Applications of evolutionary algorithms to sheet metal forming processes: a review

TL;DR: A compressive study of application of evolutionary strategies to optimize the geometry parameters such as die design and punch design, process parameterssuch as forming load, blank holder pressure and coefficient of friction, the spring back, hammering sequence etc.

Abstract: Metal forming processes are compression-tension processes involving wide spectrum of operations and flow conditions. The result of the process depends on the large number of parameters and their interdependence. The selection and optimization of various parameters is still based on trial and error methods. In this paper the authors presents a compressive study of application of evolutionary strategies to optimize the geometry parameters such as die design and punch design, process parameters such as forming load, blank holder pressure and coefficient of friction, the spring back, hammering sequence etc. Evolutionary algorithms offer many advantages over traditional methods. These are widely used now days for sheet metal industry. KeywordsSheet Metal Forming, Evolutionary strategies, Genetic algorithm Metal Forming Sheet-metal working processes have been associated with mankind since the Iron Age, when human beings first discovered that metals, especially gold and silver, can be shaped in the cold state by repetitive hammering to form thin sheets for making bowls and plates, containers, decorative items, etc. Household machines, kitchen utensils, record players, electrical appliances, toys, computers, switches and locks are some of the common household products that contain a large number of metal stampings. In stamping, drawing, or pressing, a sheet is clamped around the edge and formed into a cavity by a punch. The metal is stretched by membrane forces so that it conforms to the shape of the tools. The membrane stresses in the sheet far exceed the contact stresses between the tools and the sheet, and the throughthickness stresses may be neglected except at small tool radii. Out of these processes drawing or deep drawing process is more complicated and important with reference to the automotive industry. It is very useful in industrial field because of its efficiency. In deep drawing a sheet metal blank is drawn over a die by a punch with radius. As the blank is drawn radially inwards the flange undergoes radial tension and circumferential compression [1]. The latter may cause wrinkling of the flange if the draw ratio is large, or if the cup diameter-to-thickness ratio is high. A blank-holder usually applies sufficient pressure on the blank to prevent wrinkling. Radial tensile stress on the flange being drawn is produced by the tension on the cup wall induced by the punch force. Hence, when drawing cups at larger draw ratios, larger radial tension are created on the flange and higher tensile stress is needed on the cup wall. Bending and unbending over the die radius is also provided by this tensile stress on the cup wall. In addition, the tension on the cup wall has to help to overcome frictional resistance, at the flange and at the die radius. As the tensile stress that the wall of the cup can withstand is limited to the ultimate tensile strength of the material, the draw ratio possible in deep drawing is usually limited to about 2.1 or 2.2, to draw deeper cups recourse being made to special drawing processes such as hydroforming, hydro-mechanical forming, counterpressure deep drawing, hydraulic pressureaugmented deep drawing, etc. These processes are relatively slow (compared with the deep drawing or redrawing process) and the draw ratios are limited to 3.5 or 4 at most. However, a conventionally-drawn cup can be redrawn twice or more to obtain draw ratios of the order of 5, 6 or even larger values. Need of Optimization in Metal Forming The metal forming process is a complex operation requiring a simple geometry to be transformed into a complex one. The main goal of optimization in metal forming is to produce sound products through optimal process design, since the process material and die variables significantly influence the process. Classical approaches such as trial and error are tedious, illstructured, time consuming and costly. Dynamic programming can handle continuous and discrete variables, but is limited since the process normally involves large amount of process variables with wide range of values that may be active in the optimization problem. Also, derivative based approaches are not suitable since the objective function may possess multiple stationary points. Several authors have shown that the GA based approaches can be used to deal with these complex real world problems [1]. An outline of evolutionary computation applications in metal forming industry reported in this paper. These approaches have been shown to offer a more structured approach to process optimization problems. They also offer the benefit of cataloguing the optimal solutions for future reuse. This can save design time and effort for Applications of evolutionary algorithms to sheet metal forming processes: A review International Journal of Machine Intelligence, ISSN: 0975–2927, Volume 1, Issue 2, 2009 48 future problems. However the main problem experienced using GA in this environment is due to the expensive function evaluations. Since objective