| description abstract | The relationship between shaving and drawing or extension is discussed. For small reduction ratios, this relationship is evidenced by a transition from converging flow of the metal to shaving as the tool angle is increased. This transition is defined as the critical rake angle for shaving. An expression for the relative pressure required for orthogonal cutting is derived through the upper-bound approach. With this as a basis, an approximate upper-bound solution for shaving is obtained. This equation gives the relative stress or pressure required for shaving as a function of the process variables, both dependent and independent. The independent variables are rake angle (α), reduction ratio (R0 /Rf ), relative back stress (σzb /σ0 ), and friction factor (m). The dependent variables are defined as relative chip radius (r0 /t0 ), relative chip velocity (ωr0 /v0 ), and built-up edge angle (α1 ). Results of a computer minimization procedure for this equation are presented. In this technique, the required relative stress for shaving is determined through trial-and-error variation of the dependent variables for selected combinations of the independent variables. These results are used to predict the critical rake angle for shaving and the critical rake angle for disappearance of the built-up edge. Comparison with experimental results indicates that the prediction of the critical angle for shaving is useful. | |
