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

Friction plays an important role in metal-forming processes by pressure and largely controls material flow wear, adversely affecting the wear resistance of dies employed to form metals. Therefore, 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. Accurately determining coefficients in the Coulomb constant shear friction law is critically important for the correct assignment of the boundary conditions in the FEA of metal forming needed to develop proper dies. 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 com-pared with laboratory measurements. The model is based on an approximate solution of the equilibrium equations of elasticity, the kinematically admissible velocity field, and the distribu-tion of tangential stresses in the plastic deformation zone that meet the certain boundary condi-tions. For the zone, where a transition from the Coulomb friction law to the constant shear fric-tion law occurs, analytical formulas relating the corresponding friction coefficients have been derived. Based on the aforementioned mathematical model, an algorithm allowing us to derive the Coulomb constant shear friction law coefficients from laboratory measurements has been developed. 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 under laboratory con-ditions. The Coulomb friction coefficient µ and the constant friction factor m calculated for the model material appear to be independent of the dimension ratio and are influenced mostly by roughness and range from µ = 0.363 (w lubricant) to µ = 0.488 (w/o lubricant) and from m = 0.726 (w lubricant) to 0.99 (w/o lubricant). The relative length dominated by the Coulomb fric-tion 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 metal-working.