It has been realised that the analytical model of 3-D chip curling plays a central role in the chip formation that would predict the chip forms/shapes efficiently for the aim of chip control. The purpose of the two-part paper is to investigate and model the 3-D chip curling processes in theory. In part I, an analytical modelling procedure is described in detail and a general mathematical model for predicting chip forms/shapes in 3-D cutting processes with complex chip breaker tools is presented onthe basis of three basic chip curling patterns, i.e. up-curl, side-curl and twisting. In part II, the theoretical analysis and discussion have been done systematically based on the model presented. Therefore a group of criterions for the effects of threechip angular velocity componentsω{sub}x,ω{sub}y,ω{sub}z and chip flow angleη{sub}0 on the chip forms/shapes is derived. The varying tendency of the chip radius and chip pitch with varying ω{sub}x,ω{sub}y,ω{sub}z and η{sub}0 is discussed based onthe group of criterions. For better understanding, a group of 3-D diagrams is given to visualize the varying tendency of chip geometry. The 3-D analytical model and the group of criterions presented in part I and part II of the paper reveal new insightsin to the nature of chip curling in 3-D machining in theory and are significant for the analytical prediction of the chip curling and the chip breaking, as well as the geometric design of the chip breaker/groove.
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