Modeling of Optimization Strategies in the Incremental CNC_2004

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Modeling of Optimization Strategies in the Incremental CNCSheet Metal Forming Process

M. Bambach, G. Hirt, J. Ames

Institute of Materials Technology/Precision Forming (LWP), Saarland University, Germany

Abstract. Incremental CNC sheet forming (ISF) is a relatively new sheet metal forming process for small batch productionand prototyping. In ISF, a blank is shaped by the CNC movements of a simple tool in combination with a simplified die. Thestandard forming strategies in ISF entail two major drawbacks: (i) the inherent forming kinematics set limits on the maximumwall angle that can be formed with ISF. (ii) since elastic parts of the imposed deformation can currently not be accounted forin CNC code generation, the standard strategies can lead to undesired deviations between the target and the sample geometry.

Several enhancements have recently been put forward to overcome the above limitations, among them a multistage formingstrategy to manufacture steep flanges, and a correction algorithm to improve the geometric accuracy. Both strategies have beensuccessful in improving the forming of simple parts. However, the high experimental effort to empirically optimize the tool

paths motivates the use of process modeling techniques.This paper deals with finite element modeling of the ISF process. In particular, the outcome of different multistage

strategies is modeled and compared to collated experimental results regarding aspects such as sheet thickness and the onsetof wrinkling. Moreover, the feasibility of modeling the geometry of a part is investigated as this is of major importance withrespect to optimizing the geometric accuracy. Experimental validation is achieved by optical deformation measurement thatgives the local displacements and strains of the sheet during forming as benchmark quantities for the simulation.

INTRODUCTION

The incremental CNC sheet forming process as de-

scribed in [1-5] has been developed to meet the demands

of small batch sheet metal forming and rapid prototyp-

ing. Recent experimental work has revealed the need for

non–conventionalforming strategies to overcome currentlimitations, i.e. strategies that help optimize the tool path

to (i) produce steep flanges and (ii) reduce deviations

from the target geometry [6]. Currently, these strategies

are based on trial-and-error optimization of the tool path.

The experimental effort inherent in empirical tool path

optimization could in principle be reduced by process

modeling. The present paper provides first results of the

FE modeling of non–conventional ISF strategies.

PROCESS TECHNOLOGY

Process description

In ISF, a metal blank which is clamped into a rect-

angular blank holder is shaped by the continuous move-

ment of a simple ball-headed forming tool. The tool path

is prescribed by NC data that is generated from a CAD

model of the component to be formed. The conventional

forming strategy consists of a single forming stage where

the tool traces along a sequence of contour lines with a

vertical feed in between. Generally, a distinction is made

between "single point forming", where the bottom con-

tour of the part is supported by a rig and "two-point form-

ing", where full or partial positive dies support critical

surface areas of the part (Figure 1).

blank tool partial die

post

two-point ISFsingle point ISF

blankholder

FIGURE 1. Process variants in ISF

Process limit: sheet thinning

In conventional ISF, sheet thinning depends strongly

on the wall angle. Presuming volume constancy and a

deformation mode close to plane strain conditions, theso–called sine law

t 1

t 0

sin¡

90¢ £

α ¥

(1)

relates the initial (t 0

) and actual (t 1

) sheet thickness for

a given wall angle α . At wall angles of approximately

60¢

for Al99.5 and mild steel, a localization of the plas-

tic deformation can be observed [6]. Accordingly, wall

© 2004 American Institute of Physics 0-7354-0188-8/04/$22.00edited by S. Ghosh, J. C. Castro, and J. K. Lee

CP712, Materials Processing and Design: Modeling, Simulation and Applications, NUMIFORM 2004,

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angles of about 60-65¢

can be considered the maximum

for conventional ISF with sheets of 1–1.5 mm thickness.

This limitation on the maximum wall angle restricts the

potential scope of shapes and applications.

