A mathematical model of machining chatter has been developed through an analytical approach in order to predict dynamic cutting force from steady-state cutting tests. The model is derived from a pseudo-static geometric configuration of the cutting process by taking into account the fact that the mean friction coefficient fluctuates dynamically responding to variation of the relative speed on the chip-tool interface. The force functions through this derivation can be used to explain all three basic mechanics associated with chatter vibration, namely, velocity dependent, regenerative, and mode coupling effects.

The dynamics of a cutting process are very complex in nature. It involves not only the changes of plastic state in the intensive deformation zone but also the elastic behavior of work material surrounding the deformation zone, especially in the vicinity of the tool nose region. These changes are induced by the inner and outer modulations of the uncut chip thickness during the process and at the same time govern the variation of the cutting force. Based on these causal relationships, the transfer function between the vibration variables and the dynamic force components for a single degree-of-freedom machining system has been developed. The characterization of the mechanics of the cutting process by the new model provides more insight into the physics of the cutting dynamics. The model has been tested through computer simulation for both orthogonal wave-generating and wave-removing processes. By reference to existing experimental evidence, the theoretical predictions show a very good agreement with the test results.

Residual stress remaining in machined parts can be detrimental. Previous experimental evidence shows that hardness has a significant effect on its formation. Yet, no satisfactory explanation is available for the causes of such a phenomenon. This work seeks to understand the mechanism of residual stress formation and explain the effect of hardness on it. The analysis is based on the existence of several measurable factors that influence the stress field in the work-material during the cutting process. The sensitivity of these factors to hardness allows establishment of relationships between the hardness and the material loading cycle. The results of the analysis indicate that the residual stress pattern is correlated most strongly to the orientation of the primary deformation zone in metal cutting. This correlation provides a good explanation for the role of the material hardness on the residual stress formation.

The dynamic force model developed in the preceding paper [1] is further examined. The analysis shows a successful prediction of the forms of stability boundary over a wide range of cutting speed. It reveals that the cutting force acting on tool rake face controls the high-speed stability, while the ploughing force acting on tool nose region dominates the low-speed stability. A series of cutting tests were carried out to examine the validity of the model. The result shows a fairly good agreement between the theoretical prediction of stability limit and the experimental determination of critical width of cut when the cutting conditions are properly chosen to avoid the presence of built-up-edge on tool tip.

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