing

Abstract

Incremental sheet metal forming (ISMF) has demonstrated its great potential to form complex three-dimensional parts without using component-specific tools against the conventional stamping operation. Forming components without component-specific tooling in ISMF provides a competitive alternative for economically and effectively fabricating low-volume functional sheet metal products; hence, it offers a valid manufacturing process to match the need of mass customization, which is regarded as the future of manufacturing. In ISMF process, sheet is clamped in a fixture/frame with an opening window on a programmable machine, and a hemispherical/spherical ended tool is programmed to move in a predefined path giving shape to the clamped sheet by progressively deforming a small region in incremental steps. Although formability in incremental forming is higher than that of conventional forming, the capability to form components with desired accuracy and surface finish without fracture becomes an important requirement for commercializing the ISMF processes. This chapter presents various configurations developed to incrementally form the sheet metal components, experimental as well as numerical methods for estimating forming limits, procedures for enhancing the accuracy, and methodologies for tool path generation.

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Introduction

Evolution of manufacturing can be broadly divided into manual manufacturing, mechanization, hard automation (mass production), soft automation, and integrated manufacturing. Metal forming processes also have gone through a similar evolution process. Incremental forming is in practice from the day human began processing the metals using manual hammering for making tools and ornaments. Manual manufacturing is carried out in an integrated fashion with many limitations. For example, a blacksmith would have knowledge/information to design, fabricate, deliver, repair/service, and recycle say a plowing tool. Quality of the tool/ornament depends on the skill of technician and repeatability is not guaranteed. In addition, productivity is low. The industrial revolution and development of electrical and hydraulic machines lead to mass production of forming components using dies, resulting in traditional art of incremental processes disappear from center stage except in few cases (Groche et al. 2007). Incremental forming is characterized by small overlapping regions of deformation in desired sequence to form the intended geometry using simple tools. Hence, smaller deformation loads are sufficient at any instance. However, in the recent past, industry has witnessed a renewed interest in incremental forming (bulk as well as sheet metal) processes due to change in consumer psychology, emergence of individualism which led the market towards mass customization, change in market dynamics, reducing product prices and increasing product features and product variety forcing industry to reduce costs in order to stay competitive, and the possibility of developing numerical control machines with complex kinematics. The conventional production methods used in mass production are no longer able to fulfill the challenging demand of flexibility and agility at competitive prices. In incremental forming the shape of product is defined by kinematics of the tools instead of part-specific dies and punches. Tooling costs and subsequent investment in tool storage, space required to store dedicated tools and dies, and cost associated with maintenance of tools are low in incremental forming. Based on the surface area to volume ratio of material being deformed, incremental forming processes can be broadly classified into incremental bulk metal forming (IBMF) and incremental sheet metal forming (ISMF). It is well known that in IBMF, surface area to volume ratio is smaller than that of ISMF. This chapter will discuss the developments related to ISMF only.

Incremental Sheet Metal Forming and Configurations

Sheet metal forming covers a variety of processes wherein shearing, bending, stretching, and drawing or their combinations are used to produce parts for a wide variety of applications. Most of the conventional sheet metal forming operations require component-specific and costly tooling, and their design and fabrication add to the lead time. Hence, these forming processes are suitable for mass production to offset for the tool costs. Societal changes impacted manufacturing including other engineering fields. Earlier industrialized economies were on mass production; however, a combination of advances in technology and information is making it increasingly possible to manufacture the customized products. In the competitive world market, customers are demanding for more flexible and personal design in quality, performance, services, and aesthetics of the products with approximately same cost (if not lesser) and quality (if not higher). To be competitive in the global economy and to satisfy customer demand without much lead time, majority of manufacturers are using computer-aided tools such as computer-aided design (CAD), computer-aided engineering (CAE), computer-aided process planning (CAPP), computer-aided manufacturing (CAM), computer-aided inspection (CAI), etc., leading to integrated manufacturing without any physical boundaries between different functional departments of an organization. Development of neutral data exchange standards led to proper integration of CAX tools. To be competitive in mass customization era, one shall be able to convert the ideas quickly into products using flexible and rapid prototyping and manufacturing as well as computer-aided technologies. In addition, some traditional technologies also may have to be used. For mass customization (manufacturing system shall be agile to consumers with customized products at mass production prices with equivalent or higher quality and lesser lead time), manufacturing processes have to be flexible with minimum change over time and tooling costs. Manufacturers worldwide now attempt to grow by competing on product differentiation as much as on price. This trend leads to short product life cycles, low volume of a chosen product model, and profitability that is as much dependent on the speed at which new models and products are introduced as on the control of direct cost. This trend in manufacturing sector led to the development of flexible manufacturing technologies including layered manufacturing and particularly in the area of machining to changeover between different products with the help of fully automated systems. However, developments in the area of flexible forming (Allwood and Utsunomiya 2006) have not kept pace with machining mainly because of the requirement of component-specific tooling in many of the operations.

Conventional sheet metal forming operations require component-specific and costly tooling, and their design and fabrication add to the lead time. Incremental forming is one of the technologies that have emerged as an alternative to some of the conventional sheet metal forming processes for mass customization. Incremental sheet metal forming (ISMF) is commonly regarded as a die-less sheet metal forming process which can form complex three-dimensional parts using relatively simple tools. It is receiving attention from the engineering community due to its flexibility and low cost. This unique combination enables the rapid prototyping of functional sheet metal parts before mass production. In addition, it offers a valid manufacturing process to match the need of mass customization, which is regarded as the future of manufacturing (Wulf 2007). In ISMF process, sheet is clamped in a fixture/frame with an opening window on a commercial computer numerical control (CNC) machine, and a hemispherical/spherical ended tool is programmed to move in a predefined path giving shape to the clamped sheet by progressively deforming a small region in incremental steps. As the forming tool moves and deforms a small portion at a time, the overall time to produce one component is comparatively more, but for small batch sizes and prototyping, ISMF demonstrated its potential of being cost competitive. Existing experimental configurations for incremental sheet metal forming can be broadly classified into two categories: with (full/partial) and without die/pattern (Jeswiet 2001) support.

Negative die-less incremental forming, also known as single-point incremental forming (SPIF), is the earliest form of incremental forming. Figure 1 shows the block diagram of SPIF with a spherical tool. In SPIF, tool generally comes in contact with the sheet close to the clamped boundary at a programmed location and moves down by an amount equivalent to chosen incremental depth or a fraction of that depending on the type of tool path used. Figure 2a, b depicts the contour and spiral tool paths. In both the cases, tool moves along the programmed path peripherally.

