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AFDEX, INTELLIGENT METAL FORMING SIMULATOR
METAL FORMING SIMULATION
The figure on the front cover is a
symbolic representation of the hot forging
process with the M standing for an upper
die, the S a lower die, and the F a
workpiece deformed from a simple
cylinderical billet. The initial temperature
of each is respectively 500, 200, and
1200° C. The axi-symmetric process
producing the letter F is also made out of the acronym for Metal
Forming Simulation (MFS). The figure suggests what MFS can do.
It can simulate not only metal flow lines and temperature
distribution but also various state variables including stresses,
strains, strain-rates, die pressures and stresses, die wears,
forming loads, damages and the like.
MFS technologies replaced costly and time-consuming trialand-error approaches in metal forming processes two decades
ago. MFS technologies have led to innovations in metal-forming
process design, and their influence now extends even to quality
control of metal-formed products, as well as to cost reduction and
productivity enhancement in the development of metal-forming
processes. In the near future, major customers of automobile
manufacturers may demand simulation results before purchasing
metal-formed products.
For example, small and midsized forging companies in Korea
have been using MFS technologies for much of the past decade,
and most of the leading Korean forging companies are now using
these technologies. As a result, dependency on metal-forming
technology of leading countries for processes and die design has
been drastically lowered, and forging industries have made
significant contributions to enhancing the global competitiveness
of the Korean automobile industry.
AFDEX
AFDEX, an Intelligent Metal Forming Simulator
AFDEX is a general-purpose metal forming simulator, which
meets the following requirements for intelligent bulk-metalforming (BMF) simulation (BMFS):
Solutions should be accurate, and volume loss or change due
to the numerical procedure should be minimized and
acceptable.
Intelligent meshing or remeshing capabilities should minimize
solution inaccuracies during remeshing and smoothing state
variables.
Optimized or adaptive meshing density capabilities should be
adopted to obtain a solution within a reasonable computational
time and without solution inaccuracy. Also, one should be able
to successfully mesh complex geometries.
Characteristic boundaries (or edges) and workpiece-die
interface boundaries should be accurately traced during
simulation and remeshing to minimize changes in the
boundary value problem due to remeshing. (This is particularly
important in MFS.)
Multi-stage BMF processes (especially multi-stage forging
processes) should be simulated automatically to reduce the
total simulation time (including both computational time and
user processing time between the stages).
The simulator should be convenient and user friendly.
Currently, AFDEX is theoretically based on the rigidthermoviscoplastic finite element method. As summarized in Table
1, there are a number of modules, including AFDEX 2D, AFDEX
3D, AFDEX 3D/OPEN, AFDEX HEXA/RING, AFDEX
HEXA/RFORM, AFDEX 2D/DIE, AFDEX 3D/DIE, AFDEX MAT,
AFDEX 2D/3D, AFDEX 2D/PRE/POST, AFDEX 3D/PRE/POST,
AFDEX DB, and AFDEX Web.
AFDEX 2D and AFDEX 2D/DIE use quadrilateral finite
elements. AFDEX 3D, AFDEX 3D/OPEN, and AFDEX 3D/DIE
employ tetrahedral elements, whereas AFDEX HEXA employs
hexahedral elements. AFDEX 2D/DIE and AFDEX 3D/DIE are
integrated die structural analysis programs that accompany the
respective BMF simulators, AFDEX 2D and AFDEX 3D. AFDEX
MAT provides users with highly accurate true stress-strain curves
for the materials in use at room temperature. AFDEX 2D/3D
allows combined 2D and 3D simulations to be carried out, and
permits 2D results to be more vividly visualized via a powerful 3D
computer graphic utility. AFDEX DB provides material and
process information, including flow stresses, forming machines,
and the like. Flow stresses for most commercial materials are
available with a wide range of state variables, including
temperature and effective strain. AFDEX Web is a special web
version of the simulator that can be used online by small or large
academic, commercial, and research communities. In the near
future, small or midsized Korean forging companies will be
supported with the AFDEX web version.
