Negative Aluminium Sheets

8/12/2019 Negative Aluminium Sheets

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Negative Dieless Incremental Forming Process: the effect of process

parameters and friction on formability

Matteo Strano, Nicandro Di Meo

[email protected] Dipartimento di Ingegneria Industriale, Università di Cassino, 03043 Cassino (FR), Italy

In negative dieless incremental forming, a small punch plastically deforms a sheet metal, by following spiral-like or concentric trajectories, in

contact with the concave side of the desired part geometry, while the sheet is clamped at the periphery onto a support frame. It is well

recognized that severe deformations can occur before fracture, with negligible necking, thanks to the local shear state of strain induced by

the process. The occurrence of fracture and the quality of the part mainly depend on the part geometry (particularly on the vertical inclination

of the part wall α and on the feed rate f z) but they are also affected by the design of the punch.

The purpose of the present study is to quantitatively investigate the effect of several process parameters on formability, i.e. on the

occurrence of fracture. More particularly, the paper will present, the effect of feed rate f z, conicity α (Section 3), punch geometry (Section 4),

and friction conditions (Section 5), on formability.

It will be shown that formability may increase if using a nearly cylindrical punch, instead of a spherical punch. Besides, a moderate change in

friction forces does not significantly influences formability, whereas a relevant increase in the friction makes formability significantly

decrease.The study is carried out by analyzing the results of several incremental forming experiments, executed with a robotic incremental forming

cell. Most experiments have been executed with 3-axis spiral-like trajectories, but the effect of 4-axis interpolation (X, Y, Z plus Z-rotation)

has been evaluated. Some FEM simulations have been run with a commercial code in order to further understand the results of the

experiments.

KEYWORDS: sheet metal, dieless incremental forming,formability, robotic cell

1. Introduction

Two main variants of the dieless incremental forming process are known: the so-called “negative forming

process” and the “positive forming” process. In negative

incremental forming (Fig. 1), a ball punch moves on a

sheet metal, according to a programmed tool path. The

sheet is clamped at the periphery by bolts on a support

frame [1]. In positive forming, the central part of the

workpiece is supported by a fixed counterpunch (or

mandrel) and the tool-workpiece interface is located on

the convex side of the shape to be formed. The sheet can

be fixed at the periphery [2] by a blankholder, or set free.

Fig. 1: setup of the negative dieless incremental forming process[1]

The dieless incremental forming process is mainly

performed by pure shear deformations [3]. It is well

recognized that material formability is greatly increased

by these local, quite uniform and incremental shear

deformations. In fact, the FLDs (Forming Limit

Diagrams) obtained by incremental forming experiments

are usually located at higher position than those obtained

by traditional sheet forming processes [4], [5] and they

are approximately linear, with a strong negative slope in

the first (tension-tension) quadrant (Fig. 2). It is to be

observed that the experimental determination of FLDs is

usually obtained by means of a circle grid analysis, and

that an almost linear FLD with negative slope, as the one

pictured in Fig. 2, can be obtained if using a sufficiently

fine circle grid. In other words, when the deformation

can be considered uniform within each whole ellipse

generated by a deformed circle, the FLD becomes a

fracture limit, rather than a necking limit [6] [7], and it

resembles those obtained by incremental forming. As a

matter of fact, in incremental forming the overall

deformation is quite uniform across the workpiece,

except at sharp corners and, as a consequence, a linear

FLD with negative slope can be obtained even if using a

coarse circle grid.

Due to this particular shape of the FLDs, a very good

indication of the forming ability of a specific process can be given by the ratio εmin/εmax. When the process is

perfectly pure shear formability is maximum and the

minor deformation is null. When the process deviates

from pure shear, formability decreases and the ratio

εmin/εmax increases.

The formability induced by a specific process depends

on several parameters: some of them are geometrical

(e.g. the part slope α and curvature ρ, as defined in Fig.

3), others are tooling or process related (e.g. the punch

radius r and the feed rate f z). When shear strain is the

prevailing deformation mode, the sin law of thickness

applies, i.e. the instantaneous wall thickness t is equal to

t=t0*sin(α), where t0 is the initial thickness [3]. The

effect of the part curvature ρ (Fig. 3a) in a plane

perpendicular to the z-axis has been seldom investigated,



in explicit terms. However, it is known that, in negative

forming, the shear strain is no longer prevailing at sharp

corners (i.e. for very small values of ρ), where the

deformation is tensile on both principal axes and fracture

is more likely to appear [3], [8].