Fig. 1

Single-point incremental forming (SPIF)

Fig. 2

Contour and helical tool paths

In contour tool path, tool moves down by an amount equivalent to incremental depth at the starting of each contour, whereas in spiral tool path, tool gradually moves down and completes the downward movement equal to incremental depth by the time tool completes 360° movement along the spiral, and the same can be clearly seen in Fig. 2a, b. Note that in contour tool path, tool disengages at the end of each contour, moves to the starting point of next contour, and plunges down equivalent to incremental depth from its original location at the end of earlier contour whereas in case of spiral tool path, tool disengages only after completely forming the component. Figure 2c, d shows the components produced using contour as well as spiral paths, and a distinct mark connecting all the start/end points of each contour can be noticed in case of contour tool path. Bending between the clamped region and component periphery can be clearly seen from these figures and is one of the reasons of inaccuracy. Allwood et al. (2005) have designed and built a dedicated SPIF machine at Cambridge University and its block diagram is shown in Fig. 3. They have designed a tool-mounting system that allows free rotation of tool passively and for ease of mounting and un-mounting of tools. Provision for measurement of load(s) is provided by mounting the fixture on load cells.

Fig. 3

Block diagram of SPIF developed at Cambridge University (Allwood et al. 2005)

Positive die-less incremental forming, also referred to as two-point incremental forming (TPIF), is another variant of ISMF and is known to be first attempted by Matsubara (2001). In this process (Fig. 4), clamped sheet can move up and down. One can clearly see from Fig. 4 that the sheet metal is restrained at two locations (other than the clamping), i.e., at one location by forming tool and the second location is the static support. This static support can be a partial die or a full die. Full die can be either a negative one as shown in Fig. 4b or a positive die. Most of the above configurations are realized by mounting the required tools on stand-alone NC machines. Amino Corporation of Japan has developed a commercial machine for incremental sheet metal forming with pattern support and is shown in Fig. 5. Note that only movements in two directions are provided to tool and the third movement necessary to form the component is provided to the fixture, and in addition, the fixture can move up and down.

Fig. 4

Two-point incremental forming (TPIF) configurations: (a) partial support and (b) full support

Fig. 5

Configuration of commercial machine developed by Amino Corporation (http://www.aminonac.ca/product_e_dieless.asp)

Recently, a variant of TPIF (Fig. 6) in which, instead of partial or full die, another independently controlled forming tool is used which provides further flexibility to the process as features on both the sides of initial plane of the sheet can be formed. This variant is named as double-sided incremental forming (DSIF) . Here, the deforming and supporting roles of each tool will keep changing depending on the geometry being formed at the instant and the geometry that has to be formed later. This configuration enhances the complexity of the components that can be formed and reduces many of the limitations associated with incremental forming.

Fig. 6

Double-sided incremental forming (DSIF)

Modifications of the process setup have been made by various research groups, for example, to form doubly curved surface, Yoon and Yang (2001) have used a movable punch. Their setup (Fig. 7) consists of a movable punch and a supporting tool that has four hemispherical-headed cylindrical pins arranged in a grid. The sheet is placed between punch and supporting tool without clamping; hence, the deformation in this arrangement is mainly due to bending. The downward movement of punch bends the sheet, and the movement of sheet on the support tool changes the deformation location. Each bending operation produces a spherical shape and their combination gives doubly curved surface. The sequence of operations in this process is shown in Fig. 7c. Required curvature (R), during the deformation, is controlled by selecting the downward movement (Δz) of the punch from the initial plane of the sheet and grid size (2a) and is given by:

Fig. 7

Setup proposed by Yoon and Yang (2001) to form doubly curved surface

$$ R=\frac{a^2}{2\ast \Delta z} $$

(1)

Meier et al. (2011) have used two robots (Fig. 8) to control different tools on either side of sheet and termed the process as duplex incremental forming (DPIF). They used position control for the forming tool and combination of force and position control for the support tool to maintain continuous contact. Many people (International Patent 1999; Jurisevic et al. 2003; Emmens 2006) have tried water jet as a forming tool along with die/pattern support. Note that water jet system is force controlled, whereas the NC tool systems generally used for incremental forming are displacement controlled.

Fig. 8

Configuration of duplex incremental forming

The first patent on incremental sheet metal forming is by Leszak (1967) way back in 1967. In this invention, a turning machine with a backing plate and a pair of clamping rings (to hold the sheet) mounted on the machine turntable and a roller tool mounted on carriage as shown in Fig. 9 is used. The sheet is rotated on turntable, while the roller moving on the carriage applies pressure on the sheet. This methodology can only be used to produce axisymmetric components. More recently, Emmens et al. (2010) reviewed the available literature, especially patents, available on different variants of ISF. Starting from the inception the chronological developments in ISF have been summarized by them. It can be seen from their review that all patents are on different forms of SPIF and TPIF with or without partial or full dies (four variants as shown in Figs. 1, 4, and 6). All such kinds of ISF process variants are able to form simple to complex geometries but having features only on one side of the initial plane of sheet metal workpiece.

Fig. 9

Schematic showing the apparatus used by Leszak (1967)

First comprehensive review article on ISMF has appeared in Annals of CIRP by Jeswiet et al. (2005a). Based on the work presented in literature, they provided many useful observations and guidelines for incremental forming, as summarized below:

• Formability in SPIF increases with decrease in tool size as well as incremental step-down.

• Anisotropy has an influence on formability, greater formability being achieved with smaller diameter tools in the transverse direction.

• Formability decreases with sheet thickness.

• Large incremental step-down increases the roughness.

• Increase in the incremental step-down and tool size increases forming forces.

• There is a limitation on the maximum draw angle that can be formed in one pass; hence, multiple pass methodologies are preferred for forming large angle components.

• Spiral tool path is preferred over contour one, but the tool path generation is difficult.

Most of the attempts on all variants of ISMF are experimental in nature. Experimental observations/measurements of both single- and two-point incremental forming have shown that using spiral tool path for simple and reasonably complex geometries with small to moderate wall angles, deformation is close to plane strain, i.e., strain in one direction is zero. Material does not deform significantly in the peripheral direction, i.e., strain is negligible in the peripheral direction (tool movement direction). Assuming that the strain in the peripheral direction is principal one, the thickness strain (reduction in thickness during the deformation) has to be equal to the meridional strain (increase in length) with opposite sign to satisfy the volume constancy. Based on the above discussion, for a constant wall angle cone shown in Fig. 10, the relationship between the wall thickness after deformation and the original sheet thickness in terms of wall angle can be written as

Fig. 10

Sine law for thickness prediction in incremental forming

$$ {t}_f={t}_0 \sin \left(90-\alpha \right) $$

(2)

The above relation is very well known as sine law in ISMF. In case of continuously varying geometries, thickness can be obtained at any location by using the local wall angle. However, thickness measurement of a wide variety of components formed using single- and two-point incremental forming has shown that there is a considerable difference between the measured values and those predicted by sine law. Note that the sine-law expression for predicting the thickness is derived under the ideal deformation conditions as shown in Fig. 10 where there is no radial displacement of any through-thickness section of the material. Thickness calculated using the sine law (Eq. 2) can only serve as a rough and an average approximate estimate.

To understand the above mentioned conclusions and insight into various aspect of ISMF, details of each aspect to a reasonable extent are presented in this chapter.

