Date of Award


Document Type


Degree Name

Master of Science (MS)

Legacy Department

Mechanical Engineering


Thompson, Lonny L

Committee Member

Ziegert , John C

Committee Member

Li , Gang


During high speed rolling of a non-pneumatic wheel, vibration may be produced by the interaction of collapsible spokes with a shear deformable ring as they enter the contact region, buckle and then snap back into a state of tension. In the present work, a 2D planar finite element model with geometric nonlinearity and explicit time-stepping is used to simulate rolling of the non-pneumatic wheel. Vibration characteristics are measured from the FFT frequency spectrum of the time-signals of perpendicular distance of marker nodes from the virtual plane of the spoke, thickness change in the ring between spokes, and ground reaction forces. Both maximum peak amplitudes and RMS measures are considered as measures of vibration.
In the present work, a systematic study of the effects of six key geometric design parameters is presented using Orthogonal Arrays. Orthogonal Arrays are part of a design process method developed by Taguchi which provides an efficient way to determine the effects of variable levels and a guide to optimal combinations of design variables. Two complementary Orthogonal Arrays are evaluated. The first is the L8 orthogonal array which considers the six geometric design variables evaluated at lower and higher limiting values for a total of eight experiments defined by statistically efficient variable combinations. Based on the results from the L8 orthogonal array, a second L9 orthogonal array experiment evaluates the nonlinear effects in the four parameters of greatest interest, (a) spoke length, (b) spoke curvature, (c) spoke thickness, and (d) shear beam thickness. The L9 array consists of nine experiments with efficient combinations of low, intermediate, and high value levels. Results from the Orthogonal Array experiments were used to find combinations of parameters which significantly reduce peak and RMS amplitudes, and suggest which variables have the greatest effect on vibration amplitudes.
The results of orthogonal arrays indicate that spoke length and spoke curvature were the most influential parameters on the amplitude of vibration for all three vibration measures. The optimal configuration predicted for these two parameters is a wheel with short spokes with large curvature. The order of influence and optimal levels of the other four variables varies according to the measure of vibration. The results show that there was effectively no interaction between spoke length and spoke thickness. However there are interactions between other variables in the system, and this interaction is stronger when non-linear variable levels were considered from the L9-array. Geometries are presented that minimize vibration for each source, and an optimal geometry is suggested that significantly reduces vibration for all measures of vibration considered.
A study of natural frequency and mode shapes extracted from the operational state of the system suggest that geometries with high amplitude peaks in the FFT spectrum for spoke vibration show a correlation with spoke vibration mode shapes. For other geometries, spoke vibration amplitude peaks coincided with ring flower-pedal modes.