# Static and Modal Models of Automotive Wheel Hubs Based on Lightweight Design and Cost-Effectiveness
## 3 Results and Discussion  
### Static Analysis of the Wheel Hub  
The static analysis of the wheel hub enables the determination of the deformation distribution under loading conditions. This helps in assessing the stiffness and deformation characteristics of the wheel hub, providing insights into the shape changes and magnitude of deformation under load. After applying the forces and constraints shown in Figure 3, the overall deformation result of the wheel hub is illustrated in Figure 4. Figure 4a represents the deformation result when the support force is acting directly on the wheel spoke. From the graph, it can be observed that under multiple loads and fixed constraints, the maximum displacement of the wheel hub is 0.30926 mm, with the maximum displacement occurring in the region near the inner side of the wheel hub where the support force is applied. The deformation at the connection between the wheel hub and the bolts was minimal. Figure 4b depicts the deformation result when the support force is acting on the ventilation opening. In this case, the maximum displacement of the wheel hub is 0.29096 mm, slightly smaller compared to the scenario with the support force acting on the wheel spoke, as shown in Figure 4a. Again, the maximum displacement occurred in the region near the inner side of the wheel hub where the support force was applied. Under the above two working conditions, the maximum displacement of the wheel hub is 0.30926 mm, less than 1 mm, which meets the design requirements of the automobile wheel hub. This indicates that the wheel hub structure design chosen in this study is reasonable and capable of meeting the requirements for automotive applications. The results of static analysis allowed for the identification of areas in the wheel hub that experience high stress and significant deformation. Based on this information, structural optimization can be performed, including adjusting the material distribution, enhancing the stiffness of high-stress regions, improving connection methods, and so on, in order to enhance the performance and quality of the wheel hub.  
Figure 3: Initial conditions and constraints. (**a**) P\({}_{1}\) is acting on the wheel spoke; (**b**) P\({}_{1}\) is acting on the wheel spoke ventilation opening; (**c**) P\({}_{2}\) acts on the wheel rim, and T acts on the bolt hole surface; (**d**) The fixed constraints imposed on the wheel hub.  
The equivalent stress of the wheel hub is shown in Figure 5. From Figure 5a, it can be observed that when the support force is acting directly on the wheel spoke, the maximum equivalent stress is 39.879 MPa, significantly lower than the yield strength of the selected material (205 MPa). The primary stress ranged from 4.4436 MPa to 26.591 MPa, distributed in a ring on the wheel rim near the point where the support force was applied, which falls within the safe range. As shown in Figure 5b, when the support force is acting on the ventilation opening, the maximum equivalent stress on the wheel hub is 45.946 MPa, still significantly lower than the yield strength of the selected material (205 MPa). The stress is within the safe range of 10.22 MPa and 30.635 MPa, and the rim is distributed in a ring near the support point. Based on the stress obtained for the wheel hub, the stress was mainly concentrated in the region near the applied force point on the wheel rim, particularly in the smaller fillet areas. Therefore, appropriately increasing the fillet radius can improve the stress distribution. By analyzing simulation results, the stress distribution in various parts of the wheel hub can be obtained, including the location of maximum stress and areas of stress concentration. This helps evaluate the strength and stability of the wheel hub under loading conditions.