Formability and Thinning

Literature (Jeswiet et al. 2005a) indicates that formability in incremental sheet metal forming is much higher than the one reported in deep drawing. Most of the studies related to formability in ISMF are experimental in nature. Capability to form components with desired accuracy and surface finish without fracture becomes an important requirement for commercializing the ISMF processes. Accurate prediction of formability helps in assisting better design of part geometry and corresponding tool path. It has been well accepted that conventional forming limits are not suitable for incremental forming even when path dependency of strains are considered. The forming limit of a sheet metal in conventional forming is defined to be the state at which a localized thinning of sheet initiates when it is formed into a product shape in a stamping process. Formability of sheet metals in conventional forming is at present characterized by the Forming Limit Diagram (FLD) introduced in 1960s by Keeler and Backhofen (1964). The forming limit is conventionally described as plot of major principal strain vs. minor principal strain. It must cover as much as possible the strain domain which occurs in industrial sheet metal forming processes. The curves are established by experiments that provide pair of the values of limiting major and minor principal strains obtained for various loading patterns (equi-biaxial, biaxial, plane strain and uniaxial). A schematic representation comparing the forming limit curves of conventional forming (stamping/deep drawing) with that of single-point incremental forming is shown in Fig. 11a. It can be clearly seen that the forming limit curve for incremental forming is a straight line with a negative slope in the positive region of minor strain whereas the conventional one is present in both the regions of minor strain. Deformed grid obtained during incremental forming shown in Fig. 11b, c indicates that the deformation that occurs varies from plane strain to biaxial stretching.

Fig. 11

Schematic representation of forming limit curve in SPIF against conventional forming

Iseki and Kumon (1994) have proposed an incremental sheet metal stretch test (Fig. 12a) to estimate the forming limits in incremental forming using a rolling ball and formed a groove shown in Fig. 12b. It can be seen that both plane strain and biaxial stretching states are captured during the experiment. Shim and Park (2001) experimentally investigated the formability (of fully annealed Al-1050 sheets) in incremental forming (IF) using a tool having freely rotating ball tip similar to that used by Iseki and Kumon (1994) and generated strain-based forming limit curves (FLC) for incremental forming by measuring the major and minor strains using a deformation grid. Different tool path strategies are used to study various strain paths and their suitability to generate forming limit curves for incremental forming. They recommended an alternate imposition of vertical and horizontal displacements to form a deep straight groove (similar to that formed by Iseki and Kumon (1994)) at the central portion of a square specimen clamped peripherally. Recommended methodology is depicted pictorially in Fig. 13. It is realized by them also that biaxial stretching occurs near the start and end of groove and plane stretching occurs along a straight path and tendency of cracking is reported to be greater at the ends due to biaxial stretching. They formed components having different shapes starting from triangular opening to octagonal opening and then a circular opening and observed that deformation is close to equi-biaxial at the corners and plane strain in the straight regions. Failure conditions of the abovementioned geometries were in good agreement with the forming limit curve generated by them using the groove test.

Fig. 12

Groove test to obtain formability in incremental forming (Iseki and Kumon 1994): (a) schematic and (b) formed groove

Fig. 13

Groove test: (a) tool path and (b) forming limit curve (FLC)

Kim and Park (2002) have used the groove test mentioned above to study the effect of different process parameters on the formability of fully annealed Al-1050 sheets by conducting experiments, and their trends are presented in Fig. 14. It is also reported that the use of freely rotating ball tool enhances the formability as the friction along the tool work interface reduces. Formability decreases with increase in tool diameter and incremental depth. In addition, they carried out finite element analysis using PAMSTAMP – explicit to understand the effect of process parameters on the deformation.

Fig. 14

Variation of formability with tool diameter and incremental depth during groove test

Filice et al. (2002) have proposed experimental tests aiming at achieving different straining conditions that occur in incremental forming to study the formability. They formed a truncated pyramid to obtain the conditions of plane strain deformation and proposed a geometry with two straight grooves perpendicular to each other (tool path shown in Fig. 15) to achieve almost pure biaxial stretching condition at the center of the geometry. In addition, they proposed to form truncated cone geometry with a spiral tool path explained earlier to achieve the conditions between plane strain and biaxial states. In all the cases, they formed the components using hemispherical ended tool (not a freely rotating ball tool) till failure and generated the forming limit curves for incremental forming. Later, Fratini et al. (2004) have carried out experimental study to understand the effect of material properties on the formability in SPIF for commonly used sheet materials, namely, copper, brass, high-strength steel, deep drawing quality steel, AA1050-O, and AA6114-T4, in sheet metal industry. They measured strain-hardening constant (K), strain-hardening exponent (n), normal anisotropy index (R), ultimate tensile strength, and percentage elongation (%PE) of all the materials by conducting tensile tests. Truncated cones and pyramids of varying wall angles were formed till failure, to study the influence of abovementioned process parameters on formability of incremental forming and perform statistical analysis. Based on the analysis, they concluded that strain-hardening exponent, strain-hardening constant, and normal anisotropy index have high, medium, and low influence respectively. Ultimate tensile strength has negligible influence, whereas percentage elongation has medium influence. Among the interactive terms, only interaction between strain-hardening exponent with strain-hardening constant and percentage elongation are significant, whereas the others are insignificant. In addition, they reported the influence of same process parameters on conventional forming limit diagram also.

Fig. 15

Tool path to achieve biaxial stretching at the center of two perpendicular straight grooves

Ham and Jeswiet (2006) used two fractional factorial designs of experiments to study the effect of process variables on formability of AA3003. First set of design (wall angle, vertical step size/incremental depth, base/component opening diameter, component depth, feed rate, and spindle speed) indicates that feed rate, spindle rotation speed, step size, and forming angle decide whether a part can be successfully formed or not. It was also reported that faster spindle rotation speed improves formability. Second set of experiments (vertical step size, sheet thickness, and tool diameter) reveals that vertical step size (they used 0.05, 0.127, and 0.25 mm) has little effect on the maximum forming angle. Material thickness, tool size, and the interaction between material thickness and tool size have a considerable influence on maximum forming angle. Later they (Ham and Jeswiet 2007) used Box-Behnken design of experiments to study the forming limits in SPIF. They considered five parameters, namely, material type (three different aluminum alloys), thickness, formed shape (cone, pyramid, and dome), tool size, and incremental step size, at three levels for the experimentation. Material type has significant effect; the one having lower ultimate tensile strength will have greater formability. Shape also has some influence on the formability as the type of deformation is dependent on geometry. Allwood et al. (2007) conducted experiments using Al 5251-H22 sheets to explain the reasons behind higher forming limits observed in incremental forming and shown that the lines joining corresponding points on the upper and lower surfaces of sheet formed by SPIF remain almost normal to the surface in meridional plane (Fig. 16), indicating that the deformation in this plane is predominantly pure bending and stretching. Whereas measurements indicated that there is a relative movement between corresponding points parallel to the tool movement direction, suggesting that shear occurs in this direction. Above observations indicate that an appreciable amount of through-thickness shear occurs during incremental forming in the direction parallel to tool motion. Due to the presence of through-thickness shear, the tensile stresses responsible for fracture get reduced; hence, formability is higher in incremental forming.