functions are often analytically unknown, function evaluations can only be achieved through costly computer simulations. The slow convergence criteria to near-optimal solution with very small tolerance accompanied with the large population of solutions required for the evolutionary process result in expensive evaluations. Advantages of Evolutionary Algorithms Evolutionary algorithms always work with population, facilitating simultaneous search and optimization. These work with probabilistic approach rather than deterministic. These algorithms are often viewed as global optimization methods although convergence to a global minimum is only guaranteed in a weak probabilistic sense. A global optimum is not guaranteed, although near optimal solutions are found easily. However, one of the strengths of evolutionary strategies is that they perform well on noisy functions where there may be multiple local optima and evolutionary strategies tend not to get stuck on a local minimum. Another strength is that these methods do not require a gradient of the objective cost function as a search direction. These approaches show certain advantages over the classical optimization procedures e.g. they are robust, highly parallelizable, and suitable for optimizing multimodal functions without requiring gradient information[1]. Evolutionary strategies with self-adaptation mutation operators are used to tackle the nonlinear structural optimization problem. Another important feature of evolutionary strategies is that they can compute multiple, independent objective function evaluations simultaneously in an effort to accelerate the search process. Thus, this approach can take advantage of parallel and distributed computing multiprocessing architectures. Optimization of Hammering Sequence In an incremental forming process, a sheet metal is progressively bent by a set of comparatively simple hammer and die. The sheets are formed into a great variety of shapes by repeating local deformation due to the hammering. This process is expected as an approach of flexible forming for small lot production. Since the degree of freedom for deformation in the incremental forming is large, it is not easy to determine the hammering sequences. The use of the finite element simulation for the determination is unrealistic because it takes an extremely long computing time to calculate local deformation due to the hammering repeatedly. The hammering sequences are generally determined by a trial and error experiment. The development of a method for determining the hammering sequences is required for the establishment of incremental forming processes [1].The genetic algorithms have been recently applied as an approach for combinatorial optimization problems in the field of manufacturing. It is impossible in the combinatorial optimization problems to obtain the solution from the differentiation of the objective function because the design variables have discontinuous values. In the genetic algorithms, the combination is optimized on the basis of probabilistic transition rules. In addition, the genetic algorithms can deal with a complicated objective function in the optimization because the differentiation of the objective function is not necessary. Optimization of blank dimensions to Reduce Springback in the Flexforming process The sheet metal forming process involves a combination of elastic–plastic bending and stretch deformation of the work piece. These deformations may lead to a large amount of spring back of the formed part. It is desired to predict and reduce spring back so that the final part dimensions can be controlled as much as possible. Ayres suggested the use of a multiple step process to reduce spring back in stamping operations. Liu proposed to vary the binder forces during the forming process thereby providing tensile pre-loading to reduce the spring back in the formed part. Techniques that are used in practice to reduce spring back include stretch forming, arc bottoming and the pinching die technique[2]. However, all these techniques transmit high tensile stresses to the walls of the deforming part thereby increasing the risk of failure by tearing, mainly in parts with complex geometries. Several analytical methods have been proposed to predict the change in radius of curvature and included angle due to spring back for plane-strain conditions and simple Axisymmetric shapes. These methods are approximate and associate the source of spring back to non-uniform distribution of strain and bending moment upon unloading. The finite element method (FEM) is used widely to predict spring back in research and industry. Chinghua studied the influence of process variables of the methods used in practice to reduce spring back by an optimization technique for U channel parts. Karafillis and Boyce developed a deformation transfer function for changing the shape of the tool to compensate for spring back in sheet metal forming using FEM [

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International Journal of Machine Intelligence, ISSN: 0975–2927, Volume 1, Issue 2, 2009, pp- 47-49
Copyright © 2009, Bioinfo Publications, International Journal of Machine Intelligence, ISSN: 0975–2927, Volume 1, Issue 2, 2009
Applications of evolutionary algorithms to sheet metal forming processes:
A review
Kakandikar G.M.*
1
,
Darade P.D.
2
and Nandedkar V.M.
