Size Effect Investigation on Lateral Vibrations of a Micro Drill Subjected to an Axial Load Using the Modified Couple Stress Theory

In this paper, the modified couple stress theory is used to capture size effect on dynamic behavior in a micro drill subjected to an axial load and a concentrated mass which is attached at its free end. Governing equations of lateral vibrations of the system and also associated boundary conditions are derived by obtaining the total kinetic and potential energies of the system and then using Hamilton’s principle. The Assumed Modes method has been applied to transform the governing partial differential equations into a set of infinite ordinary differential equations. Considering two terms of the equations, first two natural frequencies and also instability rotational speeds of the micro drill system are determined semi-analytically. Finally, numerical results of natural frequencies and also the threshold of instability speeds of the system are presented with respect to different values of the system parameters such as rotational speed, axial load, rotor length, concentrated mass, and also material length scale. The results show that the material length scale parameter is extremely effective on natural frequencies and also the threshold of instability speeds of the micro drill.