Of course, AFDEX completely satisfies the aforementioned
requirements for intelligent MFS. In what follows, characteristics
and typical applications of AFDEX are discussed in terms of its
intelligence.
Table 1 - AFDEX modules
Module
AFDEX 2D
AFDEX 3D
AFDEX 3D/OPEN
AFDEX HEXA/RING
AFDEX HEXA/RFORM
AFDEX 2D/DIE
AFDEX 3D/DIE
AFDEX MAT
AFDEX 2D/3D
AFDEX 2D/PRE/POST
AFDEX 3D/PRE/POST
AFDEX DB
AFDEX Web
Capability
2D MFS
3D MFS for most processes
Open die forging simulation
Ring rolling simulation
Roll forming simulation
2D die structural analysis
3D die structural analysis
Material identification
2D/3D combining capabilities
2D pre and post-processor
3D pre and post-processor
Database for material, etc.
Web version of AFDEX
Verification and Accuracy of AFDEX
Figure 1(a) shows the metal flow lines and effective strain
predictions generated during tensile tests for two specially preheat treated steels ESW95 and ESW105 and a special steel
SCM435. Figure 1(b) compares the results of tensile tests for
three different materials with predictions obtained from AFDEX.
The flow stress information used in the predictions was obtained
from AFDEX MAT. It can be seen from Figure 1(b) that the
engineering stress-strain predictions are so close to the
experimental results that the errors can be negligible, especially
from the necking point to the fracture point.
SCM435
ESW95
(a) Effective strain and metal flows
ESW105
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Experiment
1200
Experiment
Analysis
Experiment
Analysis
Experiment
Analysis
1000
Analysis
(SCM435)
SCM435
SCM435
(SCM435)
(ESW95)
ESW95
ESW95
(ESW95)
ESW105
(ESW105)
ESW105
(ESW105)
800
600
400
200
0
0
0.1
0.2
0.3
0.4
Engineering strain (mm/mm)
(b) Engineering stress-strain
(a) Metal flow lines carved in a first-generation hub-bearing race
Internal crack
Figure 1 - Comparison of predicted and experimental engineering
stress-strain curves in a tensile test
Figure 2 compares the difference in deformed shapes between
the experiments and predictions in cylinder compression and
forward extrusion of two different materials of SCM435 and
ESW105, indicating that the experiments closely match the
predictions.
Experiment
Analysis
Experiment
Analysis
Damage
Metal flow and temperature
(b) Cracks and their possible causes
Figure 3 - Comparison of predictions and experiments (2D, hot
forging, bearing race)
SCM435
ESW105
(a) Cylinder compression
Experiment
Analysis
Experiment
SCM435
Analysis
Figure 4 compares the predictions and experimental results for
an automatic five-stage cold forging process, showing that the
predictions are sufficiently accurate that costly process design
tryouts can again be eliminated or minimized. It should be
emphasized that even though the product has a comparatively
simple shape, the simulation of this kind of process is much more
difficult than it seems, as it not only requires very high precision
but also involves an intermediate piercing stage. Note that
simulation of automatic multistage-forging processes (sometimes
called fastener forming processes or former processes) should be
supported by more sophisticated capabilities of BMF simulators
(compared with common press forging processes), as their
consecutive stages are closely related, and the die-workpiece
tolerance at each stage is very tight.
ESW105
(b) Forward extrusion
Figure 2 - Comparison of deformed shapes
Figure 3(a) compares the experimental and predicted metal flow
lines generated by an automatic three-stage hot-forging of bearing
parts, in which a product quality depends on the soundness of the
metal flow lines. As this figure indicates, the predictions are
accurate enough to permit engineers to eliminate costly and timeconsuming process design tryouts that have traditionally been
deemed essential to the development of hot-forging processes for
bearing parts and other such items. Figure 3(b) shows the internal
cracks of the product with their possible causes in terms of metal
flow lines and temperature distribution.
Figure 4 - Comparison of predictions and experiments (2D, cold
forging, automotive part)
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A coupled analysis of both temperature and deformation was
carried out for a hammer forging process for a ship engine using a
counter-blow hammer forging machine with a capacity for
predicting the number of blows attempted. The predictions and
experimental results were in very close agreement in terms of the
final product shape, as shown in Figure 5 and the predicted
number of blows was also acceptable.
