incremental sheet metal forming processes...automation (mass production), soft automation, and...

Incremental Sheet Metal Forming Processes

Venkata Reddy Nallagundlaa*, Rakesh Lingama and Jian CaobaDepartment of Mechanical and Aerospace Engineering, Indian Institute of Technology Hyderabad, Hyderabad, AndhraPradesh, IndiabDepartment of Mechanical Engineering, Northwestern University, Evanston, IL, USA

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 oper-ation. Forming components without component-specific tooling in ISMF provides a competitivealternative 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 isregarded as the future of manufacturing. In ISMF process, sheet is clamped in a fixture/frame with anopening window on a programmable machine, and a hemispherical/spherical ended tool isprogrammed to move in a predefined path giving shape to the clamped sheet by progressivelydeforming a small region in incremental steps. Although formability in incremental forming ishigher than that of conventional forming, the capability to form components with desired accuracyand surface finish without fracture becomes an important requirement for commercializing the ISMFprocesses. This chapter presents various configurations developed to incrementally form the sheetmetal components, experimental as well as numerical methods for estimating forming limits, pro-cedures for enhancing the accuracy, and methodologies for tool path generation.

Introduction

Evolution of manufacturing can be broadly divided into manual manufacturing, mechanization, hardautomation (mass production), soft automation, and integrated manufacturing. Metal formingprocesses also have gone through a similar evolution process. Incremental forming is in practicefrom the day human began processing the metals using manual hammering for making tools andornaments. Manual manufacturing is carried out in an integrated fashion with many limitations. Forexample, 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 oftechnician and repeatability is not guaranteed. In addition, productivity is low. The industrialrevolution and development of electrical and hydraulic machines lead to mass production of formingcomponents using dies, resulting in traditional art of incremental processes disappear from centerstage except in few cases (Groche et al. 2007). Incremental forming is characterized by smalloverlapping regions of deformation in desired sequence to form the intended geometry using simple

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Handbook of Manufacturing Engineering and TechnologyDOI 10.1007/978-1-4471-4976-7_45-5# Springer-Verlag London 2014

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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 markettowards mass customization, change in market dynamics, reducing product prices and increasingproduct 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. Theconventional production methods used in mass production are no longer able to fulfill the challeng-ing demand of flexibility and agility at competitive prices. In incremental forming the shape ofproduct is defined by kinematics of the tools instead of part-specific dies and punches. Tooling costsand subsequent investment in tool storage, space required to store dedicated tools and dies, and costassociated with maintenance of tools are low in incremental forming. Based on the surface area tovolume ratio of material being deformed, incremental forming processes can be broadly classifiedinto incremental bulk metal forming (IBMF) and incremental sheet metal forming (ISMF). It is wellknown that in IBMF, surface area to volume ratio is smaller than that of ISMF. This chapter willdiscuss the developments related to ISMF only.

Incremental Sheet Metal Forming and Configurations

Sheet metal forming covers a variety of processes wherein shearing, bending, stretching, anddrawing or their combinations are used to produce parts for a wide variety of applications. Mostof 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 formass production to offset for the tool costs. Societal changes impacted manufacturing includingother engineering fields. Earlier industrialized economies were on mass production; however,a combination of advances in technology and information is making it increasingly possible tomanufacture the customized products. In the competitive world market, customers are demandingfor more flexible and personal design in quality, performance, services, and aesthetics of theproducts with approximately same cost (if not lesser) and quality (if not higher). To be competitivein the global economy and to satisfy customer demand without much lead time, majority ofmanufacturers are using computer-aided tools such as computer-aided design (CAD), computer-aided engineering (CAE), computer-aided process planning (CAPP), computer-aided manufactur-ing (CAM), computer-aided inspection (CAI), etc., leading to integrated manufacturing without anyphysical boundaries between different functional departments of an organization. Development ofneutral data exchange standards led to proper integration of CAX tools. To be competitive in masscustomization era, one shall be able to convert the ideas quickly into products using flexible andrapid prototyping and manufacturing as well as computer-aided technologies. In addition, sometraditional technologies also may have to be used. For mass customization (manufacturing systemshall be agile to consumers with customized products at mass production prices with equivalent orhigher quality and lesser lead time), manufacturing processes have to be flexible with minimumchange over time and tooling costs. Manufacturers worldwide now attempt to grow by competing onproduct differentiation as much as on price. This trend leads to short product life cycles, low volumeof a chosen product model, and profitability that is as much dependent on the speed at which newmodels and products are introduced as on the control of direct cost. This trend in manufacturingsector led to the development of flexible manufacturing technologies including layered manufactur-ing and particularly in the area of machining to changeover between different products with the helpof fully automated systems. However, developments in the area of flexible forming (Allwood and


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Utsunomiya 2006) have not kept pace with machining mainly because of the requirement ofcomponent-specific tooling in many of the operations.

Conventional sheet metal forming operations require component-specific and costly tooling, andtheir design and fabrication add to the lead time. Incremental forming is one of the technologies thathave emerged as an alternative to some of the conventional sheet metal forming processes for masscustomization. Incremental sheet metal forming (ISMF) is commonly regarded as a die-less sheetmetal forming process which can form complex three-dimensional parts using relatively simpletools. 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 massproduction. In addition, it offers a valid manufacturing process to match the need of mass custom-ization, which is regarded as the future of manufacturing (Wulf 2007). In ISMF process, sheet isclamped 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 predefinedpath giving shape to the clamped sheet by progressively deforming a small region in incrementalsteps. As the forming tool moves and deforms a small portion at a time, the overall time to produceone component is comparatively more, but for small batch sizes and prototyping, ISMF demon-strated its potential of being cost competitive. Existing experimental configurations for incrementalsheet metal forming can be broadly classified into two categories: with (full/partial) and withoutdie/pattern (Jeswiet 2001) support.

