Machining with tool-chip contact on the tool secondary rake face—Part I: a new slip-line model

Given the growing number of applications of groove-type chip breaker tools in modern machining, it is becoming increasingly important to study the tool-chip contact on the tool secondary rake face. This type of tool-chip contact significantly changes not only the state of stresses in the plastic deformation region, but also changes the distribution of forces and temperatures over the tool rake face. A new slip-line model accounting for the tool-chip contact on the tool secondary rake face is proposed in this paper. The model also takes into account chip curl and incorporates seven slip-line models developed for machining during the last six decades as special cases. Dewhurst and Collins's matrix technique for numerically solving slip-line problems and Powell's algorithm of nonlinear optimization are employed in the mathematical formulation of the model. The inputs of the model include (a) the tool primary rake angle γ₁, (b) the tool secondary rake angle γ₂, (c) the tool land length h, (d) the undeformed chip thickness t₁, (e) the ratio of hydrostatic pressure P_A to the material shear flow stress k, (f) the ratio of frictional shear stress τ₁ on the tool primary rake face to the material shear flow stress k, and (g) the ratio of frictional shear stress τ₂ on the tool secondary rake face to the material shear flow stress k. The outputs of the model include (a) the cutting force F_c/kt₁w and the thrust force F_t/kt₁w, (b) the chip up-curl radius R_u, (c) the chip thickness t₂, and (d) the natural tool-chip contact length l_n.