Tailgate Hinge Stiffness Design using Topology Optimization

Transcription

1 Tailgate Hinge Stiffness Design using Topology Optimization Yunsik Yang Department of Mechanical Engineering, Graduate School Kongju National University (KNU) Euy Sik Jeon Department of Mechanical Engineering, Graduate School Kongju National University (KNU) Abstract This study presents an implementation of topology optimization design of a tailgate hinge optimized for use as a pickup truck cargo lift. As the number of pickup truck users has increased, convenience in loading and unloading has become an important concern. When a tailgate cargo lift is applied for this purpose, stiffness design of the hinge is of vital importance. Conventional tailgate hinges lack the stiffness to carry a tailgate s self-weight and cargo. To develop a suitable stiffness design, we first performed strength testing on a conventional hinge. Based on the strength test results, we then performed structural analysis to improve weak parts and derived a design direction from the test and analysis results to enhance the strength of the hinge. Finally, we performed topology optimization on the new design, thereby setting and determining the hinge shape having the minimum necessary volume. Based on the final results, we designed a tailgate hinge applicable to lift devices for pickup trucks and performed structural analysis, thus validating the design. Keywords: Tailgate, Hinge, Bending point, Stiffness design, Topology optimization INTRODUCTION Driven by economic recovery, low oil pricing, and their versatility, pickup truck sales are increasing in the USA. A pickup truck provides its user with the comfort of a sedan for commuting and the convenience of a truck for leisure activities and cargo transport using its deck. In South Korea, pickup trucks are limited to models produced by Company S, but their sales keep increasing and their market share is expected to grow. With the number of pickup truck users growing constantly, the issue of convenience when using pickup decks is attracting increased attention. Despite customer needs, however, R & D activities related to easy-to-use pickup truck structures in South Korea lag behind their international counterparts and currently their applications are limited to deck opening and closing. These deck opening and closing structures aim to prevent theft or displacement, but not to enhance user convenience. One of the devices for improving user convenience is a cargo lift mounted on the tailgate for easy loading and unloading of heavy items. The tailgate is a gate attached to the rear end of a pickup truck s deck, and its automatic lifting and lowering is being researched currently. Its two major parts are the gate and the hinge. The hinge consists of a bracket plate, bracket body, torsion springs, pins, and bearings. Since the tailgate loading acts directly on the hinge, it must have high strength and durability. Research on automotive part optimization should be preceded by the following preliminary processes: identifying structural characteristics such as tensile strength and yield strength through strength tests and checking the test results against finite-element analysis (FEA) results to validate the parts [1, 2]. Bendsoe and Kikuchi [3] performed a study on topology optimization of continuous structures with the purpose of improving the stiffness of the hinge plate. They introduced the homogenization method to derive a correlation between density and modulus of elasticity using a microstructure with rectangular holes in a permanently recurring iterative scheme. Then they computed the density distribution that maximizes the stiffness of a structure under the given boundary conditions and loading. Extending this method, Bendsoe, Diaz, and Kikuchi [4, 5] mathematized the method of simultaneous optimization under various loading and boundary conditions. Since then, following the introduction of the density method using the modulus of rigidity of isotropic mass, many research approaches have been adopted depending on analysis objects, e.g., selective applications to specified elements [6 11]. In this study, the design direction was set by means of numerical analysis to enhance hinge stiffness and topology optimization was performed, thereby limiting the optimization domain to the additional design elements. First, we performed strength testing to determine the baseline strength of a conventional hinge. Structural analysis was then performed to improve the weak parts identified in the strength test, and a new design direction oriented towards enhancing the strength of the hinge was set on the basis of the test and analysis results. The design direction was subjected to topology optimization so that the hinge shape could be optimized while maintaining a minimum necessary volume. Finally, based on the optimization results, we designed a tailgate hinge applicable to pickup truck cargo lift devices and validated the design by performing structural analysis. Figure 1: Pick-up truck tailgate 9776