Process limit: geometric accuracy

A second process limit stems from the elastic portion

of the deformation. The tool path is generated exclu-

sively according to geometric information specified by

the CAD model of the desired part. Since the elastic por-

tion of the deformation (including backstresses induced

by the cyclic loading history) are neglected, experimental

work shows undesired deviations from the target geome-

try (see Figure 2).

mild steel (t0=0.8mm)

>3.00

2.25 – 3.00

1.50 – 2.25

0.75 – 1.50

0.00 – 0.75

-0.75 – 0.00

-1.50 – -0.75

-2.25 – -1.50

-3.00 – -2.25

< -3.00

deviation [mm]

stainless steel (t0=1.0mm)

FIGURE 2. Deviations from the target geometry for ademonstator part

OPTIMIZATON STRATEGIES

Multistage forming

Inspired by the ideas for multistage forming strategies

for axisymmetric components [9], a modified multistage

forming strategy (Figure 3) has been developed for non-

axisymmetric parts.

The multistage strategy can be described as follows:

• In the first "preforming stage" (Figure 3a) a preform

with a shallow wall angle (45¢

in this example)

is produced by using the conventional two–point

forming.

• Then, a number of stages follow in which the pitch

motion of the forming tool alternates from upward

(Figure 3b) to downward (Figure 3c).

• From one stage to the next the tool path is generally

designed with an increase in angle of 3¢

or 5¢

. This

means that 7 to 12 stages are needed to produce

components with an angle of about 80¢

.

The described forming strategy introduces a number of

new process variables such as the shape of the preform,

tool

partial die

blankholder

before forming during forming stage

down

α

preforming

stage

a

fixture

up upward

stage

b

down downward

stage

c

FIGURE 3. Multistage forming strategy

and the shape and number of intermediate stages. The

number of intermediate stages should be as low as pos-

sible to avoid the occurrence of surface wear [7] and to

reduce the process time. It should be noted that reducing

the number of intermediate shapes increases the risk of

sheet rupture and wrinkling (Figure 4).

31

2

(3) wear

(1) wrinkling

(2) rupture

FIGURE 4. Multistage forming strategy

Correction algorithm

Reducing geometric deviations can be considered an

optimization problem of finding a tool path that yields

the desired part with a specified geometric tolerance. Dueto the fact that the ISF process is very reproducible, a

general correction algorithm has been developed (Fig-

ure 5). First, a part is produced based on the uncorrected

tool path. Then, "deviation vectors" pointing from a set

of target points to the corresponding points on the actual

geometry are determined using a coordinate measuring

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actual position

targetcontour

actualcontour

target point

corrected point

correctedcontour

ci

¦

ti

¦

ai

¦

c⋅di

¦

di

¦

x

z

y

targetcontour

part

actualcontour

x

z

y

FIGURE 5. correction algorithm

machine. These vectors are inverted and scaled by a cor-

retion factor c, yielding a new trial tool path to produce a

further part. The correction module can be considered a

proportional controller. It can be applied repeatedly until

a specified tolerance is met. Figure 6 shows the reduced

deviations after applying the correction algorithm once.

deviation [mm]

>2.52.5 – 2.02.0 – 1.51.5 – 2.01.0 – 1.50.5 – 1.00.0 – 0.5-0.5 – -1.0-1.0 – -1.5-1.5 – -2.0-2.0 – -2.5<-2.5

uncorrected component

corrected component (c=0.7)

FIGURE 6. Comparison between uncorrected and correctedpart geometry

PROCESS MODELING

In earlier work ([8],[9]), a modeling framework in

ABAQUS/Explicit has been successfully used to model

aspects in conventional ISF, e.g. sheet thinning, stress

and strain fields under the action of the tool as well as

damage evolution during forming. The present paper fo-

cuses on finite element modeling of the following aspects

of non–conventional ISF strategies:

• For multistage forming it is important to find a com-

bination of process parameters that avoids the limi-tations shown in Figure 4. Here, we will restrict our-

selves to the prediction of wrinkling and compare

two different variants to produce the same compo-

nent by multistage ISF.

• Since the correction algorithm presented above acts

as a proportional controller, convergence and thus

the experimental effort involved depend crucially on

the correction factor c. In order to reduce the experi-

mental effort by simulation, the finite element mod-

eling must predict the part geometry as accurately

as possible, i.e. at least as good as the desired ge-

ometric tolerance. This will be investigated later in

this paper by comparing modeling results to relatedoptical deformation measurement.

