Int. I. Mach. Tools Manufact. Vol. 27. No. 3. pp. 357-365, 1987. Printed in Great Britain 11891~6tt55tS753.tXl + .IKI Pcrgaraon Journals Ltd. A SIMPLE PREDICTIVE MODEL OF ORTHOGONAL METAL CU'ITING I. YELLOWLEY* Received 3 September 1986) NOMENCLATURE 0.4 ° [3s ° ~,° F~ F~ F~ ho h~ K KB KB~ L W apparent angle of friction on tool rake face (°) angle of friction in elastic contact zone on tool rake face (°) rake angle (°) angle between simple shear plane and cutting velocity vector (°) power consuming component of tool force in orthogonal cutting (N) normal component of force acting upon elastic region of rake face contact (N) thrust component of tool force, (perpendicular to F~.), in orthogonal cutting (N) undeformed chip thickness (mm) deformed chip thickness (ram) shear yield stress of work material (N/mm 2) length of plastic contact between chip and tool (mm) length of sliding contact between chip and tool (mm) length of straight portion of initial boundary (ram) width of cut, assumed unity in most of the analysis (mm) 1. INTRODUCTION THE MECHANICS of orthogonal metal cutting have consumed what would seem an inordinate amount of research effort. Several types of approach have been taken to the problem most notably the following: (a) Minimum energy [1]. (b) Slip line field analysis [2-5]. (c) Boundary equilibrium [6-7]. Despite the effort expended it would appear that there is still a lack of simple models which allow the prediction of the influence of machining conditions on the practical parameters, i.e. tool forces, chip-tool contact length, energies and hence the tool temperature. The purpose of this paper is the extension of a previous boundary equilibrium model through the consideration of chip moment. The model to be used has been previously described for a zero rake angle and varying extents of work- hardening [7]; it includes the elastic components of the tool rake face force, which have been shown in previous work [8], to exert considerable influence on the process. Since the model has been described in detail earlier only a brief recapitulation is given in the following section. In the analysis which follows it is assumed that the work material exhibits negligible work-hardening. 2. A SIMPLE FORCE EQUILIBRIUM MODEL OF ORTHOGONAL CUTTING AND ITS EXTENSION TO INCLUDE MOMENT EQUILIBRIUM The model (see Fig. 1) assumes that the rake face may be divided into two zones; in the first zone (AB), there is plastic contact with close-to-sticking friction prevailing; in the second (BC), elastic sliding with an average friction angle (13s) is assumed. The boundary taken across the primary deformation zone (DEFA), is taken to be a direction of maximum shear stress, meeting the free surface at "rr/4 and being parallel to the simple shear plane between E and F, then curving to meet the rake face at A at ~r/2. The line BF represents, for force equilibrium purposes, the boundary of the secondary *Department of Mechanical Engineering, McMaster University, Hamilton, Ontario, Canada, LSS 4L8. 357