Evaluating the strength condition of frame and pallet structures, and optimizing structure of support bracket of mobile weapons and equipment storage using finite element analysis

Hóa học và Kỹ thuật môi trường N. T. Hue, , N. V. Dong, “Evaluating the strength using finite element analysis.” 162 EVALUATING THE STRENGTH CONDITION OF FRAME AND PALLET STRUCTURES, AND OPTIMIZING STRUCTURE OF SUPPORT BRACKET OF MOBILE WEAPONS AND EQUIPMENT STORAGE USING FINITE ELEMENT ANALYSIS Nguyen Tien Hue 1* , Phan Hoang Cuong 2 , Dang Van Thuc 2 , Ho Ngoc Minh 1 , Do Dinh Trung 1 , Vu Dinh Thao 2 , Ong Xuan Thang 3 , Nguyen Van Dong 1 Abstract: In this paper, an evaluation on the strength condition of pallet and frame is presented, then a structure of support bracket of mobile storage for weapons and equipment using finite element analysis is optimized. The maximum equivalent stresses in frame, pallet, and support bracket structures must satisfy a condition that these values are always less than or equal to the allowable stress of materials. The result of the checking shows that the maximum equivalent stress appears at the support bracket, therefore, this structure is optimized. The minimum mass and maximum equivalent stress is selected for the objective functions of structural optimization. Finally, the manufacturing model is obtained and compared with the original model to the maximum equivalent stress and mass reduction. Keywords: Strength condition; Structural optimization; Frame; Pallet; Mobile storage; Supporting bracket; Finite element analysis; Minimum mass; Maximum equivalent stress. 1. INTRODUCTION To enhance the training and combat readiness of soldiers in river areas, mobile storage for weapons and equipment is designed and manufactured. This system is shown in Figure 3, which consists of a pallet, a frame, leather, wheels, support brackets, and support legs. The pallet and frame structures carry on the main functions of the system; hence, it is needed to check the strength condition to ensure their performances. As can be seen from Figure 3b, the frame structure is made of CT38 structural steel. This structure covers the entire boxes of ammunition and accessories before the impact of the environment such as storm, humidity, flood, and other factors. In more detail, when the system places on wind speed up to force 12 the frame will be oscillated and deformed, so that does not meet the given requirements and the leather cover can be torn up. Figure 3c shows the pallet structure, this is made of CT38 structural steel. Various features of the pallet that are a rigid frame to support the entire bag system, other components, accessories of the inner system; preserving and ensuring safety for the entire system and internal equipment during transportation and storage; making jigs, racks during the process of deploying and recovering the system. There are two significant reasons to illustrate why the support bracket shown in Figure 4 is chosen to optimize. The first reason lies in the fact is that since the support bracket plays a major role in the supporting frame of mobile weapons and equipment storage, where the force applies directly to it, thus it is necessary to check the strength condition at this component. The second reason results from the fact are that the support bracket is made from steel plate; hence it is easy to optimize and manufacture this part than other components of the system. To get a lightweight structure has been one of the most challenges in the structural engineering industry since it relates closely to the structural performance, reliability, and manufacturing cost. Several researchers have put their efforts to optimize and create a better structural component, i.e., the bracket as shown in [1–8]. Besides, topology optimization has been discussed by researchers in terms of pursuing a lightweight structure [6, 9, 10]. That is a very powerful method to reduce the Nghiên cứu khoa học công nghệ Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san Viện Hóa học - Vật liệu, 9 - 2020 163 weight of a component without losing its best performance. The result of those studies shows that the optimized structure meets the stiffness requirement, as well as improves vibration performance. One of the applications of topology optimization is that it has been used for improving spacecraft design for years. The study by Orme et al. [11] utilizes additive manufacturing and topology optimization to develop space flight hardware. Moreover, various other studies also state that this method is very useful to create lighter components in precision engineering [12], composite material [13], and civil engineering application [14, 15]. However, a study on the application of topology optimization on the supporting frame of mobile weapons and equipment storage seems to be lacking. 2. METHODS In general, the research methodology shows in the flowchart in Figure 1 and Figure 2. Figure 1 reveals a flowchart of the design and manufacturing process of the system. In this flowchart, all the parts should satisfy the strength condition before manufacturing the final products. Figure 2 shows a flowchart of the structural optimization of the support bracket. In this flowchart, the optimization process starts with an original model then is optimized by several constraints to get the final model that can be used to manufacture. Figure 1. Flowchart of the design and manufacturing process of the system. Hóa học và Kỹ thuật môi trường N. T. Hue, , N. V. Dong, “Evaluating the strength using finite element analysis.” 