A ROTARY DRAW BENDING OF RECTAGULAR TUBES: …€¦ · PAPER REF: 5639 A ROTARY DRAW BENDING OF RECTAGULAR TUBES: EXPERIMENTS AND NUMERICAL ANALYSES Simone Ancellotti1(*), Matteo

Proceedings of the 6th International Conference on Mechanics and Materials in Design,

Editors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Azores, 26-30 July 2015

-137-

PAPER REF: 5639

A ROTARY DRAW BENDING OF RECTAGULAR TUBES:

EXPERIMENTS AND NUMERICAL ANALYSES

Simone Ancellotti1(*)

, Matteo Bendetti1, Vigilio Fontanari

1, Marco Tassan

2, Stefano Slaghenaufi

2

1Department of Industrial Engineering University of Trento, Via Sommarive 9, 38123 Trento (Italy) 2R&D EMEA Product Development Product Engineering Vehicle Research & Innovation, Via della Stazione,

27, 38123 Mattarello - Trento (Italy) (*)Email: [email protected]

ABSTRACT

This paper is aimed at investigating the rotary draw bending of rectangular tubes. For this

purpose, tubes with rectangular cross section of 20x40 mm, thickness 1.5mm, made of steel

Fe430 were bent, both the “hard way” and the “easy way”, to form a nominal angle of 90°. A

A Finite Element (FE) model was developed to perform the process simulation based on an

explicit dynamic time integration scheme using the commercial code ABAQUS. The FE

outcomes have been validated by comparison with experimental results. Specifically, a

Coordinate Measuring Machine (CMM) was used to determine the degree of bend as well as

the radius, the profile and the wall thickness of the bent sections. The obtained results showed

the capability of the FE modelling to predict the material deformation process.

Keywords: draw bending, tube, FEM, elastic mandrel, thickness

INTRODUCTION

Rotary draw bending of tubes is a very important production method adopted in different

industrial branches, such as automobile, aircraft, air conditioner, gas plans, fluid lines, etc. In

the majority of applications, round tubes are bent because the axisymmetry of the part helps

reduce any type of distortion. However, some structural applications, like roll-over protection,

frameworks, bumpers, playground equipment, require to bend rectangular tubes. This is not

an easy task, in fact the bending of rectangular tubing can result in distortion, the most

common of which is concavity on the inside diameter of the section. Tube bending can be

performed by different techniques such as tube compression, press bending, roll bending, etc.

[Vollertsen, 1999] [Yang, 2012]. Rotary draw bending will be considered in this work

because it particularly suitable for thin-walled tubes. Such manufacturing process is not

simple to investigate through analytical models or experiments because it includes material

and geometries nonlinearity; hence, the rectangular shape of tubes adds more complexities to

the problem.

The operating components used in the process are: bend die, clamp die, pressure die, wiper

die and mandrel; the last one is a component having adaptive form, which prevents the tube

section from distortion and collapse due to buckling. In the usual bending of round tubes, the

mandrel consists of a fixed part connected to a row of rounded rigid metal blocks jointed each

other [Xue, 2015]. Usually, the same mandrel can be conveniently shaped to fit to rectangular

pipes, but recent developments suggest substituting it with an internal mandrel of high-

density-plastic, pressed against the bent sections.

Elastic spring back needs to be compensated by overbending the tube, but the extent of the

angular displacement to apply to the workpiece is not known a priori. Therefore, the setting of

Track_A

Analytical and Numerical Tools

the process parameters is usually tackled

based on expensive experimental campaigns

process outcome, numerical analyses based on finite elements (FE) simulations can be very

effective. [He, 2009] [Heng, 2007] [Jafari, 2013]. However, FE simulations are high

nonlinear and strongly dependent on the time variable. Under these conditions, a critical issue

of the simulation is represented by the computational heaviness, since, if compared with

conventional processes, the modeling of tools paths is very time exp

hard dynamic analysis. For this purpose, a move towards the use of dynamic explicit time

integration schemes has appeared to be promising in the literature [Zhao, 2009], as, owing to

the strong nonlinear events occurring during t

converge.

In the present paper, a numerical and experimental approach has been adopted, based on the

development of a finite element model able to simulate the entire tools trajectory during the

forming process. The computational model has been implemented and validated by a specific

experimental investigation covering the production of sample geometry on a workbench

specifically developed.