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

In contour tool path, tool moves down by an amount equivalent to incremental depth at thestarting of each contour, whereas in spiral tool path, tool gradually moves down and completes thedownward movement equal to incremental depth by the time tool completes 360� movement alongthe spiral, and the same can be clearly seen in Fig. 2a, b. Note that in contour tool path, tooldisengages at the end of each contour, moves to the starting point of next contour, and plunges downequivalent to incremental depth from its original location at the end of earlier contour whereas incase 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 markconnecting 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 thesefigures and is one of the reasons of inaccuracy. Allwood et al. (2005) have designed and built

Fig. 1 Single-point incremental forming (SPIF)


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a dedicated SPIF machine at Cambridge University and its block diagram is shown in Fig. 3. Theyhave designed a tool-mounting system that allows free rotation of tool passively and for ease ofmounting and un-mounting of tools. Provision for measurement of load(s) is provided by mountingthe fixture on load cells.

Positive die-less incremental forming, also referred to as two-point incremental forming (TPIF), isanother 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 isrestrained at two locations (other than the clamping), i.e., at one location by forming tool and thesecond location is the static support. This static support can be a partial die or a full die. Full die canbe either a negative one as shown in Fig. 4b or a positive die. Most of the above configurations arerealized by mounting the required tools on stand-alone NC machines. Amino Corporation of Japanhas developed a commercial machine for incremental sheet metal forming with pattern support andis shown in Fig. 5. Note that only movements in two directions are provided to tool and the thirdmovement necessary to form the component is provided to the fixture, and in addition, the fixture canmove up and down.

Fig. 2 Contour and helical tool paths

Fig. 3 Block diagram of SPIF developed at Cambridge University (Allwood et al. 2005)


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

Modifications of the process setup have been made by various research groups, for example, toform 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 cylindricalpins 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 ofpunch bends the sheet, and the movement of sheet on the support tool changes the deformationlocation. Each bending operation produces a spherical shape and their combination gives doublycurved surface. The sequence of operations in this process is shown in Fig. 7c. Required curvature

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)


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http://www.aminonac.ca/product_e_dieless.asp

http://www.aminonac.ca/product_e_dieless.asp

(R), during the deformation, is controlled by selecting the downward movement (Dz) of the punchfrom the initial plane of the sheet and grid size (2a) and is given by:

R ¼ a2

2 � Dz (1)

Meier et al. (2011) have used two robots (Fig. 8) to control different tools on either side of sheetand termed the process as duplex incremental forming (DPIF). They used position control for theforming tool and combination of force and position control for the support tool to maintaincontinuous 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

Fig. 6 Double-sided incremental forming (DSIF)

Fig. 7 Setup proposed by Yoon and Yang (2001) to form doubly curved surface


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force controlled, whereas the NC tool systems generally used for incremental forming are displace-ment controlled.

The first patent on incremental sheet metal forming is by Leszak (1967) way back in 1967. In thisinvention, 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

Fig. 8 Configuration of duplex incremental forming

Fig. 9 Schematic showing the apparatus used by Leszak (1967)


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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 differentvariants of ISF. Starting from the inception the chronological developments in ISF have beensummarized by them. It can be seen from their review that all patents are on different forms ofSPIF and TPIF with or without partial or full dies (four variants as shown in Figs. 1, 4, and 6). Allsuch kinds of ISF process variants are able to form simple to complex geometries but having featuresonly on one side of the initial plane of sheet metal workpiece.

First comprehensive review article on ISMF has appeared in Annals of CIRP by Jeswietet al. (2005a). Based on the work presented in literature, they provided many useful observationsand 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 observa-tions/measurements of both single- and two-point incremental forming have shown that using spiraltool 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 deformsignificantly in the peripheral direction, i.e., strain is negligible in the peripheral direction (toolmovement direction). Assuming that the strain in the peripheral direction is principal one, thethickness strain (reduction in thickness during the deformation) has to be equal to the meridionalstrain (increase in length) with opposite sign to satisfy the volume constancy. Based on the abovediscussion, for a constant wall angle cone shown in Fig. 10, the relationship between the wallthickness after deformation and the original sheet thickness in terms of wall angle can be written as

tf ¼ t0 sin 90� að Þ (2)

The above relation is very well known as sine law in ISMF. In case of continuously varyinggeometries, 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-pointincremental forming has shown that there is a considerable difference between the measured valuesand those predicted by sine law. Note that the sine-law expression for predicting the thickness is

Fig. 10 Sine law for thickness prediction in incremental forming


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derived under the ideal deformation conditions as shown in Fig. 10 where there is no radialdisplacement of any through-thickness section of the material. Thickness calculated using the sinelaw (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, detailsof 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 ismuch higher than the one reported in deep drawing. Most of the studies related to formability inISMF are experimental in nature. Capability to form components with desired accuracy and surfacefinish without fracture becomes an important requirement for commercializing the ISMF processes.Accurate prediction of formability helps in assisting better design of part geometry andcorresponding tool path. It has been well accepted that conventional forming limits are not suitablefor incremental forming even when path dependency of strains are considered. The forming limit ofa sheet metal in conventional forming is defined to be the state at which a localized thinning of sheetinitiates when it is formed into a product shape in a stamping process. Formability of sheet metals inconventional forming is at present characterized by the Forming Limit Diagram (FLD) introduced in1960s by Keeler and Backhofen (1964). The forming limit is conventionally described as plot ofmajor principal strain vs. minor principal strain. It must cover as much as possible the strain domainwhich occurs in industrial sheet metal forming processes. The curves are established by experimentsthat provide pair of the values of limiting major and minor principal strains obtained for variousloading patterns (equi-biaxial, biaxial, plane strain and uniaxial). A schematic representationcomparing the forming limit curves of conventional forming (stamping/deep drawing) with that ofsingle-point incremental forming is shown in Fig. 11a. It can be clearly seen that the forming limitcurve for incremental forming is a straight line with a negative slope in the positive region of minorstrain whereas the conventional one is present in both the regions of minor strain. Deformed gridobtained during incremental forming shown in Fig. 11b, c indicates that the deformation that occursvaries from plane strain to biaxial stretching.

