# Cross-Sectional Shape Optimization of Cylindrical Elastomer Spring for Sensitive Cargo Container
## 1 Introduction  
Commonly used transportation methods for high-value-added sensitive cargo (e.g., electronics, LEDs, semiconductors, etc.) are vibration-free cargo trucks on roads. Although the transportation system of sensitive cargoes can be accessed conveniently from the origin to the destination, there are some issues, such as expensive freight charges, road traffic congestion, limited mass transport, and environmental problems (air pollution). These problems can be improved by incorporating the freight train (hereinafter, freight car) transport method from the perspective of modal shift. Sensitive cargoes are damaged by low-frequency vibrations and shocks that occur during trans-shipment between road and rail transport. As an alternative to shock-absorbing packaging or installing a specific internal device to address vibration and shocks, containers for sensitive cargo are used [1]. However, damage to the rubber spring causes a large cost loss due to damage to the sensitive cargo. As shown in Figure 1, the rubber spring for containers consists of cylindrical natural rubber, an upper circular carbon steel plate, and a lower fixing support. Therefore, in order to develop a device with high reliability ofrail transportation for sensitive cargo during operation, nonlinear finite element analysis (NFEA) is required considering rubber characteristics representing hyperelastic behavior [2]. It should also be an optimal structural design that satisfies the design target stiffness and strength of this spring in a road/railroad operating environment. The existing research on rubber springs for railway vehicles has mainly focused on the truck suspension device of railway vehicles [3; 4; 5; 6; 7; 8; 9]. In the work of [PERSON] et al. [3], based on a nonlinear quasi-static model analysis of rubber springs, techniques were used to superimpose residual stresses and consider material fatigue to predict damage to rubber springs. [PERSON] et al. [4] proposed an effective stress tensor as a parameter for fatigue damage considering all compression, tensile, and shear stress range to study the effective fatigue evaluation of rubber mounts for railway vehicles. [PERSON] et al. [5] determined the strength of the primary suspension rubber spring through finite element analysis of the rubber spring. In addition, a study was conducted to design a rubber spring of the required strength and verify its validity by verifying the stiffness value through tests. [PERSON] et al. [6] performed structural optimization based on finite element method (FEM) and support vector regression (SVR) models for air springs for railway vehicles. [PERSON] et al. [7] analyzed the frequency dependence and amplitude dependence characteristics of rubber springs for railway vehicles under low and high-temperature conditions. [PERSON] et al. [8] analyzed the effect of geometrical parameters on the fatigue life of conical rubber springs using an orthogonal numerical test method. [PERSON] et al. [9] presented an optimization model through NFEA and optimization for conical rubber springs in railway vehicles, and the strain is reduced by about 7% compared to the initial model. [PERSON] et al. [10] studied a non-hyperelastic elliptic analysis model of EMU rubber springs based on the experimental data of rubber springs to describe the non-hyperelastic properties of rubber springs. [PERSON] et al. [11] analyzed the axial vibration according to the effects of mass and stiffness on the laminated rubber-metal spring. [PERSON] et al. [12] conducted a study on components necessary for models expressing the mechanical behavior of rubber springs for high-speed rail vehicles. [PERSON] et al. [13] performed finite element simulations on the static characteristics of rubber mounts for vehicles. [PERSON] et al. [14] conducted finite element analysis and structure optimization to improve the fatigue life of rubber mounts.