2 (a) Hinge model (b) Hinge Figure 2: Hinge structure STRENGTH TEST Tailgate hinge strength testing As shown in Fig. 1, a pickup truck tailgate prevents cargo from shifting while driving and exiting the rear end of the deck while opening and closing. The hinges placed at the two side ends of the tailgate should have sufficient stiffness to support the weight of the tailgate and cargo. When designing a tailgate cargo lift to enhance user convenience, the conventional tailgate hinge shape should be redesigned so as to provide elevated stiffness. Fig. 2(a) is a schematic representation of a conventional tailgate hinge, and (b) shows a specimen fabricated for the hinge strength test. Strength testing and result analysis The tailgate hinge under investigation was tested using a strength gauge at a speed of 3 mm/min and compressive loading of 120 kg, taking into account the tailgate s self-weight and cargo weight exerted on the hinges. Fig. 3(a) shows the experimental setup before applying compressive loading on the hinge plate. Fig. 3(b) shows the postloading deformation incurred by the hinge plate. The strength test results revealed that deformation occurred at the bending point on the hinge plate ahead of the deformation of the hinge body and pins. From the standpoint of friction resistance of pins and bearings connected to springs as well, the bending part of the hinge plate was identified experimentally as the weakest part. The strength test results are presented in Fig. 4. The maximum loading applicable to the hinge plate was found to be N, resulting in the maximum displacement of mm. Given that hinges for a tailgate cargo lift should have sufficient stiffness to bear heavy loads and ensure safety during the lifting and lowering of cargo, we set the target strength at 130% of that for conventional hinges. Figure 4: Load-distance curve of test result STRUCTURAL ANALYSIS AND SETTING THE DESIGN DIRECTION Structural analysis and results The strength test revealed the hinge bending part to be the weakest part of the hinge plate. We performed a static loading analysis using the finite-element method (FEM) to explore measures to improve the stiffness of weak parts. The hinge plate, which was identified to be the weakest part among all hinge parts, thus requiring size optimization, was simulated in a static FEA. The static analysis conditions were configured taking into account the direction and point of application of external force transferred to the hinge body under full constraint of the bolt joint on the hinge plate. A maximum loading of 2.4 kn, which corresponds to the sum of tailgate self-weight and cargo load, was applied to the hinge as a bending moment. Table 1 outlines the physical properties of the hinge material (STD 4) that were reflected in the structural analysis. Fig. 5 depicts the static FEA results of the conventional hinge plate. The structural analysis of the conventional hinge plate revealed that its maximum stress (799 MPa) lies outside the tolerable range and that the average stress distribution (500 MPa) was concentrated on the bending part. That stress is concentrated on the bending part of the hinge plate is a clear indication of the structural weakness of conventional hinges, which confirms the need to correct their shape in order to improve their stiffness. Table 1: Material properties Mechanical properties Unit STD4 SM45C Density kg/m3 7,872 7,850 Poisson s ratio Young s modulus GPa Tensile yield strength MPa Tensile ultimate strength MPa (a) Preparation state (b) Result Figure 3: Strength testing and result 9777