Fig. 16

Deformation behavior in meridional plane

Ambrogio et al. (2005a) made an attempt to predict the sheet thinning in SPIF using finite element analysis (implicit) and compared with that of experimental values and concluded that the predictions using FEA as well as measured experimental values are less than that of sine-law thickness prediction over most of the deformed region. In addition, experimental values are lower than the values predicted using FEA. Ambrogio et al. (2006) used a force-based strategy that can be used online to predict formability/failure. They measured the vertical component (thrust force on the tool) of the forming force by mounting the incremental forming fixture on top of a dynamometer similar (Chintan 2008) to that as shown in Fig. 17a. They used the force gradient (monotonically decreasing curves, Fig. 17b) as a criterion for failure. Later, Szekeres et al. (2007) observed the similar force trends while forming cone but not for pyramid shape; hence, they indicated that tool force measurement may not be very reliable. Many researchers have conducted experimental study on the forming forces by forming a cone using SPIF (Jeswiet et al. 2005b; Jeswiet and Szekeres 2005; Duflou et al. 2005, 2007a, b, 2008a; Filice et al. 2006; Ambrogio et al. 2007a; Aerens et al. 2009; Henrard et al. 2011). It is reported that the forming forces increase with tool diameter, wall angle, incremental step size, and sheet thickness as shown in Fig. 18. Increasing direction of the parameter is shown using arrow. Note that force in the tool axial direction reaches peak value and then attains steady state in all cases.

Fig. 17

Force measurement and force trend before failure

Fig. 18

Variation of vertical component of force with (a) tool diameter, (b) wall angle, (c) incremental depth, and (d) sheet thickness

To reduce the number of experiments required to test the forming limits, Hussain and Gao (2007) considered an axisymmetric component with varying wall angles along the depth direction. The cross section of the component parallel to the incremental depth direction is chosen as circular profile, and the same is shown schematically in Fig. 19. Components are formed till the failure depth and quantified the formability as wall angle at that height. Later conical components with failure angle obtained using varying angle components mentioned above are formed, and it is concluded that formable wall angles obtained by forming conical cups are more accurate but time-consuming. This work is extended (Hussain et al. 2007a) by forming components with different cross-sectional profiles, namely, elliptical, exponential, and parabolic, and found that the forming limits are different for different profiles (lowest for circular and highest for exponential). Based on the above observation, they concluded that the forming limits depend on history of forming in ISMF.

Fig. 19

Funnel geometry to evaluate formability

Hamilton and Jeswiet (2010) studied and analyzed the effect of forming at high feed rate and tool rotational speed in SPIF. They concluded that tool rotational speed does not have significant effect during SPIF and forming at high feed (5,080–8,890 mm/min) produced similar thickness distribution as of low feed. Thus, higher feed rate (less forming time) can be used to reduce the forming time, making ISMF process suitable for industrial applications. During the study of the microstructure, it was observed that the change in grain size after forming is dependent on the step size, spindle rotation speed, and feed rate. Cao et al. (2008) presented a comprehensive review along with the advances and challenges in incremental forming including formability. They used Oyane criterion (Oyane 1980) along with FEA as well as simple force equilibrium analysis to predict the forming limits. The Oyane model includes the effect of hydrostatic stress history on occurrence of the ductile fracture as given below:

$$ I=\frac{1}{c_2}{\displaystyle {\int}_0^{{\overline{\varepsilon}}_f}\left({c}_1+\frac{\sigma_m}{\overline{\sigma}}\right)\ d\overline{\varepsilon}} $$

(3)

Here constants c ₁ and c ₂ have to be obtained experimentally. They conducted the necessary experiments and obtained the values of c ₁ and c ₂ for AA5052-O material. The FLC experiments for the SPIF were carried out on a CNC machining center using straight groove geometry and tool path similar to the one shown in Fig. 13. Malhotra et al. (2012a) analyzed the fracture behavior in SPIF by using a fracture model in FEA to predict forming forces, thinning, and fracture. The material model was calibrated using the forming force history for a cone shape. The model was validated using a funnel shape (Hussain and Gao 2007; Hussain et al. 2007a) (varying wall angles as depth increases) by comparing experimental forming forces, thinning, and fracture depths with predicted values from FEA. It was concluded that fracture in SPIF is controlled by both local bending and shear. Local stretching and bending of sheet around the hemispherical tool causes higher plastic strain on the outer side of the sheet resulting in increased damage on the outer side as compared to the inner side. Greater shear in SPIF only partially explains the increased formability as compared to conventional forming. The local nature of deformation in SPIF is the root cause of increased formability as compared to conventional forming.

Bhattacharya et al. (2011) conducted experiments to study the effect of incremental sheet metal forming process variables on maximum formable angle. Box-Behnken method is used to design the experiments for formability study. From the experimental results it was concluded that during incremental forming, the formability decreases with increase in tool diameter. The formable angle first increases and then decreases with incremental depth. The variation in the formable angle is not significant in the range of incremental depths that are used in their work to produce good surface finish. To predict thickness during the SPIF, a simple model is proposed considering the overlap in deformation (Fig. 20a) and thus estimated the deformed sheet thickness more accurately. They used the proposed thickness prediction model along with a simple analytical model based on the force equilibrium to obtain the stress components at any section during SPIF. Ratio of mean stress value to the yield stress value for all the experiments conducted for formability study at the maximum formable angle is calculated by them using the force equilibrium analysis, and its value is found to be very close to unity at all conditions, hence, used the same as the failure criterion. Maximum formable angles predicted using a triaxiality criterion mentioned above for plane stretching conditions are in very good agreement with the experimental results (Fig. 20b). Duflou et al. (2007b, 2008a) have demonstrated that the use of local heating (using NdYAG laser) ahead of tool reduces the forming forces and enhances the formability of the material. They used TiAl6V4 sheets of 0.6 mm thickness. Cone with 56° wall angle and 30 mm depth is successfully formed with local heating, whereas the maximum angle that could be formed without heating using the same parameters is only 32°.

Fig. 20

(a) Schematic showing the consideration of overlap in thickness calculation. (b) Comparison of predictions of formable angle using triaxiality criterion with the experimental results

Park and Kim (2003) studied the formability of annealed aluminum sheet by forming different shapes using both positive and negative incremental forming. While forming a truncated pyramid with negative single-point incremental forming, cracks occurred at the corners due to biaxial deformation, but no cracks appeared during positive forming (in positive forming a suitable jig support is used – Fig. 21). Strain measurements with the help of a grid indicated that in negative forming both plane strain and biaxial stretching are present whereas in positive forming only plain strain stretching is present. Further extending their work to more complex geometries using positive forming, they concluded that the formability in positive incremental forming is better as the deformation occurs under plane strain conditions in addition to providing the capability to form sharp corners. Designing of support jig is a challenging task and depends on the components geometry. One can make use of pattern support to replace the jig necessary during positive incremental forming.