Iseki and Kumon (1994) have proposed an incremental sheet metal stretch test (Fig. 12a) toestimate the forming limits in incremental forming using a rolling ball and formed a groove shown inFig. 12b. It can be seen that both plane strain and biaxial stretching states are captured during the

Fig. 11 Schematic representation of forming limit curve in SPIF against conventional forming


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experiment. Shim and Park (2001) experimentally investigated the formability (of fully annealedAl-1050 sheets) in incremental forming (IF) using a tool having freely rotating ball tip similar to thatused by Iseki and Kumon (1994) and generated strain-based forming limit curves (FLC) forincremental forming by measuring the major and minor strains using a deformation grid. Differenttool path strategies are used to study various strain paths and their suitability to generate forminglimit curves for incremental forming. They recommended an alternate imposition of vertical andhorizontal 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 method-ology is depicted pictorially in Fig. 13. It is realized by them also that biaxial stretching occurs nearthe start and end of groove and plane stretching occurs along a straight path and tendency of crackingis reported to be greater at the ends due to biaxial stretching. They formed components havingdifferent shapes starting from triangular opening to octagonal opening and then a circular openingand observed that deformation is close to equi-biaxial at the corners and plane strain in the straightregions. Failure conditions of the abovementioned geometries were in good agreement with theforming limit curve generated by them using the groove test.

Kim and Park (2002) have used the groove test mentioned above to study the effect of differentprocess 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 toolenhances the formability as the friction along the tool work interface reduces. Formability decreases

Fig. 12 Groove test to obtain formability in incremental forming (Iseki and Kumon 1994): (a) schematic and (b) formedgroove

Fig. 13 Groove test: (a) tool path and (b) forming limit curve (FLC)


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with increase in tool diameter and incremental depth. In addition, they carried out finite elementanalysis using PAMSTAMP – explicit to understand the effect of process parameters on thedeformation.

Filice et al. (2002) have proposed experimental tests aiming at achieving different strainingconditions that occur in incremental forming to study the formability. They formed a truncatedpyramid to obtain the conditions of plane strain deformation and proposed a geometry with twostraight grooves perpendicular to each other (tool path shown in Fig. 15) to achieve almost purebiaxial stretching condition at the center of the geometry. In addition, they proposed to formtruncated cone geometry with a spiral tool path explained earlier to achieve the conditions betweenplane strain and biaxial states. In all the cases, they formed the components using hemisphericalended tool (not a freely rotating ball tool) till failure and generated the forming limit curves forincremental forming. Later, Fratini et al. (2004) have carried out experimental study to understandthe 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 allthe materials by conducting tensile tests. Truncated cones and pyramids of varying wall angles wereformed till failure, to study the influence of abovementioned process parameters on formability ofincremental forming and perform statistical analysis. Based on the analysis, they concluded that

Fig. 14 Variation of formability with tool diameter and incremental depth during groove test

Fig. 15 Tool path to achieve biaxial stretching at the center of two perpendicular straight grooves


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strain-hardening exponent, strain-hardening constant, and normal anisotropy index have high,medium, and low influence respectively. Ultimate tensile strength has negligible influence, whereaspercentage elongation has medium influence. Among the interactive terms, only interaction betweenstrain-hardening exponent with strain-hardening constant and percentage elongation are significant,whereas the others are insignificant. In addition, they reported the influence of same processparameters on conventional forming limit diagram also.

Ham and Jeswiet (2006) used two fractional factorial designs of experiments to study the effect ofprocess 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 spindlespeed) indicates that feed rate, spindle rotation speed, step size, and forming angle decide whethera part can be successfully formed or not. It was also reported that faster spindle rotation speedimproves formability. Second set of experiments (vertical step size, sheet thickness, and tooldiameter) reveals that vertical step size (they used 0.05, 0.127, and 0.25 mm) has little effect onthe maximum forming angle. Material thickness, tool size, and the interaction between materialthickness and tool size have a considerable influence on maximum forming angle. Later they (Hamand Jeswiet 2007) used Box-Behnken design of experiments to study the forming limits in SPI-F. 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 threelevels for the experimentation. Material type has significant effect; the one having lower ultimatetensile strength will have greater formability. Shape also has some influence on the formability as thetype of deformation is dependent on geometry. Allwood et al. (2007) conducted experiments usingAl 5251-H22 sheets to explain the reasons behind higher forming limits observed in incrementalforming and shown that the lines joining corresponding points on the upper and lower surfaces ofsheet formed by SPIF remain almost normal to the surface in meridional plane (Fig. 16), indicatingthat the deformation in this plane is predominantly pure bending and stretching. Whereas measure-ments indicated that there is a relative movement between corresponding points parallel to the toolmovement direction, suggesting that shear occurs in this direction. Above observations indicate thatan appreciable amount of through-thickness shear occurs during incremental forming in the direc-tion parallel to tool motion. Due to the presence of through-thickness shear, the tensile stressesresponsible for fracture get reduced; hence, formability is higher in incremental forming.

Ambrogio et al. (2005a) made an attempt to predict the sheet thinning in SPIF using finite elementanalysis (implicit) and compared with that of experimental values and concluded that the predictionsusing FEA as well as measured experimental values are less than that of sine-law thicknessprediction over most of the deformed region. In addition, experimental values are lower than thevalues predicted using FEA. Ambrogio et al. (2006) used a force-based strategy that can be usedonline 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 decreasingcurves, Fig. 17b) as a criterion for failure. Later, Szekeres et al. (2007) observed the similar forcetrends while forming cone but not for pyramid shape; hence, they indicated that tool force

Fig. 16 Deformation behavior in meridional plane


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measurement may not be very reliable. Many researchers have conducted experimental study on theforming 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 parameteris shown using arrow. Note that force in the tool axial direction reaches peak value and then attainssteady state in all cases.

