View
1
Download
0
Category
Preview:
Citation preview
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: simone.ancellotti@unitn.it
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
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 expensive and requires a very
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 the process, the implicit methods often fail to
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
s. The computational model has been implemented and validated by a specific
experimental investigation covering the production of sample geometry on a workbench
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
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
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
process outcome, numerical analyses based on finite elements (FE) simulations can be very
effective. [He, 2009] [Heng, 2007] [Jafari, 2013]. However, FE simulations are highly
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
ensive and requires a very
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
he process, the implicit methods often fail to
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
s. The computational model has been implemented and validated by a specific
experimental investigation covering the production of sample geometry on a workbench
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 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 obtained results showed
he material deformation process.
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
-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
Analytical and Numerical Tools
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-
upon the distance from the weld centre. It can be noted that the fusion material displays a
higher than the parent metal, ranging between 280 HV
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
ling after welding.
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
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
sliding. For simplicity, this latter component will be not considered in the present work. The
upon the distance from the weld centre. It can be noted that the fusion material displays a
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
region of about 2 mm width comprised between BM and WM. Apparently, WM and HAZ are
Hardness profile measured along a direction normal to the weld seam.
The functional layout of the CNC machine used for the rotary draw bending tests is shown in
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
sliding. For simplicity, this latter component will be not considered in the present work. The
Proceedings of the 6th International Conference on Mechanics and Materials in Design,
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.
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
-141-
"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 study, the BD’s groove, having radial
rectangular section, is designed for the specific tube’s section and the required bending
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
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
tube, etc.), is one of the main issues in tube bending and is
investigated by several researchers [Kourosh, 2013]
One of the most promising way to reduce wrinkling and distortions is the adoption of a
that averts the flattering at the outer wall OFG [Jun Fang, 2013]. This component,
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
The rotary draw bending tests were performed by imposing to the linear and rotary actuators
the paths illustrated in Fig. 6a and 6b, for EW and HW bending, respectively. Specifically, the
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
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.
"Clamp Die" clamps the tube against the "Bending die" (BD). The last one rotates about its
study, the BD’s groove, having radial
rectangular section, is designed for the specific tube’s section and the required bending
EW or HW). The mean radius determines the final middle curvature of the tube.
w friction alloy, for instance bronze; it reduces the
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
tube, etc.), is one of the main issues in tube bending and is
, 2013] [Gangyao Zhao,
One of the most promising way to reduce wrinkling and distortions is the adoption of a
at the outer wall OFG [Jun Fang, 2013]. This component,
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 practice to avoid its use
when the bending die radius is small because of excessive thinning of the walls at the
The rotary draw bending tests were performed by imposing to the linear and rotary actuators
for EW and HW bending, respectively. Specifically, the
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
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
Analytical and Numerical Tools
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
negligible transversal shear deformation in the material during the drawing process.
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
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 principal axis. The contribution of the
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
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
negligible transversal shear deformation in the material during the drawing process.
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
been refined after a convergence analysis. The optimal element size has been found to be
principal axis. The contribution of the
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
Proceedings of the 6th International Conference on Mechanics and Materials in Design,
Editors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Az
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.
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
-143-
neglecting the presence of the weld seam. This issue will be addressed at the end of the paper.
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-body-constrain with infinite stiffness
are imposed to the cylindrical support, which works as an axial prismatic joint on the tube
clamp die, the bending die, the pressure die, and the wiper. This seems reasonable in view of
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
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.
is distance between mandrel’s tip and bending die’s axis, projected along
principal tube’s axis the mandrel. This parameter specifies how much the component
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.
The tube characteristic dimensions used in the model slightly differ from the nominal ones
constrain with infinite stiffness
works as an axial prismatic joint on the tube, the
clamp die, the bending die, the pressure die, and the wiper. This seems reasonable in view of
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
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 plastic
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.
’s axis, projected along
principal tube’s axis the mandrel. This parameter specifies how much the component
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
Analytical and Numerical Tools
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
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
, as shown in Fig. 7.
Tube Profile in EW Bending, section plane defined in (a) ���� 10�� and
As index of the accuracy of the numerical results in representing the actual tube shape, we the
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
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
(b) ���� 20��;
As index of the accuracy of the numerical results in representing the actual tube shape, we the
Square (RMS) of the deviation of FEM results with respect to
Proceedings of the 6th International Conference on Mechanics and Materials in Design,
Editors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Az
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
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
-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��;
Figure 12d shows the comparison between the numerical and experimental evaluation of the
IFG and OFG wall thickness scanned as a function of the angular position
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
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°;
Figure 12d shows the comparison between the numerical and experimental evaluation of the
of the angular position αsec. As expected,
the outer surface experience a wall thinning that may affect its mechanical resistance.
In this paragraph the outcomes of the analysis of the HW Bending are presented following the
The profiles present great
the previous one, as shown in
Track_A
Analytical and Numerical Tools
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-
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.
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��
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, the higher
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
defined in (a) ����
and (e) ���� 160°;
Proceedings of the 6th International Conference on Mechanics and Materials in Design,
Editors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Az
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
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
-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
proportional to the hardness HV, the following equation is used to estimate the yield stress of
�
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.
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 - 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
proportional to the hardness HV, the following equation is used to estimate the yield stress of
(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
.
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 !"&' and
�&' and ��
#$%. See
2]
606.2527
524.6471
329.6845
Track_A
Analytical and Numerical Tools
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-
The mechanical properties of the three regions of the weld joint are implemented in the FE
Welding joint is divided in three regions in the FE model
6a 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
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
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
ess, especially if the weld joint is located on the inner surface of the bent tube. In the next
The mechanical properties of the three regions of the weld joint are implemented in the FE
6a 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
RMS deviation in HW Bending, assuming welding seam’s
���� 9��; (b) Tube
tion 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
ess, especially if the weld joint is located on the inner surface of the bent tube. In the next
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
-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
Analytical and Numerical Tools
-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.
Recommended