art%3a10.1007%2fs00170-011-3208-7

7/29/2019 art%3A10.1007%2Fs00170-011-3208-7

http://slidepdf.com/reader/full/art3a1010072fs00170-011-3208-7 1/17

ORIGINAL ARTICLE

Investigation of the effect of roll forming pass design on main

redundant deformations on profiles from AHSS

John Paralikas & Konstantinos Salonitis &

George Chryssolouris

Received: 7 June 2010 /Accepted: 31 January 2011 /Published online: 29 March 2011# Springer-Verlag London Limited 2011

Abstract The tooling design in the roll forming process

plays a major role in the quality and successful mass production of a variety of complex profiled products, in

many industrial sectors. The roll forming line is

comprised of consecutive forming passes. Each roll

forming pass consists of a set of rotating rollers able to

bend the material as it passes through them. The roll

forming pass design plays a major role in the production

of profiles. The introduction of advanced high strength

steels (AHSS), such as the DP-series and TRIP-series,

has also posed new challenges for the design of the roll

passes. The current paper exploits explicitly the finite

elements (FE) method and investigates the effect of the

roll forming passes design on main redundant deforma-

tions, such as longitudinal stains at the edge of the

profile, shear strains on strips plane, thickness reduction,

and final produced cross section with springback. The

profiles discussed are symmetrical V- and U-sections

from the AHSS Dual Phase series (DP780). The gradual

lowering of the flower pattern design, known as

“downhill pass flow”, is discussed. The calculated

decrease in the peak longitudinal strains of up to 28%,

and the decrease in thickness of up to 38% are also

presented and discussed.

Keywords Cold roll forming . Modeling . AHSS . Pass

design . Downhill pass flow . Redundant deformations

1 Introduction

Cold roll forming is a major forming process for the mass

production of a variety of complex profiles from a wide

spectrum of materials and thicknesses. According to

Chryssolouris [1] and Lange [2] the roll forming process

is classified into the category of sheet metal forming by

bending with rotary tool motion. The plastic deformation of

a solid body is achieved by means of a bending load. The

metal strip enters into the roll forming mill, in a precut or

coil form, and it is gradually formed through consecutive

contoured rolls into complex shapes. Three dimensional

deformations of the material include transversal bending

and other additive redundant deformations. Panton et al. [3]

calculated analytically the development of longitudinal and

shear strains during the roll forming process. He stated that

longitudinal stains are produced at the flange, as the outer

edge travels a greater distance than the web does through

successive rollers (Fig. 1).

Panton et al. [3] have also discussed that both the

longitudinal and the shear strains cannot be simultaneously

minimized, but instead, a compromise between them should

be made. Defects on products such as camber, warping

(bow), twisting, edge waviness (buckling), and edge

cracking are caused mainly on these redundant deforma-

tions, namely the longitudinal bending and elongation, the

transversal elongation and the shear in strip's plane and

thickness direction [4] (Fig. 2).

Rolls are the tools that form the strip into the desired

shape and turn it into roll-formed products. Several factors

have to be taken under consideration when designing the

rolls that would form a particular product. These include

the number of passes required, the material width, the

flower design, the roll design parameters, and the roll

material [5]. The number of passes required is estimated,

J. Paralikas : K. Salonitis : G. Chryssolouris (*)

Laboratory for Manufacturing Systems and Automation,

Department of Mechanical Engineering and Aeronautics,

University of Patras,

Patras 265 00, Greece

e-mail: [email protected]

Int J Adv Manuf Technol (2011) 56:475–491

DOI 10.1007/s00170-011-3208-7

7/29/2019 art%3A10.1007%2Fs00170-011-3208-7


based on material properties, thickness of the strip, and

complexity of the profile to be produced [4] [5]. The strip

width can be calculated from the profile drawing, based onthe bend allowances calculated, the arc lengths of the

curved elements, and the straight lengths of the shape [6].

The flower design and orientation comprise the initial step

of the roll tooling design and represent the designated flow

of material into the mill, based on the number of passes

required. The roll design parameters include the design of

the rolls around each overlay of the flower pattern, and the

considerations for the diameter of the rolls as well as the

desired tolerances [4].

The scope of current study is to provide a simulation

model capable of predicting main redundant deformations

during the roll forming process. Moreover, current study

investigates the effect of the roll passes design consider-

ations on main redundant deformations, such as longitudi-

nal and shear strains at the edge of the profile, reduction of

thickness, and final produced cross section with springback.

Investigation of design considerations for roll forming

passes is mainly focused on the flower design, the study

of downhill flow of the material into the mill, and the

variable bending radius along the forming passes for

symmetrical V- and U-sections profiles from advancedhigh strength steel (AHSS) Dual-Phase series and more

specifically DP780 with 1.2 mm thickness.

2 Critical review on cold roll forming simulation

Several studies have been carried out for the simulation of

the roll forming process. Over the last decade, the interest

in simulating and accurately predicting the deformations

during the roll forming and the geometrical characteristics

on the final product has been increased. The introduction of

new materials, such as the AHSS, into an “old” process has

brought about new challenges and accentuated existing

processing limitations. Paralikas et al. [7] and Salonitis et

al. [8] prepared a simulation model for the roll forming

process that can predict redundant deformations, such as

transverse and longitudinal strains and distribution onto the

cross section, as well as the final produced geometry. The

LS-Dyna code was used along with the solid elements for

the deformable strip. A V symmetrical section was

simulated, as the strip was pulled through the rigid rolls.

The main process parameters, such as line velocity, roll

gap, rolls diameter, friction, and distance between the

passes, were investigated as to their effect on undesired

Fig. 2 Main defects caused by redundant deformations on roll-formed

products [4]

Fig. 1 Outer edge travels

greater distance than web

through successive rollers

Fig. 3 A typical flower pattern design for a top-hat profile [6]

476 Int J Adv Manuf Technol (2011) 56:475–491

7/29/2019 art%3A10.1007%2Fs00170-011-3208-7


deformations during roll forming. It was concluded that the

inter-distance of the forming passes has a major influence

on the magnitude of the main redundant deformations.

Paralikas et al. [9] prepared an optimization method of the

roll forming process based on semi-empirical approach and

the Taguchi method. The responsibility of main rollforming process parameters on main redundant deforma-

tions was calculated for a U-shaped profile. Jeong et al.

[10] has carried out a simulation analysis for the roll

forming process so as to compare two different flower

patterns for the upper member of a rail mechanism. The

design of the two flower patterns was performed and then

simulated with the use of the SHAPE-RF. This roll forming

analysis program exploits the rigid-plastic finite element

method. Prediction of longitudinal strains along the roll

forming direction and the estimation of straightness were

compared for the two flower designs leading to a

conclusion for the prevention of defects on the roll-formed product. Bui et al. [11] presented a three-

dimension finite element analysis in order to simulate the

roll forming process. The simulation results, for longitudi-

nal strains at the edge of the strip, were compared with the

experimental ones, and were found in good comparison. A

U-shaped section was studied by using a rigid-plastic model

and Swift 's isotropic strain hardening law so as for the

material's behavior to be described. A parametric study was

implemented where the yield limit and work-hardeningexponent play a major role on the product 's quality. The

forming speed and the friction were found to have less

influence on the product 's quality. Lindgren [12] prepared a

simulation model in order to investigate the change in the

longitudinal peak membrane strain, at the flange edge, and

the deformation length when the yield strength increased.