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. Thecross section of the component parallel to the incremental depth direction is chosen as circularprofile, and the same is shown schematically in Fig. 19. Components are formed till the failure depthand quantified the formability as wall angle at that height. Later conical components with failureangle obtained using varying angle components mentioned above are formed, and it is concludedthat formable wall angles obtained by forming conical cups are more accurate but time-consuming.

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


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This work is extended (Hussain et al. 2007a) by forming components with different cross-sectionalprofiles, namely, elliptical, exponential, and parabolic, and found that the forming limits are differentfor different profiles (lowest for circular and highest for exponential). Based on the above observa-tion, they concluded that the forming limits depend on history of forming in ISMF.

Hamilton and Jeswiet (2010) studied and analyzed the effect of forming at high feed rate and toolrotational speed in SPIF. They concluded that tool rotational speed does not have significant effectduring SPIF and forming at high feed (5,080–8,890 mm/min) produced similar thickness distribu-tion 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, itwas observed that the change in grain size after forming is dependent on the step size, spindlerotation speed, and feed rate. Cao et al. (2008) presented a comprehensive review along with theadvances 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 forminglimits. The Oyane model includes the effect of hydrostatic stress history on occurrence of the ductilefracture as given below:

I ¼ 1

c2

ðef0

c1 þ sms

� �de (3)

Here constants c1 and c2 have to be obtained experimentally. They conducted the necessaryexperiments and obtained the values of c1 and c2 for AA5052-O material. The FLC experiments forthe SPIF were carried out on a CNC machining center using straight groove geometry and tool pathsimilar to the one shown in Fig. 13. Malhotra et al. (2012a) analyzed the fracture behavior in SPIF byusing a fracture model in FEA to predict forming forces, thinning, and fracture. The material modelwas calibrated using the forming force history for a cone shape. The model was validated usinga funnel shape (Hussain and Gao 2007; Hussain et al. 2007a) (varying wall angles as depthincreases) by comparing experimental forming forces, thinning, and fracture depths with predictedvalues from FEA. It was concluded that fracture in SPIF is controlled by both local bending andshear. Local stretching and bending of sheet around the hemispherical tool causes higher plasticstrain on the outer side of the sheet resulting in increased damage on the outer side as compared to theinner side. Greater shear in SPIF only partially explains the increased formability as compared toconventional forming. The local nature of deformation in SPIF is the root cause of increasedformability as compared to conventional forming.

Bhattacharya et al. (2011) conducted experiments to study the effect of incremental sheet metalforming process variables on maximum formable angle. Box-Behnken method is used to design theexperiments for formability study. From the experimental results it was concluded that duringincremental forming, the formability decreases with increase in tool diameter. The formable angle

Fig. 19 Funnel geometry to evaluate formability


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first increases and then decreases with incremental depth. The variation in the formable angle is notsignificant in the range of incremental depths that are used in their work to produce good surfacefinish. To predict thickness during the SPIF, a simple model is proposed considering the overlap indeformation (Fig. 20a) and thus estimated the deformed sheet thickness more accurately. They usedthe proposed thickness prediction model along with a simple analytical model based on the forceequilibrium to obtain the stress components at any section during SPIF. Ratio of mean stress value tothe yield stress value for all the experiments conducted for formability study at the maximumformable angle is calculated by them using the force equilibrium analysis, and its value is found to bevery close to unity at all conditions, hence, used the same as the failure criterion. Maximum formableangles predicted using a triaxiality criterion mentioned above for plane stretching conditions are invery good agreement with the experimental results (Fig. 20b). Duflou et al. (2007b, 2008a) havedemonstrated that the use of local heating (using NdYAG laser) ahead of tool reduces the formingforces 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 themaximum angle that could be formed without heating using the same parameters is only 32�.

Park and Kim (2003) studied the formability of annealed aluminum sheet by forming differentshapes using both positive and negative incremental forming. While forming a truncated pyramidwith negative single-point incremental forming, cracks occurred at the corners due to biaxialdeformation, but no cracks appeared during positive forming (in positive forming a suitable jig

Fig. 20 (a) Schematic showing the consideration of overlap in thickness calculation. (b) Comparison of predictions offormable angle using triaxiality criterion with the experimental results


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support is used – Fig. 21). Strain measurements with the help of a grid indicated that in negativeforming both plane strain and biaxial stretching are present whereas in positive forming only plainstrain stretching is present. Further extending their work to more complex geometries using positiveforming, they concluded that the formability in positive incremental forming is better as thedeformation occurs under plane strain conditions in addition to providing the capability to formsharp corners. Designing of support jig is a challenging task and depends on the componentsgeometry. One can make use of pattern support to replace the jig necessary during positiveincremental forming.

Recently, Jackson and Allwood (2009) have conducted experimental study to explain thedeformation mechanism in SPIF (Fig. 22a) and TPIF (Fig. 22b, with full pattern support) to thatof forming the same geometry using conventional pressing operation and to evaluate the validity ofsine law and in turn to relate the thickness measurements to the deformation mechanics. For theabovementioned purpose, they used copper plate of 3 mm thickness, cut into two halves. Cut section

Fig. 21 Tool configuration used to form truncated pyramid in positive forming

Fig. 22 Incremental forming configurations used for experimental study and grid for measuring


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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 formingconical components by SPIF, TPIF, and pressing. After forming the components are heated toseparate the two halves. Then the formed geometry, thickness, and strains are measured. One half ofthe component with grid pattern is shown in Fig. 22c. Note that the measurements ofabovementioned quantities can be carried out before joining the sheets together and after separatingthem 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 thegrid before and after the deformation. Local coordinate system shown in Fig. 22c is used for strainmeasurement, where m, y, and t are meridional, tool movement, and thickness directions, respec-tively. After analyzing the measured thickness, geometry, and strains, they concluded that in bothSPIF and TPIF, deformation is a combination of stretching as well as shear and the same increaseswith the successive tool laps in the meridional direction with the greatest strain component beingshear in the tool movement direction and shear occurs perpendicular to the tool movement directionin both SPIF and TPIF but is more significant in SPIF. Deformation mechanism in SPIF and TPIF issignificantly different from the idealized mechanism of shear spinning on which sine-law thicknessis proposed. One can easily realize the same in SPIF as there is no support similar to spinning but thesupport is present in TPIF. Critical analysis of measurements indicated that grid lines in the thicknessdirection more or less remain axial in ideal mechanism, but not after TPIF. In addition, circumfer-ential shear is present in TPIF which is absent in the ideal mechanism. Above observations clearlyindicate 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.

