CHEN Xin , MA Fangwu WANG Dengfeng and XIE Chen

1 State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130022, China

2 Zhejiang Geely Automobile Research Institute Co. Ltd, Hangzhou 311228, China

1 Introduction

The weight of body-in-white (BIW) is about 30%–40%of the total car’s, so carbody lightweighting plays an important role in reducing the car curb mass. The lighter body is also environment friendly[1]. To get a lighter car,structural lightweighting design is an important and practical way, along with the material substitution and new manufacturing process[2–3].

Currently, the prevailing research in this field has focused on modifying panel thickness, finding new substitute materials and processing[4]. GAO, et al[5],researched the structural thickness modifications of car body. LONG, et al[6], investigated the joints of mechanical clinching on steel aluminum hybrid structure. FU, et al[7],studied the performance of adhesive joints in an automotive composite structure. And MA, et al[8], discussed boron steel for hot forming and its application. Most of the light weight improvements in the later stage of car development can not solve all the weight problems caused by the early stage design inconsideration. Besides, the main analytic ways used in carbody structural lightweighting are topology and sensitivity of structures[5,9], for example, the topology relations, section dimension, location, and so on. However,most research cares detailed questions too much in one discipline rather than the overall performance coordination based on multidisciplinary design optimization (MDO).

In order to reduce carbody weight maximumly, the design idea of structural lightweighting should be integrated as soon as possible into the early stage of concept body model[10]. In the design idea of structural lightweighting, the engineers can determine a series of varieties and plans to analyze and evaluate the initial concept structure via CAE technology[11].

CAE technology based on finite element method (FEM)provides a good way to analyze and simulate the lightweighting application instead of doing components experiments[12]. The dominant structural lightweighting design needs a complicated FE model including much more detailed structural model building and preprocessing.What’s more, CAD or FE model are not flexible enough to adjust to continual modification in the concept development stage. In other words, the modifications of CAD and FE structure model cannot be realized in the synchronization process[13].

Implicit parameterized structural model by SFE CONCEPT is put forward to fast update carbody lightweighting structural modification[14–15]. Different from the common CAD or FE model, the SFE model is composed of implicit parameterized subsystems, which are built by SFE CONCEPT tools. This implicit parameterized model can use few design parameters to revise car body structure, in both detailed model and whole carbody model,and it can also quickly generate the FE model and provide better technical support for body structure multidisciplinary optimization[16–17]. The SFE implicit parameterized modeling is able to shorten the modification time of CAE model, which enables CAE and MDO to lead the design activities instead of reacting to it[18–19]. This implicit parameterized model is very effective in helping engineers to determine the best design way and balance the shape,size and thickness by the integrated analysis and optimization on multi performances of a light-weight carbody structure.

2 Implicit Parameterized Modeling

Based on the implicit parameterization idea, many simple elements construct the implicit parameterized structure, and it is the result of topological description, not of a CAD or CAE tool construction. The typical elements in implicit parameterized model are influenced by points,base lines, cross sections, beams, joints, simple surface domains, maps, and so on, among which the relations make the complete and consistent geometrical modifications in a very fast and efficient manner.

The SFE model built by point location, line curvature and the shape of cross-section is assembled by the established maps. All the SFE model parts are united logically by the implicit parameters. Any change in one parameter will automatically lead to the changes of other associated parameters. The whole SFE model is assembled by dozens of elements, and for certain analysis, the logical parametric change can cause the SFE model to change rapidly.

Lightweighting design requires the engineers to devise the SFE model optimization factors based on design characteristics and experience, such as material properties,thickness, section shape, size, and the relative location of the parts. According to the predetermined implicit parameters, the implicit parameterized model can quickly generate the FE model of BIW for the analysis on modal,stiffness, safety, and so on. With optimization tools, the implicit parameterized model can continuously generate FE model for the multidisciplinary analysis of the calculation solver. The optimization result may help the engineers find the best balance between body structural performances and its weight.

Fig. 1 shows the process of implicit parameterized modeling for carbody structure lightweighting.

Fig. 1. Processes of implicit parameterized modeling for carbody structure lightweighting

3 Case Study of SFE Implicit Parameterized Structural Model and Its Validation

A new implicit parameterized structural model can be evolved from a FE or CAD model[13]. Usually, an FE model available is improved to build an implicit parameterized model[20]. Fig. 2 shows an implicit parameterized model of BIW.

