Thermal modeling of the metal cutting process: Part I — Temperature rise distribution due to shear plane heat source

The model of an oblique band heat source moving in the direction of cutting, first introduced by Hahn (Proceedings of First U.S. National Congress of Applied Mechanics 1951. p. 661–6) for an infinite medium in 1951 and subsequently modified by Chao and Trigger (Transactions of ASME 1953;75:109–20) in 1953 for a semi-infinite medium, is extended in this investigation by including appropriate image heat sources. It is used for the determination of the temperature rise distribution in the chip and the work material near the shear plane caused by the main shear plane heat source in orthogonal machining of a continuous chip. A new approach is taken in that the analysis is made in two separate parts, namely, the workmaterial side and the chip side of the shear plane and then combined. The workmaterial (or the chip) is extended past the shear plane as an imaginary region for continuity to determine the temperature distribution in the workmaterial (or the chip) near the shear plane. The imaginary regions are the regions either of the workmaterial that was cut by the cutting tool prior to this instance and became the chip or will be cut by the cutting tool prior to becoming the chip. An appropriate image heat source with the same intensity as the shear plane heat source is considered for each case. The temperature distributions in the chip and the workmaterial were determined separately by this method and combined to obtain isotherms of the total temperature distribution (and not merely the average temperatures). It appears that the significance of Hahnʹs ingenious idea and his general solution have not been fully appreciated; instead, an approximate approach involving heat partition between the chip and the work was frequently used (Trigger and Chao. Transactions of ASME 1951;73:57–68; Loewen and Shaw. Transactions of ASME 1954;71:217–31; Leone. Transactions of ASME 1954;76:121–5; Nakayama. Bulletin of the Faculty of Engineering National University of Yokohama, Yokohama, Japan, 1956;21:1–5; Boothroyd. Proceedings of the Institution of Mechanical Engineers (Lon) 1963;177(29):789–810). It may be noted that in utilizing Hahnʹs modified solution, it is not necessary to make an explicit a priori assumption regarding partitioning of heat between the workmaterial and the chip, as was common in most prior work. Instead, this information is provided as part of the solution. The results obtained with the exact analysis were compared with other methods using the experimental data available in the literature to point out some of the discrepancies in the simplified models. It may be pointed out that these models assume the temperature rise at the chip–tool interface to be nearly uniform and equals the average temperature rise in this volume. A comparison of the calculated temperature rise by these methods with the exact analysis indicates that the differences can be quite significant (∼50% or higher). It is hoped that future researchers would recognize the significance and the versatility of the exact analysis in determining the temperature distribution in the shear zone in metal cutting.