Rotordynamic behaviour of a micro-turbine rotor on air bearings: modelling techniques and experimental verification

Current trends in micro-turbomachinery stress the need for adequate rotordynamic models. These models should allow accurate prediction of critical speeds, imbalance response and stable operation range of microturbomachinery rotor-bearing systems. This paper gives an overview of the total rotordynamic modelling process of a micro-turbine rotor supported on aerostatic bearings. A both accurate and efficient modelling technique is outlined to obtain static and dynamic air bearing properties. These bearing coefficients serve as input for a rotordynamic model yielding damped natural frequencies, unbalance response and stability limits. Experimental verification confirms a good agreement with the predicted critical speeds. Nomenclature Ao annular curtain area at gap entrance [m2] c journal bearing nominal radial clearance [μm] cij bearing damping coefficient [N s/μm or Nm s/rad] Cd entrance flow coefficient of discharge f external force acting on rotor [N] h thrust bearing nominal clearance [μm] H normalised film height It rotor transverse moment of inertia [gmm2] Ip rotor polar moment of inertia [gmm2] kij bearing stiffness coefficient [N/μm or Nm/rad] L journal bearing length [mm] Lb distance between journal bearing centres [mm] Lp distance between measurement planes [mm] Ltot total rotor length [mm] m rotor mass [g] ṁ mass flow [g/s] ṁo gap entrance flow [g/s] pa atmospherical pressure [Pa] po gap entrance pressure [Pa] ps supply pressure [Pa]