# Type C Rolling Friction

The Type C rolling friction model, proposed by Ai et al. (2011), goes beyond the standard EDEM rolling friction model by including a non-viscous term in the damping torque equation (Eq. 1).

 (1)

Where Mr  is the total damping torque vector, Mrk  is the non-viscous damping torque vector and  Mrd  is the viscous damping torque vector.

The non-viscous damping torque vector is a function of the relative particle rotation angle and the rolling stiffness as defined in Equations 2 and 3.

 (2) (3)

Where k r  is the rolling stiffness, θ r  is the relative rotation angle, R r  is the equivalent rolling radius, k n  is the normal contact stiffness and μ r  is the coefficient of rolling friction.

It should be noted that the non-viscous torque magnitude is limited according to Equation 4.

 (4)

Where F n  is the normal contact force.

The viscous damping torque vector is defined in Equation 5 and is function of the relative rotational velocity vector at the contact point and the rolling viscous damping ratio.

 (5)

Where η  is the rolling viscous damping ratio, I r  is the equivalent moment of inertia for the rotational vibration mode about the contact point and ω  is the relative rotational velocity vector at the contact point.

It should be noted that the viscous damping torque is only applied if the non-viscous torque magnitude is below the limit defined in Equation 4.

In cases where significant non-viscous rolling resistance is expected at particle contacts such as when contact forces are high or the modeled material consists of predominantly angular particles, the use of Type C rolling friction may result in a more physically accurate behavior and greater stability of the EDEM model.