(a) Bending
(b) sizing
Figure 7 - Comparison of predictions and experiments (3D, cold
forging, rotor pole)
A bevel gear enclosed die forging process was simulated. As
this is a representative process in net shape manufacturing, a
precision simulation is required. Figure 8 compares the
predictions and experimental results, and a close similarity
between the simulation and experiment is once again
demonstrated.
Figure 5 - Comparison of predictions and experiments (3D,
hammer forging, ship engine crankshaft)
A hot ring-rolling process was simulated using AFDEX
HEXA/RING, and Figure 6(a) shows a good match between the
predictions and experimental results. A cold ring-rolling process of
a taper roller bearing race was also simulated, and the reason for
the under-filling defect formation was shown in Figure 6(b).
Figure 8 - Comparison of predictions and experiments (3D, cold
forging, bevel gear enclosed die forging)
(a) Hot ring rolling
Solution Sensitivity – Adaptive and Intelligent Mesh
Generation
Remeshing capability in BMFS is of great importance because it
governs program generality, solution accuracy, and even user
friendliness, all of which are essential for intelligent BMFS. The
quadrilateral mesh generator of AFDEX 2D and the tetrahedral
mesh generator of AFDEX 3D were developed specifically for
BMFS and are therefore optimized for that purpose.
(b) Non-symmetric cold ring rolling (taper roller bearing race)
Figure 6 - Comparison of predictions and experiments (3D, ring
rolling)
Figure 7 compares the predictions and experimental results of a
rotor pole forging process, composed of a bending stage and a
final sizing stage, revealing that the predictions reflect the most
important features of the experiments.
(a) Die mesh
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(a) 2D
(b) Workpiece mesh
Figure 9 - Intelligent quadrilateral remeshing
Figures 9 and 10 illustrate several typical quadrilateral mesh
systems and tetrahedral mesh systems, respectively. It should be
emphasized that the deviation between the desired and generated
mesh densities and the number of transition elements or regions
is minimized during mesh generation or remeshing. Additionally,
mesh quality (i.e., mesh regularity and normality near the
workpiece-die interface) is optimized to reduce numerical
inaccuracies. As Figure 10 illustrates, the mesh density of the
generated tetrahedrons is in close agreement with the desired
mesh density, which is one of the greatest advantages of the
automatic remeshing capability of AFDEX. These features help
AFDEX to ensure solution accuracy and provide sophisticated
simulations of precision BMF processes.
Generated mesh system
(b) 3D
Figure 11 - Examples of specially constructed mesh systems
0.1
0.2
0.2
0.8
0.6
0.3
0.1
0.3
Desired mesh density
0.2
0.3
0.70.5
0.9 0.4
During remeshing, it is inevitable that the workpiece shape will
be subject to numerical smoothing, especially near characteristic
lines or surfaces (including sharp corners), which naturally leads
to numerical volume loss. Accordingly, mesh density control
capability, especially near sharp edges, is of great importance in
precision simulation of metal forming processes. In AFDEX,
geometrical aspects (e.g., surface curvature, workpiece-die
interface, sharp edges) and state variables (e.g., strain, strain
rate, temperature gradient) are used to determine the optimal
mesh density. Figure 12 shows a typical tetrahedral mesh system,
namely the final configuration used to predict the spiral bevel gear
forging process.
0.7
0.3 0.2
0.5
0.3
0.8 0.2
0.9
0.5
0.1
0.2
Figure 10 - Intelligent tetrahedral remeshing
Of course, the mesh density for special problems can be
manually set by users, and a local remeshing capability is
available that requires user intervention during remeshing. Figure
11 shows some specially constructed mesh systems during
automatic and manual simulations.
Figure 12 - Precision simulation of a spiral bevel gear forging
process
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Figures 13(a) and 13(b) show the edges generated in hot and
cold forging, respectively. It should be emphasized that a detailed
description of the workpiece geometry is a very important part of
MFS if one is to obtain the sort of accurate results shown in Figure
13. The mesh system shown in Figure 13(b) describes the
chamfered corner clearly and accurately with the limited number
of tetrahedral elements.
