Paper Number 3.5
Use of Orthogonal Arrays for Efficient Evaluation of Geometric Designs
for Reducing Vibration of
a Non-Pneumatic Wheel during High-Speed Rolling
William Rutherford[1]
Shashank Bezgam
Lonny Thompson
John C. Ziegert
Department of Mechanical Engineering
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Timothy B. Rhyne
Steven M. Cron
Michelin Americas Research Company
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 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 optimal combinations of
design variables. 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. 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 use of the Orthogonal Array experiments were used to
find combinations of parameters that significantly reduce peak and RMS
amplitudes, and suggest that spoke length has the greatest effect on vibration
amplitudes.