Dynamic analysis of a micro drilling system by the modified transfer matrix method

Normally, breakage is the main cause of failure of a micro drilling system, of which coupling effect of lateral and torsional displacements plays the most important role. This research developed a modified transfer matrix method to investigate the dynamics of a micro drilling system focusing on displacements induced by not only lateral, shear, torsional deformations, but also the coupling effect between lateral and torsional vibrations. The micro drilling system is modeled as pre-twisted rotating Timoshenko beam elements with a continuous-system concept. Each element includes components of linear bearings, axial drilling force, gyroscopic moments, and eccentricity. The overall transfer matrix of the system is developed to determine the state vector of the system including displacements and forces. Finally, a numerical example was presented, where the lateral and torsional displacements and critical speed of the micro drilling system at the micro drill's tip were presented.