Robust Optimization Design for the Cylindrical Helical Spring Based on the Improved Particle Swarm Algorithm

High reliability is one of the most important criterions for the design of the spring; however, due to complex and diverse factors, each type of spring requires a different design formulation. In order to make full use of the capability of materials and obtain higher reliability of the cylindrical helical spring, a multiobjective optimal model is established based on robust and reliability optimization design theory. The objective was to obtain a spring with minimum mass and maximum natural vibration frequency and minimum reliability sensitivity. Some parameters of the spring are taken as random variables in this model and the reliability target is taken as the constrained condition. This multiobjective optimal problem is transformed into a single-objective optimal problem by using the multiplication and division method. Further, an improved swarm algorithm which can reasonably deal with hybrid discrete variables is used to solve this problem. The proposed method is applied to a practical example. The results show that this method is practical, reliable, and effective for obtaining parameters of robust optimization design for reliability.