Re-evaluation of the basic mechanics of orthogonal metal cutting: velocitydiagram, virtual work equation and upper-bound theorem

This paper re-evaluates the known velocity relationships expressed in the f orm of a velocity diagram in orthogonal metal cutting, arguing that the met al cutting process be considered as cyclic and consisting of three distinct ive stages. The velocity diagrams for the second and third stages of a chip -formation cycle are discussed. The fundamentals of the mechanics of orthog onal cutting, which are the upper-bound theorem applied to orthogonal cutti ng and the real virtual work equation, are re-evaluated using the proposed velocity diagram and corrected relationships are proposed. To prove the the oretical results, the equation for displacements in the deformation zone is derived using the proposed velocity relationships, To prove that the displ acements in the deformation zone follow the derived equation and that this zone consists of two unequal parts, a metallographical study of chip struct ures has been carried out. To estimate the variation of stress and strain i n the deformation zone quantitatively, a microhardness scanning test was co nducted. Because it is proved that the chip formation process is cyclic, its frequen cy is studied. It is shown that when the noise due to various inaccuracies in the machining system is eliminated from the system response and thus fro m the measuring signal, and when this signal is then properly processed, th e amplitude of the peak at the frequency of chip formation is the largest i n the corresponding autospectra. (C) 2001 Elsevier Science Ltd. All rights reserved.