# Influence of Aging Time on Vertical Static Stiffness of Air Spring
## 5 Simulation on Vertical Static Stiffness of Air Springs with Aging Time
### Effects of Rubber Aging  
The simulation analysis results of the air spring vertical static stiffness, only considering the curtain aging, are shown in Figure 6. The figure shows that the gradually aging curtain line gradually increases the air spring vertical static stiffness, which increased by 5.3% at 12 days compared with that before aging.  
The vertical static stiffness of the air spring is proportional to its effective area, so one can compare the lateral displacement on the airbag node, the lateral displacement of the air spring, and the larger effective area. The curve of the lateral displacement of the node on the air spring airbag, shown in Figure 5, with the analysis step time is shown in Figure 7. As Figure 7a shows, when considering rubber aging only, the lateral displacement  
Figure 6: Consider the vertical static stiffness of an air spring affected by rubber aging and cord aging only.  
of the node during the first load step inflation increases; then, the air pressure decreases because the node moves inward at this position, with the deformation of the airbag. With the increase in aging time, the lateral displacement of the node on the airbag decreases significantly--that is, the effective bearing area of the air spring decreases. As shown in Figure 7b, the lateral displacement of the node on the airbag increases slightly. In other words, the effective bearing area of the air spring becomes larger, but the change amount is less obvious than when only rubber aging is considered.  
The vertical stiffness of the air spring and the internal pressure of the airbag are proportional, and the internal pressure of the airbag volume is inversely proportional to the change in the shape of the airbag, which directly reflects the change in the airbag volume, so the shapes of the airbag before and after aging can be compared. Figure 8 shows a diagram comparing the shapes of the air bag cross-section before and after aging. As Figure 8a shows, when considering the rubber aging only, the airbag volume after 12 days of aging is significantly smaller, causing a large internal pressure, and the impact of the large internal pressure is greater than the impact of a smaller effective area, so the empty spring vertical to the static stiffness increases. Compared with the shape change of the airbag before and after rubber aging, it can be observed from Figure 8b that the airbag section area change after curtain aging is relatively small, so the airbag volume change is also small; thus, the internal pressure change of the airbag is also smaller. Figure 8 shows the curve of the maximum air pressure during loading time under different conditions. As Figure 9 shows, when considering the curtain aging only, the internal pressure increase of the airbag is less than the air pressure increase of the rubber aging, so the impact of curtain aging on the air spring stiffness is less than that of rubber aging. In summary, it is considered that the effective area reduces the vertical static stiffness, the internal pressure of the airbag increases, and the internal pressure of the airbag plays a leading role. Therefore, the air spring gradually increases, but the increase is less than the value of rubber aging.  
Figure 7: The lateral displacement of the joint varies with the time of the analysis step: (**a**) considering the rubber aging, the lateral displacement of the node varies with the analysis step time; (**b**) considering the aging of the cord, the lateral displacement of the node varies with the analysis step time.