Misalignment in turbomachinery is commonly thought to produce two-times-running-speed (2N) response. The source of 2N vibration response was investigated, starting with the development of finite-element models for three flexible disc-pack couplings (4-bolt, 6-bolt, and 8-bolt couplings). Parallel and angular misalignments were analyzed. The resultant lateral stiffness terms had 1N, 2N, and 3N harmonic components versus the shaft rotation angle. The 4-bolt coupling had large 1N stiffness components under angular and parallel misalignment. The 6-bolt coupling had only a 1N reaction component under angular misalignment, while parallel misalignment showed a strong 2N reaction component, larger than either the 1N or 3N components. Under angular misalignment, the 8-bolt model produced large 1N reaction components. Under parallel misalignment, it produced 1N, 2N, and 3N components that were similar in magnitude. All the couplings behaved linearly in the range studied.

Some experts attribute observed 2N response to nonlinear bearing forces produced by bearings at high unit loads. Static tests for a 5-pad tilting-pad journal bearing with unit loads up to 34.5bars produced small 2N motion components that did not grow with increasing unit load.

A Jeffcott-rotor model with shaft stiffness orthotropy and a fixed-direction side load predicts that 2N response depends on three related factors: (1) the degree of orthotropy (the 1N stiffness variation magnitude), (2) the magnitude of the side load, and (3) the relative ratio of running speed to rotor 1st natural frequency, (ω/ωn). The 2N response magnitude is largest when ω is close to ωn/2. The side load is required to create 2N response due to shaft stiffness orthotropy. Misaligned couplings create precisely the same (very old) physical model as a two-pole turbogenerator rotor with a gravity side load (gravity critical speed).

The response of a 2-rotor/coupling system with parallel and angular misalignment was simulated using a time-transient code. When the frequency ratio was 0.5, the system response with the 4-bolt and 6-bolt coupling had a synchronous 1N component as well as a significant 2N component. Parallel misalignment at a coupling produces stiffness orthotropy and a fixed-direction side load. For ranges of running speed near ωn/2, these two elements can combine to produce 2N response.

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