In particular, tubes made of steel Fe430

and thickness 1.5 mm were bent both

“hard way” or HW (about y-y axis)

relation to the bending-direction.

Fig. 1 - Cross-Section of rectangular tube: (a) Nominal dimensions in mm; (b) wall

The FE outcomes have been validated by comparison with experimental results. Specifically,

a Coordinate Measuring Machine (CMM) was used to determine the degree of bend as well as

the radius, the profile and the wall thickness of the bent sections.

the capability of the FE modelling to predict t

-138-

usually tackled and partially solved by trial-and

ensive experimental campaigns [Zhu, 2013]. In order to efficiently predict the


effective. [He, 2009] [Heng, 2007] [Jafari, 2013]. However, FE simulations are high



conventional processes, the modeling of tools paths is very time expensive and requires a very



the strong nonlinear events occurring during the process, the implicit methods often fail to



s. The computational model has been implemented and validated by a specific


In particular, tubes made of steel Fe430 with rectangular section of 20x4

and thickness 1.5 mm were bent both the “easy way” or EW (about the x

y axis), in order to study the different tube bending resistance in

direction.

tion of rectangular tube: (a) Nominal dimensions in mm; (b) wall



radius, the profile and the wall thickness of the bent sections. The obtained results showed

the capability of the FE modelling to predict the material deformation process.

and-error approaches

[Zhu, 2013]. In order to efficiently predict the


effective. [He, 2009] [Heng, 2007] [Jafari, 2013]. However, FE simulations are highly



ensive and requires a very



he process, the implicit methods often fail to



s. The computational model has been implemented and validated by a specific


x40 mm (see Fig.1a)

about the x-x axis) and the

, in order to study the different tube bending resistance in

tion of rectangular tube: (a) Nominal dimensions in mm; (b) wall-names



The obtained results showed

he material deformation process.



-139-

EXPERIMENTAL MATERIAL

Rolling forming and welding manufacture is the process adopted to obtain the specimen-

tubes.

Taking in account the usual denominations, the four walls of rectangular pipe are named inner

flange IFG, outer flange OFG, right web RWB and left web LWB (see Fig 1b); The first and

the second one are the closest and the furthest wall to bending axis, respectively. The

remaining two, perpendicular to the same axis, work as lateral supports for the section.

The tube is made of construction steel Fe430, whose monotonic tensile proprieties were

determined in [Benedetti, 2015] and are displayed in Table 1. The alloy is assumed isotropic

for simplicity, implementing elastic and plastic behaviours. Table 1 - Fe430 properties

Fe430

Proprieties

Unit Value

Density Kg/m3

7800

Young modulus GPa

206

Poisson’s ratio 0.3

Yield stress MPa 330

As shown in Fig. 3, the welding seam is located along the centre line of the tube web.

Fig. 3 - Tube photograph showing the welding seam along the center line of the tube web.

The influence of the weld joint on the local mechanical properties of the tube is evaluated by

means of microhardness measurement. Specifically, the cross-weld hardness profile is

obtained using a Vickers microhardness tester. An indentation load of 500 g and a time-dwell

of 10 s are used. The indentations are spaced 0.2 mm apart, covering base material (BM), heat

affected zone (HAZ) and weld metal (WM). Fig. 4 illustrates the microhardness dependence

Track_A


upon the distance from the weld centre. It can be noted that the fusion material displays a

microhardness significantly higher than the parent metal, ranging between 280 HV

and 160 HV0.5 in the BM. The microhardness markedly increases in the HAZ, i.e. a transition

region of about 2 mm width comprised between BM and WM. Apparently, WM and HAZ are

hardened due to cooling after welding.

Fig. 4 - Hardness profile measured along a direction normal to the weld seam.

EXPERIMENTAL PROCEDURES

The functional layout of the CNC machine used for the rotary draw bending tests is shown in

Fig. 5.

Fig. 5 - Functional layout of

a circular cross

The "pressure die" or "Travelling

wall (OFG) without any normal relative motion. It helps reduce galling and marking

tube by alleviating the drag occurring

Sometimes the rear side of tube is sustained by a rear “booster” in order to control

sliding. For simplicity, this latter component will be not considered in the present work. The

-140-


higher than the parent metal, ranging between 280 HV

in the BM. The microhardness markedly increases in the HAZ, i.e. a transition


ling after welding.

