Self-synchronization of transient rotations in multiple shaft systems

self-synchronization of shafts is a well-known nonlinear phenomenon, whereby two (or more) unbalanced shafts on a common movable structure may rotate synchronously due to interaction via structural vibrations only, even in the absence of any direct kinematic coupling. The phenomenon had been studied extensively by asymptotic methods to predict possible (multiple) steady-state rotational motions and to evaluate their stability-mostly with application to the design of vibrators with a reduced number of driving motors. Certain cases of undesirable shaft self-synchronization in engineering had also been studied, but only steady-state motions were analyzed. This paper presents results of numerical simulation for transient self-synchronization of rotating shafts, one potential application being gas turbine engines with multiple shafts. While the shafts' design rotation speeds are usually different, they may "cross over" in transient motions-such as during coastdown of one of the shafts in an emergency situation (e.g., due to loss of a blade). But even if a stable steady-state synchronous rotation is possible at this rotation speed, it may not necessarily be implemented. Depending on their relative acceleration (or deceleration) rate, the shafts may either become captured (tangled) in a steady-state synchronous rotation or pass it. The case of two shafts on a rigid translating foundation with relatively soft suspension springs is considered, with one of these shafts rotating with a constant speed as governed by a given torque-speed characteristic of the motor and the other one coasting down from the higher original speed. A parametric study is made for the passage/capture threshold for this pair of shafts.