Date of Award


Document Type


Degree Name

Master of Science (MS)

Legacy Department

Mechanical Engineering

Committee Chair/Advisor



Extensive studies have been conducted in the past to show that the characteristics of a non-pneumatic structure, the TweelTM are the same as the pneumatic tires. These characteristics include low contact pressure, low stiffness, low energy loss from obstacle impacts, low mass, and high load-carrying capacity. The TweelTM consists of a ring shaped shear beam comprised of two inextensible membranes separated by a relatively low modulus elastic material. This shear beam is connected to the hub by thin elastic spokes.
When used for high speed rolling applications, the TweelTM produces unacceptably high levels of acoustic noise. It has been suggested that this noise source was not a forced vibration due to the wheel rotational speed but rather a self-excited vibration of some portion of the TweelTM. It was hypothesized that spokes are the source for this vibration. As the spokes enter the contact region they buckle and snap back into a state of tension as they leave the contact region. This transition may excite a resonant vibration of spokes which is relatively independent of the wheel speed.
This thesis focuses on four aspects: 1) Creating the finite element model of a rolling TweelTM which is in contact with a rigid plane to observe the spoke vibrations. 2) Investigating the effect of rolling speed on the observed spoke vibration frequencies. 3) Investigating the effect of spoke thickness on spoke vibration frequencies. 4) Creating a three-dimensional TweelTM spoke to investigate both the in-plane and out-of-plane spoke vibrations.
In this work, a planar finite element model of a TweelTM was created by Michelin in a computer aided engineering software called ABAQUS using a plug-in user interface. Two-dimensional plane stress/plane strain models were created with hyperelastic materials for the shear band and spokes, and orthotropic elastic materials for the inextensible membranes. Simulation of the cooling which takes place following the casting of the TweelTM during manufacturing was performed using coupled displacement-temperature analysis with ABAQUS/Standard solver and the results were imported into ABAQUS/Explicit for performing the dynamic simulations using dynamic coupled displacement-temperature analysis. In order to reduce the computational time an initial linear velocity was defined for the ground and an initial angular velocity for the TweelTM, thus eliminating the time required to accelerate the TweelTM from rest to its final speed. The profile of the spoke length versus time was plotted to see the spoke buckle as it enters the contact region and snaps back in tension when leaving the contact region. The frequency spectrum of the observed spoke vibrations was computed. It was noted that one of the dominant vibration frequencies does not change with vehicle speed. The effects of spoke thickness on the spoke vibration frequencies were studied and it was observed that change in spoke thickness has an impact on the amplitudes of the spoke vibration but not on the frequency.
The two-dimensional model of the TweelTM can only capture in-plane vibrations. Therefore, a three-dimensional TweelTM spoke model was created in order to capture both the in-plane and out-of-plane spoke vibrations. The spoke length vs. time profile obtained from the two-dimensional model was given as an input to the three-dimensional spoke model and the resulting vibrations were studied.
Finally, improved computational modeling strategies like coupling of spoke vibrations to ring vibrations, using beam elements for spokes, effect of material damping on spoke response, sensitivity of spoke vibration frequency to variations in spoke thickness along its length and spoke curvature are identified as possible areas of future work.



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