DOE Based Multidisciplinary Design Optimization of

International Journal of Manufacturing, Industrial & Management Engineering
Volume 2, Number 1 (2014), pp.87-94
© Delton Books
http://www.deltonbooks.com
DOE Based Multidisciplinary Design Optimization of a
Vehicle Frontal Structure
Gunti Ranga Srinivas
Indian Institute of Science
Sachin Phalaksha
Siddaganga Institute of Technology
Dr. Anindya Deb
Indian Institute of Science
Dr. R S Kadadevaramath
Siddaganga Institute of Technology
Abstract:
Multidisciplinary Design Optimization is of great significance in the design of
an automotive passenger car. The present work is concerned with the objective
of cross-functional optimization (i.e. MDO) of automotive body. The
thickness of the front end structural components namely inner rail, outer rail
and bumper beam are considered as design variables. The main goal adopted
here is minimizing the weight of the body meeting NVH (noise, vibration &
harshness), durability, crash safety and manufacturing requirements. The
stated goal is achieved using factorial method. The design of experiments is
generated using Minitab and the numerical simulations are performed using
“Optistruct” and “LS-Dyna”. The factorial equations for the NVH, crash
safety and durability parameters are developed using Minitab. Using factorial
equations, design and manufacturing constraints, optimization is performed in
MATLAB.
Introduction:
Numerical simulations for vehicle occupant safety assessment and durability
improvement have been greatly integrated in to vehicle design process. The increase in safety
standards can be attributed to the improvement of structural crashworthiness performance
through finite element analysis. Although still in its infancy, mathematical optimization
techniques are increasingly being applied to the crashworthiness design of vehicles. There is
increasing interest in the coupling of other disciplines into the optimization process,
especially for complex engineering systems like aircraft and automobiles. Different methods
have been proposed when dealing with multidisciplinary design optimization. The
conventional or standard approach is to evaluate all disciplines simultaneously in one
integrated objective and constraint set by applying an optimizer to the multidisciplinary
analysis. The standard method has been called multidisciplinary feasible, as it maintains
feasibility with respect to the multidisciplinary analysis. In order to design and develop a
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Gunti Ranga Srinivas et al.
competitive vehicle, there is a need to meet multiple attributes of a vehicle like NVH,
durability, crash safety, manufacturing and cost targets. Hence, it is necessary to develop
efficient MDO (Multidisciplinary Design Optimization) methods. Achieving the objective of
minimizing weight meeting various parameters like NVH, durability, crash safety and
manufacturing aspects using metamodeling techniques in development of industrial vehicle
with good aesthetics and ergonomics is of great significance and also poses an enormous
challenge.
The topic of automotive structural optimization has been explored by several authors,
e.g. Hong-Seok Park and Xuan-Phuong Dang [1] studied and explained about metamodeling
methods and have given integration between CAD, CAE and Optimization. Larsgunnar
Nilsson and Marcus Redhe [6] compared different methods of optimization with regards to
their efficiency and applicability in crashworthiness design and have developed a novel
method of optimization J Forsberg and L Nilsson [5] investigated crashworthiness
optimization problem using classic response surface and kriging methods. Crashworthiness
optimization using foam-filled thin walled structures by Hanfeng Yin et al. [7] and Geometric
optimization using pultruded composites by Giovanni Belingardi et al. [14] have been
studied. The majority of the authors have used response surface and other methods of
optimization and restricted their study to either one or two attributes. The present work deals
with optimization of automotive structure using factorial method with consideration of more
than two attributes like NVH, Durability, Crash safety and Manufacturing constraint. Deb et
al. [8], and Deb, Naravane and Chou [9] suggested a practical MDO method that can be
applied to weight optimization of automotive structures by specifying constraints on
frequency and crash performance. The present work deals with factorial method based MDO
that can be applied to weight optimization of automotive structures by specifying constraints
on NVH, Durability, Crash performance and manufacturing aspects.
Doe Based Approach:
Multidisciplinary Design Optimization
by Minimizing Mass
Design of Experiments Using Minitab
( Full Factorial Design)
Perform Numerical Simulation
NVH
Durability
Crash Safety
Obtain Factorial Equations
Optimization in Matlab Using Factorial Equations
and Constraints (Nvh, Durability, Crash Safety And
Manufacturing Targets)
DOE Based Multidisciplinary Design Optimization of a Vehicle….
