heal.abstract |
High speed rotors on gas foil bearings (>200kRPM) are applications of increasing interest due to their potential to increase the power to weight ratio in machines and also establish oil-free design solutions. The gas lubrication principles render lower – compared to oil – power losses and increase the threshold speed of instability in rotating systems. However, self-excited oscillations may still occur at DN (Diameter [mm] X Rotating Speed [RPM]) values much lower than the speed of sound [DN<6.5e6], these being usually triggered through Hopf bifurcation of a fixed point equilibrium (fully balanced rotor) or secondary Hopf (Neimark-Sacker) bifurcation of periodic limit cycles (unbalanced rotor). Bifurcation-free operation is a target in the dynamic design of high-speed machines like automotive turbosystems, turbopumps for rocket propulsion, small jet engines for drones or UAVs, and others; this is not always achievable with conventional rotor-bearing design.
In this work, an active gas foil bearing is presented as a novel configuration including a number of piezoelectric actuators which shape the foil component through linear feedback control. At first, an enhanced finite element model for the thin foil mounted in a number of PZTs, is developed in order to avoid shear lock effect. Second, the gas-structure interaction (FSI) is modeled through Reynolds equation for compressible flow. A simple rotor model consisting of a rigid rotor and 2 gas foil bearings is then defined, and the dynamic system is composed with its unique source of nonlinearity to be the nonlinear impedance forces from the gas to the rotor and to the foil. The third milestone includes a linear feedback control scheme to stabilize (pole placement) the dynamic system, linearized around a speed depended equilibrium (balanced rotor). Linear control is found to be insufficient to stabilize the system when certain perturbations apply. Further to that, unbalanced rotor systems (most common case) follow trajectories which extend far from fixed point equilibria, emerging strong nonlinear impedance forces from the bearings. Linear feedback control is applied in the dynamic system utilizing polynomial feedback functions in order to overcome the problem of instability. Case studies include a small (30mm) and a large (100mm) bearing, both at operating range with upper bound of speed at DN = 6.5e6; different foil thickness is also included in the case study. |
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