A universal slip-line model with non-unique solutions for machining with curled chip formation and a restricted contact tool

A universal slip-line model and the corresponding hodograph for two-dimensi onal machining which can account for chip curl and chip back-flow when mach ining with a restricted contact tool are presented in this paper, Six major slip-line models previously developed for machining are briefly reviewed. It is shown that all the six models are special cases of the universal slip -line model presented in this paper. Dewhurst and Collins's matrix techniqu e for numerically solving slip-line problems is employed in the mathematica l modeling of the universal slip-line field. A key equation is given to det ermine the shape of the initial slip-line. A non-unique solution for machin ing processes when using restricted contact tools is obtained. The influenc e of four major input parameters, i.e. (a) hydrostatic pressure (P-A) at a point on the intersection line of the shear plane and the work surface to b e machined; (b) ratio of the frictional shear stress on the tool rake face to the material shear yield stress (tau /k); (c) ratio of the undeformed ch ip thickness to the length of the tool land (t(1)/h); and (d) tool primary rake angle (gamma (1)), upon five major output parameters, i.e. (a) four sl ip-line field angles (theta, eta (1), eta (2), psi); (b) non-dimensionalize d cutting forces (F-c/kt(1)w and F-t/kt(1)w); (c) chip thickness (t(2)); (d ) chip up-curl radius (R-u); and (e) chip back-flow angle (eta (b)), is the oretically established. The issue of the "built-up-edge" produced under cer tain conditions in machining processes is also studied. It is hoped that th e research work of this paper will help in the understanding of the nature and the basic characteristics of machining processes. (C) 2000 Elsevier Sci ence Ltd. All rights reserved.