A finite groove approach (FGA), based on the finite element method (FEM), is used for analyzing the static and dynamic behavior of spiral-grooved aerodynamic journal bearings at different eccentricities, number of grooves, and compressibility numbers. The results of the FGA are compared with the narrow-groove theory (NGT) solutions. For the rotating-groove case, a novel time-periodic solution method is presented for computing the quasi-steady-state and dynamic pressure profiles. The new method offers the advantage of avoiding time-consuming transient integration, while resolving a finite number of grooves. The static and dynamic solutions of the NGT and FGA approach are compared, and they show good agreement, even at large eccentricities (ε=0.8) and high compressibility numbers (Λ = 40). Stability maps at different eccentricities are presented. At certain operation points, a stability decrease toward larger eccentricities is observed. The largest stability deviations of the NGT from the FGA solutions occur at large groove angle, low number of grooves, and large compressibility numbers.

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The dynamic behavior of spiral-grooved gas bearing supported 4DoF rotors is investigated by means of linearized bearing force coefficients and full time-integrated transient analysis. The two methods are compared for a variation of test rotors and bearing geometries in a given compressibility number interval of Lambda = [0,40]. The limitations and weaknesses of the linearized model are presented. It is shown that shafts with two symmetric herringbone-groove journal bearings have their maximum stability and load capacity if the center of gravity lays in the middle of the two bearings. For symmetric rotors (la/lb = 1) the two rigid modes, cylindrical and conical, are present and are influenced by the mass and transverse moment of inertia independently. For asymmetric rotors (la/lb < 1) the stability region decreases and the modes have a mixed shape. It is no longer possible to clearly distinguish between pure cylindrical and pure conical mode shapes. The two methods predict the critical mass and critical transverse moment of inertias within a difference of < 7%. A quasi-linear unbalance module for rigid gas bearing supported rotors is presented, which considers eccentricity dependent bearing force coefficients, allowing to speed up the unbalance response analysis by four orders of magnitude. The unbalance module is compared with the full transient orbital analysis, suggesting that the quasi-linear module predicts the non-linear unbalance response with <6% deviation for amplitudes up to e < 0.5 within the complete compressibility number range.

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The dynamic behavior of spiral-grooved gas bearing supported 4DoF rotors is investigated by means of linearized bearing force coefficients and full time-integrated transient analysis. The transient method consists of a state-space representation, which couples the equations of motion with the compressible thin film fluid equation. The linearized method is based on the perturbation analysis around a given eccentric shaft position ε, allowing to compute the static and linear dynamic bearing force coefficients at different excitation frequencies. The two methods are compared for a variation of test rotors and bearing geometries in a given compressibility number interval of Λ = [0,40]. The limitations and weaknesses of the linearized model are presented. It is shown that shafts with two symmetric herringbone-groove journal bearings have their maximum stability and load capacity if the center of gravity lays in the middle of the two bearings. For symmetric rotors (la/lb = 1) the two rigid modes, cylindrical and conical, are present and are influenced by the mass and transverse moment of inertia independently. For asymmetric rotors (la/lb < 1) the stability region decreases and the modes have a mixed shape. It is no longer possible to clearly distinguish between pure cylindrical and pure conical mode shapes. The two methods predict the critical mass and critical transverse moment of inertias within a difference of < 7%. A quasi-linear unbalance module for rigid gas bearing supported rotors is presented, which considers eccentricity dependent bearing force coefficients, allowing to speed up the unbalance response analysis by four orders of magnitude. The unbalance module is compared with the full transient orbital analysis, suggesting that the quasi-linear module predicts the non-linear unbalance response with < 6 % deviation for amplitudes up to ε < 0.5 within the complete compressibility number range.