164 Figure 2. Flowchart of the structural optimization of the support bracket. 2.1. Checking the strength condition of the system Modeling of the pallet and frame of mobile storage for weapons and equipment is shown in Figure 3. Both the frame and pallet are manufactured from CT38 structural steel which has chemical compositions and mechanical properties shown in Table 1 and Table 2. (a) (b) (c) Figure 3. Modeling of the system: (a) Mobile storage for weapons and equipment; (b) Frame; c) Pallet. Table 1. Chemical composition of CT38 structural steel. C (%) Si (%) Mn (%) P (%) S (%) 0.14÷0.22 0.12÷0.30 0.40÷0.65 ≤ 0.04 ≤ 0.04 Nghiên cứu khoa học công nghệ Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san Viện Hóa học - Vật liệu, 9 - 2020 165 Table 2. Mechanical properties of CT38 structural steel. Density Young’s modulus Bulk modulus Yield strength Tensile ultimate strength Poisson’s ratio Minimum elongation g/cm 3 GPa GPa MPa MPa % 7.85 190÷210 140 240÷280 380÷420 0.27÷0.30 ≥ 21 The support bracket is made of SM415 alloy steel grade, as seen in Figure 4. Figure 4. Modeling of the support bracket. Chemical composition and mechanical properties of SM415 alloy structural steel are shown in Table 3 and Table 4. Table 3. Chemical composition of SM415 alloy structural steel. C (%) Si (%) Mn (%) P (%) S (%) Cr (%) Mo (%) 0.38÷0.43 0.15÷0.35 0.75÷1.00 ≤ 0.035 ≤ 0.035 0.80÷1.10 0.15÷0.25 Table 4. Mechanical properties of SM415 alloy structural steel. Density Young’s modulus Bulk modulus Yield strength Tensile ultimate strength Poisson’s ratio Minimum elongation g/cm 3 GPa GPa MPa MPa % 7.8 200÷215 140 415 655 0.27÷0.30 ≥ 16 The allowable stress is given by [16]: [ ] ultimate n    (1) where, ultimate is the tensile ultimate strength of the materials. 1 2 3n n .n .n (2) where n is a safety factor [16]; n1 is a coefficient that takes into account that can be determined the accuracy of load and stress, normally n1 selected in the range of 1.2 ÷ 1.5; n2 is a coefficient that considers the mechanical uniformity of the material, for structural steel, n2=1.5; n3 is a coefficient that takes into account special requirements for safety, for important parts and components, n3=1.2 ÷ 1.5. Since it can be exactly determined of load, n1=1.4; components of the pallet and frame Hóa học và Kỹ thuật môi trường N. T. Hue, , N. V. Dong, “Evaluating the strength using finite element analysis.” 166 are manufactured from CT38 structural steel and SM415 alloy structural steel, n2=1.5; the system plays an important role to cover and transport ammunition from the harsh condition of the environment, n3=1.3. Constituting these values into Eq. (2), n 2.73 . From Eq. (1), the allowable stresses of CT38 structural steel and SM415 alloy structural steel are 147 MPa and 240 MPa, respectively. a. Checking the strength condition of the frame In the hardest condition of the environment when the system is directly placed on the wind speed which is defined the Beaufort Scale up to force 12. In order to determine forces and moments acting on the system, it is necessary to simulate the model of the whole system by using Ansys Fluent to know the aerodynamic coefficients. The result of the mesh; drag, lift, and lateral forces; and moments of the simulation is shown in Figure 5. (a) (b) (c) Figure 5. a) Meshing the system; b) Normal forces acting on the frame; c) Normal moments acting on the frame. As can be seen from Figure 5a and Figure 5b, the result reveals that when the iterations are large enough then the forces and moments are converging. The values of forces on the x and y axes and moments on the y and z axes are approximately zero. The values of force on the z-axis and moment on the x-axis are negative, which means opposites in a positive direction. These results are the input to simulate the structure of the frame. b. Checking the strength condition of the pallet The system is designed to cover and transport 72 boxes of the ammunition of 120 PM 43 mortar. Each ammunition box weighs 49 kg, so that the total force of gravity of the ammunition is 72 1 . 72.49.9.81 34610 (N)i i F m g     (3) Nghiên cứu khoa học công nghệ Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san Viện Hóa học - Vật liệu, 9 - 2020 167 As mentioned in the previous section the forces and moments acting on the frame are transferred from the frame to the pallet; However, these values are too small in comparison with the force of gravity of the ammunition, therefore, these are neglected. The result of the simulation is shown in Figure 7. c. Checking the strength of the original support bracket A mesh discretization and refinement strategy are generated in the Ansys Workbench environment. Mesh refinement is applied at particular locations, i.e., the hole purposely to obtain more accurate results. These locations are very important as the place where the force is first applied (bolt hole and shaft). The mesh refinement is also made in the support bracket body to provide sufficient discretization for topology optimization purposes. From the mesh resolution setting, the model has the