Mathematical formulae are derived for normal and tangential components of the contact force that depend not only on the proximity of the two surfaces but also the rate of approach and relative sliding. The development of the contact model is based on the asperity shoulder-shoulder contact leading to slanted asperity contact force. Thus an asperity force contains both normal and tangential components. Three dimensional consideration of asperity contact force yields directionally dependence of both the normal and tangential force components. A previously reported statistical approach is employed in which the dependence of the asperity normal and tangential contact force components on relative tangential velocity of two asperities are cast as corrective factors in the mathematical description of normal and tangential force components. The two corrective coefficients are the force directionality corrective coefficient and the force-velocity directionality corrective coefficient. Approximate equations are found for each of the normal and half-plane tangential force components that achieve accuracy within five (5) percent error.

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