An optimal design of micro-drill from the aspect of vibration analysis
This paper presents an approach to optimize the structure of a micro-drill for reducing its lateral vibration, which has a strong effect on the quality of drilled holes during the cutting process. The micro-drill and the spindle of a micro-drilling spindle system are modeled as Timoshenko’s beam elements. Each element with five degrees of freedom at each node comprehensively includes the effects of continuous mass eccentricity, shear deformation, gyroscopic moments, rotational inertia with external thrust force and torque, and coupling torsional and lateral effect. The finite element method is used to determine the lateral amplitude response at the micro-drill point, which is considering the objective function during the optimization of the micro-drill by the interior-point approach. The diameters and the lengths of drill segments are chosen as the design variables with nonlinear constraints in the constant mass, mass center location, and torsional deformation of the drill. The in-house finite element code-integrated optimization environment is implemented in MATLAB to solve the optimal problem. The results showed that compared with the original micro-drill, the lateral amplitude response at the drill point of the optimal one is reduced by 91.89% at an operating speed of 50 000 rounds per minute (r/min), and its first critical speed and the corresponding amplitude response exceed those of the original one.