This could provide the estimation of the passes and distance

between them required for each material to be roll formed.

The finite element program MARC/MENTAT was used

with the material modeled as elasto-plastic, with the

isotropic material hardening rule and the Von Misses yield

surface as well as the associated flow rule. The simulation

results predicted that the longitudinal peak membrane strain

decreased and the deformation length increased when the

yield strength was increased. Tehrani et al. [13] used finite

element simulation in order to predict localized edge

Fig. 6 Initial V-Flower1 design and downhill pass line of V-Flower2

development into the mill side and frontal views

Fig. 5 Flower pattern design for the “V-Flower2” with 8 forming

stations (0 – 5 – 10 – 20 – 30 – 40 – 50 – 55 – 60° bending angles), with down-

hill pass line of 3 mm

Fig. 4 Flower pattern design for the “V-Flower1” with 8 forming

stations (0 – 5 – 10 – 20 – 30 – 40 – 50 – 55 – 60° bending angles)

Fig. 7 V-Flower1 schematic for forming station 2 (10°) to forming

station 3 (20°)

Int J Adv Manuf Technol (2011) 56:475–491 477

7/29/2019 art%3A10.1007%2Fs00170-011-3208-7


buckling, as a limiting factor in the cold roll forming of a

circular tube section. ABAQUS 6.4 was used for the

simulation models built with S4R shell elements. Thesimulation results showed that if the profile angle, in the

first station, exceeded a particular limit, the reverse

bending applied by the rolls of the second station might

induce local edge buckling. Boman et al. [14] used the

Arbitrary Lagrangian Eulerian formalism in order to

compute the steady state of the U-shaped cold roll forming

process. This method allowed for refining meshing near

the tools, giving in that way an accurate contact prediction

all along the simulation with a limited number of

elements. During simulation, each time step is divided

into two phases: the first one is purely Lagrangian and the

second one the ALE phase. The ability of managing

efficiently the free surfaces of the sheet has been proven.

Han et al. [15] presented a B3-spline finite strip method

that can investigate the effects of the main roll forming

process parameters, such as bend angle increment, strip

thickness, material yield limit, flange length, web width,

and the distance between the roll stations, on the

longitudinal strain at the edge of the profile. The B3-spline

finite strip method (B-FMS) divides the displacement function

into two parts. The first is the transverse Hermitian cubic

polynomials and the second is the longitudinal B3-spline

function that describes the boundary conditions of the strip.

The analytical results were in agreement with the practice of

roll forming, as the longitudinal strain increased by

increasing the bend angle increment, strip thickness, material

yield limit, flange length, and the web width. Decreasing thedistance between the rolls could bring a decrease in the

longitudinal strains at the edge. Lindgren [16] investigated

the longitudinal strains at the flange and the prediction of the

deformation length during the forming of a U-channel.

Longitudinal strains in the flange of the profile can emerge

since the material in the flange travels a greater distance

during the roll forming, through successive rollers. These

redundant deformations should not enter the plastic region in

order for the plastic strains, in that direction, and the defects

in the finished profile, such as camber, bow, and twist to be

avoided.

3 Critical review on roll forming passes design

The roll passes design may be the most important step for

the preparation of the roll forming mill. The orientation of

the part is initially decided by the designer. The term

orientation is defined as the position of the profile at the

exit of the last pass. After that, the designer may estimate

the number of passes required. Given the number of passes,

the designer then, establishes the flow of the material. The

flow of material into the mill is established by the flower

pattern. The flower pattern is the station-by-station overlay

of progressive section contours (Fig. 3). This flower pattern

shows graphically, the number of passes, required to form a

given profile and the way that the material flows into the

mill. Next, the designer is able to draw each roller onto the

flower pattern for every roll station [4-6].

Several studies have been carried out for the roll pass

design and the optimization of the flow of material during

Fig. 8 V-Flower2 schematic for forming station 2 (10°) to forming

station 3 (20°)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

00-05 05-10 10-20 20-30 30-40 40-50 50-55 55-60

Bending angles (Degrees)

E l a s t i c L o n g i t u d i n a l

S t r a i n

a t e d g e ( % )

V-Flower1 V-Flower2

F ig . 9 Elastic longitudinal

strains (percentage) calculated

for bending angles for V-

Flower1 and V-Flower2


7/29/2019 art%3A10.1007%2Fs00170-011-3208-7


the roll forming process. Techniques that were used for

aiding the design of the roll passes were among others, the

response surface method, the artificial neural networks, and

the knowledge-based expert systems. Zeng et al. [17]

investigated the optimization of the roll passes design of

the cold roll forming process, based on the response surface

method. The response surface method was used for

building mathematical models that represent the effect of

forming angle increment, roll radius on springback angle,

and maximum edge longitudinal strains. In the optimization

process, the springback angle and the maximum edge

longitudinal strains at each stand were set as the objective

function and constraint condition, respectively. Minimiza-

tion of the springback could bring an optimized forming

angle and a roll radius on each forming station, as linking

them to the optimum design of the forming passes. Zhang

et al. [18] introduced a procedure for estimating the way

that the roller locating errors influenced the roll forming of

a quadrate steel tube. This investigation is based on the

formulation of the stream of variation (SOV) model of

roller dimensional errors using the CAD/CAPP parameters

of the process. Such a model was used for simulating the

variation propagation during the process. The SOV model

is also experimentally tested in a two-station case with three

different products. Li et al. [19] presented an intelligent

optimization approach that integrated machine learning and

optimization techniques. The intelligent response surface

methodology and the gradient-based optimization scheme

are presented. The optimization algorithms have been

implemented in order to identify the optimal design results.