3
*1, 2
Mechanical Engineering Department, Vidya Pratishthan’s College of Engineering, Baramati, Pune, Maharashtra, India,
kakandikar@yahoo.co.in ; pradipd2006@rediffmail.com ; Mob: 91-9860641885
3
Professor in Production Engineering Department & Dean, Students Affairs, Shri Guru Gobind Singhji Institute of
Engineering and Technology, Nanded, Maharashtra, India, vilas.nandedkar@gmail.com
Abstract- Metal forming processes are compression-tension processes involving wide spectrum of
operations and flow conditions. The result of the process depends on the large number of parameters and
their interdependence. The selection and optimization of various parameters is still based on trial and error
methods. In this paper the authors presents a compressive study of application of evolutionary strategies to
optimize the geometry parameters such as die design and punch design, process parameters such as
forming load, blank holder pressure and coefficient of friction, the spring back, hammering sequence etc.
Evolutionary algorithms offer many advantages over traditional methods. These are widely used now days
for sheet metal industry.
Keywords- Sheet Metal Forming, Evolutionary strategies, Genetic algorithm
Metal Forming
Sheet-metal working processes have been
associated with mankind since the Iron Age,
when human beings first discovered that metals,
especially gold and silver, can be shaped in the
cold state by repetitive hammering to form thin
sheets for making bowls and plates, containers,
decorative items, etc. Household machines,
kitchen utensils, record players, electrical
appliances, toys, computers, switches and locks
are some of the common household products
that contain a large number of metal stampings.
In stamping, drawing, or pressing, a sheet is
clamped around the edge and formed into a
cavity by a punch. The metal is stretched by
membrane forces so that it conforms to the
shape of the tools. The membrane stresses in the
sheet far exceed the contact stresses between
the tools and the sheet, and the through-
thickness stresses may be neglected except at
small tool radii. Out of these processes drawing
or deep drawing process is more complicated
and important with reference to the automotive
industry. It is very useful in industrial field
because of its efficiency. In deep drawing a sheet
metal blank is drawn over a die by a punch with
radius. As the blank is drawn radially inwards the
flange undergoes radial tension and
circumferential compression [1]. The latter may
cause wrinkling of the flange if the draw ratio is
large, or if the cup diameter-to-thickness ratio is
high. A blank-holder usually applies sufficient
pressure on the blank to prevent wrinkling. Radial
tensile stress on the flange being drawn is
produced by the tension on the cup wall induced
by the punch force. Hence, when drawing cups at
larger draw ratios, larger radial tension are
created on the flange and higher tensile stress is
needed on the cup wall. Bending and unbending
over the die radius is also provided by this tensile
stress on the cup wall. In addition, the tension on
the cup wall has to help to overcome frictional
resistance, at the flange and at the die radius. As
the tensile stress that the wall of the cup can
withstand is limited to the ultimate tensile
strength of the material, the draw ratio possible in
deep drawing is usually limited to about 2.1 or
2.2, to draw deeper cups recourse being made to
special drawing processes such as hydro-
forming, hydro-mechanical forming, counter-
pressure deep drawing, hydraulic pressure-
augmented deep drawing, etc. These processes
are relatively slow (compared with the deep
drawing or redrawing process) and the draw
ratios are limited to 3.5 or 4 at most. However, a
conventionally-drawn cup can be redrawn twice
or more to obtain draw ratios of the order of 5, 6
or even larger values.
Need of Optimization in Metal Forming
The metal forming process is a complex
operation requiring a simple geometry to be
transformed into a complex one. The main goal
of optimization in metal forming is to produce
sound products through optimal process design,
since the process material and die variables
significantly influence the process. Classical
approaches such as trial and error are tedious, ill-
structured, time consuming and costly. Dynamic
programming can handle continuous and discrete
variables, but is limited since the process
normally involves large amount of process
variables with wide range of values that may be
active in the optimization problem. Also,
derivative based approaches are not suitable
since the objective function may possess multiple
stationary points. Several authors have shown
that the GA based approaches can be used to
deal with these complex real world problems [1].
An outline of evolutionary computation
applications in metal forming industry reported in
this paper. These approaches have been shown
to offer a more structured approach to process
optimization problems. They also offer the benefit
of cataloguing the optimal solutions for future re-
use. This can save design time and effort for

Applications of evolutionary algorithms to sheet metal forming processes: A review
International Journal of Machine Intelligence, ISSN: 0975–2927, Volume 1, Issue 2, 2009
48
future problems. However the main problem
experienced using GA in this environment is due
to the expensive function evaluations. Since
objective functions are often analytically
unknown, function evaluations can only be
achieved through costly computer simulations.