3 Figure 5: Analysis result of the hinge plate Dimension optimization design Based on structural analysis results, we present a mathematical model to enhance the stiffness of the hinge plate in order to increase its bending moment resistance and determined its crosssectional shape and dimension according to the design direction set previously. A numerical analysis of the hinge plate was performed without taking into account the influence of other hinge parts and assuming that the self-weight portion of the entire loading is applied in the Z direction. As shown in Fig. 6, the hinge plate s cross-sectional variables to be set were thickness (t), height (h), and width (d), and the properties imparted by the cross-sectional shape were validated numerically. Under the assumption that the stress occurring under a force exerted externally on the hinge plate lies within the elastic range, the neutral axis passes the centroid of the cross section. Since stress is inversely proportional to the area moment of inertia, the shape design of the hinge plate cross section should implement an increase in the area moment of inertia that resists the y-axis bending moment. y I c y 1 A 0 h x 0 h 2 yda da As expressed by the equation above, the magnitude of the area moment of inertia I y of the hinge plate cross section is influenced by y c, the height of the plane parallel to the y-axis, and influenced more strongly by h and t than by d. Fig. 7 presents the numerical validation of the centroid position, which influences the plane height, according to changes in the design variables. Regarding the centroid position, the height of the center of gravity was found to increase in proportion to t and h, and the thinner the t, the more markedly the center of gravity is influenced by the change in h. Fig. 8 shows the cross-sectional changes with respect to changes in t and h. An increase in t increased the sensitivity to changes in h. Fig. 9 demonstrates that the change in the area moment of inertia is associated more closely with changes in t than in h, whereby the increase in t makes the moment more sensitive to changes in h. Fig. 10 confirms the changes in the area moment of inertia depending on t and h within design constraints. The area moment of inertia increases in proportion to the value of t, and its sensitivity to change increases as the value of t increases. Since the bending moment resistance increases as the area moment of inertia increases, stress induced by force exerted externally on the cross section decreases. Given that the hinge plate is produced in uniform thickness, an increase in t leads to an increase in the cross-sectional area, resulting in the linear increase of the total volume. Adding 1 mm to a 4-mm-thick conventional hinge plate results in an increase of about 20% in the area moment of inertia, and adding 1 mm of height results in an increase of about 30% in the area moment of inertia. Altering the thickness is an easy way to improve stiffness without changing the hinge s external shape, but doing so greatly affects volume. In contrast, altering the height of the hinge can minimize the change in volume and enhance stiffness. In order to increase the area moment of inertia, we set thickness and height as the design variables, limiting the ranges of thickness and height at 3 6 mm and mm, respectively. The thickness- and height-dependent maximum possible changes in the area moment of inertia were estimated at about 40% and 130%, respectively. The hinge plate design direction was set to derive the design variables capable of maximizing the area moment of inertia within the specified ranges of design variables while minimizing the volume change. t Sectional view h y c t hinge plate d hinge body z x pin y Figure 6: Design variables of the hinge plate Figure 7: Distances to centroid 9778

4 In order to derive meaningful structural shapes from topology optimization results, the design space should be segmented into a sufficient number of elements. Additionally, topology optimization dealing with a large number of design variables requires efficient rules for improvement. One of the design constraints commonly considered is the volume of the entire structure. We implemented a minimum-volume design, i.e., with volume as the design constraint, using homogeneous material. Figure 8: Sectional area Topology optimization and results We employed topology optimization to determine a heightdependent shape for the purpose of implementing a minimum-volume design within design constraints. We simultaneously conducted topology optimization of width to control the stress distribution of the bending part identified in the structural analysis. Minimize =static stress of the added support subject to Volume fraction 0.25 Moment of inertia [mm 4 ] Figure 9: Moment of inertia The objective function aimed to minimize the stress occurring in the design space by changing the shape of the hinge plate and to minimize the volume of the entire hinge plate. We applied the optimization process in an iterative scheme until the volume of the modified hinge part fell to 25% of the analysis domain. The convergence process for the topology of the support added to the hinge plate design during optimization is illustrated in Fig. 11(a). Fig. 11(b) depicts the process of the hinge plate s stress minimization. Fig. 12 presents the results of the hinge plate derived through topology optimization. We conducted a static analysis of the support s shape and checked its stress distribution against the baseline model prior to topology optimization. The stress distributions of the two models are presented in Fig. 13. As shown in Fig. 14, the volume of the topology optimization model showed an 18% increase with respect to the conventional hinge plate model. When only thickness was altered, the volume increased by 25%, and the final model showed a volume increase of 23%. As shown in Fig. 15, reduction of the maximum stress distribution achieved was 40% for the topology optimization model, 30% when only the thickness was altered, and 34% in the final model h [mm] 3 t [mm] Figure 10: Moment of inertia Iteration 1 Iteration 4 TOPOLOGY OPTIMIZATION Attempts to change topology are being made in design space because designs revolving around dimensions and external shapes cannot achieve satisfactory effects in the face of the lightweight trend of structures. Iteration 7 Iteration 10 (a) Topology change of the hinge support 9779