Fig. 21

Tool configuration used to form truncated pyramid in positive forming

Recently, Jackson and Allwood (2009) have conducted experimental study to explain the deformation mechanism in SPIF (Fig. 22a) and TPIF (Fig. 22b, with full pattern support) to that of forming the same geometry using conventional pressing operation and to evaluate the validity of sine law and in turn to relate the thickness measurements to the deformation mechanics. For the abovementioned purpose, they used copper plate of 3 mm thickness, cut into two halves. Cut section passes through the center of the component. Faces of each half are machined flat and 1.5 mm × 1.5 mm grid pattern was marked. Later these plates were brazed together and used for forming conical components by SPIF, TPIF, and pressing. After forming the components are heated to separate the two halves. Then the formed geometry, thickness, and strains are measured. One half of the component with grid pattern is shown in Fig. 22c. Note that the measurements of abovementioned quantities can be carried out before joining the sheets together and after separating them once the component is formed. Hence, evolution of strain at any instance cannot be measured, but the final strains representing the final geometry with respect to initial geometry can be measured. Strain values were calculated by measuring the relative movement of the points of intersection of the grid before and after the deformation. Local coordinate system shown in Fig. 22c is used for strain measurement, where m, θ, and t are meridional, tool movement, and thickness directions, respectively. After analyzing the measured thickness, geometry, and strains, they concluded that in both SPIF and TPIF, deformation is a combination of stretching as well as shear and the same increases with the successive tool laps in the meridional direction with the greatest strain component being shear in the tool movement direction and shear occurs perpendicular to the tool movement direction in both SPIF and TPIF but is more significant in SPIF. Deformation mechanism in SPIF and TPIF is significantly different from the idealized mechanism of shear spinning on which sine-law thickness is proposed. One can easily realize the same in SPIF as there is no support similar to spinning but the support is present in TPIF. Critical analysis of measurements indicated that grid lines in the thickness direction more or less remain axial in ideal mechanism, but not after TPIF. In addition, circumferential shear is present in TPIF which is absent in the ideal mechanism. Above observations clearly indicate that there is a radial movement of through-thickness sections during deformation; hence, there is a significant difference in measured and ideal thickness values in both the processes.

Fig. 22

Incremental forming configurations used for experimental study and grid for measuring

Single-pass SPIF can successfully form wall angles up to 70° for various aluminum as well as steel sheets of 1 mm initial thickness (Jeswiet et al. 2005a) using suitable process parameters such as incremental depth, tool diameter, and forming speed. However, forming a wall angle close to 90° using SPIF is challenging. There have been a few attempts to increase the maximum formable angle by using multi-pass single-/two-point incremental forming (Hirt et al. 2004; Skjoedt et al. 2008; Duflou et al. 2008b). Hirt et al. (2004) proposed and implemented a multi-pass forming strategy with partial support die (Fig. 23) to form components with steep walls which cannot be formed using single-pass incremental forming. The stages involved in their strategy are:

Fig. 23

Multistage forming strategy using TPIF to increase formable wall angle

• 1. First, form the shallow angle component with final desired component height (Fig. 23b).

• 2. Next, the wall angle is increased in steps of 3–5° by moving the forming tool alternatively upwards and downwards as shown in Fig. 23c, d.

Using the above strategy, first, they made a pyramidal component with 45° wall angle in the stage 1 and then formed up to 81° wall angle. Thickness measured by them revealed that the thickness at any location along the wall is more than the thickness predicted by sine law for 81°. This can be attributed to the availability of more material as the component is formed to the final desired height in stage 1 and upward movement of tool in later stages. In addition, they performed finite element analysis along with damage criterion of Gurson-Tvergaard-Needleman to predict the damage evolution during incremental forming process and predicted that the damage increases with increase in tool diameter as well as incremental depth.

Skjoedt et al. (2008) proposed a five-stage strategy as shown in Fig. 24 to form a cylindrical cup with a wall angle of 90° with height/radius ratio equal to one but the components fractured in either the fourth stage or fifth stage. They used two approaches, namely, Down-Down-Down-Up (DDDU, Fig. 24a) and Down-Up-Down-Down (DUDD, Fig. 24b). They demonstrated that the thickness variation is dependent not only on tool path but also on its direction (downwards or upwards) in each stage. In one of the above strategies, i.e., DUDD, component failed in the fourth stage, while in the other one, i.e., DDDU, it was successful up to the fourth stage, but the component formed did not confine to the designed shape. In addition, they used the profiles for all the stages with the required component depth similar to that used by Hirt et al. (2004). Note that the component height is constrained by the jig used in TPIF (Hirt et al. 2004) but the material shifts down during down pass and results in more depth than the required component in SPIF.

Fig. 24

Multi-pass strategies used by Skjoedt et al. (2008)

Duflou et al. (2008b) stated that the only way to achieve large wall angles was to aim for material redistribution by shifting material from other zones in the blank to inclined wall regions. They deformed the region of the workpiece area that was originally unaffected in single-pass SPIF tool paths (Fig. 25) to form vertical walls without leading to failure. Their tool paths always moved from the periphery towards the center of the sheet and all the stages are to a depth of required component. Hence, the stepped features (Abhishek 2009) have resulted using the tool path used by (Duflou et al. 2008b). Multistage incremental forming consists of a number of intermediate stages to form the desired geometry. To propose intermediate stages, it is very important to predict the shape that actually forms after each intermediate stage to select the profile for next stage as well as the direction of tool movement (i.e., in-to-out or out-to-in). It is very well known that when the tool is moved from out-to-in during any stage, the material which is present ahead of it moves down like a rigid body. The stepped feature formed at the bottom of the final component (Skjoedt et al. 2008; Duflou et al. 2008b) during multistage SPIF is a result of accumulated rigid body translation during the deformation of the intermediate shapes. Abhishek (2009) and Malhotra et al. (2011a) have proposed a methodology using a combination of out-to-in (OI) and in-to-out (IO) tool paths (Fig. 26) in one pass and by selectively deforming certain regions in an intermediate pass. Here, “OI tool path” refers to the tool moving from the outer periphery of the sheet towards the center of the sheet while moving down in the z-direction. The “IO tool path” refers to the tool moving from the center of the sheet towards the outer periphery while moving up or staying at a constant depth in the z- direction. They (Abhishek 2009; Malhotra et al. 2011a) used a seven-stage strategy to successfully form a cylindrical component with height to radius ratio equivalent to one. For each tool path the first number denotes the stage number, the number after the dash denotes the order of execution, and the arrow shows the direction of tool path. Note that some regions are not deformed in stages 4, 5, and 7. Abhishek (2009) has extended the methodology to make hemispherical and ellipsoidal components. Note that stepped features are avoided in the works of Abhishek (2009) and Malhotra et al. (2011a). Very recently, rigid body movement during in-to-out and out-to-in tool paths is modeled analytically and validated using finite element simulation for different materials (Xu et al. 2012).

