Local resonance of crack-imbalance orientations and orbital evolution to detect rotor cracks: Part 1, numerical analysis

Vibration peaks occurring at rational fractions of the fundamental rotating critical speed, here named Local Resonances, facilitate cracked shaft detection during machine shut-down. A modified Jeffcott-rotor on journal bearings accounting for gravity effects and oscillating around nontrivial equilibrium points is employed. Modal parameter selection allows this linear model to represent first mode characteristics of real machines, and yield comparable results to similar non-linear models. Orbit evolution and vibration patterns are analyzed yielding useful results. Unless cracks are unrealistically deep, stability are generally ruled by the common bearing oil-whip limit. For crack detection results (not previously reported) indicate that, instead of 1x and 2x components, analysis of the remaining local resonances should have priority, this is due to crack-residual imbalance interaction and to 2x multiple induced origins. Local resonances at critical speed and around 1/2, 1/3, 1/4 of it, are emphasized; also phase angles variation at post-critical speeds below the stability threshold are important. Extensive simulation analysis validates previous statements.