What is eccentricity in steam turbine shaft?

Eccentricity is the deflection in the shaft away from truly straight. The turbine shaft when not turning will settle into a bowed shape (measured in thousandths of an inch), this is the deflection from straight. Large turbines are placed on turning gears as they are cooled or warmed up to minimize this deflection. As a turbine is started this eccentricity produces vibration as the deflection changes rotational position, if the turbine is started up too quickly this deflection will increase as a result of inertia trying to deflect the weight of the deflected shaft outward. Eventually the deflection, as a result of rolling the turbine up slowly, will straighten to the true center of the turbine shaft.