Fig. 25

(a) Five stages of tool path to form vertical walls. (b) Stepped features (Abhishek 2009)

Fig. 26

Successful multistage strategy to form vertical wall without formation of stepped features: (a) tool path, (b) profile comparison, and (c) sectional view of component

Kim and Yang (2000) compared two double-pass strategies for SPIF. One was based on linear blending, i.e., the intermediate shape was calculated to be at a height of 0.5 times the final height. In the other approach, they calculated the intermediate shape so that highly deformed regions in the final shape were subjected to lesser deformation in the intermediate shapes. Their methodologies yielded better thickness distributions than single-pass forming. They concluded that the double-pass forming method results in improved formability as well as higher mechanical strength of the formed component. Young and Jeswiet (2004) experimentally studied the effect of single-pass and double-pass forming strategies on the thickness distribution in forming a 70° wall angle cone. They concluded that double-pass strategy causes marked thinning at the flange near the backing plate. In addition, they concluded that the sine law will not predict the thicknesses correctly when multiple passes are used for forming angles exceeding 40°. For better understanding of formability in terms of wall angle for different materials and process variables, a Table 1 is provided below:

Table 1 Maximum formed wall angle for various parameters

Accuracy and Surface Finish

Accuracy of the component during incremental sheet metal forming is affected by bending of sheet between the clamped boundary and component opening, continuous local springback that occurs as soon as tool moves away from a point, and global springback that occurs after the tool retraction and unclamping of the component. Comparison between the ideal geometry and the possible final geometry during SPIF due to the abovementioned effects is schematically represented in Fig. 27. One can reduce the deviation between the ideal and formed geometries due to bending that occurs close to clamped boundary in SPIF by providing a suitable support/backup or can be eliminated by using a pattern support.

Fig. 27

Schematic representation of ideal and formed profiles

Hirt et al. (2004) proposed an iterative method to improve geometrical accuracy. First, the formed component was measured using coordinate measuring machine (CMM) and compared with intended geometry. Deviation vector between measured and target points is generated and the same is used to modify the tool path. Ambrogio et al. (2004) have studied the effect of tool diameter and incremental depth on the geometrical accuracy in SPIF by conducting series of experiments and concluded that the accuracy is better while using smaller diameter tools and lower incremental depth. Note that the use of lower incremental depth increases the forming time. In addition, they also stated that elastic springback and bending in absence of a backing plate/die is the major cause for geometrical inaccuracies. Importance of a proper tool path for obtaining desirable geometrical accuracies in the formed component is emphasized, and a modified tool path is proposed to enhance the accuracy by forming a component with higher wall angle than the desired angle up to some depth and then forming the remaining component with the desired angle. Conical components formed using the above strategy enhanced the accuracy by reducing the bending near component opening (Fig. 28). Note that the modified tool path with larger angle than the desired starts deforming the sheet at somewhat distance away from the clamping region than the ideal tool path. Ambrogio et al. (2007b) studied the influence of process parameters (tool diameter, step size, sheet thickness) on springback and pillow effect (Fig. 29) in SPIF by forming a truncated pyramid with square base. Pillow effect is compensated by overbending. This in turn increases the bending at the opening region although it reduces the deviation in the wall region.

Fig. 28

Schematic representation of tool path strategy adopted by Ambrogio et al. (2004) to reduce bending in SPIF

Fig. 29

Schematic illustrating bending and pillow effect observed during SPIF

Tanaka et al. (2007) have used a backup tool that comes in contact with the work piece intermittently (following sinusoidal path) during SPIF. Finite element analysis has demonstrated that this strategy reduces the residual stress gradients and in turn enhances the component accuracy. Duflou et al. (2007b, 2008a) made an attempt to improve the geometrical accuracy by applying local heating principle. Improvement in geometrical accuracy was realized by achieving more localized forming effect (due to local heating) and reduced residual stress levels which reduces the springback effects (Fig. 30).

Fig. 30

Schematic to show the effect of local heating on accuracy

Allwood et al. (2009) suggested a closed-loop control strategy (Fig. 31) that uses spatial impulse responses to enhance the product accuracy in single-point incremental forming with feedback provided by a stereovision camera. They used a Weibull distribution curve to impulse responses from a set of experiments for a conical component and then used the same to form similar conical components with ± 0.2 mm accuracy prior to unclamping the component. They measured and reported that the formed component deviate around 2–3 mm from that of intended, without using the feedback. Their strategy requires an iterative process in which a few trials were first conducted for a component, and based on the spatial impulses obtained, tool path compensation was done to obtain a better component.

Fig. 31

Block diagram of closed-loop strategy proposed by Allwood et al. (2009)

Behera et al. (2013) proposed a compensated tool path generation methodology for SPIF to improve the accuracy by using multivariate adaptive regression splines (MARS) as an error prediction tool. The MARS generates continuous error response surfaces for individual features and feature combinations. Two types of features (planar and ruled) and two feature interactions (combinations of planar features and combinations of ruled features) were studied with parameters and algorithms to generate response surfaces. The method has two stages: (i) training stage and (ii) MARS model generation stage. In training stage formed components are scanned to generate point cloud and are compared with available point cloud of stereolithography (STL) model to generate accuracy reports and used the same to build MARS engine (Fig. 32). Feature-assisted single-point incremental forming (FSPIF) module detects the features and MARS engine adjusts these features and generates adjusted STL models in second stage (Fig. 33). The components formed from these adjusted models are again compared with original STL model to generate reports for validation. The validation results show average deviation of less than 0.3 mm, and the maximum deviation for horizontal nonplanar feature is of 0.72–0.99 mm. Although the methodology reasonably enhances the part accuracy, the process of implementation of MARS system is difficult and limited. Also, for parts with wall angles close to maximum formable angle, the compensation of the STL file results in a compensated geometry having zones with wall angle greater than maximum formable angle.

Fig. 32

Flowchart illustrating the generation and use of strategy proposed by Behera et al. (2013) to improve accuracy in SPIF – generation stage

Fig. 33

Flowchart illustrating the generation and use of strategy proposed by Behera et al. (2013) to improve accuracy in SPIF – usage stage

Twist is observed in incremental forming of components and its quantity is dependent on the type of configuration and other process parameters involved. Twist in incrementally formed sheet metal components is first reported by Matsubara (2001) while forming cone as well as pyramid shapes using two-point incremental forming (TPIF) . Note that in TPIF, tool moves from inside (starting from fixed/support tool) to outside. Due to this reason, already formed region of the part is compelled to tilt/rotate about the fixed tool. Here, fixed tool acts like a pivot. Matsubara (2001) reported twist as high as 30° in TPIF when the tool path direction is kept same during each step. To reduce this twist, tool path direction is reversed between consecutive contours. Alternative tool movement directions are used by many researchers to reduce the twist in incremental forming (Jeswiet et al. 2005a). Although twist accumulation can be reduced by alternating the tool path direction, it also results in the deterioration of surface quality at the location of contour transition. In addition, spiral tool path (Jeswiet et al. 2005a) is better for product quality and to enhance formability. Very recently, Duflou et al. (2010) and Vanhove et al. (2010) have studied the twist in SPIF of pyramid and conical shapes using unidirectional tool path. Note that in SPIF, tool moves from outside to inside and no fixed tool or any support is present as in TPIF. Twist quantified by them (Duflou et al. 2010; Vanhove et al. 2010) is in terms of angle by drawing appropriate lines (radial lines in case of cone) prior to forming and measuring its deviation after forming. They classified the twist in two categories, namely, conventional (that occurs at low wall angles) and reverse (close to formability limits). They concluded that at lower wall angles, tangential force on the deforming sheet results in twist in the tool path direction and is named as conventional twist. Asymmetric strain distribution along the meridional direction at higher wall angles for pyramidal structures was observed and the twist started reducing and even reversal is reported. They also concluded that the geometrical features like ribs/corners have significant influence on the twist. However, they reported that the twist is independent of tool diameter, rotation speed of the tool, and tool feed rate. They concluded that the twist along tool movement direction increases with wall angle up to some value and then the trend reverses with further increase in wall angle. Asghar et al. (2012) have carried out experimental and numerical analysis to study the effect of process variables on twist in incremental forming and concluded that the twist increases with increase in incremental depth and decrease in tool diameter and sheet thickness. Feed rate effect is insignificant. Numerical predictions are in good qualitative agreement with experimental results.