Single-pass SPIF can successfully form wall angles up to 70� for various aluminum as well assteel sheets of 1 mm initial thickness (Jeswiet et al. 2005a) using suitable process parameters such asincremental 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 angleby 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 withpartial support die (Fig. 23) to form components with steep walls which cannot be formed usingsingle-pass incremental forming. The stages involved in their strategy are:

Fig. 23 Multistage forming strategy using TPIF to increase formable wall angle


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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 stage1 and then formed up to 81� wall angle. Thickness measured by them revealed that the thickness atany location along the wall is more than the thickness predicted by sine law for 81�. This can beattributed to the availability of more material as the component is formed to the final desired heightin stage 1 and upward movement of tool in later stages. In addition, they performed finite elementanalysis along with damage criterion of Gurson-Tvergaard-Needleman to predict the damageevolution during incremental forming process and predicted that the damage increases with increasein 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 cupwith a wall angle of 90� with height/radius ratio equal to one but the components fractured in eitherthe 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 thicknessvariation is dependent not only on tool path but also on its direction (downwards or upwards) in eachstage. In one of the above strategies, i.e., DUDD, component failed in the fourth stage, while in theother one, i.e., DDDU, it was successful up to the fourth stage, but the component formed did notconfine to the designed shape. In addition, they used the profiles for all the stages with the requiredcomponent depth similar to that used by Hirt et al. (2004). Note that the component height isconstrained by the jig used in TPIF (Hirt et al. 2004) but the material shifts down during down passand results in more depth than the required component in SPIF.

Duflou et al. (2008b) stated that the only way to achieve large wall angles was to aim for materialredistribution by shifting material from other zones in the blank to inclined wall regions. Theydeformed the region of the workpiece area that was originally unaffected in single-pass SPIF tool

Fig. 24 Multi-pass strategies used by Skjoedt et al. 2008)


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paths (Fig. 25) to form vertical walls without leading to failure. Their tool paths always moved fromthe 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 Duflouet al. 2008b). Multistage incremental forming consists of a number of intermediate stages to form thedesired geometry. To propose intermediate stages, it is very important to predict the shape thatactually forms after each intermediate stage to select the profile for next stage as well as the directionof tool movement (i.e., in-to-out or out-to-in). It is very well known that when the tool is moved fromout-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; Duflouet al. 2008b) during multistage SPIF is a result of accumulated rigid body translation during thedeformation of the intermediate shapes. Abhishek (2009) andMalhotra et al. (2011a) have proposeda methodology using a combination of out-to-in (OI) and in-to-out (IO) tool paths (Fig. 26) in onepass and by selectively deforming certain regions in an intermediate pass. Here, “OI tool path” refersto the tool moving from the outer periphery of the sheet towards the center of the sheet while movingdown in the z-direction. The “IO tool path” refers to the tool moving from the center of the sheettowards 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

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


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a cylindrical component with height to radius ratio equivalent to one. For each tool path the firstnumber denotes the stage number, the number after the dash denotes the order of execution, and thearrow shows the direction of tool path. Note that some regions are not deformed in stages 4, 5, and7. Abhishek (2009) has extended the methodology to make hemispherical and ellipsoidal compo-nents. Note that stepped features are avoided in the works of Abhishek (2009) and Malhotraet al. (2011a). Very recently, rigid body movement during in-to-out and out-to-in tool paths ismodeled analytically and validated using finite element simulation for different materials(Xu et al. 2012).

Kim and Yang (2000) compared two double-pass strategies for SPIF. One was based on linearblending, i.e., the intermediate shape was calculated to be at a height of 0.5 times the final height. Inthe other approach, they calculated the intermediate shape so that highly deformed regions in thefinal shape were subjected to lesser deformation in the intermediate shapes. Their methodologiesyielded better thickness distributions than single-pass forming. They concluded that the double-passforming method results in improved formability as well as higher mechanical strength of the formedcomponent. 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. Theyconcluded 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 multiplepasses are used for forming angles exceeding 40�. For better understanding of formability in terms ofwall angle for different materials and process variables, a Table 1 is provided below:

Accuracy and Surface Finish

Accuracy of the component during incremental sheet metal forming is affected by bending of sheetbetween the clamped boundary and component opening, continuous local springback that occurs as

Table 1 Maximum formed wall angle for various parameters

S. No. MaterialSheet thickness Tool diameter Incremental depth Formed anglet (mm) D(mm) Dz (mm) (degrees)

1 Al 3003-O 2.1 – – 78.1 (Jeswiet et al. 2005a)

2 1.3 – – 72.1 (Jeswiet et al. 2005a)

3 1.21 – – 71 (Jeswiet et al. 2005a)

4 0.93 – – 67 (Jeswiet et al. 2005a)

5 Al 5754-O 1.02 – – 62 (Jeswiet et al. 2005a)

6 Al 5182-O 0.93 – – 63 (Jeswiet et al. 2005a)

7 AA 3003-O 2.1 4.76 1.3 77 (Ham and Jeswiet 2006)

8 1.3 12.7 75 (Szekeres et al. 2007)

9 1.2 10 0.5 73 (Ambrogio et al. 2007a)

10 AA 1050-O 1.0 18.0 0.3 70 (Ambrogio et al. 2006)

11 1 12 1 70 (Ambrogio et al. 2007a)

12 Aluminum 0.91 8.0 0.15 70 (Hussain et al. 2007a)

(exponential profile)

13 Steel-DDQ 1.0 – – 70 (Jeswiet et al. 2005a)

14 Steel-DC04 1 12 1 70 (Ambrogio et al. 2007a)

15 LY 12 M 0.91 8.0 0.15 66.0 (Hussain et al. 2007b)


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soon as tool moves away from a point, and global springback that occurs after the tool retraction andunclamping of the component. Comparison between the ideal geometry and the possible finalgeometry 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 occursclose to clamped boundary in SPIF by providing a suitable support/backup or can be eliminated byusing a pattern support.

