Vibration of a Spinning Rotationally Periodic Rotor

This paper studies the vibrations of a spinning, rotationally periodic (also known as cyclic symmetric) rotor through theoretical analysis and experimental studies. The theoretical analysis consists of two parts. The first part is Fourier analysis of mode shapes of a stationary rotor with periodicity N. A periodic mapping of the n-th mode shape shows that its k-th Fourier coefficient is generally zero, except when k ± n is an integer multiple of N. The second part is to apply the derived mode shapes through a unified algorithm developed by Shen and Kim [1] to predict primary and secondary resonances of spinning, rotationally periodic rotors. The experimental study focuses on vibration measurements of a spinning disk carrying 4 pairs of evenly spaced brackets mounted on a high-speed air-bearing spindle. Initially, experimentally measured waterfall plots do not agree well with those from theoretical predictions. Further numerical studies show that mistune of rotationally periodic rotors could substantially change their waterfall plots. After the mistune is modeled, experimental and theoretical results agree very well with a difference of only 0.8% in natural frequencies observed in the ground-based coordinates.