Force and Moment Response of Pneumatic Tires to Lateral Motion Inputs

Equations of motion applicable to a “running-band” model of the pneumatic tire, as developed by von Schlippe, are transformed to the frequency domain, and side-force and aligning-moment responses are determined for a tire undergoing sinusoidal (a) lateral oscillations of the wheel center plane; (b) steering oscillations with no lateral motion of the wheel center plane; and (c) lateral and yawing motions phased so that the wheel center plane is always aligned with the direction of motion, i.e., the slip angle is zero. The analytical results obtained for the postulated model show that the side force and aligning moment caused by a steering oscillation (namely, the motion described by (b) above) is equal to that produced by pure side-slipping (i.e., (a) above) plus that caused by pure yawing (i.e., (c) above). Numerical evaluation of the derived frequency-response expressions yields an aligning-moment response to steering judged to be extremely significant in view of the unstable behavior often exhibited by wheels with a steering degree of freedom. Comparison of theoretical predictions with experimental data obtained recently by Saito indicates that the “running-band” model is a good first-order approximation of the lateral nonstationary characteristics of pneumatic tires.