Derivation of the Coefficients in the Coulomb Constant Shear Friction Law from Experimental Data on the Extrusion of a Material into V-Shaped Channels with Different Convergence Angles: New Method and Algorithm

Abstract

The combined Coulomb constant shear friction law is widely used in commercial and research software for the finite-element analysis (FEA) of metalworking and is naturally more flexible and hence, more relevant to real-life manufacturing than the individual Coulomb and constant shear friction laws. In this work, a new mathematical model of coefficients in the Coulomb constant shear friction law for extruding a metal through narrow V-shaped channels with small convergence angles has been developed and evaluated and compared with laboratory measurements. The extrusion of the model material (lead) through narrow V-shaped channels with small convergence angles varying from 0 to 3.5 degrees has been studied. The Coulomb friction coefficient µ and the constant friction factor m appear to be independent of the dimension ratio and are influenced mostly by roughness and range from µ = 0.363 (with lubricant) to µ = 0.488 (without lubricant) and from m = 0.726 (with lubricant) to 0.99 (without lubricant). The relative length dominated by the Coulomb friction law is less than 1%, and the Coulomb’s coefficient of friction can be approximated as ½ the constant shear friction factor for all tested cases. The developed method and algorithm can be used in both FEA of manufacturing processes and efficiency tests for lubricants used in metalworking.