The slow convergence criteria to near-optimal
solution with very small tolerance accompanied
with the large population of solutions required for
the evolutionary process result in expensive
evaluations.
Advantages of Evolutionary Algorithms
Evolutionary algorithms always work with
population, facilitating simultaneous search and
optimization. These work with probabilistic
approach rather than deterministic. These
algorithms are often viewed as global
optimization methods although convergence to a
global minimum is only guaranteed in a weak
probabilistic sense. A global optimum is not
guaranteed, although near optimal solutions are
found easily. However, one of the strengths of
evolutionary strategies is that they perform well
on noisy functions where there may be multiple
local optima and evolutionary strategies tend not
to get stuck on a local minimum. Another strength
is that these methods do not require a gradient of
the objective cost function as a search direction.
These approaches show certain advantages over
the classical optimization procedures e.g. they
are robust, highly parallelizable, and suitable for
optimizing multimodal functions without requiring
gradient information[1]. Evolutionary strategies
with self-adaptation mutation operators are used
to tackle the nonlinear structural optimization
problem. Another important feature of
evolutionary strategies is that they can compute
multiple, independent objective function
evaluations simultaneously in an effort to
accelerate the search process. Thus, this
approach can take advantage of parallel and
distributed computing multiprocessing
architectures.
Optimization of Hammering Sequence
In an incremental forming process, a sheet metal
is progressively bent by a set of comparatively
simple hammer and die. The sheets are formed
into a great variety of shapes by repeating local
deformation due to the hammering. This process
is expected as an approach of flexible forming for
small lot production. Since the degree of freedom
for deformation in the incremental forming is
large, it is not easy to determine the hammering
sequences. The use of the finite element
simulation for the determination is unrealistic
because it takes an extremely long computing
time to calculate local deformation due to the
hammering repeatedly. The hammering
sequences are generally determined by a trial
and error experiment. The development of a
method for determining the hammering
sequences is required for the establishment of
incremental forming processes [1].The genetic
algorithms have been recently applied as an
approach for combinatorial optimization problems
in the field of manufacturing. It is impossible in
the combinatorial optimization problems to obtain
the solution from the differentiation of the
objective function because the design variables
have discontinuous values. In the genetic
algorithms, the combination is optimized on the
basis of probabilistic transition rules. In addition,
the genetic algorithms can deal with a
complicated objective function in the optimization
because the differentiation of the objective
function is not necessary.
Optimization of blank dimensions to Reduce
Springback in the Flexforming process
The sheet metal forming process involves a
combination of elastic–plastic bending and
stretch deformation of the work piece. These
deformations may lead to a large amount of
spring back of the formed part. It is desired to
predict and reduce spring back so that the final
part dimensions can be controlled as much as
possible. Ayres suggested the use of a multiple
step process to reduce spring back in stamping
operations. Liu proposed to vary the binder
forces during the forming process thereby
providing tensile pre-loading to reduce the spring
back in the formed part. Techniques that are
used in practice to reduce spring back include
stretch forming, arc bottoming and the pinching
die technique[2]. However, all these techniques
transmit high tensile stresses to the walls of the
deforming part thereby increasing the risk of
failure by tearing, mainly in parts with complex
geometries. Several analytical methods have
been proposed to predict the change in radius of
curvature and included angle due to spring back
for plane-strain conditions and simple
Axisymmetric shapes. These methods are
approximate and associate the source of spring
back to non-uniform distribution of strain and
bending moment upon unloading. The finite
element method (FEM) is used widely to predict
spring back in research and industry. Chinghua
studied the influence of process variables of the
methods used in practice to reduce spring back
by an optimization technique for U channel parts.
Karafillis and Boyce developed a deformation
transfer function for changing the shape of the
tool to compensate for spring back in sheet metal
forming using FEM [2]. The objective of this study
was to estimate and reduce for spring back of
axisymmetric part manufactured by flexforming
process. The manufacturer selected the die and
blank dimensions based on the experience and
trial-and-error. However, the dimensions of the
final part could not meet the design specifications
due to its spring back after forming. Thus, finite

Kakandikar GM, Darade PD and Nandedkar VM
Copyright © 2009, Bioinfo Publications, International Journal of Machine Intelligence, ISSN: 0975–2927, Volume 1, Issue 2, 2009
49
element analysis was used to predict spring back
in the existing manufacturing set-up. Then GA is
used to optimize it.