The optimization of the roll diameters of a U-channel roll-

formed section was implemented as a criterion of the

uniform longitudinal strains along the cross section. The

final optimal design was made after 300 generations and the

longitudinal strains were compared with the initial and the

optimum designs. Downes et al. [20] developed a technique

using an artificial neural network to assist in the design of

the roll forming tools. The system developed has 63 storage

locations to find integral shapes and provides a method of

studying the roll-forming tools, which have been used in

previous designs, and may help formulate a better solution

into the current design task. Moreover, the system can

guide an inexperienced designer and it can be used as a

training aid for the tooling design. Mynors et al. [21]

examined the design process and the way that a company

could put in place a design production control that would

allow the ranking of designs, in terms of quality and

efficiency. Benefits, such as enhanced understanding of

their design process route and its inconsistencies and

failings, have emerged and savings have occurred. The

DataM Software [22] developed a complete solution for

design and analysis of the roll forming process. The Copra ®

0.1057

0.105750.1058

0.10585

0.1059

0.10595

0.106

0.10605

0.1061

0.10615

0.1062

0.10625

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Downhill Displacement (mm)

E l a s t

i c L o n g i t u d i n a l S t r a i n

( % )

Fig. 10 Elastic longitudinal

strain (percentage) at edge of the

V-Flower2 versus the downhill

displacement (millimeters)

0

0.1

0.2

0.3

0.4

0.5

0.60.7

0.8

40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210

Flange width (mm)

E l a s t i c L o n g i t u d i n a l S t r a i n

( % )

V-Flower1 V-Flower2

Fig. 11 Comparison of the two

flower pattern designs (VFlo-

wer1 and VFlower2) for elastic

longitudinal strains (percentage)

as the flange width A (milli-

meters) increased, for a value of

the downhill displacement

( D=10 mm)


7/29/2019 art%3A10.1007%2Fs00170-011-3208-7


Roll Design Husk (H1) allows for the accurate designing of

the flower pattern and the roll tooling. The Copra ®

FEA RF

is a Finite Elements Analysis tool for the roll forming

process, that automatically generates a computing model

from the flower pattern and the roll tooling design in

Copra ®. The roll forming services [23] offer a solution to

the designing of the rolls tooling, referred to as “Simply roll

design”, an easy to use software. Ubeco [24] offers the

profil roll forming design software as it provides quicker

working, planning, design and calculation for the drawingof the profile and the tooling, as a first step. The second

step is the Profile Stress Analysis, as a calculation tool for

lengthening and shortening the edges and the expected

strain development. The third step is the virtual roll forming

machine that integrates the finite elements analysis, with

the use of the abaqus explicit, and enables the accurate

prediction of stress and strain within the profile, while it

travels into the mill.

4 Geometry of the profiles — flower patterns design

4.1 V-section profile geometry

In the current study, three profiles have been investigated.

These are a V-section, a U-section and non-symmetrical U-

section profiles from AHSS DP780 and 1.2 mm thickness.

Several flower pattern designs have been investigated by

utilizing the finite-elements technology and the LS-Dyna

code. The flow of material into the mill and the downhill pass

line, the bending radius strategy along with the orientation of

the profiles have been discussed, investigated and analyzed.

Regarding the flow of material into the mill, it was the

effect of the flower pattern design that was studied on

redundant deformations for three different case studies. The

gradual lowering of the flow of material into the mill,

referred to as downhill, is a major design technique for the

improvement of the flower pattern design. When rollforming of a section takes place, the straight bend lines

travel in the horizontal plane, and the edges travel not only

horizontally but also upwards at the same time [4]. Thus,

the edges travel a longer distance than the straight lines do

on the web. Consequently, the longitudinal strains are

developed on the edges of the profile (Fig. 1). If

longitudinal strains at the edge exceed the yield limit of

the material, then defects, such as edge waviness, will be

presented on the finished profile. Lowering the flower

pattern gradually, referred to as a downhill pass line, the

natural flow of the material into the mill could be estimated.

Figures 4 and 5 present the flower patterns design for the V-Section of 60° bending angle. A common flower pattern

design, referred to as V-Flower1, was designed with eight

forming stations and with 0 – 5 – 10 – 20 – 30 – 40 – 50 – 55 – 60°

bending angles. For the design of the improved flower

pattern design, named V-Flower2, the pattern was gradually

lowered with a 3-mm-vertical difference from forming a

station to station and the same bending sequence was

followed (0 – 5 – 10 – 20 – 30 – 40 – 50 – 55 – 60°).

This gradual lowering, referred to as downhill pass line,

of the flower pattern design of the V-Flower2 resulted in the

decrease of the maximum vertical distance of the initial

horizontal strip plane, from 59 to 36.1 mm (22.9-mm

difference). This can also be seen in Fig. 6, as the pass line

was developed in the roll forming mill, and the two flower

pattern designs were compared. The downhill was set as

3 mm, and the inter-distance between the forming stations

was set at 300 mm.

Figure 6 presents the flow of the material into the mill

for the two different flower pattern designs. The “downhill

flow” is compared versus the conventional flow for the

Fig. 12 Deformation length during roll forming of a U-channel

section [16]

0

0.1

0.2

0.3

0.4

0.5

50 100 150 200 250 300 350 400 450 500 550 600 650

Inter-distance between the forming passes (mm)

E l a s t i c L o n g i t u d i n a l

S t r a i n ( % )

V-Flower1 V-Flower2

Fig. 13 Comparison of the two

flower pattern designs (VFlo-

wer1 and VFlower2) for elastic

longitudinal strains (%) as the

inter-distance between the

forming passes L0 (millimeters)

increased, for a value of the

downhill displacement

( D=10 mm)


7/29/2019 art%3A10.1007%2Fs00170-011-3208-7


roll forming of the V-section profile with a total bending

angle of 60°. Practically, this “downhill flow” could be

achieved in two ways. Firstly, for the roll forming

machines, with the drive shaft in one level, the mill

should have rolls of a larger diameter in the first passes.

This is not so practical, as the first rolls, of the larger

diameter, will run the material faster, and buckling could

occur between the passes. The second way is to have a roll

forming machine with adjustable up and bottom rollers in

a vertical direction. This could allow the use of the

appropriate roll diameters, as for buckling to be avoided.

Universal machines with universal joints on the shafts

could be used, and the height of the roll stations could be

adjusted in order for this “downhill flow” of the profile's

roll forming to be achieved.

The development of the longitudinal strain, at the edge of

the V-section profile, could be investigated. For the calcula-

tion of the longitudinal strain, the comparison of the strip 's

length in the middle, referred to as L0, could be made

considering the length calculated and that the edge travels

from one forming station to the other, referred to as L. Thus,

the longitudinal strain can be estimated, as the engineering or

nominal strain based on Lange [2] and Hosford et al. [25]:

e ¼ L À L0ð Þ L0 ¼ Δ L L0== ð1Þ

The definition of the true or logarithmic strain, ε, can be

defined as:

d " ¼ dL L= ) " ¼

Z dL L= ¼ ln L L0=ð Þ ¼ ln 1 þ eð Þ ð2Þ

Assumptions for the calculation of the longitudinal

strain, at the edge of the profile, could be made. The

bending radius of the profile was ignored, the flow of the

material from one forming station to the other was assumed

as linear, and only the geometric constrains have been taken

into account.