5 (b) Convergence history of the objective function Fig. 11 Topology analysis Figure 14: Results for volume of the hinge plate Figure 12: The topology optimization result of the hinge plate Figure 15: Results for Maximum stress of hinge plate (a) Analysis results of the hinge plate support CONCLUSION The following summarizes the process of topology optimization we performed to design tailgate hinges with improved stiffness. 1) A strength test of the conventional hinge confirmed the need to enhance the stiffness of the hinge plate to make it feasible for use in tailgate cargo lifting. 2) Structural strength analysis performed on the basis of strength testing to reinforce weak parts also identified the bending part of the hinge plate as the weakest part of the hinge plate, consistent with strength test results. 3) A new design direction was set after confirming the sensitivity of the area moment of inertia to changes in cross-sectional thickness and height by performing a numerical analysis. 4) Topology optimization was performed to determine the shape that implements the support, which is a part added to the hinge plate s design, with minimum necessary volume. As a result, we achieved a designed shape that incurs minimal stress without altering its thickness. (b) Post-processed hinge plate Figure 13: Analysis results of the hinge plate ACKNOWLEDGMENT This work was supported by the Human Resource Training Program for Regional Innovation and Creativity through the Ministry of Education and National Research Foundation of 9780

6 Korea (NRF-2015H1C1A ) Also, this research was financially supported by the Ministry of Trade, Industry & Energy(MOTIE) and Korea Institute for Advancement of Technology(KIAT) through the Leading Industries of Economic Cooperation Region. REFERENCES [1] Nguyen Duc Toan, Choi Seogou, Park Junyoung, Suh Yeongsung, and Kim Youngsuk., "Finite Element Method Simulations to Improve Press Formability of Door Hinge", Vol. 18, 2008, pp [2] T. Zou, S. Mahadevan, Z. Mourelatos, P. Meernik, "Reliability analysis of automotive body-door subsystem", Reliability Engineering and System Safety, 78, 2002, pp [3] Bendsoe, M. P. and Kikuchi, N., Generating Optimal Topologies in Structural Design Using a Homogenization Method, Computer Methodes in Applied Mechanics and Engineering, 71, 1988, pp. 187~224 [4] Bendsoe, M. P. Diaz, A. R. and Kikuchi, N., Topology and Generalized Layout Optimization of Elastic Structures, in Topology Design of Structures(eds. M. P. Bendsoe and C. A. Mota Soares) Kluwer Academic publishers, Amsterdam, 1993, pp. 159~205 [5] Katsuyuki Suzuki, Noboru Kikuchi., "A homogenization method for shape and topology optimization", Computer Methods in Applied Mechanics and Engineering, Vol. 93, Issue 3, 1991, pp [6] Rajan, S., "Sizing, Shape, and Topology Design Optimization of Trusses Using Genetic Algorithm", Journal of Structural Engineering, Vol. 121, Issue 10, 1995 [7] Kalyanmoy Deb, Surendra Gulati, "Design of trussstructures for minimum weight using genetic algorithms", Finite Elements in Analysis and Design, Vol. 37, 2001, pp [8] P. Hajela, E. Lee., "Genetic Algorithms in Truss Topological Optimization", Int. J. Solids Structures, Vol. 32, 22, 1995, pp [9] Yang, R. J, Chahande, A. I., "Automotive Applications of Topology Optimization", Structural Optimization, Vol. 9, 1995, pp. 245~249 [10] Fukushima, J., Suzuki K., Kikuchi, N., "Shape and Topology Optimization of a Car Body with Multiple Loading Conditions", SAE Paper, No , 1992 [11] Fredricson, H., "Topology Optimization of Frame Structures - Joint Penalty and Material Selection", Structural and Multidisciplinary Optimization, Vol. 30, No.3, 2005, pp. 193~200 [12] Jang, G. W., Yoon, M. S., Park, J. H., "Lightweight Flatbed Trailer Design by Using Topology and Thickness Optimization", Structural and Multidisciplinary Optimization, Vol. 41, No. 2, pp.295~