Multiobjective sequential optimization for a vehicle ...

Original Article

Multiobjective sequential optimization for a vehicle door using hybrid materials tailor-welded structure

Proc IMechE Part C: J Mechanical Engineering Science 0(0) 1–9 ! IMechE 2015 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0954406215607901 pic.sagepub.com

Jianguang Fang1,3, Yunkai Gao1, Guangyong Sun2, Chengmin Xu1 and Qing Li3

Abstract To achieve lightweight vehicle door, this paper presents a novel design with a hybrid material tailor-welded structure (HMTWS). A multiobjective optimization procedure is adopted to generate a set of solutions, in which the door stiffness and mass are taken as objective functions, and the material types and plate thicknesses are regarded as the discrete and continuous design variables, respectively. To improve the optimization efficiency, Kriging algorithm is used for generating surrogate model through a sequential sampling strategy. The non-dominated sorting genetic algorithm II (NSGA-II) is employed to perform the multiobjective optimization. It is found that for the same computational cost, the sequential sampling strategy can yield more accurate optimization results than the conventional one-step sampling strategy. Most importantly, HMTWS is found more competent than the traditional thin-walled configurations made of steel or other lighter mono-materials for maximizing the usage of materials and stiffness of the vehicular door structures. Keywords Hybrid materials tailor-welded structure, tailor-welded blank, vehicular door, sequential sampling, multiobjective optimization, Kriging model Date received: 21 April 2015; accepted: 1 September 2015

Introduction Lightweight design of vehicle structures has become an increasingly critical issue for energy concern and environment conservation nowadays. To achieve a lighter structure, the applications of proper tailorwelded blanks (TWB) structures have proven rather effective in automotive industry.1 Particular effort was made to the design of TWB structure for an automotive door using topology, shape, and size optimizations and/or design of experiments (DoE).2–5 In this regard, Song and Park6 conducted a multidisciplinary optimization (MDO) of a vehicular front door using a TWB structure for the stiffness, natural frequency and side impact crashworthiness criteria. Shi et al.7 developed a lightweight design for automotive front side rails based on TWB configuration, in which the criteria of strength, bending stiffness and torsion rigidity of the TWB structure were taken into account in order to determine the sheet thicknesses. Pan et al.8 proposed a metamodel-based lightweight design of Bpillar with TWB structure subjected to the crashworthiness constraints in vehicular roof crush and side impact. Recently, there is increasing interest in aluminum and magnesium alloys in automotive industry

attributable to their unique material properties, especially lightweight. In this regard, Hosseini-Tehrani and Nikahd9 found that a hybrid front side rail structure made of steel and aluminum had better characteristics from the perspectives of passenger safety and material efficiency. Logan10 developed a hybrid material configuration by using magnesium and aluminum and achieved a more than 40% weight reduction whilst improving mechanical performance significantly compared with conventional steel bodyin-white structure. Cui et al.11 proposed to design lightweight vehicular body assemblies using multimaterial construction with low cost penalty, where 1

School of Automotive Studies, Tongji University, Shanghai, China State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Hunan University, Changsha, China 3 School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, Australia 2

Corresponding author: Yunkai Gao, School of Automotive Studies, Tongji University, Shanghai 201804, China. Email: [email protected] Guangyong Sun, State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Hunan University, Changsha 410082, China. Email: [email protected]

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different materials, such as aluminum, magnesium, steel and carbon fiber, were utilized as the potential candidates for selection. Ince et al.12 investigated the impact behaviors of the crash boxes made of steel and aluminum materials experimentally and numerically, and they then optimized the hybrid crash box to minimize the weight. To achieve better combination of dissimilar materials, substantial efforts have been devoted to the development of different tailored welding technologies. For example, Schubert et al.13 exemplified the prototype structures made of aluminum, titanium, magnesium and their combinations by using laser beam joint technology. Merklein and Giera14 performed butt joints of dissimilar steel and aluminum sheets with laserassisted friction stir welding. Shigematsu et al.15 explored TWBs comprised of aluminum and magnesium alloys, in which friction stir welding process was employed. Sahin16 welded austenitic stainless steel and aluminum materials using the friction welding technology. Although there have been some studies available on joining dissimilar materials, the investigations into optimization of TWB structures with hybrid materials in automotive industry have not been well reported yet in literature. Most (if not all) real-life engineering problems are characterized by multiple conflicting requirements, between which an appropriate trade-off should be made through multiobjective optimization (MOO).17–19 Instead of seeking a unique optimal solution, MOO often generates a spectrum of solutions to provide decision-makers with more insightful information.

This paper takes into account both TWB configuration and hybrid material usage, aiming to design a novel hybrid materials tailor-welded structure (namely, HMTWS) for vehicle door structure using MOO, in which the Kriging surrogate technique and sequential sampling-based optimization work together to reduce the computational cost. The rest of the paper is organized as follows. The following section describes the finite element modeling of TWB and hybrid materials tailor-welded structure as well as defines the specific optimization problem. The Design optimization methodology section 3 presents the methodology adopted in the door design case, including the Non-dominated Sorting Genetic Algorithm II (NSGA-II), Kriging approximation, and sequential sampling-based MOO. The next section provides the results and discussions of the TWB door structural design with hybrid materials. Finally, some conclusions are drawn in the last section.

