# Topology optimization model of multi gear rocker box in shearer cutting section

Structural optimization is the application of optimization algorithm in mechanical design. According to different optimization variables and levels, it can be roughly divided into size optimization, shape optimization and topology optimization. Among them, the size optimization takes the structural cross-section size and shell thickness as the optimization variables; the shape optimization seeks the optimal rib distribution for the sheet stamping parts, and the material is not deleted in the optimization process; the topology optimization takes the material distribution in the space as the optimization variables, which has the maximum design freedom.

Variable density method is one of the most promising topology optimization algorithms in engineering. Its basic idea is to introduce a hypothetical variable density material. The material density of each unit is regarded as the design variable, which changes continuously from 0 to 1. 0 and 1 represent the absence and existence of element materials respectively, and the median value represents the hypothetical material density, so the structural topology optimization problem is transformed into the optimal distribution problem of materials. In the optimization, a penalty factor is introduced into the middle density of the cell to suppress the cell with relative density between 0 and 1, and the cell density is aggregated to the two endpoints of 0 and 1 through iteration. Most practical problems can get clear topological results by using this method. In this study, the topology optimization model of rocker box is established and solved in the Optistruct module of HyperMesh

Establish the finite element model

In this step, three-dimensional model import, geometry cleaning and finite element mesh generation of rocker box are completed. Due to the weak 3D modeling ability of HyperMesh, it usually imports the built 3D model from the outside. Before the model is imported, it should be simplified properly, and the small structures such as chamfer, groove and screw hole should be deleted. These structures have no effect on the deformation of the main structure, but increase the number of finite element mesh and reduce the efficiency of topology optimization. Generally, there are a few geometric defects in the imported 3D model, which can be meshed after manual repair. In order to simplify the modeling process and grasp the focus of the analysis task, tetrahedral element is used to divide the finite element mesh. The grid size is 65 mm, which has been verified by grid independence in previous research.

Defining optimization problems

The essence of defining optimization problem is to define design variables, constraints and objective functions. To define the design variables is to specify the areas on the rocker box that you want to optimize and improve. These areas are called the design domain. The remaining areas, such as bearing holes, mounting surfaces and other areas that bear assembly functions, do not participate in the optimization process, which is called non design areas. Taking the total mass and static stress as constraint conditions, it is required that the total mass after optimization does not increase, and the static stress under limit load condition does not exceed 224 MPa (slightly increased compared with the original structure, because the original structure has more safety factor). The natural frequency of the rocker box is taken as the optimization objective, and the highest natural frequency is taken as the objective function.

Zg25mn2 – Ⅱ is used as the material of rocker arm box. Its tensile strength is 770 MPa and yield limit is 370 MPa. In the early analysis of the project, it is known that the maximum equivalent stress of the original structure under rated load and ultimate load is 113.43 MPa and 212.8 MPa respectively. Considering the yield strength, if the material partial safety factor is 1.1, the safety factors of the original structure under the two loading conditions are 2.97 and 1.58 respectively, which are relatively redundant. Therefore, the upper limit of static stress is 224 MPa and the corresponding safety factor is 1.5.

Result analysis

After defining the optimization problem, the problem is submitted and solved by Optistruct’s own optimization solver. The solver combines parameter sensitivity analysis to accelerate the convergence of the results. The objective function of the topology optimization model converges after 27 iterations, and the optimization results are shown in the figure below. The color code in the figure shows the relative density values represented by different colors, in which the bottom blue represents that the relative density is close to 0, and the top red represents that the relative density is close to 1. If the cell density is large, the material at the location is important to the objective function; if the cell density is small, the material at the location is not important to the objective function.

Therefore, the following conclusions can be drawn from the unit density cloud of the graph

1) Increasing the thickness of the box at the free end of the roller is not helpful to improve the natural frequency of the structure;

2) Increasing the material of the four sides of the rocker box is more conducive to improving the natural frequency of the structure than increasing the material of the four sides.

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