2373 Structural optimization of the automobile frontal ...
Transcript of 2373 Structural optimization of the automobile frontal ...
Structural optimization of the automobilefrontal structure for pedestrian protectionand the low-speed impact testM-K Shin1, S-I Yi2, O-T Kwon2, and G-J Park3*1BK21 Division, Hanyang University, Ansan City, Republic of Korea2Department of Mechanical Engineering, Hanyang University, Ansan City, Republic of Korea3Division of Mechanical and Information Management Engineering, Hanyang University, Ansan City, Republic of Korea
The manuscript was received on 15 December 2007 and was accepted after revision for publication on 29 August 2008.
DOI: 10.1243/09544070JAUTO788
Abstract: A variety of regulations are involved in the design of an automobile frontalstructure. The regulations are pedestrian protection, the Federal Motor Vehicle Safety Standard(FMVSS) part 581 bumper test, and the Research Council for Automobile Repairs (RCAR) test.The frontal structure consists of the bumper system and a crash box that connects the bumpersystem and the main body. The detailed design of the bumper system is performed to meet twoconditions: first, regulation for pedestrian protection (lower-legform impact test); second,FMVSS part 581. In the two regulations, the stiffness requirements of the bumper systemconflict with each other. In order to meet lower leg protection, a relatively soft bumper systemis required, while a relatively stiff system is typically needed to manage the pendulum impact. Anew bumper system is proposed by adding new components and is analysed by using the non-linear finite element method. An optimization problem is formulated to incorporate theanalysis results. Each regulation is considered as a constraint from a loading condition, and twoloading conditions are used. Response surface approximation optimization is utilized to solvethe formulated problem. RCAR requires reduction in the repair cost when an accident happens.The repair cost in a low-speed crash could be reduced by using an energy-absorbing structuresuch as the crash box. The crash box is analysed by using the non-linear finite element method.An optimization problem for the crash box is formulated to incorporate the analysis results.Discrete design using orthogonal arrays is utilized to solve the formulated problem in a discretespace.
Keywords: structural optimization, automobile frontal structure, pedestrian protection, low-speed impact test
1 INTRODUCTION
Many automobile companies and governments have
made much effort to enhance the safety of the dri-
vers and passengers. As a result, the number of casu-
alties and occupants’ injuries during an automobile
accident has decreased [1–4]. However, research
in certain areas is still lacking. Few studies have
examined vehicle–pedestrian accidents. It is essen-
tial to explore the design of the automobile frontal
structure to protect a pedestrian in a vehicle–pedes-
trian accident. Recently, many issues have been dis-
cussed in an effort to protect pedestrians in a vehicle–
pedestrian accident [5, 6], and the United Nations
Economic Commission for Europe/Working Party 29
(UNECE/WP29) has established pedestrian regula-
tions, which are global technical regulations (GTRs)
[7].
Various regulations are related to the automobile
frontal structure. They are pedestrian protection, the
East European Constitutional Review (ECER) 42 [8],
the Federal Motor Vehicle Safety Standard (FMVSS)
*Corresponding author: Department of Mechanical Engineering,
Hanyang University, 1271, Sa 1-Dong, Ansan City, Kyeonggi Do,
426-791, Republic of Korea. email: [email protected]
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part 581 bumper test [9], and the Research Council
for Automobile Repairs (RCAR) test [10]. ECER 42,
FMVSS part 581, and the RCAR test are carried out at
a low speed. These regulations require a stiff bumper
for protecting the occupants and reducing the repair
cost; however, the bumper should be soft to reduce
pedestrian injuries.
According to the establishment of the GTR, many
researchers have examined vehicle design for pedes-
trian protection. Many studies proposed designing
methods for the frontal structures to meet pedes-
trian protection [3, 11, 12]. McMahon et al. [13]
performed structural design of the bumper energy
absorber to satisfy pedestrian protection. However,
since the stiffness of the bumper decreases, it is
difficult to satisfy other bumper regulations. Glasson
et al. [14] reported that it is difficult to meet various
regulations simultaneously through the structural
design of the front end module of the car. Therefore,
a new design method is needed to achieve this.
A design process is proposed for structural optim-
ization of the frontal structure of the vehicle. The
proposed design process has two steps. As men-
tioned earlier, the frontal structure is composed of a
bumper system and a crash box. Each compon-
ent is designed to satisfy different regulations.
First, a new bumper system is proposed in order
to satisfy the pedestrian protection test as well as the
FMVSS part 581 bumper test. The proposed bumper
system is designed by adding a thin plate and three
springs to meet the two regulations simultaneously.
A thin-plate structure is added between a bumper
energy absorber and a bumper rail and is connected
to the bumper rail by three springs. The thicknesses
of the plate and spring coefficients are determined
through size optimization. Each regulation is con-
sidered as a constraint in the optimization process.
