A Note Concerning the Inadmissibility of Applying the Minimum Work Principle to Metal Cutting

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Abstract
In his formulation of a mathematical model of the orthogonal cutting process, Merchant [1] assumed that the workpiece material is sheared as it approaches a plane extending ahead of the tool from the cutting edge to the free surface of the workpiece. In addition, he proposed the hypothesis that this plane would assume such an inclination as would ensure that the work performed in the cutting process would be a minimum. Deductions from this hypothesis were found to be at variance with experimental observation and on this basis its validity has been questioned but it has never been disproved up to now. In the present work it is shown that the minimum work hypothesis leads to a condition which cannot be fulfilled physically. Further, it is shown that the less demanding hypothesis that the shear plane inclination is such as to ensure that the least work is dissipated in metal cutting is likewise at variance with empirical observation. Accordingly, it is concluded that the minimum work hypothesis is inapplicable to metal cutting.

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