Nonlinear Free Vibration Analysis in Micro-Rotating Systems

Abstract

Rotating machinery with flexible shafts finds application across a broad spectrum, ranging from everyday household appliances to heavy-duty industrial setups. These machines harness substantial rotational energy, which in turn induces vibrations. In step with industrial progress, modern devices are becoming smart, intelligent, and compact, with the help of microscopic devices known as Micro-Electro-Mechanical Systems (MEMS), incorporating electrical and moving mechanical parts. One noteworthy category within MEMS is Power MEMS. Operating at speeds exceeding a million revolutions per minute, these systems are employed in compact energy supply solutions for small-scale electronics, diminutive ground robots and unmanned airborne vehicles, all of which demand efficient power sources. This paper addresses the rotor dynamics associated with micro-rotating systems. The intricate dynamics and nonlinear issues witnessed in macro-scale systems are equally relevant to these tiny systems. This is why recognizing the traits and behavior of these small-scale systems and analyzing their dynamic actions within the operational context becomes a fundamental topic that influences design, control, maintenance, and safety considerations. Incorporating low friction bearings and rotor dynamics into mathematical formulation yields results that are nearly perfect models. Therefore, this study aims to conduct a comprehensive nonlinear analysis of the micro-rotor, considering the nonlinearity arising from the substantial deformation of the shaft. The influence of small-scale effects, which hold significance at the micron scale, is addressed utilizing modified couple stress theory. The study employs the Euler–Bernoulli beam theory while accounting for the axial stretching effect under conditions of significant deformation. The dynamics of the rotor, including essential parameters like spin speed, disk placement, and size dependency, are thoroughly investigated through a comprehensive parametric study presented in this work.