Hirt et al. (2004) proposed an iterative method to improve geometrical accuracy. First, the formedcomponent was measured using coordinate measuring machine (CMM) and compared withintended geometry. Deviation vector between measured and target points is generated and thesame is used to modify the tool path. Ambrogio et al. (2004) have studied the effect of tool diameterand incremental depth on the geometrical accuracy in SPIF by conducting series of experiments andconcluded that the accuracy is better while using smaller diameter tools and lower incrementaldepth. Note that the use of lower incremental depth increases the forming time. In addition, they alsostated that elastic springback and bending in absence of a backing plate/die is the major cause forgeometrical inaccuracies. Importance of a proper tool path for obtaining desirable geometricalaccuracies in the formed component is emphasized, and a modified tool path is proposed to enhancethe accuracy by forming a component with higher wall angle than the desired angle up to some depthand then forming the remaining component with the desired angle. Conical components formedusing 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 thesheet at somewhat distance away from the clamping region than the ideal tool path. Ambrogioet 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 openingregion although it reduces the deviation in the wall region.

Tanaka et al. (2007) have used a backup tool that comes in contact with the work pieceintermittently (following sinusoidal path) during SPIF. Finite element analysis has demonstratedthat 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 localheating principle. Improvement in geometrical accuracy was realized by achieving more localizedforming effect (due to local heating) and reduced residual stress levels which reduces the springbackeffects (Fig. 30).

Allwood et al. (2009) suggested a closed-loop control strategy (Fig. 31) that uses spatial impulseresponses to enhance the product accuracy in single-point incremental forming with feedback

Fig. 27 Schematic representation of ideal and formed profiles


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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

Fig. 30 Schematic to show the effect of local heating on accuracy


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provided by a stereovision camera. They used a Weibull distribution curve to impulse responsesfrom a set of experiments for a conical component and then used the same to form similar conicalcomponents with � 0.2 mm accuracy prior to unclamping the component. They measured andreported that the formed component deviate around 2–3 mm from that of intended, without using thefeedback. Their strategy requires an iterative process in which a few trials were first conducted fora component, and based on the spatial impulses obtained, tool path compensation was done to obtaina better component.

Behera et al. (2013) proposed a compensated tool path generation methodology for SPIF toimprove the accuracy by using multivariate adaptive regression splines (MARS) as an errorprediction tool. The MARS generates continuous error response surfaces for individual featuresand 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 parametersand 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 generatepoint cloud and are compared with available point cloud of stereolithography (STL) model togenerate accuracy reports and used the same to build MARS engine (Fig. 32). Feature-assistedsingle-point incremental forming (FSPIF) module detects the features and MARS engine adjuststhese features and generates adjusted STLmodels in second stage (Fig. 33). The components formedfrom these adjusted models are again compared with original STL model to generate reports forvalidation. The validation results show average deviation of less than 0.3 mm, and the maximumdeviation for horizontal nonplanar feature is of 0.72–0.99 mm. Although the methodology reason-ably enhances the part accuracy, the process of implementation of MARS system is difficult andlimited. Also, for parts with wall angles close to maximum formable angle, the compensation of the

Fig. 31 Block diagram of closed-loop strategy proposed by Allwood et al. (2009)


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STL file results in a compensated geometry having zones with wall angle greater than maximumformable angle.

Twist is observed in incremental forming of components and its quantity is dependent on the typeof configuration and other process parameters involved. Twist in incrementally formed sheet metalcomponents is first reported by Matsubara (2001) while forming cone as well as pyramid shapesusing two-point incremental forming (TPIF). Note that in TPIF, tool moves from inside (startingfrom fixed/support tool) to outside. Due to this reason, already formed region of the part iscompelled 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

Fig. 32 Flowchart illustrating the generation and use of strategy proposed by Behera et al. (2013) to improve accuracyin SPIF – generation stage

Fig. 33 Flowchart illustrating the generation and use of strategy proposed by Behera et al. (2013) to improve accuracyin SPIF – usage stage


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reduce this twist, tool path direction is reversed between consecutive contours. Alternative toolmovement 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 pathdirection, it also results in the deterioration of surface quality at the location of contour transition. Inaddition, spiral tool path (Jeswiet et al. 2005a) is better for product quality and to enhanceformability. Very recently, Duflou et al. (2010) and Vanhove et al. (2010) have studied the twist inSPIF of pyramid and conical shapes using unidirectional tool path. Note that in SPIF, tool movesfrom 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 (radiallines in case of cone) prior to forming and measuring its deviation after forming. They classified thetwist in two categories, namely, conventional (that occurs at low wall angles) and reverse (close toformability limits). They concluded that at lower wall angles, tangential force on the deforming sheetresults in twist in the tool path direction and is named as conventional twist. Asymmetric straindistribution along the meridional direction at higher wall angles for pyramidal structures wasobserved and the twist started reducing and even reversal is reported. They also concluded thatthe geometrical features like ribs/corners have significant influence on the twist. However, theyreported 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 somevalue and then the trend reverses with further increase in wall angle. Asghar et al. (2012) havecarried out experimental and numerical analysis to study the effect of process variables on twist inincremental forming and concluded that the twist increases with increase in incremental depth anddecrease in tool diameter and sheet thickness. Feed rate effect is insignificant. Numerical predictionsare in good qualitative agreement with experimental results.

