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.

Improvement of Adaptive GAs and Back Propagation ANNs Performance in Condition Diagnosis of Multiple Bearing System Using Grey Relational Analysis

Condition diagnosis of multiple bearings system is one of the requirements in industry field, because bearings are used in many equipment and their failure can result in total breakdown. Conditions of bearings commonly are reflected by vibration signals data. In multiple bearing condition diagnosis, it will involve many types of vibration signals data; thus, consequently, it will involve many features extraction to obtain precise condition diagnosis. However, large number of features extraction will increase the complexity of the diagnosis system. Therefore, in this paper, we presented a diagnosis method which is hybridization of adaptive genetic algorithms (AGAs), back propagation neural networks (BPNNs), and grey relational analysis (GRA) to diagnose the condition of multiple bearings system. AGAs are used in the diagnosis algorithm to determine the best initial weights of BPNNs in order to improve the diagnosis accuracy. In addition, GRA is applied to determine and select the dominant features from the vibration signal data which will provide good diagnosis of multiple bearings system in less features extraction. The experiments results show that AGAs-BPNNs with GRA approaches can increase the accuracy of diagnosis in shorter processing time, compared with the AGAs-BPNNs without the GRA.