A numerical modeling method for predicting chip form and power requirements in three-dimensional cutting processes is described. The method is based on variational (energy) results from the theory of rigid-plastic materials and is applicable to the steady-state cutting of ductile metals. The analysis involves mainly material behavior assumptions and for simple material models yield results similar to the widely-used minimum work approach. In Part I the theoretical basis of the method and the appropriate numerical algorithm (gradient search or steepest descent) for implementation in specific processes are described. Results for the oblique end turning and drilling processes are compared with experimental data in Part II.

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