Hardness profile measured along a direction normal to the weld seam.

EXPERIMENTAL PROCEDURES


Functional layout of the CNC machine used for the rotary draw bending tests

a circular cross-section tube is shown for illustrative purpose

Travelling pressure die" (PD) is always in contact with the tube's outer

ithout any normal relative motion. It helps reduce galling and marking

occurring during bending and wall thinning on the external wall.

Sometimes the rear side of tube is sustained by a rear “booster” in order to control



higher than the parent metal, ranging between 280 HV0.5 in WM

in the BM. The microhardness markedly increases in the HAZ, i.e. a transition


Hardness profile measured along a direction normal to the weld seam.


the CNC machine used for the rotary draw bending tests; here,

" (PD) is always in contact with the tube's outer

ithout any normal relative motion. It helps reduce galling and marking of the

wall thinning on the external wall.

Sometimes the rear side of tube is sustained by a rear “booster” in order to control the linear



Editors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Az

"Clamp Die" clamps the tube against the "Bending die" (BD). The last one rotates about its

principal rotation axis drawing the tube with it. In this

rectangular section, is designed for the specific tube’s section and the required bending

direction (EW or HW). The mean radius determines the final middle curvature of the tube.

The “wiper” is usually made up of a lo

wrinkling phenomenon and distortions of tube’s IFG before getting in contact with the

bending die. Wrinkling, caused by several operating conditions (material anisotropy, wiper

position, clearance mandrel-tube, etc.), is one of the main issues in tube bending and is

currently thoroughly investigated by several researchers [

2010].

One of the most promising way to reduce wrinkling and distortions is the adoption of a

“Mandrel” that averts the flattering

placed inside the tube, operates like a core, which, during the working process, “supports” the

sliding tube’s walls and avoids their relative collapse. It is common practi

when the bending die radius is small because of excessive thinning of the walls at the

stretched zone.

The rotary draw bending tests were performed by imposing to the linear and rotary actuators

the paths illustrated in Fig. 6a and 6b,

BD tool rotates by an angle 90° and 93°, in HW and EW, respectively. Usually, overbending

is applied to compensate the springback so as to reach the target bending angle. The bending

radius is 98 mm and 74 mm for HW and EW, respectively.

Fig. 6 - Angular/linear position v.s Time of BD and PD for EW Bending with “overbending” (a) and HW

The final shape of the tubes after forming is evaluated using a

(CMM). For this purpose, the outer and the inner surface were scanned along paths at

different distances �� from the lateral surface of the tube, as schematically shown in Fig. 7.

Moreover, CMM is used to scan the external perimeter of tube cross

different angular positions ��

walls after sectioning the tubes along the midplane.



-141-


principal rotation axis drawing the tube with it. In this study, the BD’s groove, having radial


EW or HW). The mean radius determines the final middle curvature of the tube.

The “wiper” is usually made up of a low friction alloy, for instance bronze; it reduces the



tube, etc.), is one of the main issues in tube bending and is

investigated by several researchers [Kourosh, 2013]


that averts the flattering at the outer wall OFG [Jun Fang, 2013]. This component,


sliding tube’s walls and avoids their relative collapse. It is common practi



the paths illustrated in Fig. 6a and 6b, for EW and HW bending, respectively. Specifically, the



d 74 mm for HW and EW, respectively.

Angular/linear position v.s Time of BD and PD for EW Bending with “overbending” (a) and HW

Bending (b);

tubes after forming is evaluated using a Coordinate Measuring Machine

r this purpose, the outer and the inner surface were scanned along paths at

from the lateral surface of the tube, as schematically shown in Fig. 7.

