Use of Orthogonal Arrays for Efficient Evaluation of Geometric Designs for Reducing Vibration of a Non-Pneumatic Wheel during High-Speed Rolling

Abstract

Abstract During high speed rolling of a nonpneumatic 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 two-dimensional planar finite element model with geometric nonlinearity and explicit time-stepping is used to simulate rolling of the nonpneumatic 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, 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 which significantly reduce peak and RMS amplitudes, and suggest that spoke length has the greatest effect on vibration amplitudes.