For the V-Flower1 the following nomenclature was

followed (Fig. 7):

A1 Bending angle in the second forming station (10°)

A2 Bending angle in the third forming station (20°)

A3 Angle of the strip's edge from the second to the third

forming station

L0 Initial length as the material travels in the middle of

the profile

L Edge length as it travels along the edge of the profile

Y 1 Height of the edge's tip in the second forming station

(10°)

Y 2 Height of the edge's tip in the third forming station

(20°)

A Flange width

The heights, Y 1 and Y 2, of the edge's tip in the two

forming stations, can be calculated:

Y 1 ¼ A sin A1ð Þ ; Y 2 ¼ A sin A2ð Þ ð3Þ

The angle of the strip's edge from the second to the third

forming station, A3, can then be calculated:

A3 ¼ tanÀ1 Y 2 À Y 1

L0

ð4Þ

So the edge length, L, can be calculated:

L ¼Y 2 À Y 1

sin A3

ð5Þ

The correction factor f c could be introduced here, as the

estimation of friction, thickness of the material, etc. The

value of correction factor f c was set to f c=1.2. This value

was estimated based on the longitudinal strain values

attained in experimental and simulation work reported in

the literature [4, 9-11]. Thus, the longitudinal strain, at the

Fig. 14 Flower pattern design for the “U-Flower1” with eight forming stations (0 – 5 – 15 – 25 – 40 – 55 – 70 – 80 – 90° bending angles),

and bending radius of 6 mm

Fig. 15 Flower pattern design for the “U-Flower2” with eight

forming stations (0 – 5 – 15 – 25 – 40 – 55 – 70 – 80 – 90° bending angles),

with downhill pass line of 3 mm and bending radius of 6 mm

Fig. 16 Flower pattern design for the“

U-Flower3”

with eight forming stations (0 – 5 – 15 – 25 – 40 – 55 – 70 – 80 – 90° bending angles),

with downhill pass line of 3 mm and variable bending radius

(1,000 – 350 – 200 – 100 – 50 – 25 – 12 – 6 mm)


7/29/2019 art%3A10.1007%2Fs00170-011-3208-7


edge of the strip, can be calculated based on Eq. 2 as

follows:

"1 ¼ lnL

L0

» f c ¼ ln

Y 2ÀY 1ð Þsin A3

L0

» f c

¼ ln

Y 2ÀY 1ð Þ

sin tanÀ1Y 2 ÀY 1ð Þ

L0

h i L0

» f c ð6Þ

For the V-Flower2 the following nomenclature was

followed (Fig. 8):

A1 Bending angle in the second forming station (10°)

A2 Bending angle in the third forming station (20°)

A3 Angle of the strip's edge from the second to the third

forming station

Ad Angle of the horizontal strip plane with the line

traveling in the middle of the profile

L0 Inter-distance between the forming stations

L0* Initial length as the material travels in the middle of

the profile

L Edge length as the length travels along the edge of the

profile

Y 1 Height of the edge's tip in the second forming station

(10°)

Y 2 Height of the edge's tip in the third forming station

(20°)

A Flange width

D Downhill displacement

The heights, Y 1 and Y 2, of the edge's tip in the two

forming stations can be calculated, based on Eq. 3. The

angle of the horizontal with the line traveling in the middle

of the profile, Ad, can be calculated as:

Ad ¼ tanÀ1 D

L0

ð7Þ

The initial length as the material travels in the middle of

the profile, L0*

, can be calculated as:

L»

0 ¼D

sin Ad

ð8Þ

The angle of the strip's edge from the second to the third

forming station, A3, can then be calculated as:

A3 ¼ tanÀ1 Y 2 À Y 1

L»

0 ! ð9Þ

Fig. 17 Springback after

bending of sheet metal [27]

Fig. 18 Shell163 and through

thickness integration points [29]

Table 1 Material properties used for DP780 and rigid rolls [ 31] [29]

Material properties for AHSS DP780

Initial strip thickness 1.2 mm

Friction coefficient 0.2

Density 7,860 kg/m3

Young modulus of elasticity 2.1 GPa

Poison ratio 0.3

Yield stress limit (0.2%) 495.33 MPa

Tangent modulus 2.26 GPa

Hardening parameter 1 (isotropic hardening)

Strain rate parameter C 196,815.04

Strain rate parameter P 4.09168

Failure strain 0.1808

Material properties for rigid rolls

Density 7,580 kg/m3

Young Modulus of Elasticity 2.07 GPa

Poison ratio 0.3


7/29/2019 art%3A10.1007%2Fs00170-011-3208-7


Thus, the edge length as the length travels along the

edge of the profile, L, is:

L ¼Y 2 À Y 1

sin A3

ð10Þ

The correction factor f c could be introduced here as the

estimation of friction, thickness of the material, etc. The

value of correction factor f c was set to f c=1.2. This value

was estimated based on the longitudinal strain values

attained in experimental and simulation activities in

literature. Again, the longitudinal strain, at the edge of the

strip, can be calculated based on Eq. 2 as follows:

"1 ¼ lnL

L»

0

» f c ¼ ln

Y 2ÀY 1ð Þsin A3

L»

0

» f c ¼ ln

Y 2ÀY 1ð Þ

sin tanÀ1Y 2ÀY 1ð Þ

L»

0

L

»

0

» f c

ð11Þ

Assuming the values for: A1=10°, A2=20°, D=3 mm, L=

300 mm, A=75 mm, the elastic longitudinal strains (percent-

age) for the two flower pattern designs can be calculated. The

results calculated for the elastic longitudinal strains (percent-

age) for V-Flower1 and V-Flower2 can be seen in Fig. 9.

It can be observed that for greater forming angles (10°), the

magnitude of the longitudinal strains calculated increased in

comparison with the smaller forming angles (5°). Moreover, it

can be seen from Fig. 9 that in V-Flower2, the longitudinal

strains have been significantly decreased in comparison with

V-Flower1, due to the “downhill pass line”. A more significant

decrease has been calculated for the greater forming angles.

The effect of downhill displacement on the longitudinal

strain at the strip's edge was calculated (Fig. 10). The

increase of downhill displacement can decrease the longi-

tudinal strain at the edge.

Moreover, it was calculated that with the increase of the

flange width ( A in millimeters) the longitudinal strain at the

edge of the strip was also increased. There was a

comparison made of the longitudinal strains, the V-

Flower1 and the V-Flower2 for the increase of the flange

width, for a given value of the downhill displacement for

D=10 mm (Fig. 11). It was calculated that for the increased

flange width, the difference of the longitudinal strain peak

between the two flower pattern designs has been increased.

It has been stated in literature by both Lindgren [16] and

Panton et al. [26] that the longitudinal strain is proportional

to the square of the distance from the bend line and it can

be calculated using the following equation:

" Ls ¼1

2r 2

d q

dz

2

ð12Þ

Where, r is the distance from the bend along flange

width, dz is an infinitesimal element of the length and d θ is

an infinitesimal element of the angle change.

