Helical springs have been widely used in various engineering applications for centuries. For many years, there is no significant development in the design methods of helical springs. Recently, a renewed interest is raised from the industry in exploring new designs for the helical springs with novel configurations due to the requirements of customised properties, such as specific spring stiffness and natural frequency for better performance of valve train systems. In this paper, an innovative method which combines the techniques of Finite Element Analysis (FEA), constrained Latin Hypercube sampling (cLHS) and Genetic Programming (GP) is developed to design and analyse helical springs with arbitrary shapes. cLHS method is applied to generate 300 sets of spring samples within a constrained design domain, and FE analysis is conducted on these spring samples. Two meta-models are developed from the 300 sets of FE results by using GP. They successfully describe the relationships between the design parameters and the overall mechanical performances including compression force and fundamental natural frequency of helical springs. The results show that the developed models have robust abilities on designing helical springs with arbitrary shapes, which significantly expands the design domain of the engineering design methods and potential for precise optimization of helical springs.

螺旋弹簧已经在多个工程应用中广泛使用了几个世纪。多年来，螺旋弹簧的设计方法没有重大的发展。最近，由于定制特性（例如特定的弹簧刚度和固有频率，以使气门机构系统具有更好的性能）的要求，业界对开发具有新颖配置的螺旋弹簧的新设计提出了新的兴趣。本文提出了一种创新方法，该方法结合了有限元分析（FEA），约束拉丁超立方体采样（cLHS）和遗传编程（GP）的技术，可以设计和分析任意形状的螺旋弹簧。cLHS方法用于在受约束的设计域内生成300套弹簧样本，对这些弹簧样品进行有限元分析。使用GP从300套有限元结果中建立了两个元模型。他们成功地描述了设计参数与整体机械性能（包括螺旋弹簧的压缩力和基本固有频率）之间的关系。结果表明，所开发的模型具有设计任意形状的螺旋弹簧的强大能力，这极大地扩展了工程设计方法的设计领域，并为精确优化螺旋弹簧提供了潜力。