Date of Award


Document Type


Degree Name

Master of Science (MS)

Legacy Department

Mechanical Engineering


Thompson, Lonny L

Committee Member

Biggers , Sherrill

Committee Member

Ziegert , John C


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 pedal 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 studies have 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) was considered which uses a hyperelastic Marlow material model for both ring and spokes based on uni-axial test data for Polyurethane (PU). Changes in material properties on static load-deflection curves and vibrations of spoke and ground force reaction during high-speed rolling are studied. In addition, energy loss upon impact with an obstacle is also studied.
For static load deflection studies, a new analysis procedure is developed which allows for a cooling step to proceed prior to loading, and yet maintains continuous contact with the ground. For the dynamic rolling studies, a direct analysis procedure is developed, where the Tweel is accelerated from rest. This procedure avoids potential numerical difficulties when defining nonzero initial speeds as used in previous studies. 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 Mooney-Rivlin and Neo-Hookean models obtained from a least-squares fit of the uni-axial stress-strain data. A total of 6 different material models are examined together with the original Marlow model. The 6 material models are divided into 2 sets and each set has 3 levels (unchanged and plus/minus 25% change in shear modulus).
Upon evaluation of the uniaxial data, the results show that on increasing the shear modulus, the tangent slope of the normal stress-strain curve increases; whereas with decreasing shear modulus, the slope decreases. 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 diverges significantly from the Marlow curve. 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, the vertical displacement in the static load-deflection curves increases upon loading. The 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 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 a optimal value is somewhere between the plus/minus 25% stiffness limits.
To study energy loss the 3D finite element model of the Tweel is rolled over an obstacle whose height is 7.5% of the radius of the Tweel. Energy loss is measured by the reduction in axial hub velocities and kinetic energies (KE) relative to an analytical rigid wheel with the same mass, moment of inertia and initial velocity. Results show that the reference Tweel with Marlow material properties, after traversing the obstacle, resulted in an average reduction in axial velocity and total kinetic energy of only 1.3% and 2.3%, respectively. Results show that for Mooney Rivlin, a decrease in shear modulus caused a decrease in energy loss. Conversely, for Neo Hookean, a decrease in shear modulus resulted in an increase in energy loss and an increase in shear modulus resulted in a decrease in energy loss.