Another crucial geometric condition of the roll forming

process is the inter-distance between the forming passes. As

Fig. 19 Meshing zones on deformable strip for half geometry of the

U-section profiles

Fig. 20 Simulation model into ANSYS LS-Dyna for the U-section

profile (half geometry due to symmetry of the profile)

Fig. 21 CAD of the model for verification (half geometry due to

symmetry of the profile)

Table 2 Material properties and model conditions [33], [34]

Model conditions

Material AISI 1015

Initial strip thickness 4.0 mm

Initial width 236.0 mm

Roll velocity 0.1 m/sec

Friction coefficient 0.2


7/29/2019 art%3A10.1007%2Fs00170-011-3208-7


Bui et al. [11] stated by increasing the distance between the

forming stations, a more progressive deformation is allowed

to develop in the strip flange. Thus, a higher recovery of the

strain is obtained and the plastic longitudinal strain, at the

edge, can be reduced. This can also be calculated by Eq. 6

and 11, as by increasing the inter-distance between the

forming stations, the longitudinal strain at the strip's edge is

reduced. For greater values of the inter-distance between the

forming passes, the longitudinal strains are not reduced in the

same way, since there is a critical length, referred to as

“deformation length”. Above this critical value of the

“deformation length”, the effect of the inter-distance,

between the forming passes on longitudinal strains at the

edge, is minimized. This “deformation length” is calculated

based on the minimization of the energy, required for the

bending and stretching in a roll station. It is much dependent

on the flange length, a, bending angle increment, Δθ, and on

the thickness of the material (Fig. 12).

The longitudinal strains are calculated and compared

for the two flower pattern designs, the V-Flower1 and the

V-Flower2, for a given value of the downhill displace-

ment. It was shown, in Fig. 13 that for reduced inter-

distance between the forming passes the longitudinal

strains were significantly reduced due to the downhill

flow pass. This is due to the fact that the angle of the

horizontal plane with the line traveling in the middle of

profile, Ad , is increased and the initial length as the

material travels in the middle of the profile, L0*

, is also

increased and affects the calculation of the longitudinalstrain at the edge of the profile.

4.2 U-section profile geometry

The second flower design studied is a standard U-section

profile with 90° bending angle. This is also a symmetrical

profile with eight forming stations (0 – 5 – 15 – 25 – 40 – 55 – 70 –

80 – 90° bending angles). Three designs have been proposed,

first with the strip formed in the horizontal plane, named U-

Flower1, second, with the application of the downhill pass

flow with downhill displacement of 3 mm, named U-Flower2,

and third, the same as the second one but with a variable bending radius, named as U-Flower3. The three U-section

flower designs are shown in Fig. 14 and 16.

The downhill flow of the pass line into the mill is also

investigated in the U-Flower2, but with different bending

angles. It was shown that the maximum height of the flower

pattern design was reduced from 50 mm to about 29 mm.

Thus, this reduction in the maximum height of about 21 mm

can influence the distance that the edge travels into the mill, as

discussed when comparing the V-Flowers (Fig. 15).

Another effect examined in the current study is the“variable

bending radius”, since the bending radius from one forming

station to the other is not the same, but it is gradually decreased

until the desired value has been reached. A larger bending

radius means that the compression and the stretching area are

larger. This can also affect the springback, as the springback in

the bending process, as well as in the roll forming process, is

influenced mainly from the bending radius, the material

thickness and the material properties (Fig. 16).

The springback is mainly caused by the elastic recovery

of the material. The springback in the bending process is a

function of yield stress, strain hardening and pre-straining.

As stated from Lange [2], the springback after the sheet

metal bending can be calculated from:

r ¼ a f À a i ¼1

K À 1

a i; where K ¼

a f

a i¼

r i þ t 2

r f þ t 2

ð13Þ

Where, ρ is the calculated amount of springback, ai is

the initial angle after bending, af is the final angle after

springback, r i is the bending radius before springback, r f is the bending radius after springback, t is the sheet

thickness and K is the springback ratio. The springback

ratio is influenced also from the material properties

(Fig. 17).

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0 250 500 750 1000 1250 1500 1750Roll Forming direction (mm)

L o n g i t u d i n a l S t r a i n %

Simulation Exper imental

Fig. 22 Longitudinal strains (percentage) along roll forming direction

comparison with experimental [33], [34]

Fig. 23 Contour of nodal solution for total strains in thickness

direction for U-section profile


7/29/2019 art%3A10.1007%2Fs00170-011-3208-7


5 Modeling of roll forming process

5.1 Comparison of the implicit with explicit finite element methods

Over the last decade, the roll forming process was modeled

with the use of finite elements. The roll forming process is

classified, like other sheet metal forming processes, as a

non-linear quasi-static problem. There are two finite

element equation solution methods for solving such prob-

lems, the implicit and the explicit.

The explicit finite element method was preferred in

the current study for the simulation of the roll forming

process, since many contact entities and large non-linear

dynamic phenomena exist. The ANSYS program withthe LS-Dyna explicit finite element code was used for

the non-linear dynamic analysis of the roll forming

process, in three dimensions. The implicit finite element

method and the ANSYS program were used for the

springback analysis of the roll-formed profiles. The

results from the LS-Dyna explicit analysis were imported

into an implicit analysis and springback was calculated,

as a fully elastic non-linear analysis. Recovery of the

elastic stresses has been induced.

5.2 Element type

For the simulation of the roll forming process, the shell

elements were used for both the deformable strip and the rigid

rolls. The fully integrated Belytschko-Lin-Tsay shell element,

referred to as Shell163, was used. The Shell163 element is

based on a combined co-rotational and velocity-strain formu-

lation [28]. Such an element is defined by four corner nodes.

These four corner nodes define the mid surface, and the

integration points are stacked vertically at the centroid of the

element [29], as shown in Fig. 18. Five integration points

through thickness were used for the analysis of the deformablestrip with the Gauss quadrature rule. This Gauss quadrature

rule provides the location of each integration point.

5.3 Material model and meshing

For the modeling of the material behavior of the deformable

strip, the elastic plastic isotropic and kinematic hardening

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400

Roll Forming Direction (mm)

E l a s t i c L o n g i t u

d i n a l S t r a i n ( % ) @ e

d g e

V Flower 1 V Flower 2 DP780 YP (%)

F ig. 24 Longitudinal strain

(percentage) at edge along roll

forming direction for V-section

profiles

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400

Roll Forming direction (mm)

S h e a r S t r a i n i n S t r i p ' s P l a n e

( % )

V Flower 1 V Flower 2

Fig. 25 Shear strain (percent-

age) in strip's plane along roll

forming direction for V-section

profiles


7/29/2019 art%3A10.1007%2Fs00170-011-3208-7


with strain rate dependency and failure, named as plastic

kinematic model, was used. The strain rate is taken into

account with the use of the Cowper – Symonds strain rate

parameters, which scale the yield stress by a strain rate

dependent factor [28].For the modeling of the non-deformable rolls, it was

the rigid material model used. The tooling elements,

which are considered as rigid, are bypassed into the

element processing and there is no storage allocated for

history variables, thus, making such elements very cost

efficient [28, 30].

For the simulation of the deformable strip in current

study, the DP780 steel was used with 1.2 mm thickness.

Data for the material properties of the strip and the rigid

rolls have been quoted in Table 1.

