Analytical method for determining cutting forces during orthogonal turning of C45 steel

Abstract

The authors present a method for determining cutting forces during orthogonal turning of C45 steel. The method utilizes Oxley’s chip formation model as well as Johnson-Cook (J-C) constitutive equation and is based on the assumption that the tool is perfectly sharp and the chip formation process is continuous. It is also assumed that the heat exchange between the workpiece, the tool and the chip is carried out by conduction with negligibly small loses caused by convection and radiation and that the thickness of the chip contacting the rake face is constant. The adoption of the above assumptions, together with the knowledge of cutting parameters (including the tool rake angle) as well as of material constants of J-C equation, allows to estimate the thermal-mechanical state of the cutting process and to determine feed and tangential components of the cutting force. Average values of feed and tangent components of the cutting force are calculated using an algorithm implemented in the Matlab environment. The method is based on iterative determination of the minimum difference between stress values in the secondary shear zone. Considered tangential and normal stress values are expressed by formulas based on Oxley's cutting mechanics and the J-C model. The cutting force components obtained in the described method have been compared with the results obtained during experimental studies and with the results obtained in computer simulations using the FEM numerical calculation method.