initial mass of this model is 4.16 kg. The mesh model of the original structure is shown in Figure 8a. The mesh size is chosen as 3 mm and the element number is 18600. In addition, the boundary conditions and load of 10063 N are applied to the hole for the static analysis as shown in Figure 8b. 2.2. Topology optimization of the support bracket Topology optimization is implemented to the original numerical model to reduce mass and maximum equivalent stress as two main objectives. The first one is the mass reduction at 60%, and the other is the maximum equivalent stress in the support bracket at 60 MPa. The procedure of this stage follows in Figure 2. Figure 9a and Figure 9b show the optimized model and final design model. The final design model is designed based on the result of the optimized model as well as the ability to manufacture the support bracket. 3. RESULTS AND DISCUSSIONS 3.1. Results Figure 6. The total deformation and equivalent stress of the frame. Figure 7. The total deformation and equivalent stress of the pallet. Hóa học và Kỹ thuật môi trường N. T. Hue, , N. V. Dong, “Evaluating the strength using finite element analysis.” 168 (a) (b) (c) Figure 8. a) Mesh model; b) Boundary and load conditions; c) Stress results of the original model. (a) (b) (c) Figure 9. a) Optimized model; b) Final design model; c) Stress results of the final design model. 3.2. Discussions It is clear from Figure 5 and Figure 6 that the maximum equivalent stresses in frame and pallet structures are 46.16 MPa and 39.87 MPa, respectively. These values are much less than the allowable stress which is 147 MPa; therefore, these structures are met the strength condition. The final design model and the original model of the support bracket are compared for the maximum equivalent stress and mass reduction. Figure 8c illustrates the maximum equivalent stress distributes in the vicinity of the hole of the support bracket while in other areas the values approximately zero. On the other hand, the result in Figure 9c shows the equivalent stress is nearly uniformly distributed in all the working areas of the support bracket. In this case, the maximum equivalent stress concentrates on the corner of both sides of the bar. As can be seen from Table 5, under the applied loads, the maximum equivalent stresses of the final design and original model are 61 MPa (Figure 8c) and 55.51 MPa (Figure 9c), respectively. The maximum equivalent stress is increased by a rate of 9.9%; thus, this value is acceptable. Furthermore, the mass of the original model and final design model are 4.12 kg and 2.47 kg. It is true that the mass of the final design model reduces roughly 40% in comparison with the original model. Table 5. Comparison of the original and final design model of the support bracket. Name of objectives Original model Final design model Absolute deviation Maximum equivalent stress (MPa) 55.51 61 9.9% Mass (kg) 4.12 2.47 40% Nghiên cứu khoa học công nghệ Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san Viện Hóa học - Vật liệu, 9 - 2020 169 4. CONCLUSIONS The main conclusions from the research results of the current work can be drawn as follows. By using finite element analysis in Workbench Ansys, the models for simulating the frame, pallet, and support bracket structures to check the strength condition are established in this paper. The results of the simulation show that the maximum equivalent stresses of these structures are much smaller than the allowable stress. 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Thin Walled Struct. 2019, 139, 372–388. [15]. Jewett, J.L.; Carstensen, J.V. “Topology-optimized design, construction and experimental evaluation of concrete beams”. Autom. Constr. 2019, 102, 59–67. [16]. Nguyễn Văn Yến. “Giáo trình chi tiết máy”. Nhà xuất bản Giao thông Vận tải. TÓM TẮT ĐÁNH GIÁ BỀN KẾT CẤU KHUNG, PALLET VÀ TỐI ƯU HÓA KẾT CẤU GIÁ ĐỠ CỦA HỆ THỐNG KHO BẢO QUẢN VŨ KHÍ DI ĐỘNG BẰNG PHÂN TÍCH PHẦN TỬ HỮU HẠN Bài báo trình bày bài toán kiểm nghiệm bền khung, pallet và tối ưu hóa kết cấu chi tiết giá đỡ của hệ thống kho bảo quản vũ khí - khí tài di động bằng phương pháp phân tích phần tử hữu hạn. Giá trị ứng suất tương đương lớn nhất trong hệ thống cần phải thỏa mãn điều kiện bền đó là giá trị này luôn nhỏ hơn hoặc bằng ứng suất cho phép của vật liệu được chế tạo. Kết quả mô phỏng chỉ ra rằng ứng suất tương đương lớn nhất trong kết cấu xuất hiện tại vị trí chi tiết giá đỡ, do đó, chi tiết này được lựa chọn để tối ưu hóa kết cấu. Tối thiểu hóa khối lượng và ứng suất tương đương lớn nhất được lựa chọn làm các hàm mục tiêu cho tối ưu hóa kết cấu. Kết quả phân tích là mô hình, kết cấu hợp lý dùng để chế tạo, thử nghiệm. Kết cấu này được so sánh với mô hình gốc ban đầu theo các chỉ tiêu là ứng suất tương đương lớn nhất và giảm khối lượng minh chứng cho việc tính toán tối ưu hóa thiết kế. Từ khóa: Đánh giá điều kiện bền kết cấu; Tối ưu hóa thiết kế; Khung; Pallet; Kho bảo quản di động; Giá đỡ; Phân tích phần tử hữu hạn; Khối lượng nhỏ nhất; Ứng suất tương đương lớn nhất. Received 12 th July 2020 Revised 10 th August 2020 Published 24 th August 2020 Author affiliations: 1 Institute of Chemical - Material, Academy of Military Science and Technology; 2 Le Quy Don Technical University; 3 Air defense - Air force Academy. *Corresponding author: huenguyentien@gmail.com.