From the standpoint of applied mathematics, the BMFS problem
is a typical boundary and/or initial value problem. When the finite
element method is employed, the boundary conditions vary from
time to time. It should be noted that remeshing inevitably causes
changes in a boundary value problem (in particular, changes in
the boundary conditions), which can cause varying degrees of
solution inaccuracy. Therefore, intelligent BMFS technology
should be assisted by a function that minimizes changes in
boundary condition during remeshing. AFDEX 2D and AFDEX 3D
always maintain the boundary conditions of the workpiece-die
interface during automatic remeshing. Figure 14 shows the
variations in the workpiece-die interface according to stroke, with
emphasis on mesh quality along the boundary. By using this
function, the disappearance of cavities enclosed by workpiece and
dies can be traced in detail, which ensures solution accuracy.
Moreover, solution accuracy and volume changes are greatly
improved, and the function helps users to easily obtain valuable
information, thanks to its compatibility with the workpiece
geometry.
Top
(a) Hot forging
Bottom
(a) Top and bottom
(b) Cold forging
Figure 13 - Sensitivity of the predictions near the characteristic
boundaries or edges
(b) Front
Figure 15 - Robustness of remeshing
Robustness of mesh generation is essential to realizing a fully
automatic simulation (without any user intervention). For
engineering purposes, most users prefer to simulate their die
designs without any simplifications. Some die and process
designs can create very difficult problems for automatic mesh
generation (e.g., very thin flashes and delicate, complicated die
surfaces). Hence, robustness is one of the essential requirements
to make an intelligent forging simulator adaptable to such
situations. Experience has given us confidence in the robustness
of the mesh generators adopted by AFDEX. Figure 15 illustrates
the robustness of mesh generation in AFDEX 3D.
Useful and User-friendly Functions
Contact area
Free surface
Figure 14 - Mesh density control along the workpiece-die interface
area
An intelligent forging simulator should have the capability of
automatically simulating a sequence of multi-stage forging
processes to minimize the total simulation time, including both
computational time and user processing time between stages.
Figures 16 and 17 show predictions for an axisymmetric automatic
five-stage cold forging process and a three-dimensional sevenstage compound hot metal forming process obtained using the
automatic execution function of AFDEX 2D and AFDEX 3D,
respectively. The predictions were obtained with only one return
key operation.
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Stage 1
Stage 4
Stage 2
Stage 3
AFDEX 3D can read an AFDEX 2D results files either directly or
by means of a simple connection program, and thus 2D and 3D
combined simulations can easily be carried out. Of course, the 2D
results can be viewed by the 3D post-processor with more
powerful graphics functions. Figure 18 shows the predictions of a
five-stage precision cold forging process involving one piercing
stage and a final three-dimensional stage, obtained by using the
2D and 3D combined simulation capability with minimum user
intervention (i.e., with only an initial run and one connection run).
It should be noted that this capability is especially efficient for
fastener forming process simulation. 2D and 3D combined
simulation is strongly recommended for enhancing computational
time, solution reliability, and engineering productivity when
relatively few stages are three-dimensional.
Stage 5
Figure 16 - Results obtained by automatic 2D simulation
(a) Process design
(a) Roll forging
(b) Bending
(c) Forging
Figure 17 - Results obtained by automatic 3D simulation
0.91kg
Non-optimized
0.82kg
Optimized
(b) Product design
(a) 2D results
Figure 19 - Metal flow lines in process and product design
(b) 3D results
Figure 18 - 2D and 3D combined simulation
Figure 20 - Predictions of 3D metal flow lines
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Metal flow lines in metal formed products have great influence
on their strength and thus they are the most important in process
design. Even the externally sound products often have decisive
internal defects due to bad metal flow lines. Therefore the
consumers usually impose some constraints on the internal metal
flow lines for most power transmission parts including gears,
bearings and the like. As a consequence, precision prediction of
metal flow lines and convenient visualization are important so
much. AFDEX is powerful in this point as shown in Figure 19 and
Figure 20, showing 2D and 3D metal flow lines formed in metal
forming, respectively.
