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

Abstract

In this paper, the modi ed couple stress theory is used to capture size e ect on dynamic behavior of a micro-drill subjected to an axial load and a concentrated mass, which is attached to its free end. Governing equations of lateral vibrations of the system and associated boundary conditions were derived by rst, obtaining the total kinetic and potential energy of the system and then, using Hamilton's principle. The Assumed Modes method was applied for transforming the governing partial di erential equations into a set of in nite ordinary di erential equations. Considering two terms of the equations, the rst two natural frequencies and instability rotational speeds of the micro-drill system were determined semi-analytically. Finally, numerical results of natural frequencies and the threshold of instability speeds of the system were derived with respect to di erent values of the system parameters such as rotational speed, axial load, rotor length, concentrated mass, and material length scale. The results showed that the material length scale parameter was extremely e ective on natural frequencies and the threshold of instability speeds of the micro-drill.

Vibration Behavior of Misaligned Rotor with the Asymmetric Shaft Using Theory of Timoshenko Beam

“…The responses showed that the super-synchronous component in the frequency of 2X is important to identify and diagnose misalignment of the rotor. Rahi [27] used the improved couple stress theory to see the size effect on dynamic response in a micro drill that is under the effect of a mounted mass at its free end.…”