# Static and Modal Models of Automotive Wheel Hubs Based on Lightweight Design and Cost-Effectiveness
## 3 Results and Discussion
### Optimization Design of the Wheel Hub  
The optimization of wheel hub structure size adopted ANSYS software to realize parametric modeling and parameter optimization. By setting the corresponding range of input parameters, such as boundary conditions and initial conditions, the hub size parameters can be optimized. The input parameters were set to the rim thickness and spoke thickness, and the output parameters were set to the minimum safety factor, maximum mass, maximum deformation and maximum stress. The conditions were set with a minimum safety factor greater than 2 and a maximum deformation of less than 1 mm. The rim thickness range was set to 3-5 mm, and the spoke thickness range was set to 25-40 mm. Based on the static analysis results for the wheel hub of a certain vehicle model, it was observed that the spokes of the wheel hub experience minimal stress, deformation, and almost zero strain. Therefore, this part exhibited sufficient strength and stiffness. By reducing the thickness of the spoke, increasing the area of ventilation openings, and removing the spoke material, the lightweight design goal can be achieved. These modifications not only served the purpose of ventilation but also reduced the weight of the wheel hub. Additionally, they enhanced the aesthetic appeal of the wheel hub to some extent. In locations where there was significant deformation and stress concentration, the thickness of the wheel hub and the fillets at the connections can be increased appropriately. Simultaneously, the thickness of other parts can be reduced to alter the stress distribution and reduce the weight of the wheel hub. Based on these optimization ideas, the preliminary optimized structure and approximate dimensions are shown in Figure 7. For example, the inner thickness of the rim was reduced to 6 mm, the corner radius of the ventilation opening was increased to 20 mm, and an elliptical ventilation hole with a major axis of 100 mm and a minor axis of 36 mm was created on the spoke. For the optimized structure mentioned above, the deformation results at different loading positions are shown in Figure 8, and the corresponding equivalent stress results are shown in Figure 9. In Figures 8a and 9a, the left subfigures represent the case where the support force is acting on the wheel spoke, while in Figures 8b and 9b, the support force is acting on the ventilation opening. By comparing the force distribution in Figures 8 and 9, it can be seen that the maximum deformation of the optimized hub is 0.40256 mm, and the stress distribution on the hub is more uniform than that before optimization. The maximum stress in the optimized wheel hub was 39.862 MPa, which was significantly lower than the yield strength of the material (205 MPa), indicating that the optimized wheel hub met the design requirements. The results of the modal analysis for modes 1 to 6 of the optimized wheel hub are shown in Figure 10a-f, respectively. According to the modal analysis results, the modal frequencies of the optimized wheel hub ranged from 366.39 Hz to 676.47 Hz, which was significantly different from the maximum external excitation frequency of 200 Hz, effectively avoiding resonance phenomena. Based on the comprehensive static and modal analysis results, it can be concluded that the optimized wheel hub meets the strength requirements, and its vibration frequencies are well separated from the external excitation frequencies. It is obvious that the maximum deformation of the optimized hub has increased, but the weight of the hub at this time is only 10.952 kg, which is about 15.6% lower than the weight of the non-optimized hub (12.979 kg). By optimizing the design of the hub, it is possible to improve the stability of a car during operation, which plays a crucial role in reducing air resistance and enhancing fuel efficiency. Figure 7: Preliminary optimized dimensions of the wheel hub. Figure 8: Deformation at different loading positions after optimization.