89
Implementation Of Doe-Based Optimization:
Multidisciplinary design optimization of a full vehicle to minimize mass while complying
with crashworthiness, NVH (Noise, Vibration and Harshness), Durability and Manufacturing
constraint is performed using factorial method. Initially Minitab helps in obtaining the design
points (DOE) with respect to the baseline values of design variables selected for optimization.
The parameters expressed as a function of design variables are the lowest modal frequency
which is obtained by performing modal frequency analysis using Optistrut, fatigue factor of
safety by evaluating stress amplitudes using Optistruct and peak value of crash pulse obtained
by performing crash analysis in LS Dyna. Mass equation has been useful in prediction of
mass with respect to design variables. Using the lowest natural frequency of the front end,
fatigue factor of safety, peak deceleration from the NCAP crash pulse and manufacturing
aspect (thickness of two plates spot welded should be less than 3 mm) as constraint
parameters, gages of inner rails, outer rails and bumper beam as design variables, the mass of
frontal structure (i.e. the total mass of the design variables considered) is optimized using
MATLAB.
Objective Function for Minimization:
Design variables:
i.
ii.
iii.
1.1 mm < T1 (thickness of inner rails, figure 1(a)) < 1.7
mm;
1.2 mm < T2 (thickness of outer rails, figure 1(b)) < 1.8 mm;
1.1 mm < T3 ( thickness of bumper beam, figure 1(c)) < 1.7 mm;
Constraints:
i.
ii.
iii.
iv.
Lowest (first) modal natural frequency > 16 Hz
Fatigue factor of safety > 1.1
Peak deceleration < 43G
(TI + T2) < 3 mm ( i.e. thickness of two plates spot welded should be less than or
equal to 3mm)
Figure 1(a): Front inner rails (T1)
Figure 1(b): Front outer rails (T2)
Figure 1(c): Bumper beam (T3)
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Gunti Ranga Srinivas et al.
Bumper beam (T3)
Front rails (T1 & T2
Figure 1(d): Components of vehicle frontal structure selected for optimization
As mentioned earlier, the design points obtained by DOE are based on Cube Design which
gives runs based on levels and factors (i.e.
= runs). In a full factorial experiment,
responses are measured at all combinations of the experimental factor levels. The
combinations of factor levels represent the conditions at which responses will be measured.
Each experimental condition is a called a "run" and the response measurement an
observation. The entire set of runs is the "design". In a two-level full factorial design, each
experimental factor has only two levels (high & low). The experimental runs include all
combinations of these factor levels. Because two-level factorials can indicate major trends, it
can be used to provide direction for further experimentation. Figure (2) represents a Cube
= 8 runs); vertices are the response measurement
Design with 2 levels and 3 factors (i.e.
points, the volume within is the interference space.
Figure 2: Distribution of design points (T1, T2, and T3) according to a cube design scheme
Based on the design points obtained, the finite element model is subjected to modal
frequency analysis, Durability analysis and crash analysis. The results obtained from the
analysis have been tabulated in
Table 1.
T2
T3
CASE T1
NO. (mm) (mm) (mm)
1
2
3
4
5
6
7
8
1.7
1.1
1.1
1.7
1.7
1.1
1.7
1.1
1.8
1.8
1.2
1.2
1.2
1.2
1.8
1.8
1.7
1.7
1.1
1.1
1.7
1.7
1.1
1.1
Lowest modal natural
frequency, ω
(Hz)
16.29
15.97
16.39
16.66
16.12
15.83
16.81
16.49
Fatigue factor of
safety (n)
1.49
1.02
0.96
1.41
1.40
0.95
1.49
1.03
Peak
deceleration, α
(G’s)
46.65
41.51
30.42
40.20
46.01
47.15
37.17
32.25
DOE Based Multidisciplinary Design Optimization of a Vehicle….
