An the real machining operations are of non-free-cutting, which is cha
racterized by the interference of the chip ejections from different se
gments of the cutting edges. The rapid advancing of modern cutting tec
hnology makes the non-free-cutting processes even more complex. Powerf
ul theories are badly needed for explaining, understanding and predict
ing the intricate phenomena arising in non-free-cutting operations. In
the paper, a ''Hypothesis of Minimum Energy'' is suggested based on t
he results of experiments. In the light of the hypothesis, the natural
chip ejection vector of a free-oblique-cutting tool and the interfere
nce and compromise among chip ejections upon non-free-cutting were mat
hematically modeled. The model is capable of predicting the ejection v
elocity and direction of the common chip as an integrity, the chip def
ormation and the cutting force of a non-free-cutting process. Good agr
eements between predictions and experiments were identified. The crite
ria for realizing free cutting and for chip splitting are also present
ed and discussed in this paper.