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Integrate Topology/Shape/Size Optimization into Upfront Automotive Component Design

Chin-Jung Chen* and Calvin Young.† Visteon Corporation, Dearborn, MI, 48120

Design optimization has gained significant reputation in the automotive industry because of its capabilities on helping cost cutting, weight reduction, and performance improvements for various products. It has become a valuable tool in the product development processes, and many CAE codes are developing or integrating the design optimization capabilities into their solvers to meet users' demand. Topology, shape and size optimization has been widely used to improve the product performance from the structural perspective. Topology optimization explores the initial topology of various product designs with constrained packaging spaces and design requirements. The technique can be easily applied to shell structure with shell design domain or 3D solid structures with 3D solid design domains, even though it takes extra effort to interpret the final topology optimization results for manufacturability. Nevertheless, it is still a considerable challenge to explore shell like structures with 3D solid design domains by using topology optimization tools. Manufacturing consideration such as injection molding is another challenge in developing shell like structures from 3D packaging spaces using optimization; currently there are no tools available address these types of problems directly. Manufacturing constraints like extrusion has recently become available in some commercial optimization codes. It provides some help on addressing the manufacturing issue but it did not provide any solution to the posed problem⎯develop shell like structures from 3D solid design domains. This paper proposes a two-stage topology optimization approach to develop optimal shell like structures from 3D solid design domains. The final topological design from the two-stage topology optimization analysis was then revised by designers to include design features. After that shape and size optimization was utilized to further improve the design. An injection molded plastic carbon canister bracket has been used to demonstrate the proposed approach. The main function of the carbon canister bracket is to carry the carbon canister, fuel tank isolation valve, canister vent valve, and dust box; the bracket must also meet vehicle durability requirements for dynamic load without loss of any component functions or developing any cracks. From a given 3D package space, an optimal bracket design was found based on the proposed topology optimization approach. A production ready design was created based on the topology optimization results and design features from Knowledge Based Engineering (KBE) library. Shape and size optimization was utilized to further improve the bracket design. The final design showed much better performance than the original design. The collaboration among CAD designers, product engineers and CAE engineers played a crucial role to the success of the proposed design approach.

Nomenclature f = natural frequency w = weighting factor ρ = material density V = volume a = acceleration W = weight

* Technical Fellow, Design and Manufacturing Simulation, 17000 Rotunda Dr., Suite C191-29, Dearborn, MI 48120. † CAE Product Engineer, Design and Manufacturing Simulation.

10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference30 August - 1 September 2004, Albany, New York

AIAA 2004-4594

Copyright © 2004 by Chin-Jung Chen. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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I. Introduction ANY automotive applications have demonstrated the benefits of using design optimization tools to

accomplish cost-saving target and improve product performance [1-5]. Today design optimization analyses have been extensively utilized in product development processes, and they have become one of the must-be options in Computer Aided Engineering (CAE) software. Topology optimization [6,7] has been widely used to explore the initial topology of different product designs with constrained packaging space. The technique can be easily applied to shell structure with shell design domain. It is also commonly used to explore 3D solid structures with 3D solid design domains, even though it takes extra effort to interpret the final topology optimization results for their manufacturability. Nevertheless, it is still a considerable challenge to explore shell structure designs with 3D solid design package spaces by using topology optimization tools. Because of the nature of the topology optimization methodology, it tends to gather massive material in the critical areas during the design processes. It is not easy to obtain a shell like structure from a 3D solid design domain. Manufacturing consideration for shell like structure such as injection molding is another challenge to develop shell like structures from 3D package spaces. Recently, some commercial optimization codes [8,9] have developed new capabilities to include the manufacturing constraints like extrusion while using topology optimization to explore different design options. This new feature may help address the manufacturing issue for applications with the same design intent and design domain. However, it still does not directly help resolve the issue that we just posed–developing shell like structures from 3D solid domains.

This paper proposes a two-stage topology optimization approach to develop shell structures from 3D solid design domains. The first stage is to find the initial topology of the shell structure and the second stage is to find the optimal rib deployment on the shell structure. The final topological design then was revised by designer to include the design features from KBE library. After that, the shape and size optimization was utilized to further refine and improve the design for meeting the design requirements. An injection molded plastic carbon canister bracket is used to demonstrate the proposed approach. The bracket is used to support the canister that is part of the vehicle fuel and storage system; the canister system plays an important role for vehicle to meet federal emission standard. Its main function is to absorb fuel vapor from fuel tank and prevent it from leaking into the atmosphere. The bracket carries several components and needs to survive the vigorous dynamic loading conditions. It was found that the initial design of the carbon canister bracket, from the two-stage topology optimization results, might be too stiff. The sequential shape and size optimization provides an avenue to relax the stiffness of the carbon canister bracket and meet the vehicle durability requirements.

