The effect of misalignment on rotor vibrations

Rotors with three or more fluid-film bearings (or fluid seals) have "redundant" supports, and therefore, interdependent bearing loads that are generally unknown both in magnitude and direction. The steady-state bearing eccentricities and the dynamic stiffness and damping coefficients of the bearings are, therefore, also unknown since both are functions of the bearing loads. Thus, the dynamic behavior of multibearing rotors generally cannot be predicted with good accuracy without access to a procedure for calculating the steady-state bearing loads and eccentricities. This paper outlines such a procedure in terms of both the influence coefficient method, the transfer matrix method, and the finite element method. Radial bearing misalignment and flexibility of the bearing back-lip structures are accounted for. Once the eccentricities are available, the bearing stiffness and damping coefficients can be calculated in the usual walt and used to predict critical speeds, instability threshold speed, and rotor response to imbalance. A numerical example is presented that illustrates some of the nonlinear effects of bearing support redundancy, notably the large variations in instability threshold speed with radial bearing misalignment. The example shows how the method can be used to determine the level of bearing misalignment that leads to optimum rotor stability. Ir is concluded that no simple guide lines exist by which optimum stability can be achieved. Neither perfect bearing alignment nor equal load sharing between bearings necessarily lead to optimum stability.