Surface finish of the formed component is of equal importance as that of accuracy. Hagan and Jeswiet (2004) carried out experimental study by forming conical parts with contour tool paths to measure surface roughness in SPIF. Incremental depths varying from 0.051 to 1.3 mm are used to form a conical component of 45° wall angle using 12.7 mm tool diameter with a feed rate of 25 mm/s. Peak to valley heights measured between 5 and 25 μ correspond to incremental depths between 0.051 and 1.3 mm. In addition, spindle speeds varying from 0 to 2,600 rpm were used. They concluded that it does not have significant effect, but a minimum surface roughness was observed around 1,500 rpm. Ham et al. (2009) carried out experiments to study the effect of incremental depth and tool diameter on the surface roughness of components formed using contour tool paths and observed that usage of smaller tools results in more distinctive cusps. As the tool size increases, the increased contact area between the tool and work for the same incremental depth results in greater overlap of the tool with the previously formed material; hence, the surface cusps become indistinguishable with increase in tool diameter. Singh (2009) and Bhattacharya et al. (2011) have studied the influence of wall angle (20, 40, and 60°), tool diameter (4, 6, and 8 mm), and incremental depth (0.2, 0.6, and 1 mm) on surface finish by forming conical components with spiral tool path keeping sheet thickness, feed rate, and other parameters constant. Design of experiments was carried out using full factorial design and the best surface finish (in terms of R_a) obtained by them in the range of parameters used is 0.3 μ. Empirical equation that relates surface roughness (Ra) to process variables is reproduced below:

$$ \begin{array}{l}{\mathrm{R}}_{\mathrm{a}}=8.41-0.069\upalpha -2.14\mathrm{d}+9.13\Delta \mathrm{z}+0.0035\upalpha \mathrm{d}+0.0191\upalpha \Delta \mathrm{z}\ \\ {}\kern3.5em -0.417\mathrm{d}\Delta \mathrm{z}+\mathrm{0.00005.7}{\upalpha}^2+0.153{\mathrm{d}}^2-4.66{\Delta \mathrm{z}}^2\end{array} $$

(4)

They concluded that surface roughness decreases with increase in tool diameter for all incremental depths and it happens due to the increase in overlap between the neighboring tool paths with increase in tool diameter. In addition, up to certain wall angle, surface roughness value initially increased with increase in incremental depth and then decreased. With further increase in angle, surface roughness increased with increase in incremental depth. It was observed that the undeformed region between successive tool paths is more at lesser wall angles and higher incremental depth. Note that the overlap increases with increase in wall angle whereas contact area of the tool reduces for a given incremental depth. The average surface roughness (R_a) achieved by SPIF at different process parameters is summarized in Table 2.

Table 2 Average surface roughness at different process variables in SPIF

Double-Sided Incremental Forming

Double-sided incremental forming (DSIF) uses one tool each on either side of the sheet. As stated earlier, the deforming and supporting roles of each tool will keep changing depending on the geometry. DSIF configuration enhances the complexity of the components that can be formed and reduces many of the limitations associated with incremental forming. Cao et al. (2008) mounted two tools on a single rigid C-frame (Fig. 34) to demonstrate DSIF to form features on both sides of initial plane of sheet. They introduced squeeze factor as ratio between tool gap and initial sheet thickness and reported that decrease in squeeze factor improves the dimensional accuracy of the formed component (relative error of 46.6–28.4 %, for squeeze of 0–40 % sheet thickness). Their group (Malhotra et al. 2011b) further studied the effect of squeezing on geometrical accuracy for conical component with fillet (65° wall angle, depth 36 mm) using two independently moving tools on either side of the sheet. Note that the squeeze factor definition here is the ratio between tool gap at any instant and the expected thickness using sine law at that location. The contact condition of the bottom tool (support tool) is improved with decrease in squeeze factor, but the effect of squeeze factor on part accuracy is not consistent.

Fig. 34

Double-sided incremental forming using a C-clamp to mount both the tools (Cao et al. 2008)

Malhotra et al. (2012b) have proposed another DSIF strategy (accumulative DSIF) using in-to-out (IO) tool path strategy (Malhotra et al. 2011a) with displacement controlled forming and support tools. Using ADSIF, they formed cones of 40° and 50° angles and reported maximum shape deviation of 1.15 mm. Forming time, using ADSIF, increases drastically to achieve the desired depth and geometry of the component as it uses only in-to-out tool paths. Meier et al. (2011) used two robots to control different tools on either side of sheet and termed the process as duplex incremental forming (Fig. 8). They used position control for the forming tool and combination of force and position control for the support tool to maintain continuous contact. They used a vision-based measurement technique to estimate deviations from ideal profile and modified the tool path to reduce the deviation. They made use of FEA predictions also to modify the tool path and reported significant improvement of accuracy in the wall region. But, the improvement in accuracy in component opening region and bottom regions is marginal (deviation in the range of 0.5–1.0 mm). Due to the superimposed pressure from support tool, 12.5 % increase in formability has been reported. Meier et al. (2012) presented an integrated CAx (CAD, CAM, CAE) process chain (Fig. 35) for the robot-assisted incremental forming process, called as roboforming , to quickly realized the path planning and simultaneously raise the geometrical accuracy using different compensation methods. Commercial CAM system with additional features has been developed for two synchronized tool paths according to different forming strategies. A simulation model uses this tool path for animation of robot movements and to ensure the experimental safety. Forming results are forecasted using the tool path in an established FEM model, which are fed back to the CAM program. After the comparison with the target geometry, the geometrical deviations were used to adjust the tool paths. They reported reduction of profile deviation from 1.08 to 0.2 mm, but FEA consumes about 10 h for simulation; thus, the real-time compensation is difficult to implement. Recently, DSIF machine has been designed and developed at Indian Institute of Technology Kanpur and many studies are in progress (Srivastsava 2010; Koganti 2011; Asghar 2012; Shibin 2012; Lingam 2012). Very recently, Northwestern University, Evanston, has also developed a DSIF machine.