CMM is used to scan the external perimeter of tube cross-sections l

�� (Fig. 7) and to measure the thickness of the outer and inner

walls after sectioning the tubes along the midplane.


study, the BD’s groove, having radial


EW or HW). The mean radius determines the final middle curvature of the tube.

w friction alloy, for instance bronze; it reduces the



tube, etc.), is one of the main issues in tube bending and is

, 2013] [Gangyao Zhao,


at the outer wall OFG [Jun Fang, 2013]. This component,


sliding tube’s walls and avoids their relative collapse. It is common practice to avoid its use



for EW and HW bending, respectively. Specifically, the



Angular/linear position v.s Time of BD and PD for EW Bending with “overbending” (a) and HW

Coordinate Measuring Machine

r this purpose, the outer and the inner surface were scanned along paths at

from the lateral surface of the tube, as schematically shown in Fig. 7.

sections located at

(Fig. 7) and to measure the thickness of the outer and inner

Track_A


THE FINITE ELEMENT MODEL

The FE Model, shown in Fig. 8, is developed in Abaqus CAE environment and represents a

conceptual simplification of the draw

The very small ratio between

using shell elements, even th

negligible transversal shear deformation in the material during the drawing process.

The use of brick element introduces

unfavourable element aspect ratio and

heaviness of the analysis, being the time step

dimension. Shell elements were therefore adopted

model.

The tube was discretized using 4

type of flexural theory, characterised by reduced integration scheme,

deformation large-strain [ABAQUS, 2012].

and the clamp die are meshed with linear brick 8

been refined after a convergence analysis. The optimal element size has been found to be

about 5x1 mm, the longest side is parallel to the tube

fillet at the junctions between the tube walls is neglected; hence the tube section is modeled

with sharp edges. Initially, the tube material has been assumed to be homogeneous, thus

-142-

Fig. 7 - References for tube’s sections

THE FINITE ELEMENT MODEL

Fig. 8, is developed in Abaqus CAE environment and represents a

conceptual simplification of the draw-bending machine components involved in the process.

ratio between the thickness and the other dimensions of the

, even though the use of brick elements could account for the not


The use of brick element introduces however some problems concern

aspect ratio and produces a significant increment of the com

, being the time step strictly influenced by the

were therefore adopted in the present case for building up the

The tube was discretized using 4-nodes shell element (S4R) that enforces

, characterised by reduced integration scheme, hence

[ABAQUS, 2012]. Instead, the cylindrical support, the pressure die

and the clamp die are meshed with linear brick 8-nodes elements (C3D8R). The mesh has


about 5x1 mm, the longest side is parallel to the tube principal axis. The contribution of the



Fig. 8, is developed in Abaqus CAE environment and represents a

bending machine components involved in the process.

other dimensions of the tube suggests

h the use of brick elements could account for the not


some problems concerning the very

f the computational

strictly influenced by the smallest element

for building up the

nodes shell element (S4R) that enforces a Mindlin-Reissner

hence suitable for large

support, the pressure die

nodes elements (C3D8R). The mesh has


principal axis. The contribution of the





neglecting the presence of the w

The tube characteristic dimensions used in the model slightly differ from the nominal ones

and have been measured with caliper and CMM.

To model the kinematics of the machining tools, rigid

are imposed to the cylindrical support, which

clamp die, the bending die, the pressure die, and the wiper. This seems reasonable in view of

the much higher compliance o

The wiper is modeled as an ideal undeformable shell.

The "Mandrel", made of extruded polyamide 6, is a

section. It is fixed and constrained inside the tube with a clearance of about 0.25 mm. In the

numerical analysis, it is meshed with the brick elements C3D8R. The material is assumed

completely linear elastic, because the relative deformations are not enough to produce pla

strains. The mechanical properties are taken as those declared by the supplier company.

The relative position of the mandrel with respect to the bending die is shown in Fig. 9.

Accordingly, �� is distance

principal tube’s axis the mandrel. This parameter specifies how much the component

protrudes with respect to the zero position (

the cylindrical surface of BD. During EW bending, t

�� 30 mm, while; in the HW process more structural stiffness respect to the previous one, therefore the thin walls shall not

collapse.



-143-

neglecting the presence of the weld seam. This issue will be addressed at the end of the paper.


and have been measured with caliper and CMM.

To model the kinematics of the machining tools, rigid-body-constrain with infinite stiffness

are imposed to the cylindrical support, which works as an axial prismatic joint on the tube


the much higher compliance of the tube and the conspicuous reduction in computational cost.

The wiper is modeled as an ideal undeformable shell.

