Coupled lateral and torsional vibrations of the micro-drilling spindle systems

In this research, the coupled lateral and torsional micro-drilling spindle system was analyzed by the finite element method (FEM). The Timoshenko beam finite element with five degrees of freedom at each node is applied to perform dynamic analysis of the system containing cylinder, conical symmetric elements, and flute asymmetric elements. The three-dimensional flute of the Union MDS drill with 0.1 mm diameter is defined by specifying the Cartesian coordinates of the specific points. In addition, the system model comprehensively includes the effects of continuous mass eccentricity, shear deformation, gyroscopic moments, and rotational inertia with external thrust force and torque during machining. In particular, the consideration of continuous mass eccentricity gives a more realistic model for system investigation. The Hamilton’s equations of the system involving both symmetric and asymmetric elements were established and utilized to find shape functions of each element. The transient and steady-state lateral and torsional responses of drill point were estimated by Newmark’s method. Simulation studies were attentively conducted to investigate the coupled lateral and torsional effect on the system vibration behavior. The results show that during design stage, the coupled lateral and torsional vibration associated with the above external forces should be considered carefully to prevent unexpected damage to the spindle system.