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 Collinsʹs matrix technique for numerically solving slip-line problems and Powellʹs 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 PA 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 Fc/kt1w and the thrust force Ft/kt1w, (b) the chip up-curl radius Ru, (c) the chip thickness t2, and (d) the natural tool–chip contact length ln.