## 5 Conclusions  
In this study, it was proposed that equations for predicting the change in the ply angle by a radius position based on the ply angle and the initial radius during manufacturing of the air spring. Based on the thickness direction deformation, the maximum and minimum values of the ply angle change were presented, and an angle prediction equation using Poisson's ratio was proposed. It was confirmed that the proposed equations were valid by comparing with the measurement angle of the diaphragm-type air spring. For sleeve-type springs in which the initial angle can be easily set for a finite element simulation, the ply angle change during deformation was calculated using the rebar element, and the prediction equations were shown to be valid by comparing them with the angle-prediction equation.  
Finally, the spring stiffness and shape change were compared between the case where a constant angle was input for the diaphragm-type air spring and the angle input by the prediction equations. There was no difference in the vertical load, stiffness, and shape in both cases, but the difference in lateral stiffness and torsional stiffness was 24.3% and 30.2%, respectively. It was found that for accurate prediction, the variable ply angle had to be input differently for each location.  
In the simulation of the air spring to predict the spring characteristics and deformation shape, it is necessary to trace the change in angle and input an appropriate angle according to the initial position. Otherwise, it may be possible to predict the load or stiffness in the vertical direction, but it is highly likely to fail in the prediction of the stiffness in the lateral and torsional directions. Practically, the angle in the initial shape can be obtained by measuring it after manufacturing, but it can be predicted in advance using the formula presented in this paper. According to the shape of the airbag, it is suggested that the angle for each position can be calculated by a formula, so air-spring researchers will be able to easily adopt it. In the air spring analysis, the angle should be entered based on the cylinder coordinate system, and the airbag section should be divided into regions and setup as suggested in this paper. In addition, it was suggested that the full air bag should be modeled for air spring analysis by confirming the occurrence of reaction torque at the fixed point.  
Figure 15: Variation of torque at fixed point with respect to analysis steps according to angle distribution.  
**Author Contributions:** Conceptualization, H.L. and C.-S.K.; methodology, H.L.; software, H.L.; validation, H.L. and C.-S.K.; writing--original draft preparation, H.L.; writing--review and editing, C.-S.K.; project administration, C.-S.K. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by Ministry of Land, Infrastructure and Transport of South Korea (Project No: RS-2020-KA162811).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Acknowledgments:** This work was supported by DHM Co., Ltd. (dhm-korea.com, accessed on 1 July 2022). The authors would like to express their gratitude.  
**Conflicts of Interest:** The authors declare no conflict of interest.