A Stability Solution for the Axial Contour-Turning Process

This paper presents an investigation of the stability variations in contour turning process. An equivalent chip-area formulation has been developed, and is used to model the dynamic machining forces. In order to establish a frequency domain solution for stability in the presence of geometric and structural variations along the tool path, the tool path is discretized into a finite number of portions, each of which possess constant geometric and structural properties. The stability solution developed here is capable of accommodating the effects of cutting conditions (axial and radial feed, depth of cut, and spindle speed), tooling geometry (lead angle and corner radius), workpiece geometry (contour tool path) and structural parameters (the mass, stiffness, damping ratio and orientation of the dominant mode). The stability solution is experimentally validated by machining a workpiece with a concave-convex contour combination. The solution has been applied to achieve productivity improvements via spindle speed regulation. A case study that includes contour turning of an aluminum wheel is also presented.@DOI: 10.1115/1.1480415# Recently, there has been attention given to the complexities of axial, radial, and combined axial-radial contour turning @1,2# driven in large part by the desire to machine complex part geometries via turning. In contour turning, workpiece geometric variations, and variations in depth of cut, feedrate, cutting velocity and effective lead angle, along the tool path produce large dynamic force variations, which induce variations in process stability. In order to increase productivity while maintaining part quality, an increased understanding and predictability of the stability phenomenon must be forthcoming. Since the 1950s, chatter phenomenon in machining has been investigated by several researchers. Chatter arises from the selfexcited vibrations through regeneration @3# and /or mode coupling @4# mechanisms, both of which depend on the interaction between the machining process and the machine-tool system structure. In regeneration, the tool encounters a wavy uncut work-surface left from the previous cut, and the interaction between the current and the previous wave patterns determines the stability. In mode coupling ~positional coupling!, two mutually perpendicular, closely coupled modes of the machine-tool system cause an elliptical motion of the tool-tip, which determines the stability. Graphical @5,6#, analytical @7‐11#, and numerical @12# solutions have been developed for the stability determination. More recent investigations have been geared towards including the effects of real process geometry parameters into the stability solution, including tool nose ~corner! radius @11,13‐16#, feedrate and lead angle @11,17#, and mode orientation @11,18#. The stability variations in contour turning are caused by 1! the variations of the mode orientation relative to the workpiece surface, 2! the changes in the modal parameters that arise from the workpiece ~provided that the dominant mode arises from the workpiece at one or more locations along the tool path!, and 3! the process-geometry variations. The process-geometry variations include the changes in the uncut chip geometry and effective tool angles @1#, both of which are determined by the changes in workpiece geometry along the tool path. These geometric variations cause the amount of regeneration and the cutting stiffness to change, and thus alter the stability behavior along the tool path. None of the above investigations have considered these stability variations in contour turning. While simple turning solutions may seem applicable, such schemes fail to predict the stability limit changes along the contour, and could result in local chatter zones leading to part rejection. This paper presents an investigation of the stability variations in contour turning. The dynamic chip-area variations are determined via an equivalent chip formulation, which is shown to accurately represent the actual chip area variations. The stability solution for the process is developed by discretizing the tool path into a finite number of smaller sections. The stability data is presented and experimentally verified for a workpiece with concave-convex contours. The reasons for the stability variations along the tool path are analyzed in more detail. Application of the stability solution for productivity improvement via changes in the cutting conditions is also discussed. A case study that includes contour turning of a wheel is also conducted.