Predicting stability of synchronous nonlinear vibration in vertical rotating shaft system with journal bearing

Journal bearings (JBs) play a vital role in rotating machines across various fields. In vertical rotating shaft systems with JB, synchronous vibration experiences stages of destabilization and stabilization as rotational speed increases due to self-excited vibration. The onset speed of instability (OSI1) can be predicted via conventional eigenvalue analysis around static equilibrium positions. However, conventional analysis cannot determine the stabilizing and destabilizing speeds (OSS and OSI2) at which self-excited vibration disappears and reappears; numerical and experimental methods suffice. No other theory adequately explains these phenomena. This paper proposes an analytical method based on linearizing JB force and generalized eigenvalue analysis to efficiently predict synchronous vibration stability in vertical rotating shaft systems. The extended eigenvalue analysis directly determines synchronous orbit stability. Demonstrating accuracy and efficiency, a characteristic curve representing stability changes within an unbalance range is calculated, compared with numerical results. Our method serves as an input to rotor dynamic software, calculating rotating shaft-bearing stability thresholds.