Numerical simulation of three‐dimensional steady‐state rolling by the reproducing kernel particle method

This paper presents a numerical approach for analysing three‐dimensional steady‐state rolling by means of the reproducing kernel particle method (RKPM). The approach is based on the flow formulation for slightly compressible materials and a detailed description of RKPM and its numerical implementation is presented with the objective of providing the necessary background. Special emphasis is placed on the construction of shape functions and their derivatives, enforcement of the essential boundary conditions and treatment of frictional effects along the contact interface between the workpiece and the roll. The effectiveness of the proposed approach is discussed by comparing the theoretical predictions with the finite element calculations and experimental data found in the literature.