91
Table 1: DOE cases analyzed for formulating factorial equations
With the aid of Minitab statistical analysis software and data in Table 1, a linear factorial
equation can be generated for the three constraint variables i.e. lowest modal natural
frequency (ω ), fatigue factor of safety (n) and peak value (α ) of NCAP crash pulse. The
factorial equations are formulated below:
ω = 17.253 + 0.1T1 - 0.2204 T2 - 1.25T3 + 0.2407T1T2 + 0.1667T1T3 + 0.2130T2T3
- 0.0926 T1T2T3
(1)
n = - 0.0172 + 0.7778T1 + 0.1421T2 + 0.0444T3 - 0.0231T1T2 - 0.0555T1T3 - 0.0509T2T3
+ 0.0463T1T2T3
(2)
α = - 178.641 + 133.944T1 + 103.130T2 + 154.228T3 - 70.2315T1T2 - 92.2222T1T3
- 77.4815T2T3 + 51.5741T1T2T3
(3)
As mentioned earlier, to obtain the objective of optimizing the mass, it is important to
generate the mass (m) equation to predict the total mass of the parts at various design points
as in Table 1; it has been verified that this relation accurately predicts the mass of the parts
obtained in Hypermesh when gages of the parts pertaining to inner rail, outer rail and bumper
beam are varied. The mass equation generated has been formulated below:
m = - 0.0506 + 4.1278T1 + 2.7393T2 + 3.4611T3 - 0.0509T1T2 - 0.0556T1T3 - 0.0509T2T3
+ 0.0463T1T2T3
(4)
The finite element models of a compact car (Dodge Neon, Model Year 1995) that were used
for carrying out modal frequency analysis, durability analysis and crash analysis in
generation of factorial equations are shown in figures 3(a), 3(b) and 3(c) respectively . Figure
3(a) pertaining to BIW of the front structure contains 75,314 elements and is used for modal
frequency analysis with all nodes along the cut section of the body constrained from
movement, thus the front structure of a body behaves as a cantilever with respect to the
remaining part of the vehicle and has bending (longitudinal and lateral) and torsional modes
of vibration. Figure 3(b) represents the full car model containing 280,653 elements and is
used for fatigue life prediction. The nodes corresponding to suspension mounting areas are
constrained from movement and 3G bump loads are considered to evaluate stress amplitudes
and subsequently to calculate fatigue factor of safety. Figure 3(c) represents the truncated car
model containing 109,504 elements is subjected to normal impact against a rigid wall with a
speed of 35 mph (56kph). A slab of rigid solid elements with a fictitious mass is attached to
the cut cross-section of the vehicle resulting in a total mass of the truncated model being
equal to that of the full vehicle.
Figure 3(a)
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Gunti Ranga Srinivas et al.
Figure 3(b)
Figure 3(c)
Figure 3: (a) FE model of BIW of vehicle front end structure for NVH analysis
(b) FE model of the full car for durability analysis, and
(c) FE model with lumped mass for NCAP full frontal impact simulation
Using the fatorial equations (1) through (4) along with constraints as mentioned earlier,
optimization based on traditional gradient-based search algorithm is carried out using
MATLAB function (fmincon). Fmincon attempts to find a constrained minimum of a scalar
function of several variables starting at an initial estimate. The final values of design
variables obtained after optimization are: T1 = 1.2844 mm, T2 = 1.2124 mm and T3 = 1.1
mm.
Summary of DOE Based Optimization:
The results obtained from DOE (factorial method) based MDO approach are compared with
the baseline model and are summarized in Table 2. Factorial method with the use CAE
(Computer-aided engineering) tools achieves the objective of reduction in weight of about
16%.
Design Case
T1
(mm)
1.4
1.2844
Design Summary
T2
(mm)
1.522
1.2124
T3
(mm)
1.420
1.1
Mass, m
(kg)
14.62
12.23
Baseline
DOE-based
MDO results
Table 2: A comparison of baseline and weight optimized solution
Conclusion:
Present study deals with one of the methods of Multidisciplinary design optimization (MDO)
of a automotive structure with the aid of certain statistical and analysis packages. Statistical
packages helps in obtaining the mathemetical relations between design variables and
objective functions, and subsequently solving them. Analysis packages helps in solving the
finite element model of a compact commercial car, Dodge Neon. In today’s scenario, it is
important for automotive sectors to deliver quality products which are cost effective, this can
be achieved by using multidisciplinary approaches like DOE based MDO technique. Present
work deals with MDO by minimizing the weight of the automotive body with consideration
of constraints belonging to NVH, Durability, full frontal impact safety(crash analysis) and
manufacturing requirements. Finally, the DOE based MDO approach achieves the objective
of optimiztion by reduction in mass by around 16 percent in total on considered parts for
optimization meeting both design and manufacturing requirements as mentioned earlier. The
DOE Based Multidisciplinary Design Optimization of a Vehicle….
93
proposed DOE based MDO method can further be used by increasing the number of design
variables and constraints.
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