For the meshing of the deformable strip, the strategy

of separating the strip into zones was followed. Threezones were defined, the web zone, the bending zone

and the flange zone. The bending zone has the densest

meshing (element edge size=1), followed by the flange

mes hing z on e (elemen t e dg e s iz e = 1 .5 ). T he web

meshing zone has the smallest number of elements

(element edge size=5), due to the fact that this area is

not deformed. The quadrilateral shell elements were

used for the meshing procedure. This strategy was

followed for all the profiles studied in the current study. For the V-section, the web meshing zone does

not exist due to geometry. For the meshing of the rigid

rolls the automatic mesh procedure has been followed

(Fig. 19).

Based on this meshing strategy, for the V-section profile

model, 4,900 elements were used for the deformable strip,

in total and 9,765 elements for the rigid rolls. For the U-

section profile model, 8,016 elements were used for the

deformable strip and 8,551 elements for the rigid rolls. For

the calculation of the time step, the procedure followed was

that described in [32] and [29].

5.4 Contact, boundary, and loading conditions

For the contact of the deformable strip with the rigid roll, the

automatic surface-to-surface option was followed. The friction

-18

-16

-14

-12

-10

-8

-6

-4

-2

00 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Profile Width (mm) T o t a l S t r a i n

i n T h i c k n e s s D i r e c t i o n

( % )

V Flower 1 V Flower 2

Fig. 26 Total strain in thickness

direction (percentage) to the

final produced cross section of

the V-section profiles

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30 35 40 45 50

Horizontal Displacement (mm)

V e r t i c a l D i s p l a c e m e n t ( m m )

V Flower 1_Springback V Flower 2_Springback

V Flower 1_Formed V Flower 2_Formed

Fig. 27 Final produced cross

section and springback results

for the V-section profiles


7/29/2019 art%3A10.1007%2Fs00170-011-3208-7


coefficient was set for 0.2, as stated also into Bui et al. [11], inorder for the friction between the elements to be simulated.

For the loading conditions, the rolls were fully con-

strained and the deformable strip was pulled through them

with a constant velocity. The velocity used for the roll

forming simulation was V =350 mm/sec, as it is a common

velocity in the roll forming industry [4] [5]. The velocity

vector was not applied to all the nodes of the deformable

strip, as the relief design and the split rolls techniques were

followed for the V- and U-sections. Thus, only in the

bending meshing zone for the V-section and in the web

meshing zone for the U-section, the loading conditions

were applied.The V- and U-sections were modeled for the half

geometry, exploiting the symmetry of the geometries. This

led to computational time being saved, and to more robust

and accurate results. The deformable strip was constrained

in lateral displacements (Y -axis) only on the nodes of the

symmetry's line.

The overview of the model is shown in Fig. 20 for the

U-section profile geometry.

5.5 Model verification

Verification of the model was performed with a U-channel,which comprises three roll stations of 30°

– 60° – 90° bending

angles and a first non bending station with flat rolls used as

straightening station of the line, as shown in Fig. 21.

Experimental data are reported by Darm [33] and Hong et

al. [34] for longitudinal strains distribution along roll

forming direction. Material properties and modeling con-ditions are shown into Table 2. SHELL163 elements were

used for the rigid rolls, and for the deformable strip for the

verification.

The simulation results were compared with the experi-

mental ones from Darm [33], and Hong et al. [34] for the

longitudinal strains (percentage) at the edge of the strip

along the roll forming direction. The results were longitu-

dinal strains of a streamlines 1.5 cm away from the edge.

The simulation results were in good agreement with the

experimental ones, regarding the peaks of the longitudinal

strains at the edge of the profile (Fig. 22).

6 Results and discussion

The roll forming process was modeled based on the procedure

described in previous sections, utilizing the explicit finite

element method and the LS-Dyna code. Two models were

prepared for the V-section profile and three models for the U-

section profile, all exploiting the symmetry of the profiles. The

results gathered from the post-processing of the models

include the elastic longitudinal strain history at the edge of

the deformable strip along the roll forming direction, the shear

strain history at the strip's plane, along the roll formingdirection, the strain in thickness direction (Fig. 23), and

finally, the produced profile cross section as it was formed

and with a springback.

The longitudinal and shear strain history results were

calculated from the edge node, 24 mm away from the

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.160.18

0.2

0.22

0.24

0.26

0.28

0.3

0 150 300 450 600 750 900 1050 1200 1350 1500 1650 1800


E l a s t i c L o n g i t u d i n a l S t r a i n ( % ) @ E

d g e

U Flower 1 U Flower 2 U Flower 3 DP780 YP (%)

F ig. 28 Longitudinal strain

(percentage) at edge along roll

forming direction for U-section

profiles

Profile ID Angle before springback Angle after springback Springback angle

V-Flower1 59.83° 54.25° 5.58°

V-Flower2 60.083° 55.46° 4.61°

Differences 0.253° 1.35° 0.97°

Table 3 Calculation of spring-

back angles for V-section

profiles


7/29/2019 art%3A10.1007%2Fs00170-011-3208-7


frontal edge of each profile. This is due to the fact that the

first “hitting” of the deformable strip's frontal edge could

cause excessive distortion and significant “noise” to the

results.

6.1 V-section profiles results

For the V-section profiles, the V-Flower1 and the V-Flower2 pattern designs were studied. The difference

between these designs is the application of the downhill

pass flow of the V-Flower2, as shown in Fig. 5.

The longitudinal strains (percentage) at the edge of the

deformable strip, along the roll forming direction, were

calculated. The peaks of both profiles per forming stations

were recorded. The main issue of the elastic strains, in

longitudinal direction, is for the yield limit of the material

not to be surpassed. Remaining in the elastic region, there is

no residual plastic strain, in longitudinal direction, accu-

mulated. Accumulation of such plastic strain can cause

major defects on the roll formed products. In the current study, with the application of the downhill pass flow, the

peaks of strains in longitudinal direction, in magnitude,

were reduced in almost all the roll forming stations, as

shown in Fig. 24.

Especially, in the sixth forming station (50° bending

angle), the V-Flower1 seems to be surpassing the yield limit

of the material (DP780). With the application of the

downhill flow pass, all the peaks of strains in longitudinal

direction are kept under the yield limit of the material, and

the defects were prevented in the roll formed V-section.

Reduction of about 28% in the peaks of strains, in

longitudinal direction, was achieved with the application

of the downhill pass flow.

Shear strains (percentage) at the edge of the deformable

profile in the strip's plane direction were calculated along

the roll forming direction, as shown in Fig. 25. The shear strain is induced due to stretching and compressing of the

strip in a transverse direction. Reduction in the maximum

peak of shear strains by 19.55% has been achieved with the

application of the downhill pass flow in the V-Flower2.

Thickness reduction is another major result of the roll

forming simulation. The total strain (percentage) in thickness

direction results could predict reduction in thickness. With the

application of the downhill pass flow for the V-Flower2, the

thickness reduction was reduced by 38% against V-Flower1.

Moreover, the distribution of the total strain in thickness

direction along the final roll formed profile has been made

more uniform, with the peak to have been calculated in themiddle of the profile, as shown in Fig. 26.

The result calculated for the V-section profiles, is the final

produced cross section. These final last roll formed cross

sections ofV-Flower1 and V-Flower2 were plotted after the

roll forming process (explicit solution) and after the spring-

back analysis (implicit solution), as shown in Fig. 27.

