Thickness Distribution and Design of a Multi-stage Process for Sheet Metal Incremental Forming

8/18/2019 Thickness Distribution and Design of a Multi-stage Process for Sheet Metal Incremental Forming

1/8

ORIGINAL ARTICLE

Thickness distribution and design of a multi-stage process

for sheet metal incremental forming

Junchao Li & Jianbiao Hu & Junjie Pan & Pei Geng

Received: 24 August 2011 /Accepted: 9 December 2011 /Published online: 23 December 2011# Springer-Verlag London Limited 2011

Abstract Sheet incremental forming (ISF) is a promising

technology. It is inexpensive and does not require particular dies. Sheet thinning, however, has always been one of the

forming defects which impede the process’s wide applica-

tion. Although a multi-stage forming process is supposed to

be effective to deal with this problem, it is still uncertain

how the process can reduce thickness thinning and there is

no applicable rule to determine the favorable number of

forming stages. In this work, based on a truncated cone, a

finite element method (FEM) model for a double-pass form-

ing was established first. Unlike simplifications in previous

studies, with the process of the three-dimensional coordi-

nates in numerical controlled (NC) machining code, the tool

trajectory in this simulation model is the same as that in real

work. With this approach, it was expected to gain reliability

of the simulation result, and then this simulation result and a

single-pass forming result were analyzed. The results of the

analysis indicate that more uniform thickness distribution in

the double-forming process largely benefits from the in-

crease of the total plastic deformation zone. Finally, under

the condition of constant volume in deformation, an equa-

tion was proposed to work out the right number of necessary

forming stages and the rule of this equation was verified

with a relatively complex product.

Keywords Incremental forming . Thickness distribution .

Double-pass forming . FEM

1 Introduction

Compared with the conventional stamping process for mass

produc tio n of var ious pro ducts whi ch nee ds specia lly

designed dies, sheet metal incremental forming (ISF), a

flexible manufacturing process, takes shorter lead time,

costs less and requires no dedicated dies. It satisfies the

increasing demands for the production of small batch prod-

ucts or customized parts [1, 2]. This technology originated

in rapid prototyping and it can be easily implemented by

using a three-axis numerical controlled (NC) milling ma-

chine [3, 4]. In this process, a forming tool, which moves

along a series of contour lines at a constant depth increment

in vertical direction generally, deforms a flat or circular

metal sheet into a designed product gradually. These contour

lines constitute the machining path of the forming tool. The

machining path is often programmed and edited by comput-

er aided manufacturing (CAM) software, and then submitted

to an NC milling machine for execution.

As the tool path can be conveniently modified by comput-

er, sheet incremental forming is more flexible than other metal

forming processes. Because of this, growing academic inter-

ests have been focused on incremental forming. Significant

achievements have also been achieved over the past years,

especially after finite element method (FEM) simulations

were used to analyze process mechanism. Iseki [5] applied

an FEM model to calculate the bulging height, the strain and

stress distributions based on the shell theory, and it indicates a

plane-strain deformation. Kim and Park [6] utilized PAM-

STAMP for the FEM analyses to investigate the effect of

process parameters on the formability. Costantino et al. [7]

carried out an explicit numerical analysis to verify the effec-

tiveness of incremental forming. Ma and Mo [8] employed

brick element to establish a simplified FEM model of a

truncated pyramid in DEFORM to analyze the deformation

J. Li (*) : J. Hu : J. Pan : P. Geng

College of Material Science and Engineering,

ChongQing University,

ChongQing 400044, China

e-mail: [email protected]

Int J Adv Manuf Technol (2012) 62:981 – 988

DOI 10.1007/s00170-011-3852-y


2/8

pattern, but the model needs more simulation time than the

one based on shell element. In spite of these accomplishments,

the application of incremental forming has not been popular-

ized mainly for two puzzles, the severe thickness thinning for

products with steep slopes and limited geometric accuracy

because of spring back phenomenon [9]. Multi-stage forming

is generally considered an effective way to deal with the two

puzzles. Bambach et al. [9] improved a pyramid’s geometricaccuracy by changing the size of round corners gradually. Hirt

et al. [10] made a pyramid with a wall angle (α) of 81° based

on a preformed shape (α045°) with an increase in angle of 3°

or 5° at each stage, which achieved a more homogeneous

thickness distribution. And similar results were obtained by

double-pass forming [11, 12]. However, there is still no def-

inite rule for multi-stage forming design, for the previous

investigations depended on experiences or trial and error

methods more or less. As a result, a further research on

multi-stage forming is extraordinarily necessary.

