Type C Rolling Friction

The Type C Rolling friction model, proposed by Ai et al. (2011) is an extension of the standard EDEM Rolling Friction model that includes a non-viscous term in the damping torque equation.

here  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)
	(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 non-viscous torque magnitude is limited according to Equation 4, where Fn  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.

The viscous damping torque is only applied if the non-viscous torque magnitude is below the limit as 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.

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