Size optimization is performed by using response
surface approximate optimization (RSAO) [15, 16].
In general, since a crash problem has high non-
linearity and oscillation, sensitivity information is
difficult to calculate. Therefore, approximated meth-
ods, such as response surface methods (RSMs), are
widely used to solve the optimization problem [15].
RSAO is a type of RSM.
Second, a new type of crash box is proposed
to meet the RCAR test which evaluates the repair
cost of the frontal structure. If the crash box absorbs
more impact energy, the repair cost is expected to
be reduced. The shape of the proposed crash box
is determined in a discrete space. Thus, a detailed
shape of the crash box is determined to maximize
energy absorption by using discrete design using
orthogonal arrays (DOA) [17, 18]. LS-DYNA3D is
used for non-linear finite element analysis [19], and
VisualDOC is used for structural optimization using
RSAO [20].
2 REGULATIONS RELATED TO THE FRONTALSTRUCTURE
2.1 The frontal structure of a vehicle
In the case of a collision at a low speed, the frontal
structure of a vehicle should efficiently absorb the
impact energy to prevent occupants from injury and
to reduce damage to the car. Figure 1 presents a
schematic view of the frontal structure of a vehicle.
The structure consists of a bumper cover, a bumper
energy absorber, a bumper rail, a crash box, etc. [21].
In this research, the bumper system is defined as the
frontal structure in front of the crash box. Thus, the
frontal structure consists of the bumper system and
the crash box.
Figure 2 presents the frontal structure of an exist-
ing vehicle model. This is for a compact car which
is currently on the market. According to the pilot
study, the existing model does not satisfy pedes-
trian protection while satisfying FMVSS part 581,
which is for the stiffness of the bumper. The pedes-
trian protection regulation requires a soft bumper.
However, if the stiffness of the frontal structure
is low, it would be difficult to meet the other reg-
ulations. Therefore, a new frontal structure of the
vehicle is needed to satisfy the conflicting regula-
tions simultaneously. An improved design is pur-
sued on the basis of the existing frontal structure
model.
Fig. 1 A schematic diagram of the frontal structure ofa vehicle
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2.2 Regulations for pedestrian protection
Since 1987, pedestrian regulations such as GTRs
have been developed [5–7, 22]. In pedestrian reg-
ulations, pedestrian protection tests are classified
into a headform impact test, an upper-legform im-
pact test, and a lower-legform impact test. Of the
three tests, the lower-legform impact test is the most
important in designing the frontal structure of the
vehicle. Figure 3 shows the lower-legform impact
test with a lower-legform impactor. The lower-
legform impactor has two rigid parts: a femur sec-
tion and a tibia section covered with foams. The
legform impactor has a mass of 13.4 kg. The femur
section and the tibia section are connected by a knee
joint. During the lower-legform impact test, the
impactor hits the frontal bumper of the vehicle. The
number of target points should be more than three
including the centre and the side of the bumper. The
impact speed is 40 km/h. According to the GTR, the
requirements are as follows: first, the dynamic knee
bending angle should be less than 19u; second,
the knee shearing displacement should be less
than 6 mm; third, the acceleration at the upper
tibia should be less than 170g [7]. These conditions
should be considered to reduce the leg injury and
they are used as constraints in the optimization
process of a bumper system.
2.3 Low-speed vehicle test: FMVSS part 581
The National Highway Traffic Safety Administration
(NHTSA) has proposed the strength requirement of
the frontal structure in FMVSS part 581. In general,
the regulation has two kinds of test: the barrier test
and the pendulum impact test. Figure 4 illustrates
the FMVSS part 581 bumper test. The target points of
the test are the centre of the bumper, 300 mm offset
from the centre of the bumper, and 30u corner side.
In Fig. 4(b), h is the height of the centre of the pen-
dulum from the ground. In the case of the pendulum
impact test, the height h of the pendulum should
be located between 0.4 m and 0.5 m (between 16 in
and 20 in). The speed of the impact test is 8 km/h
(5 mile/h). Both the frontal and the rear bumper im-
pact tests are performed [9].
As illustrated in Fig. 5, an intrusion and a deflec-
tion are defined for judging damage to the vehicle
during the impact test. The intrusion is the relative
displacement of the front centre of the bumper rail
Fig. 3 Lower-legform impact test
Fig. 2 Frontal structure of an existing vehicle model
Fig. 4 Side view of the FMVSS 581 bumper test
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with respect to the rear end of the crash box during
the impact test. The intrusion is used for judging
damage to the outer part of the vehicle, such as
the leading edge of the hood. The deflection is the
relative displacement of the rear centre of the
bumper rail with respect to the rear end of the crash
box during the impact test. The deflection is used for
judging damage to the inner part of the vehicle, such
as the radiator. The distance is measured from the
front bumper cover to the leading edge of the hood.
