## 4 Effect of Angle Distribution on Air Spring Constants
### Analysis Conditions and Results  
In order to analyze the effect of the ply angle distribution on the characteristics of the air spring, a diaphragm-type air spring with the shape shown in Figure 4 was analyzed. The airbag used a full model without symmetry. This part will be explained through the results. The longitudinal direction of the airbag was divided into 110 shell elements, and the circumferential direction was divided into 50 pieces at intervals of 7.5 degrees. Since theply angle using the rebar element is input for each element, the airbag was divided into a total of 110 element sets by grouping the elements in the circumferential direction into one set. The angle was written to the input file using programming. The airbag was divided into three regions by the method of the previous section, and the ply angle was entered according to the angle setting method in each region. The diameter of the reinforced fibers was 0.54 mm, and the spacing between fibers was inputted as 28 EPI (EA/inch) at the inner bead part and 9 EPI at the outer bead part. The thickness for each location was obtained through measurement. The average thickness of the airbag, excluding the vicinity of the upper and lower beads, is 4.7 mm, and has a maximum thickness of 13 mm at the lower bead and 8.5 mm at the maximum at the upper bead. The thickness distribution is shown in Figure 11a. The reinforcing fiber was nylon 66, and the reference [12] for mechanical properties was used. Figure 10: Rebar element direction (vector of sky-blue color) in the shell element: (**a**) setup with angle of 0 degree; (**b**) setup with variable ply angles. Figure 9: Domain definition of an air bag for variable ply angle setup. The angle at the maximum radial position of the airbag was measured as 16 degrees. For the constant angle model, 16 degrees was set based on the maximum angle of the airbag. In order to obtain the angle calculated for each position, 267 mm, which is the radius of the upper bead, was used for the initial radial position, and 11 degrees was used for the initial angle to set the maximum angle of the airbag to 16 degrees. Using Equation (3) with the Poisson's ratio of 0.5, the ply angle with respect to the radial position was obtained, as shown in Figure 3. The result of applying the angle to the rebar element is shown in Figure 11b using a vector. For analysis, after pressurizing to 6 bars, vertical compression, lateral deflection, and rotational twist were applied, sequentially. The rebar force distribution on the ply for each step of the variable ply angle case is shown in Figure 12, and the constant angle case is shown in Figure 13.  
Figure 11: Initial conditions of air spring analysis: (**a**) Distribution of thickness; (**b**) Vector distribution for ply angles in variable ply angle model. Figure 12: Distribution of rebar force (RBFOR) during analysis at variable ply angle distributions: (**a**) inflation; (**b**) vertical compression; (**c**) lateral deflection; (**d**) torsional rotation. In Figure 12, where the angle is assigned as a constant, the maximum force applied to the ply appears in the airbag in the area close to the bottom plate. In the change of angle shown in Figure 3, the angle decreases toward the lower plate and should be placed parallel to the longitudinal axis by approximately 3 degrees. Therefore, when stretched in the circumferential direction by the internal pressure, the ply receives a large force. This has the effect of increasing the stiffness in the circumferential direction at the position of the inner airbag close to the bottom plate. The rebar force appears larger at a constant angle model, especially in torsion, which is 44.51N and 58.86N, which is up to 32% larger. The characteristic diagram of the air spring is shown in Figure 14. As the internal pressure increases, the vertical force increases. In both cases, similar values are shown.