## 3 Design of Elastomeric Bearing Considering Large Load and Nonlinear Motion
### Sizing Equation of Elastomeric Bearing Structure  
Through Equation (4), the compressive strain and compressive stress of the elastomeric bearing can be determined.  
\[\varepsilon_{C}=\frac{(47.555)\sin\delta_{i}(FA)}{E_{C}(RS)^{2}(\sin^{3}\delta_{i }-\sin^{3}\delta_{o})},\ \sigma_{C}=\
icefrac{{\epsilon_{C}\cdot E_{C}}}{{100}} \tag{4}\]  
The ratio of the spring in the axial direction is shown in Equation (5).  
\[K_{A}=\frac{(2.094)E_{C}(RS)^{2}}{t_{R}(RS)^{2}}(\sin^{3}\delta_{i}-\sin^{3} \delta_{o}) \tag{5}\]  
Here, \(\delta_{i}\): Angle from horizontal to inner diameter, deg;  
\(\varepsilon_{\text{max}}\): 150-250% at static limit motion, \(t_{\text{R}}\): rubber thickness;  
T\({}_{\text{R}}\): Total rubber thickness, \(\varepsilon_{\text{max}}\): Compression strain, FA: Axial force;  
E\({}_{\text{c}}\): Static compression modulus, K\({}_{A}\): Axial spring rate, \(\sigma_{\text{c}}\): Compression stress;  
RS: Spherical radius.  
The ratio of torsion and cocking spring can be expressed by Equations (6) and (7).  
\[R_{T}=\frac{(0.04)G(RS)^{4}}{t_{R}}(\sin\delta_{i}\cos^{3}\delta_{i}+2\sin \delta_{i}-\sin\delta_{o}\cos^{2}\delta_{o}-2\sin\delta_{o}) \tag{6}\]  
\[R_{C}=\frac{(0.02)G(RS  
used to interpret the main elements of elastomer bearings and maintain consistency with existing analysis results. Figure 6 shows the shape of the designed elastomer bearing. The design values described in Chapter 3 were applied to the material properties of laminated rubber. The essential value of Aluminum Alloy provided by Ansys was used for the metal shim plate. For the accuracy of the analysis, a three-dimensional structural solid was used as the SOLID 197 element. The element network size was automatically created, the number of nodes was 198,970, and the total number of elements was 91,569. Figure 7 represents the generated finite element model. As for the boundary conditions, the lower part of the model was fixed, as shown in Figure 7. A design displacement of 2.52 mm was given to the upper surface in the direction of the Y-axis of the vertical displacement of the elastomeric bearing, and the reaction force value was obtained and compared with the design load value. The analyzed reaction force value for vertical displacement was 226,180 N, which was interpreted to be about 1.77 times smaller than the design load of 400,000 N. Figure 8 shows the max displacement of the elastomeric bearing when the centrifugal force of the helicopter blade is applied. A significant amount of displacement occurred due to the nature of Shim, which overlaps rubber and metal materials. This is because the displacement of rubber is much larger than that of metal materials. Figure 9 shows the strain received by the elastomeric bearing due to compressive stress. It can be seen that the flexible body bearing secures a structural safety margin of the metal material when the axial load is applied.  
Figure 6: Design model with axial vertical displacement.  
Figure 8: Deformation with axial vertical displacement of elastomeric bearing.  
Figure 7: Single finite element model of elastomeric bearing.