Multi-Objective Optimization of the Geometry of a Non-Pneumatic Tire for Three-Dimensional Stiffness Adaptation

Non-pneumatic tires (NPTs) have been widely used for their advantages of no run-flat, no need for air maintenance, and unique stiffness characteristics. This study focuses on the design of a spoke of a Fibonacci spiral non-pneumatic tire (FS-NPT) based on its properties of three-dimensional stiffness. Finite element (FE) models, parametric studies, designs of experiments (DOEs), and sensitivity analyses are conducted to study the effect on the three-dimensional stiffness considering three design variables: (a) the thickness of the spokes, (b) the radius of the first Fibonacci spiral of the spoke, and (c) the width of the spokes of the FS-NPT. The results show that variation in all three design parameters had no considerable effect on the lateral stiffness. The results from the DOE are used to create a response surface model (RSM) for the multi-objective function (minimal SSD) and a constraint on the weight of the FS-NPT. The analytical RSM functions are optimized for minimizing the SSD subjected to the given constraint. The results indicate that all three design variables of the spoke had a significant effect on the vertical stiffness. The spoke radius had no potential effect on the longitudinal stiffness of the NPT. Hence, the three-dimensional stiffness of the FS-NPT has a certain independent design. This work demonstrates the advantages of non-pneumatic tires, especially FS-NPTs, in three-dimensional stiffness decoupling. This study guides the industrial production of flexible-spoke bionic NPTs by providing a very simple spoke structure. The optimization results show that FS-NPTs have a large stiffness design range. The different stiffness targets can be achieved by adjusting different combinations of the design variables, and the tire mass does not increase significantly.