Analytical estimation of maximum amplitude during passage through resonance of a flexible rotor

Abstract

A rotor is a critical component in our modern-day lives and its applications range from heavy-duty industry to transportation and domestic applications. There are two different types of rotors. Rigid rotors operate below their critical speed and flexible rotors operate above at least one of its critical speeds. Flexible rotors possess critical speeds that may lead to large vibration amplitudes during run-up. The maximum radial displacement during passage through resonance is defined by the stiffness, mass and damping of the rotor and its bearings as well as the acceleration of the run-up characteristic. Higher resonance in flexible rotors is caused by low stiffness, rotordynamic and gyroscopic effects, limited damping, shaft support interactions and unbalance acting as an excitation source near critical speeds. The higher the acceleration, the lower the maximum displacement becomes. The underlying equations of motion of a Jeffcott rotor cannot be solved in closed form. An analytical approximation is derived for the maximum radial amplitude during passage through resonance. The derived formula is bench-marked against the exact numerical solution of a specific example. The error percentage between numerical values and analytical values from the derived expression lies below 7.1% for varying angular acceleration and below 13% for varying shaft stiffness, confirming the usefulness of the formula for a first design