If the intrusion is shorter than the distance, the
leading edge of the hood would not be damaged by
the impact. Another distance is measured from the
rear centre of the bumper rail to the radiator. If the
deflection is shorter than the distance, the radiator
would not be damaged by the impact [23]. The
intrusion and the deflection are used as constraints
in the optimization process of the bumper system.
2.4 Research Council for Automobile Repairs test
The RCAR is an international organization working
towards reducing insurance costs by improving
automotive damageability, repairability, safety, and
security [10]. The objectives of RCAR are to evaluate
the cost of the motor insurance for insurers and
to make motor vehicles safer, less damageable, and
more cost effective to repair after an accident occurs
[24].
Among a series of the RCAR tests, there is a test for
designing the frontal structure of a vehicle. It is
considered when designing the frontal structure of
a vehicle. The crash box and the side rail should
efficiently absorb the impact energy in a low-speed
impact to protect the interior components of the
vehicle and to reduce the repair cost. A computer
simulation is performed for describing the impact
test as illustrated in Fig. 6. The frontal structure
without the bumper cover and foam hits a flat rigid
barrier, and the impact speed is 15 km/h. In this
paper, the design process of the crash box is per-
formed to maximize the absorbed impact energy.
The absorbed impact energy is measured by the
strain energy of the frontal structure. If the strain
energy is maximized, the impact energy transmitted
to the other parts of the vehicle would decrease [25,
26]. This leads to lower repair costs. In achieving this
goal, a new crash box is proposed and a detailed
design process is carried out by DOA.
3 BACKGROUND THEORIES FOROPTIMIZATION
3.1 Response surface approximationoptimization
An optimization formulation of a design problem
with constraints is expressed as follows. Find
b [Rn ð1aÞ
to minimize
f bð Þ ð1bÞ
Fig. 6 A view of the RCAR test
Fig. 5 The intrusion and deflection distances
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subject to
hi bð Þ~0 i~1, 2, � � � , lð Þ ð1cÞ
gj bð Þ¡0 j~1, 2, � � � , mð Þ ð1dÞ
bL¡b¡bU ð1eÞ
where b [Rn is the design variable vector, f(b) is the
objective function, hi(b) is the ith equality con-
straint, gj is the jth inequality constraint, n is the
number of design variables, l is the number of
equality constraints, m is the number of inequality
constraints, and bL and bU are the vectors for the
lower bound and upper bound respectively.
In general, the sensitivity information is difficult to
calculate in the optimization process of equations
(1). Therefore, approximation methods, such as the
RSM, are frequently used to solve the optimization
problem. In the RSM, the functions in equations (1b)
to (1d) are approximated to explicit functions [18,
27]. First, candidate design points are selected, and
the functions in equations (1b)–(1d) are calculated at
the candidate points. The explicit functions are gen-
erated from the function values through a curve-
fitting technique. The least-squares fitting method
is generally used for curve fitting. The optimization
process is performed by using approximated func-
tions.
RSAO is one of the engineering algorithms for
optimization [15, 16, 20]. It is a modified method
of the general RSM. The RSAO generates response
surfaces with a few selected candidate design points.
An optimum from the approximated surfaces is ob-
tained and added to the set of candidate points. New
response surfaces are made again and the process
continues in an iterative manner until the new
candidate point does not change. As the iteration
proceeds, constant, linear, and quadratic terms are
sequentially produced for the approximated func-
tions. Since RSAO is a kind of RSM, it has the advan-
tage of reducing the number of function calls.
Because RSAO utilizes an approximated function
instead of a real function, it may not find a
mathematical optimum satisfying the Kuhn–Tucker
necessary condition. However, since a useful solu-
tion can be found with a small number of analyses,
this method can be exploited in a crash problem,
which has high non-linearity and difficulty in calcul-
ating sensitivity. Structural optimization of the frontal
structure of the vehicle is carried out by RSAO.
The algorithm is installed in a commercial optim-
ization software system called VisualDOC, which is
used for structural optimization.
3.2 Discrete design using an orthogonal array
Generally, the formulation in equations (1) is for
problems where the design variables are defined in a
continuous space. However, in many practical prob-
lems, the design variables exist in a discrete space.
In other words, the design variables have certain
discrete values. A design problem of this research
is defined in a discrete space with the formulation
in equation (1).
Design of experiments (DOE) is employed to
determine the design variables in a discrete space.
