Deformation Index–Based Modeling of Transient, Thermo-mechanical Rolling Resistance for a Nonpneumatic Tire

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ABSTRACT When competing in performance with their pneumatic counterparts, nonpneumatic tires should have several critical features, such as low energy loss when rolling over obstacles, low mass, low stiffness, and low contact pressure. In recent years, a nonpneumatic tire design was proposed to address each of these critical issues [1]. In this study, the steady state and transient energy losses due to rolling resistance for the proposed nonpneumatic tire are considered. Typically, such an analysis is complex because of the coupling of temperature on the structural deformation and the viscoelastic energy dissipation, which requires an iterative procedure. However, researchers have proposed a simplified analysis by using the sensitivity of the tire's elastic response to changes in material stiffness through a deformation index [2–4]. In the current study, the method is exploited to its full potential for the nonpneumatic tire due to the relatively simple nature of deformation in the tire's flexible ring and the lack of several complicating features present in pneumatic tires, namely, a heated air cavity and the complex stress state due to its composite structure. In this article, two models were developed to predict the transient and steady-state temperature rise. The first is a finite element model based on the deformation index approach, which can account for thermo-mechanical details in the tire. Motivated by the simplicity of the thermo-behavior predicted by this finite element model, a simple lumped parameter model for temperature prediction at the center of the shear band was developed, which in many cases compares very well with the more detailed finite element approach due to the nature of the nonpneumatic tire. The finite element model can be used to, for example, explore the design space of the nonpneumatic tire to reach target temperatures by modifying heat transfer coefficients and/or material properties.