Tool length-dependent stability surfaces

This article describes the development of three-dimensional stability surfaces, or maps, that combine the traditional dependence of allowable (chatter-free) chip width on spindle speed with the inherent dependence on tool overhang length, due to the corresponding changes in the system dynamics with overhang. The tool point frequency response, which is required as input to existing stability lobe calculations, is determined analytically using Receptance Coupling Substructure Analysis (RCSA). In this method, a model of the tool, which includes overhang length as a variable, is coupled to an experimental measurement of the holder/ spindle substructure through empirical connection parameters. The assembly frequency response at the tool point can then be predicted for variations in tool overhang length. Using the graphs developed in this study, the technique of tool tuning, described previously in the literature, can then be carried out to select a tool overhang length for maximized material removal rate. Experimental results for both frequency response predictions and milling stability are presented.