The full factorial design in a discrete space can
find the best solution. However, it is an extrem-
ely expensive method because experiments should
be conducted for all combinations. The fractional
design is utilized to save cost since the factorial
design requires a large number of experiments. A
subset of the full factorial design is considered in
the fractional design. Among the fractional designs,
a method which directly uses orthogonal arrays is
selected. The method using an orthogonal array is
a type of DOE. This paper utilizes a method called
DOA to reduce the number of experiments. This
method can find a solution with a small number of
experiments (function calls) [28]. The method using
orthogonal arrays is defined for unconstrained prob-
lems. However, the general design problem formula-
ted in equations (1) has many constraints. There-
fore, a constrained problem must be transformed
into an unconstrained problem. For the transforma-
tion, an augment function Y(b) is introduced. An
augment function Y(b) is defined as [18]
Y bð Þ~f bð ÞzP bð Þ ð2Þ
P bð Þ~sXn
i~1
max 0, gj
� �, j~1, 2, � � � , m ð3Þ
where Y(b) is the characteristic function for con-
sidering the constraint violation, s is the scale fac-
tor, and P(b) is a penalty function to include the
maximum violation of constraints. The scale factor is
imposed in order to emphasize the constraint
violation. An excessive scale factor leads to neglect-
ing the effect of the objective function while the
penalty function with a small scale factor can cause
an infeasible design.
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Using Y(b), equations (1) are changed to an un-
constrained problem as follows. Find
b [Rn ð4aÞ
to minimize
Y bð Þ ð4bÞ
subject to
bL¡b¡bU ð4cÞ
Therefore, the formulation in equations (4) is used
in the design of the crash box. In solving a discrete
design problem with constraints, the steps of DOA
are as follows [18].
Step 1. An appropriate orthogonal array is selected
according to the number of design variables and
the number of levels. In this paper, the L9(34)
orthogonal array is used and shown in Table 1. In
L9(34), the number of rows is 9, the number of
levels is 3, and the number of design variables is 4.
Step 2. The objective function Y(b) is calculated for
each row of the selected orthogonal array. This
process is called a matrix experiment.
Step 3. A one-way table is made for each design
variable. The one-way table is the process where
the levels of design variables with the smallest
objective function are found. Table 2 shows an
example of the one-way table of results from the
orthogonal array in Table 1.
Step 4. Using the one-way table, a new combination
of the design variables is chosen. In each row of the
one-way table, the smallest variable is selected.
Step 5. The solution of step 4 is verified by a confir-
mation experiment where the objective function
and constraints are evaluated. The confirmation
experiment is needed because the interaction
effect is ignored in the above matrix experiment.
The results of Table 1 and the confirmation ex-
periment are compared and the best result which
has the least object function without constraint
violation is finally selected.
4 STRUCTURAL OPTIMIZATION OF THEFRONTAL STRUCTURE OF THE VEHICLE
4.1 Overall design process of the frontal structureof the vehicle
As explained earlier, pedestrian protection and the
low-speed impact test are taken into account in
order to design the frontal structure of the vehicle.
Through many analyses, it has been found that the
existing bumper model does not fulfil all the reg-
ulations. Therefore, this research proposes a new
bumper system and a new type of crash box to
satisfy the regulations. Detailed designs of the new
bumper system and the new crash box are per-
formed using optimization. Based on the results of
several analyses, it has been found that the stiff-
ness of the crash box does not have much impact
on pedestrian protection and the bumper test. Con-
Table 1 L9(34) orthogonal array
Experiment
Column number assigned for the following design variables
Characteristic function YA B C D
1 1 1 1 1 Y1
2 1 2 2 2 Y2
3 1 3 3 3 Y3
4 2 1 2 3 Y4
5 2 2 3 1 Y5
6 2 3 1 2 Y6
7 3 1 3 2 Y7
8 3 2 1 3 Y8
9 3 3 2 1 Y9
Table 2 An example of the one-way table for an orthogonal array
Design variable
Value for the following levels
1 2 3
A mA1~ 1
3 Y1zY2zY3ð Þ mA2~ 1
3 Y4zY5zY6ð Þ mA3~ 1
3 Y7zY8zY9ð ÞB mB1
~ 13 Y1zY4zY7ð Þ mB2
~ 13 Y2zY5zY8ð Þ mB3
~ 13 Y3zY6zY9ð Þ
C mC1~ 1
3 Y1zY6zY8ð Þ mC2~ 1
3 Y2zY4zY9ð Þ mC3~ 1
3 Y3zY5zY7ð ÞD mD1
~ 13 Y1zY5zY9ð Þ mD2
~ 13 Y2zY6zY7ð Þ mD3
~ 13 Y3zY4zY6ð Þ
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sequently, the design process for the frontal struc-
ture of the vehicle has two steps. First, the bumper
system is designed while considering pedestrian
protection and FMVSS part 581. Second, the crash
box is designed to satisfy the RCAR test, at the de-
sign of step 1.
Figure 7 presents the overall design process of the
frontal structure, which is proposed in the present
study. First, a detailed design of the newly proposed
bumper system is carried out by using RSAO. A new
plate structure and springs are added to the existing
model. The design variables are the thicknesses of
the plate and the bumper rail, and the stiffness of
the springs. The mass of the bumper system is
considered as the objective function and minimized.
