# RVD Rolling Friction

In this model, the rolling friction depends on relative rotational velocity of a pair of elements in contact in a manner suggested in (Zhou, et al. 1999).

This Relative Velocity Dependent (RVD) Rolling Friction model is offered as a 3D generalization of the “Type A: Directional Constant Torque” model type discussed in the paper (Ai, et al. 2011) with one difference in the method of calculating the relative rotational velocity of two elements in contact. While in reference (Ai, et al. 2011) the relative rotational velocity is evaluated from tracking the point of contact, in the EDEM RVD Rolling Friction model, the relative rotational velocity is calculated from the values of instantaneous rotational velocities of two elements in contact as described below. This implementation detail insured proper functionality in three dimensions without affecting the computational time.

In particular, this contact model accounts for rolling friction by applying a constant torque to the contacting surfaces. The torque depends on the relative rotational velocity of two particles in contact, particle i and particle j, as follows:

With μ_{r }the coefficient of rolling friction, and R* is the equivalent radius of two elements in contact. The unit vector of relative rotational velocity, ω_{rel}, is calculated as follows:

Here n_{ij }is a unit vector pointing from particle i to the point of contact as shown in the following figure:

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