Finite elemet modeling of multistage

forming

Problem definition

We consider two different variants of multistage ISF

for the forming of a four–sided pyramid with a flange

angle of 81¢

(Figure 7).

final shape α=81°

preforming stages

(α=45°)

variant 1 variant 2

FIGURE 7. Multistage forming of variants 1 and 2

The different variants can be described as follows:

1. In variant 1, a constant corner radius of 15 mm isused throughout all forming stages.

2. For variant 2, a variable corner radius is used. The

preform has a bottom radius of 60 mm which de-

creases continously to a top radius of 15 mm. The

corner radii are gradually reduced to yield a con-

stant edge radius of 15 mm (from top to bottom)

after the final stage.

For both variants, the wall angle on the flat side walls

is increased by 3¢

per stage (yielding 12 stages after the

preform). Under the described conditions, both variants

should produce the same final shape, using different

shapes for the preform and the intermediate stages.

Finite element model

Modeling of ISF is computationally very intensive,

mainly due to the fact that the ISF process has a time

range of minutes or hours in reality. Since the tool path

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consists of a large number of points (104£

106) even

for demonstrator components, the FE model has to deal

with a huge number of contact situations. In the case

of multistage forming, the process duration is further

increased. With 12 stages in the example to be presented,

the process time is increased by a factor 12 with respect

to the conventional process.Consequently, in order to reduce model complexity

and calculation time, only a quarter of the pyramid is

considered (Figure 8), with symmetry boundary condi-

tions applied to the cutting edges. Considering a quarter

pyramid introduces disturbances in the stress and strain

fields as compared to a full pyramid, but test calculations

have shown that these deviations are small and restricted

to the immediate vicinity of the cutting edges, i.e. far

away from the region where wrinkling occurs.

sheet

tool

partial

die

tool path

1 2

3

symmetry b.c.

in 2-directionsymmetry b.c.

in 1-direction

FIGURE 8. FE model for multistage forming of a pyramid

The partial die used for the experiments has a length

of 72 mm, a width of 52 mm and a 9 mm edge radius,

yielding a quarter die with edge lengths of 36 mm and

of 26 mm, respectively, for the simulation. The sheet

has a size of 130x140 mm and is meshed with 2912

shell elements. In the experiments, 1.5 mm A1050-H14

aluminum sheets have been used. Since previous results

have shown that anisotropy has a negligible effect on

the outcome of the forming operation [9], isotropic J 2

plasticity with isotropic hardening has been used.

Results and discussion

The outcome of the simulation of the different mul-

tistage ISF variants is given in Figure 9 (both parts are

shown from the inside). For variant 1, the simulationpredicts excessive wrinkling in the corner region of the

pyramid at stage 9 of 12 stages. This corresponds well

to experimental results (Figure 10). On the contary, the

simulation predicts that variant 2 enables forming with-

out wrinkling. This is also found in the corresponding

experiment, where a pyramid with a final wall angle of

81¢

has been successfully formed (Figure 10).

thickness

[mm]

variant 1 variant 2

wrinkling no wrinkling2.2

1.9

1.6

1.3

1.0

0.7

0.4

FIGURE 9. FE modeling of forming variants 1 and 2

wrinkling

wrinkling successful strategy

FIGURE 10. Pyramid with a wall angle of 81 §

Two factors are crucial for wrinkling:

• In order to allow for steep flanges to be formed,

the perimeter of the part at an arbitrary z–level¡

0¨

z© £

60mm¥

is gradually reduced, and addi-

tional material from the preform is included into the

forming of the part. The reduction of the perimeter

causes compressive stresses in circumferential di-

rection that can entail wrinkling.

• At a fixed stage, the considered variants differ in the

shape of the corner region. The constant corner ra-

dius of variant 1 leads to a smaller inclination of the

side wall compared to the inclination of variant 2

for the preform. Thus, for all stages, the sheet vol-

ume included in the forming of the corner region is

bigger for variant 1, yielding a larger sheet thick-

ness and thus stiffness than variant 2. Since the flat

side walls have the same wall angle for both variants

and consequently the same sheet thickness, variant

1 shows a steeper increase in stiffness at the junc-

tion between side wall and corner region and is thus

more susceptible to wrinkling.