The conditions for pedestrian protection and FMVSS
part 581 are used as constraints. Simulations of both
the lower-legform impact test and the pendulum
impact test are performed to generate the response
surfaces. As mentioned earlier, acceleration at the
upper tibia is measured in the lower-legform impact
test, and the intrusion and deflection are measured
in the pendulum impact test. The measured prop-
erties are used as constraints in the optimization
process. Since the two impact tests are carried out
in the time domain, the acceleration, intrusion, and
deflection should be considered with respect to all
the time steps. A response surface is generated at
each time step: thus, the number of constraints for
each property is the same as that of the time steps of
the analysis.
When the optimization process is conducted by
RSAO, an optimum is obtained; the function values
from the response surfaces could be different from
Fig. 7 The flow chart of the frontal structure of the vehicle (ANOM, analysis of means)
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real values. Therefore, a confirmation experiment
should be performed. Both impact tests are evalu-
ated again at the optimum. If the test results do
not satisfy the regulations, another bumper system
should be proposed again. Otherwise, the design pro-
cess for the bumper system terminates.
After completing the design of the bumper system,
the crash box is designed for the RCAR test. First,
a new type of crash box is proposed, and its
detailed shape is determined by using DOA. It is
difficult to perform mathematical shape optimiza-
tion with crash analysis because of costly sensitivity
analysis. Thus, shape design is carried out in the
discrete space by using DOA. Design variables are
the shape of the crash box and the thickness of the
crash box. For this purpose, the design variables
should be discretized. The objective of the RCAR test
is to reduce the repair costs. As mentioned earlier,
the strain energy is considered as an objective
function because, if the strain energy is maximized,
the impact energy transmitted to the other parts of
the vehicle would be decreased. It leads to lower
repair costs. After designing the crash box, the de-
sign process for the frontal structure of the vehicle
terminates since the stiffness of the crash box does
not have much impact on pedestrian protection and
the bumper test.
4.2 Design of the bumper system
4.2.1 Proposed bumper system
As defined in section 4.1, a bumper system is first
designed to satisfy both the regulations of pedestrian
protection and FMVSS part 581. A stiff bumper on
the market can typically manage the pendulum im-
pact (FMVSS part 581); however, this stiff system does
not satisfy pedestrian protection. Many previous
studies proposed soft bumpers in order to meet
pedestrian protection; however, soft bumpers do not
satisfy the pendulum test. In general, the frontal
structure of the vehicle needs sufficient space to de-
crease the lower leg injury (pedestrian protection),
but it is difficult to secure enough space in the fron-
tal structure because of the styling of the vehicle.
Therefore, a new bumper system is needed to meet
the two regulations.
Figure 8 presents the configuration for the pro-
posed bumper system. Figure 9 illustrates the finite
element model for a pendulum test of the entire
bumper system. The finite element model is utilized
for non-linear dynamic finite element analysis us-
ing LS-DYNA3D [19]. The finite element model for
the bumper system analysis consists of 33 645 shell
elements, 3476 solid elements, and three spring
elements. Finite element analyses for the bumper
system are conducted for the 200 pendulum test at
a speed of 8 km/h (5 mile/h) and the pedestrian
legform test. Table 3 shows the material properties
for parts of the vehicle front structure. As mentioned
earlier, a thin-plate structure is connected to the
bumper rail by three springs. The plate structure
helps to reduce the impact to the pedestrian in a
vehicle–pedestrian crash, and it also protects the
vehicle in a low-speed impact. Because of the plate
structure, a certain space is needed between the
bumper energy absorber and the bumper rail. This
space could have a negative influence on the vehicle’s
styling. To compensate for this increased space, the
crash box is shortened afterward. Figure 10 illustrates
the new plate structure. The initial shape of the plate
structure including a reinforcement bead is deter-
mined by trial and error. The detailed design of the
new bumper system to satisfy pedestrian protection
and FMVSS part 581 is carried out while the mass of
the system is minimized.