Fig. 2. An implicit parameterized model of BIW

Table 1 is the contrast data between FE model generated by SFE model and the original FE model. All the deviation is less than 3.8%. So, the SFE structural model and its generating FE model are validated, and they both can be applied in further CAE optimization.

Table 1. Contrast data between SFE model (its generating FE model) and the original FE model

The grid generated rapidly by the validated SFE model can be applied to analyze modal, stiffness, safety, etc.Driven by OPTIMUS, the SFE CONCEPT is linked to the solver, such as NASTRAN, LS-DYNA, PAM-CRASH, and so on[21]. Therefore, MDO is available in the loop composed of the optimizer, SFE tools and FE solvers.

Fig. 3 shows an optimization loop. In the loop, the response relationships can be acquired between the lightweighting parameters and the structural characteristics[22], which guides how to reduce the carbody structural weight. Since the optimization target is the lightest body weight and the constraints are multi-performance, the solver in the loop would reach a good parameters’ combination via complicated calculation process for the lightest weight.

Fig. 3. An optimization loop

4 Optimization Case on Carbody Structural Lightweighting

The SFE carbody implicit parameterized model is shown in Fig. 2, with material properties assigned and map relations defined. This SFE BIW model can be meshed rapidly by SFE built-in tool.

In this MDO case, the target of optimization is the minimum mass. The constraint conditions are the 1st order torsion frequency and bending frequency, which are not less than 39.2 Hz and 41.2 Hz, respectively, and the torsion stiffness and bending stiffness are not less than 11.5 kN ? m/(°) and 11.8 kN/mm, respectively.

The total variables are 90, including 68 thickness variables and 22 shape/location variables selected by the experienced structural engineers.

To reduce the large-scale calculating for the massive variables, the optimization is divided into 2 rounds. The 1st round is to find the more sensitive or potential variables from the 90 variables. The 2nd round is to further carbody lightweighting by using the variables selected in the 1st round.

Fig. 4 displays the flow chart of the 1st round of optimization.

Fig. 4. Flow chart of the 1st round of optimization

The 30 variables, that is, 24 thickness variables and 6 shape/location variables, are picked by correlation analysis of the 1st round of DOE (Design of Experiment), which are regarded as the new input design variables of the 2nd round of optimization.

Fig. 5 is the flow chart of the 2nd round of optimization.

Fig. 5. Flow chart of the 2nd round of optimization

Latin hypercube sampling (LHS) is used in the design of experiment (DOE), and the first-order linear least squares model is built as the approximate model for the further analysis on the characteristics of modal, stiffness and mass.

Table 2 is the accuracy of approximate model. In the table, the response regression of the simulation output R^2_press is close to 1 and no less than 0.9, so the accuracy meets the requirements for further analysis.

Table 2. Accuracy of approximate model

Fig. 6 gives a scatter diagram of approximate model.

Fig. 6. Scatter diagram of approximate model

Under the constraints of performances of modal and stiffness, the minimum mass of carbody can be calculated by using the approximate model via the SAE(Self-Adaptive Evolution) algorithm in the optimization loop.

Fig. 7 shows the iterative process of several variables approaching the optimization results. The ordinate is the value range of certain thickness variable or location variable, whose physical quantity unit is usually mm. The abscissa represents the number of iterations.

Fig. 7. Iterative process of several variables

Table 3 shows the results of two rounds of optimization.

Table 3. Optimization results

Fig. 8 and Fig. 9 show the 1st modal shapes. Fig. 10 and Fig. 11 show the overall stiffness shapes.

Fig. 8. 1st order bending modal shapes

Fig. 9. 1st order torsion modal shapes

From Table 3, and Figs. 8–11, it can be drawn that the differences of performance data and the shapes between the SFE model and the 2nd round model are relatively small(slightly decreased less than 2.9%). While, it is very significant for carbody lightweighting, because 5% of carbody weight loss (about 15.7 kg) greatly outweighs the slight performances decline.

Fig. 10. Overall bending stiffness shapes

Fig. 11. Overall torsion stiffness shapes

5 Conclusions

(1) Carbody lightweighting can be realized by implicit engineering parameterized model in a considerable degree(15.7 kg) rather than by material substitution and expensive new manufacturing process, but the performances may change little.

(2) The automatic carbody lightweighting can be carried out with SFE implicit engineering parameterized model in the MDO loop integrated by optimizer and FE solvers.

(3) Implicit parameterized modeling makes performancedriven design and quick MDO possible, and it saves the development time and cuts down the costs.

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