# Type C Rolling Friction

here *
Mr
* is the total damping torque vector, *
Mrk
* is the non-viscous damping torque vector and

*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.*

*Mrd*(2) | |

(3) | |

(4) |

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.

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.

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.

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