Quasi steady-state conditions for transient vibration of a Jeffcott rotor during acceleration

Since flexible rotor systems normally operate above their first several critical speeds, much attention is paid to transient vibration problems resulting from their passing through critical speeds during acceleration in order to reach their operating speed. When an unbalanced Jeffcott rotor system accelerates passing through its critical speeds, it will have transient vibration caused by the imbalance-induced harmonic excitation whose frequency changes as the rotating speed. In this paper, this vibration under constant acceleration is solved by using the analytic method; moreover, with varying rotating speed discretized, a series of its general responses with the harmonic excitation whose frequency is one of all the discretized constant rotating speeds are applied to represent approximately its transient vibration in each time step. Comparing numerical simulations of these two methods, appropriate qualitative conditions known as the quasi steady-state conditions for transient vibration of this rotor are established under which the analytic solution can be replaced by the results from the approximate method. Through searching the quasi steady-state conditions, what are special requirements can be found in order for one to use continuous active balancing operations with a sequence of finite constant rotating speeds to perform active balancing of a rotor during acceleration.