Analytical determination of friction resistance as a function of normal load and geometry of surface irregularities

A mathematical modeling and simulation of friction during steady state sliding of metals, based on the upper-bound approach, is demonstrated. The existence of wedge-shaped protrusions on the tool surface is assumed. Pressing these protrusions onto the workpiece and sliding the tool along the workpiece produces asperities on the surface of the workpiece. These asperities move in a wave-like motion along the surface layer and cause plastic deformation through a specified depth under the surface. This plastic deformation combines with local friction between the tool and the workpiece along the asperity interface to produce resistance to sliding. The relation between the normal pressure and the sliding resistance is established for the entire range of pressure levels from zero to infinity. The apparent Coulomb coefficient of friction for lower levels of normal pressure and the constant friction factor for excessive load levels are determined. The transition region from Coulomb coefficient of friction to constant friction factor also becomes clear. A mathematical determination is obtained by means of a force equilibrium considering the concept of a contact surface friction ratio. The force of resistance to sliding is related both to the geometry of the asperity of the surface of the tool and to the constant friction factor, which is used for measuring a local frictional force along the interface of each asperity.