In this paper, based on FEM model and experimental

verification, we made efforts to investigate on deformationcharacteristics of multi-stage forming of incremental form-

ing. In the mentioned FEM researches, most of the studies

were based upon simplified FEM models to simulate ISF

process, for the complicated three-dimensional (3-D) move-

ments of the forming tool are quite difficult to be imple-

mented in FEM analysis. In addition, the previous

simulation models were mostly aimed at single-pass form-

ing. For this reason, in our study, an FEM model of double-

pass incremental forming was proposed first, in which the

tool’s motion trajectory was the same as in actual working

condition. After that, the simulation results were analyzed

and experimentally verified. Then, a method to determine

the suitable number of forming stages was put forward and

proved applicable with a relatively complex model as an

example.

2 Methods

2.1 Multi-stage forming

The ISF process is fully characterized by a localized defor-

mation which is restricted to a small area between the

moving tool and the workpiece. And the forming zone is

mainly subjected to shear deformation confirmed by other

studies [11, 13]. As a result, the sine law originated from

shear forming has been adopted to predict the ultimate sheet

thickness:

t ¼ t 0 sin a ð1Þ

where t 0 is the initial sheet thickness, t is the ultimate sheet

thickness, and α is the wall angle.

In view of the sine law, it is impossible for a straight wall

part (α00°) to be formed through a conventional single-pass

forming. Previous studies have shown that for a given

material with a certain sheet thickness, the minimum wall

angle of a successfully formed part is far more than 0° [14,

15]. On the other hand, even though a product with steep

slope was successfully formed, the sheet often suffers severe

thickness reduction. Faced with these problems, multi-stageforming has been proposed to form parts with steep slope

and to reduce sheet thinning [10].

A kind of multi-stage forming processes is sketched in

Fig. 1. For a model with a wall angle of α, if the tool path is

directly generated from α, the process is a single-pass form-

ing. On the contrary, if the tool deforms the sheet from some

intermediate shapes to the final part, multi-stage forming

strategy is used. Each intermediate shape represents a form-

ing stage and in each process, the deformation procedure

equals a single-pass incremental forming.

In order to make it easy to understand multi-stage form-

ing, take double-pass forming (n02) as an example. Ap- proximately, the size of the deformation area will change

from L2 + L4 to L1 + L4 during the process. Therefore,

according to shear deformation mechanism, the principal

strain can be expressed by the following equation.

"m ¼ ln L1 þ L4 L2 þ L4

ð2Þ

Similarly, as for a single-pass process, the principal strain

is:

"s ¼ ln L1 L2

ð3Þ

Thus,

"m "s ¼ ln L1 þ L4ð Þ

L2 þ L4ð Þ ln

L1

L2¼ ln

L1 L2 þ L2 L4 L1 L2 þ L1 L4

ð4Þ

Fig. 1 Sketch of multi-stage forming

982 Int J Adv Manuf Technol (2012) 62:981 – 988


3/8

It is obvious that L1 > L2, so εm < εs. That is, the

thickness reduction using a multi-stage forming is smaller

than that which uses a single-pass process. It might result

from the increase of the forming zone from L2 to L2 + L4shown in Fig. 1. Therefore, when it is difficult to meet the

requirements of wall thickness or strength with traditional

process, multi-pass forming is likely a good choice.

2.2 Designed part and process parameters

In this paper, a frustum of cone, with a height of 50 mm and

a major diameter of 160 mm, was taken into account.

Meanwhile, the wall angle is 30°.The blank used in the

experiment was a DC56 sheet and was 1 mm thick by

400×400 mm, and the main material parameters of DC56

are listed in Table 1.

In order to analyze the influence of forming stages on

blank formability, a preformed shape with wall angle of 45°

was designed. According to previous studies, process

parameters play an important part in blank formability [16,17]. In this paper, the utilized process parameters of the

preformed shape and the final part are shown in Table 2.

