Mathematical Modelling of Residual Stresses in End Milling

Abstract

During end milling, the residual stresses is developed from two sources which includes, stresses due to plastic deformation of material and then stresses due to thermal energy generated. This work looks into the two sources combined into one and then predicts how to best combine the machining parameters in order to minimize the residual stresses in the components. The aim of this work is to develop a mathematical model that can be used to predict the residual stresses in milling. Analytical method was used in developing this model; the model captured the mechanical stress and the thermal stress. The simulation was done with MATLAB and from the results obtained; it was observed that mill cutter with nose radius of 0.4mm and a constant cutting speed of 3m/min while the depth of cut varies from 0.1mm to 0.4mm, the resulting residual stress varied from 50MPa to 150MPa respectively. From the graphs it was also observed that the value of the residual stress at a particular depth of cut is the same in both the x-x and z-z directions and that the stress reduces exponentially as it approaches zero.