Fig. 8 - FEM model in ABAQUS

The "Mandrel", made of extruded polyamide 6, is a parallelepiped with chamfered terminal

xed and constrained inside the tube with a clearance of about 0.25 mm. In the


completely linear elastic, because the relative deformations are not enough to produce pla



is distance between mandrel’s tip and bending die’s axis, projected along


protrudes with respect to the zero position (�� 0), which corresponds to the tangent to the cylindrical surface of BD. During EW bending, the mandrel is positioned at a distance

in the HW process �� is set to 0 because that configuration shows

more structural stiffness respect to the previous one, therefore the thin walls shall not

eld seam. This issue will be addressed at the end of the paper.


constrain with infinite stiffness

works as an axial prismatic joint on the tube, the


f the tube and the conspicuous reduction in computational cost.

with chamfered terminal

xed and constrained inside the tube with a clearance of about 0.25 mm. In the


completely linear elastic, because the relative deformations are not enough to produce plastic



’s axis, projected along


corresponds to the tangent to

he mandrel is positioned at a distance

is set to 0 because that configuration shows

more structural stiffness respect to the previous one, therefore the thin walls shall not

Track_A


RESULTS FOR EASY WAY BENDING

In fig. 11a and 11b, the numerical and experimental profiles of OFG and IFG for EW bending

are plotted on different section planes normal to BD’s rotational axis. The position of section

plane is defined by ��, as shown in Fig. 7.

Fig. 11 - Tube Profile in EW Bending, section

As index of the accuracy of the numerical results in representing the actual tube shape, we the

have evaluated the Root-Mean

experimental data; the outcomes are shown in Table 2.

-144-

Fig. 10 - Mandrel position ��

RESULTS FOR EASY WAY BENDING



, as shown in Fig. 7.

Tube Profile in EW Bending, section plane defined in (a) �� 10�� and


Mean-Square (RMS) of the deviation of FEM results with respect to

experimental data; the outcomes are shown in Table 2.

Table 2 - RMS deviation in EW Bending

hsez

[mm]

RMS dev.

[mm]

Mean Err.

[mm]

10 0.5045 0.4397

20 0.6297 0.5175



(b) �� 20��;


Square (RMS) of the deviation of FEM results with respect to



Moreover, numerical and experimental estimations of the cross

different angular position are compared in

agreement.

Fig. 12 - EW Bending results: Tube Cro

Thickness Profile on section plane

Figure 12d shows the comparison between the numerical and experimental evaluation of the

IFG and OFG wall thickness scanned as a function

the outer surface experience a wall thinning that may affect its mechanical resistance.

RESULTS FOR HARD WAY BENDING

In this paragraph the outcomes of the analysis of the HW Bending are presented following the

same procedures, concepts and references of the previous one.

deviations from the experimental points in comparison

Table 3 and Fig. 13.

Table



-145-

eover, numerical and experimental estimations of the cross-section profiles taken at

different angular position are compared in Figures 12a, 12b and 12c, showing a good

EW Bending results: Tube Cross-Section in (a) �� 114°, (b) �� 140°

Thickness Profile on section plane �� 14��;


IFG and OFG wall thickness scanned as a function of the angular position


RESULTS FOR HARD WAY BENDING


ame procedures, concepts and references of the previous one. The profiles present great

deviations from the experimental points in comparison with the previous one, as shown in

Table 1 - RMS deviation in HW Bending

hsez

[mm]

RMS dev.

[mm]

Mean Err.

[mm]

5 1.485 1.468

9 1.126 1.014

section profiles taken at

Figures 12a, 12b and 12c, showing a good

and (b) �� 160°;


of the angular position αsec. As expected,



The profiles present great

the previous one, as shown in

Track_A


Instead, thickness is correctly evaluated and it follows the same trend. This unsatisfactory

agreement is imputed to the presence of the weld joint on the inner surface. In fact,

hardness of HAZ and WM suggests that the inner surface hinders the plastic flow involved in

the metal forming in a greater extent than that modeled in numerical analyses. This issue will

be addressed in the following Section.

