## 5 Model Reconstruction and Secondary Optimization
### Lightweight Design of Subframe Based on OptiStruct  
The main technical approach to lightweight design is structural optimization, which mainly includes topology optimization, shape optimization and size optimization. The transmission path of the subframe force was obtained through the completed subframe topology optimization. Relying on the completed model reconstruction, for the further lightweight design of the subframe, to increase the vehicle's driving range and reduce energy consumption, further optimize the subframe.  
Figure 11: Number of iterations.  
By applying the size optimization technology of Optistruct, weight reduction optimization is achieved in the subframe design stage. Parameter adjustment technology, also known as size optimization method, focuses on finely adjusting various parameters of the three-dimensional model without changing the mesh structure, in order to achieve size optimization of the finite element model of mechanical components, such as precise control of plate thickness. This method is dedicated to achieving the lightweight design of the subframe to the greatest extent within the limitations of existing materials and manufacturing processes [16; 17].  
The relevant parameters for subframe size optimization are:  
Objective function:  
\[V_{min}(x_{1},x_{2},x_{3},x_{4},x_{5}),f_{max1}(x_{1},x_{2},x_{3},x_{4},x_{5}) \tag{15}\]  
Figure 12: Three-view view of the subframe.  
Constraint conditions:  
\[\delta\leq 306\;\text{MPa}\] \[Y\leq 1\;\text{mm} \tag{16}\] \[f_{1}\geq 100\;\text{Hz}\]  
Design variable:  
\[1\;\text{mm}\leq x_{1},x_{2},x_{3},x_{4},x_{5}\leq 5\;\text{mm} \tag{17}\]  
In the formula, \(V\) represents the volume of the subframe; \(\delta\) represents the subframe stress; Y represents the maximum deformation of the subframe; \(x_{1}\) represents the thickness of the front crossbeam of the subframe; \(x_{2}\) indicates the thickness of the rear crossbeam of the subframe; \(x_{3}\) represents the thickness of the side beams of the subframe. \(x_{4}\) represents the thickness of the subframe pipe string; \(x_{5}\) is the connection plate of the lower swing arm.  
The study was constructed using SAPH440 material. It was assumed that the density distribution was balanced and the weight of the subframe was positively correlated with its volume. Based on this, volume reduction is taken as the core goal of the optimized design. The subframe mode needs to avoid the road excitation frequency and the engine excitation frequency. Then, the maximum frequency of the first-order mode is set as the second objective function. If the yield strength of SAPH440 material is 306 Mpa, then the stress under the constraint condition needs to be less than 306 Mpa. The other first-order mode needs to avoid the engine frequency and the road excitation frequency. Therefore, the range of the first-order mode is set to be greater than 80 Hz. When designing the subframe, the deformation is required to be less than 1 mm. Set the thickness of each part of the subframe as the design variable of the subframe. Meanwhile, set the convergence tolerance at 0.5%. When choosing design variables, consider taking the thickness of the side beams of the subframe, the front crossbeam, the rear crossbeam, the lower swing arm connection plate and the pipe string as the design variables for achieving lightweight. These ten working conditions are selected as the reference conditions for strength constraints and stiffness constraints.  
After the secondary optimization, the subframe is shown in Figure 13. The wall thickness of the left and right vertical beams is 3.3 mm, the thickness of the front crossbeam and pipe string is 1.3 mm, the thickness of the rear crossbeam is 1.6 mm, and the wall thickness of the lower swing arm mounting plate is 3.6 mm. You can view it by opening mass calc in the home page Tool in Hypermesh. Figure 11 shows the optimized quality.