Figure 21 - Flow stresses obtained from AFDEX DB
AFDEX prov ides the material properties of almost all
commercial materials, including steels and aluminums. Properties
of some special alloy materials are also provided. Figure 21
shows typical flow stress information obtained from AFDEX DB.
AFDEX DB also includes special functions for accommodating
user input (for example, space for a machine database, frictional
conditions, and the like).
In the past, interest in BMFS technology was limited to a small
number of experts in research or academia. Recently, however,
BMF simulators have become essential even for small-sized
companies, especially in Korea, that manufacture critical
automotive parts. User friendliness is therefore of great
importance, as many users are not proficient in the theory of
plasticity or numerical approaches to mechanics, even though
they are experts in the field of BMF process design. AFDEX
provides the recommended initial default values for any process
when users enter fundamental process information, such as
problem type, number of stages, material type, machine type, die
geometries, and the like. AFDEX also provides powerful computer
graphics support, as shown in Figure 22. AFDEX can, of course,
be linked to any CAD system via the DXF file format for 2D and
the STL format for 3D.
Ease of use is one of the essential requirements or an
intelligent metal forming simulator. In developing AFDEX, we
incorporated advice from related industries, and thus our pre- and
post-processors are believed to be very user friendly. Experience
convinces us that one or two days are sufficient for process
design engineers to learn how to use the simulators if they are
proficient at utilizing CAD software. A user manual is not
essential, as AFDEX can be learned heuristically by interfacing
with the pre- and post-processors. Of course, AFDEX provides
various ways for specialized users to modify the default values or
define professional constants.
· Post-processor
· Pre-processor
Figure 22 - User friendliness of PRE/POST processors
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APPLICATIONS
Typical applications
Ring Rolling
Extrusion
Rolling
(b) Fracture formation after the fracture point has been reached
Figure 23 - Predictions of a tensile test
Example 2: Enclosed die forging of a bevel gear
Drawing
Forging
AFDEX was applied to various metal forming processes beginning
15 years ago: some of these applications are illustrated on the
back cover. Most of the examples in the figure were studied
during the early developmental stage of AFDEX, and their details
can be found on the AFDEX website and in related literature.
During its development, AFDEX was tested on examples drawn
mostly from related industries, usually involving problems in
process design and various considerations for process
improvement. It is noteworthy that this lengthy and specialized
development process involving close user-developer cooperation,
has allowed us to incorporate valuable ideas and capabilities
gleaned from many process design experts in the field, which in
turn enable AFDEX to provide cutting-edge creative support to the
current generation of users.
Special Applications
Enclosed die forging is a typical method for net-shape precision
forging, and thus its simulation should be accomplished under
very sophisticated process and simulator considerations. In a
precision simulation of enclosed die forging, care must be taken to
keep the numerical volume loss below the maximum allowable
value to enable prediction of tiny under-filling regions. Figure 24
shows the prediction obtained for an enclosed die forging process
for a bevel gear, with emphasis on the mesh quality around the
teeth-die contact area.
Contact area
Free surface
Example 1: Fracture in a tensile test
Simulation of tensile tests is very important because application
engineers or researchers can not only obtain insights or
confidence in solution accuracy but can also understand the
plastic or fracture behavior of the materials. Figure 23 shows our
unique predictions for a tensile test for low carbon steel. The
predictions exactly reflect the plastic behavior of the tensile test
specimen (in the engineering sense) before reaching the fracture
point, and the predicted fracture phenomena match the
experimental results qualitatively.
Figure 24 - Enclosed die forging process for a bevel gear
Example 3: Roll forging
Roll forging is a special metal forming process in which plastic
deformation of the workpiece is caused by the motion of the threedimensional rolls. In a roll forging simulation, careful consideration
should be given to workpiece handling. Figure 25 shows the
prediction for a typical application.