Fig. 8 Configuration of the new bumper system and design variables for optimization
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4.2.2 Design formulation
In section 4.2.1, a new bumper system is proposed to
satisfy the regulations for pedestrian protection and
FMVSS part 581. As mentioned earlier, the number
of target points for impact should be more than
three, including the centre and the side of the
bumper. In a pilot study, the lower-leg injury is the
highest at the centre of the bumper among the three
targets. Thus, only the centre point is selected for
the lower-legform impact test. GTR for the lower-leg
injury has three requirements: the dynamic knee
bending angle, the knee shearing displacement, and
the acceleration at the upper tibia. These conditions
should be considered to reduce leg injury. Previous
research has found that the design to meet the
dynamic knee bending angle can be obtained by
adding a lower stiffener and modifying the lower part
Table 3 Material properties used in the analysis of the front structure of a vehicle
Part name
Material properties
Material name Density (kg/mm3) Young’s modulus Yield strength (MPa)
Crash box Steel (SAPH440) 7.856103 210 230Rail Steel (SAPH590) 7.856103 210 480Plate Steel (SAPH370) 7.856103 207 235Energy absorber Foam (EPP) 87 48.3 3.1
Fig. 9 Model for finite element analysis of the frontal structure
Fig. 10 Shape of the plate
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of the bumper cover [3]. Also, if a design meets the
requirements for the dynamic knee bending angle
and the acceleration at the upper tibia, the design
would meet the knee shearing displacement [29].
Therefore, this research only considers the accelera-
tion at the upper tibia.
FMVSS part 581 has two tests: the barrier test and
the pendulum impact test. In both tests, the target
points are the centre of the bumper and the side of
the vehicle. In the pendulum impact test, a vehicle is
hit by a pendulum weighing as much as the vehicle
and located between 0.4 m and 0.5 m (16 in and
20 in) height from the ground. In the pilot study, an
intrusion and a deflection are highest when the
pendulum at 0.5 m (20 in) height hits the centre of
the vehicle. Thus, only this condition is used in this
research, and the intrusion and deflection are used
as constraints in the optimization process. The
intrusion and deflection are illustrated in Fig. 5.
The intrusion is the distance from the front bumper
cover to the leading edge of the hood. The distance is
measured as 75 mm. If the intrusion is less than
75 mm, the leading edge of the hood would not be
damaged by impact. The deflection is the distance
from the rear centre of the bumper rail to the
radiator. The distance is measured as 35 mm. If the
deflection is less than 35 mm, the radiator would not
be damaged by impact.
Design variables are determined as illustrated in
Fig. 8. They are the thickness (t1) of the plate, the
thickness (t2) of the bumper rail, the spring coef-
ficient (k1) of the centre spring, and the spring
coefficient (k2) of the side springs. The objective
function is the mass of the bumper system. In the
pedestrian impact test, the acceleration at the upper
tibia should be less than 170g as indicated in the
GTR. In the pendulum impact test, the intrusion
should be less than 75 mm and the deflection should
be less than 35 mm. In the optimization process, the
safety factor is defined as 10 per cent. Therefore, the
acceleration at the upper tibia should be less than
153g, the intrusion should be less than 67.5 mm, and
the deflection should be less than 31.5 mm. These
values are considered as the constraint values. The
values should be satisfied at all the time steps. An
optimization formulation of the design problem is
expressed as follows. Find
t1, t2, k1, k2 ð5aÞ
to minimize
mass ð5bÞ
subject to
ai¡153g i~1, � � � , nð Þ ð5cÞ
I j¡67:5 mm j~1, � � � , mð Þ ð5dÞ
Dj¡31:5 mm j~1, � � � , mð Þ ð5eÞ
where a is the acceleration at the upper tibia, I is
the intrusion, D is the deflection, n is the number of
time steps in the lower-legform impact test, and m
is the number of time steps in FMVSS part 581. The
problem in equations (4) is solved by using RSAO as
explained before.
4.2.3 Optimization results
An optimization design process is carried out to
meet the two regulations by using RSAO. RSAO gen-
erates response surfaces based on the experiments.
An optimum solution is obtained in 16 iterations.
During the optimization, the number of non-linear
finite element analyses is 25 for each impact test.
The optimum solutions are as follows.
1. The thickness of the plate is 1.76 mm.
2. The thickness of the bumper rail is 0.915 mm.
3. The spring coefficient of the centre spring is
56.08 N/mm.
4. The spring coefficient of both side springs is
39.23 N/mm.
Figure 11 presents the history of the objective
function. The objective function values are normal-
ized by the initial value. The mass of optimum plate
structure is reduced by 26.6 per cent compared with
the initial model.
Fig. 11 History of the objective function value
2382 M-K Shin, S-I Yi, O-T Kwon, and G-J Park
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Based on the proposed process in section 4.1, a
confirmation experiment is performed. Both regula-
tions are well satisfied in the confirmation experi-
ment. Thus, the design of the bumper system is
completed, and the design of the crash box is made.
4.3 Design of the crash box
4.3.1 Proposed crash box
After the design of the new bumper system, the crash
box design is carried out for the RCAR test. The goal
of the RCAR test is to reduce insurance costs by
improving automotive damageability, repairability,
safety, and security. If a device absorbs most of the
energy of an impact, it can be expected that the
other parts are not deformed during an accident.
When the energy-absorbing device is removable,
then the other parts do not have to be disassembled
for repair and the repair cost is reduced [30, 31].
