Centrifugal Effects in Inflated, Rotating Bias-Ply Tires

Abstract

An equation is derived which governs the dynamic equilibrium contour taken by an inflated and rotating, but otherwise unloaded, bias-ply tire. This equation, which is in the form of a hyperelliptic integral, is based on the membrane theory of shells and the netting analysis of composite materials. Results are obtained for the meridional geom etry of a typical two-ply automobile tire, which are in reasonable agreement with ex perimental measurements. This integral, which describes the dynamic equilibrium contour of the tire, is then used to obtain an algebraic cord load formula. The formula shows how the cord tension at any location is dependent on mass distribution, angular velocity, inflation pressure, deformed tire geometry, and number of cords in the tire. Centrifugal effects, as they influence cord tension, are more pronounced in the bead region than in the crown region. Cord forces are experimentally measured up to 1600 rpm, using the tirecord tension transducer which is a strain-gage instrumented tension link embedded in the tire and placed in series with the cord. Agreement between the theoretically predicted and ex perimentally measured cord forces is good, especially in the range of angular velocities and inflation pressures used in service.