Decreasing the feed rate fz (as defined in Fig. 3b) has

a positive effect on formability, both in negative and

positive incremental forming [9], [10]. In positiveincremental forming without blankholder, the process is

limited not only by the possible occurrence of cracks, but

also by the possible occurrence of wrinkling in the

flange. In a previous work [11] the authors showed that,

if using a spherical punch with radius r on aluminum,

formability increases as the radius r increases.

Fig. 2:schematic representation of FLDs for the incremental formingprocess (a); fracture and necking FLDs [6] (b)

Fig. 3: geometrical parameters of the formed part: curvature

radius ρ, vertical slope α, instantaneous thickness t (a); definitionof feed rate f z and tool radius r (b)

2. Description of the experiments

A robotic cell for negative incremental forming has

been implemented and used for the execution of several

experiments on thin commercially pure aluminum sheets

(AA 1050-O, t0=0.6 mm). The cell, shown in Fig. 4, is

composed by an anthropomorphic robot, a tool-holder, a

small sized tempered steel punch with a semi-spherical

end, a supporting frame (work area: 500×500 mm) and a

square blankholder. Several aluminum cups have been

incrementally formed until fracture, by continuous spiral

tool trajectories, with changing feed rate value f z. The

cups have different dimensions and shape. Each cup isrotationally symmetric, with variable cross section, i.e.

with variable conicity angle α.

Fig. 4: robotic incremental forming cell

3. The effect of feed rate f z and conicity on

formability

If the sin law applies, i.e. if the circumferential strain

εmin is null and the deformation is completely due to pure

shear, the nominal thinning εt is equal to:

( ) ( )

( )( )[ ] z sent

z t z t α ε lnln

0

=

= (1)

A technological forming limit for a thin (0.6 mm)

commercially pure aluminum has been found by the

authors, giving the probability of having a sound part Ps

as an empirical function of the part slope α, the

horizontal curvature ρ, the part depth z and the feed ratef z.

;

46.22722.6125.111

ln

*

*

ρ

ε

z f f with

f P

P

z z

z t

s

s

⋅=

⋅−⋅+=

− (2)

This empirical model is graphically reported in Fig. 6,

with the nominal thinning εt on the abscissa axis and the

corrected feed rate f z*=f z⋅(z/ρ)1/2

on the ordinate. The

straith curve plotted is the locus of points where the

probability Ps of having a sound part is equal to 80 %.The model has been built basing on the analysis of 230

experimental observations (215 were sound parts, 15

fractured), with r=1.3 mm. The process parameters used

in the experiments were as reported in Table 1.

Table 1: Maximum and minimum tested values for processparameters and material data

minimum maximum no. of values

maximum depth zmax 4.2 mm 82 mm 20

initial radius ρ(0) 40 mm 100 mm 9

final part radius ρ(z) 16 mm 99 mm 66

punch radius r 1.1 mm 1.5 mm 2

Angles α(z) 14 deg 75 deg 36

feed rate f z(z) 0.15 mm/rev 1.7 mm/rev 17



0

0.05

0.10.15

0.2

0.25

0.3

0.35

0.4

0.45

-1.5 -1 -0.5 0

sound

fractured

Ps=80%

t

f z*

0

0.05

0.10.15

0.2

0.25

0.3

0.35

0.4

0.45

-1.5 -1 -0.5 0

sound

fractured

Ps=80%

t

f z*

Fig. 5: experimental data in the εt-f z

* plane for AA 1050-O,

t0= 0,6 mm.

0.0

0.1

0.2

0.3

0.4

0.5

-2.0 -1.5 -1.0 -0.5 0.0

sound

fractured

Ps=80%

t

f z*

0.0

0.1

0.2

0.3

0.4

0.5

-2.0 -1.5 -1.0 -0.5 0.0

sound

fractured

Ps=80%

t

f z*

Fig. 6: experimental data in the εt-f z

* plane for AA 1050-O,

t0= 1 mm.

A similar trend has been found for a different sheet

thickness as well (t0=1 mm), as shown in Fig. 6. It is to

be noted that figures 5 and 6 provide a technologicalforming limit, i.e. nominal values of the process

parameters are used. A more intrinsic forming limit can

be obtained if, instead of using the nominal thickness

strain εt, the actual measured thickness strain ε is

considered. If one compares the theoretical values of

thickness strain (i.e. calculated wiht equation 1) to the

actual measured values, the graph in Fig. 7 can be

obtained (using the fractured experimental data of Fig.