2.3 FEM model

2.3.1 A FEM model of double-pass forming

A 3-D elastic – plastic finite element model for incremental

forming in this experiment was established based on Aba-

qus/Explicit. The flow chart of setting up a double-pass

forming model is depicted in Fig. 2. First, an FEM model

of the preformed shape (α045°) was established and then

submitted for analysis. Next, the deformed mesh and mate-

rial state of blank could be successfully transferred to the

FEM model of the final part by defining a preliminary state

field in Abaqus. Meanwhile, the new tool with other com-

pone nts in cludin g su pport and bind er co uld al so be

imported and relocated. In this way, when the FEM model

of the final shape runs, the model can inherit the previous

analysis results at the beginning and an FEM model to

realize a more-than-two pass forming process could be

implemented. In addition, the material was assumed to be

of isotropic property and was meshed with four-node shell

elements (Abaqus type S4R) with five integration points

through the thickness. Coulomb’s friction law was applied

with a friction coefficient of 0.1 between the blank and the

tool, and a friction coefficient of 0.25 between the blank and

other parts including the partial die and the binder. At the

same time, a master – slave contact algorithm was employed.

Moreover, the process parameters in the two models were

Table 1 Properties of DC56Item Value

Yield strength (MPa) 135.27

Elastic modulus

(MPa)

207

Density (kg m−3) 7,850

Poisson ratio 0.28

Strain-hardeningexponent

0.23

Table 2 Process parameters for double pass ISF

Process parameter Value

Preformed

shape

Final part

Wall angle, α (°) 45 30

Tool diameter, D (mm) 16 10

Depth increment, Δ z (mm) 1 0.5

Fig. 2 Establishment of a double-pass forming FEM model

toolupper binder

supportlow binder

blank

Fig. 3 The FEM model of the preformed shape

Int J Adv Manuf Technol (2012) 62:981 – 988 983


4/8

set according to Table 2. Figure 3 shows the FEM model of

the preformed shape.

2.3.2 Boundary condition of tool path

Boundary conditions should be defined in the FEM model,

for an intermediate shape or a final part. In spite of the

definition of blank holder force between the binders, tool

path definition has always been a puzzle in FEM analysis as

it often consists of a series of spatial curves [ 18, 19].

Because of this, most studies were just concerned with

simplified tool trajectory to analyze the process of incre-

mental forming and to investigate certain problems [7, 8].

This can give rise to a deviation between an FEM model and

an actual process. To deal with it, in this paper, the tooltrajectory in FEM model was defined by adding the 3-D

displacement coordinates of the moving tool in real working

condition. And the procedure of tool path definition is

described in Fig. 4. At first, the 3-D coordinates ( x, y, z ) in

APT (automatically programmed tools) file which was gen-

erated by CAM program were obtained. Assuming that the

tool moved at a constant speed, a time series could be

generated by Matlab programming because the distance

between two adjacent points along the tool path was known.

Thus, three time-coordinate arrays were obtained and were

used to create displacement constraints of the forming tool

in FEM model. As a result, the tool path in the simulation

model is the same as that in real work. However, as men-

tioned in previous researches, long calculation time has

always been a crucial problem for ISF simulation because

of the complicated tool path [20]. To tackle this problem, the

tool speed was artificially increased below a critical value in

this study and the total calculation time was sharplyreduced.

3 Results

3.1 Simulation results

The thickness cloud image of the preformed shape and the

final part are illustrated in Fig. 5. Obviously, there are several

consequent strain rings around the circumference of the ulti-

mate truncated cone. To examine sheet thickness variations at

different areas of the final part further, the thickness distribu-

tion along with the sectional outline in the radial direction was

obtained, as shown in Fig. 6. Meanwhile, the simulation result

of the same part using a single-pass process was also com-

pared, and process parameters in the single-pass process were

identical with those of the latter stage of the double-pass

forming. It was noted that the minimum thicknesses of the

double-pass and single-pass formed part were 0.58 and

0.5 mm, respectively. The maximum thinning rate of the

double-pass process was largely reduced compared with the

single-pass method. In terms of the thickness variations in the

radial direction, the whole deformation area could be divided

into three distinct parts: OA, AB and BC regions. The sheet

thickness continuously reduces from point O to point A. Then,

the thickness increases gradually to 1 mm at point C with an

inflexion point of B.