Fig. 13 – HW Bending without welded material assumption; Profiles on section

5�� and (b) �� 9��; Tube Cro

(f) Thickness Profile on section plane

-146-


agreement is imputed to the presence of the weld joint on the inner surface. In fact,



be addressed in the following Section.

ding without welded material assumption; Profiles on section plane defined in

Tube Cross-Section in (c) �� 114°, (d) �� 140° and (e)

(f) Thickness Profile on section plane �� 8��


agreement is imputed to the presence of the weld joint on the inner surface. In fact, the higher



defined in (a) ��

and (e) �� 160°;



EFFECT OF THE WELD JOINT

The results of the microhardness tests

of the weld joint to be implemented in the FE simulations. Since the yield stress

proportional to the hardness HV, the following equation is used to estimate the yield stress of

the weld metal ��:

�� ∝ HV

��

HV�

HV�

∙ ��

where:

HV� is the hardness of weld metal;

HV� and �� are, respectively, original hardness and yield stress of the base material (BM);

The monotonic tensile curve of the weld material is obtained by increasing

up to the local yield stress value

compensate the offset due to the residual

Fig. 14

For the sake of simplicity, the weld joint is divided into a weld metal (WM) zone and heat

affected zone (HAZ), as shown in Fig. 15, where the hardness is indicated as

!"#$%, respectively; the predicted yielding stresses are respectively

Table 4.

Table

Location

WM

HAZ

Base Material



-147-

EFFECT OF THE WELD JOINT

The results of the microhardness tests have been used to reconstruct the mechanical properties

of the weld joint to be implemented in the FE simulations. Since the yield stress


�

is the hardness of weld metal;

are, respectively, original hardness and yield stress of the base material (BM);

c tensile curve of the weld material is obtained by increasing

up to the local yield stress value �� and appropriately shifting the hardening curve in order to

compensate the offset due to the residual deformation, as shown in Fig. 14.

Fig. 14 – Curve stress-strain, “shifting” due to welding.


affected zone (HAZ), as shown in Fig. 15, where the hardness is indicated as

, respectively; the predicted yielding stresses are respectively ��&'

Table 4 - Welding Seam zones proprieties

Young Module

[N/mm2]

HV averge

[HV]

()

[N/mm2

206000 282.79 606.2527

206000 244.7246 524.6471

Base Material 206000 153.7833 329.6845

have been used to reconstruct the mechanical properties

of the weld joint to be implemented in the FE simulations. Since the yield stress �� is nearly


(1)

(2)

are, respectively, original hardness and yield stress of the base material (BM);

c tensile curve of the weld material is obtained by increasing the elastic regime

and appropriately shifting the hardening curve in order to

.


affected zone (HAZ), as shown in Fig. 15, where the hardness is indicated as !"&' and

�&' and ��

#$%. See

2]

606.2527

524.6471

329.6845

Track_A


The mechanical properties of the three regions of the weld joint are implemented in the FE

model.

Fig. 15 - Welding joint is divided in three regions in the FE model

Table 5 and Figures 16a and 16b demonstrates that accounting for the local mechanical

properties of the weld joints permits to improve the accuracy of the estimation of the tube

profile and cross-section.

Table 5 - RMS deviation in HW Bending, assuming welding seam’s

Fig. 16 –-HW Bending, assuming welding seam;

CONCLUSIONS

A Finite Element simulation of rotary draw bending of rectangular tubes has been developed

and validated. The tubes were obtained through rolling forming and welding of steel sheets.

We found that the mechanical properties of the weld joint significantly affects the forming

process, especially if the weld joint is located on the inner surface of the bent tube. In the next

-148-


Welding joint is divided in three regions in the FE model

6a and 16b demonstrates that accounting for the local mechanical


RMS deviation in HW Bending, assuming welding seam’s

effect

hsez

[mm]

RMS dev.

[mm]

Mean Err.

[mm]

5 0.725 0.699

9 0.795 0.755

HW Bending, assuming welding seam; (a) Profiles on section plane defined in �

Cross-Section in �� 140°

tion of rotary draw bending of rectangular tubes has been developed



ess, especially if the weld joint is located on the inner surface of the bent tube. In the next


6a and 16b demonstrates that accounting for the local mechanical


RMS deviation in HW Bending, assuming welding seam’s

�� 9��; (b) Tube

tion of rotary draw bending of rectangular tubes has been developed



ess, especially if the weld joint is located on the inner surface of the bent tube. In the next



-149-

future we propose to investigate the effect of other process parameters, such as the position of

the mandrel, the clearance tube-mandrel and tube-wiper, bending radius, material anisotropy

and friction coefficient.

ACKNOWLEDGMENTS

The authors gratefully acknowledge Fiat Research Company for the support and BLM Group

s.p.a for the execution of experiments and for availability showed.

