Stiffness analysis and structural optimization design of an air spring for ships

An air spring (AS) for ships must have the structural strength of its bellows enhanced considerably to ensure its reliability under high internal pressure and strong impact. In this case, the stiffness of the bellows gradually dominates the overall stiffness of the AS. Nevertheless, the parameterization calculation of stiffness for an AS mainly focuses on its pneumatic stiffness. The bellows stiffness is normally analyzed by virtue of equivalent simplification or numeric simulation. There is not an effective parameterization calculation model for the stiffness of the bellows, making it difficult to achieve the structural optimization design of the bellows. In this paper, the shell theory was borrowed to build a mechanical model for the bellows. Subsequently, the state vector of the bellows was solved by precision integration and boundary condition. Iteration was conducted to identify the complex coupling relationship between the vector of the bellows and other parameters. On this basis, the parameterization calculation method was introduced for the stiffness of the bellows to obtain the vertical and horizontal stiffness of the AS. After that, a dual-membrane low-stiffness structure was designed to analyze the dominating factors affecting the strength and stiffness of the AS, which highlighted the way to the low-stiffness optimization design of high-strength ASs. In the end, three prototypes and one optimized prototype were tested to verify the correctness of the parameterization design model for stiffness as well as the effectiveness of the structural optimization design.