Effects of Material Properties on Static Load-Deflection and Vibration of a Non-Pneumatic Tire During High-Speed Rolling

The Michelin Tweel tire structure has recently been developed as an innovative non-pneumatic tire which has potential for improved handling, grip, comfort, low energy loss when impacting obstacles and reduced rolling resistance when compared to a traditional pneumatic tire. One of the potential sources of vibration during rolling of a non-pneumatic tire is the buckling phenomenon and snapping back of the spokes in tension when they enter and exit the contact zone. Another source of noise was hypothesized due to a flower petal ring vibration effect due to discrete spoke interaction with the ring and contact with the ground during rolling as the spokes cycle between tension and compression. Transmission of vibration between the ground force, ring and spokes to the hub was also considered to be a significant contributor to vibration and noise characteristics of the Tweel. Previous work studied spoke vibration, ground vibration and related geometrical factors on a two-dimensional (2D) Tweel model. In the present work, a three-dimensional finite element model of a non-pneumatic tire (Tweel) is considered which uses a hyperelastic Marlow material model for both ring and spokes based on uni-axial test data for Polyurethane (PU). Changes in the shear modulus on vertical stiffness and vibration of spoke and ground force reaction for a non-pneumatic tire during high-speed rolling are studied. A three-dimensional finite element model with hyperelastic Marlow material properties for both ring and spokes based on uni-axial test data for Polyurethane (PU) is used for the numerical experiments. In order to study the effect of changes in shear modulus for the ring and spokes while keeping the ratio of volumetric bulk modulus to shear modulus unchanged, the value of shear modulus is varied from unchanged to plus/minus 25% for the Mooney-Rivlin and Neo-Hookean models obtained from a nonlinear least-squares fit of the uni-axial stress-strain data. For tensile stresses and strains, the Mooney-Rivlin best matches the original Marlow material model, compared to the simpler Neo-Hookean model. However, for large compressive stresses, the Mooney-Rivlin model diverges significantly from the results obtained with Marlow properties. The simple Neo-Hookean model is able to fit the Marlow curve better for compression, but is less accurate in tension. As a result of decreasing shear modulus in the ring of the non-pneumatic tire, the vertical displacement in the static load-deflection curves increases upon loading. The softer Neo-Hookean model resulted in decrease in stiffness when compared to the Mooney-Rivlin and original Marlow model. The effects of material changes on spoke vibration as measured by changes in perpendicular distance and vibration in ground interaction measured by FFT frequency response of vertical reaction force during rolling are also reported. Results show a trend where the vibration decreased when the stiffness of the Mooney Rivlin and the Neo Hookean models was increased from +25% to −25%. Conversely, the vibration increased when the stiffness decreased between the extreme limits. However, in several of the material models for the ring and spokes, the unchanged stiffness gave the lowest vibration amplitude, suggesting that an optimal value is somewhere between the plus/minus 25% stiffness limits.