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

Abstract This paper re-evaluates the known velocity relationships expressed in the form of a velocity diagram in orthogonal metal cutting, arguing that the metal cutting process be considered as cyclic and consisting of three distinctive stages. The velocity diagrams for the second and third stages of a chip-formation cycle are discussed. The fundamentals of the mechanics of orthogonal cutting, which are the upper-bound theorem applied to orthogonal cutting and the real virtual work equation, are re-evaluated using the proposed velocity diagram and corrected relationships are proposed. To prove the theoretical results, the equation for displacements in the deformation zone is derived using the proposed velocity relationships. To prove that the displacements in the deformation zone follow the derived equation and that this zone consists of two unequal parts, a metallographical study of chip structures has been carried out. To estimate the variation of stress and strain in the deformation zone quantitatively, a microhardness scanning test was conducted. Because it is proved that the chip formation process is cyclic, its frequency 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 from the measuring signal, and when this signal is then properly processed, the amplitude of the peak at the frequency of chip formation is the largest in the corresponding autospectra.

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