Role of strain softening and viscoelastic memory for the rolling friction of two tire tread compounds

Rolling friction is of great importance for many applications, such as tires and conveyor belts. We study the rolling friction for hard cylinders rolling on flat rubber sheets. The rolling friction depends on the number of rolling cycles, the rolling speed, and the temperature. We show that when the rubber is cooled down below the glass transition temperature, the deformations of the rubber surface are frozen-in, resulting in a non-flat rolling track where uphill and downhill rolling movements strongly affect the rolling force. The experimental data are analyzed using the Persson rolling friction theory; good agreement with the experiments is obtained when the non-linear (strain-softening) properties of the viscoelastic modulus are taken into account.