Therefore, it is important to have an efficient energy-
absorbing part, and the crash box in Fig. 2 is utilized
for this purpose. In this section, the crash box is
designed concerning the RCAR test. The detailed
design of the newly proposed crash box is performed
by using the algorithm of DOA, which was intro-
duced in section 3.2.
As explained in section 2, a frontal barrier impact
test at a speed of 15 km/h is considered in the RCAR
test. Figure 12 presents a new type of the proposed
crash box [12]. The proposed crash box has a bellows
shape with a rectangular section. The initial shape
of the crash box is determined by trial and error.
The initial shape is determined by the number of
wrinkles, the length of the interval, and the shape of
the section. As illustrated in Fig. 12, the length of the
initial model is 180 mm, which is 50 mm shorter than
the existing model in order to compensate for the
previously increasing space between the bumper
energy absorber and the bumper rail. The role of the
crash box is to absorb the impact energy as much as
possible, and this leads to preventing the interior
parts of the vehicle from being damaged.
4.3.2 Design formulation
A shape optimization process of the crash box is
needed to determine the detailed shape of the crash
box. As mentioned earlier, mathematical shape opti-
mization with crash analysis is extremely difficult.
Thus, in this research, shape design is conduc-
ted in a discrete space by using DOA. Since DOA
uses an orthogonal array, it has the advantage of
finding a solution with a small number of experi-
ments (function calculation).
Figure 12 illustrates three design variables: the
thickness t, the width w, and the height h of the
crash box. The width and the height are defined at
the rear part box because it is difficult to change the
sizes of the front part. Thus, the crash box has a stair
shape. The number of levels for each design variable
is three and an orthogonal array L9(34) is selected.
The candidate values of the design variables are
selected by considering the space of the vehicle. As
shown in Table 1, the combination of the design
variables is made for each row of the orthogonal
array. The first three columns are used. For each
row, a finite element model is constructed.
The strain energy is selected as an objective
function (characteristic function). The strain energy
and reaction force at the end of the crash box are
used as constraints. These constraints are defined to
improve the energy-absorbing capability compared
with the existing model. In other words, the trans-
mitted impact energy to the interior part of the veh-
icle is less than that of the existing model. The strain
energy of the existing model is 7.066106 N mm,
and the reaction force at the end of the crash box
is 177.8 kN. An optimization formulation is defined
as follows. Find
w, h, t ð6aÞ
to maximize
Estrain ð6bÞ
subject to
Eexistingstrain {Estrain¡0 ð6cÞ
Freaction{Fexistingreaction¡0 ð6dÞFig. 12 Configuration of the crash box and initial
values of the design variables
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where the candidate values are
w [ 61 mm, 91 mm, 121 mmf gh [ 63:3 mm, 93:3 mm, 123:3 mmf g
t [ 1:2 mm, 1:4 mm, 1:6 mmf g
where Estrain is the strain energy, Freaction is thereaction force at the end of the crash box, and thesuperscript ‘existing’ means the existing model. Asexplained before, an augmented function Y(b) inequation (2) is used to consider the constraints. Theoptimization formulation of equations (6) is changedto the following. Find
w, h, t ð60aÞto minimize
Y bð Þ~f bð ÞzP bð Þ
~1
Estrainzs max 0, E
existingstrain {Estrain
� �h
zmax 0, Freaction{Fexistingreaction
� �ið60bÞ
where s is the scale factor. The formulation in equ-
ations (69) is solved by using DOA.
4.3.3 Optimization results
The shape optimization process is performed us-
ing DOA. Table 4 shows the levels of each design
variable. Since the number of design variables is 3
and the number of levels is 3, the L9(34) orthogonal
array as shown in Table 1 is selected. As shown in
Table 5, each design variable is allocated to the
variable in Table 1. An experiment is carried out for
each row, and the best one is A2B1C3 of the fourth
row. Table 6 is the one-way table for Table 5 and the
smallest values are selected. The solution is A2B3C1
and a confirmation experiment is performed. In
the confirmation experiment, Y of the combination
A2B3C1 is 1.06102 and the constraints are violated.
Therefore, the final solution is A2B1C3 in the fourth
row of Table 5.