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Experiment
Prediction
10
8
6
4
2
0
0
2
4
Elongation [mm]
6
8
(a) Comparison of engineering stress-strain curves with emphasis
on fracture region
Figure 25 - Roll forging process for an aluminum preform
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Example 4: Ring rolling
Example 5: Radial forging
From the simulation standpoint, ring rolling presents some
distinctive characteristics, including a small contact region relative
to workpiece size, large stroke, and geometrical identity. To cope
with these features, a proper analysis model is essential, and
some special functions should be developed specifically for ring
rolling simulation. For example, we adopted hexahedral elements
to enhance the solution accuracy and computational time at the
expense of program generality. Figure 26 shows three typical
applications of AFDEX HEXA/RING. Figure 26(a) illustrates a
bearing race ring rolling process, Figure 26(b) a wind tower flange
ring rolling process, and Figure 26(c) a profiled ring rolling
process.
Radial forging is an open die forging technology, and its
simulation poses the most sophisticated problem among existing
metal forming processes. In radial forging, cyclic motions of tools
or dies and a carefully developed modeling capability for the
manipulator should be supported. Automatic simulation of multistage processes and some special functions for manufacturing
stepped or hollow shafts may also be of great importance in some
applications. Figure 27(a) shows the predictions of a simple round
rod radial forging process and Figure 27(b) the predictions for a
profiled round rod radial forging process.
Pass 1
Pass 3
Pass 2
Prediction
(a) Bearing race
Experiment
(a) Simple round rod
(b) Profiled round rod
Figure 27 - Radial forging processes
(b) Profiled ring
Example 6: Roll piercing
Roll piercing is a special rolling technology for manufacturing
hollow shafts or pipes without any weld lines and is one of the
more complicated metal forming processes. Of course, the
piercing process itself generates numerous remeshings, which
can lead to significant numerical volume change and adversely
affect the solution accuracy. Hence, particular care must be taken
to model the actual process in a roll piercing simulation. Also, a
special updating scheme should be applied to minimize numerical
volume loss while in updating the rotating workpiece and tools.
Figure 28 shows a typical prediction for a roll piercing process.
(c) Tower flange
Figure 26 - Ring rolling processes
Figure 28 – Roll piercing process
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Example 7: Swaging
Swaging is an incremental metal forming technology for
manufacturing profiled pipes and long products with various
shapes. In a swaging simulation, periodic description of tool
movement and workpiece handling is of great importance, and
minimization of artificial volume loss should be considered. In
addition, special attention should be paid to modeling the
workpiece feeding system to reflect the elastic response,
especially when the inclined dies are pressing against the
workpiece and pushing it backward especially in the early stage of
forming. Figure 29 shows an example of a swaging process
prediction.
Figure 31 - Hollow cylinder axial lengthening process
Example 9: Micro-forming or large-scaled workpiece
forming
A micro-formed part is a small mechanical part with more than
two dimensions less than 1.0mm. In this instance, dimensional
extremity may cause numerical errors or a somewhat greater
volume change, leading to more or less deterioration in solution
accuracy, as most simulators have been designed for
conventional processes. The same difficulty arises in large-scale
workpiece forming process. For these cases, AFDEX provides a
user-defined unit system that can eliminate errors caused by too
small or large dimensional magnitude. Figure 32 shows
predictions obtained for a micro-forming process, together with
experimental results for comparison.
Figure 29 - Swaging process
Example 8: Hollow cylinder diametrical expansion
and axial lengthening
Hollow cylinder diametrical expansion and axial lengthening
process is one of open die forging technologies, a special
incremental forming process which is aimed at increasing the
diameter or length of a hollow cylinder. The tool is usually
composed of a mandrel and a punch, and the workpiece is hung
on the mandrel. The forming sequence consists of a forming
stroke by the punch and consecutive workpiece rotation by the
mandrel. Thus, a special function for rotating the workpiece
according to the rotational motion of the mandrel should be
supported to simulate this process. The process may be
inherently subject to excessive numerical volume change during
simulation due to the considerable amount of swaying or rotational
motion. Accordingly, AFDEX has adopted a special updating
scheme to reduce the artificial volume change while updating the
solution step. Figure 30 and Figure 31 show the predictions
obtained for a hollow cylinder diametrical expansion and axial
lengthening process, respectively.
