Influence of frequency dependent flexible bearing supports on rotor stability

A common method for performing stability analyses of turbomachinery is the linear transfer matrix method. A serious limitation of the transfer matrix method is an inability to adequately handle branched systems. A system is considered branched when the differential equation describing an element is not strictly dependent on two adjacent elements. Two byproducts of branching are singularities and rotor-bearing cross talk. Singularities are the result of exact dynamic reduction, a method used to incorporate additional degrees of freedom into the rotor model. Singularities, points in the complex plane which approach infinity, bias the gradient descent search methods used to find system eigenvalues. Rotor cross talks, coupling between bearings through a flexible casing, create a dependence on unknown rotor states. The transfer matrix method breaks down due to numerical convergence problems associated with singularities in the eigenvalue search space and dependence on unknown rotor states. Methods of eliminating these problems are introduced and demonstrated to be effective through typical industrial examples.

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