Design optimization of a HMTWS vehicle door Numerical modeling and experimental validation of the door structure19 As illustrated in Fang et al.,19 the finite element (FE) models of a vehicle door, subjected to four different load conditions, i.e. lower lateral, upper lateral, vertical sag, and free–free boundary conditions, and the first three are established in Figure 1. The FE models are run in commercial code MSC.NASTRAN.20

Figure 1. Loading conditions for door stiffness analyses. (a) Lower lateral, (b) upper lateral, and (c) vertical sag.

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Table 1. Result comparison between FEA and physical tests. Indicator

Simulation

Experiment

Difference

Mass (m) Vertical sag (Dsag) Natural frequency (f) Upper lateral (Dupper) Lower lateral (Dlower)

22.13 kg 4.49 mm 40.45 Hz 2.86 mm 1.67 mm

22.20 kg 4.53 mm 40.71 Hz 2.83 mm 1.68 mm

0.32% 0.88% 0.64% 1.06% 0.60%

Table 1 provides the comparison between finite element analysis (FEA) results and experimental data19 of the conventional steel door structure. All the FE results are found to agree very well with the experimental results. Therefore, the FE models are considered accurate for the subsequent design optimization.

Optimization for a HMTWS vehicle door As a simple treatment on the weld line, the coincident node method8 is generally used to tie adjacent shell elements around the weld zone of the two connecting sheet components. Note that although the welding connection between two disparate parts with different thicknesses and materials could play a significant role in affecting local mechanical properties,1,21 it can be modeled by a simplified approach without accounting for local effects of welding properties because the blank size is much larger than the size of heat-affected zones (HAZs) in practical applications.22,23 Thus, the geometric details and specific material properties of the weld line can be approximately neglected in the design model. Although the partition of weld line of the inner door panel may be determined by topology optimization,2,24 the locations of weld lines of the inner door panel are assumed to be a given condition in this study. Four thicknesses (T1, T2, T3, and T4) and the corresponding materials (M1, M2, M3, and M4) at different locations (see Figure 2) are taken as the design variables of the inner door panel. Besides, the thickness and material of the outer panel are also considered to be the design variables, i.e. T5 and M5 as in Figure 2. To achieve the lightweight design to a large extent, each material can be selected from either aluminum or magnesium in addition to the conventional steel in this study, indicating the discrete variables. The mechanical properties of these three materials are summarized in Table 2. This study aims to simultaneously maximize the vertical sag stiffness and to minimize the structural mass, while constraining other stiffness indices at certain levels. Thus, the multiobjective optimization problem for the door structure is formulated as a standard mathematical form in terms of mixed variables (i.e. continuous thickness variables and discrete material type variables), objectives and constraints as

Figure 2. Design variables.

Table 2. Material properties for TWB door structure. ID

Material

Elastic modulus (GPa)

Poisson’s ratio

Density (kg/m3)

1 2 3

Steel Aluminum Magnesium

210 72 45

0.30 0.33 0.37

7850 2720 1840

follows   8 m, Dsag f 540:45Hz > > > > D < upper 42:86mm Dlower 41:67mm > s:t: > > > > > > 0:6mm4T > i 43:0mmi ¼ 1, 2, . . . , , 5 > > : : Mj ¼ 1, 2, 3j ¼ 1, 2, . . . , , 5 8 Min > > > > > >
> > > f 540:45Hz < > > < : Dupper 42:86mm > s:t: > > D 41:67mm > > > : : lower 0:6mm4Touter , Tinner 43:0mm

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Table 4. Optimal solutions. No.

M1

M2

M3

M4

M5

T1

T2

T3

T4

T5

1 2 3 4 5 6 7 8 9 10 11

3 2 2 3 3 3 3 3 3 3 3

1 1 1 2 2 2 2 2 2 2 2

1 1 1 1 1 1 1 1 1 1 2

1 1 1 1 1 2 3 3 3 3 3

1 1 2 3 3 3 3 3 3 3 3

3.00 1.67 1.96 1.34 1.42 1.61 2.47 2.91 2.70 3.00 2.81

2.45 2.09 2.89 3.00 3.00 2.60 2.91 3.00 3.00 3.00 3.00

3.00 3.00 3.00 3.00 3.00 3.00 3.00 2.85 2.63 2.32 3.00

3.00 3.00 3.00 2.80 2.30 3.00 2.80 2.23 2.26 2.34 2.65

3.00 2.40 3.00 2.82 1.93 2.45 1.62 1.73 1.81 1.84 2.07

Table 5. Objectives of the optimal solutions. M

Dsag

No.

