A new approach is introduced to model 3-D turning operations that are used for the stability analysis of long slender bars. This approach utilizes the unique relationship between externally created feed direction tool displacements (input) and the resultant thrust direction workpiece vibrations (output) to estimate stability limits in three-dimensional turning operations from the data of a single dynamic cutting test. In this paper, this unique relationship is referred to as the “Unified Transfer Function ” (UTF) and its expressions are derived from conventional cutting and structural dynamics transfer functions. For the stability analysis, the uncut chip area variations of oblique cutting are represented by a linear model having different coefficients at different depths of cuts. These coefficients are found by using a tool geometry simulation program. An iterative procedure is developed for the stability analysis. The proposed approach considers in-process structural and cutting dynamics and can be automatically implemented without any input from the operator for the traverse turning of a long slender bar. Experimental studies have validated the proposed modeling and stability analysis techniques. The UTFs can also be used to monitor machine tool structure, tool wear, and the machinability of the material.

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