A method is described for calculating the coupled torsional-lateral vibrations in a geared system of rotors. It considers both forced vibrations, caused by mesh errors or by mass unbalance, and free, damped vibrations whose complex eigen frequencies define the damped critical speeds and the stability of the rotor system. The rotors, supported in fluid-film bearings, are calculated independently, using the Holzer method for torsional vibrations and the Myklestad-Prohl method for lateral vibrations, after which they are coupled through impedance matching at the gear meshes. The resulting equations are solved for the unknown mesh contact forces, and the roots of the coefficient matrix determinant give the eigenvalues of the system. The method is efficient and readily programmed.

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