Preliminary design and numerical verification of a coaxial tuned mass damper integrated into a tool holder for CNC milling chatter mitigation

This study presents the preliminary design and numerical verification of a coaxial ring-type tuned mass damper (TMD) integrated into a BT40-ER32 tool holder to mitigate chatter in CNC milling. A uniform hollow shaft was used to validate Euler-Bernoulli beam theory against ANSYS finite element analysis and MATLAB dynamic simulation. The first bending frequency was 249.69 Hz analytically and 241.89 Hz numerically, corresponding to a 3.12% deviation, while mesh-convergence variation remained below 0.02%. The target mode was reduced to an equivalent single-degree-of-freedom system, and the designed TMD had a mass of 0.0162 kg, stiffness of 41,128.78 N/m, and damping coefficient of 5.895 N•s/m. The model predicted a 57.3% reduction in peak receptance and a 3.88-fold increase in normalized stability limit.