Figure 32 - Micro-forming
Example 10: Tube drawing with back pressing
Drawing looks simple, but it is not easy, especially when the
reduction of area is nearly critical. The most serious problem in a
drawing simulation is artificial change in reduction of area due to
numerical changes in the workpiece diameter at the entry or exit,
which may be caused by both theoretical limits and numerical
inaccuracies. This is especially important because reduction of
area has a very strong influence on drawability. Thus, a precision
simulation technique should be employed in this case.
Stage 1
Stage 2
Stage 3
Figure 30 - Hollow cylinder diametrical expansion process
(a) Three-stage pipe drawing
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Example 12: Extrusion with chevron cracks
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Because of inferior process design and/or material, cold
extrusion may be subject to the dangerous central bursting defect
known as a chevron crack. Detailed simulation of chevron crack
formation can help engineers to understand the material fractures
that occur during metal forming. To predict the chevron crack, a
proper damage model is necessary, which differs from material to
material. Figure 35 is a typical chevron crack predicted by AFDEX.
This prediction is believed to be quite similar to a real crack,
especially as regards the shape of the crack.
1422 N
0.8
0.6
Upper_Die
Lower_Die
0.4
= 30º
R.A.=18
=0.03
0.2
= 30º
R.A.=30
=0.03
1422 N
0
0
20
40
Stroke (mm)
60
80
(b) Forming load, back pressing force
Figure 33 - Tube drawing process with back pressing
AFDEX utilizes the artificial body force approach to handle back
tension or pressing in drawing, the optimized step-size
determination scheme to minimize the numerical volume change
and the artificial bulge-removing scheme to eliminate numerical
bulging resulting from the rigid-plasticity assumption. Figure 33(a)
shows the predictions obtained for a three-stage tube drawing
process. A plug is used in the third stage, and back pressing
forces of 1422 N are exerted in both the second and third stages,
which can be inferred from the forming load difference of the
predictions in Figure 33(b).
Example 11: Thread rolling
Thread rolling simulation is an extreme case because it requires
a great many remeshings of a geometrically complicated
workpiece. Figure 34 shows the predictions obtained for a thread
rolling process for manufacturing high strength flange bolts,
together with experimental results. Global simulation over the
entire domain (as shown in Figure 34(a)) is not economical in
thread rolling, but local simulation for a sliced workpiece with endsymmetry conditions can sometimes provide much better results
(in the engineering sense), as shown in Figure 34(b), which was
obtained after 450 remeshings.
Figure 35 - Chevron crack prediction in cold forward extrusion
Example 13: Pore closing
In open die forging, the initial cast materials usually have many
pores, which can cause various problems during being metal
formed or in their service. To simulate the pore closing
phenomena, proper analysis models to reflect the real situations
are necessary. Of course, the models should be assisted by
powerful intelligent remeshing capabilities together with precision
simulation capability because pore closing phenomena
themselves are geometrically very complex. AFDEX can simulate
the pore closing phenomena. Figure 36 shows the predictions of
pore closing phenomena in upsetting and cogging or radial
forging.
(a) Upsetting
(a) Entire model
(b) Local model
(b) Radial forging, cogging
Figure 34 - Thread rolling
Figure 36 - Pore closing prediction in upsetting and cogging
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Example 14: Plate forging
Plate forging is characterized by the shape of the workpiece
(i.e., the plate). Plate forging simulations are intermediate
between sheet MFS and bulk MFS. Unfortunately, sheet MFS
technologies are sometimes inappropriate for plate forging
problems, as they cannot accurately handle plastic deformation in
the thickness direction, which is of great importance, especially
near the corners of the workpiece. Figures 37(a) and (b) show
predictions for a cold plate forging process and a hot plate forging
process, respectively, obtained via BMFS techniques.