3.2 Experimental verification

A verification test for the double-pass forming process was

carried out on a three-axis milling machine along with a

self-made set-up for incremental forming. During the

Fig. 4 Tool path definition in FEM model

thickness thickness

α=45°(preformed part) α=30°(final part)

Fig. 5 Thickness distributions

after a double-pass forming

simulation



5/8

experiment, hemispherical end tools were applied. The tra-

jectories of the tools were the same with those in FEM

model, which were achieved by CAM module of Unigra-

phics NX. The tool speeds for the preformed stage, and the

final stage were set to 1,000 and 1,500 mm/min, respective-

ly. In addition, other process parameters, such as tool diam-

eter and depth increment, strictly equaled those in

simulation model. Meanwhile, oil was applied to minimize

the friction. Figure 7a shows the forming set-up. The exper-

imental thickness result as well as the numerical result of the

final stage is depicted in Fig.7b. It was found that both of the

thickness distributions in the radial direction were generally

in accordance with each other despite a little acceptable

discrepancy. Accordingly, the FEM model in this paper

and its corresponding results proved effective.

4 Discussion

4.1 Influence on thickness distribution

As illustrated in Fig. 6, the deformation area from point O to

point C has been divided into three regions. In the OA region,

the average thickness of the double-pass formed part is sig-

nificantly larger than that of the single-pass formed part.However, the case is just the reverse in AB and BC regions.

Specifically, as for the single-pass process, the thickness

increases sharply to its initial value from point A to point B

and remains invariable in BC region, where there is no plastic

deformation occurring. With regard to the double-pass pro-

cess, however, the deformation occurs over the whole AC

area. In addition, it should be observed further that there is

no difference between the preformed process and the final

process in thickness distribution in BC region. It indicates that

the material in BC region would never experience further

deformation during the second forming stage. At the same

time, considering that BC region does not deform at all in thesingle-pass forming process, this region during a double-pass

process is expected to be served as an auxiliary deformation

area to reduce the thickness thinning of the sloping surface

OA and to avoid or to delay the crack occurrence there. It

seems that if a multi-pass process beyond twice is adopted, the

size of the auxiliary region would vary slightly, but a more

uniform thickness distribution would be accomplished. As a

consequence, for decisive areas where the minimum thickness

is required, the auxiliary deformation regions should be well

designed at places without critical thickness expectations.

4.2 Strain history

Figure 8 shows strain histories for nodes A, B, C and D. As

shown, whether in the single-pass process or in the double-

pass process, the strain paths are characterized by a series of

cascades. This is fully in accord with the previous result

[21]. The difference is that each strain path goes through

two segments of cascading increase in the double-pass

process.

Distance from the center R /mm

Single-pass

Final stage

Preformed stage

Preformed

stage

Final stage

T

h i c k n e s s t / m m

H e i g h t H / m m

α=30°

α=45°

α=30°

Fig. 6 Thickness distribution and outline in the radial direction

Simulation

result

Experimental

result

(a) Forming set-up (b) Thickness distribution comparisonsFig. 7 Experimentalverification for the double-pass

forming



6/8

Moreover, node A is the first to undergo deformation

because of its location at the top, but it reaches a minor

strain for the reason that it only deforms when the tool

moves along the original several contours. Other nodes are

subjected to more tool actions and consequently have larger

strain values. In addition, the maximum stains for nodes A,

B and C reduces by 66.2%, 81.9% and 36.0%, respectively,

while the maximum strain for node D increases a little. The

only exception for node D is mainly because it has experi-

enced a double deformation process. As a whole, in a

double-pass process, the sheet strain is reduced largely and

less thickness fluctuation is achieved.

