Ground-Based Response of a Spinning, Cyclic Symmetric Rotor Assembled to a Flexible Stationary Housing Via Multiple Bearings

This paper is to study ground-based response of a spinning, cyclic symmetric rotor assembled to a flexible housing via multiple bearings. In particular, interaction of the spinning rotor and the flexible housing is manifested theoretically, numerically, and experimentally. In the theoretical analysis, we show that the interaction primarily appears in coupled rotor–bearing–housing modes whose response is dominated by the housing. Specifically, let a housing-dominant mode have natural frequency $ω(H)$ and the spin speed of the rotor to be ω₃. In rotor-based coordinates, response of the spinning rotor for the housing-dominant mode will possess frequency splits $ω(H)±ω3$⁠. In ground-based coordinates, response of the spinning rotor will possess alternative frequency splits $ω(H)-(k+1)ω3$ and $ω(H)-(k-1)ω3$⁠, where k is an integer determined by the cyclic symmetry of the rotor and the housing-dominant mode of interest. In the numerical analysis, we study a benchmark model consisting of a spinning slotted disk mounted on a stationary square plate via two ball bearings. The numerical model successfully confirms the frequency splits both in the rotor-based and ground-based coordinates. In the experimental analysis, we conduct vibration testing on a rotor–bearing–housing system that mimics the numerical benchmark model. Test results reveal two housing-dominant modes. As the rotor spins at various speed, measured waterfall plots confirm that the housing-dominant modes split according to $ω(H)-(k+1)ω3$ and $ω(H)-(k-1)ω3$ as predicted.