(b) Superplastic sheet metal forming
Figure 38 - Sheet MFS
Example 16: Roll forming
(a) Cold plate forging
Roll forming is a manufacturing technology for making ducts,
stringers and the like using metal sheets. Usually so-called flower
patterns can be simulated under the plane strain assumption.
Figure 39(a) shows the predictions of deformation of the flower
patterns employed in roll forming of an aircraft stringer. Figure
39(b) shows 3D non-steady state predictions of the deformation.
(a) Flower pattern simulation
(b) Hot plate forging
Figure 37 - Plate forging
Example 15: Sheet metal forming
Sheet metal forming is characterized by the thinness of the
workpiece. In most cases, the conventional sheet MFS provides
valuable information. However, it is useful or inevitable to apply
BMFS to some situations in which thickness variation is important.
Figure 38(a) shows the predictions obtained for a common deep
drawing process, and Figure 38(b) shows predictions for a
superplastic forming process.
(b) 3D non-steady state simulation
Figure 39 - Roll forming simulation
Example 17: Die structural analysis
(a) Square cup deep drawing
AFDEX provides two kinds of the die structural analysis
modules linked directly to the metal forming simulators. The one is
used for simple die structural analysis without any geometrical
modification of the dies while the other is for detailed structural
analysis of the dies which is stored in the output file after dies are
modified geometrically and mechanically for the purpose of
assigning preload due to shrink fit or adding or modifying shrink
ring parts or other die mechanical parts. Figure 40 shows a typical
13
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[Unit:MPa]
700
application example. Figure 40(a) shows the predicted forging
with effective strain and stress vector on the workpiece-die
interface obtained under assumption of rigid dies and Figure 40(b)
shows the corresponding effective stresses of the shrink fitted die.
Figure 41 shows die effective stresses obtained by 3D die
structural analysis.
622
544
467
389
311
233
156
78
0
Max:913
Min : 0
(b) Hot forging, die
Figure 41 - 3D die structural analysis
Example 18: Die fracture prediction
Figure 42 reveals the reason for a die fracture near the region
marked “A” occurring during ball-stud cold forging with a highstrength material ESW105 (see Figure 1). It seems that the
circumferential stress near the marked region increases
remarkably, which contrasts to the case when the special steel
SCM435 is used, the maximum circumferential stress (-20MPa)
remains in compression. The increase in the circumferential stress
up to 870MPa in tension is believed to cause the longitudinal
fracture of the brittle die material of tungsten-carbide as shown in
Figure 42(a).
(a) Process
Punch
A
Shrink
ring
Die
insert
(a) Problem description
(b) Die with shrink rings
CL
Figure 40 - 2D die structural analysis
Effective stress: MPa
3800
3400
3000
2600
2200
1800
1400
1000
600
SCM435
2850MPa
871MPa
200
Effective stress: MPa
4000
3600
3200
2800
2400
2000
1600
1200
ESW125
(a) Cold forging, punch
800
400
(b) Effective stress
(c) circumferential stress
Figure 42 - Analysis of die fracture
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14
Collections of Recent Representative Simulations
Figure 43 shows several typical AFDEX applications for the year 2008-2009, including an electric upsetting process, a open die forging
process, a porthole extrusion process, a three-dimensional extrusion process, a cross wedge rolling process, a bearing race ring rolling
process, a hammer forging process, a steering pinion (helical gear) extrusion process, a roll forging process, a thread rolling process, an
arbitrary rolling process and spiral bevel gear and precision bevel gear forging processes.
Figure 43 - Representative AFDEX applications for the year (2008-2009)
Figure 44 also shows several typical AFDEX applications for the year 2009-2010, including a profile ring rolling process, a wind tower
flange ring rolling process, a radial forging process, a superplastic sheet metal forming process, a hollow cylinder diametrical expansion
and axial lengthening process, a sheet metal forming process, a swaging process, a spinning process, a pipe drawing process with back
pressing, and a specially designed roll forming process for curved roll formed products.
In addition to the examples mentioned above, AFDEX has been used for solving numerous problems in related industries, some of
which can be found on the AFDEX Web site.
Figure 44 - Representative AFDEX applications for the year (2009-2010)