4.3 Forming stages needed

Multi-stage forming has been verified to avoid severe sheet

thinning in an incremental forming process in this work and

other researches. However, for any product, how many

necessary forming stages are needed? Too many stages

mean an unacceptable work cycle and too little stages indi-

cate inability to meet thickness requirements. An effective

method to define the appropriate number of forming stages

is quite necessary. As thinning rate R is always one of the

striking demands for a product, it was applied in this paper

to find out the right number of stages.In terms of the rule that volume remains constant during

ISF process, there is a relationship between the thickness

thinning Ri (i01, 2, …, n) of each forming stage and the

total thickness thinning R0 as follows:

ln 1 R1ð Þ þ ln 1 R2ð Þ þ . . . þ ln 1 Rnð Þ ¼ ln 1 R0ð Þ ð5Þ

Assuming that R1 0 R2 0 … 0 Rn 0 R′, then the total

number of forming stages

n ¼ ln 1 R0ð Þ

ln 1 R0ð Þ ð6Þ

The result of n can be regarded as an estimate of the

number of stages in real work. For instance, for a model

1-D

1-C

1-A

1-B

2-C

2-D

2-A

2-B

1-single-pass

2-double-pass

T /s

E q u i v a l e n t p l a s t i c s t r a i n ε

Fig. 8 Strain histories for selected nodes

thickness

(b) Result of the first stagethickness

(c) Result of the second stage (d) Result of the third stage

(a) A designed partthickness

Fig. 9 Verification of the

algorithm of necessary forming

stages



7/8

shown in Fig. 9a , of which the thinning rate was requested

to be less than 0.7, R′00.33 was made and n was calculated

to be 3, in reference to Eq. 6. Then, the real thickness

reduction ratios of the three forming stages should be ad-

justed from small to large. Thus, R1, R2 and R3 were set to

0.23, 0.3 and 0.46, respectively. In this case, for a DC56

sheet with a thickness of 2.4 mm, the thickness of each

forming stage is expected to be more than 1.85, 1.3 and0.7 mm in turn. Thus, the minimum walls at the first two

intermediate stages, 50.4° and 44.4°, were determined based

on the arrangement of Ri (i01, 2, 3) and the sine law. With

this, addendum surfaces taken as auxiliary deformation

areas were also designed. The FEM model of this three-

pass process was set up in the same way as shown in Fig. 2.

The tool diameters in three models were 20, 16 and 10 mm.

Figure 9 presents the simulation results. The minimum

thicknesses of three stages are 1.85, 1.29 and 0.66 mm,

which are nearly consistent with the expected values. But

at the final stage, the sheet thickness reaches its maximum

value of 3.08 mm, having a tendency of wrinkling. This can be solved by partly modifying addendum surfaces. Consid-

ering the agreeable numerical results, expression 6 was

applicable to work out the necessary forming stages.

5 Conclusions

FEM has been widely used to investigate the incremental

forming process so far. However, FEM models were

often simplified because it was hard to define complex

tool trajectories. In this work, the tool path was loaded by building up the displacement boundary condition of

the moving tool on the basis of the tool’s three dimen-

sional coordinates which come from APT file. Therefore,

there were no differences between the simulation model

and the real work in tool path, which will lead to more

accurate results.

In addition, a double-pass forming process along with a

single-pass technology for a truncated cone was analyzed

based on an FEM model which was verified effective by a

trail on a three-axis milling machine. The result indicates

that the thickness thinning reduction in a double-pass pro-

cess is due to an existing auxiliary deformation area. That is,

more uniform thickness distribution in critical parts of a

product largely results from the enlargement of the whole

plastically deforming zone.

Finally, for any product of which thickness requirements

were difficult to satisfy in a single-pass process, an expres-

sion to estimate the necessary number of forming stages was

proposed, and the expression was verified by simulation of a

relatively complex product. Future work will be focused on

testing the achievable accuracy of this prediction rule for

more kinds of products. Furthermore, reasonable designs of

addendum surfaces should also be emphasized.

Acknowledgements The authors would like to acknowledge finan-

cial support by the Fundamental Research Funds for the Central

Universities, under grant No.CDJZR10130006.