Kriging (kg)

FEA (kg)

Error (%)

Kriging (mm)

FEA (mm)

Error (%)

1 2 3 4 5 6 7 8 9 10 11

46.21 41.63 33.27 27.62 24.02 19.28 16.62 16.17 16.03 15.85 15.07

46.18 41.62 33.19 27.60 24.04 19.31 16.61 16.18 16.03 15.86 15.05

0.06 0.01 0.22 0.06 0.08 0.14 0.09 0.05 0.02 0.03 0.12

1.39 1.40 1.42 1.46 1.54 1.59 1.71 1.88 2.05 2.33 2.67

1.39 1.40 1.42 1.46 1.54 1.59 1.71 1.88 2.04 2.33 2.68

0.17 0.02 0.15 0.28 0.02 0.01 0.06 0.04 0.04 0.02 0.03

Table 6. Constraints of the optimal solutions. f

1 2 3 4 5 6 7 8 9 10 11

Dlower

Dupper

No. Kriging (Hz)

FEA (Hz)

Error (%)

Kriging (mm)

FEA (mm)

Error (%)

Kriging (mm)

FEA (mm)

Error (%)

58.69 57.09 64.29 60.68 58.60 63.91 58.19 58.73 59.33 59.34 60.97

59.52 57.34 65.10 61.95 58.90 63.72 58.14 58.86 59.36 59.38 61.14

1.39 0.44 1.24 2.04 0.51 0.30 0.09 0.22 0.04 0.07 0.28

1.43 1.59 1.63 2.28 2.55 2.52 2.83 2.85 2.86 2.86 2.86

1.47 1.60 1.64 2.26 2.53 2.54 2.83 2.85 2.86 2.86 2.86

2.25 0.08 0.65 1.00 0.84 0.50 0.19 0.16 0.03 0.16 0.15

0.73 0.77 0.82 0.98 1.15 1.21 1.50 1.65 1.64 1.64 1.58

0.73 0.77 0.82 0.97 1.14 1.21 1.50 1.65 1.64 1.64 1.58

0.32 0.03 0.03 1.04 0.52 0.22 0.16 0.16 0.06 0.04 0.02

The Pareto frontiers of structures made of three mono-materials and HMTWS are displayed together in Figure 9. Apparently, HMTWS is much more promising than any of mono-material structures, i.e.

either better sag stiffness can be obtained for the same mass or lower mass can be obtained for the same sag stiffness. Besides, a simple substitution of steel with lighter materials, such as magnesium or

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Proc IMechE Part C: J Mechanical Engineering Science 0(0) The non-dominated sorting genetic algorithm II (NSGA-II) was employed to generate Pareto frontiers, integrated with the sequential sampling-based metamodeling technique. From the optimization results, we can come to the following specific conclusions.

4

3.305

3.5

3.300

Dsag / mm

3

3.295

2.5

15.915

15.920

15.925

15.930

Steel Aluminium Magnesium HMTWS

2

1.5

1 15

20

25

30 35 m / kg

40

45

50

Figure 9. Pareto frontier comparison of HMTWS and different single-material structures.

aluminum, can reduce the mass only within a very narrow range of sag vertical stiffness as shown in the Pareto space. In other words, compared with steel, a magnesium door can reduce the mass only when vertical sag deformation is around 3.3 mm, and an aluminum door can do so only when vertical sag deformation lies in between 2.4 and 2.7 mm. It should be pointed out that in the sequential sampling and modeling procedure, these 11 validation points are selected from the current Pareto frontier uniformly. Addition of these optimal validation points to the training data set allows to particularly enhance the modeling accuracy near the optimum domain. Such a sampling bias is generally considered positive to the design optimization and it enables a more accurate final solution as shown in this study. Note that although the results of this door design case study demonstrated the potential of using HMTWS, the extra economic issues during the forming and joining process of fabricating the structures should be also evaluated in the design. Nevertheless, this is beyond the scope of this paper.

Concluding remarks To achieve the lightweight design for a vehicle door, we presented a novel hybrid material tailor-welded structure (HMTWS) by taking into account both tailor-welded blank (TWB) structure and hybrid use of different materials. To make a proper trade-off between the structural mass and vertical sag stiffness subjected to static and dynamic stiffness constraints, the multiobjective optimization (MOO) approach was adopted. In this study, the thicknesses and material types of the inner and outer panels were regarded as the continuous and discrete variables, respectively.

1. Compared with the conventional steel and other single lighter material structures, the novel HMTWS door with both TWB technique and hybrid materials can significantly improve the design objectives of vertical sag stiffness and lightweight, while satisfying all the other stiffness constraints. 2. Compared with the one-step sampling strategy that has the similar computational cost, the sequential sampling strategy yielded more accurate and realistic optimal solutions. Declaration of Conflicting Interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The supports from the National Natural Science Foundation of China (51575172), the Hunan Provincial Science Foundation of China (13JJ4036), the Doctoral Fund of Ministry of Education of China (20120161120005) are acknowledged. The first author is a recipient of the doctoral scholarships from both China Scholarship Council (CSC) and the University of Sydney.

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