Figure 13 presents a comparison between the
initial model and the optimum model of the crash
box. Through the optimization process, the width
and thickness of the crash box increase compared
with the initial model. The height of the crash box
does not change. At the optimum, the strain energy
is 1.026107 N mm, and the reaction force at the end
of the crash box is 169.6 kN. The strain energy
increases by 44.5 per cent and the reaction force
Table 4 Levels of each design variable
Designvariable
Value for the following levels
1 2 3
A (w) A1 5 61 mm A2 5 91 mm A3 5 121 mmB (h) B1 5 63.3 mm B2 5 93.3 mm B3 5 123.3 mmC (t) C1 5 1.2 mm C2 5 1.4 mm C3 5 1.6 mm
Table 6 A one-way table of the orthogonal array
Design variable
Value for the following levels
1 2 3
A mA1~ 1
3 Y1zY2zY3ð Þ~2:07|104
mA2~ 1
3 Y4zY5zY6ð Þ~1:28|104
mA3~ 1
3 Y7zY8zY9ð Þ~3:33|104
B mB1~ 1
3 Y1zY4zY7ð Þ~3:45|104
mB2~ 1
3 Y2zY5zY8ð Þ~3:02|104
mB3~ 1
3 Y3zY6zY9ð Þ~2:09|104
C mC1~ 1
3 Y1zY6zY8ð Þ~4:24|104
mC2~ 1
3 Y2zY4zY9ð Þ~5:46|104
mC3~ 1
3 Y3zY5zY7ð Þ~4:34|104
Table 5 Matrix experiment results for the crash box
Experiment
Value of the following design variables
Characteristic function YA (w) B (h) C (t) D
1 61 mm 63.3 mm 1.2 mm 1 1.1061027
2 61 mm 93.3 mm 1.4 mm 2 1.176104
3 61 mm 123.3 mm 1.6 mm 3 5.056104
4 91 mm 63.3 mm 1.4 mm 3 9.8461028
5 91 mm 93.3 mm 1.6 mm 1 4.116104
6 91 mm 123.3 mm 1.2 mm 2 6.236104
7 121 mm 63.3 mm 1.6 mm 2 3.856104
8 121 mm 93.3 mm 1.2 mm 3 3.776104
9 121 mm 123.3 mm 1.4 mm 1 5.116104
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decreases compared with the existing model. In
other words, the optimum model is absorbing more
impact energy than the existing crash box model,
and it could lead to a reduction in the repair costs.
Based on the proposed design process in section 4.1,
the design process for the frontal structure of the
vehicle terminates since the stiffness of the crash box
does not have much impact on pedestrian protec-
tion and the bumper test.
5 CONCLUSIONS
Various regulations are related to the automotive
frontal structure. The regulations are pedestrian
protection, the FMVSS part 581 bumper test, and
the RCAR test. In these regulations, the stiffness
requirements of the bumper system disagree with
each other. In this research, a design method for a
new bumper system and the crash box is proposed
to satisfy the regulations related to the front struc-
ture of the vehicle. Consequently, the bumper sys-
tem satisfies the pedestrian protection test as well
as the FMVSS part 581 bumper test. Also, the crash
box satisfies the requirement to lower the repair cost
concerning the RCAR test. Computer simulation is
employed to describe the impact tests.
Analyses for the bumper system and the crash box
are highly non-linear and sensitivity information is
extremely difficult to calculate. Therefore, an ap-
proximate optimization algorithm such as RSAO and
DOE are used in the design process.
A design process is proposed in order to design the
frontal structure of the vehicle while the regulations
related to the frontal structure are satisfied. Accor-
ding to the design process, a detailed shape of the
bumper system and the crash box are determined.
The design process consists of two steps. First, a
new bumper system is proposed to satisfy the reg-
ulations for pedestrian protection as well as the
FMVSS part 581 bumper test. Detailed design of the
bumper system is carried out using RSAO. Second,
a new type of crash box is proposed, and the detailed
shape of the crash box is determined by DOA. Using
RSAO, the mass of the proposed bumper system
is minimized while both regulations of pedestrian
protection and FMVSS part 581 are satisfied. When
using DOA, the strain energy of the crash box is
maximized because the strain energy is the cap-
ability to absorb the impact energy. Using DOA, the
strain energy increases by 44.5 per cent and the
increasing strain energy leads to absorption of the
impact energy. In conclusion, the frontal structure
of the vehicle is improved through the proposed
design process.
ACKNOWLEDGEMENTS
This work was supported by a Korea Science andEngineering Foundation grant and supported by theKorean government’s Ministry of Education, Scienceand Technology, Republic of Korea (Grant R01-2008-000-10012-0). The authors are grateful to Mrs MiSunPark for her correction of the manuscript.
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APPENDIX
Notation
a acceleration at the upper tibia
b design variables
bL, bU lower and upper limits respectively
for design variables
D deflection distance
Estrain strain energy of the crash box
f(b) objective function
Freaction reaction force at the end of the crash
box
gj(b) inequality constraint
h height of the crash box
hi(b) equality constraint
I intrusion distance
k1, k2 spring constants
m number of time steps in the Federal
Motor Vehicle Safety Standard part
581
n number of time steps in the
lower-legform impact test
P(b) penalty function defined by the
maximum violation of the constraint
s scale factor
t, t1, t2 thickness
w width of the crash box
Y(b) characteristic function, objective
function in the design of experiments
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