Analysis of stationary displacement patterns in rotating machinery subject to local harmonic excitation

Rotor vibration and stationary displacement patterns observed in rotating machineries subject to local harmonic excitation are analysed for improved understanding and dynamic characterization. The analysis stresses the importance of coordinate transformation between rotating and stationary frame of reference for accurate results and estimation of dynamic properties. A generic method which can be used for various rotor applications such as machine tool spindle and turbo machinery vibration is presented. The phenomenon shares similarities with stationary waves in rotating disks though focuses on vibration in shafts. The paper further proposes a graphical tool, the displacement map, which can be used for selection of stable rotational speed for rotating machinery. The results are validated through simulation of dynamic response of a milling cutter, which is a typical example of a variable speed rotor operating under different load conditions.