Surface finish of the formed component is of equal importance as that of accuracy. Hagan andJeswiet (2004) carried out experimental study by forming conical parts with contour tool paths tomeasure surface roughness in SPIF. Incremental depths varying from 0.051 to 1.3 mm are used toform a conical component of 45� wall angle using 12.7 mm tool diameter with a feed rate of25 mm/s. Peak to valley heights measured between 5 and 25 m correspond to incremental depthsbetween 0.051 and 1.3 mm. In addition, spindle speeds varying from 0 to 2,600 rpmwere used. Theyconcluded that it does not have significant effect, but a minimum surface roughness was observedaround 1,500 rpm. Ham et al. (2009) carried out experiments to study the effect of incremental depthand tool diameter on the surface roughness of components formed using contour tool paths andobserved that usage of smaller tools results in more distinctive cusps. As the tool size increases, theincreased contact area between the tool and work for the same incremental depth results in greateroverlap of the tool with the previously formed material; hence, the surface cusps become indistin-guishable with increase in tool diameter. Singh (2009) and Bhattacharya et al. (2011) have studiedthe 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 keepingsheet thickness, feed rate, and other parameters constant. Design of experiments was carried outusing full factorial design and the best surface finish (in terms of Ra) obtained by them in the range ofparameters used is 0.3 m. Empirical equation that relates surface roughness (Ra) to process variablesis reproduced below:

Ra ¼ 8:41� 0:069a� 2:14dþ 9:13Dzþ 0:0035adþ 0:0191aDz� 0:417dDzþ 0:00005:7a2 þ 0:153d2 � 4:66Dz2

(4)

They concluded that surface roughness decreases with increase in tool diameter for all


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incremental depths and it happens due to the increase in overlap between the neighboring tool pathswith increase in tool diameter. In addition, up to certain wall angle, surface roughness value initiallyincreased 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 undeformedregion 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 reducesfor a given incremental depth. The average surface roughness (Ra) achieved by SPIF at differentprocess parameters is summarized in Table 2.

Double-Sided Incremental Forming

Double-sided incremental forming (DSIF) uses one tool each on either side of the sheet. As statedearlier, the deforming and supporting roles of each tool will keep changing depending on thegeometry. DSIF configuration enhances the complexity of the components that can be formed andreduces many of the limitations associated with incremental forming. Cao et al. (2008) mounted twotools on a single rigid C-frame (Fig. 34) to demonstrate DSIF to form features on both sides of initialplane of sheet. They introduced squeeze factor as ratio between tool gap and initial sheet thickness

Table 2 Average surface roughness at different process variables in SPIF

S. No. MaterialWall angle(degrees)

Tool diameter(mm)

Incremental depth(mm)

Surface roughness (Ra)(microns)

1 Al 3003 45 12.7 0.051 0.5 (Hagan and Jeswiet 2004)

2 45 12.7 1.3 5.0 (Hagan and Jeswiet 2004)

3 AA 5052-O 60 4 1.0 2.99 (Singh 2009)

4 60 8 0.2 0.30 (Singh 2009)

5 40 4 1.0 3.91 (Singh 2009)

6 40 8 0.2 0.34 (Singh 2009)

7 20 4 1.0 4.28 (Singh 2009)

8 20 8 0.2 1.75 (Singh 2009)

Fig. 34 Double-sided incremental forming using a C-clamp to mount both the tools (Cao et al. 2008)


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and reported that decrease in squeeze factor improves the dimensional accuracy of the formedcomponent (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 conicalcomponent with fillet (65� wall angle, depth 36mm) using two independently moving tools on eitherside of the sheet. Note that the squeeze factor definition here is the ratio between tool gap at anyinstant and the expected thickness using sine law at that location. The contact condition of thebottom tool (support tool) is improved with decrease in squeeze factor, but the effect of squeezefactor on part accuracy is not consistent.

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 supporttools. Using ADSIF, they formed cones of 40� and 50� angles and reported maximum shapedeviation of 1.15 mm. Forming time, using ADSIF, increases drastically to achieve the desireddepth and geometry of the component as it uses only in-to-out tool paths. Meier et al. (2011) usedtwo robots to control different tools on either side of sheet and termed the process as duplexincremental forming (Fig. 8). They used position control for the forming tool and combination offorce 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 toreduce the deviation. They made use of FEA predictions also to modify the tool path and reportedsignificant improvement of accuracy in the wall region. But, the improvement in accuracy incomponent opening region and bottom regions is marginal (deviation in the range of0.5–1.0 mm). Due to the superimposed pressure from support tool, 12.5 % increase in formabilityhas been reported. Meier et al. (2012) presented an integrated CAx (CAD, CAM, CAE) processchain (Fig. 35) for the robot-assisted incremental forming process, called as roboforming, to quicklyrealized the path planning and simultaneously raise the geometrical accuracy using differentcompensation methods. Commercial CAM system with additional features has been developedfor two synchronized tool paths according to different forming strategies. A simulation model usesthis tool path for animation of robot movements and to ensure the experimental safety. Forming

Fig. 35 Block diagram showing the interaction of different modules to generate the tool path for roboforming (Meieret al. 2012)


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results are forecasted using the tool path in an established FEM model, which are fed back to theCAM program. After the comparison with the target geometry, the geometrical deviations were usedto adjust the tool paths. They reported reduction of profile deviation from 1.08 to 0.2 mm, but FEAconsumes 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 Kanpurand many studies are in progress (Srivastsava 2010; Koganti 2011; Asghar 2012; Shibin 2012;Lingam 2012). Very recently, Northwestern University, Evanston, has also developed a DSIFmachine.

