On the decrease in contact area for spheres and cylinders rolling on a viscoelastic plane

A theory is presented for predicting the variation with speed of the contact area for spheres and cylinders rolling on a dry, viscoelastic plane. Two distinct effects are shown to occur, due to size and shape variations respectively. The size effect is an overall reduction in contact area because of elastomer stiffening at very high forward speeds, whereas the shape effect produces contact asymmetry at lower speeds. Both effects are a manifestation of the hysteresis properties of the viscoelastic plane. A complex Voigt model with variable parameters is used to simulate the dynamic performance of the plane, and there is close agreement with experimental data. An important application is the rolling behaviour of pneumatic tyres on rough road surfaces.