An improved tool–holder model for RCSA tool-point frequency response prediction

In addition to the precise kinematic motions of the machine tools and spindles, machining accurate parts necessitates controlling the dynamic behavior of the tool tip with respect to the workpiece. High-fidelity models of tool-tip dynamics can be used to select operating parameters that improve the accuracy by reducing the effect of vibrations. To effectively model the tool-tip dynamics for arbitrary tool-and-holder combinations using the receptance coupling substructure analysis (RCSA) technique, highly accurate and numerically efficient models of the tool–holder dynamics are needed. In this paper, we present a tool–holder model that incorporates a spectral-Tchebychev technique with the Timoshenko beam equation to obtain a completely parameterized solution. Comparison of the tool–holder model to a three-dimensional finite elements solution shows that the dynamic behavior is captured with sufficient accuracy. The tool–holder model is then coupled with the experimentally determined spindle–machine dynamics through RCSA to realize a model of the tool-tip dynamics. The coupled model is validated through experiments for three different tool overhang lengths. The presented technique can be used to predict the tool-tip dynamics for different tool-and-holder combinations and for optimization studies without the need for extensive experimentation.