Explain rotordynamic analysis for pumps and factors affecting rotor stability.

Rotordynamic analysis predicts pump rotor vibration behavior under operating conditions. Key aspects: (1) Lateral analysis: calculates critical speeds (natural frequencies), mode shapes, unbalance response, and stability; must avoid operating near critical speeds (separation margin >15%). (2) Stiffness and damping: from bearings (sleeve, tilting pad), seals (wear rings, balance drum), and fluid interaction. (3) Cross-coupled stiffness from annular seals and impellers can cause subsynchronous instabilities when destabilizing forces exceed damping. Lomakin effect in wear rings provides stiffness proportional to pressure drop. (4) API 610/617 require rotordynamic analysis for between-bearing pumps. Stability analysis using eigenvalue approach predicts log decrement (>0.1 required). Mitigation: swirl brakes, anti-swirl devices, optimized seal geometry, damper bearings.