Abstract
This work considers analysis of sustained impacting cycles of rotating shafts with potentially many disks. The insight that this is an internal resonance phenomena makes this an ideal system to be studied with the method of normal forms. However, the presence of arbitrary non smooth nonlinearities due to impact and rub mean that the method must be extended by incorporating an Alternating Frequency/Time (AFT) step to capture nonlinear forces. The process results in an elegant formulation that can model a very wide variety of rotor systems and is demonstrated by comparing against simulation of a contacting overhung rotor.
Highlights
Contact between rotating machinery and surrounding stators is an issue that can effect a wide variety of engineered systems, from pumps to turbines and drilling rigs
Recent work by the authors identified that sustained bouncing cycles can be seen as an internal resonance that is identifiable in the rotating coordinate system [5], unlike the phenomena in [4], which are explained in the stationary frame
The systems under consideration have the following form in a coordinate system that rotates with the shaft: Mq + ΩGq + Kq + Cq + Kcq + nq(q, q ) = b (1)
Summary
Contact between rotating machinery and surrounding stators is an issue that can effect a wide variety of engineered systems, from pumps to turbines and drilling rigs. Recent work by the authors identified that sustained bouncing cycles can be seen as an internal resonance that is identifiable in the rotating coordinate system [5], unlike the phenomena in [4], which are explained in the stationary frame. After transformation into complex modal rotating system coordinates, and the normal forms transformation, the system typically becomes represented by just two complex modal amplitudes, which are solved with two transformed harmonic balance equations. This is a very powerful and elegant method to reduce nonlinear problems in rotating shafts that can potentially handle large problems with complex nonlinearities
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