Modeling the part geometry

Due to the presence of elastic waves, the explicit FEmethod is generally considered ill–suited to predict the

shape of the sheet after springback (i.e. the geometric

accuracy). The implicit method, on the contrary, is well–

suited for springback analyzes, but a small time step has

to be chosen in order to deal with the huge number of

contact situations in simulations of the ISF process. This

leads at present to an unacceptable computational effort.

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In the following, a benchmark example is considered to

investigate the feasibility of our explicit FE model for

springback analysis:

We consider single–point forming of a four–sided

pyramid made of 1.5 mm aluminum sheet A1050-H14.

The pyramid has a square bottom contour of 200

200

mm with a 15 mm radius at the corners, a side wall angleof 50

¢

and a height of 60 mm. The corresponding finite

element model is given in Figure 11.

tool

rig

sheet

2 0 0 m

m2 0 0 m m

1 0 0 m

m 1 0 0 m m

vertical pitch/

break point

observed

area

FIGURE 11. FE model for comparison with optical defor-mation measurement

During forming, the part geometry is analyzed by means

of an optical deformation measurement system consist-

ing of two calibrated CCD cameras. The cameras record

the deformation on the underside of the sheet. Since

bulging occurs primarily on the unsupported side walls

of the pyramid, a square of 100 mm edge length that

completely contains one side wall has been observed by

deformation measurement.

In order to reduce the number of cycles to be recorded,

a tool path with a relatively coarse vertical pitch of 1 mm

has been chosen. The G–code file for the CNC control is

designed in such a way that the machine is halted aftereach cycle of the tool just before the vertical feed motion

is carried out so that the deformation after each cycle can

be evaluated. In order to synchronize the FE simulation

with the experiment, the tool path information specified

in the G–code file has been translated into input data

for ABAQUS/Explicit. By maintaining the break points

set in the experiments, we generate field outputs of the

calculated displacements and strains for exactly the same

time points as in the experiment.

The finite element mesh is depicted in Figure 12 for

a forming depth of 50 mm. The mesh consists of 6,400

shell elements with 5 integration points over the sheet

thickness. The mesh region that corresponds to the area

observed with optical deformation measurement is high-lighted. The results given next compare the FE model

with experimental data along the depicted centered sec-

tion, where the maximum amount of bulging occurs.

The comparison between the results obtained by sim-

ulation and deformation measurement is shown in Figure

13 for six stages from 10 mm to 60 mm forming depth.

mesh region corresponding to

the area observed by

deformation measurement

centered section for

the comparison with

deformation measurement

FIGURE 12. FE model for comparison with optical defor-mation measurement

In almost all cases, side wall bulging is underestimated

in the finite element simulation. For the final stage (z =

-60 mm), a maximum deviation of 4 mm between defor-

mation analysis and simulation has been found.

0 20 40 60−30

−20

−10

0z = −10 mm

z

0 20 40 60−30

−20

−10

0z = −20 mm

0 20 40 60−40

−20

0z = −30 mm

z

0 20 40 60−40

−20

0z = −40 mm

0 20 40 60−60

−40

−20

0z = −50 mm

y

z

0 20 40 60−60

−40

−20

0z = −60 mm

y

simulationexperiment

FIGURE 13. Comparison between the geometry predictedby FEM and related deformation measurement

Since the misfit to the experimental results is partially

due to the the presence of elastic waves, the analysis

has been restarted and a viscous pressure load has been

applied to the surface of the shell elements to damp out

transient wave effects. Quasi–static equilibrium can be

reached quickly by calculating one additional second of

process time, which is a negligible effort compared to

the 300 seconds of process time that have been taken for

the simulation of whole process. Figure 14 compares the

geometry of the part along the centered section for the

final stage (z=-60mm).