6). The figure shows that:

• Measured strain data are consistently closer to

zero than calculated. Indeed, if the trajectories

followed by the robot are designed in order toform a certain angle α(z), the actual angle α(z)’

measured on the part will often be significantly

different (up to even 30 degrees in the worst

cases), due to a non completely plastic

deformation of the cup and, therefore, due to the

absence of a supporting die.

• Measured strain data at fracture seem to be

independent on the feed rate (the linear regression

R 2 is only 0.25), whereas the theoretical values of

strain at the fracture location are dependent on the

process parameters. In other words, there seem to

be an intrinsic value of minimum thickness strain

where fracture occurs.

R2 = 0.68

R2 = 0.25

-2.0

-1.5

-1.0

-0.5

0.0

0.0 0.5 1.0 1.5

f z

theoretical

measured

Fig. 7: experimental fracture data in the εt-f z

* plane for AA 1050-

O, t0= 1 mm.

4. The effect of the punch geometry on

formability

All the experiments described in the previous Sectionwere run with hemispherical end punches (r=1.1 mm and

r=1.5 mm) and applying a viscous liquid lubricant,

abundantly sprayed on the part surface before forming.

The radius of the spherical punch is expected to be

relevant in determining the deformation mode. If the

punch radius is small in respect of the sheet thickness, a

reduction of the diameter generates a concentration of

stress which might favor tearing by shear. Besides, if the

radius is small enough, the punch will not only deform

the sheet on the cup wall side, but also on the inner side,

generating an undesired local bulging, as shown in Fig.

8. On the other end, if the punch radius is large in respect

of the sheet thickness, an enlargement on the sphericalend diameter makes the deformation mode can shift from

pure shear conditions to drawing condition, thus

reducing the material forming limits.

Fig. 8: local bulge induced by the incremental forming punch.

Therefore, it seems that a good compromise might be

using a punch shaped as the one pictured in Fig. 9a. This

punch does not show a spherical end, but rather:

• a double curvature: a small curvature radius (1.3

mm) on the outer edge, where the plastic

deformation takes place and localized and shear

strains should be favored;

• a flatter geometry (radius 5 mm) on the central part,

in order to reduce the local bulging effect shown in

Fig. 8.



Fig. 9: double radius punch (a); punch with spherical roller, freely

rotating (b)

In order to test the efficacy of the newly designed

punch, a specific experiment has been designed,

executed and replicated three times. The cup obtained by

these three repeated experiments was formed using

decreasing nominal conicity angle α (from 38 to 24.6

degrees), and an increasing feed rate f z (from 0.9 to 1.56

mm). In other words, the path followed by the robot was

such that the probability Ps of having a sound partdecreases with increasing the forming depth z. The

planned path, if represented in the plane εt-f z*, creates a

line moving up-left towards decreasing Ps values, as

pictured in Fig. 10, which clearly shows that the new

punch greatly increased the process formability.

0

0.1

0.2

0.3

0.4

0.5

0.6

-1.5 -1 -0.5 0

sound

fractured

Ps=80%

new punch

t

f z*

0

0.1

0.2

0.3

0.4

0.5

0.6

-1.5 -1 -0.5 0

sound

fractured

Ps=80%

new punch

t

f z*

Fig. 10: tooling path represented in the εt-f z* plane for the punchshown in Fig. 9

5. The effect of friction on formability

In order to evaluate the effect of friction, several

experiments have been planned and executed withdifferent tribological conditions. Friction has been

changed in different ways.

• By controlling the amount of liquid lubricant. Some

experiments have been run without any lubricant

(condition L0), some with a deposition of an initial

layer of lubricant on the sheet (condition L1) and

some with a continuous feed (condition L2).

• By controlling the rotation of the tool around the

vertical “z” axis. Some experiments have been run

without any rotation (condition R0) and some with

a clockwise tool rotation (R1). Since the tool

trajectory was followed clockwise as well, thisincreses the relative motion (and thus the friction

forces) between the tool and the sheet.

In order to evaluate the different conditions in terms of

tribological conditions, a friction test has been

developed, based on the following considerations. When

a conical part is incrementally formed using, e.g.

clockwise trajectories, the undeformed bottom of the part

slowly follows a clockwise rigid body rotation, only as a

consequence of friction forces, as well shown by the

FEM results in Fig. 11. The simulation has been run witha friction coefficient f=0.12 and a constant feed rat f z=1

mm. After only 18 spirals (18 mm depth), with a punch

radius r=5 mm, the bottom of the cup showed a rigid

rotation about the z-axis equal to φ=0.23 degrees. Thus,

the rotation angle φ can be used as an indirect measure of

the friction coefficient f.

