Prediction of sticking and sliding lengths on the rake faces of tools using cutting forces

The algebraic relationships between friction force F and normal force N on the rake face of a tool, and between average stress distributions q(F) and q(N) are derived for an assumed power law stress distribution of the normal contact pressure p between chip and rake face, i.e. for p=p(o)(x/L)(n), as used by Zorev, where x is measured towards the tip of the tool from an origin at the end of the contact region of length L, and P-o is the maximum pressure at the cutting edge. The derived expressions suggest a novel method of determining quantitatively the lengths s of stuck regions on the rake face, and unstuck lengths (L-s), just from the cutting forces without the use of special devices such as split tooling. Calculations for the variations of (s/L) and mu(apparent)=q(F)/q(N) with uncut chip thickness t automatically give the variation in values of P-o and n. The theory is tested using experimental cutting force data in the literature from a wide range of materials in different thermomechanical states and the predictions are compared with independent data. It is demonstrated that the usually-illustrated version of the Zorev pressure distribution where the contact pressure rises 'exponentially' to the cutting edge (i.e. where n > 1) applies only when (s/L) is less than about 0.5. When the sticking length s is a larger proportion of L, n < 1 giving the experimentally known different type of pressure distribution that levels out towards the cutting edge. Theory and experiments show that q(F) plots non-linearly against q(N) for all combinations of uncut chip thickness t and rake face contact length L. The plot emanates from the origin with an initial slope of mu(Coulomb). As soon as the sticking length s begins to increase, the slope diminishes and when (s/L)=1 at complete sticking, the local slope of the q(F) vs q(N) is zero. Increasing (s/L) corresponds to a reduction in (L/t) that may be achieved using restricted contact tools, but even in full-face cutting where L=L-ff there is some sticking near the cutting edge at the largest (L-ff/t). Plots of friction force F vs normal force N along the rake face are also predicted to be non-linear and emanate from the origin with slope mu(Coulomb). While some experimental results display this shape, most F vs N experimental data for full-face cutting follow linear F=F-o+pi N' relations (having high correlation coefficients). It is shown that such linear plots with intercepts are tangents to the more general non-linear relations, and are caused by the relatively small range of q(F) and q(N) encountered in full-face cutting which is caused by the interplay between rates of increase of cutting forces as t increases, and rates of change of L-ff/t with increasing t. How (slap. and n may be determined from such plots without knowledge of mu(coulomb) is explained and calculations from experiments are made. The loads expected to be measured by split tools having a Zorev contact pressure distribution are also predicted and compare favourably with experiment. (C) 2014 Elsevier Ltd. All rights reserved.