Fig. 35

Block diagram showing the interaction of different modules to generate the tool path for roboforming (Meier et al. 2012)

Tool Path Planning

In incremental forming, tool path plays a significant role on the forming limits, component accuracy, surface quality, thickness variation, and forming time. Many attempts have been made to study various tool path strategies (contour, spiral, radial, and multiple passes – in-to-out and/or out-to-in) and their effect on forming limits, thickness distribution, accuracy, and surface quality in various variants of incremental forming (SPIF, TPIF, DSIF), and the same has been presented in the earlier sections. Hence, certain aspects are not discussed in detail in this section. As presented earlier, there are two types of tool path used for ISMF process , namely, contour and spiral (Fig. 2a, b). Most of those tool paths have been generated using surface milling modules of commercial CAM packages developed for machining. Deformation is biaxial at the starting and end points of each contour in contour tool path and is near to plane strain in between; hence, the tendency for fracture at the start and end points of each contour is higher. Contour tool path leaves stretch marks at the start points of each contour (Fig. 2c). To avoid equi-biaxial stretching and the tool marks at the end points of each contour, Filice et al. (2002) have suggested the use of a spiral tool path (Fig. 2b). In SPIF, tool (either contour or spiral) moves from out-to-in and represented as conventional strategy in Fig. 36a. Bambach et al. (2005) have proposed a conical strategy in addition to conventional strategy. In conical strategy, tool movement starts at the center and opens up with increasing depth. They studied two in-plane tool movement strategies (contour, Fig. 36b, and radial, Fig. 36c) coupled with two z-movement strategies, conventional and conical strategies. Considering the time required for producing the part and the uniformity of sheet thickness throughout the part, they concluded that the conventional/contour strategy is better (2 min production time with comparable thickness distribution) as compared to radial strategies (9 min for cone/radial and 40 min for conventional radial trajectory). Time required to form the component reported by them can be easily understood with the schematic representations presented in Fig. 36.

Fig. 36

Different tool path strategies used by Bambach et al. (2005): (a) conventional and conical, (b) contour tool path , (c) radial tool path, (d) conventional-contour, and (e) conical-contour strategies

Kopac and Kampus (2005) studied the effect of various in-plane tool movement strategies for axisymmetric components. They examined four procedures in terms of tool movement, namely, (A) from exterior to interior, (B) from interior to exterior, (C) first in the center then from exterior to interior, and (D) first in the center then from interior to exterior, and reported that the maximum depth of forming can be achieved with case D, i.e., first in the center then from interior to exterior. Ambrogio et al. (2005b) developed a tool path modification strategy by integrating an on-line measuring system and tool path to be followed for forming the remaining portion of the component under consideration. For achieving the same, they utilized the combination of online measuring techniques, numerical simulation (Deform3D), and optimization techniques to modify the tool path. Their path-correcting methodology makes use of the measurement of the previous reference point on a given section of the spiral and its comparison to the desired position at the final and current step. Three-dimensional spiral tool paths for forming asymmetric components (Skjoedt et al. 2007) are generated by first generating contour tool paths using the milling module available in Pro/ENGINEER and then interpolating between the individual contours to produce a single 3D spiral. They used constant incremental depth for generating the contour tool path. Stereolithography (STL) files are used to develop an iterative tool path generation methodology (contour tool path was generated using a combination of forming, scanning, and reforming) (Verbert et al. 2007). It is well known that STL format has inherent chordal errors and iterative nature increases time. Attanasio et al. (2006, 2008) have investigated two types of tool paths, one with a constant incremental depth (Δz) and the other with a constant scallop height (h) (Fig. 37). It was reported that the surface quality of the formed component improved by decreasing the values of incremental depth (Δz). A shortcoming of their approach is that when the value of Δz is arbitrarily reduced to a very small value, the forming time increases, especially when larger components are to be formed. This kind of approach does give the designer the freedom to form a component quickly with acceptable surface finish.

Fig. 37

Schematic of tool path with (a) constant incremental depth and (b) constant scallop height

Malhotra (2008), Malhotra et al. (2010) developed and implemented a platform-independent methodology for generation of contour and spiral tool paths for an arbitrary component formable by SPIF. The methodology takes neutral part format STEP AP203/AP214 of CAD model as input. Adaptive slicing techniques used in layered manufacturing (Pandey et al. 2003) and 3D spiral tool path generation methodology for surface milling of freeform shapes with constant scallop height (Lee 2003) have been modified and used for generating tool paths. Tool path methodology developed by them for single-point incremental forming addresses the trade-off that exists between geometric accuracy, surface finish, and forming time. Steps involved in their tool path generation methodology are:

• 1. Generation of contour tool path with a constant incremental depth.

• 2. Calculation of volumetric errors and scallop heights to form components with good accuracy and surface finish.

• 3. Usage of adaptive slicing criterion to evaluate the need for new contour insertion.

  • (a) Repeat steps 2–4 for the inserted contour and the one above when the new contour is inserted.

  • (b) Otherwise move down to the next pair of contours and perform steps 3 and 4 till all the contours are finished.

• 4. Perform deletion of slices to get the final contours. Here, extra slices are deleted, which will not adversely affect the accuracy by evaluating the volumetric error percentage between slice n and slice n + 1.

• 5. Generation of final spiral path using the finalized contours.

• 6. Apply the tool radius compensation (Fig. 38) using local geometrical conditions and generate the tool path for forming the components.

Fig. 38

Schematic showing the importance of tool radius compensation

The adaptive slicing methodology along with volumetric error criterion enhances the conformity between the formed and the desired components and the same can be seen from Fig. 39.

Fig. 39

Comparison of ideal and measured profiles: (a) with and (b) without tool radius compensation

Azaouri and Lebaal (2012) proposed a tool path optimization strategy for SPIF for finding the shortest tool path (less forming time) which distributes the material as evenly as possible throughout the part. As a consequence of volume conservation, the part with the lowest reduction in sheet thickness would have a homogeneous distribution of thickness. FEA, in combination with response surface method and sequential quadratic programming algorithm, was used for determining the optimal forming strategy. The authors reported a better thickness distribution (minimum thickness: 0.91–0.96 mm with optimization and 0.79 mm without optimization, for an initial sheet thickness of 1.5 mm) and less forming forces. However, in order to achieve the shortest path, the accuracy and surface finish of the component get deteriorated. Many (Cao et al. 2008; Hirt et al. 2004; Skjoedt et al. 2008, 2010; Duflou et al. 2008b; Abhishek 2009; Malhotra et al. 2011a; Xu et al. 2012; Kim and Yang 2000; Young and Jeswiet 2004) have proposed tool paths for other variants of incremental forming, and their details are presented in earlier sections dealing with formability, thickness distribution, and accuracy.

Summary

Incremental sheet metal forming is gaining importance in automobile (Governale et al. 2007), aerospace (Jeswiet et al. 2005a), and biomedical industries (Ambrogio et al. 2005c) and even for processing recycling panels (Jackson et al. 2007; Takano et al. 2008) and producing dies/molds quickly using complex sheet metal surfaces produced by incremental forming at very less expense (Allwood et al. 2006). Accuracy of the component during incremental sheet metal forming is affected by bending of sheet between the clamped boundary and component opening, continuous local springback that occurs as soon as tool moves away from a point, and global springback that occurs after the tool retraction and unclamping of the component. Predicting springback using numerical analysis and compensating for the same during tool path generation is a time-consuming process due to the nature of process. Development of DSIF enhanced the product complexity to form parts with double curvature on both sides of the initial sheet plane without any additional setups with better accuracy than other incremental forming configurations.