II. Topology Optimization In this paper, a shell structure of an automotive component–plastic carbon canister bracket–was explored through

the use of the proposed topology optimization approach. The design domain is a 3D solid package space. The carbon canister bracket is usually made of plastic material and has thickness around 3.0 mm. The purpose of the carbon canister bracket is to support the carbon canister, fuel tank isolation valve, canister vent valve, and dust box to meet the vehicle durability requirements for dynamic load without loss of component functions. The bracket itself should pass the durability test without any cracks. There are several concerns while designing the canister bracket. First, the bracket should be stiff enough to support all the previous cited components without any cracks. Second, the bracket should not be too stiff because it could cause the carbon bed in the canister to break down due to high acceleration loads on the carbon bed.

Brackets are usually designed to meet durability requirements of dynamic loading by stiffening the structure (increasing its natural frequencies). However, it may not be the best strategy to design the canister bracket. Figure 1 shows a typical carbon canister assembly. The bracket for this assembly is made of a large

M

T bracket

Canister bracket

Figure 1. A carbon canister system

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plastic bracket and a small steel T-bracket, with foam pads on the underside of the canister to decrease vehicle vibration impact. There are six attachment locations for this canister bracket. The first and second natural frequencies of the carbon canister system are 19.8 Hz, and 23.0 Hz, respectively, as shown in Figure 2.

A new design for the carbon canister system was proposed, and the new design has only four attachment locations. The package space was identified by the designer. A design domain was created based on the design packaging space, as shown in Fig. 3(a). The design domain reserves several pocket spaces for various components. 3D solid elements are created in the design domain. Figure 3(b) shows the finite element (FE) model of the carbon canister system that includes various components in the model.

A two-stage topology optimization approach is proposed in this paper to develop a shell like structure from a 3D solid design domain. The first stage is to find the initial topology of the shell structure and the second stage is to

find the optimal rib deployment on the shell structure. The procedures are given as followings: 1. Identify the design package space and attachment locations for the product. 2. Deploy solid element in the design package space, and include the non-design components in the FE model. 3. Formulate the optimization problem based on selective design requirements. 4. Run the first stage topology optimization analysis to find optimal geometry of the structure. 5. Create the initial shell structure based on the first stage topology optimization results and manufacturing

constraints. 6. Deploy solid and shell elements on the initial shell structure at the potential rib locations. 7. Formulate the optimization problem based on the design requirements.

Figure 2. (a) First frequency 19.8 Hz (b) Second frequency 23.0 Hz.

Figure 3. (a) Design package space (b) FE model of the canister system

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8. Run the second stage topology optimization analysis to find optimal rib deployment for the shell structure. 9. Create the final shell structure based on the second stage topology optimization results and output surface

data. Figure 4 shows the flowchart of the proposed two-stage topology optimization approach. The proposed two-stage topology optimization was applied to the canister bracket design. The first stage

topology optimization is to maximize the first natural frequency of the carbon canister system subject to material fraction constraint, and the extrusion constraint is incorporated in the design processes. The optimization formulation is given in Equations (1) and (2). GENESIS [8] was used to perform the topology optimization analysis.

Maximize: ∑=

1

1iii fw (1)

Subject to: 25.0≤∫ dVρ (2)

Develop solid meshin package space

Perform first topology optimization

Create bracket based on the 1st

optimization results

Develop FE modelFor 2nd topology

optimization

Deploy ribs based on the 2nd

optimization results

Perform second topology optimization

Create finalbracket design

Output surfaceData to CAD

CAD provides surface data

based on package space

Develop solid meshin package space

Develop solid meshin package space

Perform first topology optimization

Perform first topology optimization

Create bracket based on the 1st

optimization results

Create bracket based on the 1st

optimization results

Develop FE modelFor 2nd topology

optimization

Develop FE modelFor 2nd topology

optimization

Deploy ribs based on the 2nd

optimization results

Deploy ribs based on the 2nd

optimization results

Perform second topology optimization

Perform second topology optimization

Create finalbracket design

Create finalbracket design

Output surfaceData to CAD

Output surfaceData to CAD

CAD provides surface data

based on package space

CAD provides surface data

based on package space

Figure 4. A two-stage topology optimization approach.

Figure 5. First topology optimization results Figure 6. First bracket design

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Figure 5 shows the first topology optimization results, and figure 6 shows the proposed canister bracket based on the first topology optimization results. The first and second natural frequencies of the first bracket design are 25.2 Hz and 26.8 Hz, respectively. To further improve the stiffness of the bracket, the second-stage topology optimization was executed. The design domains are defined at the pocket spaces underneath the bracket and some bottom surfaces of the bracket. Solid elements are filled in the pocket spaces and shell like rib structure was added to the bottom surfaces of the bracket, as shown in Figure 7. Again the design objective is to maximize the first

natural frequency of the bracket with material constraint. The optimal design is shown in Fig. 8, and a proposed design based on the second stage topology optimization results is shown in Fig. 9. The proposed canister bracket

shifts the first frequency of the carbon canister assembly from 19 Hz to 38 Hz ⎯ offering one hundred percent improvement in the stiffness over the previous design; it also eliminates the need for foam pads. The proposed method shows a promising solution to design shell like structures with solid design domains.