There seem not to be great differences or distortion in

the predicted final cross sections after the roll forming

-0.3-0.25-0.2

-0.15-0.1

-0.050

0.050.1

0.150.2

0.250.3

0 200 400 600 800 1000 1200 1400 1600 1800


S h e a r S t r a i n i n S t r i p ' s P l a n e ( % )

U Flower 1 U Flower 2 U Flower 3

Fig. 29 Shear strain (percent-

age) in strip's plane along roll

forming direction for U-section

profiles

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

00 10 20 30 40 50 60 70 80 90 100

Profile Width (mm) T o t a l S t r a i n i n T h i c k n e s s D i r e c t i o n

( % )

U Flower 1 U Flower 2 U Flower 3

Fig. 30 Strain in thickness di-

rection (percentage) to the final

produced cross section of the U-

section profiles


7/29/2019 art%3A10.1007%2Fs00170-011-3208-7


process. The springback calculated angles, based on Eq. 13,

for the two flower pattern designs are quoted in Table 3:

The difference on the springback angle between the two

V-section profiles is less than 1°, which is of minor

importance. This can confirm that springback is only a

function of material properties, thickness of the strip and bending radius.

6.2 U-section profiles results

The same results were also calculated for the U-section

profiles. In this type of the profile, the downhill pass flow

and the variable bending radius along the roll forming

progression were also studied.

The elastic longitudinal strains (percentage), at the edge

of the strip, along the roll forming line direction of the three

flower pattern designs, are shown in Fig. 28. A significant

increase in the elastic longitudinal strains of the U-Flower3

has been calculated. Such strains pass into the plastic region

for almost all the forming stations. This means that the

plastic strain at the edge is accumulated in longitudinal

direction, and defects may occur to the final roll formed

product using the U-Flower3 flower pattern design. The U-

Flower2 has the lowest peak of longitudinal strains, at the

edge of the profile, with 6.36% reduction from the U-

Flower1 and 33.78% reduction from the U-Flower3.

The shear strains (percentage) in the strip's plane were

calculated along the roll forming direction, as shown into

Fig. 29. Once more, the U-Flower3 shows increased shear

strain accumulation in almost all of the forming stations.

This is due to the fact that the increased bending radius can

cause increased stretching in the strip's plane direction.

Predicted calculated values for the shear strains have shown

again minimum peak values for the U-Flower2 with 10.42%

reduction from the U-Flower1 and 15.26% reduction from

the U-Flower3.

The calculated values of the total strain (percentage) in

thickness direction, as a reduction in thickness, for all the U-

section flower pattern designs are shown in Fig. 30. A

significant decrease in thickness was calculated for the U-Flower3 with 136.35% reduction against the U-Flower1 and

107.66% reduction against the U-Flower2. The difference of

thickness reduction between the U-Flower2 and U-Flower1

is 13.81%, with the U-Flower1 having the greatest value of

thinning in thickness direction. Smaller value for thinning in

the thickness direction results in such a U-section profile,

with the downhill pass flow applied and a variable bending

radius along the roll forming progression.

The calculated results for the final cross section and

springback angles of the U-Flower2 and U-Flower3 are

shown in Fig. 31. The U-Flower1 was not compared with

the other flower pattern design, as it had been proven from previous results of the V-sections that the springback

differences between the V-Flower1 and V-Flower2 were

minor. Thus, only U-Flower2 and U-Flower3 were com-

pared, since the effect of the variable bending radius, along

the forming stations, will be discussed here.

It was calculated that the springback was increased

significantly for the U-Flower3. Results of the angles

before and after the springback have been quoted in

Table 4.

This means that the designated bending radius, from one

forming station to the other, would have an effect on the

final produced roll formed product. As more material is

“ pushed” into the corner, during the continuous bending

operation, the recovery of the elastic stresses would have a

greater effect on the final springback angle.

7 Conclusions and future work

The effect of the flower pattern design on the main redundant

deformations and the final produced cross section was studied

in the current paper. The design of the flower patterns included

the application the downhill pass flow and the variable

bending radius along the roll forming passes. Two symmet-

rical profiles were studied analytically and the finite element

methods were utilized. The explicit finite element method was

0

5

10

15

20

25

30

35

40

45

50

55

0 5 10 15 20 25 30 35 40 45 50 55

Horizontal Displacement (mm)

V

e r t i c a l D i s p l a c e m e n t ( m m )

U Flower 2 Formed U Flower 2 Springback

U Flower 3 Formed U Flower 3 Springback

Fig. 31 Final produced cross section and springback results for the U-

section profiles

Profile ID Angle before springback Angle after springback Springback angle

V-Flower2 89.99° 88.42° 1.57°

V-Flower3 89.77° 86.64° 3.13°

Differences 0.22° 1.78° 1.56°

Table 4 Calculation of spring-

back angles for U-section

profiles


7/29/2019 art%3A10.1007%2Fs00170-011-3208-7


used for the simulation of the roll forming process, as a non-

linear dynamic problem, while the implicit finite element

method was used for the prediction of the profiles' springback,

as a fully elastic non-linear problem.

A calculation of the elastic longitudinal strains was

implemented, based on the geometric constraints, and as proven the longitudinal strains are proportional to the

flange width and to the bending angle increment. The

downhill pass flow effect was calculated for the V-section

profiles, and the effects of the flange width and inter-

distance between the forming passes has shown that the

application of the downhill pass flow could reduce the

longitudinal strains at the edge. The results from the finite

element analyses (Table 5) have shown reduction in the

elastic longitudinal strains by about 28% on the V-section

profiles and by about 6.36% on the U-section profiles only

with the application of the downhill pass flow technique on

the flower pattern design. Proportional effects were also

calculated for the shear strains on the strip 's plane at the

edge of the profile. Moreover, the reduction of thickness

was improved for the cross sections under study, by 38%

for the V-sections and by 13.81% for U-sections, with the

application of the downhill pass flow. The springback has

shown that it remained unaffected from the application of

the downhill pass flow. Another investigation on the flower

pattern design was the application of the downhill pass flow

and in the meantime, the variable bending radius along the

forming passes. This has shown significant improvements

on the thickness reduction by 107.66%, but negative effects

on other redundant deformations as well as on the final

produced profile with an increased springback angle. More

specifically the results have been summarized into the

following table for different profiles and concepts and the

achievements based on the model responses.

The next steps to be taken for the forming passes

design would be the investigation of more complex and

non-symmetrical profiles. Moreover, the study of the

effect of the forming passes design techniques could

involve more materials, as well as investigate the effect

of each material on the main redundant deformations and

on the springback.

Acknowledgment The work reported in this paper was partially

supported by CEC/FP6 NMP Programme, “Integration Multi-

functional materials and related production technologies integratedinto the Automotive industry of the future-FUTURA” (FP6-2004-

NMP-NI-4-026621).

