A general method is presented for obtaining the unbalance response orbit of a gear-coupled two-shaft rotor-bearing system, based on the finite element approach. Specifically, analytical solutions of the maximum and minimum radii of the orbit are proposed. The method has been applied to the unbalance response analysis of a 600 kW turbo-chiller rotor-bearing system, having a bull-pinion speed increasing gear. Bumps in the unbalance responses have been observed at the first torsional natural frequency because of the coupling between the lateral and torsional dynamics due to gear meshing. In addition, the analytical solutions have been validated with results obtained by a full numerical approach. The proposed method can be generally applied to an analysis of the unbalance response orbits of dual-shaft rotor-bearing systems coupled by bearings as well, which are often found in aerospace gas turbine engines.

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