Deformation Index–Based Modeling of Transient, Thermo-mechanical Rolling Resistance for a Nonpneumatic Tire
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.ABSTRACT
Flowchart for conventional method of handling coupled thermo-mechanical analysis, reproduced from [4].
Flowchart for the deformation index method of handling coupled thermo-mechanical analysis, reproduced from [4].
Description of the model for structural finite element analysis.
Axis-symmetric model for thermal finite element analysis for nonpneumatic tire.
Experimental data of candidate tire material. Rectangular portion indicates operating temperature range of tire.
Deformation index example from Mars [21]. (a) Springs in series. (b) Deformation index as a function of the ratio of spring stiffness.
Finite element model results of the deformation index through the thickness of shear band using 10 elements.
Comparison of experimental rolling resistance from drum tests with finite element calculations from the drum boundary condition and straight ground.
Sensitivity of deformation index on temperature profile for (a) constant m = −0.20, −0.40, −0.60, −0.80, and −1.00 and (b) varying the deformation index m through cross section according to Fig. 6.
Lumped parameter prediction of rolling resistance versus time at constant speed.
Lumped parameter and finite element predictions of temperature rise and cool down for inner radius and centerline of tire.
Simulation of temperature change for centerline of shear band for urban driving cycle. (a) EPA urban driving schedule. (b) Centerline temperatures for FEA and lumped parameter model.
Temperature along centerline and side of tire for EPA driving schedule using an FEA model with varying m through the thickness and convective heat loss out the sides, compared with temperature from the lumped parameter model with constant m and insulated sides.
Temperature profile at the end of EPA driving schedule (a) across the width of the tire from the free surface to centerline and (b) across the thickness of the tire at the free surface and across the thickness of the tire at centerline.
Results of thermal analysis for a constant rolling speed. (a) Transient temperature rises for finite element and lumped parameter model at the inner radius of the shear band and the midpoint of thickness in the shear band. (b) Steady-state temperature profile across the thickness of the shear band for the finite element and lumped parameter model on the air-exposed ends.
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