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

Abstract

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 γ 1, (b) the tool secondary rake angle γ 2, (c) the tool land length h, (d) the undeformed chip thickness t 1, (e) the ratio of hydrostatic pressure P A to the material shear flow stress k, (f) the ratio of frictional shear stress τ 1 on the tool primary rake face to the material shear flow stress k, and (g) the ratio of frictional shear stress τ 2 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/ kt 1 w and the thrust force F t/ kt 1 w, (b) the chip up-curl radius R u, (c) the chip thickness t 2, and (d) the natural tool–chip contact length l n.