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 studyvarious 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 variousvariants of incremental forming (SPIF, TPIF, DSIF), and the same has been presented in the earliersections. Hence, certain aspects are not discussed in detail in this section. As presented earlier, thereare two types of tool path used for ISMF process , namely, contour and spiral (Fig. 2a, b). Most ofthose tool paths have been generated using surface milling modules of commercial CAM packagesdeveloped for machining. Deformation is biaxial at the starting and end points of each contour incontour tool path and is near to plane strain in between; hence, the tendency for fracture at the startand end points of each contour is higher. Contour tool path leaves stretch marks at the start points ofeach contour (Fig. 2c). To avoid equi-biaxial stretching and the tool marks at the end points of eachcontour, Filice et al. (2002) have suggested the use of a spiral tool path (Fig. 2b). In SPIF, tool (either

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


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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. Inconical strategy, tool movement starts at the center and opens up with increasing depth. They studiedtwo in-plane tool movement strategies (contour, Fig. 36b, and radial, Fig. 36c) coupled with twoz-movement strategies, conventional and conical strategies. Considering the time required forproducing the part and the uniformity of sheet thickness throughout the part, they concluded thatthe conventional/contour strategy is better (2 min production time with comparable thicknessdistribution) as compared to radial strategies (9 min for cone/radial and 40 min for conventionalradial trajectory). Time required to form the component reported by them can be easily understoodwith the schematic representations presented in Fig. 36.

Kopac and Kampus (2005) studied the effect of various in-plane tool movement strategies foraxisymmetric 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 tointerior, and (D) first in the center then from interior to exterior, and reported that the maximumdepth 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-linemeasuring system and tool path to be followed for forming the remaining portion of the componentunder consideration. For achieving the same, they utilized the combination of online measuringtechniques, numerical simulation (Deform3D), and optimization techniques to modify the tool path.Their path-correctingmethodologymakes use of the measurement of the previous reference point ona 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) aregenerated by first generating contour tool paths using the milling module available inPro/ENGINEER and then interpolating between the individual contours to produce a single 3Dspiral. 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 wasgenerated using a combination of forming, scanning, and reforming) (Verbert et al. 2007). It is wellknown that STL format has inherent chordal errors and iterative nature increases time. Attanasioet al. (2006, 2008) have investigated two types of tool paths, one with a constant incremental depth(Dz) and the other with a constant scallop height (h) (Fig. 37). It was reported that the surface qualityof the formed component improved by decreasing the values of incremental depth (Dz).

Fig. 37 Schematic of tool path with (a) constant incremental depth and (b) constant scallop height


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A shortcoming of their approach is that when the value of Dz is arbitrarily reduced to a very smallvalue, the forming time increases, especially when larger components are to be formed. This kind ofapproach does give the designer the freedom to form a component quickly with acceptable surfacefinish.

Malhotra (2008), Malhotra et al. (2010) developed and implemented a platform-independentmethodology for generation of contour and spiral tool paths for an arbitrary component formable bySPIF. 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 toolpath 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 methodologydeveloped by them for single-point incremental forming addresses the trade-off that exists betweengeometric accuracy, surface finish, and forming time. Steps involved in their tool path generationmethodology 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 notadversely affect the accuracy by evaluating the volumetric error percentage between slice n andslice 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.

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

Fig. 38 Schematic showing the importance of tool radius compensation


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Azaouri and Lebaal (2012) proposed a tool path optimization strategy for SPIF for finding theshortest tool path (less forming time) which distributes the material as evenly as possible throughoutthe part. As a consequence of volume conservation, the part with the lowest reduction in sheetthickness would have a homogeneous distribution of thickness. FEA, in combination with responsesurface method and sequential quadratic programming algorithm, was used for determining theoptimal forming strategy. The authors reported a better thickness distribution (minimum thickness:0.91–0.96 mmwith optimization and 0.79 mmwithout optimization, for an initial sheet thickness of1.5 mm) and less forming forces. However, in order to achieve the shortest path, the accuracy andsurface finish of the component get deteriorated. Many (Cao et al. 2008; Hirt et al. 2004; Skjoedtet al. 2008, 2010; Duflou et al. 2008b; Abhishek 2009; Malhotra et al. 2011a; Xu et al. 2012; Kimand Yang 2000; Young and Jeswiet 2004) have proposed tool paths for other variants of incrementalforming, and their details are presented in earlier sections dealing with formability, thicknessdistribution, 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 forprocessing recycling panels (Jackson et al. 2007; Takano et al. 2008) and producing dies/moldsquickly 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 isaffected by bending of sheet between the clamped boundary and component opening, continuouslocal springback that occurs as soon as tool moves away from a point, and global springback thatoccurs after the tool retraction and unclamping of the component. Predicting springback usingnumerical analysis and compensating for the same during tool path generation is a time-consumingprocess due to the nature of process. Development of DSIF enhanced the product complexity to formparts with double curvature on both sides of the initial sheet plane without any additional setups withbetter accuracy than other incremental forming configurations.

References

Abhishek K (2009) Multi-stage tool path strategies for single point incremental forming. M.Tech.thesis, Indian Institute of Technology, Kanpur

Fig. 39 Comparison of ideal and measured profiles: (a) with and (b) without tool radius compensation


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Aerens R, Eyckens P, Bael AV, Duflou JR (2009) Force prediction for single point incrementalforming deduced from experimental and FEM observations. Int J Adv Manuf Technol46:969–982

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Index Terms:

Accuracy in IF 20–21Biaxial stretching 9, 11, 16Compensations 23, 27, 30Contour tool path 4, 28, 30Double sided incremental forming (DSIF) 5–6, 26Formability in IF 10Groove test for IF 9–11Incremental sheet metal forming (ISMF) 3, 28Multi stage forming 17, 19Pillow effect 21–22Plain strain stretching 16Roboforming 27Sine law for IF 8Single point incremental forming (SPIF) 3–4, 17Spiral tool path 8, 28, 30Spring back in IF 20–21Surface finish in IF 25Through thickness shear 12Twist 24Two point incremental forming (TPIF) 4–5, 24


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incremental sheet metal forming processes...automation (mass production), soft automation, and...

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