Prediction of Shear Angle in Oblique Cutting with Maximum Shear Stress and Minimum Energy Principles

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Abstract
A new shear angle prediction theory is proposed for oblique cutting operations. Oblique cutting mechanics are described by two components of shear angle, two angles defining direction of resultant cutting force, and chip flow angle. The five unknown parameters describe the geometry of chip deformation, velocities and forces in oblique cutting. When combined with the material dependent shear stress and average chip—rake face friction coefficient, cutting forces in three Cartesian directions can be predicted. In this paper, the mechanics of oblique cutting are described by five expressions. Three of the expressions are derived from the kinematics of oblique cutting, and the remaining two are derived either by applying Maximum Shear Stress or Minimum Energy Principle on the process. Unlike the previous solutions, the proposed methods do not require any intuitive or empirical assumptions, but use only the material properties, tool geometry and the physical laws of deformation. The oblique cutting parameters and forces predicted by the proposed models agree well with the empirical and experimental results reported in the classical cutting literature. The proposed models are experimentally verified in predicting forces in helical end milling which has oblique cutting mechanics.

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