Generalized method for the analysis of bending, torsional and axial receptances of tool-holder-spindle assembly

Existing researches for the prediction of tool point receptances have focused on developing dedicated methods for cutting tools used in each single cutting operation such as milling and drilling processes. This paper presents a generalized method for the analysis of the tool point receptances of cutting tools suitable for being mounted on a rotating spindle. Translational and rotational dynamic responses related to all axes (X, Y and Z) are simultaneously modeled in a unified way to predict the tool point bending, torsional and axial receptances of all kinds of rotating tools, such as milling, drilling and boring cutters. To facilitate modeling, the tool-holder-spindle assembly is divided into four substructures, i.e., spindle-holder subassembly, shank of tool, fluted part of tool and tool-holder joint interface. The fluted part of tool is modeled as a three-dimensional Timoshenko beam with varying cross-section, while the tool-holder joint interface is regarded as a zero-thickness distributed layer and modeled as a joint substructure composed of a set of independent spring-damper elements. Assembling criterion is derived to couple the dynamic responses of all substructures to calculate the tool point receptances. Meanwhile, compared with past experimental means, a measurement procedure to eliminate the adapter's mass effect on torsional and axial receptances is designed. The proposed method is experimentally proven for two kinds of rotating tools, i.e., mills and drills.