Analytical predictions and experimental validation of cutting force ratio, chip thickness, and chip back-flow angle in restricted contact machining using the universal slip-line model

This paper presents analytical predictions and experimental validation of a recently developed universal slip-line model for machining with restricted contact cut-away tools. Three important machining parameters, i.e. the cutting force ratio, chip thickness, and chip back-flow angle, are predicted on the basis of: (1) the universal slip-line model; (2) a maximum value principle for determining the state of stresses in the plastic region in restricted contact machining; (3) Dewhurst and Collins' matrix technique for numerically solving slip-line problems; and (4) Powell's algorithm for non-linear optimizations. All predictions are based on purely theoretical calculations with no experimental/empirical data as input. The extensive comparisons between theory and experiments show a reasonable agreement. Major new research findings from this study include: (1) the applicable ranges of an extreme friction slip-line model and of Johnson's and Usui and Hoshi's slip-line models; and (2) the general rule of the variation of tool-chip friction conditions. Tool-chip contact in machining with restricted contact cut-away tools is categorized into three broad cases. A theoretical method is also presented in the paper to distinguish different tool-chip contact cases in practical machining situations.