References

1. Jeswiet J, Micari F, Hirt G, Bramley A, Duflou J, Allwood J (2005)

Asymmetric single point incremental forming of sheet metal. CIRP

Ann Manuf Technol 54(2):623 – 649

2. Allwood JM, King GPF, Duflou J (2005) A structured search for

applications of the incremental sheet-forming process by product

segmentation. Proc IMechE B J Eng Manuf 219(2):239 – 244

3. Filice L, Fratini L, Micari F (2002) Analysis of material formabil-

ity in incremental forming. CIRP Ann Manuf Technol 51(1):199 –

202

4. Jackson KR, Allwood JM, Landert M (2008) Incremental

forming of sandwich panels. J Mater Process Technol 204(1 –

3):290 – 303

5. Iseki H (2001) An approximate deformation, analysis and FEM

analysis for the incremental bulging of sheet metal using a spher-

ical roller. J Mater Process Technol 111(1 – 3):150 – 154

6. Kim YH, Park JJ (2002) Effect of process parameters on formability

in incremental forming of sheet metal. J Mater Process Technol

130:42 – 46

7. Costantino I, Ambrogio G, De Napoli L, Filice L, Fratini L,

Muzzupappa M (2004) Influence of some relevant process param-

eters on the dimensional accuracy in incremental forming: a nu-

merical and experimental investigation. J Mater Process Technol

153:501 – 507

8. Ma LW, Mo JH (2008) Three-dimensional finite element method

simulation of sheet metal single-point incremental forming and the

deformation pattern analysis. Proc IMechE B J Eng Manuf 222

(3):373 –

3809. Bambach M, Taleb Araghi B, Hirt G (2009) Strategies to improve

the geometric accuracy in asymmetric single point incremental

forming. Prod Eng Res Devel 3(2):145 – 156

10. Hirt G, Ames J, Bambach M, Kopp R (2004) Forming strategies

and process modelling for CNC incremental sheet forming. CIRP

Ann Manuf Technol 53(1):203 – 206

11. Jeswiet J, Young D (2004) Wall thickness variations in single-point

incremental forming. Proc IMechE B J Eng Manuf 218(11):1453 –

1459

12. Yang DY, Kim TJ (2000) Improvement of formability for the

incremental sheet metal forming process. Int J Mech Sci 42

(7):1271 – 1286

13. Matsubara S (1994) Incremental backward bulge forming of a

sheet metal with a hemispherical head tool — a study of a numerical

control forming system II. Jpn Soc Tech Plast 35:1311 –

131114. Jeswiet J, Hagan E (2004) Analysis of surface roughness for parts

formed by computer numerical controlled incremental forming.

Proc IMechE B J Eng Manuf 218(10):1307 – 1312

15. Silva MB, Nielsen PS, Bay N, Martins PAF. Failure mechanisms in

single-point incremental forming of metals. Int J Adv Manuf

Technol. doi:10.1007/s00170-011-3254-1

16. Hussain G, Gao L, Zhang Z (2008) Formability evaluation of a

pure titanium sheet in the cold incremental forming process. Int J

Adv Manuf Technol 37(9):920 – 926

17. Ziran X, Gao L, Hussain G, Cui Z (2010) The performance of flat

end and hemispherical end tools in single-point incremental form-

ing. Int J Adv Manuf Technol 46(9):1113 – 1118


http://dx.doi.org/10.1007/s00170-011-3254-1http://dx.doi.org/10.1007/s00170-011-3254-1


8/8

18. Lee SG, Kim HC, Yang MY (2008) Mesh-based tool path gener-

ation for constant scallop-height machining. Int J Adv Manuf

Technol 37(1):15 – 22

19. Zhu H, Liu Z, Fu J (2011) Spiral tool-path generation with constant

scallop height for sheet metal CNC incremental forming. Int J Adv

Manuf Technol 54:911 – 919

20. Hirt G, Ames J, Bambach M (2005) A new forming strategy to

realise parts designed for deep-drawing by incremental CNC sheet

forming. Steel Res Int 76(2 – 3):160 – 166

21. Han F, Mo J (2008) Numerical simulation and experimental inves-

tigation of incremental sheet forming process. J Cent South Univ T

15(5):581 – 587


Thickness Distribution and Design of a Multi-stage Process for Sheet Metal Incremental Forming

Documents

Transcript of Thickness Distribution and Design of a Multi-stage Process for Sheet Metal Incremental Forming