Slip-line modeling of built-up edge formation in machining

Abstract

Extensive investigations on built-up edge (BUE) formation in machining have been conducted in the past. However, very little effort has been made to quantitatively predict the size of the BUE and its effect on chip flow and cutting forces under different machining conditions. This prediction is important because it is the key to predicting the fluctuation of cutting forces and provides better rationale for explaining various machining phenomena associated with BUE formation. A new slip-line model for machining with BUE formation and its associated hodograph are proposed in this paper. Consisting of four slip-line sub-regions, the new slip-line model meets both the stress equilibrium and velocity requirements of material flow. The new model simultaneously predicts the length and height of the BUE, cutting and thrust forces, chip up-curl radius, chip thickness, and tool–chip contact length. Dewhurst and Collins's matrix technique for numerically solving the slip-line problem is employed in the mathematical formulation of the model, with non-unique solutions being obtained. It is demonstrated that one of the four slip-line angles included in the new model directly governs the size and surface shape of the BUE. Compared with the well-known Lee and Shaffer's model, the new model predicts a much longer BUE covering a larger portion of the tool rake face. A small tool rake angle tends to generate a large BUE. The predicted trends of the variation of relevant machining parameters are consistent with experimental observations.