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In an effort to develop tires with low rolling resistance, nonpneumatic tires (NPTs) with low viscoelastic energy loss materials are receiving more attention. For better design of NPTs on fuel efficiency, one may need to analyze rolling energy loss of NPT at a component level. The objective of this study is to develop a tool to quantify rolling energy loss and the corresponding internal heat generation of NPTs at a component level. For varying vehicle loads and rolling speeds, we suggest a thermo-mechanical model of an NPT with hexagonal cellular spokes and investigate temperature distribution of the NPT generated by hysteresis and convection loss into air. Using a hyper-viscoelastic material model developed from uniaxial (tensile and compression) tests and dynamic mechanical analysis (DMA), a thermo-mechanical model is developed by combining a longitudinal shear deformation induced hysteresis and a cooling procedure exposed to air.

Due to the relatively high freedom of selection of materials associated with a simple manufacturing method, a nonpneumatic tire (NPT) can be manufactured with a low viscoelastic energy loss material. A highly increasing demand to reduce greenhouse gases drives engineers to explore NPTs. NPTs consisting of flexible spokes and the shear band are still at an early stage of research and development. An optimization study of NPTs' geometry needs to be conducted, which is the objective of this paper. Parametric studies and design of experiments (DOE) of an NPT are conducted with a hyper-viscoelastic finite element (FE) model to determine the effects of three design variables on rolling resistance: the thickness of cellular spokes, the cell angle, and the shear band thickness. Considering vehicle load carrying capacity and riding comfort, ranges of vertical deflection between 18 and 20mm and contact pressure between 0.6 and 0.8MPa are selected as constraints for the optimization.