The Analytical Imbalance Response of Jeffcott Rotor During Acceleration

The characteristics of the transition vibration of a rotor system when it passes its critical speeds during acceleration are of great interest for active vibration control, active real-time balancing @1#, and rotor design. In the past, a few analyses @2‐8# have dealt with speed varying transient rotor dynamics. These researchers used numerical integration techniques to calculate numerical solutions to the transient dynamic model. Although these models can be used to predict the transient vibration for a complicated rotor system, it remains hard to obtain the quantitative characteristics of the transient vibration. Lewis @9# and Dimentberg @10# presented an analytical solution of the problem of running a rotor system through its critical speeds at a uniform acceleration. The basic characteristic of the ‘‘envelope’’ ~amplitude! of the transient vibration was studied by an approximation method. In this paper, their work is extended. An analytical expression of the motion of the geometric center of a simple Jeffcott rotor is derived. The exact ‘‘envelope’’ and ‘‘phase’’ of the transient vibration are presented. As stated in Dimentberg @10#, it is found that the transient vibration through critical speeds consists of free vibration and synchronous vibration. Explicit expressions of these two components are presented in this paper.