References

1. Chryssolouris G (2005) Manufacturing systems-theory and prac-

tice, 2nd edn. Springer-Verlag, New York

2. Lange K (1985) Handbook of metal forming. McGraw-Hill, New

York

3. Panton SM, Duncan JL, Zhu SD (1996) Longitudinal and shear

strain development in cold roll forming. J Mater Process Technol

60:219 – 224

4. Halmos GT (2006) Roll forming handbook. CRC, New York 5. Wick C, Benedict J, Veilleux R (1984) Tool and manufacturing

engineers handbook, Volume 2 Forming, SME

6. Alvarez W (2006) Roll form tool design. Industrial Press Inc,

New York

7. Paralikas J, Salonitis K, Chryssolouris G (2009) Investigation of

the roll forming process parameters ' effect on the quality of an

AHSS open profile. Int J Adv Manuf Technol 44:223 – 237.

doi:10.1007/s00170-008-1822-9

8. Salonitis K, Paralikas J, Chryssolouris G (2008) Roll Forming of

AHSS: Numerical Simulation and investigation of effects of main

process parameters on quality, 1st International Conference of

Engineering Against Fracture, Patras, Greece

9. Paralikas J, Salonitis K, Chryssolouris G (2010) Optimization of the

roll forming process parameters — a semi empirical approach. Int J

Adv Manuf Technol 47:1041 –

1052. doi:10.1007/s00170-009-2252-z10. Jeong SH, Lee SH, Kim GH, Seo HJ, Kim TH (2007) Computer

simulation of U-channel for under-rail roll forming using rigid-

plastic finite element methods. J Mater Process Tech. doi:10.1016/

j.jmatprotec.2007.11.130

11. Bui QV, Ponthot JP (2007) Numerical simulation of cold roll-

forming processes. J Mater Process Tech. doi:10.1016/j.

jmatprotec.2007.08.0 73

12. Lindgren M (2007) Cold roll forming of a U-channel made of high

strength steel. J Mater Process Tech. doi:10.1016/j.jmatprotec.2006.12.017

13. Tehrani MS, Naeini HM, Hartley P, Khademizadeh H (2006)

Localized edge buckling in cold roll-forming of circular tube

section. J Mater Process Technol 177:617 – 620

Table 5 Summary of the results and achievements for different profiles and concepts

Profile/concept Model response/measurement Achievement

V-section/downhill flow Peaks of elastic longitudinal strain at edge 28% reduction

U-section/downhill flow 6.36% reduction

U-section/downhill flow and variable bending radius 33.78% increase

V-section/downhill flow Thickness reduction at the bending corner 38% reduction

U-section/downhill flow 13.81% reduction

U-section/downhill flow and variable bending radius 107.66% reduction

V-section/downhill flow Springback angle effect Minor effect

U-section/downhill flow Minor effect

U-section/downhill flow and variable bending radius 3.13° increase of springback


http://dx.doi.org/10.1007/s00170-008-1822-9

http://dx.doi.org/10.1007/s00170-009-2252-z

http://dx.doi.org/10.1016/j.jmatprotec.2007.11.130










http://dx.doi.org/10.1007/s00170-009-2252-z

http://dx.doi.org/10.1007/s00170-008-1822-9

7/29/2019 art%3A10.1007%2Fs00170-011-3208-7


14. Boman R, Papeleux L, Bui QV, Ponthot JP (2006) Application of

the Arbitrary Lagrangian Eulerian formulation to the numerical

simulation of cold roll forming process. J Mater Process Technol

177:621 – 625

15. Han Z-W, Liu C, Lu W-P, Ren L-Q, Tong J (2005) Spline finite

strip analysis of forming parameters in roll forming a channel

section. J Mater Process Technol 159:383 – 388

16. Lindgren M (2005) Modeling and simulation of the roll forming

process, Licentiate thesis, Lulea University of technology

17. Zeng G, Li SH, Yu ZQ, Lai XM (2008) Optimization design of roll profiles for cold roll forming based on response surface

method. Journal of Materials and Design. doi:10.1016/j.

matdes.2008.09.018

18. Zhang L, Ni J, Lai X (2008) Dimensional errors of rollers in the

stream of variation modeling in cold roll forming process of

quadrate steel tube. Int J Adv Manuf Technol 37:1082 – 1092

19. Li DY, Peng YH, Yin JL (2007) Optimization of metal-forming

process via a hybrid intelligent optimization technique. Struct

Multidisc Optim 34:229 – 241. doi:10.1007/s00158-006-0075-1

20. Downes A, Hartley P (2006) Using an artificial neural network to

assist roll design in cold roll-forming processes. J Mater Process

Technol 177:319 – 322

21. Mynors DJ, English M, Castellucci M (2006) Controlling the cold

roll forming design process. Annals of the CIRP 55/1/2006, p. 271

22. DataM Software GmbH, Copra ® Roll Forming, URL: http://www.roll-design.com

23. Roll Forming Services (RFS), URL: http://www.rollformingservices.

com

24. Ubeco, Profil Roll Forming Design Software, URL: http://www.

ubeco.com/profil.htm

25. Hosford WF, Caddell RM (2007) Metal forming mechanics and

metallurgy, 3rd edn. Cambridge University Press, Cambridge

26. Panton SM, Zhu SD, Duncan JL (1992) Geometricconstraints on the

forming path in roll forming channel sections, Proceedings of the

Institution of Mechanical Engineers. J Eng Manuf 206:113 – 118

27. Altan T (2003) Predicting springback in air bending, straight

flanging, Stamping Journal, URL: http://www.thefabricator.com/

PressTechnology/PressTechnology _ Article.cfm?ID=73528. Hallquist JO (2006), LS-Dyna Theory manual, Livermore Soft-

ware Technology Corp

29. ANSYS Release 10.0 (2005), ANSYS LS-Dyna User Guide,

ANSYS Inc

30. Rojeka J, Zienkiewiczb OC, Onatec E, Posteka E (2001)

Advances in FE explicit formulation for simulation of metal-

forming processes. J Mater Process Technol 119:41 – 47

31. FUTURA internal report, (2008), MFMs' processing and environ-

mental specifications; Material characterization database

32. Harewood FJ, McHugh PE (2007) Comparison of the implicit and

explicit finite element methods using crystal plasticity. Comput

Mater Sci 39:481 – 494

33. Darm K (1989) Determination of longitudinal strains in roll

forming of standard section in a multi-stand machine, Institute for

Production Technology34. Hong S, Lee S, Kim N (2001) A parametric study on forming

length in roll forming. Journal of Materials Processing Technol-

ogy 113(1):774 – 778


http://dx.doi.org/10.1016/j.matdes.2008.09.018


http://dx.doi.org/10.1007/s00158-006-0075-1

http://www.roll-design.com/


http://www.rollformingservices.com/


http://www.ubeco.com/profil.htm


http://www.thefabricator.com/PressTechnology/PressTechnology_Article.cfm?ID=735












http://dx.doi.org/10.1007/s00158-006-0075-1



art%3a10.1007%2fs00170-011-3208-7

Documents