With damping the misfit has been reduced to a maxi-mum deviation of 1.5 mm. While this can be considered

a good conformance, it is still a considerable misfit as

measured by the demands of the correction module. It

is worth mentioning that the influence of the discretiza-

tion and shell element formulation has been carefully

checked in a series of test calculations.

1973



y

z

experimentsimulation as issimulation with viscous pressure load

0

-10

-20

-30

-40

-50

-600 10 20 30 40 50 60

FIGURE 14. Comparison between the geometry predictedby FEM and related deformation measurement

Reasons for the remaining deviations can be:

• The strong dependence of the results on the elas-tic modulus. Since we assume isotropic elastic be-

haviour and since the elastic modulus of the unde-

formed sheet can only be determined with limited

accuracy, this could have a considerable influence

on the result. Furthermore, we do not account for

the decrease of the elastic modulus due to damage

evolution in the sheet. Since decreasing the elastic

modulus increases the elastic part of the deforma-

tion, accounting for this effect could improve the

prediction of geometric accuracy.

• The constitutive framework used in this work does

not account for kinematic hardening and the build–

up of backstresses. Accounting for kinematic hard-

ening should provide a better prediction of spring-

back than the isotropic hardening law used here.

• The blank holder is at present modeled by constrain-

ing the corresponding translational and rotational

degrees of freedom along the edges of the sheet. A

realistic modeling of the clamping conditions could

further improve the results.

SUMMARY AND OUTLOOK

In this paper finite element calculations for non–

conventional forming strategies in incremental sheet

forming have been presented. The enclosed non–conventional forming strategies aim at optimizing the

tool path to enable the production of steep flanges and to

reduce geometric deviations. Since these strategies are

at present based on trial–and–error optimization, finite

element calculations could in principle help reduce the

experimental effort. In particular, two different variants

for the multistage forming of a pyramid shape have been

compared. The occurrence of wrinkling in one of the

variants has been modeled successfully. Furthermore, the

evolution of the geometry of a part during forming has

been tracked using optical deformation measurement.

The related finite element calculation with an explicit

code could describe side wall bulging fairly well afterthe elastic waves have been damped out using a viscous

pressure load. However, the remaining maximum devia-

tion of 1.5 mm between model and experiment is still too

large to allow for an optimization of the part geometry.

Future work will focus on the role of the elasic modulus

and the build–up of internal stresses in order to improve

the prediction of the part geometry.

ACKNOWLEDGMENTS

This research is supported by the German Research

Foundation (DFG) in the framework of SPP 1146: Mod-

eling of incremental forming operations.

REFERENCES

1. Kitazawa, K., Incremental Sheet Metal Stretch-ExpandingWith CNC Machine Tools, Advanced Technology of Plasticity (1993).

2. Amino, H., Makita, K., and Maki, T., Sheet Fluid Forming And Sheet Dieless NC Forming, International Conference"New Developments in Sheet Metal Forming", Fellbach,Germany (2000).

3. Matsubara, S., A Computer Numerically Controlled Dieless Incremental Forming of A Sheet Metal, Proc.Instn. Mech. Engrs Vol. 215 Part B, pp. 959–966 (2001).

4. Filice, L., Fratini, L., and Micari, F., New Trends in Sheet Metal Stamping Processes, Proc. of 1th Int. Seminar of Progress in Innovative Manufacturing Engineering, SestriLevante, Italy (2001).

5. Hirt, G., and Junk, S., Surface Quality, GeometricPrecision and Sheet Thinning in Incremental Sheet Forming, Proceedings of Materials Week 2001, Munich,1–3 October 2001, Paper No. 442 G3 (2002).

6. Junk, S., Hirt, G., and Chouvalova, I., Forming Strategiesand Tools in Incremental Sheet Forming, 11th InternationalConference on Sheet Metal, Belfast, April 2003

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9. Bambach, M., Hirt, G., Junk, S., Modelling and Experimental Evaluation of the Incremental CNC Sheet Metal Forming Process, VII International Conference onComputational Plasticity, COMPLAS 2003, Barcelona7-10 April 2003, eds. Oñate E., Owen D. R. J.

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Modeling of Optimization Strategies in the Incremental CNC_2004