Nonlinear dynamic analysis of a tilting pad journal bearing subjected to pad fluttering

This work brings an overview of the nonlinear dynamics of four-segment tilting pad journal bearings (TPJB) in load-between-pads configuration supported on flexible pivots. We focus primarily on analysing the sub-synchronous motion of statically unloaded pads, also called pad fluttering. In this particular case, the motion deviates between chaotic and periodic due to 1:4, 1:5, 1:6 and 1:7 internal resonances. The response is analysed with bifurcation diagrams and characterised with estimates of the largest Lyapunov exponents. Unlike previous works, we show that pad fluttering disappears at relative eccentricities lower than 0.34. This behaviour is enabled due to a fixed point trajectory that is not predicted by analysing static equilibria. The observation is crucial for high-speed rotating machinery supported on TPJBs, including pinions in multi-stage compressors and microturbines. The analysis is performed using a verified computational model which includes fluid-structure interaction and potential Hertzian contacts between individual parts of the TPJB. This model exploits local and auxiliary coordinate systems for a straightforward description of acting forces. Furthermore, we provide a detailed step-by-step discussion regarding the model formulation employing the finite difference method to solve hydrodynamic lubrication.