Best thanks to Nicolò Corsentino and Marco Cazzolli, Ph.D. of the University of Trento, for

the measures by CMM and Vickers hardness measurements.

REFERENCES

[1]-ABAQUS Analysis User's Manual., Version 6.11, Simulia 2012

[2]-M. Benedetti, V. Fontanari, B. Monelli, M. Tassan, (2015), “Single Point Incremental

Forming of Sheet Metals: Experimental Study and Numerical Simulation”, University of

Trento (Italy)

[3]-He, Y., Jing, Y., Mei, Heng, Z., and Yongle, L. K., “3D numerical study on wrinkling

characteristics in NC bending of aluminum alloy thin-walled tubes with large diameters under

multi-die constraints”, Computational Materials Science, 2009, pp. 1052- 1067. V

[4]-Heng, L., He, Y. Z., MeiZhicao, S., and Ruijie, G., “Role of mandrel in NC precision

bending process of thin-walled tube”, Int. J. of Machine Tools & Manufacture, 2007, pp.

1164-1175.

[5]-Jafari Nedoushan, Reza, “Effect of Mandrel, Its Clearance and Pressure Die on Tube

Bending Process via Rotary Draw Bending Method. International Journal of Advanced

Design and Manufacturing Technology”, [S.l.], v. 5, n. 5, apr. 2013, p. 47-52.

[6]-Jun Fang, Shiqiang Lu, Kelu Wang, Jianmei Xu, Xiaomei Xu, and Zhengjun Yao, “Effect

of Mandrel on Cross-Section Quality in Numerical Control Bending Process of Stainless Steel

2169 Small Diameter Tube,” Advances in Materials Science and Engineering, vol. 2013,

Article ID 849495, 9 pages, 2013. doi:10.1155/2013/849495

[7]-Kourosh Hasanpour, Mahmoud Barati, Behnaz Amini and Mehrdad Poursina, “The effect

of anisotropy on wrinkling of tube under rotary draw bending”, Journal of Mechanical

Science and Technology 27 (3) (2013) 783~792.

[8]-Gangyao Zhao, Yuli Liu, He Yang, “Effect of clearance on wrinkling of thin-walled

rectangular tube in rotary draw bending process”, Int J Adv Manuf Technol (2010) 50:85–92, DOI 10.1007/s00170-009-2508-7

[9]-Rohit Agarwal, “Tube Bending with axial pull and internal pressure”, Master Thesis,

Texas A&M University, May 2004.

[10]-Vollertsen F, Sprenger A, Kraus J, Arnet H (1999) “Extrusion, channel, and profile

bending: a review”. J Mater Process Technol 87:1–27

[11]-X. Xue, J. Liao, G. Vincze, J.J. Gracio, Modelling of mandrel rotary draw bending for

accurate twist springback prediction of an asymmetric thin-walled tube, Journal of Materials

Processing Technology, Volume 216, February 2015, Pages 405-417, ISSN 0924-0136,

http://dx.doi.org/10.1016/j.jmatprotec.2014.10.007.

Track_A


-150-

[12]-Yang H, Li H, Zhang ZY, Zhan M, Liu J, Li G (2012) “Advances and trends on tube

bending forming technologies”. Chin J Aeronaut 25(1):1–12. doi:10.1016/S1000-

9361(11)60356-7

[13]-Zhao, G. Y., Liu, Y. L., Yang, H., Lu, C. H., and Gu, R. J., “Three-dimensional finite-

elements modeling and simulation of rotary-draw bending process for thin-walled rectangular

tube”, Materials Science and Engineering, 2009, pp. 257-261. V

[14]-Y.X. Zhu, Y.L. Liu, H. Yang, H.P. Li, Improvement of the accuracy and the

computational efficiency of the springback prediction model for the rotary-draw bending of

rectangular H96 tube, International Journal of Mechanical Sciences, Volume 66, January

2013, Pages 224-232, ISSN 0020-7403, http://dx.doi.org/10.1016/j.ijmecsci.2012.11.012.

Documents

A ROTARY DRAW BENDING OF RECTAGULAR TUBES: …€¦ · PAPER REF: 5639 A ROTARY DRAW BENDING OF RECTAGULAR TUBES: EXPERIMENTS AND NUMERICAL ANALYSES Simone Ancellotti1(*), Matteo