Optimization of metal forming processes
Nowadays, the finite element method (FEM) has
proven its efficiency and usefulness simulating
steady and non-steady metal forming processes.
It allows to test and to compare several process
candidates. When the modeling approaches are
deterministic requiring the introduction of several
input data such as geometry, mesh, non-linear
material behavior laws, loading cases, friction
laws, thermal laws, etc., then the computation of
process evolution and final results is called a
direct problem. Since efficient numerical methods
have already been developed, these direct
problems using FEM have reached some level of
maturity. Then it becomes possible to solve more
complex problems, namely the inverse
problems[3]. The goal of these inverse problems
is to determine one or more of the direct problem
input data, leading to a given result. One of these
inverse problems deals with the initial geometry
and tool shape design parameters in forming
processes. It consists in determining the initial
shape of the work-piece in one stage forming or
the shape of the forming tools in multi-stage
forming, in order to provide the desired final
geometry of the forged piece. This problem can
be formulated as an optimization problem. The
goal is to minimize an objective function
considering among other factors the total forming
energy and the gap between the FEM results for
the final geometry and the desired one. The
development of inverse techniques has resulted
in several realizations in 2D and 3D optimization
algorithms where the geometry parameter update
considers gradients and sensitivity analysis of the
objective function. Recently, evolutionary genetic
algorithms have been proposed in order to
optimize shape design parameters in forming
processes[3]. Then the optimal solutions are not
gradient dependent and consequently do not
present numerical errors resulting from non-
accurate sensitivity calculations. Furthermore,
shape and non-shape, discrete and continuous
variables can be simultaneously optimized using
genetic algorithms.
Optimal designs of metal forming die
surfaces
Computer-based systematic approach for
optimum design of geometric and process
parameters in industrial sheet metal forming
simulations is proposed here. Today, most of the
automotive Industry uses sheet metal forming
simulations during the vehicle development
process in order to accelerate the design cycles
and to reduce development costs [4]. The
simulations are applied to assess the feasibility of
part geometries during the product design phase,
to try out prototype and production tooling during
the die development process, and to optimize
process parameters for maximum efficiency,
reliability and quality. Therefore, many similar
simulations must be carried out with different
process parameters and different tool
geometries. Furthermore, it is not sure whether
the optimal process parameters and tool
geometries have been found, even after having
carried out several simulations. There is thus an
urgent need for a reliable integrated computer-
based optimization approach to modify geometry
and process parameters and to automatically find
their optimal combination. Recent evolutionary
strategies simulated annealing and genetic
algorithms have attracted attention amongst the
engineering design optimization community. This
has given rise to the Evolutionary Automatic
Design [EAD] of process and geometry
parameters [4]. Important phases are fast
parametric design of the tool surfaces, the choice
of actuator design variables and relevant
objective cost functions by practical process
engineers, and the integration of evolutionary
strategies into the computer-based systematic
approach. The main components of an integrated
computer based system are: (1) an automatic
parametric tool design generated from the CAD
surface data of the sheet metal part; (2) the
optimum design problem (objective function,
design variables and constraints involved in the
optimization); (3) the evolutionary strategy as
optimization algorithm; and (4) the integrated
objective function evaluation by applying the
implicit infinite element sheet metal forming
simulation software package Auto Form-
Incremental, where a single simulation may take
anywhere from few minutes to several hours of
computation on a single processor.
Summary
With the recent developments in sheet metal
forming processes and composite materials that
are being used now days, it is possible to form
more complicated products. This involves more
complicated process variables. The evolutionary
algorithms have proved themselves more useful
to be applied for optimization in these situations.
References
[1] Mori K., Yamamoto M., Osakada K. (1996)
Journal of Materials Processing Technology
60, 463-468.
[2] Naceur H., Guob Y.Q., Batoz J.L. (2004) Journal
of Materials Processing Technology 151,
183–191.
[3] Hariharasudhan Palaniswamy, Gracious Ngaile,
Taylan Altan (2004) Journal of Materials
Processing Technology 146, 28–34.
[4] Posta J., Klaseboera G., Stinstrab E., van
Amstela T., Huetinkc J. (2009) Journal of
materials processing technology 209, 2648–
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