In order to test if a difference in the lubrication condition

may have an impact on formability, several formability

experiments have been run, using the tool path shown in

Fig. 13. Each experiments has been replicated 2 or 3

times and the maximum obtained value of f z* before

fracture has been recorded. The results of these tests aresummarised in Fig. 13. They show that a change in

friction might have a negative influence on formability,

but only for large variation (condition L1-R0 vs.

condition L0-R0). When friction increases, formability

might decrease due to different reasons:

• some abrasion on the sheet metal surface might

occur, especially for small values of punch radius r;

• undesired shear strains can appear in the sheet plane,

as testified by the rotation of the cup bottom.

Fig. 11: FEM plot (top and side view) of an incrementally formedconical cup, with variable feed rate and conicity; the top viewshows a clockwise rotation oh the elemental edges on thebottom of the cup.



0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

-1.5 -1 -0.5 0

t

f z*

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

-1.5 -1 -0.5 0

t

f z*

Fig. 12: tool path used for the formability tests

Fig. 13: relation between the angle φ obtained by the friction testand the maximum

6. Conclusions

The results of some experiments and FEM simulations

of negative dieless incremental forming on 1050

aluminium sheets have been presented and discussed.

The experiments showed that:

• For a given material and thickness, the forming limit

can be represented as a line in the εt - f z* plane (where εt

= ln(t/t0) and f z* =f z⋅(z/ρ)1/2

.

• Formability increases if using a punch with a double

curvature radius, i.e. with a nearly flat bottom and a

small forming radius, as the one pictured in Fig. 9.

• A moderate change in friction forces does not

significantly influences formability.

• A relevant increase in the friction makes formability

significantly decrease.

7. References

[1] M. Strano, 2003. Incremental forming processes: current and

potential applications, SME technical paper No. MF03-114.[2] Park J.-J., Kim Y.-H., 2003. Fundamental studies on the

incremental sheet metal forming technique, J. of Material Proc.

Tech., 140 pp. 447-453.

[3] Kim T.J., Yang D.Y., 2000. Improvement of formability for the

incremental sheet metal forming process, International Journal of

Mechanical Sciences 42 pp. 1271-1286.

[4] Shim M.S., Park J.-J., 2001. The formability of aluminum in

incremental forming, J. of Material Proc. Tech., 113 pp. 654-658

[5] Iseki H., 2001. An approximate deformation analysis and FEM

analysis for the incremental bulging of a sheet metal using a

spherical roller, J. of Material Proc. Tech., 111 pp. 150-154.

[6] W. F. Hosford, J. L. Duncan, 1999, Sheet Metal Forming: A

Review, JOM, 51 (11), pp. 39-44.

[7] Banabic, Bunge, Pohlandt, Tekkaya, 2000. Formability of

Metallic Materials, Springer-Verlag.

[8] Filice L., Fratini L., Pantano F., 2001. CNC incremental formingof Aluminum alloy sheets, 5th Italian AITEM Conference, Bari.

[9] Kim Y.-H., Park J.-J., 2003. Effect of process parameters on

formability in incremental forming of sheet metal, J. of Material

Proc. Tech., 130-131 pp. 42-46.

[10] Wong, C.C., Dean, T.A., Lin, J. 2003. A review of spinning,

shear forming and flow forming processes. International Journal

of Machine Tools and Manufacture, 43, 14, pp. 1419-1435.

[11] Strano M., Ruggiero M., Carrino L., 2004. Representation of

Forming Limits for Negative Incremental Forming of Thin Sheet

Metals. International Deep Drawing Research Group 2004

Conference.

[12] L. H. Amino, K. Makita, T. Maki, 2000. Sheet Fluid Forming

and Sheet Dieless NC Forming, New Developments in Sheet

Metal Forming (Institute for Metal Forming Technology of the

University of Stuttgart), pp. 39-66.

Fz*

0.46

0.48

0.50

0.52

0.54

0.56

0 1 2 3 4 5

0.4704.40R0L0

0.4852.56R1L1

0.4852.03R1L2

0.5381.34R0L1

mmdeg lubr. cond.

Fz*

0.4704.40R0L0

0.4852.56R1L1

0.4852.03R1L2

0.5381.34R0L1

mmdeg lubr. cond.

Fz*

Negative Aluminium Sheets

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