Four attachment locationsFour attachment locations

Rib Elements

Solid elements

Rib Elements

Solid elements

Need adding ribs

Material on the bracket can be removed

Need adding ribs

Material on the bracket can be removed

Figure 7. Design model for second topologyoptimization results

Figure 8. Second stage topology optimization results.

Figure 9. Proposed design from second topology optimization results

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III. Shape and Size Optimization The surface data of the proposed design (Fig. 9) was created and given to CAD designer. The designer utilized

the geometry features in the KBE library and the surface data from topology optimization results to create the first production ready carbon canister bracket, as shown in Fig. 10. The first and second natural frequencies of the production ready bracket are 32.0 Hz and 46.88 Hz, respectively. The first natural frequency has dropped 6.6 Hz compared the proposed design in Fig. 9. This is understandable because a production ready design usually has lower stiffness in order to incorporate the design features. A further vibration analysis showed the maximum acceleration response of the canister was beyond the design limit. Therefore the shape and size optimization was used to further improve the bracket design.

When using design optimization to explore the product design, it may not be practical or possible to include all design requirements in the initial topology optimization analysis, particularly, if durability and dynamic responses are part of the design requirements. It would be a good alternative to use shape and size optimization to further improve the product design after obtaining the optimal topological design. In the previous section, the stiffness of the bracket is the main design objective for topology optimization. Here the dynamic responses of the canister bracket will be addressed through shape and size optimization. Shape and size optimization is used to improve the design of the canister bracket so the dynamic stress of the canister bracket and the acceleration response of the canister could meet the design requirements. A prescribed dynamic loading was

Figure 10. Production ready design based on topology optimization results and KBE features.

Figure 11. Shape and size design variables.

Shape 1 Shape 2

Shape 4

Shape 3

Size 1

Size 2

Size 6

Size 3Size 5

Size 4

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applied to the canister assembly. The initial results indicate the maximum dynamic stress is lower than 50% of the material yield stress but the maximum acceleration of the canister is 23% over the design limit. To reduce the acceleration of the canister, four shape design variables and five size design variables were defined, as shown in Fig. 11. HyperMorph [10] was used to morph the geometry of the canister bracket and define the shape design variables. The design objective was to minimize the weight of the canister bracket. The upper limit of the acceleration response on the canister was defined as constraint. The enforced vibration was applied at the attachment points of the canister bracket with a sinusoidal frequency sweep from 20Hz to 60Hz. Since the maximum dynamic stress is not an issue for the initial design, the dynamic stress was not included in the optimization problem. GENESIS [8] was again used for the optimization analysis.

Minimize: W (3)

Subject to: 0aa ≤ for f=20 Hz ∼ 60 Hz (4)

Figure 14. Design Comparison.

Figure 12. Optimal shape design. Figure 13. Final canister bracket design.

Original Design

Optimal Topology Design

Optimal Shape and Size Design

Shape changes

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Equations (3) and (4) show the shape and size optimization problem formulation, and a0 in Eq. (4) is the acceleration upper limit. After six design iterations, all four shape design variables were increased, and the fourth design variable reached its maximum value. The shape changes are given in Figure 12. Only first size design variable was increased to 5.0 mm; the rest of them reduced to 2.0 mm that is the lower bound of the size design variables. It indicates lower stiffness is preferred at the areas related to size design variables 2 to 4. The weight of the canister bracket remains the same, the acceleration response of the canister meets the design requirements, and the maximum dynamic stress response was also reduced as same time. Based on the optimization results, a final design was created, as shown in the Fig. 13. It meets all the design requirements. Figure 14 shows different canister bracket designs. The final design not only has less attachment points but also has better dynamic performance.

IV. Conclusions An automotive component was used to demonstrate the integration of upfront design optimization. A two-stage

topology optimization approach was proposed and applied to an injection molded plastic canister bracket to demonstrate the feasibility of developing shell like structures from 3D solid design domains. The optimal bracket design from the two-stage topology optimization shows a 100% improvement on the first natural frequency over the previous bracket design. Further incorporation of the KBE features in the bracket design has degraded the bracket stiffness but the production ready design still provides a 62% improvement over the previous design. Sequential shape and size optimization further refines the bracket design. The final bracket design meet all the design requirements. It may not be possible or practical to include the dynamic responses of the structure like the dynamic stresses and acceleration in the topology optimization analyses; however, the dynamic responses of the canister bracket can be further improved by using shape and size optimization. The final design not only shows its robustness over the original design but also provides a better NVH performance for the canister assembly. It again demonstrates the potential benefits of integrating design optimization upfront in product design processes. The proposed two-stage topology optimization method shows a promising solution to design shell like structures with solid design domains. The design optimization applications presents in this paper hope to provide some inspiration on future innovative product designs.

Acknowledgments This paper is developed out of a CAE effort for a production project-⎯"Canister Bracket Design Process". The

authors would like to thank their colleagues Jhun Lin and Christina Le who are the product engineers for their support on the project and the designer Mark Cobb for his support on developing the new canister CAD design.

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